YES Problem: __(__(X,Y),Z) -> __(X,__(Y,Z)) __(X,nil()) -> X __(nil(),X) -> X U11(tt()) -> tt() U21(tt(),V2) -> U22(isList(activate(V2))) U22(tt()) -> tt() U31(tt()) -> tt() U41(tt(),V2) -> U42(isNeList(activate(V2))) U42(tt()) -> tt() U51(tt(),V2) -> U52(isList(activate(V2))) U52(tt()) -> tt() U61(tt()) -> tt() U71(tt(),P) -> U72(isPal(activate(P))) U72(tt()) -> tt() U81(tt()) -> tt() isList(V) -> U11(isNeList(activate(V))) isList(n__nil()) -> tt() isList(n____(V1,V2)) -> U21(isList(activate(V1)),activate(V2)) isNeList(V) -> U31(isQid(activate(V))) isNeList(n____(V1,V2)) -> U41(isList(activate(V1)),activate(V2)) isNeList(n____(V1,V2)) -> U51(isNeList(activate(V1)),activate(V2)) isNePal(V) -> U61(isQid(activate(V))) isNePal(n____(I,n____(P,I))) -> U71(isQid(activate(I)),activate(P)) isPal(V) -> U81(isNePal(activate(V))) isPal(n__nil()) -> tt() isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__i()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() __(X1,X2) -> n____(X1,X2) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(activate(X1),activate(X2)) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X Proof: Matrix Interpretation Processor: dim=1 interpretation: [u] = 2, [o] = 2, [i] = 4, [e] = 2, [a] = 2, [n__u] = 2, [n__o] = 2, [n__i] = 4, [n__e] = 2, [n__a] = 2, [isNePal](x0) = 2x0 + 1, [isQid](x0) = 2x0 + 1, [n____](x0, x1) = x0 + x1 + 2, [n__nil] = 2, [U81](x0) = x0 + 1, [U72](x0) = x0, [isPal](x0) = 2x0 + 2, [U71](x0, x1) = 2x0 + 2x1, [U61](x0) = x0, [U52](x0) = x0, [U51](x0, x1) = x0 + 4x1, [U42](x0) = x0 + 3, [isNeList](x0) = 4x0 + 2, [U41](x0, x1) = x0 + 4x1 + 5, [U31](x0) = 2x0, [U22](x0) = x0 + 6, [isList](x0) = 4x0 + 5, [activate](x0) = x0, [U21](x0, x1) = x0 + 4x1 + 7, [U11](x0) = x0 + 3, [tt] = 5, [nil] = 2, [__](x0, x1) = x0 + x1 + 2 orientation: __(__(X,Y),Z) = X + Y + Z + 4 >= X + Y + Z + 4 = __(X,__(Y,Z)) __(X,nil()) = X + 4 >= X = X __(nil(),X) = X + 4 >= X = X U11(tt()) = 8 >= 5 = tt() U21(tt(),V2) = 4V2 + 12 >= 4V2 + 11 = U22(isList(activate(V2))) U22(tt()) = 11 >= 5 = tt() U31(tt()) = 10 >= 5 = tt() U41(tt(),V2) = 4V2 + 10 >= 4V2 + 5 = U42(isNeList(activate(V2))) U42(tt()) = 8 >= 5 = tt() U51(tt(),V2) = 4V2 + 5 >= 4V2 + 5 = U52(isList(activate(V2))) U52(tt()) = 5 >= 5 = tt() U61(tt()) = 5 >= 5 = tt() U71(tt(),P) = 2P + 10 >= 2P + 2 = U72(isPal(activate(P))) U72(tt()) = 5 >= 5 = tt() U81(tt()) = 6 >= 5 = tt() isList(V) = 4V + 5 >= 4V + 5 = U11(isNeList(activate(V))) isList(n__nil()) = 13 >= 5 = tt() isList(n____(V1,V2)) = 4V1 + 4V2 + 13 >= 4V1 + 4V2 + 12 = U21(isList(activate(V1)),activate(V2)) isNeList(V) = 4V + 2 >= 4V + 2 = U31(isQid(activate(V))) isNeList(n____(V1,V2)) = 4V1 + 4V2 + 10 >= 4V1 + 4V2 + 10 = U41(isList(activate(V1)),activate(V2)) isNeList(n____(V1,V2)) = 4V1 + 4V2 + 10 >= 4V1 + 4V2 + 2 = U51(isNeList(activate(V1)),activate(V2)) isNePal(V) = 2V + 1 >= 2V + 1 = U61(isQid(activate(V))) isNePal(n____(I,n____(P,I))) = 4I + 2P + 9 >= 4I + 2P + 2 = U71(isQid(activate(I)),activate(P)) isPal(V) = 2V + 2 >= 2V + 2 = U81(isNePal(activate(V))) isPal(n__nil()) = 6 >= 5 = tt() isQid(n__a()) = 5 >= 5 = tt() isQid(n__e()) = 5 >= 5 = tt() isQid(n__i()) = 9 >= 5 = tt() isQid(n__o()) = 5 >= 5 = tt() isQid(n__u()) = 5 >= 5 = tt() nil() = 2 >= 2 = n__nil() __(X1,X2) = X1 + X2 + 2 >= X1 + X2 + 2 = n____(X1,X2) a() = 2 >= 2 = n__a() e() = 2 >= 2 = n__e() i() = 4 >= 4 = n__i() o() = 2 >= 2 = n__o() u() = 2 >= 2 = n__u() activate(n__nil()) = 2 >= 2 = nil() activate(n____(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = __(activate(X1),activate(X2)) activate(n__a()) = 2 >= 2 = a() activate(n__e()) = 2 >= 2 = e() activate(n__i()) = 4 >= 4 = i() activate(n__o()) = 2 >= 2 = o() activate(n__u()) = 2 >= 2 = u() activate(X) = X >= X = X problem: __(__(X,Y),Z) -> __(X,__(Y,Z)) U51(tt(),V2) -> U52(isList(activate(V2))) U52(tt()) -> tt() U61(tt()) -> tt() U72(tt()) -> tt() isList(V) -> U11(isNeList(activate(V))) isNeList(V) -> U31(isQid(activate(V))) isNeList(n____(V1,V2)) -> U41(isList(activate(V1)),activate(V2)) isNePal(V) -> U61(isQid(activate(V))) isPal(V) -> U81(isNePal(activate(V))) isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() __(X1,X2) -> n____(X1,X2) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(activate(X1),activate(X2)) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X Matrix Interpretation Processor: dim=3 interpretation: [0] [u] = [0] [1], [0] [o] = [1] [1], [0] [i] = [0] [1], [0] [e] = [0] [1], [0] [a] = [0] [1], [0] [n__u] = [0] [0], [0] [n__o] = [1] [0], [0] [n__i] = [0] [0], [0] [n__e] = [0] [0], [0] [n__a] = [0] [0], [1 0 0] [0] [isNePal](x0) = [0 0 0]x0 + [1] [0 0 0] [1], [1 0 0] [0] [isQid](x0) = [0 0 0]x0 + [1] [0 0 0] [0], [1 1 0] [1 1 0] [0] [n____](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1] [0 0 1] [0 0 0] [0], [0] [n__nil] = [0] [0], [1 0 1] [U81](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [U72](x0) = [0 1 0]x0 [0 1 0] , [1 0 0] [1] [isPal](x0) = [0 0 1]x0 + [0] [0 0 1] [0], [1 0 0] [0] [U61](x0) = [0 0 0]x0 + [1] [0 0 0] [0], [1 1 0] [U52](x0) = [0 1 0]x0 [0 1 0] , [1 0 0] [1 0 0] [1] [U51](x0, x1) = [0 1 0]x0 + [1 1 1]x1 + [0] [0 0 0] [1 1 0] [0], [1 0 0] [1] [isNeList](x0) = [0 0 0]x0 + [0] [0 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] [1] [U31](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [1 0 0] [1] [isList](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [0] [activate](x0) = x0 + [0] [1], [1 0 0] [U11](x0) = [0 0 0]x0 [0 0 0] , [0] [tt] = [1] [0], [0] [nil] = [0] [1], [1 1 0] [1 1 0] [0] [__](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1] [0 0 1] [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] __(__(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] = __(X,__(Y,Z)) [0 0 1] [0 0 0] [0 0 0] [0] [0 0 1] [0 0 0] [0 0 0] [0] [1 0 0] [1] [1 0 0] [1] U51(tt(),V2) = [1 1 1]V2 + [1] >= [0 0 0]V2 + [0] = U52(isList(activate(V2))) [1 1 0] [0] [0 0 0] [0] [1] [0] U52(tt()) = [1] >= [1] = tt() [1] [0] [0] [0] U61(tt()) = [1] >= [1] = tt() [0] [0] [0] [0] U72(tt()) = [1] >= [1] = tt() [1] [0] [1 0 0] [1] [1 0 0] [1] isList(V) = [0 0 0]V + [0] >= [0 0 0]V + [0] = U11(isNeList(activate(V))) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1] [1 0 0] [1] isNeList(V) = [0 0 0]V + [0] >= [0 0 0]V + [0] = U31(isQid(activate(V))) [0 0 0] [0] [0 0 0] [0] [1 1 0] [1 1 0] [1] [1 0 0] [1 0 0] [1] isNeList(n____(V1,V2)) = [0 0 0]V1 + [0 0 0]V2 + [0] >= [0 0 0]V1 + [0 0 0]V2 + [0] = U41(isList(activate(V1)),activate(V2)) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 0] [0] [1 0 0] [0] isNePal(V) = [0 0 0]V + [1] >= [0 0 0]V + [1] = U61(isQid(activate(V))) [0 0 0] [1] [0 0 0] [0] [1 0 0] [1] [1 0 0] [1] isPal(V) = [0 0 1]V + [0] >= [0 0 0]V + [0] = U81(isNePal(activate(V))) [0 0 1] [0] [0 0 0] [0] [0] [0] isQid(n__a()) = [1] >= [1] = tt() [0] [0] [0] [0] isQid(n__e()) = [1] >= [1] = tt() [0] [0] [0] [0] isQid(n__o()) = [1] >= [1] = tt() [0] [0] [0] [0] isQid(n__u()) = [1] >= [1] = tt() [0] [0] [0] [0] nil() = [0] >= [0] = n__nil() [1] [0] [1 1 0] [1 1 0] [0] [1 1 0] [1 1 0] [0] __(X1,X2) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = n____(X1,X2) [0 0 1] [0 0 0] [0] [0 0 1] [0 0 0] [0] [0] [0] a() = [0] >= [0] = n__a() [1] [0] [0] [0] e() = [0] >= [0] = n__e() [1] [0] [0] [0] i() = [0] >= [0] = n__i() [1] [0] [0] [0] o() = [1] >= [1] = n__o() [1] [0] [0] [0] u() = [0] >= [0] = n__u() [1] [0] [0] [0] activate(n__nil()) = [0] >= [0] = nil() [1] [1] [1 1 0] [1 1 0] [0] [1 1 0] [1 1 0] [0] activate(n____(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = __(activate(X1),activate(X2)) [0 0 1] [0 0 0] [1] [0 0 1] [0 0 0] [1] [0] [0] activate(n__a()) = [0] >= [0] = a() [1] [1] [0] [0] activate(n__e()) = [0] >= [0] = e() [1] [1] [0] [0] activate(n__i()) = [0] >= [0] = i() [1] [1] [0] [0] activate(n__o()) = [1] >= [1] = o() [1] [1] [0] [0] activate(n__u()) = [0] >= [0] = u() [1] [1] [0] activate(X) = X + [0] >= X = X [1] problem: __(__(X,Y),Z) -> __(X,__(Y,Z)) U51(tt(),V2) -> U52(isList(activate(V2))) U61(tt()) -> tt() U72(tt()) -> tt() isList(V) -> U11(isNeList(activate(V))) isNeList(V) -> U31(isQid(activate(V))) isNeList(n____(V1,V2)) -> U41(isList(activate(V1)),activate(V2)) isNePal(V) -> U61(isQid(activate(V))) isPal(V) -> U81(isNePal(activate(V))) isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__o()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() __(X1,X2) -> n____(X1,X2) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(activate(X1),activate(X2)) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X Matrix Interpretation Processor: dim=3 interpretation: [1] [u] = [1] [0], [0] [o] = [0] [0], [0] [i] = [0] [0], [0] [e] = [0] [0], [0] [a] = [0] [0], [1] [n__u] = [0] [0], [0] [n__o] = [0] [0], [0] [n__i] = [0] [0], [0] [n__e] = [0] [0], [0] [n__a] = [0] [0], [1 0 0] [1] [isNePal](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [1 0 0] [isQid](x0) = [0 0 1]x0 [0 1 0] , [1 0 1] [1 0 1] [0] [n____](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0] [0 0 0] [0 0 0] [1], [0] [n__nil] = [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 1 1] [1] [isPal](x0) = [0 0 0]x0 + [1] [1 0 1] [1], [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 0] , [1 0 0] [1 0 1] [1] [U51](x0, x1) = [0 0 0]x0 + [0 1 0]x1 + [0] [0 0 0] [0 0 0] [1], [1 0 1] [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 1 0] [U31](x0) = [0 0 0]x0 [0 0 0] , [1 0 1] [1] [isList](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [1 0 0] [activate](x0) = [1 1 0]x0 [0 0 1] , [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 1] [1 0 1] [0] [__](x0, x1) = [1 0 1]x0 + [1 0 1]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] __(__(X,Y),Z) = [1 0 1]X + [1 0 1]Y + [1 0 1]Z + [1] >= [1 0 1]X + [1 0 1]Y + [1 0 1]Z + [1] = __(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] [1 0 1] [1] U51(tt(),V2) = [0 1 0]V2 + [0] >= [0 0 0]V2 + [0] = U52(isList(activate(V2))) [0 0 0] [1] [0 0 0] [0] [1] [0] U61(tt()) = [0] >= [0] = tt() [0] [0] [0] [0] U72(tt()) = [0] >= [0] = tt() [0] [0] [1 0 1] [1] [1 0 1] [1] isList(V) = [0 0 0]V + [0] >= [0 0 0]V + [0] = U11(isNeList(activate(V))) [0 0 0] [1] [0 0 0] [0] [1 0 1] [1 0 1] isNeList(V) = [0 0 0]V >= [0 0 0]V = U31(isQid(activate(V))) [0 0 0] [0 0 0] [1 0 1] [1 0 1] [1] [1 0 1] [1 0 0] [1] isNeList(n____(V1,V2)) = [0 0 0]V1 + [0 0 0]V2 + [0] >= [0 0 0]V1 + [0 0 0]V2 + [0] = U41(isList(activate(V1)),activate(V2)) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 0] [1] [1 0 0] [1] isNePal(V) = [0 0 0]V + [0] >= [0 0 0]V + [0] = U61(isQid(activate(V))) [0 0 0] [0] [0 0 0] [0] [1 1 1] [1] [1 0 0] [1] isPal(V) = [0 0 0]V + [1] >= [0 0 0]V + [0] = U81(isNePal(activate(V))) [1 0 1] [1] [0 0 0] [0] [0] [0] isQid(n__a()) = [0] >= [0] = tt() [0] [0] [0] [0] isQid(n__e()) = [0] >= [0] = tt() [0] [0] [0] [0] isQid(n__o()) = [0] >= [0] = tt() [0] [0] [1] [0] isQid(n__u()) = [0] >= [0] = tt() [0] [0] [0] [0] nil() = [0] >= [0] = n__nil() [0] [0] [1 0 1] [1 0 1] [0] [1 0 1] [1 0 1] [0] __(X1,X2) = [1 0 1]X1 + [1 0 1]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = n____(X1,X2) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [0] [0] a() = [0] >= [0] = n__a() [0] [0] [0] [0] e() = [0] >= [0] = n__e() [0] [0] [0] [0] i() = [0] >= [0] = n__i() [0] [0] [0] [0] o() = [0] >= [0] = n__o() [0] [0] [1] [1] u() = [1] >= [0] = n__u() [0] [0] [0] [0] activate(n__nil()) = [0] >= [0] = nil() [0] [0] [1 0 1] [1 0 1] [0] [1 0 1] [1 0 1] [0] activate(n____(X1,X2)) = [1 0 1]X1 + [1 0 1]X2 + [0] >= [1 0 1]X1 + [1 0 1]X2 + [0] = __(activate(X1),activate(X2)) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [0] [0] activate(n__a()) = [0] >= [0] = a() [0] [0] [0] [0] activate(n__e()) = [0] >= [0] = e() [0] [0] [0] [0] activate(n__i()) = [0] >= [0] = i() [0] [0] [0] [0] activate(n__o()) = [0] >= [0] = o() [0] [0] [1] [1] activate(n__u()) = [1] >= [1] = u() [0] [0] [1 0 0] activate(X) = [1 1 0]X >= X = X [0 0 1] problem: __(__(X,Y),Z) -> __(X,__(Y,Z)) U51(tt(),V2) -> U52(isList(activate(V2))) U72(tt()) -> tt() isList(V) -> U11(isNeList(activate(V))) isNeList(V) -> U31(isQid(activate(V))) isNeList(n____(V1,V2)) -> U41(isList(activate(V1)),activate(V2)) isNePal(V) -> U61(isQid(activate(V))) isPal(V) -> U81(isNePal(activate(V))) isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__o()) -> tt() nil() -> n__nil() __(X1,X2) -> n____(X1,X2) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(activate(X1),activate(X2)) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X Matrix Interpretation Processor: dim=3 interpretation: [0] [u] = [1] [0], [0] [o] = [1] [0], [0] [i] = [1] [0], [0] [e] = [1] [0], [0] [a] = [1] [0], [0] [n__u] = [0] [0], [0] [n__o] = [0] [0], [0] [n__i] = [0] [0], [0] [n__e] = [0] [0], [0] [n__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] [1 0 1] [n____](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 1] [0 0 0] , [1] [n__nil] = [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 1] [isPal](x0) = [0 0 0]x0 [1 0 0] , [1 0 0] [U61](x0) = [0 0 0]x0 [0 0 0] , [1 0 1] [U52](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 1] [1] [U51](x0, x1) = [0 0 0]x0 + [1 0 0]x1 + [0] [0 0 0] [0 0 1] [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 0] , [1 0 0] [0] [isList](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [0] [activate](x0) = x0 + [1] [0], [1 0 0] [0] [U11](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [0] [tt] = [0] [0], [1] [nil] = [1] [0], [1 0 0] [1 0 1] [__](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 1] [0 0 0] orientation: [1 0 0] [1 0 1] [1 0 1] [1 0 0] [1 0 1] [1 0 1] __(__(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 = __(X,__(Y,Z)) [0 0 1] [0 0 0] [0 0 0] [0 0 1] [0 0 0] [0 0 0] [1 0 1] [1] [1 0 0] [1] U51(tt(),V2) = [1 0 0]V2 + [0] >= [0 0 0]V2 + [0] = U52(isList(activate(V2))) [0 0 1] [0] [0 0 0] [0] [1] [0] U72(tt()) = [0] >= [0] = tt() [0] [0] [1 0 0] [0] [1 0 0] [0] isList(V) = [0 0 0]V + [0] >= [0 0 0]V + [0] = U11(isNeList(activate(V))) [0 0 0] [1] [0 0 0] [1] [1 0 0] [1 0 0] isNeList(V) = [0 0 0]V >= [0 0 0]V = U31(isQid(activate(V))) [0 0 0] [0 0 0] [1 0 0] [1 0 1] [1 0 0] [1 0 0] isNeList(n____(V1,V2)) = [0 0 0]V1 + [0 0 0]V2 >= [0 0 0]V1 + [0 0 0]V2 = U41(isList(activate(V1)),activate(V2)) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] isNePal(V) = [0 0 0]V >= [0 0 0]V = U61(isQid(activate(V))) [0 0 0] [0 0 0] [1 0 1] [1 0 0] isPal(V) = [0 0 0]V >= [0 0 0]V = U81(isNePal(activate(V))) [1 0 0] [0 0 0] [0] [0] isQid(n__a()) = [0] >= [0] = tt() [0] [0] [0] [0] isQid(n__e()) = [0] >= [0] = tt() [0] [0] [0] [0] isQid(n__o()) = [0] >= [0] = tt() [0] [0] [1] [1] nil() = [1] >= [0] = n__nil() [0] [0] [1 0 0] [1 0 1] [1 0 0] [1 0 1] __(X1,X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = n____(X1,X2) [0 0 1] [0 0 0] [0 0 1] [0 0 0] [0] [0] a() = [1] >= [0] = n__a() [0] [0] [0] [0] e() = [1] >= [0] = n__e() [0] [0] [0] [0] i() = [1] >= [0] = n__i() [0] [0] [0] [0] o() = [1] >= [0] = n__o() [0] [0] [0] [0] u() = [1] >= [0] = n__u() [0] [0] [1] [1] activate(n__nil()) = [1] >= [1] = nil() [0] [0] [1 0 0] [1 0 1] [0] [1 0 0] [1 0 1] activate(n____(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 = __(activate(X1),activate(X2)) [0 0 1] [0 0 0] [0] [0 0 1] [0 0 0] [0] [0] activate(n__a()) = [1] >= [1] = a() [0] [0] [0] [0] activate(n__e()) = [1] >= [1] = e() [0] [0] [0] [0] activate(n__i()) = [1] >= [1] = i() [0] [0] [0] [0] activate(n__o()) = [1] >= [1] = o() [0] [0] [0] [0] activate(n__u()) = [1] >= [1] = u() [0] [0] [0] activate(X) = X + [1] >= X = X [0] problem: __(__(X,Y),Z) -> __(X,__(Y,Z)) U51(tt(),V2) -> U52(isList(activate(V2))) isList(V) -> U11(isNeList(activate(V))) isNeList(V) -> U31(isQid(activate(V))) isNeList(n____(V1,V2)) -> U41(isList(activate(V1)),activate(V2)) isNePal(V) -> U61(isQid(activate(V))) isPal(V) -> U81(isNePal(activate(V))) isQid(n__a()) -> tt() isQid(n__e()) -> tt() isQid(n__o()) -> tt() nil() -> n__nil() __(X1,X2) -> n____(X1,X2) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(activate(X1),activate(X2)) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X Matrix Interpretation Processor: dim=3 interpretation: [0] [u] = [0] [0], [0] [o] = [0] [0], [0] [i] = [0] [0], [1] [e] = [0] [0], [0] [a] = [0] [0], [0] [n__u] = [0] [0], [0] [n__o] = [0] [0], [0] [n__i] = [0] [0], [1] [n__e] = [0] [0], [0] [n__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] [1 0 1] [n____](x0, x1) = [0 0 0]x0 + [0 1 0]x1 [0 0 0] [0 0 0] , [1] [n__nil] = [0] [0], [1 0 0] [U81](x0) = [1 0 0]x0 [0 0 0] , [1 0 0] [isPal](x0) = [1 0 1]x0 [0 1 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 1 1] [1] [U51](x0, x1) = [0 0 0]x0 + [0 1 0]x1 + [0] [0 0 0] [1 0 0] [0], [1 0 0] [1] [isNeList](x0) = [0 0 0]x0 + [0] [1 0 1] [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 0] , [1 0 0] [1] [isList](x0) = [0 1 0]x0 + [0] [0 0 0] [0], [activate](x0) = x0 , [1 0 0] [U11](x0) = [0 0 0]x0 [0 0 0] , [0] [tt] = [0] [0], [1] [nil] = [0] [0], [1 0 0] [1 0 1] [__](x0, x1) = [0 0 0]x0 + [0 1 0]x1 [0 0 0] [0 0 0] orientation: [1 0 0] [1 0 1] [1 0 1] [1 0 0] [1 0 0] [1 0 1] __(__(X,Y),Z) = [0 0 0]X + [0 0 0]Y + [0 1 0]Z >= [0 0 0]X + [0 0 0]Y + [0 1 0]Z = __(X,__(Y,Z)) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 1] [1] [1 0 0] [1] U51(tt(),V2) = [0 1 0]V2 + [0] >= [0 0 0]V2 + [0] = U52(isList(activate(V2))) [1 0 0] [0] [0 0 0] [0] [1 0 0] [1] [1 0 0] [1] isList(V) = [0 1 0]V + [0] >= [0 0 0]V + [0] = U11(isNeList(activate(V))) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1] [1 0 0] isNeList(V) = [0 0 0]V + [0] >= [0 0 0]V = U31(isQid(activate(V))) [1 0 1] [0] [0 0 0] [1 0 0] [1 0 1] [1] [1 0 0] [1 0 0] [1] isNeList(n____(V1,V2)) = [0 0 0]V1 + [0 0 0]V2 + [0] >= [0 0 0]V1 + [0 0 0]V2 + [0] = U41(isList(activate(V1)),activate(V2)) [1 0 0] [1 0 1] [0] [0 0 0] [0 0 0] [0] [1 0 0] [1 0 0] isNePal(V) = [0 0 0]V >= [0 0 0]V = U61(isQid(activate(V))) [0 0 0] [0 0 0] [1 0 0] [1 0 0] isPal(V) = [1 0 1]V >= [1 0 0]V = U81(isNePal(activate(V))) [0 1 0] [0 0 0] [0] [0] isQid(n__a()) = [0] >= [0] = tt() [0] [0] [1] [0] isQid(n__e()) = [0] >= [0] = tt() [0] [0] [0] [0] isQid(n__o()) = [0] >= [0] = tt() [0] [0] [1] [1] nil() = [0] >= [0] = n__nil() [0] [0] [1 0 0] [1 0 1] [1 0 0] [1 0 1] __(X1,X2) = [0 0 0]X1 + [0 1 0]X2 >= [0 0 0]X1 + [0 1 0]X2 = n____(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0] [0] a() = [0] >= [0] = n__a() [0] [0] [1] [1] e() = [0] >= [0] = n__e() [0] [0] [0] [0] i() = [0] >= [0] = n__i() [0] [0] [0] [0] o() = [0] >= [0] = n__o() [0] [0] [0] [0] u() = [0] >= [0] = n__u() [0] [0] [1] [1] activate(n__nil()) = [0] >= [0] = nil() [0] [0] [1 0 0] [1 0 1] [1 0 0] [1 0 1] activate(n____(X1,X2)) = [0 0 0]X1 + [0 1 0]X2 >= [0 0 0]X1 + [0 1 0]X2 = __(activate(X1),activate(X2)) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0] [0] activate(n__a()) = [0] >= [0] = a() [0] [0] [1] [1] activate(n__e()) = [0] >= [0] = e() [0] [0] [0] [0] activate(n__i()) = [0] >= [0] = i() [0] [0] [0] [0] activate(n__o()) = [0] >= [0] = o() [0] [0] [0] [0] activate(n__u()) = [0] >= [0] = u() [0] [0] activate(X) = X >= X = X problem: __(__(X,Y),Z) -> __(X,__(Y,Z)) U51(tt(),V2) -> U52(isList(activate(V2))) isList(V) -> U11(isNeList(activate(V))) isNeList(n____(V1,V2)) -> U41(isList(activate(V1)),activate(V2)) isNePal(V) -> U61(isQid(activate(V))) isPal(V) -> U81(isNePal(activate(V))) isQid(n__a()) -> tt() isQid(n__o()) -> tt() nil() -> n__nil() __(X1,X2) -> n____(X1,X2) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(activate(X1),activate(X2)) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X Matrix Interpretation Processor: dim=3 interpretation: [0] [u] = [1] [1], [0] [o] = [1] [1], [0] [i] = [0] [0], [0] [e] = [0] [0], [1] [a] = [0] [0], [0] [n__u] = [0] [0], [0] [n__o] = [0] [0], [0] [n__i] = [0] [0], [0] [n__e] = [0] [0], [1] [n__a] = [0] [0], [1 1 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] [1 0 0] [n____](x0, x1) = [1 0 0]x0 + [1 0 1]x1 [0 0 0] [0 0 1] , [0] [n__nil] = [0] [0], [1 0 0] [0] [U81](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [1 1 0] [1] [isPal](x0) = [1 0 0]x0 + [0] [0 0 1] [1], [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] [1] [U51](x0, x1) = [0 0 0]x0 + [1 0 1]x1 + [0] [0 0 0] [1 0 1] [0], [1 0 0] [0] [isNeList](x0) = [0 0 0]x0 + [1] [0 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] [0] [isList](x0) = [0 0 0]x0 + [1] [0 0 0] [0], [0] [activate](x0) = x0 + [1] [1], [1 0 0] [U11](x0) = [0 1 0]x0 [0 0 0] , [0] [tt] = [0] [0], [0] [nil] = [0] [0], [1 0 0] [1 0 0] [__](x0, x1) = [1 0 0]x0 + [1 0 1]x1 [0 0 0] [0 0 1] orientation: [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] __(__(X,Y),Z) = [1 0 0]X + [1 0 0]Y + [1 0 1]Z >= [1 0 0]X + [1 0 0]Y + [1 0 1]Z = __(X,__(Y,Z)) [0 0 0] [0 0 0] [0 0 1] [0 0 0] [0 0 0] [0 0 1] [1 0 0] [1] [1 0 0] U51(tt(),V2) = [1 0 1]V2 + [0] >= [0 0 0]V2 = U52(isList(activate(V2))) [1 0 1] [0] [0 0 0] [1 0 0] [0] [1 0 0] [0] isList(V) = [0 0 0]V + [1] >= [0 0 0]V + [1] = U11(isNeList(activate(V))) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] isNeList(n____(V1,V2)) = [0 0 0]V1 + [0 0 0]V2 + [1] >= [0 0 0]V1 + [0 0 0]V2 = U41(isList(activate(V1)),activate(V2)) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [1 1 0] [1 0 0] isNePal(V) = [0 0 0]V >= [0 0 0]V = U61(isQid(activate(V))) [0 0 0] [0 0 0] [1 1 0] [1] [1 1 0] [1] isPal(V) = [1 0 0]V + [0] >= [0 0 0]V + [0] = U81(isNePal(activate(V))) [0 0 1] [1] [0 0 0] [1] [1] [0] isQid(n__a()) = [0] >= [0] = tt() [0] [0] [0] [0] isQid(n__o()) = [0] >= [0] = tt() [0] [0] [0] [0] nil() = [0] >= [0] = n__nil() [0] [0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] __(X1,X2) = [1 0 0]X1 + [1 0 1]X2 >= [1 0 0]X1 + [1 0 1]X2 = n____(X1,X2) [0 0 0] [0 0 1] [0 0 0] [0 0 1] [1] [1] a() = [0] >= [0] = n__a() [0] [0] [0] [0] e() = [0] >= [0] = n__e() [0] [0] [0] [0] i() = [0] >= [0] = n__i() [0] [0] [0] [0] o() = [1] >= [0] = n__o() [1] [0] [0] [0] u() = [1] >= [0] = n__u() [1] [0] [0] [0] activate(n__nil()) = [1] >= [0] = nil() [1] [0] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] activate(n____(X1,X2)) = [1 0 0]X1 + [1 0 1]X2 + [1] >= [1 0 0]X1 + [1 0 1]X2 + [1] = __(activate(X1),activate(X2)) [0 0 0] [0 0 1] [1] [0 0 0] [0 0 1] [1] [1] [1] activate(n__a()) = [1] >= [0] = a() [1] [0] [0] [0] activate(n__e()) = [1] >= [0] = e() [1] [0] [0] [0] activate(n__i()) = [1] >= [0] = i() [1] [0] [0] [0] activate(n__o()) = [1] >= [1] = o() [1] [1] [0] [0] activate(n__u()) = [1] >= [1] = u() [1] [1] [0] activate(X) = X + [1] >= X = X [1] problem: __(__(X,Y),Z) -> __(X,__(Y,Z)) isList(V) -> U11(isNeList(activate(V))) isNeList(n____(V1,V2)) -> U41(isList(activate(V1)),activate(V2)) isNePal(V) -> U61(isQid(activate(V))) isPal(V) -> U81(isNePal(activate(V))) isQid(n__o()) -> tt() nil() -> n__nil() __(X1,X2) -> n____(X1,X2) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(activate(X1),activate(X2)) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X Matrix Interpretation Processor: dim=3 interpretation: [1] [u] = [0] [0], [0] [o] = [0] [0], [0] [i] = [0] [0], [0] [e] = [0] [0], [0] [a] = [0] [0], [1] [n__u] = [0] [0], [0] [n__o] = [0] [0], [0] [n__i] = [0] [0], [0] [n__e] = [0] [0], [0] [n__a] = [0] [0], [1 0 0] [1] [isNePal](x0) = [0 0 0]x0 + [0] [1 1 0] [0], [1 0 0] [isQid](x0) = [0 0 0]x0 [0 1 0] , [1 0 0] [1 0 0] [n____](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 1 1] [0 0 0] , [0] [n__nil] = [0] [1], [1 0 0] [U81](x0) = [0 0 0]x0 [0 0 0] , [1 1 1] [1] [isPal](x0) = [0 1 0]x0 + [1] [1 1 0] [0], [1 0 0] [U61](x0) = [0 0 0]x0 [1 0 1] , [1 0 1] [isNeList](x0) = [0 0 0]x0 [0 1 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 1 1] [0] [isList](x0) = [0 0 0]x0 + [0] [1 0 0] [1], [activate](x0) = x0 , [1 0 1] [U11](x0) = [0 0 0]x0 [0 0 0] , [0] [tt] = [0] [0], [0] [nil] = [0] [1], [1 0 0] [1 0 0] [__](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 1 1] [0 0 0] orientation: [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] __(__(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 = __(X,__(Y,Z)) [0 1 1] [0 0 0] [0 0 0] [0 1 1] [0 0 0] [0 0 0] [1 1 1] [0] [1 1 1] isList(V) = [0 0 0]V + [0] >= [0 0 0]V = U11(isNeList(activate(V))) [1 0 0] [1] [0 0 0] [1 1 1] [1 0 0] [1 1 1] [1 0 0] isNeList(n____(V1,V2)) = [0 0 0]V1 + [0 0 0]V2 >= [0 0 0]V1 + [0 0 0]V2 = U41(isList(activate(V1)),activate(V2)) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1] [1 0 0] isNePal(V) = [0 0 0]V + [0] >= [0 0 0]V = U61(isQid(activate(V))) [1 1 0] [0] [1 1 0] [1 1 1] [1] [1 0 0] [1] isPal(V) = [0 1 0]V + [1] >= [0 0 0]V + [0] = U81(isNePal(activate(V))) [1 1 0] [0] [0 0 0] [0] [0] [0] isQid(n__o()) = [0] >= [0] = tt() [0] [0] [0] [0] nil() = [0] >= [0] = n__nil() [1] [1] [1 0 0] [1 0 0] [1 0 0] [1 0 0] __(X1,X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = n____(X1,X2) [0 1 1] [0 0 0] [0 1 1] [0 0 0] [0] [0] a() = [0] >= [0] = n__a() [0] [0] [0] [0] e() = [0] >= [0] = n__e() [0] [0] [0] [0] i() = [0] >= [0] = n__i() [0] [0] [0] [0] o() = [0] >= [0] = n__o() [0] [0] [1] [1] u() = [0] >= [0] = n__u() [0] [0] [0] [0] activate(n__nil()) = [0] >= [0] = nil() [1] [1] [1 0 0] [1 0 0] [1 0 0] [1 0 0] activate(n____(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = __(activate(X1),activate(X2)) [0 1 1] [0 0 0] [0 1 1] [0 0 0] [0] [0] activate(n__a()) = [0] >= [0] = a() [0] [0] [0] [0] activate(n__e()) = [0] >= [0] = e() [0] [0] [0] [0] activate(n__i()) = [0] >= [0] = i() [0] [0] [0] [0] activate(n__o()) = [0] >= [0] = o() [0] [0] [1] [1] activate(n__u()) = [0] >= [0] = u() [0] [0] activate(X) = X >= X = X problem: __(__(X,Y),Z) -> __(X,__(Y,Z)) isList(V) -> U11(isNeList(activate(V))) isNeList(n____(V1,V2)) -> U41(isList(activate(V1)),activate(V2)) isPal(V) -> U81(isNePal(activate(V))) isQid(n__o()) -> tt() nil() -> n__nil() __(X1,X2) -> n____(X1,X2) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(activate(X1),activate(X2)) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X Matrix Interpretation Processor: dim=3 interpretation: [0] [u] = [0] [0], [0] [o] = [0] [0], [0] [i] = [0] [0], [0] [e] = [0] [0], [0] [a] = [0] [0], [0] [n__u] = [0] [0], [0] [n__o] = [0] [0], [0] [n__i] = [0] [0], [0] [n__e] = [0] [0], [0] [n__a] = [0] [0], [1 0 0] [isNePal](x0) = [0 0 0]x0 [1 0 0] , [1 0 0] [isQid](x0) = [0 0 0]x0 [0 0 0] , [1 1 0] [1 1 0] [0] [n____](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1] [0 1 1] [0 1 0] [0], [0] [n__nil] = [0] [0], [1 0 0] [1] [U81](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [1 0 0] [1] [isPal](x0) = [0 0 0]x0 + [0] [0 1 0] [1], [1 1 0] [isNeList](x0) = [0 0 0]x0 [0 0 1] , [1 0 0] [1 1 0] [U41](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 1 0] [0 0 0] , [1 1 0] [1] [isList](x0) = [0 0 1]x0 + [0] [0 0 0] [0], [activate](x0) = x0 , [1 0 0] [U11](x0) = [0 0 0]x0 [0 0 0] , [0] [tt] = [0] [0], [0] [nil] = [0] [0], [1 1 0] [1 1 0] [0] [__](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1] [0 1 1] [0 1 0] [0] orientation: [1 1 0] [1 1 0] [1 1 0] [1] [1 1 0] [1 1 0] [1 1 0] [1] __(__(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] = __(X,__(Y,Z)) [0 1 1] [0 1 0] [0 1 0] [1] [0 1 1] [0 0 0] [0 0 0] [1] [1 1 0] [1] [1 1 0] isList(V) = [0 0 1]V + [0] >= [0 0 0]V = U11(isNeList(activate(V))) [0 0 0] [0] [0 0 0] [1 1 0] [1 1 0] [1] [1 1 0] [1 1 0] [1] isNeList(n____(V1,V2)) = [0 0 0]V1 + [0 0 0]V2 + [0] >= [0 0 0]V1 + [0 0 0]V2 + [0] = U41(isList(activate(V1)),activate(V2)) [0 1 1] [0 1 0] [0] [0 0 1] [0 0 0] [0] [1 0 0] [1] [1 0 0] [1] isPal(V) = [0 0 0]V + [0] >= [0 0 0]V + [0] = U81(isNePal(activate(V))) [0 1 0] [1] [0 0 0] [1] [0] [0] isQid(n__o()) = [0] >= [0] = tt() [0] [0] [0] [0] nil() = [0] >= [0] = n__nil() [0] [0] [1 1 0] [1 1 0] [0] [1 1 0] [1 1 0] [0] __(X1,X2) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = n____(X1,X2) [0 1 1] [0 1 0] [0] [0 1 1] [0 1 0] [0] [0] [0] a() = [0] >= [0] = n__a() [0] [0] [0] [0] e() = [0] >= [0] = n__e() [0] [0] [0] [0] i() = [0] >= [0] = n__i() [0] [0] [0] [0] o() = [0] >= [0] = n__o() [0] [0] [0] [0] u() = [0] >= [0] = n__u() [0] [0] [0] [0] activate(n__nil()) = [0] >= [0] = nil() [0] [0] [1 1 0] [1 1 0] [0] [1 1 0] [1 1 0] [0] activate(n____(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = __(activate(X1),activate(X2)) [0 1 1] [0 1 0] [0] [0 1 1] [0 1 0] [0] [0] [0] activate(n__a()) = [0] >= [0] = a() [0] [0] [0] [0] activate(n__e()) = [0] >= [0] = e() [0] [0] [0] [0] activate(n__i()) = [0] >= [0] = i() [0] [0] [0] [0] activate(n__o()) = [0] >= [0] = o() [0] [0] [0] [0] activate(n__u()) = [0] >= [0] = u() [0] [0] activate(X) = X >= X = X problem: __(__(X,Y),Z) -> __(X,__(Y,Z)) isNeList(n____(V1,V2)) -> U41(isList(activate(V1)),activate(V2)) isPal(V) -> U81(isNePal(activate(V))) isQid(n__o()) -> tt() nil() -> n__nil() __(X1,X2) -> n____(X1,X2) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(activate(X1),activate(X2)) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X Matrix Interpretation Processor: dim=1 interpretation: [u] = 4, [o] = 6, [i] = 3, [e] = 3, [a] = 1, [n__u] = 2, [n__o] = 5, [n__i] = 2, [n__e] = 2, [n__a] = 1, [isNePal](x0) = x0 + 1, [isQid](x0) = 4x0 + 4, [n____](x0, x1) = x0 + x1 + 3, [n__nil] = 0, [U81](x0) = x0 + 1, [isPal](x0) = 4x0 + 2, [isNeList](x0) = 6x0 + 5, [U41](x0, x1) = x0 + x1, [isList](x0) = x0, [activate](x0) = 4x0, [tt] = 0, [nil] = 0, [__](x0, x1) = x0 + x1 + 6 orientation: __(__(X,Y),Z) = X + Y + Z + 12 >= X + Y + Z + 12 = __(X,__(Y,Z)) isNeList(n____(V1,V2)) = 6V1 + 6V2 + 23 >= 4V1 + 4V2 = U41(isList(activate(V1)),activate(V2)) isPal(V) = 4V + 2 >= 4V + 2 = U81(isNePal(activate(V))) isQid(n__o()) = 24 >= 0 = tt() nil() = 0 >= 0 = n__nil() __(X1,X2) = X1 + X2 + 6 >= X1 + X2 + 3 = n____(X1,X2) a() = 1 >= 1 = n__a() e() = 3 >= 2 = n__e() i() = 3 >= 2 = n__i() o() = 6 >= 5 = n__o() u() = 4 >= 2 = n__u() activate(n__nil()) = 0 >= 0 = nil() activate(n____(X1,X2)) = 4X1 + 4X2 + 12 >= 4X1 + 4X2 + 6 = __(activate(X1),activate(X2)) activate(n__a()) = 4 >= 1 = a() activate(n__e()) = 8 >= 3 = e() activate(n__i()) = 8 >= 3 = i() activate(n__o()) = 20 >= 6 = o() activate(n__u()) = 8 >= 4 = u() activate(X) = 4X >= X = X problem: __(__(X,Y),Z) -> __(X,__(Y,Z)) isPal(V) -> U81(isNePal(activate(V))) nil() -> n__nil() a() -> n__a() activate(n__nil()) -> nil() activate(X) -> X Matrix Interpretation Processor: dim=3 interpretation: [1] [a] = [1] [0], [0] [n__a] = [0] [0], [1 0 1] [isNePal](x0) = [0 1 0]x0 [0 0 0] , [0] [n__nil] = [1] [0], [1 0 0] [U81](x0) = [0 0 0]x0 [1 0 0] , [1 1 1] [1] [isPal](x0) = [1 0 1]x0 + [0] [1 1 1] [1], [1 1 0] [0] [activate](x0) = [0 1 0]x0 + [0] [0 0 1] [1], [0] [nil] = [1] [0], [1 0 0] [1 0 0] [0] [__](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1] [0 1 1] [0 1 0] [0] orientation: [1 0 0] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [1 0 0] [0] __(__(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] = __(X,__(Y,Z)) [0 1 1] [0 1 0] [0 1 0] [1] [0 1 1] [0 0 0] [0 0 0] [1] [1 1 1] [1] [1 1 1] [1] isPal(V) = [1 0 1]V + [0] >= [0 0 0]V + [0] = U81(isNePal(activate(V))) [1 1 1] [1] [1 1 1] [1] [0] [0] nil() = [1] >= [1] = n__nil() [0] [0] [1] [0] a() = [1] >= [0] = n__a() [0] [0] [1] [0] activate(n__nil()) = [1] >= [1] = nil() [1] [0] [1 1 0] [0] activate(X) = [0 1 0]X + [0] >= X = X [0 0 1] [1] problem: __(__(X,Y),Z) -> __(X,__(Y,Z)) isPal(V) -> U81(isNePal(activate(V))) nil() -> n__nil() activate(X) -> X Matrix Interpretation Processor: dim=3 interpretation: [1 1 0] [isNePal](x0) = [0 0 0]x0 [0 0 0] , [0] [n__nil] = [0] [0], [1 0 0] [U81](x0) = [0 0 0]x0 [1 0 0] , [1 1 0] [1] [isPal](x0) = [0 0 0]x0 + [0] [1 1 0] [0], [activate](x0) = x0 , [0] [nil] = [0] [0], [1 1 0] [1 0 0] [__](x0, x1) = [0 0 0]x0 + [0 1 1]x1 [0 0 0] [0 0 0] orientation: [1 1 0] [1 1 1] [1 0 0] [1 1 0] [1 1 0] [1 0 0] __(__(X,Y),Z) = [0 0 0]X + [0 0 0]Y + [0 1 1]Z >= [0 0 0]X + [0 0 0]Y + [0 1 1]Z = __(X,__(Y,Z)) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [1] [1 1 0] isPal(V) = [0 0 0]V + [0] >= [0 0 0]V = U81(isNePal(activate(V))) [1 1 0] [0] [1 1 0] [0] [0] nil() = [0] >= [0] = n__nil() [0] [0] activate(X) = X >= X = X problem: __(__(X,Y),Z) -> __(X,__(Y,Z)) nil() -> n__nil() activate(X) -> X Matrix Interpretation Processor: dim=3 interpretation: [0] [n__nil] = [0] [0], [activate](x0) = x0 , [1] [nil] = [0] [0], [1 0 1] [1 0 1] [0] [__](x0, x1) = [1 0 1]x0 + [0 0 1]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] __(__(X,Y),Z) = [1 0 1]X + [1 0 1]Y + [0 0 1]Z + [1] >= [1 0 1]X + [0 0 0]Y + [0 0 0]Z + [1] = __(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] nil() = [0] >= [0] = n__nil() [0] [0] activate(X) = X >= X = X problem: __(__(X,Y),Z) -> __(X,__(Y,Z)) activate(X) -> X Matrix Interpretation Processor: dim=3 interpretation: [1] [activate](x0) = x0 + [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] [1 0 0] [1 0 0] [1 0 0] [1 0 0] __(__(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 = __(X,__(Y,Z)) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1] activate(X) = X + [0] >= X = X [0] problem: __(__(X,Y),Z) -> __(X,__(Y,Z)) Matrix Interpretation Processor: dim=1 interpretation: [__](x0, x1) = 2x0 + x1 + 1 orientation: __(__(X,Y),Z) = 4X + 2Y + Z + 3 >= 2X + 2Y + Z + 2 = __(X,__(Y,Z)) problem: Qed