/export/starexec/sandbox2/solver/bin/starexec_run_ttt2 /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Problem: __(__(X,Y),Z) -> __(X,__(Y,Z)) __(X,nil()) -> X __(nil(),X) -> X and(tt(),X) -> activate(X) isList(V) -> isNeList(activate(V)) isList(n__nil()) -> tt() isList(n____(V1,V2)) -> and(isList(activate(V1)),n__isList(activate(V2))) isNeList(V) -> isQid(activate(V)) isNeList(n____(V1,V2)) -> and(isList(activate(V1)),n__isNeList(activate(V2))) isNeList(n____(V1,V2)) -> and(isNeList(activate(V1)),n__isList(activate(V2))) isNePal(V) -> isQid(activate(V)) isNePal(n____(I,__(P,I))) -> and(isQid(activate(I)),n__isPal(activate(P))) isPal(V) -> 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) isList(X) -> n__isList(X) isNeList(X) -> n__isNeList(X) isPal(X) -> n__isPal(X) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(X1,X2) activate(n__isList(X)) -> isList(X) activate(n__isNeList(X)) -> isNeList(X) activate(n__isPal(X)) -> isPal(X) 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: [n__o] = 0, [activate](x0) = x0, [n__a] = 0, [n____](x0, x1) = 5x0 + x1, [nil] = 2, [and](x0, x1) = x0 + x1, [n__e] = 0, [e] = 0, [n__u] = 0, [n__i] = 4, [i] = 4, [isList](x0) = x0, [isQid](x0) = x0, [__](x0, x1) = 5x0 + x1, [n__nil] = 2, [a] = 0, [isPal](x0) = 4x0, [isNePal](x0) = x0, [o] = 0, [u] = 0, [n__isNeList](x0) = x0, [n__isList](x0) = x0, [n__isPal](x0) = 4x0, [isNeList](x0) = x0, [tt] = 0 orientation: __(__(X,Y),Z) = 25X + 5Y + Z >= 5X + 5Y + Z = __(X,__(Y,Z)) __(X,nil()) = 5X + 2 >= X = X __(nil(),X) = X + 10 >= X = X and(tt(),X) = X >= X = activate(X) isList(V) = V >= V = isNeList(activate(V)) isList(n__nil()) = 2 >= 0 = tt() isList(n____(V1,V2)) = 5V1 + V2 >= V1 + V2 = and(isList(activate(V1)),n__isList(activate(V2))) isNeList(V) = V >= V = isQid(activate(V)) isNeList(n____(V1,V2)) = 5V1 + V2 >= V1 + V2 = and(isList(activate(V1)),n__isNeList(activate(V2))) isNeList(n____(V1,V2)) = 5V1 + V2 >= V1 + V2 = and(isNeList(activate(V1)),n__isList(activate(V2))) isNePal(V) = V >= V = isQid(activate(V)) isNePal(n____(I,__(P,I))) = 6I + 5P >= I + 4P = and(isQid(activate(I)),n__isPal(activate(P))) isPal(V) = 4V >= V = isNePal(activate(V)) isPal(n__nil()) = 8 >= 0 = tt() isQid(n__a()) = 0 >= 0 = tt() isQid(n__e()) = 0 >= 0 = tt() isQid(n__i()) = 4 >= 0 = tt() isQid(n__o()) = 0 >= 0 = tt() isQid(n__u()) = 0 >= 0 = tt() nil() = 2 >= 2 = n__nil() __(X1,X2) = 5X1 + X2 >= 5X1 + X2 = n____(X1,X2) isList(X) = X >= X = n__isList(X) isNeList(X) = X >= X = n__isNeList(X) isPal(X) = 4X >= 4X = n__isPal(X) a() = 0 >= 0 = n__a() e() = 0 >= 0 = n__e() i() = 4 >= 4 = n__i() o() = 0 >= 0 = n__o() u() = 0 >= 0 = n__u() activate(n__nil()) = 2 >= 2 = nil() activate(n____(X1,X2)) = 5X1 + X2 >= 5X1 + X2 = __(X1,X2) activate(n__isList(X)) = X >= X = isList(X) activate(n__isNeList(X)) = X >= X = isNeList(X) activate(n__isPal(X)) = 4X >= 4X = isPal(X) activate(n__a()) = 0 >= 0 = a() activate(n__e()) = 0 >= 0 = e() activate(n__i()) = 4 >= 4 = i() activate(n__o()) = 0 >= 0 = o() activate(n__u()) = 0 >= 0 = u() activate(X) = X >= X = X problem: __(__(X,Y),Z) -> __(X,__(Y,Z)) and(tt(),X) -> activate(X) isList(V) -> isNeList(activate(V)) isList(n____(V1,V2)) -> and(isList(activate(V1)),n__isList(activate(V2))) isNeList(V) -> isQid(activate(V)) isNeList(n____(V1,V2)) -> and(isList(activate(V1)),n__isNeList(activate(V2))) isNeList(n____(V1,V2)) -> and(isNeList(activate(V1)),n__isList(activate(V2))) isNePal(V) -> isQid(activate(V)) isNePal(n____(I,__(P,I))) -> and(isQid(activate(I)),n__isPal(activate(P))) isPal(V) -> 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) isList(X) -> n__isList(X) isNeList(X) -> n__isNeList(X) isPal(X) -> n__isPal(X) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(X1,X2) activate(n__isList(X)) -> isList(X) activate(n__isNeList(X)) -> isNeList(X) activate(n__isPal(X)) -> isPal(X) 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: [n__o] = 4, [activate](x0) = x0, [n__a] = 4, [n____](x0, x1) = 4x0 + x1 + 4, [nil] = 0, [and](x0, x1) = x0 + x1, [n__e] = 0, [e] = 0, [n__u] = 0, [n__i] = 5, [i] = 5, [isList](x0) = x0, [isQid](x0) = x0, [__](x0, x1) = 4x0 + x1 + 4, [n__nil] = 0, [a] = 4, [isPal](x0) = x0, [isNePal](x0) = x0, [o] = 4, [u] = 0, [n__isNeList](x0) = x0, [n__isList](x0) = x0, [n__isPal](x0) = x0, [isNeList](x0) = x0, [tt] = 0 orientation: __(__(X,Y),Z) = 16X + 4Y + Z + 20 >= 4X + 4Y + Z + 8 = __(X,__(Y,Z)) and(tt(),X) = X >= X = activate(X) isList(V) = V >= V = isNeList(activate(V)) isList(n____(V1,V2)) = 4V1 + V2 + 4 >= V1 + V2 = and(isList(activate(V1)),n__isList(activate(V2))) isNeList(V) = V >= V = isQid(activate(V)) isNeList(n____(V1,V2)) = 4V1 + V2 + 4 >= V1 + V2 = and(isList(activate(V1)),n__isNeList(activate(V2))) isNeList(n____(V1,V2)) = 4V1 + V2 + 4 >= V1 + V2 = and(isNeList(activate(V1)),n__isList(activate(V2))) isNePal(V) = V >= V = isQid(activate(V)) isNePal(n____(I,__(P,I))) = 5I + 4P + 8 >= I + P = and(isQid(activate(I)),n__isPal(activate(P))) isPal(V) = V >= V = isNePal(activate(V)) isQid(n__a()) = 4 >= 0 = tt() isQid(n__e()) = 0 >= 0 = tt() isQid(n__o()) = 4 >= 0 = tt() isQid(n__u()) = 0 >= 0 = tt() nil() = 0 >= 0 = n__nil() __(X1,X2) = 4X1 + X2 + 4 >= 4X1 + X2 + 4 = n____(X1,X2) isList(X) = X >= X = n__isList(X) isNeList(X) = X >= X = n__isNeList(X) isPal(X) = X >= X = n__isPal(X) a() = 4 >= 4 = n__a() e() = 0 >= 0 = n__e() i() = 5 >= 5 = n__i() o() = 4 >= 4 = n__o() u() = 0 >= 0 = n__u() activate(n__nil()) = 0 >= 0 = nil() activate(n____(X1,X2)) = 4X1 + X2 + 4 >= 4X1 + X2 + 4 = __(X1,X2) activate(n__isList(X)) = X >= X = isList(X) activate(n__isNeList(X)) = X >= X = isNeList(X) activate(n__isPal(X)) = X >= X = isPal(X) activate(n__a()) = 4 >= 4 = a() activate(n__e()) = 0 >= 0 = e() activate(n__i()) = 5 >= 5 = i() activate(n__o()) = 4 >= 4 = o() activate(n__u()) = 0 >= 0 = u() activate(X) = X >= X = X problem: and(tt(),X) -> activate(X) isList(V) -> isNeList(activate(V)) isNeList(V) -> isQid(activate(V)) isNePal(V) -> isQid(activate(V)) isPal(V) -> isNePal(activate(V)) isQid(n__e()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() __(X1,X2) -> n____(X1,X2) isList(X) -> n__isList(X) isNeList(X) -> n__isNeList(X) isPal(X) -> n__isPal(X) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(X1,X2) activate(n__isList(X)) -> isList(X) activate(n__isNeList(X)) -> isNeList(X) activate(n__isPal(X)) -> isPal(X) 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] [n__o] = [0] [0], [0] [activate](x0) = x0 + [1] [0], [0] [n__a] = [0] [0], [1 0 0] [1 0 0] [n____](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [0] [nil] = [0] [0], [1 0 0] [1 0 0] [1] [and](x0, x1) = [0 0 0]x0 + [0 1 1]x1 + [1] [0 0 0] [0 0 1] [0], [0] [n__e] = [0] [0], [0] [e] = [1] [0], [0] [n__u] = [0] [0], [0] [n__i] = [0] [0], [0] [i] = [1] [0], [1 1 0] [1] [isList](x0) = [0 0 1]x0 + [0] [0 0 0] [0], [1 0 0] [isQid](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [0] [__](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1] [0 0 0] [0 0 0] [0], [0] [n__nil] = [0] [0], [0] [a] = [1] [0], [1 0 0] [isPal](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [isNePal](x0) = [0 0 0]x0 [0 0 0] , [0] [o] = [1] [0], [0] [u] = [1] [0], [1 1 0] [n__isNeList](x0) = [0 0 0]x0 [0 0 0] , [1 1 0] [1] [n__isList](x0) = [0 0 1]x0 + [0] [0 0 0] [0], [1 0 0] [n__isPal](x0) = [0 0 0]x0 [0 0 0] , [1 1 0] [isNeList](x0) = [0 0 0]x0 [0 0 0] , [0] [tt] = [0] [0] orientation: [1 0 0] [1] [0] and(tt(),X) = [0 1 1]X + [1] >= X + [1] = activate(X) [0 0 1] [0] [0] [1 1 0] [1] [1 1 0] [1] isList(V) = [0 0 1]V + [0] >= [0 0 0]V + [0] = isNeList(activate(V)) [0 0 0] [0] [0 0 0] [0] [1 1 0] [1 0 0] isNeList(V) = [0 0 0]V >= [0 0 0]V = isQid(activate(V)) [0 0 0] [0 0 0] [1 0 0] [1 0 0] isNePal(V) = [0 0 0]V >= [0 0 0]V = isQid(activate(V)) [0 0 0] [0 0 0] [1 0 0] [1 0 0] isPal(V) = [0 0 0]V >= [0 0 0]V = isNePal(activate(V)) [0 0 0] [0 0 0] [0] [0] isQid(n__e()) = [0] >= [0] = tt() [0] [0] [0] [0] isQid(n__u()) = [0] >= [0] = tt() [0] [0] [0] [0] nil() = [0] >= [0] = n__nil() [0] [0] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] __(X1,X2) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 = n____(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [1 1 0] [1] [1 1 0] [1] isList(X) = [0 0 1]X + [0] >= [0 0 1]X + [0] = n__isList(X) [0 0 0] [0] [0 0 0] [0] [1 1 0] [1 1 0] isNeList(X) = [0 0 0]X >= [0 0 0]X = n__isNeList(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] isPal(X) = [0 0 0]X >= [0 0 0]X = n__isPal(X) [0 0 0] [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] [0] [0] activate(n__nil()) = [1] >= [0] = nil() [0] [0] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] activate(n____(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = __(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 1 0] [1] [1 1 0] [1] activate(n__isList(X)) = [0 0 1]X + [1] >= [0 0 1]X + [0] = isList(X) [0 0 0] [0] [0 0 0] [0] [1 1 0] [0] [1 1 0] activate(n__isNeList(X)) = [0 0 0]X + [1] >= [0 0 0]X = isNeList(X) [0 0 0] [0] [0 0 0] [1 0 0] [0] [1 0 0] activate(n__isPal(X)) = [0 0 0]X + [1] >= [0 0 0]X = isPal(X) [0 0 0] [0] [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: isList(V) -> isNeList(activate(V)) isNeList(V) -> isQid(activate(V)) isNePal(V) -> isQid(activate(V)) isPal(V) -> isNePal(activate(V)) isQid(n__e()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() __(X1,X2) -> n____(X1,X2) isList(X) -> n__isList(X) isNeList(X) -> n__isNeList(X) isPal(X) -> n__isPal(X) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(X1,X2) activate(n__isList(X)) -> isList(X) activate(n__isNeList(X)) -> isNeList(X) activate(n__isPal(X)) -> isPal(X) 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] [n__o] = [0] [0], [activate](x0) = x0 , [0] [n__a] = [0] [0], [1 0 1] [1 0 0] [n____](x0, x1) = [0 1 0]x0 + [1 0 0]x1 [0 0 0] [0 0 0] , [0] [nil] = [0] [0], [0] [n__e] = [0] [0], [0] [e] = [0] [0], [0] [n__u] = [0] [0], [0] [n__i] = [0] [0], [0] [i] = [0] [0], [1 0 1] [0] [isList](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [1 0 1] [0] [isQid](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [1 0 1] [1 0 0] [__](x0, x1) = [0 1 0]x0 + [1 0 0]x1 [0 0 0] [0 0 0] , [0] [n__nil] = [0] [0], [0] [a] = [0] [0], [1 1 1] [1] [isPal](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [1 1 1] [1] [isNePal](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [0] [o] = [0] [0], [0] [u] = [0] [0], [1 0 1] [0] [n__isNeList](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [1 0 1] [0] [n__isList](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [1 1 1] [1] [n__isPal](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [1 0 1] [0] [isNeList](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [0] [tt] = [0] [0] orientation: [1 0 1] [0] [1 0 1] [0] isList(V) = [0 0 0]V + [0] >= [0 0 0]V + [0] = isNeList(activate(V)) [0 0 0] [1] [0 0 0] [1] [1 0 1] [0] [1 0 1] [0] isNeList(V) = [0 0 0]V + [0] >= [0 0 0]V + [0] = isQid(activate(V)) [0 0 0] [1] [0 0 0] [1] [1 1 1] [1] [1 0 1] [0] isNePal(V) = [0 0 0]V + [0] >= [0 0 0]V + [0] = isQid(activate(V)) [0 0 0] [1] [0 0 0] [1] [1 1 1] [1] [1 1 1] [1] isPal(V) = [0 0 0]V + [0] >= [0 0 0]V + [0] = isNePal(activate(V)) [0 0 0] [1] [0 0 0] [1] [0] [0] isQid(n__e()) = [0] >= [0] = tt() [1] [0] [0] [0] isQid(n__u()) = [0] >= [0] = tt() [1] [0] [0] [0] nil() = [0] >= [0] = n__nil() [0] [0] [1 0 1] [1 0 0] [1 0 1] [1 0 0] __(X1,X2) = [0 1 0]X1 + [1 0 0]X2 >= [0 1 0]X1 + [1 0 0]X2 = n____(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 1] [0] [1 0 1] [0] isList(X) = [0 0 0]X + [0] >= [0 0 0]X + [0] = n__isList(X) [0 0 0] [1] [0 0 0] [1] [1 0 1] [0] [1 0 1] [0] isNeList(X) = [0 0 0]X + [0] >= [0 0 0]X + [0] = n__isNeList(X) [0 0 0] [1] [0 0 0] [1] [1 1 1] [1] [1 1 1] [1] isPal(X) = [0 0 0]X + [0] >= [0 0 0]X + [0] = n__isPal(X) [0 0 0] [1] [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] [0] [0] u() = [0] >= [0] = n__u() [0] [0] [0] [0] activate(n__nil()) = [0] >= [0] = nil() [0] [0] [1 0 1] [1 0 0] [1 0 1] [1 0 0] activate(n____(X1,X2)) = [0 1 0]X1 + [1 0 0]X2 >= [0 1 0]X1 + [1 0 0]X2 = __(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 1] [0] [1 0 1] [0] activate(n__isList(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = isList(X) [0 0 0] [1] [0 0 0] [1] [1 0 1] [0] [1 0 1] [0] activate(n__isNeList(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = isNeList(X) [0 0 0] [1] [0 0 0] [1] [1 1 1] [1] [1 1 1] [1] activate(n__isPal(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = isPal(X) [0 0 0] [1] [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] [0] [0] activate(n__u()) = [0] >= [0] = u() [0] [0] activate(X) = X >= X = X problem: isList(V) -> isNeList(activate(V)) isNeList(V) -> isQid(activate(V)) isPal(V) -> isNePal(activate(V)) isQid(n__e()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() __(X1,X2) -> n____(X1,X2) isList(X) -> n__isList(X) isNeList(X) -> n__isNeList(X) isPal(X) -> n__isPal(X) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() activate(n__nil()) -> nil() activate(n____(X1,X2)) -> __(X1,X2) activate(n__isList(X)) -> isList(X) activate(n__isNeList(X)) -> isNeList(X) activate(n__isPal(X)) -> isPal(X) 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: [n__o] = 0, [activate](x0) = 2x0, [n__a] = 0, [n____](x0, x1) = 2x0 + x1 + 2, [nil] = 0, [n__e] = 0, [e] = 0, [n__u] = 0, [n__i] = 0, [i] = 0, [isList](x0) = 4x0 + 2, [isQid](x0) = x0 + 2, [__](x0, x1) = 2x0 + x1 + 2, [n__nil] = 0, [a] = 0, [isPal](x0) = 2x0, [isNePal](x0) = x0, [o] = 0, [u] = 0, [n__isNeList](x0) = 2x0 + 2, [n__isList](x0) = 4x0 + 2, [n__isPal](x0) = 2x0, [isNeList](x0) = 2x0 + 2, [tt] = 2 orientation: isList(V) = 4V + 2 >= 4V + 2 = isNeList(activate(V)) isNeList(V) = 2V + 2 >= 2V + 2 = isQid(activate(V)) isPal(V) = 2V >= 2V = isNePal(activate(V)) isQid(n__e()) = 2 >= 2 = tt() isQid(n__u()) = 2 >= 2 = tt() nil() = 0 >= 0 = n__nil() __(X1,X2) = 2X1 + X2 + 2 >= 2X1 + X2 + 2 = n____(X1,X2) isList(X) = 4X + 2 >= 4X + 2 = n__isList(X) isNeList(X) = 2X + 2 >= 2X + 2 = n__isNeList(X) isPal(X) = 2X >= 2X = n__isPal(X) a() = 0 >= 0 = n__a() e() = 0 >= 0 = n__e() i() = 0 >= 0 = n__i() o() = 0 >= 0 = n__o() u() = 0 >= 0 = n__u() activate(n__nil()) = 0 >= 0 = nil() activate(n____(X1,X2)) = 4X1 + 2X2 + 4 >= 2X1 + X2 + 2 = __(X1,X2) activate(n__isList(X)) = 8X + 4 >= 4X + 2 = isList(X) activate(n__isNeList(X)) = 4X + 4 >= 2X + 2 = isNeList(X) activate(n__isPal(X)) = 4X >= 2X = isPal(X) activate(n__a()) = 0 >= 0 = a() activate(n__e()) = 0 >= 0 = e() activate(n__i()) = 0 >= 0 = i() activate(n__o()) = 0 >= 0 = o() activate(n__u()) = 0 >= 0 = u() activate(X) = 2X >= X = X problem: isList(V) -> isNeList(activate(V)) isNeList(V) -> isQid(activate(V)) isPal(V) -> isNePal(activate(V)) isQid(n__e()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() __(X1,X2) -> n____(X1,X2) isList(X) -> n__isList(X) isNeList(X) -> n__isNeList(X) isPal(X) -> n__isPal(X) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() activate(n__nil()) -> nil() activate(n__isPal(X)) -> isPal(X) 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] [n__o] = [0] [1], [1 0 0] [activate](x0) = [0 1 1]x0 [0 0 1] , [1] [n__a] = [0] [0], [1 0 0] [1 0 0] [n____](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [0] [nil] = [1] [0], [0] [n__e] = [0] [0], [0] [e] = [0] [0], [0] [n__u] = [0] [1], [0] [n__i] = [0] [0], [0] [i] = [0] [0], [1 1 1] [1] [isList](x0) = [1 0 0]x0 + [0] [0 0 0] [0], [1 0 0] [isQid](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [__](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [0] [n__nil] = [1] [0], [1] [a] = [0] [0], [1 0 0] [0] [isPal](x0) = [1 0 0]x0 + [1] [0 0 0] [0], [1 0 0] [isNePal](x0) = [1 0 0]x0 [0 0 0] , [0] [o] = [1] [1], [0] [u] = [1] [1], [1 1 0] [n__isNeList](x0) = [0 0 0]x0 [0 0 0] , [1 1 0] [n__isList](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [0] [n__isPal](x0) = [1 0 0]x0 + [1] [0 0 0] [0], [1 1 0] [isNeList](x0) = [0 0 0]x0 [0 0 0] , [0] [tt] = [0] [0] orientation: [1 1 1] [1] [1 1 1] isList(V) = [1 0 0]V + [0] >= [0 0 0]V = isNeList(activate(V)) [0 0 0] [0] [0 0 0] [1 1 0] [1 0 0] isNeList(V) = [0 0 0]V >= [0 0 0]V = isQid(activate(V)) [0 0 0] [0 0 0] [1 0 0] [0] [1 0 0] isPal(V) = [1 0 0]V + [1] >= [1 0 0]V = isNePal(activate(V)) [0 0 0] [0] [0 0 0] [0] [0] isQid(n__e()) = [0] >= [0] = tt() [0] [0] [0] [0] isQid(n__u()) = [0] >= [0] = tt() [0] [0] [0] [0] nil() = [1] >= [1] = n__nil() [0] [0] [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 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 1] [1] [1 1 0] isList(X) = [1 0 0]X + [0] >= [0 0 0]X = n__isList(X) [0 0 0] [0] [0 0 0] [1 1 0] [1 1 0] isNeList(X) = [0 0 0]X >= [0 0 0]X = n__isNeList(X) [0 0 0] [0 0 0] [1 0 0] [0] [1 0 0] [0] isPal(X) = [1 0 0]X + [1] >= [1 0 0]X + [1] = n__isPal(X) [0 0 0] [0] [0 0 0] [0] [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] [1] [0] [0] u() = [1] >= [0] = n__u() [1] [1] [0] [0] activate(n__nil()) = [1] >= [1] = nil() [0] [0] [1 0 0] [0] [1 0 0] [0] activate(n__isPal(X)) = [1 0 0]X + [1] >= [1 0 0]X + [1] = isPal(X) [0 0 0] [0] [0 0 0] [0] [1] [1] 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()) = [1] >= [1] = o() [1] [1] [0] [0] activate(n__u()) = [1] >= [1] = u() [1] [1] [1 0 0] activate(X) = [0 1 1]X >= X = X [0 0 1] problem: isNeList(V) -> isQid(activate(V)) isPal(V) -> isNePal(activate(V)) isQid(n__e()) -> tt() isQid(n__u()) -> tt() nil() -> n__nil() __(X1,X2) -> n____(X1,X2) isNeList(X) -> n__isNeList(X) isPal(X) -> n__isPal(X) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() activate(n__nil()) -> nil() activate(n__isPal(X)) -> isPal(X) 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] [n__o] = [0] [0], [1 0 0] [activate](x0) = [1 1 0]x0 [0 1 1] , [1] [n__a] = [0] [0], [1 0 0] [1 0 0] [n____](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1] [nil] = [0] [0], [0] [n__e] = [0] [1], [0] [e] = [0] [1], [0] [n__u] = [0] [1], [1] [n__i] = [0] [1], [1] [i] = [1] [1], [1 0 1] [0] [isQid](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [1 0 0] [0] [__](x0, x1) = x0 + [0 0 0]x1 + [1] [0 1 0] [0], [1] [n__nil] = [0] [0], [1] [a] = [0] [0], [1 1 1] [1] [isPal](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [1 0 1] [isNePal](x0) = [0 0 0]x0 [0 0 0] , [0] [o] = [0] [0], [0] [u] = [0] [1], [1 0 0] [1] [n__isNeList](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [1 1 1] [1] [n__isPal](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [1 1 1] [1] [isNeList](x0) = [0 0 0]x0 + [1] [0 0 0] [1], [0] [tt] = [0] [1] orientation: [1 1 1] [1] [1 1 1] [0] isNeList(V) = [0 0 0]V + [1] >= [0 0 0]V + [0] = isQid(activate(V)) [0 0 0] [1] [0 0 0] [1] [1 1 1] [1] [1 1 1] isPal(V) = [0 0 0]V + [0] >= [0 0 0]V = isNePal(activate(V)) [0 0 0] [0] [0 0 0] [1] [0] isQid(n__e()) = [0] >= [0] = tt() [1] [1] [1] [0] isQid(n__u()) = [0] >= [0] = tt() [1] [1] [1] [1] nil() = [0] >= [0] = n__nil() [0] [0] [1 0 0] [0] [1 0 0] [1 0 0] __(X1,X2) = X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 = n____(X1,X2) [0 1 0] [0] [0 0 0] [0 0 0] [1 1 1] [1] [1 0 0] [1] isNeList(X) = [0 0 0]X + [1] >= [0 0 0]X + [0] = n__isNeList(X) [0 0 0] [1] [0 0 0] [1] [1 1 1] [1] [1 1 1] [1] isPal(X) = [0 0 0]X + [0] >= [0 0 0]X + [0] = n__isPal(X) [0 0 0] [0] [0 0 0] [0] [1] [1] a() = [0] >= [0] = n__a() [0] [0] [0] [0] e() = [0] >= [0] = n__e() [1] [1] [1] [1] i() = [1] >= [0] = n__i() [1] [1] [0] [0] o() = [0] >= [0] = n__o() [0] [0] [0] [0] u() = [0] >= [0] = n__u() [1] [1] [1] [1] activate(n__nil()) = [1] >= [0] = nil() [0] [0] [1 1 1] [1] [1 1 1] [1] activate(n__isPal(X)) = [1 1 1]X + [1] >= [0 0 0]X + [0] = isPal(X) [0 0 0] [0] [0 0 0] [0] [1] [1] activate(n__a()) = [1] >= [0] = a() [0] [0] [0] [0] activate(n__e()) = [0] >= [0] = e() [1] [1] [1] [1] activate(n__i()) = [1] >= [1] = i() [1] [1] [0] [0] activate(n__o()) = [0] >= [0] = o() [0] [0] [0] [0] activate(n__u()) = [0] >= [0] = u() [1] [1] [1 0 0] activate(X) = [1 1 0]X >= X = X [0 1 1] problem: nil() -> n__nil() __(X1,X2) -> n____(X1,X2) isNeList(X) -> n__isNeList(X) isPal(X) -> n__isPal(X) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() activate(n__nil()) -> nil() activate(n__isPal(X)) -> isPal(X) 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] [n__o] = [0] [0], [1] [activate](x0) = x0 + [0] [0], [0] [n__a] = [0] [0], [1 0 0] [1 0 0] [n____](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1] [nil] = [0] [0], [0] [n__e] = [0] [0], [1] [e] = [0] [0], [0] [n__u] = [0] [0], [0] [n__i] = [0] [0], [1] [i] = [0] [0], [1 0 0] [1 0 0] [__](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [0] [n__nil] = [0] [0], [1] [a] = [0] [0], [1 0 0] [1] [isPal](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [1] [o] = [0] [0], [1] [u] = [0] [0], [1 0 0] [n__isNeList](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [n__isPal](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [isNeList](x0) = [0 0 0]x0 [0 0 0] orientation: [1] [0] nil() = [0] >= [0] = n__nil() [0] [0] [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 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] isNeList(X) = [0 0 0]X >= [0 0 0]X = n__isNeList(X) [0 0 0] [0 0 0] [1 0 0] [1] [1 0 0] isPal(X) = [0 0 0]X + [0] >= [0 0 0]X = n__isPal(X) [0 0 0] [0] [0 0 0] [1] [0] a() = [0] >= [0] = n__a() [0] [0] [1] [0] e() = [0] >= [0] = n__e() [0] [0] [1] [0] i() = [0] >= [0] = n__i() [0] [0] [1] [0] o() = [0] >= [0] = n__o() [0] [0] [1] [0] u() = [0] >= [0] = n__u() [0] [0] [1] [1] activate(n__nil()) = [0] >= [0] = nil() [0] [0] [1 0 0] [1] [1 0 0] [1] activate(n__isPal(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = isPal(X) [0 0 0] [0] [0 0 0] [0] [1] [1] activate(n__a()) = [0] >= [0] = a() [0] [0] [1] [1] activate(n__e()) = [0] >= [0] = e() [0] [0] [1] [1] activate(n__i()) = [0] >= [0] = i() [0] [0] [1] [1] activate(n__o()) = [0] >= [0] = o() [0] [0] [1] [1] activate(n__u()) = [0] >= [0] = u() [0] [0] [1] activate(X) = X + [0] >= X = X [0] problem: __(X1,X2) -> n____(X1,X2) isNeList(X) -> n__isNeList(X) activate(n__nil()) -> nil() activate(n__isPal(X)) -> isPal(X) activate(n__a()) -> a() activate(n__e()) -> e() activate(n__i()) -> i() activate(n__o()) -> o() activate(n__u()) -> u() Matrix Interpretation Processor: dim=3 interpretation: [0] [n__o] = [0] [0], [1 0 0] [1] [activate](x0) = [0 1 0]x0 + [0] [0 0 0] [0], [0] [n__a] = [1] [0], [1 0 0] [1 0 0] [n____](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [0] [nil] = [0] [0], [0] [n__e] = [0] [0], [0] [e] = [0] [0], [0] [n__u] = [0] [0], [0] [n__i] = [0] [0], [0] [i] = [0] [0], [1 0 0] [1 0 0] [__](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [0] [n__nil] = [0] [0], [0] [a] = [1] [0], [1 0 0] [isPal](x0) = [0 0 0]x0 [0 0 0] , [0] [o] = [0] [0], [0] [u] = [0] [0], [1 0 0] [n__isNeList](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [n__isPal](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [isNeList](x0) = [0 0 0]x0 [0 0 0] orientation: [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 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] isNeList(X) = [0 0 0]X >= [0 0 0]X = n__isNeList(X) [0 0 0] [0 0 0] [1] [0] activate(n__nil()) = [0] >= [0] = nil() [0] [0] [1 0 0] [1] [1 0 0] activate(n__isPal(X)) = [0 0 0]X + [0] >= [0 0 0]X = isPal(X) [0 0 0] [0] [0 0 0] [1] [0] activate(n__a()) = [1] >= [1] = a() [0] [0] [1] [0] activate(n__e()) = [0] >= [0] = e() [0] [0] [1] [0] activate(n__i()) = [0] >= [0] = i() [0] [0] [1] [0] activate(n__o()) = [0] >= [0] = o() [0] [0] [1] [0] activate(n__u()) = [0] >= [0] = u() [0] [0] problem: __(X1,X2) -> n____(X1,X2) isNeList(X) -> n__isNeList(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [1 0 0] [n____](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 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] , [1 0 0] [n__isNeList](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1] [isNeList](x0) = [0 0 0]x0 + [0] [0 0 0] [0] orientation: [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 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1] [1 0 0] isNeList(X) = [0 0 0]X + [0] >= [0 0 0]X = n__isNeList(X) [0 0 0] [0] [0 0 0] problem: __(X1,X2) -> n____(X1,X2) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [1 0 0] [n____](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [1 0 0] [1] [__](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0] [0 0 0] [0 0 1] [0] orientation: [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] __(X1,X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 = n____(X1,X2) [0 0 0] [0 0 1] [0] [0 0 0] [0 0 0] problem: Qed