YES Problem: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt())) -> mark(tt()) active(U21(tt(),V2)) -> mark(U22(isList(V2))) active(U22(tt())) -> mark(tt()) active(U31(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNeList(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt(),P)) -> mark(U72(isPal(P))) active(U72(tt())) -> mark(tt()) active(U81(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isNeList(V))) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isPal(V)) -> mark(U81(isNePal(V))) active(isPal(nil())) -> mark(tt()) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U61(mark(X)) -> mark(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U81(mark(X)) -> mark(U81(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(ok(X)) -> ok(U22(X)) isList(ok(X)) -> ok(isList(X)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(ok(X)) -> ok(U42(X)) isNeList(ok(X)) -> ok(isNeList(X)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(ok(X)) -> ok(U52(X)) U61(ok(X)) -> ok(U61(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isPal(ok(X)) -> ok(isPal(X)) U81(ok(X)) -> ok(U81(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Proof: Matrix Interpretation Processor: dim=1 interpretation: [top](x0) = x0, [ok](x0) = x0, [proper](x0) = x0, [u] = 1, [o] = 1, [i] = 2, [e] = 1, [a] = 1, [isNePal](x0) = x0 + 2, [isQid](x0) = x0, [U81](x0) = 2x0, [U72](x0) = x0, [isPal](x0) = 2x0 + 4, [U71](x0, x1) = 3x0 + 2x1 + 2, [U61](x0) = x0 + 2, [U52](x0) = x0, [U51](x0, x1) = x0 + x1, [U42](x0) = x0, [isNeList](x0) = x0 + 1, [U41](x0, x1) = x0 + x1, [U31](x0) = x0, [U22](x0) = x0, [isList](x0) = x0 + 1, [U21](x0, x1) = x0 + x1, [U11](x0) = x0, [tt] = 1, [nil] = 0, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = 2x0 + x1 orientation: active(__(__(X,Y),Z)) = 4X + 2Y + Z >= 2X + 2Y + Z = mark(__(X,__(Y,Z))) active(__(X,nil())) = 2X >= X = mark(X) active(__(nil(),X)) = X >= X = mark(X) active(U11(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V2)) = V2 + 1 >= V2 + 1 = mark(U22(isList(V2))) active(U22(tt())) = 1 >= 1 = mark(tt()) active(U31(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V2)) = V2 + 1 >= V2 + 1 = mark(U42(isNeList(V2))) active(U42(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V2)) = V2 + 1 >= V2 + 1 = mark(U52(isList(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 3 >= 1 = mark(tt()) active(U71(tt(),P)) = 2P + 5 >= 2P + 4 = mark(U72(isPal(P))) active(U72(tt())) = 1 >= 1 = mark(tt()) active(U81(tt())) = 2 >= 1 = mark(tt()) active(isList(V)) = V + 1 >= V + 1 = mark(U11(isNeList(V))) active(isList(nil())) = 1 >= 1 = mark(tt()) active(isList(__(V1,V2))) = 2V1 + V2 + 1 >= V1 + V2 + 1 = mark(U21(isList(V1),V2)) active(isNeList(V)) = V + 1 >= V = mark(U31(isQid(V))) active(isNeList(__(V1,V2))) = 2V1 + V2 + 1 >= V1 + V2 + 1 = mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) = 2V1 + V2 + 1 >= V1 + V2 + 1 = mark(U51(isNeList(V1),V2)) active(isNePal(V)) = V + 2 >= V + 2 = mark(U61(isQid(V))) active(isNePal(__(I,__(P,I)))) = 3I + 2P + 2 >= 3I + 2P + 2 = mark(U71(isQid(I),P)) active(isPal(V)) = 2V + 4 >= 2V + 4 = mark(U81(isNePal(V))) active(isPal(nil())) = 4 >= 1 = mark(tt()) active(isQid(a())) = 1 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 2 >= 1 = mark(tt()) active(isQid(o())) = 1 >= 1 = mark(tt()) active(isQid(u())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = 2X1 + X2 >= 2X1 + X2 = __(active(X1),X2) active(__(X1,X2)) = 2X1 + X2 >= 2X1 + X2 = __(X1,active(X2)) active(U11(X)) = X >= X = U11(active(X)) active(U21(X1,X2)) = X1 + X2 >= X1 + X2 = U21(active(X1),X2) active(U22(X)) = X >= X = U22(active(X)) active(U31(X)) = X >= X = U31(active(X)) active(U41(X1,X2)) = X1 + X2 >= X1 + X2 = U41(active(X1),X2) active(U42(X)) = X >= X = U42(active(X)) active(U51(X1,X2)) = X1 + X2 >= X1 + X2 = U51(active(X1),X2) active(U52(X)) = X >= X = U52(active(X)) active(U61(X)) = X + 2 >= X + 2 = U61(active(X)) active(U71(X1,X2)) = 3X1 + 2X2 + 2 >= 3X1 + 2X2 + 2 = U71(active(X1),X2) active(U72(X)) = X >= X = U72(active(X)) active(U81(X)) = 2X >= 2X = U81(active(X)) __(mark(X1),X2) = 2X1 + X2 >= 2X1 + X2 = mark(__(X1,X2)) __(X1,mark(X2)) = 2X1 + X2 >= 2X1 + X2 = mark(__(X1,X2)) U11(mark(X)) = X >= X = mark(U11(X)) U21(mark(X1),X2) = X1 + X2 >= X1 + X2 = mark(U21(X1,X2)) U22(mark(X)) = X >= X = mark(U22(X)) U31(mark(X)) = X >= X = mark(U31(X)) U41(mark(X1),X2) = X1 + X2 >= X1 + X2 = mark(U41(X1,X2)) U42(mark(X)) = X >= X = mark(U42(X)) U51(mark(X1),X2) = X1 + X2 >= X1 + X2 = mark(U51(X1,X2)) U52(mark(X)) = X >= X = mark(U52(X)) U61(mark(X)) = X + 2 >= X + 2 = mark(U61(X)) U71(mark(X1),X2) = 3X1 + 2X2 + 2 >= 3X1 + 2X2 + 2 = mark(U71(X1,X2)) U72(mark(X)) = X >= X = mark(U72(X)) U81(mark(X)) = 2X >= 2X = mark(U81(X)) proper(__(X1,X2)) = 2X1 + X2 >= 2X1 + X2 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X)) = X >= X = U11(proper(X)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U21(X1,X2)) = X1 + X2 >= X1 + X2 = U21(proper(X1),proper(X2)) proper(U22(X)) = X >= X = U22(proper(X)) proper(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(U31(X)) = X >= X = U31(proper(X)) proper(U41(X1,X2)) = X1 + X2 >= X1 + X2 = U41(proper(X1),proper(X2)) proper(U42(X)) = X >= X = U42(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U51(X1,X2)) = X1 + X2 >= X1 + X2 = U51(proper(X1),proper(X2)) proper(U52(X)) = X >= X = U52(proper(X)) proper(U61(X)) = X + 2 >= X + 2 = U61(proper(X)) proper(U71(X1,X2)) = 3X1 + 2X2 + 2 >= 3X1 + 2X2 + 2 = U71(proper(X1),proper(X2)) proper(U72(X)) = X >= X = U72(proper(X)) proper(isPal(X)) = 2X + 4 >= 2X + 4 = isPal(proper(X)) proper(U81(X)) = 2X >= 2X = U81(proper(X)) proper(isQid(X)) = X >= X = isQid(proper(X)) proper(isNePal(X)) = X + 2 >= X + 2 = isNePal(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 1 >= 1 = ok(e()) proper(i()) = 2 >= 2 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = 2X1 + X2 >= 2X1 + X2 = ok(__(X1,X2)) U11(ok(X)) = X >= X = ok(U11(X)) U21(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(U21(X1,X2)) U22(ok(X)) = X >= X = ok(U22(X)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) U31(ok(X)) = X >= X = ok(U31(X)) U41(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(U41(X1,X2)) U42(ok(X)) = X >= X = ok(U42(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U51(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(U51(X1,X2)) U52(ok(X)) = X >= X = ok(U52(X)) U61(ok(X)) = X + 2 >= X + 2 = ok(U61(X)) U71(ok(X1),ok(X2)) = 3X1 + 2X2 + 2 >= 3X1 + 2X2 + 2 = ok(U71(X1,X2)) U72(ok(X)) = X >= X = ok(U72(X)) isPal(ok(X)) = 2X + 4 >= 2X + 4 = ok(isPal(X)) U81(ok(X)) = 2X >= 2X = ok(U81(X)) isQid(ok(X)) = X >= X = ok(isQid(X)) isNePal(ok(X)) = X + 2 >= X + 2 = ok(isNePal(X)) top(mark(X)) = X >= X = top(proper(X)) top(ok(X)) = X >= X = top(active(X)) problem: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt())) -> mark(tt()) active(U21(tt(),V2)) -> mark(U22(isList(V2))) active(U22(tt())) -> mark(tt()) active(U31(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNeList(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(U52(tt())) -> mark(tt()) active(U72(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isNeList(V))) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isPal(V)) -> mark(U81(isNePal(V))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U61(mark(X)) -> mark(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U81(mark(X)) -> mark(U81(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(ok(X)) -> ok(U22(X)) isList(ok(X)) -> ok(isList(X)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(ok(X)) -> ok(U42(X)) isNeList(ok(X)) -> ok(isNeList(X)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(ok(X)) -> ok(U52(X)) U61(ok(X)) -> ok(U61(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isPal(ok(X)) -> ok(isPal(X)) U81(ok(X)) -> ok(U81(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dim=1 interpretation: [top](x0) = 2x0, [ok](x0) = x0, [proper](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isNePal](x0) = 4x0, [isQid](x0) = 4x0, [U81](x0) = x0 + 2, [U72](x0) = 2x0, [isPal](x0) = 4x0 + 2, [U71](x0, x1) = 2x0 + x1, [U61](x0) = x0, [U52](x0) = x0, [U51](x0, x1) = 2x0 + x1, [U42](x0) = x0, [isNeList](x0) = x0, [U41](x0, x1) = x0 + x1, [U31](x0) = x0, [U22](x0) = x0, [isList](x0) = x0, [U21](x0, x1) = 2x0 + x1, [U11](x0) = x0, [tt] = 0, [nil] = 1, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = 4x0 + x1 orientation: active(__(__(X,Y),Z)) = 16X + 4Y + Z >= 4X + 4Y + Z = mark(__(X,__(Y,Z))) active(__(X,nil())) = 4X + 1 >= X = mark(X) active(__(nil(),X)) = X + 4 >= X = mark(X) active(U11(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V2)) = V2 >= V2 = mark(U22(isList(V2))) active(U22(tt())) = 0 >= 0 = mark(tt()) active(U31(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V2)) = V2 >= V2 = mark(U42(isNeList(V2))) active(U42(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V2)) = V2 >= V2 = mark(U52(isList(V2))) active(U52(tt())) = 0 >= 0 = mark(tt()) active(U72(tt())) = 0 >= 0 = mark(tt()) active(isList(V)) = V >= V = mark(U11(isNeList(V))) active(isList(nil())) = 1 >= 0 = mark(tt()) active(isList(__(V1,V2))) = 4V1 + V2 >= 2V1 + V2 = mark(U21(isList(V1),V2)) active(isNeList(__(V1,V2))) = 4V1 + V2 >= V1 + V2 = mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) = 4V1 + V2 >= 2V1 + V2 = mark(U51(isNeList(V1),V2)) active(isNePal(V)) = 4V >= 4V = mark(U61(isQid(V))) active(isNePal(__(I,__(P,I)))) = 20I + 16P >= 8I + P = mark(U71(isQid(I),P)) active(isPal(V)) = 4V + 2 >= 4V + 2 = mark(U81(isNePal(V))) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = 4X1 + X2 >= 4X1 + X2 = __(active(X1),X2) active(__(X1,X2)) = 4X1 + X2 >= 4X1 + X2 = __(X1,active(X2)) active(U11(X)) = X >= X = U11(active(X)) active(U21(X1,X2)) = 2X1 + X2 >= 2X1 + X2 = U21(active(X1),X2) active(U22(X)) = X >= X = U22(active(X)) active(U31(X)) = X >= X = U31(active(X)) active(U41(X1,X2)) = X1 + X2 >= X1 + X2 = U41(active(X1),X2) active(U42(X)) = X >= X = U42(active(X)) active(U51(X1,X2)) = 2X1 + X2 >= 2X1 + X2 = U51(active(X1),X2) active(U52(X)) = X >= X = U52(active(X)) active(U61(X)) = X >= X = U61(active(X)) active(U71(X1,X2)) = 2X1 + X2 >= 2X1 + X2 = U71(active(X1),X2) active(U72(X)) = 2X >= 2X = U72(active(X)) active(U81(X)) = X + 2 >= X + 2 = U81(active(X)) __(mark(X1),X2) = 4X1 + X2 >= 4X1 + X2 = mark(__(X1,X2)) __(X1,mark(X2)) = 4X1 + X2 >= 4X1 + X2 = mark(__(X1,X2)) U11(mark(X)) = X >= X = mark(U11(X)) U21(mark(X1),X2) = 2X1 + X2 >= 2X1 + X2 = mark(U21(X1,X2)) U22(mark(X)) = X >= X = mark(U22(X)) U31(mark(X)) = X >= X = mark(U31(X)) U41(mark(X1),X2) = X1 + X2 >= X1 + X2 = mark(U41(X1,X2)) U42(mark(X)) = X >= X = mark(U42(X)) U51(mark(X1),X2) = 2X1 + X2 >= 2X1 + X2 = mark(U51(X1,X2)) U52(mark(X)) = X >= X = mark(U52(X)) U61(mark(X)) = X >= X = mark(U61(X)) U71(mark(X1),X2) = 2X1 + X2 >= 2X1 + X2 = mark(U71(X1,X2)) U72(mark(X)) = 2X >= 2X = mark(U72(X)) U81(mark(X)) = X + 2 >= X + 2 = mark(U81(X)) proper(__(X1,X2)) = 4X1 + X2 >= 4X1 + X2 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X)) = X >= X = U11(proper(X)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U21(X1,X2)) = 2X1 + X2 >= 2X1 + X2 = U21(proper(X1),proper(X2)) proper(U22(X)) = X >= X = U22(proper(X)) proper(isList(X)) = X >= X = isList(proper(X)) proper(U31(X)) = X >= X = U31(proper(X)) proper(U41(X1,X2)) = X1 + X2 >= X1 + X2 = U41(proper(X1),proper(X2)) proper(U42(X)) = X >= X = U42(proper(X)) proper(isNeList(X)) = X >= X = isNeList(proper(X)) proper(U51(X1,X2)) = 2X1 + X2 >= 2X1 + X2 = U51(proper(X1),proper(X2)) proper(U52(X)) = X >= X = U52(proper(X)) proper(U61(X)) = X >= X = U61(proper(X)) proper(U71(X1,X2)) = 2X1 + X2 >= 2X1 + X2 = U71(proper(X1),proper(X2)) proper(U72(X)) = 2X >= 2X = U72(proper(X)) proper(isPal(X)) = 4X + 2 >= 4X + 2 = isPal(proper(X)) proper(U81(X)) = X + 2 >= X + 2 = U81(proper(X)) proper(isQid(X)) = 4X >= 4X = isQid(proper(X)) proper(isNePal(X)) = 4X >= 4X = isNePal(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = 4X1 + X2 >= 4X1 + X2 = ok(__(X1,X2)) U11(ok(X)) = X >= X = ok(U11(X)) U21(ok(X1),ok(X2)) = 2X1 + X2 >= 2X1 + X2 = ok(U21(X1,X2)) U22(ok(X)) = X >= X = ok(U22(X)) isList(ok(X)) = X >= X = ok(isList(X)) U31(ok(X)) = X >= X = ok(U31(X)) U41(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(U41(X1,X2)) U42(ok(X)) = X >= X = ok(U42(X)) isNeList(ok(X)) = X >= X = ok(isNeList(X)) U51(ok(X1),ok(X2)) = 2X1 + X2 >= 2X1 + X2 = ok(U51(X1,X2)) U52(ok(X)) = X >= X = ok(U52(X)) U61(ok(X)) = X >= X = ok(U61(X)) U71(ok(X1),ok(X2)) = 2X1 + X2 >= 2X1 + X2 = ok(U71(X1,X2)) U72(ok(X)) = 2X >= 2X = ok(U72(X)) isPal(ok(X)) = 4X + 2 >= 4X + 2 = ok(isPal(X)) U81(ok(X)) = X + 2 >= X + 2 = ok(U81(X)) isQid(ok(X)) = 4X >= 4X = ok(isQid(X)) isNePal(ok(X)) = 4X >= 4X = ok(isNePal(X)) top(mark(X)) = 2X >= 2X = top(proper(X)) top(ok(X)) = 2X >= 2X = top(active(X)) problem: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(U11(tt())) -> mark(tt()) active(U21(tt(),V2)) -> mark(U22(isList(V2))) active(U22(tt())) -> mark(tt()) active(U31(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNeList(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(U52(tt())) -> mark(tt()) active(U72(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isNeList(V))) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isPal(V)) -> mark(U81(isNePal(V))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U61(mark(X)) -> mark(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U81(mark(X)) -> mark(U81(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(ok(X)) -> ok(U22(X)) isList(ok(X)) -> ok(isList(X)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(ok(X)) -> ok(U42(X)) isNeList(ok(X)) -> ok(isNeList(X)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(ok(X)) -> ok(U52(X)) U61(ok(X)) -> ok(U61(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isPal(ok(X)) -> ok(isPal(X)) U81(ok(X)) -> ok(U81(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dim=1 interpretation: [top](x0) = 2x0, [ok](x0) = x0, [proper](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isNePal](x0) = x0 + 6, [isQid](x0) = x0 + 2, [U81](x0) = x0, [U72](x0) = 6x0 + 4, [isPal](x0) = x0 + 6, [U71](x0, x1) = 6x0 + x1, [U61](x0) = x0, [U52](x0) = x0 + 2, [U51](x0, x1) = x0 + x1 + 1, [U42](x0) = x0, [isNeList](x0) = x0 + 1, [U41](x0, x1) = x0 + x1, [U31](x0) = 7x0 + 2, [U22](x0) = x0 + 3, [isList](x0) = x0 + 1, [U21](x0, x1) = 4x0 + x1, [U11](x0) = x0, [tt] = 2, [nil] = 0, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = 5x0 + x1 + 3 orientation: active(__(__(X,Y),Z)) = 25X + 5Y + Z + 18 >= 5X + 5Y + Z + 6 = mark(__(X,__(Y,Z))) active(U11(tt())) = 2 >= 2 = mark(tt()) active(U21(tt(),V2)) = V2 + 8 >= V2 + 4 = mark(U22(isList(V2))) active(U22(tt())) = 5 >= 2 = mark(tt()) active(U31(tt())) = 16 >= 2 = mark(tt()) active(U41(tt(),V2)) = V2 + 2 >= V2 + 1 = mark(U42(isNeList(V2))) active(U42(tt())) = 2 >= 2 = mark(tt()) active(U51(tt(),V2)) = V2 + 3 >= V2 + 3 = mark(U52(isList(V2))) active(U52(tt())) = 4 >= 2 = mark(tt()) active(U72(tt())) = 16 >= 2 = mark(tt()) active(isList(V)) = V + 1 >= V + 1 = mark(U11(isNeList(V))) active(isList(__(V1,V2))) = 5V1 + V2 + 4 >= 4V1 + V2 + 4 = mark(U21(isList(V1),V2)) active(isNeList(__(V1,V2))) = 5V1 + V2 + 4 >= V1 + V2 + 1 = mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) = 5V1 + V2 + 4 >= V1 + V2 + 2 = mark(U51(isNeList(V1),V2)) active(isNePal(V)) = V + 6 >= V + 2 = mark(U61(isQid(V))) active(isNePal(__(I,__(P,I)))) = 6I + 5P + 12 >= 6I + P + 12 = mark(U71(isQid(I),P)) active(isPal(V)) = V + 6 >= V + 6 = mark(U81(isNePal(V))) active(isQid(a())) = 2 >= 2 = mark(tt()) active(isQid(e())) = 2 >= 2 = mark(tt()) active(isQid(o())) = 2 >= 2 = mark(tt()) active(isQid(u())) = 2 >= 2 = mark(tt()) active(__(X1,X2)) = 5X1 + X2 + 3 >= 5X1 + X2 + 3 = __(active(X1),X2) active(__(X1,X2)) = 5X1 + X2 + 3 >= 5X1 + X2 + 3 = __(X1,active(X2)) active(U11(X)) = X >= X = U11(active(X)) active(U21(X1,X2)) = 4X1 + X2 >= 4X1 + X2 = U21(active(X1),X2) active(U22(X)) = X + 3 >= X + 3 = U22(active(X)) active(U31(X)) = 7X + 2 >= 7X + 2 = U31(active(X)) active(U41(X1,X2)) = X1 + X2 >= X1 + X2 = U41(active(X1),X2) active(U42(X)) = X >= X = U42(active(X)) active(U51(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U51(active(X1),X2) active(U52(X)) = X + 2 >= X + 2 = U52(active(X)) active(U61(X)) = X >= X = U61(active(X)) active(U71(X1,X2)) = 6X1 + X2 >= 6X1 + X2 = U71(active(X1),X2) active(U72(X)) = 6X + 4 >= 6X + 4 = U72(active(X)) active(U81(X)) = X >= X = U81(active(X)) __(mark(X1),X2) = 5X1 + X2 + 3 >= 5X1 + X2 + 3 = mark(__(X1,X2)) __(X1,mark(X2)) = 5X1 + X2 + 3 >= 5X1 + X2 + 3 = mark(__(X1,X2)) U11(mark(X)) = X >= X = mark(U11(X)) U21(mark(X1),X2) = 4X1 + X2 >= 4X1 + X2 = mark(U21(X1,X2)) U22(mark(X)) = X + 3 >= X + 3 = mark(U22(X)) U31(mark(X)) = 7X + 2 >= 7X + 2 = mark(U31(X)) U41(mark(X1),X2) = X1 + X2 >= X1 + X2 = mark(U41(X1,X2)) U42(mark(X)) = X >= X = mark(U42(X)) U51(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U51(X1,X2)) U52(mark(X)) = X + 2 >= X + 2 = mark(U52(X)) U61(mark(X)) = X >= X = mark(U61(X)) U71(mark(X1),X2) = 6X1 + X2 >= 6X1 + X2 = mark(U71(X1,X2)) U72(mark(X)) = 6X + 4 >= 6X + 4 = mark(U72(X)) U81(mark(X)) = X >= X = mark(U81(X)) proper(__(X1,X2)) = 5X1 + X2 + 3 >= 5X1 + X2 + 3 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X)) = X >= X = U11(proper(X)) proper(tt()) = 2 >= 2 = ok(tt()) proper(U21(X1,X2)) = 4X1 + X2 >= 4X1 + X2 = U21(proper(X1),proper(X2)) proper(U22(X)) = X + 3 >= X + 3 = U22(proper(X)) proper(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(U31(X)) = 7X + 2 >= 7X + 2 = U31(proper(X)) proper(U41(X1,X2)) = X1 + X2 >= X1 + X2 = U41(proper(X1),proper(X2)) proper(U42(X)) = X >= X = U42(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(U51(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U51(proper(X1),proper(X2)) proper(U52(X)) = X + 2 >= X + 2 = U52(proper(X)) proper(U61(X)) = X >= X = U61(proper(X)) proper(U71(X1,X2)) = 6X1 + X2 >= 6X1 + X2 = U71(proper(X1),proper(X2)) proper(U72(X)) = 6X + 4 >= 6X + 4 = U72(proper(X)) proper(isPal(X)) = X + 6 >= X + 6 = isPal(proper(X)) proper(U81(X)) = X >= X = U81(proper(X)) proper(isQid(X)) = X + 2 >= X + 2 = isQid(proper(X)) proper(isNePal(X)) = X + 6 >= X + 6 = isNePal(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = 5X1 + X2 + 3 >= 5X1 + X2 + 3 = ok(__(X1,X2)) U11(ok(X)) = X >= X = ok(U11(X)) U21(ok(X1),ok(X2)) = 4X1 + X2 >= 4X1 + X2 = ok(U21(X1,X2)) U22(ok(X)) = X + 3 >= X + 3 = ok(U22(X)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) U31(ok(X)) = 7X + 2 >= 7X + 2 = ok(U31(X)) U41(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(U41(X1,X2)) U42(ok(X)) = X >= X = ok(U42(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) U51(ok(X1),ok(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = ok(U51(X1,X2)) U52(ok(X)) = X + 2 >= X + 2 = ok(U52(X)) U61(ok(X)) = X >= X = ok(U61(X)) U71(ok(X1),ok(X2)) = 6X1 + X2 >= 6X1 + X2 = ok(U71(X1,X2)) U72(ok(X)) = 6X + 4 >= 6X + 4 = ok(U72(X)) isPal(ok(X)) = X + 6 >= X + 6 = ok(isPal(X)) U81(ok(X)) = X >= X = ok(U81(X)) isQid(ok(X)) = X + 2 >= X + 2 = ok(isQid(X)) isNePal(ok(X)) = X + 6 >= X + 6 = ok(isNePal(X)) top(mark(X)) = 2X >= 2X = top(proper(X)) top(ok(X)) = 2X >= 2X = top(active(X)) problem: active(U11(tt())) -> mark(tt()) active(U42(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(isList(V)) -> mark(U11(isNeList(V))) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isPal(V)) -> mark(U81(isNePal(V))) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U61(mark(X)) -> mark(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U81(mark(X)) -> mark(U81(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(ok(X)) -> ok(U22(X)) isList(ok(X)) -> ok(isList(X)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(ok(X)) -> ok(U42(X)) isNeList(ok(X)) -> ok(isNeList(X)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(ok(X)) -> ok(U52(X)) U61(ok(X)) -> ok(U61(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isPal(ok(X)) -> ok(isPal(X)) U81(ok(X)) -> ok(U81(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dim=1 interpretation: [top](x0) = x0 + 2, [ok](x0) = x0, [proper](x0) = x0, [u] = 1, [o] = 1, [i] = 0, [e] = 0, [a] = 4, [isNePal](x0) = 4x0 + 4, [isQid](x0) = x0 + 1, [U81](x0) = x0, [U72](x0) = 4x0 + 4, [isPal](x0) = 4x0 + 4, [U71](x0, x1) = 4x0 + x1, [U61](x0) = 2x0, [U52](x0) = 2x0, [U51](x0, x1) = x0 + 2x1 + 1, [U42](x0) = 4x0, [isNeList](x0) = x0, [U41](x0, x1) = x0 + 4x1, [U31](x0) = 2x0 + 2, [U22](x0) = 4x0 + 2, [isList](x0) = x0, [U21](x0, x1) = 4x0 + x1, [U11](x0) = x0, [tt] = 1, [nil] = 0, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = 4x0 + x1 orientation: active(U11(tt())) = 1 >= 1 = mark(tt()) active(U42(tt())) = 4 >= 1 = mark(tt()) active(U51(tt(),V2)) = 2V2 + 2 >= 2V2 = mark(U52(isList(V2))) active(isList(V)) = V >= V = mark(U11(isNeList(V))) active(isList(__(V1,V2))) = 4V1 + V2 >= 4V1 + V2 = mark(U21(isList(V1),V2)) active(isNePal(__(I,__(P,I)))) = 20I + 16P + 4 >= 4I + P + 4 = mark(U71(isQid(I),P)) active(isPal(V)) = 4V + 4 >= 4V + 4 = mark(U81(isNePal(V))) active(isQid(a())) = 5 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(o())) = 2 >= 1 = mark(tt()) active(isQid(u())) = 2 >= 1 = mark(tt()) active(__(X1,X2)) = 4X1 + X2 >= 4X1 + X2 = __(active(X1),X2) active(__(X1,X2)) = 4X1 + X2 >= 4X1 + X2 = __(X1,active(X2)) active(U11(X)) = X >= X = U11(active(X)) active(U21(X1,X2)) = 4X1 + X2 >= 4X1 + X2 = U21(active(X1),X2) active(U22(X)) = 4X + 2 >= 4X + 2 = U22(active(X)) active(U31(X)) = 2X + 2 >= 2X + 2 = U31(active(X)) active(U41(X1,X2)) = X1 + 4X2 >= X1 + 4X2 = U41(active(X1),X2) active(U42(X)) = 4X >= 4X = U42(active(X)) active(U51(X1,X2)) = X1 + 2X2 + 1 >= X1 + 2X2 + 1 = U51(active(X1),X2) active(U52(X)) = 2X >= 2X = U52(active(X)) active(U61(X)) = 2X >= 2X = U61(active(X)) active(U71(X1,X2)) = 4X1 + X2 >= 4X1 + X2 = U71(active(X1),X2) active(U72(X)) = 4X + 4 >= 4X + 4 = U72(active(X)) active(U81(X)) = X >= X = U81(active(X)) __(mark(X1),X2) = 4X1 + X2 >= 4X1 + X2 = mark(__(X1,X2)) __(X1,mark(X2)) = 4X1 + X2 >= 4X1 + X2 = mark(__(X1,X2)) U11(mark(X)) = X >= X = mark(U11(X)) U21(mark(X1),X2) = 4X1 + X2 >= 4X1 + X2 = mark(U21(X1,X2)) U22(mark(X)) = 4X + 2 >= 4X + 2 = mark(U22(X)) U31(mark(X)) = 2X + 2 >= 2X + 2 = mark(U31(X)) U41(mark(X1),X2) = X1 + 4X2 >= X1 + 4X2 = mark(U41(X1,X2)) U42(mark(X)) = 4X >= 4X = mark(U42(X)) U51(mark(X1),X2) = X1 + 2X2 + 1 >= X1 + 2X2 + 1 = mark(U51(X1,X2)) U52(mark(X)) = 2X >= 2X = mark(U52(X)) U61(mark(X)) = 2X >= 2X = mark(U61(X)) U71(mark(X1),X2) = 4X1 + X2 >= 4X1 + X2 = mark(U71(X1,X2)) U72(mark(X)) = 4X + 4 >= 4X + 4 = mark(U72(X)) U81(mark(X)) = X >= X = mark(U81(X)) proper(__(X1,X2)) = 4X1 + X2 >= 4X1 + X2 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X)) = X >= X = U11(proper(X)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U21(X1,X2)) = 4X1 + X2 >= 4X1 + X2 = U21(proper(X1),proper(X2)) proper(U22(X)) = 4X + 2 >= 4X + 2 = U22(proper(X)) proper(isList(X)) = X >= X = isList(proper(X)) proper(U31(X)) = 2X + 2 >= 2X + 2 = U31(proper(X)) proper(U41(X1,X2)) = X1 + 4X2 >= X1 + 4X2 = U41(proper(X1),proper(X2)) proper(U42(X)) = 4X >= 4X = U42(proper(X)) proper(isNeList(X)) = X >= X = isNeList(proper(X)) proper(U51(X1,X2)) = X1 + 2X2 + 1 >= X1 + 2X2 + 1 = U51(proper(X1),proper(X2)) proper(U52(X)) = 2X >= 2X = U52(proper(X)) proper(U61(X)) = 2X >= 2X = U61(proper(X)) proper(U71(X1,X2)) = 4X1 + X2 >= 4X1 + X2 = U71(proper(X1),proper(X2)) proper(U72(X)) = 4X + 4 >= 4X + 4 = U72(proper(X)) proper(isPal(X)) = 4X + 4 >= 4X + 4 = isPal(proper(X)) proper(U81(X)) = X >= X = U81(proper(X)) proper(isQid(X)) = X + 1 >= X + 1 = isQid(proper(X)) proper(isNePal(X)) = 4X + 4 >= 4X + 4 = isNePal(proper(X)) proper(a()) = 4 >= 4 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 1 >= 1 = ok(u()) __(ok(X1),ok(X2)) = 4X1 + X2 >= 4X1 + X2 = ok(__(X1,X2)) U11(ok(X)) = X >= X = ok(U11(X)) U21(ok(X1),ok(X2)) = 4X1 + X2 >= 4X1 + X2 = ok(U21(X1,X2)) U22(ok(X)) = 4X + 2 >= 4X + 2 = ok(U22(X)) isList(ok(X)) = X >= X = ok(isList(X)) U31(ok(X)) = 2X + 2 >= 2X + 2 = ok(U31(X)) U41(ok(X1),ok(X2)) = X1 + 4X2 >= X1 + 4X2 = ok(U41(X1,X2)) U42(ok(X)) = 4X >= 4X = ok(U42(X)) isNeList(ok(X)) = X >= X = ok(isNeList(X)) U51(ok(X1),ok(X2)) = X1 + 2X2 + 1 >= X1 + 2X2 + 1 = ok(U51(X1,X2)) U52(ok(X)) = 2X >= 2X = ok(U52(X)) U61(ok(X)) = 2X >= 2X = ok(U61(X)) U71(ok(X1),ok(X2)) = 4X1 + X2 >= 4X1 + X2 = ok(U71(X1,X2)) U72(ok(X)) = 4X + 4 >= 4X + 4 = ok(U72(X)) isPal(ok(X)) = 4X + 4 >= 4X + 4 = ok(isPal(X)) U81(ok(X)) = X >= X = ok(U81(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) isNePal(ok(X)) = 4X + 4 >= 4X + 4 = ok(isNePal(X)) top(mark(X)) = X + 2 >= X + 2 = top(proper(X)) top(ok(X)) = X + 2 >= X + 2 = top(active(X)) problem: active(U11(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isNeList(V))) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isPal(V)) -> mark(U81(isNePal(V))) active(isQid(e())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U61(mark(X)) -> mark(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U81(mark(X)) -> mark(U81(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(ok(X)) -> ok(U22(X)) isList(ok(X)) -> ok(isList(X)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(ok(X)) -> ok(U42(X)) isNeList(ok(X)) -> ok(isNeList(X)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(ok(X)) -> ok(U52(X)) U61(ok(X)) -> ok(U61(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isPal(ok(X)) -> ok(isPal(X)) U81(ok(X)) -> ok(U81(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dim=1 interpretation: [top](x0) = 2x0 + 4, [ok](x0) = x0, [proper](x0) = x0, [u] = 0, [o] = 4, [i] = 6, [e] = 4, [a] = 0, [isNePal](x0) = 4x0 + 1, [isQid](x0) = x0, [U81](x0) = x0 + 2, [U72](x0) = 2x0, [isPal](x0) = 4x0 + 3, [U71](x0, x1) = 6x0 + x1, [U61](x0) = x0, [U52](x0) = 4x0, [U51](x0, x1) = x0 + x1, [U42](x0) = 2x0 + 4, [isNeList](x0) = x0, [U41](x0, x1) = x0 + x1, [U31](x0) = x0, [U22](x0) = x0 + 1, [isList](x0) = 2x0, [U21](x0, x1) = x0 + 2x1, [U11](x0) = x0, [tt] = 0, [nil] = 2, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = x0 + x1 orientation: active(U11(tt())) = 0 >= 0 = mark(tt()) active(isList(V)) = 2V >= V = mark(U11(isNeList(V))) active(isList(__(V1,V2))) = 2V1 + 2V2 >= 2V1 + 2V2 = mark(U21(isList(V1),V2)) active(isNePal(__(I,__(P,I)))) = 8I + 4P + 1 >= 6I + P = mark(U71(isQid(I),P)) active(isPal(V)) = 4V + 3 >= 4V + 3 = mark(U81(isNePal(V))) active(isQid(e())) = 4 >= 0 = mark(tt()) active(__(X1,X2)) = X1 + X2 >= X1 + X2 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 >= X1 + X2 = __(X1,active(X2)) active(U11(X)) = X >= X = U11(active(X)) active(U21(X1,X2)) = X1 + 2X2 >= X1 + 2X2 = U21(active(X1),X2) active(U22(X)) = X + 1 >= X + 1 = U22(active(X)) active(U31(X)) = X >= X = U31(active(X)) active(U41(X1,X2)) = X1 + X2 >= X1 + X2 = U41(active(X1),X2) active(U42(X)) = 2X + 4 >= 2X + 4 = U42(active(X)) active(U51(X1,X2)) = X1 + X2 >= X1 + X2 = U51(active(X1),X2) active(U52(X)) = 4X >= 4X = U52(active(X)) active(U61(X)) = X >= X = U61(active(X)) active(U71(X1,X2)) = 6X1 + X2 >= 6X1 + X2 = U71(active(X1),X2) active(U72(X)) = 2X >= 2X = U72(active(X)) active(U81(X)) = X + 2 >= X + 2 = U81(active(X)) __(mark(X1),X2) = X1 + X2 >= X1 + X2 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 >= X1 + X2 = mark(__(X1,X2)) U11(mark(X)) = X >= X = mark(U11(X)) U21(mark(X1),X2) = X1 + 2X2 >= X1 + 2X2 = mark(U21(X1,X2)) U22(mark(X)) = X + 1 >= X + 1 = mark(U22(X)) U31(mark(X)) = X >= X = mark(U31(X)) U41(mark(X1),X2) = X1 + X2 >= X1 + X2 = mark(U41(X1,X2)) U42(mark(X)) = 2X + 4 >= 2X + 4 = mark(U42(X)) U51(mark(X1),X2) = X1 + X2 >= X1 + X2 = mark(U51(X1,X2)) U52(mark(X)) = 4X >= 4X = mark(U52(X)) U61(mark(X)) = X >= X = mark(U61(X)) U71(mark(X1),X2) = 6X1 + X2 >= 6X1 + X2 = mark(U71(X1,X2)) U72(mark(X)) = 2X >= 2X = mark(U72(X)) U81(mark(X)) = X + 2 >= X + 2 = mark(U81(X)) proper(__(X1,X2)) = X1 + X2 >= X1 + X2 = __(proper(X1),proper(X2)) proper(nil()) = 2 >= 2 = ok(nil()) proper(U11(X)) = X >= X = U11(proper(X)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U21(X1,X2)) = X1 + 2X2 >= X1 + 2X2 = U21(proper(X1),proper(X2)) proper(U22(X)) = X + 1 >= X + 1 = U22(proper(X)) proper(isList(X)) = 2X >= 2X = isList(proper(X)) proper(U31(X)) = X >= X = U31(proper(X)) proper(U41(X1,X2)) = X1 + X2 >= X1 + X2 = U41(proper(X1),proper(X2)) proper(U42(X)) = 2X + 4 >= 2X + 4 = U42(proper(X)) proper(isNeList(X)) = X >= X = isNeList(proper(X)) proper(U51(X1,X2)) = X1 + X2 >= X1 + X2 = U51(proper(X1),proper(X2)) proper(U52(X)) = 4X >= 4X = U52(proper(X)) proper(U61(X)) = X >= X = U61(proper(X)) proper(U71(X1,X2)) = 6X1 + X2 >= 6X1 + X2 = U71(proper(X1),proper(X2)) proper(U72(X)) = 2X >= 2X = U72(proper(X)) proper(isPal(X)) = 4X + 3 >= 4X + 3 = isPal(proper(X)) proper(U81(X)) = X + 2 >= X + 2 = U81(proper(X)) proper(isQid(X)) = X >= X = isQid(proper(X)) proper(isNePal(X)) = 4X + 1 >= 4X + 1 = isNePal(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 4 >= 4 = ok(e()) proper(i()) = 6 >= 6 = ok(i()) proper(o()) = 4 >= 4 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(__(X1,X2)) U11(ok(X)) = X >= X = ok(U11(X)) U21(ok(X1),ok(X2)) = X1 + 2X2 >= X1 + 2X2 = ok(U21(X1,X2)) U22(ok(X)) = X + 1 >= X + 1 = ok(U22(X)) isList(ok(X)) = 2X >= 2X = ok(isList(X)) U31(ok(X)) = X >= X = ok(U31(X)) U41(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(U41(X1,X2)) U42(ok(X)) = 2X + 4 >= 2X + 4 = ok(U42(X)) isNeList(ok(X)) = X >= X = ok(isNeList(X)) U51(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(U51(X1,X2)) U52(ok(X)) = 4X >= 4X = ok(U52(X)) U61(ok(X)) = X >= X = ok(U61(X)) U71(ok(X1),ok(X2)) = 6X1 + X2 >= 6X1 + X2 = ok(U71(X1,X2)) U72(ok(X)) = 2X >= 2X = ok(U72(X)) isPal(ok(X)) = 4X + 3 >= 4X + 3 = ok(isPal(X)) U81(ok(X)) = X + 2 >= X + 2 = ok(U81(X)) isQid(ok(X)) = X >= X = ok(isQid(X)) isNePal(ok(X)) = 4X + 1 >= 4X + 1 = ok(isNePal(X)) top(mark(X)) = 2X + 4 >= 2X + 4 = top(proper(X)) top(ok(X)) = 2X + 4 >= 2X + 4 = top(active(X)) problem: active(U11(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isNeList(V))) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isPal(V)) -> mark(U81(isNePal(V))) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U61(mark(X)) -> mark(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U81(mark(X)) -> mark(U81(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(ok(X)) -> ok(U22(X)) isList(ok(X)) -> ok(isList(X)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(ok(X)) -> ok(U42(X)) isNeList(ok(X)) -> ok(isNeList(X)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(ok(X)) -> ok(U52(X)) U61(ok(X)) -> ok(U61(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isPal(ok(X)) -> ok(isPal(X)) U81(ok(X)) -> ok(U81(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dim=1 interpretation: [top](x0) = 2x0 + 6, [ok](x0) = x0, [proper](x0) = x0, [u] = 0, [o] = 0, [i] = 2, [e] = 0, [a] = 0, [isNePal](x0) = 2x0, [isQid](x0) = x0, [U81](x0) = x0, [U72](x0) = x0, [isPal](x0) = 2x0, [U71](x0, x1) = x0 + x1, [U61](x0) = 2x0, [U52](x0) = 4x0, [U51](x0, x1) = x0 + x1, [U42](x0) = 2x0 + 4, [isNeList](x0) = x0, [U41](x0, x1) = 2x0 + 2x1 + 1, [U31](x0) = x0 + 5, [U22](x0) = 4x0, [isList](x0) = 4x0, [U21](x0, x1) = 4x0 + x1, [U11](x0) = 2x0, [tt] = 1, [nil] = 2, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = 4x0 + x1 orientation: active(U11(tt())) = 2 >= 1 = mark(tt()) active(isList(V)) = 4V >= 2V = mark(U11(isNeList(V))) active(isList(__(V1,V2))) = 16V1 + 4V2 >= 16V1 + V2 = mark(U21(isList(V1),V2)) active(isPal(V)) = 2V >= 2V = mark(U81(isNePal(V))) active(__(X1,X2)) = 4X1 + X2 >= 4X1 + X2 = __(active(X1),X2) active(__(X1,X2)) = 4X1 + X2 >= 4X1 + X2 = __(X1,active(X2)) active(U11(X)) = 2X >= 2X = U11(active(X)) active(U21(X1,X2)) = 4X1 + X2 >= 4X1 + X2 = U21(active(X1),X2) active(U22(X)) = 4X >= 4X = U22(active(X)) active(U31(X)) = X + 5 >= X + 5 = U31(active(X)) active(U41(X1,X2)) = 2X1 + 2X2 + 1 >= 2X1 + 2X2 + 1 = U41(active(X1),X2) active(U42(X)) = 2X + 4 >= 2X + 4 = U42(active(X)) active(U51(X1,X2)) = X1 + X2 >= X1 + X2 = U51(active(X1),X2) active(U52(X)) = 4X >= 4X = U52(active(X)) active(U61(X)) = 2X >= 2X = U61(active(X)) active(U71(X1,X2)) = X1 + X2 >= X1 + X2 = U71(active(X1),X2) active(U72(X)) = X >= X = U72(active(X)) active(U81(X)) = X >= X = U81(active(X)) __(mark(X1),X2) = 4X1 + X2 >= 4X1 + X2 = mark(__(X1,X2)) __(X1,mark(X2)) = 4X1 + X2 >= 4X1 + X2 = mark(__(X1,X2)) U11(mark(X)) = 2X >= 2X = mark(U11(X)) U21(mark(X1),X2) = 4X1 + X2 >= 4X1 + X2 = mark(U21(X1,X2)) U22(mark(X)) = 4X >= 4X = mark(U22(X)) U31(mark(X)) = X + 5 >= X + 5 = mark(U31(X)) U41(mark(X1),X2) = 2X1 + 2X2 + 1 >= 2X1 + 2X2 + 1 = mark(U41(X1,X2)) U42(mark(X)) = 2X + 4 >= 2X + 4 = mark(U42(X)) U51(mark(X1),X2) = X1 + X2 >= X1 + X2 = mark(U51(X1,X2)) U52(mark(X)) = 4X >= 4X = mark(U52(X)) U61(mark(X)) = 2X >= 2X = mark(U61(X)) U71(mark(X1),X2) = X1 + X2 >= X1 + X2 = mark(U71(X1,X2)) U72(mark(X)) = X >= X = mark(U72(X)) U81(mark(X)) = X >= X = mark(U81(X)) proper(__(X1,X2)) = 4X1 + X2 >= 4X1 + X2 = __(proper(X1),proper(X2)) proper(nil()) = 2 >= 2 = ok(nil()) proper(U11(X)) = 2X >= 2X = U11(proper(X)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U21(X1,X2)) = 4X1 + X2 >= 4X1 + X2 = U21(proper(X1),proper(X2)) proper(U22(X)) = 4X >= 4X = U22(proper(X)) proper(isList(X)) = 4X >= 4X = isList(proper(X)) proper(U31(X)) = X + 5 >= X + 5 = U31(proper(X)) proper(U41(X1,X2)) = 2X1 + 2X2 + 1 >= 2X1 + 2X2 + 1 = U41(proper(X1),proper(X2)) proper(U42(X)) = 2X + 4 >= 2X + 4 = U42(proper(X)) proper(isNeList(X)) = X >= X = isNeList(proper(X)) proper(U51(X1,X2)) = X1 + X2 >= X1 + X2 = U51(proper(X1),proper(X2)) proper(U52(X)) = 4X >= 4X = U52(proper(X)) proper(U61(X)) = 2X >= 2X = U61(proper(X)) proper(U71(X1,X2)) = X1 + X2 >= X1 + X2 = U71(proper(X1),proper(X2)) proper(U72(X)) = X >= X = U72(proper(X)) proper(isPal(X)) = 2X >= 2X = isPal(proper(X)) proper(U81(X)) = X >= X = U81(proper(X)) proper(isQid(X)) = X >= X = isQid(proper(X)) proper(isNePal(X)) = 2X >= 2X = isNePal(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 2 >= 2 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = 4X1 + X2 >= 4X1 + X2 = ok(__(X1,X2)) U11(ok(X)) = 2X >= 2X = ok(U11(X)) U21(ok(X1),ok(X2)) = 4X1 + X2 >= 4X1 + X2 = ok(U21(X1,X2)) U22(ok(X)) = 4X >= 4X = ok(U22(X)) isList(ok(X)) = 4X >= 4X = ok(isList(X)) U31(ok(X)) = X + 5 >= X + 5 = ok(U31(X)) U41(ok(X1),ok(X2)) = 2X1 + 2X2 + 1 >= 2X1 + 2X2 + 1 = ok(U41(X1,X2)) U42(ok(X)) = 2X + 4 >= 2X + 4 = ok(U42(X)) isNeList(ok(X)) = X >= X = ok(isNeList(X)) U51(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(U51(X1,X2)) U52(ok(X)) = 4X >= 4X = ok(U52(X)) U61(ok(X)) = 2X >= 2X = ok(U61(X)) U71(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(U71(X1,X2)) U72(ok(X)) = X >= X = ok(U72(X)) isPal(ok(X)) = 2X >= 2X = ok(isPal(X)) U81(ok(X)) = X >= X = ok(U81(X)) isQid(ok(X)) = X >= X = ok(isQid(X)) isNePal(ok(X)) = 2X >= 2X = ok(isNePal(X)) top(mark(X)) = 2X + 6 >= 2X + 6 = top(proper(X)) top(ok(X)) = 2X + 6 >= 2X + 6 = top(active(X)) problem: active(isList(V)) -> mark(U11(isNeList(V))) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isPal(V)) -> mark(U81(isNePal(V))) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U61(mark(X)) -> mark(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U81(mark(X)) -> mark(U81(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(ok(X)) -> ok(U22(X)) isList(ok(X)) -> ok(isList(X)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(ok(X)) -> ok(U42(X)) isNeList(ok(X)) -> ok(isNeList(X)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(ok(X)) -> ok(U52(X)) U61(ok(X)) -> ok(U61(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isPal(ok(X)) -> ok(isPal(X)) U81(ok(X)) -> ok(U81(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [top](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [ok](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [0] [proper](x0) = [0 0 0]x0 + [1] [0 0 1] [0], [0] [u] = [0] [0], [0] [o] = [0] [0], [0] [i] = [0] [1], [0] [e] = [0] [0], [0] [a] = [0] [1], [1 0 0] [isNePal](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [isQid](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [U81](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1] [U72](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [1 0 0] [1] [isPal](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [1 0 0] [1 0 0] [U71](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [1] [U61](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [1 0 0] [U52](x0) = [0 0 0]x0 [0 0 1] , [1 0 0] [1 0 0] [U51](x0, x1) = [0 1 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [1] [U42](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [1 0 0] [isNeList](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [U41](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [U31](x0) = [0 0 0]x0 [0 0 1] , [1 0 0] [U22](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1] [isList](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [1 0 0] [1 0 0] [U21](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [1] [U11](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [0] [tt] = [0] [0], [0] [nil] = [0] [0], [1 0 0] [mark](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [active](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [__](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] orientation: [1 0 0] [1] [1 0 0] [1] active(isList(V)) = [0 0 0]V + [0] >= [0 0 0]V + [0] = mark(U11(isNeList(V))) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] [1] active(isList(__(V1,V2))) = [0 0 0]V1 + [0 0 0]V2 + [0] >= [0 0 0]V1 + [0 0 0]V2 + [0] = mark(U21(isList(V1),V2)) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 0] [1] [1 0 0] active(isPal(V)) = [0 0 0]V + [0] >= [0 0 0]V = mark(U81(isNePal(V))) [0 0 0] [0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] active(__(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = __(active(X1),X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] active(__(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = __(X1,active(X2)) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1] [1 0 0] [1] active(U11(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = U11(active(X)) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] active(U21(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = U21(active(X1),X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] active(U22(X)) = [0 0 0]X >= [0 0 0]X = U22(active(X)) [0 0 0] [0 0 0] [1 0 0] [1 0 0] active(U31(X)) = [0 0 0]X >= [0 0 0]X = U31(active(X)) [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] active(U41(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = U41(active(X1),X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1] [1 0 0] [1] active(U42(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = U42(active(X)) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] active(U51(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = U51(active(X1),X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] active(U52(X)) = [0 0 0]X >= [0 0 0]X = U52(active(X)) [0 0 0] [0 0 0] [1 0 0] [1] [1 0 0] [1] active(U61(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = U61(active(X)) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] active(U71(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = U71(active(X1),X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1] [1 0 0] [1] active(U72(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = U72(active(X)) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1 0 0] active(U81(X)) = [0 0 0]X >= [0 0 0]X = U81(active(X)) [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] __(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = mark(__(X1,X2)) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] __(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = mark(__(X1,X2)) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1] [1 0 0] [1] U11(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = mark(U11(X)) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] U21(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = mark(U21(X1,X2)) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] U22(mark(X)) = [0 0 0]X >= [0 0 0]X = mark(U22(X)) [0 0 0] [0 0 0] [1 0 0] [1 0 0] U31(mark(X)) = [0 0 0]X >= [0 0 0]X = mark(U31(X)) [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] U41(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = mark(U41(X1,X2)) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1] [1 0 0] [1] U42(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = mark(U42(X)) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] U51(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = mark(U51(X1,X2)) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] U52(mark(X)) = [0 0 0]X >= [0 0 0]X = mark(U52(X)) [0 0 0] [0 0 0] [1 0 0] [1] [1 0 0] [1] U61(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = mark(U61(X)) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] U71(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = mark(U71(X1,X2)) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1] [1 0 0] [1] U72(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = mark(U72(X)) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1 0 0] U81(mark(X)) = [0 0 0]X >= [0 0 0]X = mark(U81(X)) [0 0 0] [0 0 0] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] proper(__(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 = __(proper(X1),proper(X2)) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [0] proper(nil()) = [1] >= [0] = ok(nil()) [0] [0] [1 0 0] [1] [1 0 0] [1] proper(U11(X)) = [0 0 0]X + [1] >= [0 0 0]X + [0] = U11(proper(X)) [0 0 0] [0] [0 0 0] [0] [0] [0] proper(tt()) = [1] >= [0] = ok(tt()) [0] [0] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] proper(U21(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 = U21(proper(X1),proper(X2)) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [1 0 0] [0] [1 0 0] proper(U22(X)) = [0 0 0]X + [1] >= [0 0 0]X = U22(proper(X)) [0 0 0] [0] [0 0 0] [1 0 0] [1] [1 0 0] [1] proper(isList(X)) = [0 0 0]X + [1] >= [0 0 0]X + [0] = isList(proper(X)) [0 0 0] [0] [0 0 0] [0] [1 0 0] [0] [1 0 0] proper(U31(X)) = [0 0 0]X + [1] >= [0 0 0]X = U31(proper(X)) [0 0 1] [0] [0 0 1] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] proper(U41(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 = U41(proper(X1),proper(X2)) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [1 0 0] [1] [1 0 0] [1] proper(U42(X)) = [0 0 0]X + [1] >= [0 0 0]X + [0] = U42(proper(X)) [0 0 0] [0] [0 0 0] [0] [1 0 0] [0] [1 0 0] proper(isNeList(X)) = [0 0 0]X + [1] >= [0 0 0]X = isNeList(proper(X)) [0 0 0] [0] [0 0 0] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] proper(U51(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = U51(proper(X1),proper(X2)) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 0] [0] [1 0 0] proper(U52(X)) = [0 0 0]X + [1] >= [0 0 0]X = U52(proper(X)) [0 0 1] [0] [0 0 1] [1 0 0] [1] [1 0 0] [1] proper(U61(X)) = [0 0 0]X + [1] >= [0 0 0]X + [0] = U61(proper(X)) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] proper(U71(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 = U71(proper(X1),proper(X2)) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [1 0 0] [1] [1 0 0] [1] proper(U72(X)) = [0 0 0]X + [1] >= [0 0 0]X + [0] = U72(proper(X)) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1] [1 0 0] [1] proper(isPal(X)) = [0 0 0]X + [1] >= [0 0 0]X + [0] = isPal(proper(X)) [0 0 0] [1] [0 0 0] [1] [1 0 0] [0] [1 0 0] proper(U81(X)) = [0 0 0]X + [1] >= [0 0 0]X = U81(proper(X)) [0 0 0] [0] [0 0 0] [1 0 0] [0] [1 0 0] proper(isQid(X)) = [0 0 0]X + [1] >= [0 0 0]X = isQid(proper(X)) [0 0 0] [0] [0 0 0] [1 0 0] [0] [1 0 0] proper(isNePal(X)) = [0 0 0]X + [1] >= [0 0 0]X = isNePal(proper(X)) [0 0 0] [0] [0 0 0] [0] [0] proper(a()) = [1] >= [0] = ok(a()) [1] [0] [0] [0] proper(e()) = [1] >= [0] = ok(e()) [0] [0] [0] [0] proper(i()) = [1] >= [0] = ok(i()) [1] [0] [0] [0] proper(o()) = [1] >= [0] = ok(o()) [0] [0] [0] [0] proper(u()) = [1] >= [0] = ok(u()) [0] [0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] __(ok(X1),ok(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = ok(__(X1,X2)) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1] [1 0 0] [1] U11(ok(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = ok(U11(X)) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] U21(ok(X1),ok(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = ok(U21(X1,X2)) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] U22(ok(X)) = [0 0 0]X >= [0 0 0]X = ok(U22(X)) [0 0 0] [0 0 0] [1 0 0] [1] [1 0 0] [1] isList(ok(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = ok(isList(X)) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1 0 0] U31(ok(X)) = [0 0 0]X >= [0 0 0]X = ok(U31(X)) [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] U41(ok(X1),ok(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = ok(U41(X1,X2)) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1] [1 0 0] [1] U42(ok(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = ok(U42(X)) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1 0 0] isNeList(ok(X)) = [0 0 0]X >= [0 0 0]X = ok(isNeList(X)) [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] U51(ok(X1),ok(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = ok(U51(X1,X2)) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] U52(ok(X)) = [0 0 0]X >= [0 0 0]X = ok(U52(X)) [0 0 0] [0 0 0] [1 0 0] [1] [1 0 0] [1] U61(ok(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = ok(U61(X)) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] U71(ok(X1),ok(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = ok(U71(X1,X2)) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1] [1 0 0] [1] U72(ok(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = ok(U72(X)) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1] [1 0 0] [1] isPal(ok(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = ok(isPal(X)) [0 0 0] [1] [0 0 0] [0] [1 0 0] [1 0 0] U81(ok(X)) = [0 0 0]X >= [0 0 0]X = ok(U81(X)) [0 0 0] [0 0 0] [1 0 0] [1 0 0] isQid(ok(X)) = [0 0 0]X >= [0 0 0]X = ok(isQid(X)) [0 0 0] [0 0 0] [1 0 0] [1 0 0] isNePal(ok(X)) = [0 0 0]X >= [0 0 0]X = ok(isNePal(X)) [0 0 0] [0 0 0] [1 0 0] [1 0 0] top(mark(X)) = [0 0 0]X >= [0 0 0]X = top(proper(X)) [0 0 0] [0 0 0] [1 0 0] [1 0 0] top(ok(X)) = [0 0 0]X >= [0 0 0]X = top(active(X)) [0 0 0] [0 0 0] problem: active(isList(V)) -> mark(U11(isNeList(V))) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U61(mark(X)) -> mark(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U81(mark(X)) -> mark(U81(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(ok(X)) -> ok(U22(X)) isList(ok(X)) -> ok(isList(X)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(ok(X)) -> ok(U42(X)) isNeList(ok(X)) -> ok(isNeList(X)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(ok(X)) -> ok(U52(X)) U61(ok(X)) -> ok(U61(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isPal(ok(X)) -> ok(isPal(X)) U81(ok(X)) -> ok(U81(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dim=1 interpretation: [top](x0) = x0 + 4, [ok](x0) = x0, [proper](x0) = x0, [u] = 4, [o] = 4, [i] = 4, [e] = 2, [a] = 0, [isNePal](x0) = x0 + 2, [isQid](x0) = x0 + 4, [U81](x0) = x0, [U72](x0) = 4x0, [isPal](x0) = 4x0, [U71](x0, x1) = x0 + x1 + 2, [U61](x0) = x0, [U52](x0) = 4x0, [U51](x0, x1) = 4x0 + x1, [U42](x0) = x0, [isNeList](x0) = 2x0, [U41](x0, x1) = x0 + x1, [U31](x0) = x0, [U22](x0) = 4x0 + 5, [isList](x0) = 4x0 + 1, [U21](x0, x1) = 4x0 + x1 + 4, [U11](x0) = 2x0 + 1, [tt] = 0, [nil] = 4, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = 4x0 + 2x1 + 2 orientation: active(isList(V)) = 4V + 1 >= 4V + 1 = mark(U11(isNeList(V))) active(isList(__(V1,V2))) = 16V1 + 8V2 + 9 >= 16V1 + V2 + 8 = mark(U21(isList(V1),V2)) active(__(X1,X2)) = 4X1 + 2X2 + 2 >= 4X1 + 2X2 + 2 = __(active(X1),X2) active(__(X1,X2)) = 4X1 + 2X2 + 2 >= 4X1 + 2X2 + 2 = __(X1,active(X2)) active(U11(X)) = 2X + 1 >= 2X + 1 = U11(active(X)) active(U21(X1,X2)) = 4X1 + X2 + 4 >= 4X1 + X2 + 4 = U21(active(X1),X2) active(U22(X)) = 4X + 5 >= 4X + 5 = U22(active(X)) active(U31(X)) = X >= X = U31(active(X)) active(U41(X1,X2)) = X1 + X2 >= X1 + X2 = U41(active(X1),X2) active(U42(X)) = X >= X = U42(active(X)) active(U51(X1,X2)) = 4X1 + X2 >= 4X1 + X2 = U51(active(X1),X2) active(U52(X)) = 4X >= 4X = U52(active(X)) active(U61(X)) = X >= X = U61(active(X)) active(U71(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = U71(active(X1),X2) active(U72(X)) = 4X >= 4X = U72(active(X)) active(U81(X)) = X >= X = U81(active(X)) __(mark(X1),X2) = 4X1 + 2X2 + 2 >= 4X1 + 2X2 + 2 = mark(__(X1,X2)) __(X1,mark(X2)) = 4X1 + 2X2 + 2 >= 4X1 + 2X2 + 2 = mark(__(X1,X2)) U11(mark(X)) = 2X + 1 >= 2X + 1 = mark(U11(X)) U21(mark(X1),X2) = 4X1 + X2 + 4 >= 4X1 + X2 + 4 = mark(U21(X1,X2)) U22(mark(X)) = 4X + 5 >= 4X + 5 = mark(U22(X)) U31(mark(X)) = X >= X = mark(U31(X)) U41(mark(X1),X2) = X1 + X2 >= X1 + X2 = mark(U41(X1,X2)) U42(mark(X)) = X >= X = mark(U42(X)) U51(mark(X1),X2) = 4X1 + X2 >= 4X1 + X2 = mark(U51(X1,X2)) U52(mark(X)) = 4X >= 4X = mark(U52(X)) U61(mark(X)) = X >= X = mark(U61(X)) U71(mark(X1),X2) = X1 + X2 + 2 >= X1 + X2 + 2 = mark(U71(X1,X2)) U72(mark(X)) = 4X >= 4X = mark(U72(X)) U81(mark(X)) = X >= X = mark(U81(X)) proper(__(X1,X2)) = 4X1 + 2X2 + 2 >= 4X1 + 2X2 + 2 = __(proper(X1),proper(X2)) proper(nil()) = 4 >= 4 = ok(nil()) proper(U11(X)) = 2X + 1 >= 2X + 1 = U11(proper(X)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U21(X1,X2)) = 4X1 + X2 + 4 >= 4X1 + X2 + 4 = U21(proper(X1),proper(X2)) proper(U22(X)) = 4X + 5 >= 4X + 5 = U22(proper(X)) proper(isList(X)) = 4X + 1 >= 4X + 1 = isList(proper(X)) proper(U31(X)) = X >= X = U31(proper(X)) proper(U41(X1,X2)) = X1 + X2 >= X1 + X2 = U41(proper(X1),proper(X2)) proper(U42(X)) = X >= X = U42(proper(X)) proper(isNeList(X)) = 2X >= 2X = isNeList(proper(X)) proper(U51(X1,X2)) = 4X1 + X2 >= 4X1 + X2 = U51(proper(X1),proper(X2)) proper(U52(X)) = 4X >= 4X = U52(proper(X)) proper(U61(X)) = X >= X = U61(proper(X)) proper(U71(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = U71(proper(X1),proper(X2)) proper(U72(X)) = 4X >= 4X = U72(proper(X)) proper(isPal(X)) = 4X >= 4X = isPal(proper(X)) proper(U81(X)) = X >= X = U81(proper(X)) proper(isQid(X)) = X + 4 >= X + 4 = isQid(proper(X)) proper(isNePal(X)) = X + 2 >= X + 2 = isNePal(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 2 >= 2 = ok(e()) proper(i()) = 4 >= 4 = ok(i()) proper(o()) = 4 >= 4 = ok(o()) proper(u()) = 4 >= 4 = ok(u()) __(ok(X1),ok(X2)) = 4X1 + 2X2 + 2 >= 4X1 + 2X2 + 2 = ok(__(X1,X2)) U11(ok(X)) = 2X + 1 >= 2X + 1 = ok(U11(X)) U21(ok(X1),ok(X2)) = 4X1 + X2 + 4 >= 4X1 + X2 + 4 = ok(U21(X1,X2)) U22(ok(X)) = 4X + 5 >= 4X + 5 = ok(U22(X)) isList(ok(X)) = 4X + 1 >= 4X + 1 = ok(isList(X)) U31(ok(X)) = X >= X = ok(U31(X)) U41(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(U41(X1,X2)) U42(ok(X)) = X >= X = ok(U42(X)) isNeList(ok(X)) = 2X >= 2X = ok(isNeList(X)) U51(ok(X1),ok(X2)) = 4X1 + X2 >= 4X1 + X2 = ok(U51(X1,X2)) U52(ok(X)) = 4X >= 4X = ok(U52(X)) U61(ok(X)) = X >= X = ok(U61(X)) U71(ok(X1),ok(X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = ok(U71(X1,X2)) U72(ok(X)) = 4X >= 4X = ok(U72(X)) isPal(ok(X)) = 4X >= 4X = ok(isPal(X)) U81(ok(X)) = X >= X = ok(U81(X)) isQid(ok(X)) = X + 4 >= X + 4 = ok(isQid(X)) isNePal(ok(X)) = X + 2 >= X + 2 = ok(isNePal(X)) top(mark(X)) = X + 4 >= X + 4 = top(proper(X)) top(ok(X)) = X + 4 >= X + 4 = top(active(X)) problem: active(isList(V)) -> mark(U11(isNeList(V))) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U61(mark(X)) -> mark(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U81(mark(X)) -> mark(U81(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(ok(X)) -> ok(U22(X)) isList(ok(X)) -> ok(isList(X)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(ok(X)) -> ok(U42(X)) isNeList(ok(X)) -> ok(isNeList(X)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(ok(X)) -> ok(U52(X)) U61(ok(X)) -> ok(U61(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isPal(ok(X)) -> ok(isPal(X)) U81(ok(X)) -> ok(U81(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dim=1 interpretation: [top](x0) = 2x0, [ok](x0) = x0, [proper](x0) = x0, [u] = 6, [o] = 2, [i] = 2, [e] = 2, [a] = 4, [isNePal](x0) = 2x0, [isQid](x0) = x0, [U81](x0) = 2x0 + 2, [U72](x0) = x0 + 2, [isPal](x0) = 4x0 + 4, [U71](x0, x1) = 4x0 + 4x1 + 1, [U61](x0) = 4x0, [U52](x0) = 2x0, [U51](x0, x1) = x0 + 2x1, [U42](x0) = x0 + 3, [isNeList](x0) = x0, [U41](x0, x1) = x0 + 2x1 + 4, [U31](x0) = x0 + 4, [U22](x0) = 2x0 + 2, [isList](x0) = 2x0 + 4, [U21](x0, x1) = 2x0 + 4x1 + 4, [U11](x0) = x0, [tt] = 5, [nil] = 0, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = 2x0 + x1 + 4 orientation: active(isList(V)) = 2V + 4 >= V = mark(U11(isNeList(V))) active(__(X1,X2)) = 2X1 + X2 + 4 >= 2X1 + X2 + 4 = __(active(X1),X2) active(__(X1,X2)) = 2X1 + X2 + 4 >= 2X1 + X2 + 4 = __(X1,active(X2)) active(U11(X)) = X >= X = U11(active(X)) active(U21(X1,X2)) = 2X1 + 4X2 + 4 >= 2X1 + 4X2 + 4 = U21(active(X1),X2) active(U22(X)) = 2X + 2 >= 2X + 2 = U22(active(X)) active(U31(X)) = X + 4 >= X + 4 = U31(active(X)) active(U41(X1,X2)) = X1 + 2X2 + 4 >= X1 + 2X2 + 4 = U41(active(X1),X2) active(U42(X)) = X + 3 >= X + 3 = U42(active(X)) active(U51(X1,X2)) = X1 + 2X2 >= X1 + 2X2 = U51(active(X1),X2) active(U52(X)) = 2X >= 2X = U52(active(X)) active(U61(X)) = 4X >= 4X = U61(active(X)) active(U71(X1,X2)) = 4X1 + 4X2 + 1 >= 4X1 + 4X2 + 1 = U71(active(X1),X2) active(U72(X)) = X + 2 >= X + 2 = U72(active(X)) active(U81(X)) = 2X + 2 >= 2X + 2 = U81(active(X)) __(mark(X1),X2) = 2X1 + X2 + 4 >= 2X1 + X2 + 4 = mark(__(X1,X2)) __(X1,mark(X2)) = 2X1 + X2 + 4 >= 2X1 + X2 + 4 = mark(__(X1,X2)) U11(mark(X)) = X >= X = mark(U11(X)) U21(mark(X1),X2) = 2X1 + 4X2 + 4 >= 2X1 + 4X2 + 4 = mark(U21(X1,X2)) U22(mark(X)) = 2X + 2 >= 2X + 2 = mark(U22(X)) U31(mark(X)) = X + 4 >= X + 4 = mark(U31(X)) U41(mark(X1),X2) = X1 + 2X2 + 4 >= X1 + 2X2 + 4 = mark(U41(X1,X2)) U42(mark(X)) = X + 3 >= X + 3 = mark(U42(X)) U51(mark(X1),X2) = X1 + 2X2 >= X1 + 2X2 = mark(U51(X1,X2)) U52(mark(X)) = 2X >= 2X = mark(U52(X)) U61(mark(X)) = 4X >= 4X = mark(U61(X)) U71(mark(X1),X2) = 4X1 + 4X2 + 1 >= 4X1 + 4X2 + 1 = mark(U71(X1,X2)) U72(mark(X)) = X + 2 >= X + 2 = mark(U72(X)) U81(mark(X)) = 2X + 2 >= 2X + 2 = mark(U81(X)) proper(__(X1,X2)) = 2X1 + X2 + 4 >= 2X1 + X2 + 4 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X)) = X >= X = U11(proper(X)) proper(tt()) = 5 >= 5 = ok(tt()) proper(U21(X1,X2)) = 2X1 + 4X2 + 4 >= 2X1 + 4X2 + 4 = U21(proper(X1),proper(X2)) proper(U22(X)) = 2X + 2 >= 2X + 2 = U22(proper(X)) proper(isList(X)) = 2X + 4 >= 2X + 4 = isList(proper(X)) proper(U31(X)) = X + 4 >= X + 4 = U31(proper(X)) proper(U41(X1,X2)) = X1 + 2X2 + 4 >= X1 + 2X2 + 4 = U41(proper(X1),proper(X2)) proper(U42(X)) = X + 3 >= X + 3 = U42(proper(X)) proper(isNeList(X)) = X >= X = isNeList(proper(X)) proper(U51(X1,X2)) = X1 + 2X2 >= X1 + 2X2 = U51(proper(X1),proper(X2)) proper(U52(X)) = 2X >= 2X = U52(proper(X)) proper(U61(X)) = 4X >= 4X = U61(proper(X)) proper(U71(X1,X2)) = 4X1 + 4X2 + 1 >= 4X1 + 4X2 + 1 = U71(proper(X1),proper(X2)) proper(U72(X)) = X + 2 >= X + 2 = U72(proper(X)) proper(isPal(X)) = 4X + 4 >= 4X + 4 = isPal(proper(X)) proper(U81(X)) = 2X + 2 >= 2X + 2 = U81(proper(X)) proper(isQid(X)) = X >= X = isQid(proper(X)) proper(isNePal(X)) = 2X >= 2X = isNePal(proper(X)) proper(a()) = 4 >= 4 = ok(a()) proper(e()) = 2 >= 2 = ok(e()) proper(i()) = 2 >= 2 = ok(i()) proper(o()) = 2 >= 2 = ok(o()) proper(u()) = 6 >= 6 = ok(u()) __(ok(X1),ok(X2)) = 2X1 + X2 + 4 >= 2X1 + X2 + 4 = ok(__(X1,X2)) U11(ok(X)) = X >= X = ok(U11(X)) U21(ok(X1),ok(X2)) = 2X1 + 4X2 + 4 >= 2X1 + 4X2 + 4 = ok(U21(X1,X2)) U22(ok(X)) = 2X + 2 >= 2X + 2 = ok(U22(X)) isList(ok(X)) = 2X + 4 >= 2X + 4 = ok(isList(X)) U31(ok(X)) = X + 4 >= X + 4 = ok(U31(X)) U41(ok(X1),ok(X2)) = X1 + 2X2 + 4 >= X1 + 2X2 + 4 = ok(U41(X1,X2)) U42(ok(X)) = X + 3 >= X + 3 = ok(U42(X)) isNeList(ok(X)) = X >= X = ok(isNeList(X)) U51(ok(X1),ok(X2)) = X1 + 2X2 >= X1 + 2X2 = ok(U51(X1,X2)) U52(ok(X)) = 2X >= 2X = ok(U52(X)) U61(ok(X)) = 4X >= 4X = ok(U61(X)) U71(ok(X1),ok(X2)) = 4X1 + 4X2 + 1 >= 4X1 + 4X2 + 1 = ok(U71(X1,X2)) U72(ok(X)) = X + 2 >= X + 2 = ok(U72(X)) isPal(ok(X)) = 4X + 4 >= 4X + 4 = ok(isPal(X)) U81(ok(X)) = 2X + 2 >= 2X + 2 = ok(U81(X)) isQid(ok(X)) = X >= X = ok(isQid(X)) isNePal(ok(X)) = 2X >= 2X = ok(isNePal(X)) top(mark(X)) = 2X >= 2X = top(proper(X)) top(ok(X)) = 2X >= 2X = top(active(X)) problem: active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U61(mark(X)) -> mark(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U81(mark(X)) -> mark(U81(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(ok(X)) -> ok(U22(X)) isList(ok(X)) -> ok(isList(X)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(ok(X)) -> ok(U42(X)) isNeList(ok(X)) -> ok(isNeList(X)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(ok(X)) -> ok(U52(X)) U61(ok(X)) -> ok(U61(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isPal(ok(X)) -> ok(isPal(X)) U81(ok(X)) -> ok(U81(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [top](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [ok](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [proper](x0) = [0 0 0]x0 [1 0 0] , [0] [u] = [0] [0], [0] [o] = [0] [0], [0] [i] = [0] [0], [0] [e] = [0] [0], [0] [a] = [0] [0], [1 0 0] [isNePal](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [isQid](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [U81](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [U72](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [isPal](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [U71](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [U61](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [U52](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [U51](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [U42](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [isNeList](x0) = [0 0 0]x0 [0 0 1] , [1 0 0] [1 0 0] [U41](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [U31](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [U22](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [isList](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [U21](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [U11](x0) = [0 0 0]x0 [0 0 1] , [0] [tt] = [0] [0], [0] [nil] = [0] [0], [1 0 0] [1] [mark](x0) = [0 0 0]x0 + [0] [0 0 1] [0], [1 0 0] [active](x0) = [0 0 0]x0 [1 0 0] , [1 0 0] [1 0 0] [__](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [1 0 0] orientation: [1 0 0] [1 0 0] [1 0 0] [1 0 0] active(__(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = __(active(X1),X2) [1 0 0] [1 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] active(__(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = __(X1,active(X2)) [1 0 0] [1 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] active(U11(X)) = [0 0 0]X >= [0 0 0]X = U11(active(X)) [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] active(U21(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = U21(active(X1),X2) [1 0 0] [1 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] active(U22(X)) = [0 0 0]X >= [0 0 0]X = U22(active(X)) [1 0 0] [0 0 0] [1 0 0] [1 0 0] active(U31(X)) = [0 0 0]X >= [0 0 0]X = U31(active(X)) [1 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] active(U41(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = U41(active(X1),X2) [1 0 0] [1 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] active(U42(X)) = [0 0 0]X >= [0 0 0]X = U42(active(X)) [1 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] active(U51(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = U51(active(X1),X2) [1 0 0] [1 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] active(U52(X)) = [0 0 0]X >= [0 0 0]X = U52(active(X)) [1 0 0] [0 0 0] [1 0 0] [1 0 0] active(U61(X)) = [0 0 0]X >= [0 0 0]X = U61(active(X)) [1 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] active(U71(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = U71(active(X1),X2) [1 0 0] [1 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] active(U72(X)) = [0 0 0]X >= [0 0 0]X = U72(active(X)) [1 0 0] [0 0 0] [1 0 0] [1 0 0] active(U81(X)) = [0 0 0]X >= [0 0 0]X = U81(active(X)) [1 0 0] [0 0 0] [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] [1] __(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = mark(__(X1,X2)) [0 0 0] [1 0 0] [0] [0 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] [1] __(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = mark(__(X1,X2)) [0 0 0] [1 0 0] [1] [0 0 0] [1 0 0] [0] [1 0 0] [1] [1 0 0] [1] U11(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = mark(U11(X)) [0 0 1] [0] [0 0 1] [0] [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] [1] U21(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = mark(U21(X1,X2)) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 0] [1] [1 0 0] [1] U22(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = mark(U22(X)) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1] [1 0 0] [1] U31(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = mark(U31(X)) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] [1] U41(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = mark(U41(X1,X2)) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 0] [1] [1 0 0] [1] U42(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = mark(U42(X)) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] [1] U51(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = mark(U51(X1,X2)) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 0] [1] [1 0 0] [1] U52(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = mark(U52(X)) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1] [1 0 0] [1] U61(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = mark(U61(X)) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] [1] U71(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = mark(U71(X1,X2)) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 0] [1] [1 0 0] [1] U72(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = mark(U72(X)) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1] [1 0 0] [1] U81(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = mark(U81(X)) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] proper(__(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = __(proper(X1),proper(X2)) [1 0 0] [1 0 0] [0 0 0] [1 0 0] [0] [0] proper(nil()) = [0] >= [0] = ok(nil()) [0] [0] [1 0 0] [1 0 0] proper(U11(X)) = [0 0 0]X >= [0 0 0]X = U11(proper(X)) [1 0 0] [1 0 0] [0] [0] proper(tt()) = [0] >= [0] = ok(tt()) [0] [0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] proper(U21(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = U21(proper(X1),proper(X2)) [1 0 0] [1 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] proper(U22(X)) = [0 0 0]X >= [0 0 0]X = U22(proper(X)) [1 0 0] [0 0 0] [1 0 0] [1 0 0] proper(isList(X)) = [0 0 0]X >= [0 0 0]X = isList(proper(X)) [1 0 0] [0 0 0] [1 0 0] [1 0 0] proper(U31(X)) = [0 0 0]X >= [0 0 0]X = U31(proper(X)) [1 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] proper(U41(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = U41(proper(X1),proper(X2)) [1 0 0] [1 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] proper(U42(X)) = [0 0 0]X >= [0 0 0]X = U42(proper(X)) [1 0 0] [0 0 0] [1 0 0] [1 0 0] proper(isNeList(X)) = [0 0 0]X >= [0 0 0]X = isNeList(proper(X)) [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] proper(U51(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = U51(proper(X1),proper(X2)) [1 0 0] [1 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] proper(U52(X)) = [0 0 0]X >= [0 0 0]X = U52(proper(X)) [1 0 0] [0 0 0] [1 0 0] [1 0 0] proper(U61(X)) = [0 0 0]X >= [0 0 0]X = U61(proper(X)) [1 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] proper(U71(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = U71(proper(X1),proper(X2)) [1 0 0] [1 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] proper(U72(X)) = [0 0 0]X >= [0 0 0]X = U72(proper(X)) [1 0 0] [0 0 0] [1 0 0] [1 0 0] proper(isPal(X)) = [0 0 0]X >= [0 0 0]X = isPal(proper(X)) [1 0 0] [0 0 0] [1 0 0] [1 0 0] proper(U81(X)) = [0 0 0]X >= [0 0 0]X = U81(proper(X)) [1 0 0] [0 0 0] [1 0 0] [1 0 0] proper(isQid(X)) = [0 0 0]X >= [0 0 0]X = isQid(proper(X)) [1 0 0] [0 0 0] [1 0 0] [1 0 0] proper(isNePal(X)) = [0 0 0]X >= [0 0 0]X = isNePal(proper(X)) [1 0 0] [0 0 0] [0] [0] proper(a()) = [0] >= [0] = ok(a()) [0] [0] [0] [0] proper(e()) = [0] >= [0] = ok(e()) [0] [0] [0] [0] proper(i()) = [0] >= [0] = ok(i()) [0] [0] [0] [0] proper(o()) = [0] >= [0] = ok(o()) [0] [0] [0] [0] proper(u()) = [0] >= [0] = ok(u()) [0] [0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] __(ok(X1),ok(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = ok(__(X1,X2)) [0 0 0] [1 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] U11(ok(X)) = [0 0 0]X >= [0 0 0]X = ok(U11(X)) [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] U21(ok(X1),ok(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = ok(U21(X1,X2)) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] U22(ok(X)) = [0 0 0]X >= [0 0 0]X = ok(U22(X)) [0 0 0] [0 0 0] [1 0 0] [1 0 0] isList(ok(X)) = [0 0 0]X >= [0 0 0]X = ok(isList(X)) [0 0 0] [0 0 0] [1 0 0] [1 0 0] U31(ok(X)) = [0 0 0]X >= [0 0 0]X = ok(U31(X)) [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] U41(ok(X1),ok(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = ok(U41(X1,X2)) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] U42(ok(X)) = [0 0 0]X >= [0 0 0]X = ok(U42(X)) [0 0 0] [0 0 0] [1 0 0] [1 0 0] isNeList(ok(X)) = [0 0 0]X >= [0 0 0]X = ok(isNeList(X)) [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] U51(ok(X1),ok(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = ok(U51(X1,X2)) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] U52(ok(X)) = [0 0 0]X >= [0 0 0]X = ok(U52(X)) [0 0 0] [0 0 0] [1 0 0] [1 0 0] U61(ok(X)) = [0 0 0]X >= [0 0 0]X = ok(U61(X)) [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] U71(ok(X1),ok(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = ok(U71(X1,X2)) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] U72(ok(X)) = [0 0 0]X >= [0 0 0]X = ok(U72(X)) [0 0 0] [0 0 0] [1 0 0] [1 0 0] isPal(ok(X)) = [0 0 0]X >= [0 0 0]X = ok(isPal(X)) [0 0 0] [0 0 0] [1 0 0] [1 0 0] U81(ok(X)) = [0 0 0]X >= [0 0 0]X = ok(U81(X)) [0 0 0] [0 0 0] [1 0 0] [1 0 0] isQid(ok(X)) = [0 0 0]X >= [0 0 0]X = ok(isQid(X)) [0 0 0] [0 0 0] [1 0 0] [1 0 0] isNePal(ok(X)) = [0 0 0]X >= [0 0 0]X = ok(isNePal(X)) [0 0 0] [0 0 0] [1 0 0] [1] [1 0 0] top(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X = top(proper(X)) [0 0 0] [0] [0 0 0] [1 0 0] [1 0 0] top(ok(X)) = [0 0 0]X >= [0 0 0]X = top(active(X)) [0 0 0] [0 0 0] problem: active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U61(mark(X)) -> mark(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U81(mark(X)) -> mark(U81(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(ok(X)) -> ok(U22(X)) isList(ok(X)) -> ok(isList(X)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(ok(X)) -> ok(U42(X)) isNeList(ok(X)) -> ok(isNeList(X)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(ok(X)) -> ok(U52(X)) U61(ok(X)) -> ok(U61(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isPal(ok(X)) -> ok(isPal(X)) U81(ok(X)) -> ok(U81(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dim=3 interpretation: [1 0 1] [top](x0) = [0 0 1]x0 [0 0 0] , [1 1 0] [0] [ok](x0) = [0 1 0]x0 + [0] [0 0 1] [1], [1 1 0] [0] [proper](x0) = [0 1 0]x0 + [0] [0 0 1] [1], [1] [u] = [0] [0], [0] [o] = [0] [0], [0] [i] = [0] [0], [0] [e] = [0] [0], [0] [a] = [0] [0], [1 0 1] [0] [isNePal](x0) = [0 1 0]x0 + [1] [0 1 1] [0], [1] [isQid](x0) = x0 + [0] [0], [1 0 1] [0] [U81](x0) = [0 1 0]x0 + [1] [0 0 1] [0], [U72](x0) = x0 , [isPal](x0) = x0 , [1 0 1] [0] [U71](x0, x1) = [0 1 0]x0 + x1 + [1] [0 0 0] [0], [1 0 1] [0] [U61](x0) = [0 1 0]x0 + [1] [0 0 1] [0], [1 0 1] [0] [U52](x0) = [0 1 0]x0 + [1] [0 0 1] [0], [1 0 0] [U51](x0, x1) = x0 + [0 1 0]x1 [0 0 0] , [1 0 0] [1] [U42](x0) = [0 1 0]x0 + [0] [0 1 1] [0], [1] [isNeList](x0) = x0 + [0] [0], [1 0 0] [U41](x0, x1) = x0 + [0 1 0]x1 [0 1 0] , [U31](x0) = x0 , [1] [U22](x0) = x0 + [0] [0], [1 0 0] [isList](x0) = [0 1 0]x0 [0 1 1] , [1 0 0] [U21](x0, x1) = [0 1 0]x0 + x1 [0 0 0] , [1 0 1] [0] [U11](x0) = [0 1 0]x0 + [1] [0 0 1] [0], [0] [tt] = [1] [0], [0] [nil] = [0] [0], [mark](x0) = x0 , [1 1 0] [active](x0) = [0 1 0]x0 [0 0 1] , [1 0 1] [1 0 0] [0] [__](x0, x1) = [0 1 0]x0 + [0 1 0]x1 + [1] [0 0 1] [0 0 0] [0] orientation: [1 1 1] [1 1 0] [1] [1 1 1] [1 0 0] [0] active(__(X1,X2)) = [0 1 0]X1 + [0 1 0]X2 + [1] >= [0 1 0]X1 + [0 1 0]X2 + [1] = __(active(X1),X2) [0 0 1] [0 0 0] [0] [0 0 1] [0 0 0] [0] [1 1 1] [1 1 0] [1] [1 0 1] [1 1 0] [0] active(__(X1,X2)) = [0 1 0]X1 + [0 1 0]X2 + [1] >= [0 1 0]X1 + [0 1 0]X2 + [1] = __(X1,active(X2)) [0 0 1] [0 0 0] [0] [0 0 1] [0 0 0] [0] [1 1 1] [1] [1 1 1] [0] active(U11(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = U11(active(X)) [0 0 1] [0] [0 0 1] [0] [1 1 0] [1 1 0] [1 1 0] active(U21(X1,X2)) = [0 1 0]X1 + [0 1 0]X2 >= [0 1 0]X1 + X2 = U21(active(X1),X2) [0 0 0] [0 0 1] [0 0 0] [1 1 0] [1] [1 1 0] [1] active(U22(X)) = [0 1 0]X + [0] >= [0 1 0]X + [0] = U22(active(X)) [0 0 1] [0] [0 0 1] [0] [1 1 0] [1 1 0] active(U31(X)) = [0 1 0]X >= [0 1 0]X = U31(active(X)) [0 0 1] [0 0 1] [1 1 0] [1 1 0] [1 1 0] [1 0 0] active(U41(X1,X2)) = [0 1 0]X1 + [0 1 0]X2 >= [0 1 0]X1 + [0 1 0]X2 = U41(active(X1),X2) [0 0 1] [0 1 0] [0 0 1] [0 1 0] [1 1 0] [1] [1 1 0] [1] active(U42(X)) = [0 1 0]X + [0] >= [0 1 0]X + [0] = U42(active(X)) [0 1 1] [0] [0 1 1] [0] [1 1 0] [1 1 0] [1 1 0] [1 0 0] active(U51(X1,X2)) = [0 1 0]X1 + [0 1 0]X2 >= [0 1 0]X1 + [0 1 0]X2 = U51(active(X1),X2) [0 0 1] [0 0 0] [0 0 1] [0 0 0] [1 1 1] [1] [1 1 1] [0] active(U52(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = U52(active(X)) [0 0 1] [0] [0 0 1] [0] [1 1 1] [1] [1 1 1] [0] active(U61(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = U61(active(X)) [0 0 1] [0] [0 0 1] [0] [1 1 1] [1 1 0] [1] [1 1 1] [0] active(U71(X1,X2)) = [0 1 0]X1 + [0 1 0]X2 + [1] >= [0 1 0]X1 + X2 + [1] = U71(active(X1),X2) [0 0 0] [0 0 1] [0] [0 0 0] [0] [1 1 0] [1 1 0] active(U72(X)) = [0 1 0]X >= [0 1 0]X = U72(active(X)) [0 0 1] [0 0 1] [1 1 1] [1] [1 1 1] [0] active(U81(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = U81(active(X)) [0 0 1] [0] [0 0 1] [0] [1 0 1] [1 0 0] [0] [1 0 1] [1 0 0] [0] __(mark(X1),X2) = [0 1 0]X1 + [0 1 0]X2 + [1] >= [0 1 0]X1 + [0 1 0]X2 + [1] = mark(__(X1,X2)) [0 0 1] [0 0 0] [0] [0 0 1] [0 0 0] [0] [1 0 1] [1 0 0] [0] [1 0 1] [1 0 0] [0] __(X1,mark(X2)) = [0 1 0]X1 + [0 1 0]X2 + [1] >= [0 1 0]X1 + [0 1 0]X2 + [1] = mark(__(X1,X2)) [0 0 1] [0 0 0] [0] [0 0 1] [0 0 0] [0] [1 0 1] [0] [1 0 1] [0] U11(mark(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = mark(U11(X)) [0 0 1] [0] [0 0 1] [0] [1 0 0] [1 0 0] U21(mark(X1),X2) = [0 1 0]X1 + X2 >= [0 1 0]X1 + X2 = mark(U21(X1,X2)) [0 0 0] [0 0 0] [1] [1] U22(mark(X)) = X + [0] >= X + [0] = mark(U22(X)) [0] [0] U31(mark(X)) = X >= X = mark(U31(X)) [1 0 0] [1 0 0] U41(mark(X1),X2) = X1 + [0 1 0]X2 >= X1 + [0 1 0]X2 = mark(U41(X1,X2)) [0 1 0] [0 1 0] [1 0 0] [1] [1 0 0] [1] U42(mark(X)) = [0 1 0]X + [0] >= [0 1 0]X + [0] = mark(U42(X)) [0 1 1] [0] [0 1 1] [0] [1 0 0] [1 0 0] U51(mark(X1),X2) = X1 + [0 1 0]X2 >= X1 + [0 1 0]X2 = mark(U51(X1,X2)) [0 0 0] [0 0 0] [1 0 1] [0] [1 0 1] [0] U52(mark(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = mark(U52(X)) [0 0 1] [0] [0 0 1] [0] [1 0 1] [0] [1 0 1] [0] U61(mark(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = mark(U61(X)) [0 0 1] [0] [0 0 1] [0] [1 0 1] [0] [1 0 1] [0] U71(mark(X1),X2) = [0 1 0]X1 + X2 + [1] >= [0 1 0]X1 + X2 + [1] = mark(U71(X1,X2)) [0 0 0] [0] [0 0 0] [0] U72(mark(X)) = X >= X = mark(U72(X)) [1 0 1] [0] [1 0 1] [0] U81(mark(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = mark(U81(X)) [0 0 1] [0] [0 0 1] [0] [1 1 1] [1 1 0] [1] [1 1 1] [1 1 0] [1] proper(__(X1,X2)) = [0 1 0]X1 + [0 1 0]X2 + [1] >= [0 1 0]X1 + [0 1 0]X2 + [1] = __(proper(X1),proper(X2)) [0 0 1] [0 0 0] [1] [0 0 1] [0 0 0] [1] [0] [0] proper(nil()) = [0] >= [0] = ok(nil()) [1] [1] [1 1 1] [1] [1 1 1] [1] proper(U11(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = U11(proper(X)) [0 0 1] [1] [0 0 1] [1] [1] [1] proper(tt()) = [1] >= [1] = ok(tt()) [1] [1] [1 1 0] [1 1 0] [0] [1 1 0] [1 1 0] [0] proper(U21(X1,X2)) = [0 1 0]X1 + [0 1 0]X2 + [0] >= [0 1 0]X1 + [0 1 0]X2 + [0] = U21(proper(X1),proper(X2)) [0 0 0] [0 0 1] [1] [0 0 0] [0 0 1] [1] [1 1 0] [1] [1 1 0] [1] proper(U22(X)) = [0 1 0]X + [0] >= [0 1 0]X + [0] = U22(proper(X)) [0 0 1] [1] [0 0 1] [1] [1 1 0] [0] [1 1 0] [0] proper(isList(X)) = [0 1 0]X + [0] >= [0 1 0]X + [0] = isList(proper(X)) [0 1 1] [1] [0 1 1] [1] [1 1 0] [0] [1 1 0] [0] proper(U31(X)) = [0 1 0]X + [0] >= [0 1 0]X + [0] = U31(proper(X)) [0 0 1] [1] [0 0 1] [1] [1 1 0] [1 1 0] [0] [1 1 0] [1 1 0] [0] proper(U41(X1,X2)) = [0 1 0]X1 + [0 1 0]X2 + [0] >= [0 1 0]X1 + [0 1 0]X2 + [0] = U41(proper(X1),proper(X2)) [0 0 1] [0 1 0] [1] [0 0 1] [0 1 0] [1] [1 1 0] [1] [1 1 0] [1] proper(U42(X)) = [0 1 0]X + [0] >= [0 1 0]X + [0] = U42(proper(X)) [0 1 1] [1] [0 1 1] [1] [1 1 0] [1] [1 1 0] [1] proper(isNeList(X)) = [0 1 0]X + [0] >= [0 1 0]X + [0] = isNeList(proper(X)) [0 0 1] [1] [0 0 1] [1] [1 1 0] [1 1 0] [0] [1 1 0] [1 1 0] [0] proper(U51(X1,X2)) = [0 1 0]X1 + [0 1 0]X2 + [0] >= [0 1 0]X1 + [0 1 0]X2 + [0] = U51(proper(X1),proper(X2)) [0 0 1] [0 0 0] [1] [0 0 1] [0 0 0] [1] [1 1 1] [1] [1 1 1] [1] proper(U52(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = U52(proper(X)) [0 0 1] [1] [0 0 1] [1] [1 1 1] [1] [1 1 1] [1] proper(U61(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = U61(proper(X)) [0 0 1] [1] [0 0 1] [1] [1 1 1] [1 1 0] [1] [1 1 1] [1 1 0] [1] proper(U71(X1,X2)) = [0 1 0]X1 + [0 1 0]X2 + [1] >= [0 1 0]X1 + [0 1 0]X2 + [1] = U71(proper(X1),proper(X2)) [0 0 0] [0 0 1] [1] [0 0 0] [0 0 1] [1] [1 1 0] [0] [1 1 0] [0] proper(U72(X)) = [0 1 0]X + [0] >= [0 1 0]X + [0] = U72(proper(X)) [0 0 1] [1] [0 0 1] [1] [1 1 0] [0] [1 1 0] [0] proper(isPal(X)) = [0 1 0]X + [0] >= [0 1 0]X + [0] = isPal(proper(X)) [0 0 1] [1] [0 0 1] [1] [1 1 1] [1] [1 1 1] [1] proper(U81(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = U81(proper(X)) [0 0 1] [1] [0 0 1] [1] [1 1 0] [1] [1 1 0] [1] proper(isQid(X)) = [0 1 0]X + [0] >= [0 1 0]X + [0] = isQid(proper(X)) [0 0 1] [1] [0 0 1] [1] [1 1 1] [1] [1 1 1] [1] proper(isNePal(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = isNePal(proper(X)) [0 1 1] [1] [0 1 1] [1] [0] [0] proper(a()) = [0] >= [0] = ok(a()) [1] [1] [0] [0] proper(e()) = [0] >= [0] = ok(e()) [1] [1] [0] [0] proper(i()) = [0] >= [0] = ok(i()) [1] [1] [0] [0] proper(o()) = [0] >= [0] = ok(o()) [1] [1] [1] [1] proper(u()) = [0] >= [0] = ok(u()) [1] [1] [1 1 1] [1 1 0] [1] [1 1 1] [1 1 0] [1] __(ok(X1),ok(X2)) = [0 1 0]X1 + [0 1 0]X2 + [1] >= [0 1 0]X1 + [0 1 0]X2 + [1] = ok(__(X1,X2)) [0 0 1] [0 0 0] [1] [0 0 1] [0 0 0] [1] [1 1 1] [1] [1 1 1] [1] U11(ok(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = ok(U11(X)) [0 0 1] [1] [0 0 1] [1] [1 1 0] [1 1 0] [0] [1 1 0] [1 1 0] [0] U21(ok(X1),ok(X2)) = [0 1 0]X1 + [0 1 0]X2 + [0] >= [0 1 0]X1 + [0 1 0]X2 + [0] = ok(U21(X1,X2)) [0 0 0] [0 0 1] [1] [0 0 0] [0 0 1] [1] [1 1 0] [1] [1 1 0] [1] U22(ok(X)) = [0 1 0]X + [0] >= [0 1 0]X + [0] = ok(U22(X)) [0 0 1] [1] [0 0 1] [1] [1 1 0] [0] [1 1 0] [0] isList(ok(X)) = [0 1 0]X + [0] >= [0 1 0]X + [0] = ok(isList(X)) [0 1 1] [1] [0 1 1] [1] [1 1 0] [0] [1 1 0] [0] U31(ok(X)) = [0 1 0]X + [0] >= [0 1 0]X + [0] = ok(U31(X)) [0 0 1] [1] [0 0 1] [1] [1 1 0] [1 1 0] [0] [1 1 0] [1 1 0] [0] U41(ok(X1),ok(X2)) = [0 1 0]X1 + [0 1 0]X2 + [0] >= [0 1 0]X1 + [0 1 0]X2 + [0] = ok(U41(X1,X2)) [0 0 1] [0 1 0] [1] [0 0 1] [0 1 0] [1] [1 1 0] [1] [1 1 0] [1] U42(ok(X)) = [0 1 0]X + [0] >= [0 1 0]X + [0] = ok(U42(X)) [0 1 1] [1] [0 1 1] [1] [1 1 0] [1] [1 1 0] [1] isNeList(ok(X)) = [0 1 0]X + [0] >= [0 1 0]X + [0] = ok(isNeList(X)) [0 0 1] [1] [0 0 1] [1] [1 1 0] [1 1 0] [0] [1 1 0] [1 1 0] [0] U51(ok(X1),ok(X2)) = [0 1 0]X1 + [0 1 0]X2 + [0] >= [0 1 0]X1 + [0 1 0]X2 + [0] = ok(U51(X1,X2)) [0 0 1] [0 0 0] [1] [0 0 1] [0 0 0] [1] [1 1 1] [1] [1 1 1] [1] U52(ok(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = ok(U52(X)) [0 0 1] [1] [0 0 1] [1] [1 1 1] [1] [1 1 1] [1] U61(ok(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = ok(U61(X)) [0 0 1] [1] [0 0 1] [1] [1 1 1] [1 1 0] [1] [1 1 1] [1 1 0] [1] U71(ok(X1),ok(X2)) = [0 1 0]X1 + [0 1 0]X2 + [1] >= [0 1 0]X1 + [0 1 0]X2 + [1] = ok(U71(X1,X2)) [0 0 0] [0 0 1] [1] [0 0 0] [0 0 1] [1] [1 1 0] [0] [1 1 0] [0] U72(ok(X)) = [0 1 0]X + [0] >= [0 1 0]X + [0] = ok(U72(X)) [0 0 1] [1] [0 0 1] [1] [1 1 0] [0] [1 1 0] [0] isPal(ok(X)) = [0 1 0]X + [0] >= [0 1 0]X + [0] = ok(isPal(X)) [0 0 1] [1] [0 0 1] [1] [1 1 1] [1] [1 1 1] [1] U81(ok(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = ok(U81(X)) [0 0 1] [1] [0 0 1] [1] [1 1 0] [1] [1 1 0] [1] isQid(ok(X)) = [0 1 0]X + [0] >= [0 1 0]X + [0] = ok(isQid(X)) [0 0 1] [1] [0 0 1] [1] [1 1 1] [1] [1 1 1] [1] isNePal(ok(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = ok(isNePal(X)) [0 1 1] [1] [0 1 1] [1] [1 1 1] [1] [1 1 1] top(ok(X)) = [0 0 1]X + [1] >= [0 0 1]X = top(active(X)) [0 0 0] [0] [0 0 0] problem: active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U72(X)) -> U72(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U61(mark(X)) -> mark(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U81(mark(X)) -> mark(U81(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(ok(X)) -> ok(U22(X)) isList(ok(X)) -> ok(isList(X)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(ok(X)) -> ok(U42(X)) isNeList(ok(X)) -> ok(isNeList(X)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(ok(X)) -> ok(U52(X)) U61(ok(X)) -> ok(U61(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isPal(ok(X)) -> ok(isPal(X)) U81(ok(X)) -> ok(U81(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) Matrix Interpretation Processor: dim=1 interpretation: [ok](x0) = 4x0 + 4, [proper](x0) = 6x0, [u] = 2, [o] = 3, [i] = 4, [e] = 2, [a] = 3, [isNePal](x0) = 4x0, [isQid](x0) = x0, [U81](x0) = 4x0 + 4, [U72](x0) = x0, [isPal](x0) = 2x0 + 1, [U71](x0, x1) = x0 + 4x1, [U61](x0) = 4x0 + 4, [U52](x0) = x0, [U51](x0, x1) = 2x0 + 2x1, [U42](x0) = x0, [isNeList](x0) = 4x0 + 4, [U41](x0, x1) = 2x0 + x1 + 2, [U31](x0) = 2x0 + 1, [U22](x0) = 4x0 + 1, [isList](x0) = 4x0 + 4, [U21](x0, x1) = 4x0 + x1 + 3, [U11](x0) = x0, [tt] = 2, [nil] = 3, [mark](x0) = x0 + 2, [active](x0) = 2x0, [__](x0, x1) = 4x0 + x1 + 3 orientation: active(U21(X1,X2)) = 8X1 + 2X2 + 6 >= 8X1 + X2 + 3 = U21(active(X1),X2) active(U22(X)) = 8X + 2 >= 8X + 1 = U22(active(X)) active(U31(X)) = 4X + 2 >= 4X + 1 = U31(active(X)) active(U41(X1,X2)) = 4X1 + 2X2 + 4 >= 4X1 + X2 + 2 = U41(active(X1),X2) active(U42(X)) = 2X >= 2X = U42(active(X)) active(U51(X1,X2)) = 4X1 + 4X2 >= 4X1 + 2X2 = U51(active(X1),X2) active(U72(X)) = 2X >= 2X = U72(active(X)) __(mark(X1),X2) = 4X1 + X2 + 11 >= 4X1 + X2 + 5 = mark(__(X1,X2)) __(X1,mark(X2)) = 4X1 + X2 + 5 >= 4X1 + X2 + 5 = mark(__(X1,X2)) U11(mark(X)) = X + 2 >= X + 2 = mark(U11(X)) U21(mark(X1),X2) = 4X1 + X2 + 11 >= 4X1 + X2 + 5 = mark(U21(X1,X2)) U22(mark(X)) = 4X + 9 >= 4X + 3 = mark(U22(X)) U31(mark(X)) = 2X + 5 >= 2X + 3 = mark(U31(X)) U41(mark(X1),X2) = 2X1 + X2 + 6 >= 2X1 + X2 + 4 = mark(U41(X1,X2)) U42(mark(X)) = X + 2 >= X + 2 = mark(U42(X)) U51(mark(X1),X2) = 2X1 + 2X2 + 4 >= 2X1 + 2X2 + 2 = mark(U51(X1,X2)) U52(mark(X)) = X + 2 >= X + 2 = mark(U52(X)) U61(mark(X)) = 4X + 12 >= 4X + 6 = mark(U61(X)) U71(mark(X1),X2) = X1 + 4X2 + 2 >= X1 + 4X2 + 2 = mark(U71(X1,X2)) U72(mark(X)) = X + 2 >= X + 2 = mark(U72(X)) U81(mark(X)) = 4X + 12 >= 4X + 6 = mark(U81(X)) proper(__(X1,X2)) = 24X1 + 6X2 + 18 >= 24X1 + 6X2 + 3 = __(proper(X1),proper(X2)) proper(nil()) = 18 >= 16 = ok(nil()) proper(U11(X)) = 6X >= 6X = U11(proper(X)) proper(tt()) = 12 >= 12 = ok(tt()) proper(U21(X1,X2)) = 24X1 + 6X2 + 18 >= 24X1 + 6X2 + 3 = U21(proper(X1),proper(X2)) proper(U22(X)) = 24X + 6 >= 24X + 1 = U22(proper(X)) proper(isList(X)) = 24X + 24 >= 24X + 4 = isList(proper(X)) proper(U31(X)) = 12X + 6 >= 12X + 1 = U31(proper(X)) proper(U41(X1,X2)) = 12X1 + 6X2 + 12 >= 12X1 + 6X2 + 2 = U41(proper(X1),proper(X2)) proper(U42(X)) = 6X >= 6X = U42(proper(X)) proper(isNeList(X)) = 24X + 24 >= 24X + 4 = isNeList(proper(X)) proper(U51(X1,X2)) = 12X1 + 12X2 >= 12X1 + 12X2 = U51(proper(X1),proper(X2)) proper(U52(X)) = 6X >= 6X = U52(proper(X)) proper(U61(X)) = 24X + 24 >= 24X + 4 = U61(proper(X)) proper(U71(X1,X2)) = 6X1 + 24X2 >= 6X1 + 24X2 = U71(proper(X1),proper(X2)) proper(U72(X)) = 6X >= 6X = U72(proper(X)) proper(isPal(X)) = 12X + 6 >= 12X + 1 = isPal(proper(X)) proper(U81(X)) = 24X + 24 >= 24X + 4 = U81(proper(X)) proper(isQid(X)) = 6X >= 6X = isQid(proper(X)) proper(isNePal(X)) = 24X >= 24X = isNePal(proper(X)) proper(a()) = 18 >= 16 = ok(a()) proper(e()) = 12 >= 12 = ok(e()) proper(i()) = 24 >= 20 = ok(i()) proper(o()) = 18 >= 16 = ok(o()) proper(u()) = 12 >= 12 = ok(u()) __(ok(X1),ok(X2)) = 16X1 + 4X2 + 23 >= 16X1 + 4X2 + 16 = ok(__(X1,X2)) U11(ok(X)) = 4X + 4 >= 4X + 4 = ok(U11(X)) U21(ok(X1),ok(X2)) = 16X1 + 4X2 + 23 >= 16X1 + 4X2 + 16 = ok(U21(X1,X2)) U22(ok(X)) = 16X + 17 >= 16X + 8 = ok(U22(X)) isList(ok(X)) = 16X + 20 >= 16X + 20 = ok(isList(X)) U31(ok(X)) = 8X + 9 >= 8X + 8 = ok(U31(X)) U41(ok(X1),ok(X2)) = 8X1 + 4X2 + 14 >= 8X1 + 4X2 + 12 = ok(U41(X1,X2)) U42(ok(X)) = 4X + 4 >= 4X + 4 = ok(U42(X)) isNeList(ok(X)) = 16X + 20 >= 16X + 20 = ok(isNeList(X)) U51(ok(X1),ok(X2)) = 8X1 + 8X2 + 16 >= 8X1 + 8X2 + 4 = ok(U51(X1,X2)) U52(ok(X)) = 4X + 4 >= 4X + 4 = ok(U52(X)) U61(ok(X)) = 16X + 20 >= 16X + 20 = ok(U61(X)) U71(ok(X1),ok(X2)) = 4X1 + 16X2 + 20 >= 4X1 + 16X2 + 4 = ok(U71(X1,X2)) U72(ok(X)) = 4X + 4 >= 4X + 4 = ok(U72(X)) isPal(ok(X)) = 8X + 9 >= 8X + 8 = ok(isPal(X)) U81(ok(X)) = 16X + 20 >= 16X + 20 = ok(U81(X)) isQid(ok(X)) = 4X + 4 >= 4X + 4 = ok(isQid(X)) isNePal(ok(X)) = 16X + 16 >= 16X + 4 = ok(isNePal(X)) problem: active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U72(X)) -> U72(active(X)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U42(mark(X)) -> mark(U42(X)) U52(mark(X)) -> mark(U52(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U42(X)) -> U42(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(e()) -> ok(e()) proper(u()) -> ok(u()) U11(ok(X)) -> ok(U11(X)) isList(ok(X)) -> ok(isList(X)) U42(ok(X)) -> ok(U42(X)) isNeList(ok(X)) -> ok(isNeList(X)) U52(ok(X)) -> ok(U52(X)) U61(ok(X)) -> ok(U61(X)) U72(ok(X)) -> ok(U72(X)) U81(ok(X)) -> ok(U81(X)) isQid(ok(X)) -> ok(isQid(X)) Matrix Interpretation Processor: dim=1 interpretation: [ok](x0) = 2x0 + 4, [proper](x0) = 4x0 + 2, [u] = 4, [e] = 4, [isNePal](x0) = x0, [isQid](x0) = x0, [U81](x0) = 3x0, [U72](x0) = x0, [U71](x0, x1) = x0 + x1 + 3, [U61](x0) = 2x0, [U52](x0) = x0, [U51](x0, x1) = 3x0 + 4x1 + 4, [U42](x0) = 4x0 + 4, [isNeList](x0) = x0, [isList](x0) = 4x0 + 6, [U11](x0) = 2x0 + 4, [tt] = 2, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = 2x0 + 2x1 orientation: active(U42(X)) = 4X + 4 >= 4X + 4 = U42(active(X)) active(U51(X1,X2)) = 3X1 + 4X2 + 4 >= 3X1 + 4X2 + 4 = U51(active(X1),X2) active(U72(X)) = X >= X = U72(active(X)) __(X1,mark(X2)) = 2X1 + 2X2 >= 2X1 + 2X2 = mark(__(X1,X2)) U11(mark(X)) = 2X + 4 >= 2X + 4 = mark(U11(X)) U42(mark(X)) = 4X + 4 >= 4X + 4 = mark(U42(X)) U52(mark(X)) = X >= X = mark(U52(X)) U71(mark(X1),X2) = X1 + X2 + 3 >= X1 + X2 + 3 = mark(U71(X1,X2)) U72(mark(X)) = X >= X = mark(U72(X)) proper(U11(X)) = 8X + 18 >= 8X + 8 = U11(proper(X)) proper(tt()) = 10 >= 8 = ok(tt()) proper(U42(X)) = 16X + 18 >= 16X + 12 = U42(proper(X)) proper(U51(X1,X2)) = 12X1 + 16X2 + 18 >= 12X1 + 16X2 + 18 = U51(proper(X1),proper(X2)) proper(U52(X)) = 4X + 2 >= 4X + 2 = U52(proper(X)) proper(U71(X1,X2)) = 4X1 + 4X2 + 14 >= 4X1 + 4X2 + 7 = U71(proper(X1),proper(X2)) proper(U72(X)) = 4X + 2 >= 4X + 2 = U72(proper(X)) proper(isQid(X)) = 4X + 2 >= 4X + 2 = isQid(proper(X)) proper(isNePal(X)) = 4X + 2 >= 4X + 2 = isNePal(proper(X)) proper(e()) = 18 >= 12 = ok(e()) proper(u()) = 18 >= 12 = ok(u()) U11(ok(X)) = 4X + 12 >= 4X + 12 = ok(U11(X)) isList(ok(X)) = 8X + 22 >= 8X + 16 = ok(isList(X)) U42(ok(X)) = 8X + 20 >= 8X + 12 = ok(U42(X)) isNeList(ok(X)) = 2X + 4 >= 2X + 4 = ok(isNeList(X)) U52(ok(X)) = 2X + 4 >= 2X + 4 = ok(U52(X)) U61(ok(X)) = 4X + 8 >= 4X + 4 = ok(U61(X)) U72(ok(X)) = 2X + 4 >= 2X + 4 = ok(U72(X)) U81(ok(X)) = 6X + 12 >= 6X + 4 = ok(U81(X)) isQid(ok(X)) = 2X + 4 >= 2X + 4 = ok(isQid(X)) problem: active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U72(X)) -> U72(active(X)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U42(mark(X)) -> mark(U42(X)) U52(mark(X)) -> mark(U52(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U72(X)) -> U72(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) U11(ok(X)) -> ok(U11(X)) isNeList(ok(X)) -> ok(isNeList(X)) U52(ok(X)) -> ok(U52(X)) U72(ok(X)) -> ok(U72(X)) isQid(ok(X)) -> ok(isQid(X)) Matrix Interpretation Processor: dim=1 interpretation: [ok](x0) = x0 + 2, [proper](x0) = 5x0, [isNePal](x0) = x0 + 2, [isQid](x0) = 4x0, [U72](x0) = 6x0 + 5, [U71](x0, x1) = 4x0 + x1, [U52](x0) = 6x0 + 6, [U51](x0, x1) = 2x0 + 2x1 + 2, [U42](x0) = 2x0, [isNeList](x0) = x0, [U11](x0) = 4x0 + 5, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = 4x0 + 2x1 orientation: active(U42(X)) = 2X >= 2X = U42(active(X)) active(U51(X1,X2)) = 2X1 + 2X2 + 2 >= 2X1 + 2X2 + 2 = U51(active(X1),X2) active(U72(X)) = 6X + 5 >= 6X + 5 = U72(active(X)) __(X1,mark(X2)) = 4X1 + 2X2 >= 4X1 + 2X2 = mark(__(X1,X2)) U11(mark(X)) = 4X + 5 >= 4X + 5 = mark(U11(X)) U42(mark(X)) = 2X >= 2X = mark(U42(X)) U52(mark(X)) = 6X + 6 >= 6X + 6 = mark(U52(X)) U71(mark(X1),X2) = 4X1 + X2 >= 4X1 + X2 = mark(U71(X1,X2)) U72(mark(X)) = 6X + 5 >= 6X + 5 = mark(U72(X)) proper(U51(X1,X2)) = 10X1 + 10X2 + 10 >= 10X1 + 10X2 + 2 = U51(proper(X1),proper(X2)) proper(U52(X)) = 30X + 30 >= 30X + 6 = U52(proper(X)) proper(U72(X)) = 30X + 25 >= 30X + 5 = U72(proper(X)) proper(isQid(X)) = 20X >= 20X = isQid(proper(X)) proper(isNePal(X)) = 5X + 10 >= 5X + 2 = isNePal(proper(X)) U11(ok(X)) = 4X + 13 >= 4X + 7 = ok(U11(X)) isNeList(ok(X)) = X + 2 >= X + 2 = ok(isNeList(X)) U52(ok(X)) = 6X + 18 >= 6X + 8 = ok(U52(X)) U72(ok(X)) = 6X + 17 >= 6X + 7 = ok(U72(X)) isQid(ok(X)) = 4X + 8 >= 4X + 2 = ok(isQid(X)) problem: active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U72(X)) -> U72(active(X)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U42(mark(X)) -> mark(U42(X)) U52(mark(X)) -> mark(U52(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) proper(isQid(X)) -> isQid(proper(X)) isNeList(ok(X)) -> ok(isNeList(X)) Matrix Interpretation Processor: dim=1 interpretation: [ok](x0) = x0 + 6, [proper](x0) = 4x0, [isQid](x0) = 4x0, [U72](x0) = x0, [U71](x0, x1) = 2x0 + 2x1 + 4, [U52](x0) = 2x0, [U51](x0, x1) = x0 + x1 + 4, [U42](x0) = 4x0, [isNeList](x0) = x0, [U11](x0) = 2x0 + 4, [mark](x0) = x0, [active](x0) = 4x0, [__](x0, x1) = 4x0 + x1 orientation: active(U42(X)) = 16X >= 16X = U42(active(X)) active(U51(X1,X2)) = 4X1 + 4X2 + 16 >= 4X1 + X2 + 4 = U51(active(X1),X2) active(U72(X)) = 4X >= 4X = U72(active(X)) __(X1,mark(X2)) = 4X1 + X2 >= 4X1 + X2 = mark(__(X1,X2)) U11(mark(X)) = 2X + 4 >= 2X + 4 = mark(U11(X)) U42(mark(X)) = 4X >= 4X = mark(U42(X)) U52(mark(X)) = 2X >= 2X = mark(U52(X)) U71(mark(X1),X2) = 2X1 + 2X2 + 4 >= 2X1 + 2X2 + 4 = mark(U71(X1,X2)) U72(mark(X)) = X >= X = mark(U72(X)) proper(isQid(X)) = 16X >= 16X = isQid(proper(X)) isNeList(ok(X)) = X + 6 >= X + 6 = ok(isNeList(X)) problem: active(U42(X)) -> U42(active(X)) active(U72(X)) -> U72(active(X)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U42(mark(X)) -> mark(U42(X)) U52(mark(X)) -> mark(U52(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) proper(isQid(X)) -> isQid(proper(X)) isNeList(ok(X)) -> ok(isNeList(X)) Matrix Interpretation Processor: dim=1 interpretation: [ok](x0) = 4x0 + 3, [proper](x0) = 3x0 + 2, [isQid](x0) = 4x0 + 3, [U72](x0) = 4x0 + 1, [U71](x0, x1) = 4x0 + x1 + 2, [U52](x0) = x0 + 4, [U42](x0) = 4x0 + 1, [isNeList](x0) = 6x0, [U11](x0) = 2x0 + 1, [mark](x0) = x0, [active](x0) = 7x0 + 2, [__](x0, x1) = x0 + 2x1 orientation: active(U42(X)) = 28X + 9 >= 28X + 9 = U42(active(X)) active(U72(X)) = 28X + 9 >= 28X + 9 = U72(active(X)) __(X1,mark(X2)) = X1 + 2X2 >= X1 + 2X2 = mark(__(X1,X2)) U11(mark(X)) = 2X + 1 >= 2X + 1 = mark(U11(X)) U42(mark(X)) = 4X + 1 >= 4X + 1 = mark(U42(X)) U52(mark(X)) = X + 4 >= X + 4 = mark(U52(X)) U71(mark(X1),X2) = 4X1 + X2 + 2 >= 4X1 + X2 + 2 = mark(U71(X1,X2)) U72(mark(X)) = 4X + 1 >= 4X + 1 = mark(U72(X)) proper(isQid(X)) = 12X + 11 >= 12X + 11 = isQid(proper(X)) isNeList(ok(X)) = 24X + 18 >= 24X + 3 = ok(isNeList(X)) problem: active(U42(X)) -> U42(active(X)) active(U72(X)) -> U72(active(X)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U42(mark(X)) -> mark(U42(X)) U52(mark(X)) -> mark(U52(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) proper(isQid(X)) -> isQid(proper(X)) Matrix Interpretation Processor: dim=1 interpretation: [proper](x0) = 2x0 + 1, [isQid](x0) = x0 + 1, [U72](x0) = x0, [U71](x0, x1) = x0 + x1, [U52](x0) = x0 + 4, [U42](x0) = x0, [U11](x0) = x0 + 2, [mark](x0) = x0 + 4, [active](x0) = 4x0 + 2, [__](x0, x1) = 4x0 + x1 orientation: active(U42(X)) = 4X + 2 >= 4X + 2 = U42(active(X)) active(U72(X)) = 4X + 2 >= 4X + 2 = U72(active(X)) __(X1,mark(X2)) = 4X1 + X2 + 4 >= 4X1 + X2 + 4 = mark(__(X1,X2)) U11(mark(X)) = X + 6 >= X + 6 = mark(U11(X)) U42(mark(X)) = X + 4 >= X + 4 = mark(U42(X)) U52(mark(X)) = X + 8 >= X + 8 = mark(U52(X)) U71(mark(X1),X2) = X1 + X2 + 4 >= X1 + X2 + 4 = mark(U71(X1,X2)) U72(mark(X)) = X + 4 >= X + 4 = mark(U72(X)) proper(isQid(X)) = 2X + 3 >= 2X + 2 = isQid(proper(X)) problem: active(U42(X)) -> U42(active(X)) active(U72(X)) -> U72(active(X)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U42(mark(X)) -> mark(U42(X)) U52(mark(X)) -> mark(U52(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) Matrix Interpretation Processor: dim=1 interpretation: [U72](x0) = 4x0 + 3, [U71](x0, x1) = x0 + x1 + 2, [U52](x0) = x0 + 4, [U42](x0) = x0, [U11](x0) = x0 + 6, [mark](x0) = x0 + 4, [active](x0) = x0, [__](x0, x1) = x0 + x1 orientation: active(U42(X)) = X >= X = U42(active(X)) active(U72(X)) = 4X + 3 >= 4X + 3 = U72(active(X)) __(X1,mark(X2)) = X1 + X2 + 4 >= X1 + X2 + 4 = mark(__(X1,X2)) U11(mark(X)) = X + 10 >= X + 10 = mark(U11(X)) U42(mark(X)) = X + 4 >= X + 4 = mark(U42(X)) U52(mark(X)) = X + 8 >= X + 8 = mark(U52(X)) U71(mark(X1),X2) = X1 + X2 + 6 >= X1 + X2 + 6 = mark(U71(X1,X2)) U72(mark(X)) = 4X + 19 >= 4X + 7 = mark(U72(X)) problem: active(U42(X)) -> U42(active(X)) active(U72(X)) -> U72(active(X)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U42(mark(X)) -> mark(U42(X)) U52(mark(X)) -> mark(U52(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) Matrix Interpretation Processor: dim=1 interpretation: [U72](x0) = 5x0 + 4, [U71](x0, x1) = x0 + x1 + 1, [U52](x0) = x0 + 4, [U42](x0) = 4x0 + 3, [U11](x0) = x0, [mark](x0) = x0 + 2, [active](x0) = 2x0 + 1, [__](x0, x1) = 2x0 + x1 orientation: active(U42(X)) = 8X + 7 >= 8X + 7 = U42(active(X)) active(U72(X)) = 10X + 9 >= 10X + 9 = U72(active(X)) __(X1,mark(X2)) = 2X1 + X2 + 2 >= 2X1 + X2 + 2 = mark(__(X1,X2)) U11(mark(X)) = X + 2 >= X + 2 = mark(U11(X)) U42(mark(X)) = 4X + 11 >= 4X + 5 = mark(U42(X)) U52(mark(X)) = X + 6 >= X + 6 = mark(U52(X)) U71(mark(X1),X2) = X1 + X2 + 3 >= X1 + X2 + 3 = mark(U71(X1,X2)) problem: active(U42(X)) -> U42(active(X)) active(U72(X)) -> U72(active(X)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U52(mark(X)) -> mark(U52(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [0] [U72](x0) = [0 0 1]x0 + [0] [0 1 0] [1], [1 0 0] [1 0 0] [U71](x0, x1) = [0 1 0]x0 + [0 0 0]x1 [0 0 0] [1 0 0] , [1 1 0] [U52](x0) = [0 1 1]x0 [0 1 0] , [1 0 0] [0] [U42](x0) = [0 1 1]x0 + [1] [0 0 0] [0], [1 1 0] [U11](x0) = [0 1 0]x0 [0 0 0] , [0] [mark](x0) = x0 + [1] [0], [1 1 1] [active](x0) = [0 1 0]x0 [0 0 1] , [1 0 0] [1 1 0] [__](x0, x1) = [0 0 0]x0 + [1 1 0]x1 [0 0 0] [0 0 0] orientation: [1 1 1] [1] [1 1 1] [0] active(U42(X)) = [0 1 1]X + [1] >= [0 1 1]X + [1] = U42(active(X)) [0 0 0] [0] [0 0 0] [0] [1 1 1] [1] [1 1 1] [0] active(U72(X)) = [0 0 1]X + [0] >= [0 0 1]X + [0] = U72(active(X)) [0 1 0] [1] [0 1 0] [1] [1 0 0] [1 1 0] [1] [1 0 0] [1 1 0] [0] __(X1,mark(X2)) = [0 0 0]X1 + [1 1 0]X2 + [1] >= [0 0 0]X1 + [1 1 0]X2 + [1] = mark(__(X1,X2)) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 1 0] [1] [1 1 0] [0] U11(mark(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = mark(U11(X)) [0 0 0] [0] [0 0 0] [0] [1 1 0] [1] [1 1 0] [0] U52(mark(X)) = [0 1 1]X + [1] >= [0 1 1]X + [1] = mark(U52(X)) [0 1 0] [1] [0 1 0] [0] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] U71(mark(X1),X2) = [0 1 0]X1 + [0 0 0]X2 + [1] >= [0 1 0]X1 + [0 0 0]X2 + [1] = mark(U71(X1,X2)) [0 0 0] [1 0 0] [0] [0 0 0] [1 0 0] [0] problem: U71(mark(X1),X2) -> mark(U71(X1,X2)) Matrix Interpretation Processor: dim=3 interpretation: [1 1 0] [1 0 0] [U71](x0, x1) = [0 0 1]x0 + [0 0 0]x1 [0 1 0] [0 0 0] , [0] [mark](x0) = x0 + [1] [1] orientation: [1 1 0] [1 0 0] [1] [1 1 0] [1 0 0] [0] U71(mark(X1),X2) = [0 0 1]X1 + [0 0 0]X2 + [1] >= [0 0 1]X1 + [0 0 0]X2 + [1] = mark(U71(X1,X2)) [0 1 0] [0 0 0] [1] [0 1 0] [0 0 0] [1] problem: Qed