YES Problem: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(isNeList(V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(and(isList(V1),isList(V2))) active(isNeList(V)) -> mark(isQid(V)) active(isNeList(__(V1,V2))) -> mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) -> mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) -> mark(isQid(V)) active(isNePal(__(I,__(P,I)))) -> mark(and(isQid(I),isPal(P))) active(isPal(V)) -> mark(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(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(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)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(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] = 4, [o] = 4, [i] = 4, [e] = 4, [a] = 4, [isPal](x0) = 4x0, [isNePal](x0) = 4x0, [isQid](x0) = x0, [isNeList](x0) = x0, [isList](x0) = x0 + 1, [and](x0, x1) = x0 + x1, [tt] = 4, [nil] = 3, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = x0 + x1 + 1 orientation: active(__(__(X,Y),Z)) = X + Y + Z + 2 >= X + Y + Z + 2 = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 4 >= X = mark(X) active(__(nil(),X)) = X + 4 >= X = mark(X) active(and(tt(),X)) = X + 4 >= X = mark(X) active(isList(V)) = V + 1 >= V = mark(isNeList(V)) active(isList(nil())) = 4 >= 4 = mark(tt()) active(isList(__(V1,V2))) = V1 + V2 + 2 >= V1 + V2 + 2 = mark(and(isList(V1),isList(V2))) active(isNeList(V)) = V >= V = mark(isQid(V)) active(isNeList(__(V1,V2))) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) = 4V >= V = mark(isQid(V)) active(isNePal(__(I,__(P,I)))) = 8I + 4P + 8 >= I + 4P = mark(and(isQid(I),isPal(P))) active(isPal(V)) = 4V >= 4V = mark(isNePal(V)) active(isPal(nil())) = 12 >= 4 = mark(tt()) active(isQid(a())) = 4 >= 4 = mark(tt()) active(isQid(e())) = 4 >= 4 = mark(tt()) active(isQid(i())) = 4 >= 4 = mark(tt()) active(isQid(o())) = 4 >= 4 = mark(tt()) active(isQid(u())) = 4 >= 4 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,active(X2)) active(and(X1,X2)) = X1 + X2 >= X1 + X2 = and(active(X1),X2) __(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) and(mark(X1),X2) = X1 + X2 >= X1 + X2 = mark(and(X1,X2)) proper(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 3 >= 3 = ok(nil()) proper(and(X1,X2)) = X1 + X2 >= X1 + X2 = and(proper(X1),proper(X2)) proper(tt()) = 4 >= 4 = ok(tt()) proper(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(isNeList(X)) = X >= X = isNeList(proper(X)) proper(isQid(X)) = X >= X = isQid(proper(X)) proper(isNePal(X)) = 4X >= 4X = isNePal(proper(X)) proper(isPal(X)) = 4X >= 4X = isPal(proper(X)) proper(a()) = 4 >= 4 = ok(a()) proper(e()) = 4 >= 4 = ok(e()) proper(i()) = 4 >= 4 = ok(i()) proper(o()) = 4 >= 4 = ok(o()) proper(u()) = 4 >= 4 = ok(u()) __(ok(X1),ok(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = ok(__(X1,X2)) and(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(and(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) isNeList(ok(X)) = X >= X = ok(isNeList(X)) isQid(ok(X)) = X >= X = ok(isQid(X)) isNePal(ok(X)) = 4X >= 4X = ok(isNePal(X)) isPal(ok(X)) = 4X >= 4X = ok(isPal(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(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(and(isList(V1),isList(V2))) active(isNeList(V)) -> mark(isQid(V)) active(isNeList(__(V1,V2))) -> mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) -> mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) -> mark(isQid(V)) active(isPal(V)) -> mark(isNePal(V)) 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(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(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)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(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 1 1] [ok](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [proper](x0) = [0 0 0]x0 [0 0 1] , [0] [u] = [0] [0], [0] [o] = [0] [0], [0] [i] = [0] [0], [0] [e] = [0] [0], [0] [a] = [0] [0], [1 0 0] [isPal](x0) = [0 0 0]x0 [0 1 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] [isNeList](x0) = [0 0 0]x0 [0 0 1] , [1 0 1] [isList](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [and](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 1] [0 0 0] , [0] [tt] = [0] [0], [1] [nil] = [0] [0], [1 0 0] [mark](x0) = [0 0 0]x0 [0 0 0] , [1 0 1] [active](x0) = [0 0 0]x0 [0 0 1] , [1 0 0] [1 0 0] [__](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 1] [0 1 1] orientation: [1 0 1] [1 1 1] [1 1 1] [1 0 0] [1 0 0] [1 0 0] active(__(__(X,Y),Z)) = [0 0 0]X + [0 0 0]Y + [0 0 0]Z >= [0 0 0]X + [0 0 0]Y + [0 0 0]Z = mark(__(X,__(Y,Z))) [0 0 1] [0 1 1] [0 1 1] [0 0 0] [0 0 0] [0 0 0] [1] [0] active(isList(nil())) = [0] >= [0] = mark(tt()) [0] [0] [1 0 1] [1 1 1] [1 0 1] [1 0 1] active(isList(__(V1,V2))) = [0 0 0]V1 + [0 0 0]V2 >= [0 0 0]V1 + [0 0 0]V2 = mark(and(isList(V1),isList(V2))) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 1] [1 0 0] active(isNeList(V)) = [0 0 0]V >= [0 0 0]V = mark(isQid(V)) [0 0 1] [0 0 0] [1 0 1] [1 1 1] [1 0 1] [1 0 0] active(isNeList(__(V1,V2))) = [0 0 0]V1 + [0 0 0]V2 >= [0 0 0]V1 + [0 0 0]V2 = mark(and(isList(V1),isNeList(V2))) [0 0 1] [0 1 1] [0 0 0] [0 0 0] [1 0 1] [1 1 1] [1 0 0] [1 0 1] active(isNeList(__(V1,V2))) = [0 0 0]V1 + [0 0 0]V2 >= [0 0 0]V1 + [0 0 0]V2 = mark(and(isNeList(V1),isList(V2))) [0 0 1] [0 1 1] [0 0 0] [0 0 0] [1 0 0] [1 0 0] active(isNePal(V)) = [0 0 0]V >= [0 0 0]V = mark(isQid(V)) [0 0 0] [0 0 0] [1 1 0] [1 0 0] active(isPal(V)) = [0 0 0]V >= [0 0 0]V = mark(isNePal(V)) [0 1 0] [0 0 0] [0] [0] active(isQid(a())) = [0] >= [0] = mark(tt()) [0] [0] [0] [0] active(isQid(e())) = [0] >= [0] = mark(tt()) [0] [0] [0] [0] active(isQid(i())) = [0] >= [0] = mark(tt()) [0] [0] [0] [0] active(isQid(o())) = [0] >= [0] = mark(tt()) [0] [0] [0] [0] active(isQid(u())) = [0] >= [0] = mark(tt()) [0] [0] [1 0 1] [1 1 1] [1 0 1] [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 1] [0 1 1] [0 0 1] [0 1 1] [1 0 1] [1 1 1] [1 0 0] [1 0 1] active(__(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = __(X1,active(X2)) [0 0 1] [0 1 1] [0 0 1] [0 0 1] [1 0 1] [1 0 0] [1 0 1] [1 0 0] active(and(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = and(active(X1),X2) [0 0 1] [0 0 0] [0 0 1] [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 1 1] [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 1] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] and(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = mark(and(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] proper(__(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = __(proper(X1),proper(X2)) [0 0 1] [0 1 1] [0 0 1] [0 0 1] [1] [1] proper(nil()) = [0] >= [0] = ok(nil()) [0] [0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] proper(and(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = and(proper(X1),proper(X2)) [0 0 1] [0 0 0] [0 0 1] [0 0 0] [0] [0] proper(tt()) = [0] >= [0] = ok(tt()) [0] [0] [1 0 1] [1 0 1] proper(isList(X)) = [0 0 0]X >= [0 0 0]X = isList(proper(X)) [0 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)) [0 0 1] [0 0 1] [1 0 0] [1 0 0] proper(isQid(X)) = [0 0 0]X >= [0 0 0]X = isQid(proper(X)) [0 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)) [0 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)) [0 1 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 1 1] [1 1 1] [1 0 1] [1 1 1] __(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 1 1] [1 1 1] [1 0 1] [1 0 0] and(ok(X1),ok(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = ok(and(X1,X2)) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 1] [1 0 1] isList(ok(X)) = [0 0 0]X >= [0 0 0]X = ok(isList(X)) [0 0 0] [0 0 0] [1 1 1] [1 0 1] isNeList(ok(X)) = [0 0 0]X >= [0 0 0]X = ok(isNeList(X)) [0 0 0] [0 0 0] [1 1 1] [1 0 0] isQid(ok(X)) = [0 0 0]X >= [0 0 0]X = ok(isQid(X)) [0 0 0] [0 0 0] [1 1 1] [1 0 0] isNePal(ok(X)) = [0 0 0]X >= [0 0 0]X = ok(isNePal(X)) [0 0 0] [0 0 0] [1 1 1] [1 1 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] top(mark(X)) = [0 0 0]X >= [0 0 0]X = top(proper(X)) [0 0 0] [0 0 0] [1 1 1] [1 0 1] top(ok(X)) = [0 0 0]X >= [0 0 0]X = top(active(X)) [0 0 0] [0 0 0] problem: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(isList(__(V1,V2))) -> mark(and(isList(V1),isList(V2))) active(isNeList(V)) -> mark(isQid(V)) active(isNeList(__(V1,V2))) -> mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) -> mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) -> mark(isQid(V)) active(isPal(V)) -> mark(isNePal(V)) 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(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(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)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dim=1 interpretation: [top](x0) = x0, [ok](x0) = x0, [proper](x0) = x0, [u] = 7, [o] = 0, [i] = 1, [e] = 0, [a] = 2, [isPal](x0) = 6x0 + 6, [isNePal](x0) = 4x0, [isQid](x0) = 4x0, [isNeList](x0) = 4x0, [isList](x0) = x0, [and](x0, x1) = x0 + x1, [tt] = 0, [nil] = 0, [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(isList(__(V1,V2))) = 4V1 + V2 >= V1 + V2 = mark(and(isList(V1),isList(V2))) active(isNeList(V)) = 4V >= 4V = mark(isQid(V)) active(isNeList(__(V1,V2))) = 16V1 + 4V2 >= V1 + 4V2 = mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) = 16V1 + 4V2 >= 4V1 + V2 = mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) = 4V >= 4V = mark(isQid(V)) active(isPal(V)) = 6V + 6 >= 4V = mark(isNePal(V)) active(isQid(a())) = 8 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 4 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 28 >= 0 = mark(tt()) active(__(X1,X2)) = 4X1 + X2 >= 4X1 + X2 = __(active(X1),X2) active(__(X1,X2)) = 4X1 + X2 >= 4X1 + X2 = __(X1,active(X2)) active(and(X1,X2)) = X1 + X2 >= X1 + X2 = and(active(X1),X2) __(mark(X1),X2) = 4X1 + X2 >= 4X1 + X2 = mark(__(X1,X2)) __(X1,mark(X2)) = 4X1 + X2 >= 4X1 + X2 = mark(__(X1,X2)) and(mark(X1),X2) = X1 + X2 >= X1 + X2 = mark(and(X1,X2)) proper(__(X1,X2)) = 4X1 + X2 >= 4X1 + X2 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(and(X1,X2)) = X1 + X2 >= X1 + X2 = and(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(isList(X)) = X >= X = isList(proper(X)) proper(isNeList(X)) = 4X >= 4X = isNeList(proper(X)) proper(isQid(X)) = 4X >= 4X = isQid(proper(X)) proper(isNePal(X)) = 4X >= 4X = isNePal(proper(X)) proper(isPal(X)) = 6X + 6 >= 6X + 6 = isPal(proper(X)) proper(a()) = 2 >= 2 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 7 >= 7 = ok(u()) __(ok(X1),ok(X2)) = 4X1 + X2 >= 4X1 + X2 = ok(__(X1,X2)) and(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(and(X1,X2)) isList(ok(X)) = X >= X = ok(isList(X)) isNeList(ok(X)) = 4X >= 4X = ok(isNeList(X)) isQid(ok(X)) = 4X >= 4X = ok(isQid(X)) isNePal(ok(X)) = 4X >= 4X = ok(isNePal(X)) isPal(ok(X)) = 6X + 6 >= 6X + 6 = ok(isPal(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(isList(__(V1,V2))) -> mark(and(isList(V1),isList(V2))) active(isNeList(V)) -> mark(isQid(V)) active(isNeList(__(V1,V2))) -> mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) -> mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) -> mark(isQid(V)) active(isQid(e())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(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)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(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] , [ok](x0) = x0 , [1 0 0] [proper](x0) = [0 0 1]x0 [0 0 1] , [0] [u] = [0] [0], [0] [o] = [0] [0], [0] [i] = [0] [0], [0] [e] = [0] [0], [0] [a] = [0] [0], [1 0 0] [isPal](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [isNePal](x0) = [0 0 0]x0 [0 0 1] , [1 0 0] [isQid](x0) = [0 0 1]x0 [0 0 1] , [1 0 0] [1] [isNeList](x0) = [0 0 0]x0 + [0] [1 0 1] [0], [1 0 0] [isList](x0) = [1 0 0]x0 [1 0 1] , [1 0 0] [1 0 0] [and](x0, x1) = [0 0 1]x0 + [0 0 0]x1 [0 0 1] [0 0 0] , [0] [tt] = [0] [0], [0] [nil] = [0] [0], [1 0 0] [mark](x0) = [0 0 0]x0 [0 0 1] , [active](x0) = x0 , [1 0 1] [1 0 1] [0] [__](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0] [0 0 0] [0 0 0] [1] orientation: [1 0 1] [1 0 1] [1 0 1] [1] [1 0 1] [1 0 1] [1 0 1] [1] active(__(__(X,Y),Z)) = [0 0 0]X + [0 0 0]Y + [0 0 0]Z + [0] >= [0 0 0]X + [0 0 0]Y + [0 0 0]Z + [0] = mark(__(X,__(Y,Z))) [0 0 0] [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [0 0 0] [1] [1 0 1] [1 0 1] [0] [1 0 0] [1 0 0] active(isList(__(V1,V2))) = [1 0 1]V1 + [1 0 1]V2 + [0] >= [0 0 0]V1 + [0 0 0]V2 = mark(and(isList(V1),isList(V2))) [1 0 1] [1 0 1] [1] [1 0 1] [0 0 0] [1 0 0] [1] [1 0 0] active(isNeList(V)) = [0 0 0]V + [0] >= [0 0 0]V = mark(isQid(V)) [1 0 1] [0] [0 0 1] [1 0 1] [1 0 1] [1] [1 0 0] [1 0 0] [1] active(isNeList(__(V1,V2))) = [0 0 0]V1 + [0 0 0]V2 + [0] >= [0 0 0]V1 + [0 0 0]V2 + [0] = mark(and(isList(V1),isNeList(V2))) [1 0 1] [1 0 1] [1] [1 0 1] [0 0 0] [0] [1 0 1] [1 0 1] [1] [1 0 0] [1 0 0] [1] active(isNeList(__(V1,V2))) = [0 0 0]V1 + [0 0 0]V2 + [0] >= [0 0 0]V1 + [0 0 0]V2 + [0] = mark(and(isNeList(V1),isList(V2))) [1 0 1] [1 0 1] [1] [1 0 1] [0 0 0] [0] [1 0 0] [1 0 0] active(isNePal(V)) = [0 0 0]V >= [0 0 0]V = mark(isQid(V)) [0 0 1] [0 0 1] [0] [0] active(isQid(e())) = [0] >= [0] = mark(tt()) [0] [0] [0] [0] active(isQid(o())) = [0] >= [0] = mark(tt()) [0] [0] [1 0 1] [1 0 1] [0] [1 0 1] [1 0 1] [0] active(__(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = __(active(X1),X2) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1 0 1] [1 0 1] [0] [1 0 1] [1 0 1] [0] active(__(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = __(X1,active(X2)) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1 0 0] [1 0 0] [1 0 0] [1 0 0] active(and(X1,X2)) = [0 0 1]X1 + [0 0 0]X2 >= [0 0 1]X1 + [0 0 0]X2 = and(active(X1),X2) [0 0 1] [0 0 0] [0 0 1] [0 0 0] [1 0 1] [1 0 1] [0] [1 0 1] [1 0 1] [0] __(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] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1 0 1] [1 0 1] [0] [1 0 1] [1 0 1] [0] __(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] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1 0 0] [1 0 0] [1 0 0] [1 0 0] and(mark(X1),X2) = [0 0 1]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = mark(and(X1,X2)) [0 0 1] [0 0 0] [0 0 1] [0 0 0] [1 0 1] [1 0 1] [0] [1 0 1] [1 0 1] [0] proper(__(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [0] = __(proper(X1),proper(X2)) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [0] [0] proper(nil()) = [0] >= [0] = ok(nil()) [0] [0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] proper(and(X1,X2)) = [0 0 1]X1 + [0 0 0]X2 >= [0 0 1]X1 + [0 0 0]X2 = and(proper(X1),proper(X2)) [0 0 1] [0 0 0] [0 0 1] [0 0 0] [0] [0] proper(tt()) = [0] >= [0] = ok(tt()) [0] [0] [1 0 0] [1 0 0] proper(isList(X)) = [1 0 1]X >= [1 0 0]X = isList(proper(X)) [1 0 1] [1 0 1] [1 0 0] [1] [1 0 0] [1] proper(isNeList(X)) = [1 0 1]X + [0] >= [0 0 0]X + [0] = isNeList(proper(X)) [1 0 1] [0] [1 0 1] [0] [1 0 0] [1 0 0] proper(isQid(X)) = [0 0 1]X >= [0 0 1]X = isQid(proper(X)) [0 0 1] [0 0 1] [1 0 0] [1 0 0] proper(isNePal(X)) = [0 0 1]X >= [0 0 0]X = isNePal(proper(X)) [0 0 1] [0 0 1] [1 0 0] [1 0 0] proper(isPal(X)) = [0 0 0]X >= [0 0 0]X = isPal(proper(X)) [0 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 1] [1 0 1] [0] [1 0 1] [1 0 1] [0] __(ok(X1),ok(X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = ok(__(X1,X2)) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1 0 0] [1 0 0] [1 0 0] [1 0 0] and(ok(X1),ok(X2)) = [0 0 1]X1 + [0 0 0]X2 >= [0 0 1]X1 + [0 0 0]X2 = ok(and(X1,X2)) [0 0 1] [0 0 0] [0 0 1] [0 0 0] [1 0 0] [1 0 0] isList(ok(X)) = [1 0 0]X >= [1 0 0]X = ok(isList(X)) [1 0 1] [1 0 1] [1 0 0] [1] [1 0 0] [1] isNeList(ok(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = ok(isNeList(X)) [1 0 1] [0] [1 0 1] [0] [1 0 0] [1 0 0] isQid(ok(X)) = [0 0 1]X >= [0 0 1]X = ok(isQid(X)) [0 0 1] [0 0 1] [1 0 0] [1 0 0] isNePal(ok(X)) = [0 0 0]X >= [0 0 0]X = ok(isNePal(X)) [0 0 1] [0 0 1] [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] 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(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(isList(__(V1,V2))) -> mark(and(isList(V1),isList(V2))) active(isNeList(__(V1,V2))) -> mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) -> mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) -> mark(isQid(V)) active(isQid(e())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(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)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(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] [0] [ok](x0) = [0 0 0]x0 + [1] [1 0 0] [0], [1 0 0] [0] [proper](x0) = [0 0 0]x0 + [1] [0 0 1] [1], [1] [u] = [0] [0], [1] [o] = [0] [0], [0] [i] = [0] [0], [1] [e] = [0] [0], [0] [a] = [0] [0], [1 0 0] [0] [isPal](x0) = [0 0 0]x0 + [1] [1 0 0] [0], [1 0 0] [0] [isNePal](x0) = [0 0 0]x0 + [1] [0 0 1] [0], [isQid](x0) = x0 , [isNeList](x0) = x0 , [1 0 0] [isList](x0) = [0 1 0]x0 [1 1 0] , [1 0 0] [1 0 0] [and](x0, x1) = [0 1 0]x0 + [0 0 0]x1 [1 1 0] [1 0 0] , [0] [tt] = [0] [0], [1] [nil] = [0] [0], [1 0 0] [mark](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [active](x0) = [0 1 0]x0 [1 1 0] , [1 0 0] [1 0 0] [__](x0, x1) = [0 1 0]x0 + [0 0 0]x1 [1 1 0] [1 0 0] orientation: [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] active(__(__(X,Y),Z)) = [0 1 0]X + [0 0 0]Y + [0 0 0]Z >= [0 0 0]X + [0 0 0]Y + [0 0 0]Z = mark(__(X,__(Y,Z))) [1 1 0] [1 0 0] [1 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] active(isList(__(V1,V2))) = [0 1 0]V1 + [0 0 0]V2 >= [0 0 0]V1 + [0 0 0]V2 = mark(and(isList(V1),isList(V2))) [1 1 0] [1 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] active(isNeList(__(V1,V2))) = [0 1 0]V1 + [0 0 0]V2 >= [0 0 0]V1 + [0 0 0]V2 = mark(and(isList(V1),isNeList(V2))) [1 1 0] [1 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] active(isNeList(__(V1,V2))) = [0 1 0]V1 + [0 0 0]V2 >= [0 0 0]V1 + [0 0 0]V2 = mark(and(isNeList(V1),isList(V2))) [1 1 0] [1 0 0] [0 0 0] [0 0 0] [1 0 0] [0] [1 0 0] active(isNePal(V)) = [0 0 0]V + [1] >= [0 0 0]V = mark(isQid(V)) [1 0 0] [1] [0 0 0] [1] [0] active(isQid(e())) = [0] >= [0] = mark(tt()) [1] [0] [1] [0] active(isQid(o())) = [0] >= [0] = mark(tt()) [1] [0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] active(__(X1,X2)) = [0 1 0]X1 + [0 0 0]X2 >= [0 1 0]X1 + [0 0 0]X2 = __(active(X1),X2) [1 1 0] [1 0 0] [1 1 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] active(__(X1,X2)) = [0 1 0]X1 + [0 0 0]X2 >= [0 1 0]X1 + [0 0 0]X2 = __(X1,active(X2)) [1 1 0] [1 0 0] [1 1 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] active(and(X1,X2)) = [0 1 0]X1 + [0 0 0]X2 >= [0 1 0]X1 + [0 0 0]X2 = and(active(X1),X2) [1 1 0] [1 0 0] [1 1 0] [1 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)) [1 0 0] [1 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] __(X1,mark(X2)) = [0 1 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = mark(__(X1,X2)) [1 1 0] [1 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] and(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = mark(and(X1,X2)) [1 0 0] [1 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] proper(__(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = __(proper(X1),proper(X2)) [1 1 0] [1 0 0] [1] [1 0 0] [1 0 0] [1] [1] [1] proper(nil()) = [1] >= [1] = ok(nil()) [1] [1] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] proper(and(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = and(proper(X1),proper(X2)) [1 1 0] [1 0 0] [1] [1 0 0] [1 0 0] [1] [0] [0] proper(tt()) = [1] >= [1] = ok(tt()) [1] [0] [1 0 0] [0] [1 0 0] [0] proper(isList(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = isList(proper(X)) [1 1 0] [1] [1 0 0] [1] [1 0 0] [0] [1 0 0] [0] proper(isNeList(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = isNeList(proper(X)) [0 0 1] [1] [0 0 1] [1] [1 0 0] [0] [1 0 0] [0] proper(isQid(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = isQid(proper(X)) [0 0 1] [1] [0 0 1] [1] [1 0 0] [0] [1 0 0] [0] proper(isNePal(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = isNePal(proper(X)) [0 0 1] [1] [0 0 1] [1] [1 0 0] [0] [1 0 0] [0] proper(isPal(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = isPal(proper(X)) [1 0 0] [1] [1 0 0] [0] [0] [0] proper(a()) = [1] >= [1] = ok(a()) [1] [0] [1] [1] proper(e()) = [1] >= [1] = ok(e()) [1] [1] [0] [0] proper(i()) = [1] >= [1] = ok(i()) [1] [0] [1] [1] proper(o()) = [1] >= [1] = ok(o()) [1] [1] [1] [1] proper(u()) = [1] >= [1] = ok(u()) [1] [1] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] __(ok(X1),ok(X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = ok(__(X1,X2)) [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] and(ok(X1),ok(X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = ok(and(X1,X2)) [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] [0] [1 0 0] [0] [1 0 0] [0] isList(ok(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = ok(isList(X)) [1 0 0] [1] [1 0 0] [0] [1 0 0] [0] [1 0 0] [0] isNeList(ok(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = ok(isNeList(X)) [1 0 0] [0] [1 0 0] [0] [1 0 0] [0] [1 0 0] [0] isQid(ok(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = ok(isQid(X)) [1 0 0] [0] [1 0 0] [0] [1 0 0] [0] [1 0 0] [0] isNePal(ok(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = ok(isNePal(X)) [1 0 0] [0] [1 0 0] [0] [1 0 0] [0] [1 0 0] [0] isPal(ok(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = ok(isPal(X)) [1 0 0] [0] [1 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(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(isList(__(V1,V2))) -> mark(and(isList(V1),isList(V2))) active(isNeList(__(V1,V2))) -> mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) -> mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) -> mark(isQid(V)) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(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)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(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] [0] [ok](x0) = [1 0 0]x0 + [0] [0 0 0] [1], [1 0 0] [proper](x0) = [0 1 1]x0 [1 0 0] , [1] [u] = [0] [1], [1] [o] = [1] [0], [1] [i] = [1] [0], [1] [e] = [0] [1], [1] [a] = [1] [0], [1 0 0] [isPal](x0) = [1 0 0]x0 [0 0 1] , [1] [isNePal](x0) = x0 + [1] [0], [1 0 0] [isQid](x0) = [1 0 0]x0 [0 0 1] , [1 0 0] [isNeList](x0) = [1 0 0]x0 [0 0 1] , [isList](x0) = x0 , [1 0 0] [1 0 0] [and](x0, x1) = [1 0 0]x0 + [1 0 0]x1 [0 0 1] [0 0 0] , [1] [tt] = [0] [1], [1] [nil] = [1] [0], [1 0 0] [mark](x0) = [0 0 0]x0 [0 0 0] , [active](x0) = x0 , [1 0 0] [1 0 0] [__](x0, x1) = [1 0 0]x0 + [0 1 1]x1 [0 0 1] [1 0 0] orientation: [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] active(__(__(X,Y),Z)) = [1 0 0]X + [1 0 0]Y + [0 1 1]Z >= [0 0 0]X + [0 0 0]Y + [0 0 0]Z = mark(__(X,__(Y,Z))) [0 0 1] [1 0 0] [1 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] active(isList(__(V1,V2))) = [1 0 0]V1 + [0 1 1]V2 >= [0 0 0]V1 + [0 0 0]V2 = mark(and(isList(V1),isList(V2))) [0 0 1] [1 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] active(isNeList(__(V1,V2))) = [1 0 0]V1 + [1 0 0]V2 >= [0 0 0]V1 + [0 0 0]V2 = mark(and(isList(V1),isNeList(V2))) [0 0 1] [1 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] active(isNeList(__(V1,V2))) = [1 0 0]V1 + [1 0 0]V2 >= [0 0 0]V1 + [0 0 0]V2 = mark(and(isNeList(V1),isList(V2))) [0 0 1] [1 0 0] [0 0 0] [0 0 0] [1] [1 0 0] active(isNePal(V)) = V + [1] >= [0 0 0]V = mark(isQid(V)) [0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] active(__(X1,X2)) = [1 0 0]X1 + [0 1 1]X2 >= [1 0 0]X1 + [0 1 1]X2 = __(active(X1),X2) [0 0 1] [1 0 0] [0 0 1] [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] active(__(X1,X2)) = [1 0 0]X1 + [0 1 1]X2 >= [1 0 0]X1 + [0 1 1]X2 = __(X1,active(X2)) [0 0 1] [1 0 0] [0 0 1] [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] active(and(X1,X2)) = [1 0 0]X1 + [1 0 0]X2 >= [1 0 0]X1 + [1 0 0]X2 = and(active(X1),X2) [0 0 1] [0 0 0] [0 0 1] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] __(mark(X1),X2) = [1 0 0]X1 + [0 1 1]X2 >= [0 0 0]X1 + [0 0 0]X2 = mark(__(X1,X2)) [0 0 0] [1 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] __(X1,mark(X2)) = [1 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = mark(__(X1,X2)) [0 0 1] [1 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] and(mark(X1),X2) = [1 0 0]X1 + [1 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = mark(and(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] proper(__(X1,X2)) = [1 0 1]X1 + [1 1 1]X2 >= [1 0 0]X1 + [1 1 1]X2 = __(proper(X1),proper(X2)) [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1] [1] proper(nil()) = [1] >= [1] = ok(nil()) [1] [1] [1 0 0] [1 0 0] [1 0 0] [1 0 0] proper(and(X1,X2)) = [1 0 1]X1 + [1 0 0]X2 >= [1 0 0]X1 + [1 0 0]X2 = and(proper(X1),proper(X2)) [1 0 0] [1 0 0] [1 0 0] [0 0 0] [1] [1] proper(tt()) = [1] >= [1] = ok(tt()) [1] [1] [1 0 0] [1 0 0] proper(isList(X)) = [0 1 1]X >= [0 1 1]X = isList(proper(X)) [1 0 0] [1 0 0] [1 0 0] [1 0 0] proper(isNeList(X)) = [1 0 1]X >= [1 0 0]X = isNeList(proper(X)) [1 0 0] [1 0 0] [1 0 0] [1 0 0] proper(isQid(X)) = [1 0 1]X >= [1 0 0]X = isQid(proper(X)) [1 0 0] [1 0 0] [1 0 0] [1] [1 0 0] [1] proper(isNePal(X)) = [0 1 1]X + [1] >= [0 1 1]X + [1] = isNePal(proper(X)) [1 0 0] [1] [1 0 0] [0] [1 0 0] [1 0 0] proper(isPal(X)) = [1 0 1]X >= [1 0 0]X = isPal(proper(X)) [1 0 0] [1 0 0] [1] [1] proper(a()) = [1] >= [1] = ok(a()) [1] [1] [1] [1] proper(e()) = [1] >= [1] = ok(e()) [1] [1] [1] [1] proper(i()) = [1] >= [1] = ok(i()) [1] [1] [1] [1] proper(o()) = [1] >= [1] = ok(o()) [1] [1] [1] [1] proper(u()) = [1] >= [1] = ok(u()) [1] [1] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] __(ok(X1),ok(X2)) = [1 0 0]X1 + [1 0 0]X2 + [1] >= [1 0 0]X1 + [1 0 0]X2 + [0] = ok(__(X1,X2)) [0 0 0] [1 0 0] [1] [0 0 0] [0 0 0] [1] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] and(ok(X1),ok(X2)) = [1 0 0]X1 + [1 0 0]X2 + [0] >= [1 0 0]X1 + [1 0 0]X2 + [0] = ok(and(X1,X2)) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1 0 0] [0] [1 0 0] [0] isList(ok(X)) = [1 0 0]X + [0] >= [1 0 0]X + [0] = ok(isList(X)) [0 0 0] [1] [0 0 0] [1] [1 0 0] [0] [1 0 0] [0] isNeList(ok(X)) = [1 0 0]X + [0] >= [1 0 0]X + [0] = ok(isNeList(X)) [0 0 0] [1] [0 0 0] [1] [1 0 0] [0] [1 0 0] [0] isQid(ok(X)) = [1 0 0]X + [0] >= [1 0 0]X + [0] = ok(isQid(X)) [0 0 0] [1] [0 0 0] [1] [1 0 0] [1] [1 0 0] [1] isNePal(ok(X)) = [1 0 0]X + [1] >= [1 0 0]X + [1] = ok(isNePal(X)) [0 0 0] [1] [0 0 0] [1] [1 0 0] [0] [1 0 0] [0] isPal(ok(X)) = [1 0 0]X + [0] >= [1 0 0]X + [0] = ok(isPal(X)) [0 0 0] [1] [0 0 0] [1] [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(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(isList(__(V1,V2))) -> mark(and(isList(V1),isList(V2))) active(isNeList(__(V1,V2))) -> mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) -> mark(and(isNeList(V1),isList(V2))) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(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)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dim=3 interpretation: [1 0 1] [top](x0) = [1 0 1]x0 [0 0 0] , [1 0 0] [ok](x0) = [0 0 0]x0 [0 1 1] , [1 0 0] [proper](x0) = [0 0 1]x0 [0 0 1] , [0] [u] = [0] [1], [1] [o] = [0] [1], [1] [i] = [0] [1], [1] [e] = [0] [1], [0] [a] = [0] [0], [1 0 0] [isPal](x0) = [0 0 0]x0 [0 0 0] , [isNePal](x0) = x0 , [1 0 0] [isQid](x0) = [0 0 0]x0 [1 0 1] , [0] [isNeList](x0) = x0 + [0] [1], [1 0 0] [isList](x0) = [0 0 0]x0 [0 0 0] , [1 0 1] [1 0 0] [and](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [0] [tt] = [0] [1], [1] [nil] = [0] [1], [1 0 0] [mark](x0) = [0 0 0]x0 [0 1 1] , [1 0 1] [active](x0) = [0 0 0]x0 [0 0 0] , [1 0 1] [1 0 1] [__](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] orientation: [1 0 1] [1 0 1] [1 0 1] [1 0 1] [1 0 1] [1 0 1] active(__(__(X,Y),Z)) = [0 0 0]X + [0 0 0]Y + [0 0 0]Z >= [0 0 0]X + [0 0 0]Y + [0 0 0]Z = mark(__(X,__(Y,Z))) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 1] [1 0 1] [1 0 0] [1 0 0] active(isList(__(V1,V2))) = [0 0 0]V1 + [0 0 0]V2 >= [0 0 0]V1 + [0 0 0]V2 = mark(and(isList(V1),isList(V2))) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 1] [1 0 1] [1] [1 0 0] [1 0 0] active(isNeList(__(V1,V2))) = [0 0 0]V1 + [0 0 0]V2 + [0] >= [0 0 0]V1 + [0 0 0]V2 = mark(and(isList(V1),isNeList(V2))) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [1 0 1] [1 0 1] [1] [1 0 1] [1 0 0] [1] active(isNeList(__(V1,V2))) = [0 0 0]V1 + [0 0 0]V2 + [0] >= [0 0 0]V1 + [0 0 0]V2 + [0] = mark(and(isNeList(V1),isList(V2))) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 1] [1 0 1] [1 0 1] [1 0 1] 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 1] [1 0 1] [1 0 1] [1 0 1] 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 1] [1 0 0] [1 0 1] [1 0 0] active(and(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = and(active(X1),X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 1] [1 0 1] [1 0 1] [1 0 1] __(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 1] [1 1 1] [1 0 1] [1 0 1] __(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 1 1] [1 0 0] [1 0 1] [1 0 0] and(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = mark(and(X1,X2)) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 1] [1 0 1] [1 0 1] [1 0 1] proper(__(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = __(proper(X1),proper(X2)) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1] [1] proper(nil()) = [1] >= [0] = ok(nil()) [1] [1] [1 0 1] [1 0 0] [1 0 1] [1 0 0] proper(and(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = and(proper(X1),proper(X2)) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0] [0] proper(tt()) = [1] >= [0] = ok(tt()) [1] [1] [1 0 0] [1 0 0] proper(isList(X)) = [0 0 0]X >= [0 0 0]X = isList(proper(X)) [0 0 0] [0 0 0] [1 0 0] [0] [1 0 0] [0] proper(isNeList(X)) = [0 0 1]X + [1] >= [0 0 1]X + [0] = isNeList(proper(X)) [0 0 1] [1] [0 0 1] [1] [1 0 0] [1 0 0] proper(isQid(X)) = [1 0 1]X >= [0 0 0]X = isQid(proper(X)) [1 0 1] [1 0 1] [1 0 0] [1 0 0] proper(isNePal(X)) = [0 0 1]X >= [0 0 1]X = isNePal(proper(X)) [0 0 1] [0 0 1] [1 0 0] [1 0 0] proper(isPal(X)) = [0 0 0]X >= [0 0 0]X = isPal(proper(X)) [0 0 0] [0 0 0] [0] [0] proper(a()) = [0] >= [0] = ok(a()) [0] [0] [1] [1] proper(e()) = [1] >= [0] = ok(e()) [1] [1] [1] [1] proper(i()) = [1] >= [0] = ok(i()) [1] [1] [1] [1] proper(o()) = [1] >= [0] = ok(o()) [1] [1] [0] [0] proper(u()) = [1] >= [0] = ok(u()) [1] [1] [1 1 1] [1 1 1] [1 0 1] [1 0 1] __(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 1 1] [1 0 0] [1 0 1] [1 0 0] and(ok(X1),ok(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = ok(and(X1,X2)) [0 0 0] [0 0 0] [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] [0] [1 0 0] [0] isNeList(ok(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = ok(isNeList(X)) [0 1 1] [1] [0 1 1] [1] [1 0 0] [1 0 0] isQid(ok(X)) = [0 0 0]X >= [0 0 0]X = ok(isQid(X)) [1 1 1] [1 0 1] [1 0 0] [1 0 0] isNePal(ok(X)) = [0 0 0]X >= [0 0 0]X = ok(isNePal(X)) [0 1 1] [0 1 1] [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 1 1] [1 0 1] top(mark(X)) = [1 1 1]X >= [1 0 1]X = top(proper(X)) [0 0 0] [0 0 0] [1 1 1] [1 0 1] top(ok(X)) = [1 1 1]X >= [1 0 1]X = top(active(X)) [0 0 0] [0 0 0] problem: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(isList(__(V1,V2))) -> mark(and(isList(V1),isList(V2))) active(isNeList(__(V1,V2))) -> mark(and(isNeList(V1),isList(V2))) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(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)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(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 1]x0 [0 0 0] , [1 0 1] [ok](x0) = [0 1 0]x0 [0 0 0] , [1 0 0] [proper](x0) = [0 1 0]x0 [0 0 0] , [0] [u] = [0] [0], [0] [o] = [0] [0], [1] [i] = [0] [0], [1] [e] = [0] [0], [1] [a] = [0] [0], [1 0 0] [isPal](x0) = [0 0 0]x0 [0 0 0] , [1 1 0] [isNePal](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [0] [isQid](x0) = [0 0 0]x0 + [1] [0 0 0] [0], [1 1 0] [isNeList](x0) = [0 0 0]x0 [0 0 0] , [1 1 0] [0] [isList](x0) = [0 0 0]x0 + [1] [0 0 0] [0], [1 1 0] [1 0 0] [and](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 1] [0 0 0] , [0] [tt] = [0] [0], [0] [nil] = [0] [0], [mark](x0) = x0 , [1 0 1] [active](x0) = [0 1 0]x0 [0 0 0] , [1 1 1] [1 1 1] [0] [__](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1] [0 0 0] [0 0 0] [0] orientation: [1 1 1] [1 1 1] [1 1 1] [1] [1 1 1] [1 1 1] [1 1 1] [1] active(__(__(X,Y),Z)) = [0 0 0]X + [0 0 0]Y + [0 0 0]Z + [1] >= [0 0 0]X + [0 0 0]Y + [0 0 0]Z + [1] = mark(__(X,__(Y,Z))) [0 0 0] [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0 0 0] [0] [1 1 1] [1 1 1] [1] [1 1 0] [1 1 0] [1] active(isList(__(V1,V2))) = [0 0 0]V1 + [0 0 0]V2 + [1] >= [0 0 0]V1 + [0 0 0]V2 + [0] = mark(and(isList(V1),isList(V2))) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 1 1] [1 1 1] [1] [1 1 0] [1 1 0] active(isNeList(__(V1,V2))) = [0 0 0]V1 + [0 0 0]V2 + [0] >= [0 0 0]V1 + [0 0 0]V2 = mark(and(isNeList(V1),isList(V2))) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [1 1 1] [1 1 1] [0] [1 1 1] [1 1 1] [0] active(__(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = __(active(X1),X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 1 1] [1 1 1] [0] [1 1 1] [1 1 1] [0] active(__(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = __(X1,active(X2)) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 1 1] [1 0 0] [1 1 1] [1 0 0] active(and(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = and(active(X1),X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 1] [1 1 1] [0] [1 1 1] [1 1 1] [0] __(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = mark(__(X1,X2)) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 1 1] [1 1 1] [0] [1 1 1] [1 1 1] [0] __(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = mark(__(X1,X2)) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 1 0] [1 0 0] [1 1 0] [1 0 0] and(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = mark(and(X1,X2)) [0 0 1] [0 0 0] [0 0 1] [0 0 0] [1 1 1] [1 1 1] [0] [1 1 0] [1 1 0] [0] proper(__(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = __(proper(X1),proper(X2)) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [0] [0] proper(nil()) = [0] >= [0] = ok(nil()) [0] [0] [1 1 0] [1 0 0] [1 1 0] [1 0 0] proper(and(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = and(proper(X1),proper(X2)) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0] [0] proper(tt()) = [0] >= [0] = ok(tt()) [0] [0] [1 1 0] [0] [1 1 0] [0] proper(isList(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = isList(proper(X)) [0 0 0] [0] [0 0 0] [0] [1 1 0] [1 1 0] proper(isNeList(X)) = [0 0 0]X >= [0 0 0]X = isNeList(proper(X)) [0 0 0] [0 0 0] [1 0 0] [0] [1 0 0] [0] proper(isQid(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = isQid(proper(X)) [0 0 0] [0] [0 0 0] [0] [1 1 0] [1 1 0] proper(isNePal(X)) = [0 0 0]X >= [0 0 0]X = isNePal(proper(X)) [0 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)) [0 0 0] [0 0 0] [1] [1] proper(a()) = [0] >= [0] = ok(a()) [0] [0] [1] [1] proper(e()) = [0] >= [0] = ok(e()) [0] [0] [1] [1] 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 1 1] [1 1 1] [0] [1 1 1] [1 1 1] [0] __(ok(X1),ok(X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = ok(__(X1,X2)) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 1 1] [1 0 1] [1 1 1] [1 0 0] and(ok(X1),ok(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = ok(and(X1,X2)) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 1] [0] [1 1 0] [0] isList(ok(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = ok(isList(X)) [0 0 0] [0] [0 0 0] [0] [1 1 1] [1 1 0] isNeList(ok(X)) = [0 0 0]X >= [0 0 0]X = ok(isNeList(X)) [0 0 0] [0 0 0] [1 0 1] [0] [1 0 0] [0] isQid(ok(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = ok(isQid(X)) [0 0 0] [0] [0 0 0] [0] [1 1 1] [1 1 0] isNePal(ok(X)) = [0 0 0]X >= [0 0 0]X = ok(isNePal(X)) [0 0 0] [0 0 0] [1 0 1] [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] top(mark(X)) = [0 0 1]X >= [0 0 0]X = top(proper(X)) [0 0 0] [0 0 0] [1 0 1] [1 0 1] top(ok(X)) = [0 0 0]X >= [0 0 0]X = top(active(X)) [0 0 0] [0 0 0] problem: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(isList(__(V1,V2))) -> mark(and(isList(V1),isList(V2))) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(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)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(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 1] [ok](x0) = [0 1 0]x0 [0 0 0] , [1 0 0] [proper](x0) = [0 1 0]x0 [1 0 0] , [1] [u] = [0] [0], [1] [o] = [0] [0], [0] [i] = [0] [0], [1] [e] = [0] [0], [0] [a] = [0] [0], [1 0 0] [isPal](x0) = [0 0 0]x0 [0 0 1] , [1 0 0] [isNePal](x0) = [0 1 0]x0 [0 0 0] , [1 0 0] [isQid](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [isNeList](x0) = [0 0 0]x0 [0 0 0] , [1 1 0] [isList](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 1 0] [and](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1] [tt] = [0] [0], [1] [nil] = [0] [0], [1 0 0] [mark](x0) = [0 1 0]x0 [0 0 0] , [1 0 0] [active](x0) = [0 1 0]x0 [0 0 0] , [1 1 0] [1 1 0] [0] [__](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1] [0 0 0] [0 0 0] [0] orientation: [1 1 0] [1 1 0] [1 1 0] [1] [1 1 0] [1 1 0] [1 1 0] [1] active(__(__(X,Y),Z)) = [0 0 0]X + [0 0 0]Y + [0 0 0]Z + [1] >= [0 0 0]X + [0 0 0]Y + [0 0 0]Z + [1] = mark(__(X,__(Y,Z))) [0 0 0] [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0 0 0] [0] [1 1 0] [1 1 0] [1] [1 1 0] [1 1 0] active(isList(__(V1,V2))) = [0 0 0]V1 + [0 0 0]V2 + [0] >= [0 0 0]V1 + [0 0 0]V2 = mark(and(isList(V1),isList(V2))) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [1 1 0] [1 1 0] [0] [1 1 0] [1 1 0] [0] active(__(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = __(active(X1),X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 1 0] [1 1 0] [0] [1 1 0] [1 1 0] [0] active(__(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = __(X1,active(X2)) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 0] [1 1 0] [1 0 0] [1 1 0] active(and(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = and(active(X1),X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [1 1 0] [0] [1 1 0] [1 1 0] [0] __(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 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 0] [0] [1 1 0] [1 1 0] [0] __(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = mark(__(X1,X2)) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 0] [1 1 0] [1 0 0] [1 1 0] and(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = mark(and(X1,X2)) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [1 1 0] [0] [1 1 0] [1 1 0] [0] proper(__(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = __(proper(X1),proper(X2)) [1 1 0] [1 1 0] [0] [0 0 0] [0 0 0] [0] [1] [1] proper(nil()) = [0] >= [0] = ok(nil()) [1] [0] [1 0 0] [1 1 0] [1 0 0] [1 1 0] proper(and(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = and(proper(X1),proper(X2)) [1 0 0] [1 1 0] [0 0 0] [0 0 0] [1] [1] proper(tt()) = [0] >= [0] = ok(tt()) [1] [0] [1 1 0] [1 1 0] proper(isList(X)) = [0 0 0]X >= [0 0 0]X = isList(proper(X)) [1 1 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] [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 1 0]X >= [0 1 0]X = isNePal(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] [1 0 0] [0] [0] proper(a()) = [0] >= [0] = ok(a()) [0] [0] [1] [1] proper(e()) = [0] >= [0] = ok(e()) [1] [0] [0] [0] proper(i()) = [0] >= [0] = ok(i()) [0] [0] [1] [1] proper(o()) = [0] >= [0] = ok(o()) [1] [0] [1] [1] proper(u()) = [0] >= [0] = ok(u()) [1] [0] [1 1 1] [1 1 1] [0] [1 1 0] [1 1 0] [0] __(ok(X1),ok(X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = ok(__(X1,X2)) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 1] [1 1 1] [1 0 0] [1 1 0] and(ok(X1),ok(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = ok(and(X1,X2)) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 1] [1 1 0] isList(ok(X)) = [0 0 0]X >= [0 0 0]X = ok(isList(X)) [0 0 0] [0 0 0] [1 0 1] [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 1] [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 1] [1 0 0] isNePal(ok(X)) = [0 1 0]X >= [0 1 0]X = ok(isNePal(X)) [0 0 0] [0 0 0] [1 0 1] [1 0 1] 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] top(mark(X)) = [0 0 0]X >= [0 0 0]X = top(proper(X)) [0 0 0] [0 0 0] [1 0 1] [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(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(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)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dim=1 interpretation: [top](x0) = 4x0, [ok](x0) = x0, [proper](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 2x0, [isNePal](x0) = x0, [isQid](x0) = 4x0, [isNeList](x0) = x0, [isList](x0) = 2x0, [and](x0, x1) = x0 + x1, [tt] = 0, [nil] = 0, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = 2x0 + x1 + 4 orientation: active(__(__(X,Y),Z)) = 4X + 2Y + Z + 12 >= 2X + 2Y + Z + 8 = mark(__(X,__(Y,Z))) 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(and(X1,X2)) = X1 + X2 >= X1 + X2 = and(active(X1),X2) __(mark(X1),X2) = 2X1 + X2 + 4 >= 2X1 + X2 + 4 = mark(__(X1,X2)) __(X1,mark(X2)) = 2X1 + X2 + 4 >= 2X1 + X2 + 4 = mark(__(X1,X2)) and(mark(X1),X2) = X1 + X2 >= X1 + X2 = mark(and(X1,X2)) proper(__(X1,X2)) = 2X1 + X2 + 4 >= 2X1 + X2 + 4 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(and(X1,X2)) = X1 + X2 >= X1 + X2 = and(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(isList(X)) = 2X >= 2X = isList(proper(X)) proper(isNeList(X)) = X >= X = isNeList(proper(X)) proper(isQid(X)) = 4X >= 4X = isQid(proper(X)) proper(isNePal(X)) = X >= X = isNePal(proper(X)) proper(isPal(X)) = 2X >= 2X = isPal(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)) = 2X1 + X2 + 4 >= 2X1 + X2 + 4 = ok(__(X1,X2)) and(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(and(X1,X2)) isList(ok(X)) = 2X >= 2X = ok(isList(X)) isNeList(ok(X)) = X >= X = ok(isNeList(X)) isQid(ok(X)) = 4X >= 4X = ok(isQid(X)) isNePal(ok(X)) = X >= X = ok(isNePal(X)) isPal(ok(X)) = 2X >= 2X = ok(isPal(X)) top(mark(X)) = 4X >= 4X = top(proper(X)) top(ok(X)) = 4X >= 4X = top(active(X)) problem: active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(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)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [top](x0) = [1 0 0]x0 [0 0 0] , [1 0 0] [ok](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [0] [proper](x0) = [1 0 1]x0 + [0] [0 0 0] [1], [0] [u] = [0] [0], [0] [o] = [0] [1], [0] [i] = [0] [0], [1] [e] = [0] [0], [0] [a] = [0] [0], [1 0 0] [0] [isPal](x0) = [0 0 0]x0 + [1] [0 0 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] [isNeList](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] [and](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [0] [tt] = [0] [0], [0] [nil] = [0] [1], [1 0 0] [1] [mark](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [1 0 0] [0] [active](x0) = [0 0 0]x0 + [1] [0 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 0 0] [0] [1 0 0] [1 0 0] active(__(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 = __(active(X1),X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] active(__(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 = __(X1,active(X2)) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] active(and(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 = and(active(X1),X2) [0 0 0] [0 0 0] [0] [0 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] [0 0 0] [0] [0 0 0] [0 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] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] [1] and(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = mark(and(X1,X2)) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] proper(__(X1,X2)) = [1 0 0]X1 + [1 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 = __(proper(X1),proper(X2)) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [0] [0] proper(nil()) = [1] >= [0] = ok(nil()) [1] [0] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] proper(and(X1,X2)) = [1 0 0]X1 + [1 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 = and(proper(X1),proper(X2)) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [0] [0] proper(tt()) = [0] >= [0] = ok(tt()) [1] [0] [1 0 0] [0] [1 0 0] proper(isList(X)) = [1 0 0]X + [0] >= [0 0 0]X = isList(proper(X)) [0 0 0] [1] [0 0 0] [1 0 0] [0] [1 0 0] proper(isNeList(X)) = [1 0 0]X + [0] >= [0 0 0]X = isNeList(proper(X)) [0 0 0] [1] [0 0 0] [1 0 0] [0] [1 0 0] proper(isQid(X)) = [1 0 0]X + [0] >= [0 0 0]X = isQid(proper(X)) [0 0 0] [1] [0 0 0] [1 0 0] [0] [1 0 0] proper(isNePal(X)) = [1 0 0]X + [0] >= [0 0 0]X = isNePal(proper(X)) [0 0 0] [1] [0 0 0] [1 0 0] [0] [1 0 0] [0] proper(isPal(X)) = [1 0 0]X + [1] >= [0 0 0]X + [1] = isPal(proper(X)) [0 0 0] [1] [0 0 0] [1] [0] [0] proper(a()) = [0] >= [0] = ok(a()) [1] [0] [1] [1] proper(e()) = [1] >= [0] = ok(e()) [1] [0] [0] [0] proper(i()) = [0] >= [0] = ok(i()) [1] [0] [0] [0] proper(o()) = [1] >= [0] = ok(o()) [1] [0] [0] [0] proper(u()) = [0] >= [0] = ok(u()) [1] [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 0 0] [1 0 0] [1 0 0] and(ok(X1),ok(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = ok(and(X1,X2)) [0 0 0] [0 0 0] [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] 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] 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] [0] [1 0 0] isPal(ok(X)) = [0 0 0]X + [1] >= [0 0 0]X = ok(isPal(X)) [0 0 0] [1] [0 0 0] [1 0 0] [1] [1 0 0] top(mark(X)) = [1 0 0]X + [1] >= [1 0 0]X = top(proper(X)) [0 0 0] [0] [0 0 0] [1 0 0] [1 0 0] top(ok(X)) = [1 0 0]X >= [1 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(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(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)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(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 1 0] [0] [ok](x0) = [0 0 0]x0 + [0] [0 0 1] [1], [1 1 0] [0] [proper](x0) = [0 1 0]x0 + [0] [0 0 0] [1], [0] [u] = [0] [0], [0] [o] = [0] [0], [0] [i] = [0] [0], [0] [e] = [0] [0], [0] [a] = [0] [0], [isPal](x0) = x0 , [isNePal](x0) = x0 , [isQid](x0) = x0 , [isNeList](x0) = x0 , [isList](x0) = x0 , [1 0 0] [and](x0, x1) = [0 1 0]x0 + x1 [0 0 0] , [0] [tt] = [0] [0], [0] [nil] = [1] [0], [1 0 0] [1] [mark](x0) = [0 0 0]x0 + [0] [0 0 1] [0], [1 1 0] [active](x0) = [0 1 0]x0 [0 0 1] , [1 0 0] [1 0 1] [0] [__](x0, x1) = [0 1 0]x0 + [0 1 0]x1 + [1] [0 0 0] [0 0 1] [0] orientation: [1 1 0] [1 1 1] [1] [1 1 0] [1 0 1] [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 0] [0 0 1] [0] [0 0 0] [0 0 1] [0] [1 1 0] [1 1 1] [1] [1 0 0] [1 1 1] [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 0] [0 0 1] [0] [0 0 0] [0 0 1] [0] [1 1 0] [1 1 0] [1 1 0] active(and(X1,X2)) = [0 1 0]X1 + [0 1 0]X2 >= [0 1 0]X1 + X2 = and(active(X1),X2) [0 0 0] [0 0 1] [0 0 0] [1 0 0] [1 0 1] [1] [1 0 0] [1 0 1] [1] __(mark(X1),X2) = [0 0 0]X1 + [0 1 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [0] = mark(__(X1,X2)) [0 0 0] [0 0 1] [0] [0 0 0] [0 0 1] [0] [1 0 0] [1 0 1] [1] [1 0 0] [1 0 1] [1] __(X1,mark(X2)) = [0 1 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [0] = mark(__(X1,X2)) [0 0 0] [0 0 1] [0] [0 0 0] [0 0 1] [0] [1 0 0] [1] [1 0 0] [1 0 0] [1] and(mark(X1),X2) = [0 0 0]X1 + X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = mark(and(X1,X2)) [0 0 0] [0] [0 0 0] [0 0 1] [0] [1 1 0] [1 1 1] [1] [1 1 0] [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 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1] [1] proper(nil()) = [1] >= [0] = ok(nil()) [1] [1] [1 1 0] [1 1 0] [0] [1 1 0] [1 1 0] [0] proper(and(X1,X2)) = [0 1 0]X1 + [0 1 0]X2 + [0] >= [0 1 0]X1 + [0 1 0]X2 + [0] = and(proper(X1),proper(X2)) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [0] [0] proper(tt()) = [0] >= [0] = ok(tt()) [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 0 0] [1] [0 0 0] [1] [1 1 0] [0] [1 1 0] [0] proper(isNeList(X)) = [0 1 0]X + [0] >= [0 1 0]X + [0] = isNeList(proper(X)) [0 0 0] [1] [0 0 0] [1] [1 1 0] [0] [1 1 0] [0] proper(isQid(X)) = [0 1 0]X + [0] >= [0 1 0]X + [0] = isQid(proper(X)) [0 0 0] [1] [0 0 0] [1] [1 1 0] [0] [1 1 0] [0] proper(isNePal(X)) = [0 1 0]X + [0] >= [0 1 0]X + [0] = isNePal(proper(X)) [0 0 0] [1] [0 0 0] [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 0] [1] [0 0 0] [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] [0] [0] proper(u()) = [0] >= [0] = ok(u()) [1] [1] [1 1 0] [1 1 1] [1] [1 1 0] [1 1 1] [1] __(ok(X1),ok(X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [0] = ok(__(X1,X2)) [0 0 0] [0 0 1] [1] [0 0 0] [0 0 1] [1] [1 1 0] [1 1 0] [0] [1 1 0] [1 1 0] [0] and(ok(X1),ok(X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = ok(and(X1,X2)) [0 0 0] [0 0 1] [1] [0 0 0] [0 0 1] [1] [1 1 0] [0] [1 1 0] [0] isList(ok(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = ok(isList(X)) [0 0 1] [1] [0 0 1] [1] [1 1 0] [0] [1 1 0] [0] isNeList(ok(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = ok(isNeList(X)) [0 0 1] [1] [0 0 1] [1] [1 1 0] [0] [1 1 0] [0] isQid(ok(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = ok(isQid(X)) [0 0 1] [1] [0 0 1] [1] [1 1 0] [0] [1 1 0] [0] isNePal(ok(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = ok(isNePal(X)) [0 0 1] [1] [0 0 1] [1] [1 1 0] [0] [1 1 0] [0] isPal(ok(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = ok(isPal(X)) [0 0 1] [1] [0 0 1] [1] [1 1 0] [1 1 0] top(ok(X)) = [0 0 0]X >= [0 0 0]X = top(active(X)) [0 0 0] [0 0 0] problem: active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(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)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(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] , [0] [ok](x0) = x0 + [1] [0], [1 1 0] [proper](x0) = [0 0 1]x0 [1 0 0] , [1] [u] = [0] [1], [1] [o] = [0] [1], [1] [i] = [0] [1], [1] [e] = [0] [1], [1] [a] = [0] [1], [isPal](x0) = x0 , [1] [isNePal](x0) = x0 + [0] [0], [1] [isQid](x0) = x0 + [0] [0], [isNeList](x0) = x0 , [isList](x0) = x0 , [1 1 0] [and](x0, x1) = x0 + [0 0 1]x1 [1 0 0] , [1] [tt] = [0] [1], [1] [nil] = [0] [1], [mark](x0) = x0 , [1 0 0] [0] [active](x0) = [0 1 0]x0 + [1] [1 0 0] [0], [1 1 0] [__](x0, x1) = [0 0 1]x0 + x1 [1 0 0] orientation: [1 0 0] [1 1 0] [0] [1 0 0] [1 1 0] [0] active(and(X1,X2)) = [0 1 0]X1 + [0 0 1]X2 + [1] >= [0 1 0]X1 + [0 0 1]X2 + [1] = and(active(X1),X2) [1 0 0] [1 1 0] [0] [1 0 0] [1 0 0] [0] [1 1 0] [1 1 0] __(mark(X1),X2) = [0 0 1]X1 + X2 >= [0 0 1]X1 + X2 = mark(__(X1,X2)) [1 0 0] [1 0 0] [1 1 0] [1 1 0] __(X1,mark(X2)) = [0 0 1]X1 + X2 >= [0 0 1]X1 + X2 = mark(__(X1,X2)) [1 0 0] [1 0 0] [1 1 0] [1 1 0] and(mark(X1),X2) = X1 + [0 0 1]X2 >= X1 + [0 0 1]X2 = mark(and(X1,X2)) [1 0 0] [1 0 0] [1 1 1] [1 1 0] [1 1 1] [1 1 0] proper(__(X1,X2)) = [1 0 0]X1 + [0 0 1]X2 >= [1 0 0]X1 + [0 0 1]X2 = __(proper(X1),proper(X2)) [1 1 0] [1 0 0] [1 1 0] [1 0 0] [1] [1] proper(nil()) = [1] >= [1] = ok(nil()) [1] [1] [1 1 0] [1 1 1] [1 1 0] [1 1 1] proper(and(X1,X2)) = [0 0 1]X1 + [1 0 0]X2 >= [0 0 1]X1 + [1 0 0]X2 = and(proper(X1),proper(X2)) [1 0 0] [1 1 0] [1 0 0] [1 1 0] [1] [1] proper(tt()) = [1] >= [1] = ok(tt()) [1] [1] [1 1 0] [1 1 0] proper(isList(X)) = [0 0 1]X >= [0 0 1]X = isList(proper(X)) [1 0 0] [1 0 0] [1 1 0] [1 1 0] proper(isNeList(X)) = [0 0 1]X >= [0 0 1]X = isNeList(proper(X)) [1 0 0] [1 0 0] [1 1 0] [1] [1 1 0] [1] proper(isQid(X)) = [0 0 1]X + [0] >= [0 0 1]X + [0] = isQid(proper(X)) [1 0 0] [1] [1 0 0] [0] [1 1 0] [1] [1 1 0] [1] proper(isNePal(X)) = [0 0 1]X + [0] >= [0 0 1]X + [0] = isNePal(proper(X)) [1 0 0] [1] [1 0 0] [0] [1 1 0] [1 1 0] proper(isPal(X)) = [0 0 1]X >= [0 0 1]X = isPal(proper(X)) [1 0 0] [1 0 0] [1] [1] proper(a()) = [1] >= [1] = ok(a()) [1] [1] [1] [1] proper(e()) = [1] >= [1] = ok(e()) [1] [1] [1] [1] proper(i()) = [1] >= [1] = ok(i()) [1] [1] [1] [1] proper(o()) = [1] >= [1] = ok(o()) [1] [1] [1] [1] proper(u()) = [1] >= [1] = ok(u()) [1] [1] [1 1 0] [1] [1 1 0] [0] __(ok(X1),ok(X2)) = [0 0 1]X1 + X2 + [1] >= [0 0 1]X1 + X2 + [1] = ok(__(X1,X2)) [1 0 0] [0] [1 0 0] [0] [1 1 0] [1] [1 1 0] [0] and(ok(X1),ok(X2)) = X1 + [0 0 1]X2 + [1] >= X1 + [0 0 1]X2 + [1] = ok(and(X1,X2)) [1 0 0] [0] [1 0 0] [0] [0] [0] isList(ok(X)) = X + [1] >= X + [1] = ok(isList(X)) [0] [0] [0] [0] isNeList(ok(X)) = X + [1] >= X + [1] = ok(isNeList(X)) [0] [0] [1] [1] isQid(ok(X)) = X + [1] >= X + [1] = ok(isQid(X)) [0] [0] [1] [1] isNePal(ok(X)) = X + [1] >= X + [1] = ok(isNePal(X)) [0] [0] [0] [0] isPal(ok(X)) = X + [1] >= X + [1] = ok(isPal(X)) [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(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(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 1] [ok](x0) = [0 0 0]x0 [0 0 0] , [1 1 0] [proper](x0) = [0 1 0]x0 [0 1 0] , [0] [u] = [0] [0], [0] [o] = [0] [0], [0] [i] = [0] [0], [0] [e] = [1] [0], [0] [a] = [0] [0], [1] [isPal](x0) = x0 + [0] [0], [isNePal](x0) = x0 , [1 0 0] [isQid](x0) = [0 1 0]x0 [0 0 0] , [1 0 0] [1] [isNeList](x0) = [0 1 0]x0 + [0] [0 0 0] [0], [isList](x0) = x0 , [1 0 0] [0] [and](x0, x1) = x0 + [0 1 0]x1 + [1] [0 0 0] [1], [0] [tt] = [0] [0], [0] [nil] = [0] [0], [1 0 0] [1] [mark](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [1 0 1] [active](x0) = [0 1 0]x0 [0 0 1] , [1 0 0] [1 0 0] [0] [__](x0, x1) = [0 1 0]x0 + [0 1 0]x1 + [1] [0 0 0] [0 0 0] [1] orientation: [1 0 1] [1 0 0] [1] [1 0 1] [1 0 0] [0] active(and(X1,X2)) = [0 1 0]X1 + [0 1 0]X2 + [1] >= [0 1 0]X1 + [0 1 0]X2 + [1] = and(active(X1),X2) [0 0 1] [0 0 0] [1] [0 0 1] [0 0 0] [1] [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] [1] __(mark(X1),X2) = [0 0 0]X1 + [0 1 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [0] = mark(__(X1,X2)) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [0] [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] [1] __(X1,mark(X2)) = [0 1 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [0] = mark(__(X1,X2)) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [0] [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] [1] and(mark(X1),X2) = [0 0 0]X1 + [0 1 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [0] = mark(and(X1,X2)) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [0] [1 1 0] [1 1 0] [1] [1 1 0] [1 1 0] [0] 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 1 0] [0 1 0] [1] [0 0 0] [0 0 0] [1] [0] [0] proper(nil()) = [0] >= [0] = ok(nil()) [0] [0] [1 1 0] [1 1 0] [1] [1 1 0] [1 1 0] [0] proper(and(X1,X2)) = [0 1 0]X1 + [0 1 0]X2 + [1] >= [0 1 0]X1 + [0 1 0]X2 + [1] = and(proper(X1),proper(X2)) [0 1 0] [0 1 0] [1] [0 1 0] [0 0 0] [1] [0] [0] proper(tt()) = [0] >= [0] = ok(tt()) [0] [0] [1 1 0] [1 1 0] proper(isList(X)) = [0 1 0]X >= [0 1 0]X = isList(proper(X)) [0 1 0] [0 1 0] [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 1 0] [0] [0 0 0] [0] [1 1 0] [1 1 0] proper(isQid(X)) = [0 1 0]X >= [0 1 0]X = isQid(proper(X)) [0 1 0] [0 0 0] [1 1 0] [1 1 0] proper(isNePal(X)) = [0 1 0]X >= [0 1 0]X = isNePal(proper(X)) [0 1 0] [0 1 0] [1 1 0] [1] [1 1 0] [1] proper(isPal(X)) = [0 1 0]X + [0] >= [0 1 0]X + [0] = isPal(proper(X)) [0 1 0] [0] [0 1 0] [0] [0] [0] proper(a()) = [0] >= [0] = ok(a()) [0] [0] [1] [0] proper(e()) = [1] >= [0] = ok(e()) [1] [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 1] [1 0 1] isList(ok(X)) = [0 0 0]X >= [0 0 0]X = ok(isList(X)) [0 0 0] [0 0 0] [1 0 1] [1] [1 0 0] [1] isNeList(ok(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = ok(isNeList(X)) [0 0 0] [0] [0 0 0] [0] [1 0 1] [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 1] [1 0 1] isNePal(ok(X)) = [0 0 0]X >= [0 0 0]X = ok(isNePal(X)) [0 0 0] [0 0 0] [1 0 1] [1] [1 0 1] [1] isPal(ok(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = ok(isPal(X)) [0 0 0] [0] [0 0 0] [0] [1 0 1] [1 0 1] top(ok(X)) = [0 0 0]X >= [0 0 0]X = top(active(X)) [0 0 0] [0 0 0] problem: __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(nil()) -> ok(nil()) proper(tt()) -> ok(tt()) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dim=1 interpretation: [top](x0) = x0, [ok](x0) = x0 + 3, [proper](x0) = x0 + 3, [u] = 5, [o] = 0, [i] = 0, [a] = 1, [isPal](x0) = x0, [isNePal](x0) = x0 + 2, [isQid](x0) = x0 + 5, [isNeList](x0) = x0 + 1, [isList](x0) = x0, [and](x0, x1) = x0 + x1, [tt] = 6, [nil] = 0, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = 4x0 + x1 orientation: __(mark(X1),X2) = 4X1 + X2 >= 4X1 + X2 = mark(__(X1,X2)) __(X1,mark(X2)) = 4X1 + X2 >= 4X1 + X2 = mark(__(X1,X2)) and(mark(X1),X2) = X1 + X2 >= X1 + X2 = mark(and(X1,X2)) proper(nil()) = 3 >= 3 = ok(nil()) proper(tt()) = 9 >= 9 = ok(tt()) proper(isList(X)) = X + 3 >= X + 3 = isList(proper(X)) proper(isNeList(X)) = X + 4 >= X + 4 = isNeList(proper(X)) proper(isQid(X)) = X + 8 >= X + 8 = isQid(proper(X)) proper(isNePal(X)) = X + 5 >= X + 5 = isNePal(proper(X)) proper(isPal(X)) = X + 3 >= X + 3 = isPal(proper(X)) proper(a()) = 4 >= 4 = ok(a()) proper(i()) = 3 >= 3 = ok(i()) proper(o()) = 3 >= 3 = ok(o()) proper(u()) = 8 >= 8 = ok(u()) isList(ok(X)) = X + 3 >= X + 3 = ok(isList(X)) isNeList(ok(X)) = X + 4 >= X + 4 = ok(isNeList(X)) isQid(ok(X)) = X + 8 >= X + 8 = ok(isQid(X)) isNePal(ok(X)) = X + 5 >= X + 5 = ok(isNePal(X)) isPal(ok(X)) = X + 3 >= X + 3 = ok(isPal(X)) top(ok(X)) = X + 3 >= X = top(active(X)) problem: __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(nil()) -> ok(nil()) proper(tt()) -> ok(tt()) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) Matrix Interpretation Processor: dim=3 interpretation: [ok](x0) = x0 , [1 0 1] [proper](x0) = [0 1 0]x0 [0 1 0] , [0] [u] = [1] [0], [0] [o] = [0] [0], [1] [i] = [0] [0], [1] [a] = [0] [0], [1 0 1] [0] [isPal](x0) = [0 1 0]x0 + [1] [0 1 0] [0], [1 0 1] [1] [isNePal](x0) = [0 1 0]x0 + [1] [0 1 0] [0], [1 0 1] [0] [isQid](x0) = [0 1 0]x0 + [1] [0 1 0] [1], [1 0 1] [0] [isNeList](x0) = [0 1 0]x0 + [1] [0 1 0] [0], [1 0 1] [isList](x0) = [0 1 0]x0 [0 1 0] , [1 0 1] [1 0 0] [0] [and](x0, x1) = [0 0 0]x0 + [0 1 0]x1 + [1] [0 0 1] [0 0 0] [0], [0] [tt] = [0] [0], [0] [nil] = [0] [0], [1 0 0] [0] [mark](x0) = [0 0 0]x0 + [0] [0 0 1] [1], [1 0 1] [1 0 1] [__](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 1] [0 0 1] orientation: [1 0 1] [1 0 1] [1] [1 0 1] [1 0 1] [0] __(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 1] [0 0 1] [1] [0 0 1] [0 0 1] [1] [1 0 1] [1 0 1] [1] [1 0 1] [1 0 1] [0] __(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 1] [0 0 1] [1] [0 0 1] [0 0 1] [1] [1 0 1] [1 0 0] [1] [1 0 1] [1 0 0] [0] and(mark(X1),X2) = [0 0 0]X1 + [0 1 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [0] = mark(and(X1,X2)) [0 0 1] [0 0 0] [1] [0 0 1] [0 0 0] [1] [0] [0] proper(nil()) = [0] >= [0] = ok(nil()) [0] [0] [0] [0] proper(tt()) = [0] >= [0] = ok(tt()) [0] [0] [1 1 1] [1 1 1] proper(isList(X)) = [0 1 0]X >= [0 1 0]X = isList(proper(X)) [0 1 0] [0 1 0] [1 1 1] [0] [1 1 1] [0] proper(isNeList(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = isNeList(proper(X)) [0 1 0] [1] [0 1 0] [0] [1 1 1] [1] [1 1 1] [0] proper(isQid(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = isQid(proper(X)) [0 1 0] [1] [0 1 0] [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 0] [1] [0 1 0] [0] [1 1 1] [0] [1 1 1] [0] proper(isPal(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = isPal(proper(X)) [0 1 0] [1] [0 1 0] [0] [1] [1] proper(a()) = [0] >= [0] = ok(a()) [0] [0] [1] [1] proper(i()) = [0] >= [0] = ok(i()) [0] [0] [0] [0] proper(o()) = [0] >= [0] = ok(o()) [0] [0] [0] [0] proper(u()) = [1] >= [1] = ok(u()) [1] [0] [1 0 1] [1 0 1] isList(ok(X)) = [0 1 0]X >= [0 1 0]X = ok(isList(X)) [0 1 0] [0 1 0] [1 0 1] [0] [1 0 1] [0] isNeList(ok(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = ok(isNeList(X)) [0 1 0] [0] [0 1 0] [0] [1 0 1] [0] [1 0 1] [0] isQid(ok(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = ok(isQid(X)) [0 1 0] [1] [0 1 0] [1] [1 0 1] [1] [1 0 1] [1] isNePal(ok(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = ok(isNePal(X)) [0 1 0] [0] [0 1 0] [0] [1 0 1] [0] [1 0 1] [0] isPal(ok(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = ok(isPal(X)) [0 1 0] [0] [0 1 0] [0] problem: proper(nil()) -> ok(nil()) proper(tt()) -> ok(tt()) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) Matrix Interpretation Processor: dim=3 interpretation: [ok](x0) = x0 , [1 1 1] [proper](x0) = [1 1 0]x0 [1 0 1] , [0] [u] = [0] [0], [0] [o] = [0] [0], [0] [i] = [0] [0], [0] [a] = [0] [0], [0] [isPal](x0) = x0 + [0] [1], [1 0 0] [0] [isNePal](x0) = [0 0 1]x0 + [0] [0 1 0] [1], [1 0 0] [1] [isQid](x0) = [0 0 0]x0 + [0] [0 0 1] [0], [1 0 0] [0] [isNeList](x0) = [0 0 1]x0 + [0] [0 1 0] [1], [0] [isList](x0) = x0 + [0] [1], [0] [tt] = [0] [1], [0] [nil] = [0] [1] orientation: [1] [0] proper(nil()) = [0] >= [0] = ok(nil()) [1] [1] [1] [0] proper(tt()) = [0] >= [0] = ok(tt()) [1] [1] [1 1 1] [1] [1 1 1] [0] proper(isList(X)) = [1 1 0]X + [0] >= [1 1 0]X + [0] = isList(proper(X)) [1 0 1] [1] [1 0 1] [1] [1 1 1] [1] [1 1 1] [0] proper(isNeList(X)) = [1 0 1]X + [0] >= [1 0 1]X + [0] = isNeList(proper(X)) [1 1 0] [1] [1 1 0] [1] [1 1 1] [1] [1 1 1] [0] proper(isNePal(X)) = [1 0 1]X + [0] >= [1 0 1]X + [0] = isNePal(proper(X)) [1 1 0] [1] [1 1 0] [1] [1 1 1] [1] [1 1 1] [0] proper(isPal(X)) = [1 1 0]X + [0] >= [1 1 0]X + [0] = isPal(proper(X)) [1 0 1] [1] [1 0 1] [1] [0] [0] proper(a()) = [0] >= [0] = ok(a()) [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] [0] [0] isList(ok(X)) = X + [0] >= X + [0] = ok(isList(X)) [1] [1] [1 0 0] [0] [1 0 0] [0] isNeList(ok(X)) = [0 0 1]X + [0] >= [0 0 1]X + [0] = ok(isNeList(X)) [0 1 0] [1] [0 1 0] [1] [1 0 0] [1] [1 0 0] [1] isQid(ok(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = ok(isQid(X)) [0 0 1] [0] [0 0 1] [0] [1 0 0] [0] [1 0 0] [0] isNePal(ok(X)) = [0 0 1]X + [0] >= [0 0 1]X + [0] = ok(isNePal(X)) [0 1 0] [1] [0 1 0] [1] [0] [0] isPal(ok(X)) = X + [0] >= X + [0] = ok(isPal(X)) [1] [1] problem: proper(a()) -> ok(a()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) Matrix Interpretation Processor: dim=1 interpretation: [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [u] = 7, [o] = 0, [i] = 3, [a] = 4, [isPal](x0) = 6x0 + 1, [isNePal](x0) = x0, [isQid](x0) = x0, [isNeList](x0) = x0 + 4, [isList](x0) = x0 + 7 orientation: proper(a()) = 5 >= 5 = ok(a()) proper(i()) = 4 >= 4 = ok(i()) proper(o()) = 1 >= 1 = ok(o()) proper(u()) = 8 >= 8 = ok(u()) isList(ok(X)) = X + 8 >= X + 8 = ok(isList(X)) isNeList(ok(X)) = X + 5 >= X + 5 = ok(isNeList(X)) isQid(ok(X)) = X + 1 >= X + 1 = ok(isQid(X)) isNePal(ok(X)) = X + 1 >= X + 1 = ok(isNePal(X)) isPal(ok(X)) = 6X + 7 >= 6X + 2 = ok(isPal(X)) problem: proper(a()) -> ok(a()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) Matrix Interpretation Processor: dim=1 interpretation: [ok](x0) = 2x0 + 2, [proper](x0) = x0 + 3, [u] = 1, [o] = 1, [i] = 1, [a] = 1, [isNePal](x0) = 4x0 + 5, [isQid](x0) = 2x0 + 2, [isNeList](x0) = 2x0 + 2, [isList](x0) = 4x0 + 6 orientation: proper(a()) = 4 >= 4 = ok(a()) proper(i()) = 4 >= 4 = ok(i()) proper(o()) = 4 >= 4 = ok(o()) proper(u()) = 4 >= 4 = ok(u()) isList(ok(X)) = 8X + 14 >= 8X + 14 = ok(isList(X)) isNeList(ok(X)) = 4X + 6 >= 4X + 6 = ok(isNeList(X)) isQid(ok(X)) = 4X + 6 >= 4X + 6 = ok(isQid(X)) isNePal(ok(X)) = 8X + 13 >= 8X + 12 = ok(isNePal(X)) problem: proper(a()) -> ok(a()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isQid(ok(X)) -> ok(isQid(X)) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [ok](x0) = [0 1 0]x0 [0 1 0] , [1 0 0] [1] [proper](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [0] [u] = [0] [0], [0] [o] = [0] [0], [0] [i] = [0] [0], [0] [a] = [0] [0], [1 0 0] [0] [isQid](x0) = [1 0 0]x0 + [1] [1 0 0] [1], [1 0 0] [1] [isNeList](x0) = [0 0 0]x0 + [0] [0 0 1] [0], [1 0 0] [isList](x0) = [1 0 0]x0 [1 0 0] orientation: [1] [0] proper(a()) = [0] >= [0] = ok(a()) [0] [0] [1] [0] proper(i()) = [0] >= [0] = ok(i()) [0] [0] [1] [0] proper(o()) = [0] >= [0] = ok(o()) [0] [0] [1] [0] proper(u()) = [0] >= [0] = ok(u()) [0] [0] [1 0 0] [1 0 0] isList(ok(X)) = [1 0 0]X >= [1 0 0]X = ok(isList(X)) [1 0 0] [1 0 0] [1 0 0] [1] [1 0 0] [1] isNeList(ok(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = ok(isNeList(X)) [0 1 0] [0] [0 0 0] [0] [1 0 0] [0] [1 0 0] [0] isQid(ok(X)) = [1 0 0]X + [1] >= [1 0 0]X + [1] = ok(isQid(X)) [1 0 0] [1] [1 0 0] [1] problem: isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isQid(ok(X)) -> ok(isQid(X)) Matrix Interpretation Processor: dim=3 interpretation: [0] [ok](x0) = x0 + [1] [0], [1 0 1] [isQid](x0) = [0 1 0]x0 [0 0 0] , [1 1 0] [isNeList](x0) = [0 1 1]x0 [0 1 0] , [1 1 1] [isList](x0) = [0 1 1]x0 [0 0 0] orientation: [1 1 1] [1] [1 1 1] [0] isList(ok(X)) = [0 1 1]X + [1] >= [0 1 1]X + [1] = ok(isList(X)) [0 0 0] [0] [0 0 0] [0] [1 1 0] [1] [1 1 0] [0] isNeList(ok(X)) = [0 1 1]X + [1] >= [0 1 1]X + [1] = ok(isNeList(X)) [0 1 0] [1] [0 1 0] [0] [1 0 1] [0] [1 0 1] [0] isQid(ok(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = ok(isQid(X)) [0 0 0] [0] [0 0 0] [0] problem: isQid(ok(X)) -> ok(isQid(X)) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [0] [ok](x0) = [0 0 0]x0 + [0] [0 0 1] [1], [1 0 1] [isQid](x0) = [0 0 0]x0 [0 0 1] orientation: [1 0 1] [1] [1 0 1] [0] isQid(ok(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = ok(isQid(X)) [0 0 1] [1] [0 0 1] [1] problem: Qed