/export/starexec/sandbox/solver/bin/starexec_run_ttt2 /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Problem: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt())) -> mark(tt()) active(U21(tt(),V2)) -> mark(U22(isList(V2))) active(U22(tt())) -> mark(tt()) active(U31(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNeList(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt(),P)) -> mark(U72(isPal(P))) active(U72(tt())) -> mark(tt()) active(U81(tt())) -> mark(tt()) active(isList(V)) -> mark(U11(isNeList(V))) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) -> mark(U51(isNeList(V1),V2)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),P)) active(isPal(V)) -> mark(U81(isNePal(V))) active(isPal(nil())) -> mark(tt()) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X)) -> active(U11(mark(X))) mark(tt()) -> active(tt()) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X)) -> active(U22(mark(X))) mark(isList(X)) -> active(isList(X)) mark(U31(X)) -> active(U31(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isPal(X)) -> active(isPal(X)) mark(U81(X)) -> active(U81(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X)) -> U11(X) U11(active(X)) -> U11(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X)) -> U22(X) U22(active(X)) -> U22(X) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U31(mark(X)) -> U31(X) U31(active(X)) -> U31(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) Proof: Matrix Interpretation Processor: dim=1 interpretation: [U72](x0) = 2x0 + 6, [tt] = 2, [U61](x0) = x0, [U22](x0) = x0, [active](x0) = x0, [nil] = 5, [U71](x0, x1) = x0 + 4x1 + 4, [isNePal](x0) = 2x0, [u] = 4, [U81](x0) = x0, [isPal](x0) = 2x0, [a] = 4, [U11](x0) = x0, [U41](x0, x1) = 2x0 + 2x1 + 4, [__](x0, x1) = 4x0 + x1 + 4, [isList](x0) = 2x0 + 2, [isQid](x0) = x0, [o] = 2, [U52](x0) = x0, [U42](x0) = x0 + 1, [e] = 2, [i] = 5, [isNeList](x0) = 2x0 + 1, [U31](x0) = 2x0, [U51](x0, x1) = 4x0 + 2x1 + 4, [U21](x0, x1) = 2x0 + 2x1 + 3, [mark](x0) = x0 orientation: active(__(__(X,Y),Z)) = 16X + 4Y + Z + 20 >= 4X + 4Y + Z + 8 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 4X + 9 >= X = mark(X) active(__(nil(),X)) = X + 24 >= X = mark(X) active(U11(tt())) = 2 >= 2 = mark(tt()) active(U21(tt(),V2)) = 2V2 + 7 >= 2V2 + 2 = mark(U22(isList(V2))) active(U22(tt())) = 2 >= 2 = mark(tt()) active(U31(tt())) = 4 >= 2 = mark(tt()) active(U41(tt(),V2)) = 2V2 + 8 >= 2V2 + 2 = mark(U42(isNeList(V2))) active(U42(tt())) = 3 >= 2 = mark(tt()) active(U51(tt(),V2)) = 2V2 + 12 >= 2V2 + 2 = mark(U52(isList(V2))) active(U52(tt())) = 2 >= 2 = mark(tt()) active(U61(tt())) = 2 >= 2 = mark(tt()) active(U71(tt(),P)) = 4P + 6 >= 4P + 6 = mark(U72(isPal(P))) active(U72(tt())) = 10 >= 2 = mark(tt()) active(U81(tt())) = 2 >= 2 = mark(tt()) active(isList(V)) = 2V + 2 >= 2V + 1 = mark(U11(isNeList(V))) active(isList(nil())) = 12 >= 2 = mark(tt()) active(isList(__(V1,V2))) = 8V1 + 2V2 + 10 >= 4V1 + 2V2 + 7 = mark(U21(isList(V1),V2)) active(isNeList(V)) = 2V + 1 >= 2V = mark(U31(isQid(V))) active(isNeList(__(V1,V2))) = 8V1 + 2V2 + 9 >= 4V1 + 2V2 + 8 = mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) = 8V1 + 2V2 + 9 >= 8V1 + 2V2 + 8 = mark(U51(isNeList(V1),V2)) active(isNePal(V)) = 2V >= V = mark(U61(isQid(V))) active(isNePal(__(I,__(P,I)))) = 10I + 8P + 16 >= I + 4P + 4 = mark(U71(isQid(I),P)) active(isPal(V)) = 2V >= 2V = mark(U81(isNePal(V))) active(isPal(nil())) = 10 >= 2 = mark(tt()) active(isQid(a())) = 4 >= 2 = mark(tt()) active(isQid(e())) = 2 >= 2 = mark(tt()) active(isQid(i())) = 5 >= 2 = mark(tt()) active(isQid(o())) = 2 >= 2 = mark(tt()) active(isQid(u())) = 4 >= 2 = mark(tt()) mark(__(X1,X2)) = 4X1 + X2 + 4 >= 4X1 + X2 + 4 = active(__(mark(X1),mark(X2))) mark(nil()) = 5 >= 5 = active(nil()) mark(U11(X)) = X >= X = active(U11(mark(X))) mark(tt()) = 2 >= 2 = active(tt()) mark(U21(X1,X2)) = 2X1 + 2X2 + 3 >= 2X1 + 2X2 + 3 = active(U21(mark(X1),X2)) mark(U22(X)) = X >= X = active(U22(mark(X))) mark(isList(X)) = 2X + 2 >= 2X + 2 = active(isList(X)) mark(U31(X)) = 2X >= 2X = active(U31(mark(X))) mark(U41(X1,X2)) = 2X1 + 2X2 + 4 >= 2X1 + 2X2 + 4 = active(U41(mark(X1),X2)) mark(U42(X)) = X + 1 >= X + 1 = active(U42(mark(X))) mark(isNeList(X)) = 2X + 1 >= 2X + 1 = active(isNeList(X)) mark(U51(X1,X2)) = 4X1 + 2X2 + 4 >= 4X1 + 2X2 + 4 = active(U51(mark(X1),X2)) mark(U52(X)) = X >= X = active(U52(mark(X))) mark(U61(X)) = X >= X = active(U61(mark(X))) mark(U71(X1,X2)) = X1 + 4X2 + 4 >= X1 + 4X2 + 4 = active(U71(mark(X1),X2)) mark(U72(X)) = 2X + 6 >= 2X + 6 = active(U72(mark(X))) mark(isPal(X)) = 2X >= 2X = active(isPal(X)) mark(U81(X)) = X >= X = active(U81(mark(X))) mark(isQid(X)) = X >= X = active(isQid(X)) mark(isNePal(X)) = 2X >= 2X = active(isNePal(X)) mark(a()) = 4 >= 4 = active(a()) mark(e()) = 2 >= 2 = active(e()) mark(i()) = 5 >= 5 = active(i()) mark(o()) = 2 >= 2 = active(o()) mark(u()) = 4 >= 4 = active(u()) __(mark(X1),X2) = 4X1 + X2 + 4 >= 4X1 + X2 + 4 = __(X1,X2) __(X1,mark(X2)) = 4X1 + X2 + 4 >= 4X1 + X2 + 4 = __(X1,X2) __(active(X1),X2) = 4X1 + X2 + 4 >= 4X1 + X2 + 4 = __(X1,X2) __(X1,active(X2)) = 4X1 + X2 + 4 >= 4X1 + X2 + 4 = __(X1,X2) U11(mark(X)) = X >= X = U11(X) U11(active(X)) = X >= X = U11(X) U21(mark(X1),X2) = 2X1 + 2X2 + 3 >= 2X1 + 2X2 + 3 = U21(X1,X2) U21(X1,mark(X2)) = 2X1 + 2X2 + 3 >= 2X1 + 2X2 + 3 = U21(X1,X2) U21(active(X1),X2) = 2X1 + 2X2 + 3 >= 2X1 + 2X2 + 3 = U21(X1,X2) U21(X1,active(X2)) = 2X1 + 2X2 + 3 >= 2X1 + 2X2 + 3 = U21(X1,X2) U22(mark(X)) = X >= X = U22(X) U22(active(X)) = X >= X = U22(X) isList(mark(X)) = 2X + 2 >= 2X + 2 = isList(X) isList(active(X)) = 2X + 2 >= 2X + 2 = isList(X) U31(mark(X)) = 2X >= 2X = U31(X) U31(active(X)) = 2X >= 2X = U31(X) U41(mark(X1),X2) = 2X1 + 2X2 + 4 >= 2X1 + 2X2 + 4 = U41(X1,X2) U41(X1,mark(X2)) = 2X1 + 2X2 + 4 >= 2X1 + 2X2 + 4 = U41(X1,X2) U41(active(X1),X2) = 2X1 + 2X2 + 4 >= 2X1 + 2X2 + 4 = U41(X1,X2) U41(X1,active(X2)) = 2X1 + 2X2 + 4 >= 2X1 + 2X2 + 4 = U41(X1,X2) U42(mark(X)) = X + 1 >= X + 1 = U42(X) U42(active(X)) = X + 1 >= X + 1 = U42(X) isNeList(mark(X)) = 2X + 1 >= 2X + 1 = isNeList(X) isNeList(active(X)) = 2X + 1 >= 2X + 1 = isNeList(X) U51(mark(X1),X2) = 4X1 + 2X2 + 4 >= 4X1 + 2X2 + 4 = U51(X1,X2) U51(X1,mark(X2)) = 4X1 + 2X2 + 4 >= 4X1 + 2X2 + 4 = U51(X1,X2) U51(active(X1),X2) = 4X1 + 2X2 + 4 >= 4X1 + 2X2 + 4 = U51(X1,X2) U51(X1,active(X2)) = 4X1 + 2X2 + 4 >= 4X1 + 2X2 + 4 = U51(X1,X2) U52(mark(X)) = X >= X = U52(X) U52(active(X)) = X >= X = U52(X) U61(mark(X)) = X >= X = U61(X) U61(active(X)) = X >= X = U61(X) U71(mark(X1),X2) = X1 + 4X2 + 4 >= X1 + 4X2 + 4 = U71(X1,X2) U71(X1,mark(X2)) = X1 + 4X2 + 4 >= X1 + 4X2 + 4 = U71(X1,X2) U71(active(X1),X2) = X1 + 4X2 + 4 >= X1 + 4X2 + 4 = U71(X1,X2) U71(X1,active(X2)) = X1 + 4X2 + 4 >= X1 + 4X2 + 4 = U71(X1,X2) U72(mark(X)) = 2X + 6 >= 2X + 6 = U72(X) U72(active(X)) = 2X + 6 >= 2X + 6 = U72(X) isPal(mark(X)) = 2X >= 2X = isPal(X) isPal(active(X)) = 2X >= 2X = isPal(X) U81(mark(X)) = X >= X = U81(X) U81(active(X)) = X >= X = U81(X) isQid(mark(X)) = X >= X = isQid(X) isQid(active(X)) = X >= X = isQid(X) isNePal(mark(X)) = 2X >= 2X = isNePal(X) isNePal(active(X)) = 2X >= 2X = isNePal(X) problem: active(U11(tt())) -> mark(tt()) active(U22(tt())) -> mark(tt()) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt(),P)) -> mark(U72(isPal(P))) active(U81(tt())) -> mark(tt()) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(V)) -> mark(U81(isNePal(V))) active(isQid(e())) -> mark(tt()) active(isQid(o())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X)) -> active(U11(mark(X))) mark(tt()) -> active(tt()) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X)) -> active(U22(mark(X))) mark(isList(X)) -> active(isList(X)) mark(U31(X)) -> active(U31(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isPal(X)) -> active(isPal(X)) mark(U81(X)) -> active(U81(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X)) -> U11(X) U11(active(X)) -> U11(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X)) -> U22(X) U22(active(X)) -> U22(X) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U31(mark(X)) -> U31(X) U31(active(X)) -> U31(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) Matrix Interpretation Processor: dim=3 interpretation: [1 1 0] [U72](x0) = [0 0 0]x0 [0 0 0] , [0] [tt] = [0] [0], [1 1 0] [U61](x0) = [0 0 0]x0 [0 0 0] , [1 1 0] [0] [U22](x0) = [0 0 0]x0 + [1] [0 0 0] [0], [1 1 1] [active](x0) = [0 0 0]x0 [0 0 0] , [0] [nil] = [1] [0], [1 1 0] [1 0 0] [1] [U71](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0] [0 0 0] [0 0 0] [0], [1 0 0] [1] [isNePal](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [0] [u] = [0] [0], [1 1 0] [U81](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1] [isPal](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [0] [a] = [0] [0], [1 1 0] [U11](x0) = [0 0 0]x0 [0 0 0] , [1 1 0] [1 0 0] [1] [U41](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0] [0 0 0] [0 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], [1 0 0] [isList](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [0] [isQid](x0) = [0 0 0]x0 + [1] [0 0 0] [0], [0] [o] = [0] [0], [1 1 0] [1] [U52](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [1 1 0] [U42](x0) = [0 0 0]x0 [0 0 0] , [0] [e] = [1] [0], [0] [i] = [0] [0], [1 0 0] [isNeList](x0) = [0 0 0]x0 [0 0 0] , [1 1 0] [U31](x0) = [0 0 0]x0 [0 0 0] , [1 1 0] [1 1 0] [U51](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 1 0] [1 0 0] [0] [U21](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1] [0 0 0] [0 0 0] [0], [1 1 0] [mark](x0) = [0 0 0]x0 [0 0 0] orientation: [0] [0] active(U11(tt())) = [0] >= [0] = mark(tt()) [0] [0] [1] [0] active(U22(tt())) = [0] >= [0] = mark(tt()) [0] [0] [1] [0] active(U52(tt())) = [0] >= [0] = mark(tt()) [0] [0] [0] [0] active(U61(tt())) = [0] >= [0] = mark(tt()) [0] [0] [1 0 0] [1] [1 0 0] [1] active(U71(tt(),P)) = [0 0 0]P + [0] >= [0 0 0]P + [0] = mark(U72(isPal(P))) [0 0 0] [0] [0 0 0] [0] [0] [0] active(U81(tt())) = [0] >= [0] = mark(tt()) [0] [0] [1 0 0] [1] [1 0 0] [1] active(isNePal(V)) = [0 0 0]V + [0] >= [0 0 0]V + [0] = mark(U61(isQid(V))) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1] [1 0 0] [1] active(isPal(V)) = [0 0 0]V + [0] >= [0 0 0]V + [0] = mark(U81(isNePal(V))) [0 0 0] [0] [0 0 0] [0] [1] [0] active(isQid(e())) = [0] >= [0] = mark(tt()) [0] [0] [1] [0] active(isQid(o())) = [0] >= [0] = mark(tt()) [0] [0] [1 1 0] [1 1 0] [1] [1 1 0] [1 1 0] [1] mark(__(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = active(__(mark(X1),mark(X2))) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1] [1] mark(nil()) = [0] >= [0] = active(nil()) [0] [0] [1 1 0] [1 1 0] mark(U11(X)) = [0 0 0]X >= [0 0 0]X = active(U11(mark(X))) [0 0 0] [0 0 0] [0] [0] mark(tt()) = [0] >= [0] = active(tt()) [0] [0] [1 1 0] [1 0 0] [1] [1 1 0] [1 0 0] [1] mark(U21(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = active(U21(mark(X1),X2)) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 1 0] [1] [1 1 0] [1] mark(U22(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = active(U22(mark(X))) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1 0 0] mark(isList(X)) = [0 0 0]X >= [0 0 0]X = active(isList(X)) [0 0 0] [0 0 0] [1 1 0] [1 1 0] mark(U31(X)) = [0 0 0]X >= [0 0 0]X = active(U31(mark(X))) [0 0 0] [0 0 0] [1 1 0] [1 0 0] [1] [1 1 0] [1 0 0] [1] mark(U41(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = active(U41(mark(X1),X2)) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 1 0] [1 1 0] mark(U42(X)) = [0 0 0]X >= [0 0 0]X = active(U42(mark(X))) [0 0 0] [0 0 0] [1 0 0] [1 0 0] mark(isNeList(X)) = [0 0 0]X >= [0 0 0]X = active(isNeList(X)) [0 0 0] [0 0 0] [1 1 0] [1 1 0] [1 1 0] [1 1 0] mark(U51(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = active(U51(mark(X1),X2)) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [1] [1 1 0] [1] mark(U52(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = active(U52(mark(X))) [0 0 0] [0] [0 0 0] [0] [1 1 0] [1 1 0] mark(U61(X)) = [0 0 0]X >= [0 0 0]X = active(U61(mark(X))) [0 0 0] [0 0 0] [1 1 0] [1 0 0] [1] [1 1 0] [1 0 0] [1] mark(U71(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = active(U71(mark(X1),X2)) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 1 0] [1 1 0] mark(U72(X)) = [0 0 0]X >= [0 0 0]X = active(U72(mark(X))) [0 0 0] [0 0 0] [1 0 0] [1] [1 0 0] [1] mark(isPal(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = active(isPal(X)) [0 0 0] [0] [0 0 0] [0] [1 1 0] [1 1 0] mark(U81(X)) = [0 0 0]X >= [0 0 0]X = active(U81(mark(X))) [0 0 0] [0 0 0] [1 0 0] [1] [1 0 0] [1] mark(isQid(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = active(isQid(X)) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1] [1 0 0] [1] mark(isNePal(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = active(isNePal(X)) [0 0 0] [0] [0 0 0] [0] [0] [0] mark(a()) = [0] >= [0] = active(a()) [0] [0] [1] [1] mark(e()) = [0] >= [0] = active(e()) [0] [0] [0] [0] mark(i()) = [0] >= [0] = active(i()) [0] [0] [0] [0] mark(o()) = [0] >= [0] = active(o()) [0] [0] [0] [0] mark(u()) = [0] >= [0] = active(u()) [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] = __(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] = __(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 1 1] [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,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 1 0] [1 1 1] [0] [1 1 0] [1 1 0] [0] __(X1,active(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 0] U11(mark(X)) = [0 0 0]X >= [0 0 0]X = U11(X) [0 0 0] [0 0 0] [1 1 1] [1 1 0] U11(active(X)) = [0 0 0]X >= [0 0 0]X = U11(X) [0 0 0] [0 0 0] [1 1 0] [1 0 0] [0] [1 1 0] [1 0 0] [0] U21(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = U21(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 0 0] [0] U21(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = U21(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 1 1] [1 0 0] [0] [1 1 0] [1 0 0] [0] U21(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = U21(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 1 0] [1 1 1] [0] [1 1 0] [1 0 0] [0] U21(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = U21(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 1 0] [0] [1 1 0] [0] U22(mark(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = U22(X) [0 0 0] [0] [0 0 0] [0] [1 1 1] [0] [1 1 0] [0] U22(active(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = U22(X) [0 0 0] [0] [0 0 0] [0] [1 1 0] [1 0 0] isList(mark(X)) = [0 0 0]X >= [0 0 0]X = isList(X) [0 0 0] [0 0 0] [1 1 1] [1 0 0] isList(active(X)) = [0 0 0]X >= [0 0 0]X = isList(X) [0 0 0] [0 0 0] [1 1 0] [1 1 0] U31(mark(X)) = [0 0 0]X >= [0 0 0]X = U31(X) [0 0 0] [0 0 0] [1 1 1] [1 1 0] U31(active(X)) = [0 0 0]X >= [0 0 0]X = U31(X) [0 0 0] [0 0 0] [1 1 0] [1 0 0] [1] [1 1 0] [1 0 0] [1] U41(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = U41(X1,X2) [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 0 0] [1] U41(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = U41(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 1 1] [1 0 0] [1] [1 1 0] [1 0 0] [1] U41(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = U41(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 1 0] [1 1 1] [1] [1 1 0] [1 0 0] [1] U41(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = U41(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 1 0] [1 1 0] U42(mark(X)) = [0 0 0]X >= [0 0 0]X = U42(X) [0 0 0] [0 0 0] [1 1 1] [1 1 0] U42(active(X)) = [0 0 0]X >= [0 0 0]X = U42(X) [0 0 0] [0 0 0] [1 1 0] [1 0 0] isNeList(mark(X)) = [0 0 0]X >= [0 0 0]X = isNeList(X) [0 0 0] [0 0 0] [1 1 1] [1 0 0] isNeList(active(X)) = [0 0 0]X >= [0 0 0]X = isNeList(X) [0 0 0] [0 0 0] [1 1 0] [1 1 0] [1 1 0] [1 1 0] U51(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = U51(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [1 1 0] [1 1 0] [1 1 0] U51(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = U51(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 1] [1 1 0] [1 1 0] [1 1 0] U51(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = U51(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [1 1 1] [1 1 0] [1 1 0] U51(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = U51(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [1] [1 1 0] [1] U52(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = U52(X) [0 0 0] [0] [0 0 0] [0] [1 1 1] [1] [1 1 0] [1] U52(active(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = U52(X) [0 0 0] [0] [0 0 0] [0] [1 1 0] [1 1 0] U61(mark(X)) = [0 0 0]X >= [0 0 0]X = U61(X) [0 0 0] [0 0 0] [1 1 1] [1 1 0] U61(active(X)) = [0 0 0]X >= [0 0 0]X = U61(X) [0 0 0] [0 0 0] [1 1 0] [1 0 0] [1] [1 1 0] [1 0 0] [1] U71(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = U71(X1,X2) [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 0 0] [1] U71(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = U71(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 1 1] [1 0 0] [1] [1 1 0] [1 0 0] [1] U71(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = U71(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 1 0] [1 1 1] [1] [1 1 0] [1 0 0] [1] U71(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = U71(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 1 0] [1 1 0] U72(mark(X)) = [0 0 0]X >= [0 0 0]X = U72(X) [0 0 0] [0 0 0] [1 1 1] [1 1 0] U72(active(X)) = [0 0 0]X >= [0 0 0]X = U72(X) [0 0 0] [0 0 0] [1 1 0] [1] [1 0 0] [1] isPal(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = isPal(X) [0 0 0] [0] [0 0 0] [0] [1 1 1] [1] [1 0 0] [1] isPal(active(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = isPal(X) [0 0 0] [0] [0 0 0] [0] [1 1 0] [1 1 0] U81(mark(X)) = [0 0 0]X >= [0 0 0]X = U81(X) [0 0 0] [0 0 0] [1 1 1] [1 1 0] U81(active(X)) = [0 0 0]X >= [0 0 0]X = U81(X) [0 0 0] [0 0 0] [1 1 0] [0] [1 0 0] [0] isQid(mark(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = isQid(X) [0 0 0] [0] [0 0 0] [0] [1 1 1] [0] [1 0 0] [0] isQid(active(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = isQid(X) [0 0 0] [0] [0 0 0] [0] [1 1 0] [1] [1 0 0] [1] isNePal(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = isNePal(X) [0 0 0] [0] [0 0 0] [0] [1 1 1] [1] [1 0 0] [1] isNePal(active(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = isNePal(X) [0 0 0] [0] [0 0 0] [0] problem: active(U11(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt(),P)) -> mark(U72(isPal(P))) active(U81(tt())) -> mark(tt()) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(V)) -> mark(U81(isNePal(V))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X)) -> active(U11(mark(X))) mark(tt()) -> active(tt()) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X)) -> active(U22(mark(X))) mark(isList(X)) -> active(isList(X)) mark(U31(X)) -> active(U31(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isPal(X)) -> active(isPal(X)) mark(U81(X)) -> active(U81(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X)) -> U11(X) U11(active(X)) -> U11(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X)) -> U22(X) U22(active(X)) -> U22(X) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U31(mark(X)) -> U31(X) U31(active(X)) -> U31(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) Matrix Interpretation Processor: dim=1 interpretation: [U72](x0) = x0, [tt] = 0, [U61](x0) = x0, [U22](x0) = 4x0, [active](x0) = x0, [nil] = 6, [U71](x0, x1) = x0 + 4x1 + 6, [isNePal](x0) = x0, [u] = 2, [U81](x0) = 4x0 + 4, [isPal](x0) = 4x0 + 6, [a] = 0, [U11](x0) = 2x0, [U41](x0, x1) = x0 + x1 + 2, [__](x0, x1) = x0 + x1, [isList](x0) = x0, [isQid](x0) = x0, [o] = 0, [U52](x0) = 2x0 + 2, [U42](x0) = x0 + 6, [e] = 2, [i] = 2, [isNeList](x0) = x0 + 6, [U31](x0) = 2x0 + 6, [U51](x0, x1) = 2x0 + 2x1, [U21](x0, x1) = x0 + x1, [mark](x0) = x0 orientation: active(U11(tt())) = 0 >= 0 = mark(tt()) active(U61(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),P)) = 4P + 6 >= 4P + 6 = mark(U72(isPal(P))) active(U81(tt())) = 4 >= 0 = mark(tt()) active(isNePal(V)) = V >= V = mark(U61(isQid(V))) active(isPal(V)) = 4V + 6 >= 4V + 4 = mark(U81(isNePal(V))) mark(__(X1,X2)) = X1 + X2 >= X1 + X2 = active(__(mark(X1),mark(X2))) mark(nil()) = 6 >= 6 = active(nil()) mark(U11(X)) = 2X >= 2X = active(U11(mark(X))) mark(tt()) = 0 >= 0 = active(tt()) mark(U21(X1,X2)) = X1 + X2 >= X1 + X2 = active(U21(mark(X1),X2)) mark(U22(X)) = 4X >= 4X = active(U22(mark(X))) mark(isList(X)) = X >= X = active(isList(X)) mark(U31(X)) = 2X + 6 >= 2X + 6 = active(U31(mark(X))) mark(U41(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = active(U41(mark(X1),X2)) mark(U42(X)) = X + 6 >= X + 6 = active(U42(mark(X))) mark(isNeList(X)) = X + 6 >= X + 6 = active(isNeList(X)) mark(U51(X1,X2)) = 2X1 + 2X2 >= 2X1 + 2X2 = active(U51(mark(X1),X2)) mark(U52(X)) = 2X + 2 >= 2X + 2 = active(U52(mark(X))) mark(U61(X)) = X >= X = active(U61(mark(X))) mark(U71(X1,X2)) = X1 + 4X2 + 6 >= X1 + 4X2 + 6 = active(U71(mark(X1),X2)) mark(U72(X)) = X >= X = active(U72(mark(X))) mark(isPal(X)) = 4X + 6 >= 4X + 6 = active(isPal(X)) mark(U81(X)) = 4X + 4 >= 4X + 4 = active(U81(mark(X))) mark(isQid(X)) = X >= X = active(isQid(X)) mark(isNePal(X)) = X >= X = active(isNePal(X)) mark(a()) = 0 >= 0 = active(a()) mark(e()) = 2 >= 2 = active(e()) mark(i()) = 2 >= 2 = active(i()) mark(o()) = 0 >= 0 = active(o()) mark(u()) = 2 >= 2 = active(u()) __(mark(X1),X2) = X1 + X2 >= X1 + X2 = __(X1,X2) __(X1,mark(X2)) = X1 + X2 >= X1 + X2 = __(X1,X2) __(active(X1),X2) = X1 + X2 >= X1 + X2 = __(X1,X2) __(X1,active(X2)) = X1 + X2 >= X1 + X2 = __(X1,X2) U11(mark(X)) = 2X >= 2X = U11(X) U11(active(X)) = 2X >= 2X = U11(X) U21(mark(X1),X2) = X1 + X2 >= X1 + X2 = U21(X1,X2) U21(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U21(X1,X2) U21(active(X1),X2) = X1 + X2 >= X1 + X2 = U21(X1,X2) U21(X1,active(X2)) = X1 + X2 >= X1 + X2 = U21(X1,X2) U22(mark(X)) = 4X >= 4X = U22(X) U22(active(X)) = 4X >= 4X = U22(X) isList(mark(X)) = X >= X = isList(X) isList(active(X)) = X >= X = isList(X) U31(mark(X)) = 2X + 6 >= 2X + 6 = U31(X) U31(active(X)) = 2X + 6 >= 2X + 6 = U31(X) U41(mark(X1),X2) = X1 + X2 + 2 >= X1 + X2 + 2 = U41(X1,X2) U41(X1,mark(X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = U41(X1,X2) U41(active(X1),X2) = X1 + X2 + 2 >= X1 + X2 + 2 = U41(X1,X2) U41(X1,active(X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = U41(X1,X2) U42(mark(X)) = X + 6 >= X + 6 = U42(X) U42(active(X)) = X + 6 >= X + 6 = U42(X) isNeList(mark(X)) = X + 6 >= X + 6 = isNeList(X) isNeList(active(X)) = X + 6 >= X + 6 = isNeList(X) U51(mark(X1),X2) = 2X1 + 2X2 >= 2X1 + 2X2 = U51(X1,X2) U51(X1,mark(X2)) = 2X1 + 2X2 >= 2X1 + 2X2 = U51(X1,X2) U51(active(X1),X2) = 2X1 + 2X2 >= 2X1 + 2X2 = U51(X1,X2) U51(X1,active(X2)) = 2X1 + 2X2 >= 2X1 + 2X2 = U51(X1,X2) U52(mark(X)) = 2X + 2 >= 2X + 2 = U52(X) U52(active(X)) = 2X + 2 >= 2X + 2 = U52(X) U61(mark(X)) = X >= X = U61(X) U61(active(X)) = X >= X = U61(X) U71(mark(X1),X2) = X1 + 4X2 + 6 >= X1 + 4X2 + 6 = U71(X1,X2) U71(X1,mark(X2)) = X1 + 4X2 + 6 >= X1 + 4X2 + 6 = U71(X1,X2) U71(active(X1),X2) = X1 + 4X2 + 6 >= X1 + 4X2 + 6 = U71(X1,X2) U71(X1,active(X2)) = X1 + 4X2 + 6 >= X1 + 4X2 + 6 = U71(X1,X2) U72(mark(X)) = X >= X = U72(X) U72(active(X)) = X >= X = U72(X) isPal(mark(X)) = 4X + 6 >= 4X + 6 = isPal(X) isPal(active(X)) = 4X + 6 >= 4X + 6 = isPal(X) U81(mark(X)) = 4X + 4 >= 4X + 4 = U81(X) U81(active(X)) = 4X + 4 >= 4X + 4 = U81(X) isQid(mark(X)) = X >= X = isQid(X) isQid(active(X)) = X >= X = isQid(X) isNePal(mark(X)) = X >= X = isNePal(X) isNePal(active(X)) = X >= X = isNePal(X) problem: active(U11(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt(),P)) -> mark(U72(isPal(P))) active(isNePal(V)) -> mark(U61(isQid(V))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X)) -> active(U11(mark(X))) mark(tt()) -> active(tt()) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X)) -> active(U22(mark(X))) mark(isList(X)) -> active(isList(X)) mark(U31(X)) -> active(U31(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isPal(X)) -> active(isPal(X)) mark(U81(X)) -> active(U81(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X)) -> U11(X) U11(active(X)) -> U11(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X)) -> U22(X) U22(active(X)) -> U22(X) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U31(mark(X)) -> U31(X) U31(active(X)) -> U31(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) Matrix Interpretation Processor: dim=1 interpretation: [U72](x0) = x0 + 4, [tt] = 0, [U61](x0) = x0 + 5, [U22](x0) = x0 + 4, [active](x0) = x0, [nil] = 0, [U71](x0, x1) = 4x0 + 4x1 + 4, [isNePal](x0) = 2x0 + 5, [u] = 0, [U81](x0) = x0 + 4, [isPal](x0) = 4x0, [a] = 2, [U11](x0) = x0, [U41](x0, x1) = 4x0 + x1, [__](x0, x1) = 4x0 + 2x1, [isList](x0) = x0 + 4, [isQid](x0) = 2x0, [o] = 0, [U52](x0) = x0, [U42](x0) = 2x0, [e] = 2, [i] = 4, [isNeList](x0) = x0 + 4, [U31](x0) = x0, [U51](x0, x1) = 4x0 + x1 + 4, [U21](x0, x1) = x0 + x1, [mark](x0) = x0 orientation: active(U11(tt())) = 0 >= 0 = mark(tt()) active(U61(tt())) = 5 >= 0 = mark(tt()) active(U71(tt(),P)) = 4P + 4 >= 4P + 4 = mark(U72(isPal(P))) active(isNePal(V)) = 2V + 5 >= 2V + 5 = mark(U61(isQid(V))) mark(__(X1,X2)) = 4X1 + 2X2 >= 4X1 + 2X2 = active(__(mark(X1),mark(X2))) mark(nil()) = 0 >= 0 = active(nil()) mark(U11(X)) = X >= X = active(U11(mark(X))) mark(tt()) = 0 >= 0 = active(tt()) mark(U21(X1,X2)) = X1 + X2 >= X1 + X2 = active(U21(mark(X1),X2)) mark(U22(X)) = X + 4 >= X + 4 = active(U22(mark(X))) mark(isList(X)) = X + 4 >= X + 4 = active(isList(X)) mark(U31(X)) = X >= X = active(U31(mark(X))) mark(U41(X1,X2)) = 4X1 + X2 >= 4X1 + X2 = active(U41(mark(X1),X2)) mark(U42(X)) = 2X >= 2X = active(U42(mark(X))) mark(isNeList(X)) = X + 4 >= X + 4 = active(isNeList(X)) mark(U51(X1,X2)) = 4X1 + X2 + 4 >= 4X1 + X2 + 4 = active(U51(mark(X1),X2)) mark(U52(X)) = X >= X = active(U52(mark(X))) mark(U61(X)) = X + 5 >= X + 5 = active(U61(mark(X))) mark(U71(X1,X2)) = 4X1 + 4X2 + 4 >= 4X1 + 4X2 + 4 = active(U71(mark(X1),X2)) mark(U72(X)) = X + 4 >= X + 4 = active(U72(mark(X))) mark(isPal(X)) = 4X >= 4X = active(isPal(X)) mark(U81(X)) = X + 4 >= X + 4 = active(U81(mark(X))) mark(isQid(X)) = 2X >= 2X = active(isQid(X)) mark(isNePal(X)) = 2X + 5 >= 2X + 5 = active(isNePal(X)) mark(a()) = 2 >= 2 = active(a()) mark(e()) = 2 >= 2 = active(e()) mark(i()) = 4 >= 4 = active(i()) mark(o()) = 0 >= 0 = active(o()) mark(u()) = 0 >= 0 = active(u()) __(mark(X1),X2) = 4X1 + 2X2 >= 4X1 + 2X2 = __(X1,X2) __(X1,mark(X2)) = 4X1 + 2X2 >= 4X1 + 2X2 = __(X1,X2) __(active(X1),X2) = 4X1 + 2X2 >= 4X1 + 2X2 = __(X1,X2) __(X1,active(X2)) = 4X1 + 2X2 >= 4X1 + 2X2 = __(X1,X2) U11(mark(X)) = X >= X = U11(X) U11(active(X)) = X >= X = U11(X) U21(mark(X1),X2) = X1 + X2 >= X1 + X2 = U21(X1,X2) U21(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U21(X1,X2) U21(active(X1),X2) = X1 + X2 >= X1 + X2 = U21(X1,X2) U21(X1,active(X2)) = X1 + X2 >= X1 + X2 = U21(X1,X2) U22(mark(X)) = X + 4 >= X + 4 = U22(X) U22(active(X)) = X + 4 >= X + 4 = U22(X) isList(mark(X)) = X + 4 >= X + 4 = isList(X) isList(active(X)) = X + 4 >= X + 4 = isList(X) U31(mark(X)) = X >= X = U31(X) U31(active(X)) = X >= X = U31(X) U41(mark(X1),X2) = 4X1 + X2 >= 4X1 + X2 = U41(X1,X2) U41(X1,mark(X2)) = 4X1 + X2 >= 4X1 + X2 = U41(X1,X2) U41(active(X1),X2) = 4X1 + X2 >= 4X1 + X2 = U41(X1,X2) U41(X1,active(X2)) = 4X1 + X2 >= 4X1 + X2 = U41(X1,X2) U42(mark(X)) = 2X >= 2X = U42(X) U42(active(X)) = 2X >= 2X = U42(X) isNeList(mark(X)) = X + 4 >= X + 4 = isNeList(X) isNeList(active(X)) = X + 4 >= X + 4 = isNeList(X) U51(mark(X1),X2) = 4X1 + X2 + 4 >= 4X1 + X2 + 4 = U51(X1,X2) U51(X1,mark(X2)) = 4X1 + X2 + 4 >= 4X1 + X2 + 4 = U51(X1,X2) U51(active(X1),X2) = 4X1 + X2 + 4 >= 4X1 + X2 + 4 = U51(X1,X2) U51(X1,active(X2)) = 4X1 + X2 + 4 >= 4X1 + X2 + 4 = U51(X1,X2) U52(mark(X)) = X >= X = U52(X) U52(active(X)) = X >= X = U52(X) U61(mark(X)) = X + 5 >= X + 5 = U61(X) U61(active(X)) = X + 5 >= X + 5 = U61(X) U71(mark(X1),X2) = 4X1 + 4X2 + 4 >= 4X1 + 4X2 + 4 = U71(X1,X2) U71(X1,mark(X2)) = 4X1 + 4X2 + 4 >= 4X1 + 4X2 + 4 = U71(X1,X2) U71(active(X1),X2) = 4X1 + 4X2 + 4 >= 4X1 + 4X2 + 4 = U71(X1,X2) U71(X1,active(X2)) = 4X1 + 4X2 + 4 >= 4X1 + 4X2 + 4 = U71(X1,X2) U72(mark(X)) = X + 4 >= X + 4 = U72(X) U72(active(X)) = X + 4 >= X + 4 = U72(X) isPal(mark(X)) = 4X >= 4X = isPal(X) isPal(active(X)) = 4X >= 4X = isPal(X) U81(mark(X)) = X + 4 >= X + 4 = U81(X) U81(active(X)) = X + 4 >= X + 4 = U81(X) isQid(mark(X)) = 2X >= 2X = isQid(X) isQid(active(X)) = 2X >= 2X = isQid(X) isNePal(mark(X)) = 2X + 5 >= 2X + 5 = isNePal(X) isNePal(active(X)) = 2X + 5 >= 2X + 5 = isNePal(X) problem: active(U11(tt())) -> mark(tt()) active(U71(tt(),P)) -> mark(U72(isPal(P))) active(isNePal(V)) -> mark(U61(isQid(V))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X)) -> active(U11(mark(X))) mark(tt()) -> active(tt()) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X)) -> active(U22(mark(X))) mark(isList(X)) -> active(isList(X)) mark(U31(X)) -> active(U31(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isPal(X)) -> active(isPal(X)) mark(U81(X)) -> active(U81(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X)) -> U11(X) U11(active(X)) -> U11(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X)) -> U22(X) U22(active(X)) -> U22(X) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U31(mark(X)) -> U31(X) U31(active(X)) -> U31(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) Matrix Interpretation Processor: dim=1 interpretation: [U72](x0) = x0 + 4, [tt] = 4, [U61](x0) = 2x0, [U22](x0) = 6x0, [active](x0) = x0, [nil] = 0, [U71](x0, x1) = 2x0 + 4x1 + 2, [isNePal](x0) = 4x0, [u] = 0, [U81](x0) = 4x0, [isPal](x0) = 2x0 + 1, [a] = 0, [U11](x0) = 4x0 + 1, [U41](x0, x1) = 2x0 + 2x1 + 4, [__](x0, x1) = 4x0 + 4x1, [isList](x0) = x0 + 4, [isQid](x0) = x0, [o] = 0, [U52](x0) = x0, [U42](x0) = x0, [e] = 0, [i] = 0, [isNeList](x0) = 4x0, [U31](x0) = 2x0, [U51](x0, x1) = 2x0 + x1, [U21](x0, x1) = x0 + x1, [mark](x0) = 2x0 orientation: active(U11(tt())) = 17 >= 8 = mark(tt()) active(U71(tt(),P)) = 4P + 10 >= 4P + 10 = mark(U72(isPal(P))) active(isNePal(V)) = 4V >= 4V = mark(U61(isQid(V))) mark(__(X1,X2)) = 8X1 + 8X2 >= 8X1 + 8X2 = active(__(mark(X1),mark(X2))) mark(nil()) = 0 >= 0 = active(nil()) mark(U11(X)) = 8X + 2 >= 8X + 1 = active(U11(mark(X))) mark(tt()) = 8 >= 4 = active(tt()) mark(U21(X1,X2)) = 2X1 + 2X2 >= 2X1 + X2 = active(U21(mark(X1),X2)) mark(U22(X)) = 12X >= 12X = active(U22(mark(X))) mark(isList(X)) = 2X + 8 >= X + 4 = active(isList(X)) mark(U31(X)) = 4X >= 4X = active(U31(mark(X))) mark(U41(X1,X2)) = 4X1 + 4X2 + 8 >= 4X1 + 2X2 + 4 = active(U41(mark(X1),X2)) mark(U42(X)) = 2X >= 2X = active(U42(mark(X))) mark(isNeList(X)) = 8X >= 4X = active(isNeList(X)) mark(U51(X1,X2)) = 4X1 + 2X2 >= 4X1 + X2 = active(U51(mark(X1),X2)) mark(U52(X)) = 2X >= 2X = active(U52(mark(X))) mark(U61(X)) = 4X >= 4X = active(U61(mark(X))) mark(U71(X1,X2)) = 4X1 + 8X2 + 4 >= 4X1 + 4X2 + 2 = active(U71(mark(X1),X2)) mark(U72(X)) = 2X + 8 >= 2X + 4 = active(U72(mark(X))) mark(isPal(X)) = 4X + 2 >= 2X + 1 = active(isPal(X)) mark(U81(X)) = 8X >= 8X = active(U81(mark(X))) mark(isQid(X)) = 2X >= X = active(isQid(X)) mark(isNePal(X)) = 8X >= 4X = active(isNePal(X)) mark(a()) = 0 >= 0 = active(a()) mark(e()) = 0 >= 0 = active(e()) mark(i()) = 0 >= 0 = active(i()) mark(o()) = 0 >= 0 = active(o()) mark(u()) = 0 >= 0 = active(u()) __(mark(X1),X2) = 8X1 + 4X2 >= 4X1 + 4X2 = __(X1,X2) __(X1,mark(X2)) = 4X1 + 8X2 >= 4X1 + 4X2 = __(X1,X2) __(active(X1),X2) = 4X1 + 4X2 >= 4X1 + 4X2 = __(X1,X2) __(X1,active(X2)) = 4X1 + 4X2 >= 4X1 + 4X2 = __(X1,X2) U11(mark(X)) = 8X + 1 >= 4X + 1 = U11(X) U11(active(X)) = 4X + 1 >= 4X + 1 = U11(X) U21(mark(X1),X2) = 2X1 + X2 >= X1 + X2 = U21(X1,X2) U21(X1,mark(X2)) = X1 + 2X2 >= X1 + X2 = U21(X1,X2) U21(active(X1),X2) = X1 + X2 >= X1 + X2 = U21(X1,X2) U21(X1,active(X2)) = X1 + X2 >= X1 + X2 = U21(X1,X2) U22(mark(X)) = 12X >= 6X = U22(X) U22(active(X)) = 6X >= 6X = U22(X) isList(mark(X)) = 2X + 4 >= X + 4 = isList(X) isList(active(X)) = X + 4 >= X + 4 = isList(X) U31(mark(X)) = 4X >= 2X = U31(X) U31(active(X)) = 2X >= 2X = U31(X) U41(mark(X1),X2) = 4X1 + 2X2 + 4 >= 2X1 + 2X2 + 4 = U41(X1,X2) U41(X1,mark(X2)) = 2X1 + 4X2 + 4 >= 2X1 + 2X2 + 4 = U41(X1,X2) U41(active(X1),X2) = 2X1 + 2X2 + 4 >= 2X1 + 2X2 + 4 = U41(X1,X2) U41(X1,active(X2)) = 2X1 + 2X2 + 4 >= 2X1 + 2X2 + 4 = U41(X1,X2) U42(mark(X)) = 2X >= X = U42(X) U42(active(X)) = X >= X = U42(X) isNeList(mark(X)) = 8X >= 4X = isNeList(X) isNeList(active(X)) = 4X >= 4X = isNeList(X) U51(mark(X1),X2) = 4X1 + X2 >= 2X1 + X2 = U51(X1,X2) U51(X1,mark(X2)) = 2X1 + 2X2 >= 2X1 + X2 = U51(X1,X2) U51(active(X1),X2) = 2X1 + X2 >= 2X1 + X2 = U51(X1,X2) U51(X1,active(X2)) = 2X1 + X2 >= 2X1 + X2 = U51(X1,X2) U52(mark(X)) = 2X >= X = U52(X) U52(active(X)) = X >= X = U52(X) U61(mark(X)) = 4X >= 2X = U61(X) U61(active(X)) = 2X >= 2X = U61(X) U71(mark(X1),X2) = 4X1 + 4X2 + 2 >= 2X1 + 4X2 + 2 = U71(X1,X2) U71(X1,mark(X2)) = 2X1 + 8X2 + 2 >= 2X1 + 4X2 + 2 = U71(X1,X2) U71(active(X1),X2) = 2X1 + 4X2 + 2 >= 2X1 + 4X2 + 2 = U71(X1,X2) U71(X1,active(X2)) = 2X1 + 4X2 + 2 >= 2X1 + 4X2 + 2 = U71(X1,X2) U72(mark(X)) = 2X + 4 >= X + 4 = U72(X) U72(active(X)) = X + 4 >= X + 4 = U72(X) isPal(mark(X)) = 4X + 1 >= 2X + 1 = isPal(X) isPal(active(X)) = 2X + 1 >= 2X + 1 = isPal(X) U81(mark(X)) = 8X >= 4X = U81(X) U81(active(X)) = 4X >= 4X = U81(X) isQid(mark(X)) = 2X >= X = isQid(X) isQid(active(X)) = X >= X = isQid(X) isNePal(mark(X)) = 8X >= 4X = isNePal(X) isNePal(active(X)) = 4X >= 4X = isNePal(X) problem: active(U71(tt(),P)) -> mark(U72(isPal(P))) active(isNePal(V)) -> mark(U61(isQid(V))) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X)) -> active(U22(mark(X))) mark(U31(X)) -> active(U31(mark(X))) mark(U42(X)) -> active(U42(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X)) -> U11(X) U11(active(X)) -> U11(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X)) -> U22(X) U22(active(X)) -> U22(X) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U31(mark(X)) -> U31(X) U31(active(X)) -> U31(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) Matrix Interpretation Processor: dim=1 interpretation: [U72](x0) = x0 + 1, [tt] = 7, [U61](x0) = x0 + 1, [U22](x0) = 4x0, [active](x0) = x0, [nil] = 0, [U71](x0, x1) = 2x0 + 4x1 + 1, [isNePal](x0) = 5x0 + 4, [u] = 0, [U81](x0) = 2x0, [isPal](x0) = x0, [a] = 0, [U11](x0) = 2x0 + 2, [U41](x0, x1) = 2x0 + x1, [__](x0, x1) = x0 + x1 + 2, [isList](x0) = 4x0 + 6, [isQid](x0) = x0, [o] = 2, [U52](x0) = x0 + 2, [U42](x0) = x0, [e] = 0, [i] = 0, [isNeList](x0) = 2x0, [U31](x0) = 4x0, [U51](x0, x1) = 2x0 + 2x1 + 2, [U21](x0, x1) = 4x0 + 4x1 + 6, [mark](x0) = 4x0 orientation: active(U71(tt(),P)) = 4P + 15 >= 4P + 4 = mark(U72(isPal(P))) active(isNePal(V)) = 5V + 4 >= 4V + 4 = mark(U61(isQid(V))) mark(__(X1,X2)) = 4X1 + 4X2 + 8 >= 4X1 + 4X2 + 2 = active(__(mark(X1),mark(X2))) mark(nil()) = 0 >= 0 = active(nil()) mark(U21(X1,X2)) = 16X1 + 16X2 + 24 >= 16X1 + 4X2 + 6 = active(U21(mark(X1),X2)) mark(U22(X)) = 16X >= 16X = active(U22(mark(X))) mark(U31(X)) = 16X >= 16X = active(U31(mark(X))) mark(U42(X)) = 4X >= 4X = active(U42(mark(X))) mark(isNeList(X)) = 8X >= 2X = active(isNeList(X)) mark(U51(X1,X2)) = 8X1 + 8X2 + 8 >= 8X1 + 2X2 + 2 = active(U51(mark(X1),X2)) mark(U52(X)) = 4X + 8 >= 4X + 2 = active(U52(mark(X))) mark(U61(X)) = 4X + 4 >= 4X + 1 = active(U61(mark(X))) mark(U81(X)) = 8X >= 8X = active(U81(mark(X))) mark(isQid(X)) = 4X >= X = active(isQid(X)) mark(isNePal(X)) = 20X + 16 >= 5X + 4 = active(isNePal(X)) mark(a()) = 0 >= 0 = active(a()) mark(e()) = 0 >= 0 = active(e()) mark(i()) = 0 >= 0 = active(i()) mark(o()) = 8 >= 2 = active(o()) mark(u()) = 0 >= 0 = active(u()) __(mark(X1),X2) = 4X1 + X2 + 2 >= X1 + X2 + 2 = __(X1,X2) __(X1,mark(X2)) = X1 + 4X2 + 2 >= X1 + X2 + 2 = __(X1,X2) __(active(X1),X2) = X1 + X2 + 2 >= X1 + X2 + 2 = __(X1,X2) __(X1,active(X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = __(X1,X2) U11(mark(X)) = 8X + 2 >= 2X + 2 = U11(X) U11(active(X)) = 2X + 2 >= 2X + 2 = U11(X) U21(mark(X1),X2) = 16X1 + 4X2 + 6 >= 4X1 + 4X2 + 6 = U21(X1,X2) U21(X1,mark(X2)) = 4X1 + 16X2 + 6 >= 4X1 + 4X2 + 6 = U21(X1,X2) U21(active(X1),X2) = 4X1 + 4X2 + 6 >= 4X1 + 4X2 + 6 = U21(X1,X2) U21(X1,active(X2)) = 4X1 + 4X2 + 6 >= 4X1 + 4X2 + 6 = U21(X1,X2) U22(mark(X)) = 16X >= 4X = U22(X) U22(active(X)) = 4X >= 4X = U22(X) isList(mark(X)) = 16X + 6 >= 4X + 6 = isList(X) isList(active(X)) = 4X + 6 >= 4X + 6 = isList(X) U31(mark(X)) = 16X >= 4X = U31(X) U31(active(X)) = 4X >= 4X = U31(X) U41(mark(X1),X2) = 8X1 + X2 >= 2X1 + X2 = U41(X1,X2) U41(X1,mark(X2)) = 2X1 + 4X2 >= 2X1 + X2 = U41(X1,X2) U41(active(X1),X2) = 2X1 + X2 >= 2X1 + X2 = U41(X1,X2) U41(X1,active(X2)) = 2X1 + X2 >= 2X1 + X2 = U41(X1,X2) U42(mark(X)) = 4X >= X = U42(X) U42(active(X)) = X >= X = U42(X) isNeList(mark(X)) = 8X >= 2X = isNeList(X) isNeList(active(X)) = 2X >= 2X = isNeList(X) U51(mark(X1),X2) = 8X1 + 2X2 + 2 >= 2X1 + 2X2 + 2 = U51(X1,X2) U51(X1,mark(X2)) = 2X1 + 8X2 + 2 >= 2X1 + 2X2 + 2 = U51(X1,X2) U51(active(X1),X2) = 2X1 + 2X2 + 2 >= 2X1 + 2X2 + 2 = U51(X1,X2) U51(X1,active(X2)) = 2X1 + 2X2 + 2 >= 2X1 + 2X2 + 2 = U51(X1,X2) U52(mark(X)) = 4X + 2 >= X + 2 = U52(X) U52(active(X)) = X + 2 >= X + 2 = U52(X) U61(mark(X)) = 4X + 1 >= X + 1 = U61(X) U61(active(X)) = X + 1 >= X + 1 = U61(X) U71(mark(X1),X2) = 8X1 + 4X2 + 1 >= 2X1 + 4X2 + 1 = U71(X1,X2) U71(X1,mark(X2)) = 2X1 + 16X2 + 1 >= 2X1 + 4X2 + 1 = U71(X1,X2) U71(active(X1),X2) = 2X1 + 4X2 + 1 >= 2X1 + 4X2 + 1 = U71(X1,X2) U71(X1,active(X2)) = 2X1 + 4X2 + 1 >= 2X1 + 4X2 + 1 = U71(X1,X2) U72(mark(X)) = 4X + 1 >= X + 1 = U72(X) U72(active(X)) = X + 1 >= X + 1 = U72(X) isPal(mark(X)) = 4X >= X = isPal(X) isPal(active(X)) = X >= X = isPal(X) U81(mark(X)) = 8X >= 2X = U81(X) U81(active(X)) = 2X >= 2X = U81(X) isQid(mark(X)) = 4X >= X = isQid(X) isQid(active(X)) = X >= X = isQid(X) isNePal(mark(X)) = 20X + 4 >= 5X + 4 = isNePal(X) isNePal(active(X)) = 5X + 4 >= 5X + 4 = isNePal(X) problem: active(isNePal(V)) -> mark(U61(isQid(V))) mark(nil()) -> active(nil()) mark(U22(X)) -> active(U22(mark(X))) mark(U31(X)) -> active(U31(mark(X))) mark(U42(X)) -> active(U42(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U81(X)) -> active(U81(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X)) -> U11(X) U11(active(X)) -> U11(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X)) -> U22(X) U22(active(X)) -> U22(X) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U31(mark(X)) -> U31(X) U31(active(X)) -> U31(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) Matrix Interpretation Processor: dim=1 interpretation: [U72](x0) = x0, [U61](x0) = x0, [U22](x0) = x0, [active](x0) = x0, [nil] = 4, [U71](x0, x1) = x0 + x1, [isNePal](x0) = 4x0 + 4, [u] = 5, [U81](x0) = 4x0, [isPal](x0) = x0 + 4, [a] = 0, [U11](x0) = 2x0 + 2, [U41](x0, x1) = 2x0 + 2x1 + 2, [__](x0, x1) = 4x0 + x1, [isList](x0) = 2x0 + 7, [isQid](x0) = x0, [U52](x0) = x0 + 4, [U42](x0) = x0, [e] = 0, [i] = 0, [isNeList](x0) = 4x0 + 2, [U31](x0) = 2x0, [U51](x0, x1) = 2x0 + 2x1, [U21](x0, x1) = 4x0 + x1, [mark](x0) = 4x0 orientation: active(isNePal(V)) = 4V + 4 >= 4V = mark(U61(isQid(V))) mark(nil()) = 16 >= 4 = active(nil()) mark(U22(X)) = 4X >= 4X = active(U22(mark(X))) mark(U31(X)) = 8X >= 8X = active(U31(mark(X))) mark(U42(X)) = 4X >= 4X = active(U42(mark(X))) mark(isNeList(X)) = 16X + 8 >= 4X + 2 = active(isNeList(X)) mark(U81(X)) = 16X >= 16X = active(U81(mark(X))) mark(isQid(X)) = 4X >= X = active(isQid(X)) mark(a()) = 0 >= 0 = active(a()) mark(e()) = 0 >= 0 = active(e()) mark(i()) = 0 >= 0 = active(i()) mark(u()) = 20 >= 5 = active(u()) __(mark(X1),X2) = 16X1 + X2 >= 4X1 + X2 = __(X1,X2) __(X1,mark(X2)) = 4X1 + 4X2 >= 4X1 + X2 = __(X1,X2) __(active(X1),X2) = 4X1 + X2 >= 4X1 + X2 = __(X1,X2) __(X1,active(X2)) = 4X1 + X2 >= 4X1 + X2 = __(X1,X2) U11(mark(X)) = 8X + 2 >= 2X + 2 = U11(X) U11(active(X)) = 2X + 2 >= 2X + 2 = U11(X) U21(mark(X1),X2) = 16X1 + X2 >= 4X1 + X2 = U21(X1,X2) U21(X1,mark(X2)) = 4X1 + 4X2 >= 4X1 + X2 = U21(X1,X2) U21(active(X1),X2) = 4X1 + X2 >= 4X1 + X2 = U21(X1,X2) U21(X1,active(X2)) = 4X1 + X2 >= 4X1 + X2 = U21(X1,X2) U22(mark(X)) = 4X >= X = U22(X) U22(active(X)) = X >= X = U22(X) isList(mark(X)) = 8X + 7 >= 2X + 7 = isList(X) isList(active(X)) = 2X + 7 >= 2X + 7 = isList(X) U31(mark(X)) = 8X >= 2X = U31(X) U31(active(X)) = 2X >= 2X = U31(X) U41(mark(X1),X2) = 8X1 + 2X2 + 2 >= 2X1 + 2X2 + 2 = U41(X1,X2) U41(X1,mark(X2)) = 2X1 + 8X2 + 2 >= 2X1 + 2X2 + 2 = U41(X1,X2) U41(active(X1),X2) = 2X1 + 2X2 + 2 >= 2X1 + 2X2 + 2 = U41(X1,X2) U41(X1,active(X2)) = 2X1 + 2X2 + 2 >= 2X1 + 2X2 + 2 = U41(X1,X2) U42(mark(X)) = 4X >= X = U42(X) U42(active(X)) = X >= X = U42(X) isNeList(mark(X)) = 16X + 2 >= 4X + 2 = isNeList(X) isNeList(active(X)) = 4X + 2 >= 4X + 2 = isNeList(X) U51(mark(X1),X2) = 8X1 + 2X2 >= 2X1 + 2X2 = U51(X1,X2) U51(X1,mark(X2)) = 2X1 + 8X2 >= 2X1 + 2X2 = U51(X1,X2) U51(active(X1),X2) = 2X1 + 2X2 >= 2X1 + 2X2 = U51(X1,X2) U51(X1,active(X2)) = 2X1 + 2X2 >= 2X1 + 2X2 = U51(X1,X2) U52(mark(X)) = 4X + 4 >= X + 4 = U52(X) U52(active(X)) = X + 4 >= X + 4 = U52(X) U61(mark(X)) = 4X >= X = U61(X) U61(active(X)) = X >= X = U61(X) U71(mark(X1),X2) = 4X1 + X2 >= X1 + X2 = U71(X1,X2) U71(X1,mark(X2)) = X1 + 4X2 >= X1 + X2 = U71(X1,X2) U71(active(X1),X2) = X1 + X2 >= X1 + X2 = U71(X1,X2) U71(X1,active(X2)) = X1 + X2 >= X1 + X2 = U71(X1,X2) U72(mark(X)) = 4X >= X = U72(X) U72(active(X)) = X >= X = U72(X) isPal(mark(X)) = 4X + 4 >= X + 4 = isPal(X) isPal(active(X)) = X + 4 >= X + 4 = isPal(X) U81(mark(X)) = 16X >= 4X = U81(X) U81(active(X)) = 4X >= 4X = U81(X) isQid(mark(X)) = 4X >= X = isQid(X) isQid(active(X)) = X >= X = isQid(X) isNePal(mark(X)) = 16X + 4 >= 4X + 4 = isNePal(X) isNePal(active(X)) = 4X + 4 >= 4X + 4 = isNePal(X) problem: mark(U22(X)) -> active(U22(mark(X))) mark(U31(X)) -> active(U31(mark(X))) mark(U42(X)) -> active(U42(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X)) -> U11(X) U11(active(X)) -> U11(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X)) -> U22(X) U22(active(X)) -> U22(X) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U31(mark(X)) -> U31(X) U31(active(X)) -> U31(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) Matrix Interpretation Processor: dim=1 interpretation: [U72](x0) = 2x0 + 7, [U61](x0) = 4x0 + 2, [U22](x0) = x0, [active](x0) = x0, [U71](x0, x1) = 3x0 + 2x1, [isNePal](x0) = 4x0 + 4, [U81](x0) = x0 + 6, [isPal](x0) = 4x0 + 6, [a] = 0, [U11](x0) = 2x0, [U41](x0, x1) = x0 + 4x1, [__](x0, x1) = 6x0 + x1 + 3, [isList](x0) = x0 + 4, [isQid](x0) = 2x0 + 1, [U52](x0) = 4x0 + 4, [U42](x0) = 4x0, [e] = 0, [i] = 0, [isNeList](x0) = x0, [U31](x0) = x0 + 1, [U51](x0, x1) = 2x0 + x1, [U21](x0, x1) = 4x0 + 2x1, [mark](x0) = 4x0 orientation: mark(U22(X)) = 4X >= 4X = active(U22(mark(X))) mark(U31(X)) = 4X + 4 >= 4X + 1 = active(U31(mark(X))) mark(U42(X)) = 16X >= 16X = active(U42(mark(X))) mark(U81(X)) = 4X + 24 >= 4X + 6 = active(U81(mark(X))) mark(isQid(X)) = 8X + 4 >= 2X + 1 = active(isQid(X)) mark(a()) = 0 >= 0 = active(a()) mark(e()) = 0 >= 0 = active(e()) mark(i()) = 0 >= 0 = active(i()) __(mark(X1),X2) = 24X1 + X2 + 3 >= 6X1 + X2 + 3 = __(X1,X2) __(X1,mark(X2)) = 6X1 + 4X2 + 3 >= 6X1 + X2 + 3 = __(X1,X2) __(active(X1),X2) = 6X1 + X2 + 3 >= 6X1 + X2 + 3 = __(X1,X2) __(X1,active(X2)) = 6X1 + X2 + 3 >= 6X1 + X2 + 3 = __(X1,X2) U11(mark(X)) = 8X >= 2X = U11(X) U11(active(X)) = 2X >= 2X = U11(X) U21(mark(X1),X2) = 16X1 + 2X2 >= 4X1 + 2X2 = U21(X1,X2) U21(X1,mark(X2)) = 4X1 + 8X2 >= 4X1 + 2X2 = U21(X1,X2) U21(active(X1),X2) = 4X1 + 2X2 >= 4X1 + 2X2 = U21(X1,X2) U21(X1,active(X2)) = 4X1 + 2X2 >= 4X1 + 2X2 = U21(X1,X2) U22(mark(X)) = 4X >= X = U22(X) U22(active(X)) = X >= X = U22(X) isList(mark(X)) = 4X + 4 >= X + 4 = isList(X) isList(active(X)) = X + 4 >= X + 4 = isList(X) U31(mark(X)) = 4X + 1 >= X + 1 = U31(X) U31(active(X)) = X + 1 >= X + 1 = U31(X) U41(mark(X1),X2) = 4X1 + 4X2 >= X1 + 4X2 = U41(X1,X2) U41(X1,mark(X2)) = X1 + 16X2 >= X1 + 4X2 = U41(X1,X2) U41(active(X1),X2) = X1 + 4X2 >= X1 + 4X2 = U41(X1,X2) U41(X1,active(X2)) = X1 + 4X2 >= X1 + 4X2 = U41(X1,X2) U42(mark(X)) = 16X >= 4X = U42(X) U42(active(X)) = 4X >= 4X = U42(X) isNeList(mark(X)) = 4X >= X = isNeList(X) isNeList(active(X)) = X >= X = isNeList(X) U51(mark(X1),X2) = 8X1 + X2 >= 2X1 + X2 = U51(X1,X2) U51(X1,mark(X2)) = 2X1 + 4X2 >= 2X1 + X2 = U51(X1,X2) U51(active(X1),X2) = 2X1 + X2 >= 2X1 + X2 = U51(X1,X2) U51(X1,active(X2)) = 2X1 + X2 >= 2X1 + X2 = U51(X1,X2) U52(mark(X)) = 16X + 4 >= 4X + 4 = U52(X) U52(active(X)) = 4X + 4 >= 4X + 4 = U52(X) U61(mark(X)) = 16X + 2 >= 4X + 2 = U61(X) U61(active(X)) = 4X + 2 >= 4X + 2 = U61(X) U71(mark(X1),X2) = 12X1 + 2X2 >= 3X1 + 2X2 = U71(X1,X2) U71(X1,mark(X2)) = 3X1 + 8X2 >= 3X1 + 2X2 = U71(X1,X2) U71(active(X1),X2) = 3X1 + 2X2 >= 3X1 + 2X2 = U71(X1,X2) U71(X1,active(X2)) = 3X1 + 2X2 >= 3X1 + 2X2 = U71(X1,X2) U72(mark(X)) = 8X + 7 >= 2X + 7 = U72(X) U72(active(X)) = 2X + 7 >= 2X + 7 = U72(X) isPal(mark(X)) = 16X + 6 >= 4X + 6 = isPal(X) isPal(active(X)) = 4X + 6 >= 4X + 6 = isPal(X) U81(mark(X)) = 4X + 6 >= X + 6 = U81(X) U81(active(X)) = X + 6 >= X + 6 = U81(X) isQid(mark(X)) = 8X + 1 >= 2X + 1 = isQid(X) isQid(active(X)) = 2X + 1 >= 2X + 1 = isQid(X) isNePal(mark(X)) = 16X + 4 >= 4X + 4 = isNePal(X) isNePal(active(X)) = 4X + 4 >= 4X + 4 = isNePal(X) problem: mark(U22(X)) -> active(U22(mark(X))) mark(U42(X)) -> active(U42(mark(X))) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(mark(X)) -> U11(X) U11(active(X)) -> U11(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X)) -> U22(X) U22(active(X)) -> U22(X) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U31(mark(X)) -> U31(X) U31(active(X)) -> U31(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 1] [U72](x0) = [0 0 0]x0 [1 0 1] , [1 0 0] [1] [U61](x0) = [0 0 0]x0 + [1] [0 0 0] [0], [1 0 1] [0] [U22](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [1 1 0] [active](x0) = [1 0 0]x0 [0 0 1] , [1 0 0] [1 0 0] [U71](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [0] [isNePal](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [1 0 0] [U81](x0) = [0 0 0]x0 [1 0 1] , [1 0 0] [isPal](x0) = [0 0 0]x0 [1 0 0] , [0] [a] = [0] [1], [1 0 1] [0] [U11](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 1] [1 0 0] [__](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [1 0 0] [0 0 0] , [1 0 0] [isList](x0) = [0 0 0]x0 [0 0 0] , [1 0 1] [isQid](x0) = [1 0 1]x0 [0 0 0] , [1 0 0] [0] [U52](x0) = [0 0 0]x0 + [1] [0 0 0] [0], [1 0 1] [0] [U42](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [0] [e] = [1] [1], [0] [i] = [1] [1], [1 0 1] [0] [isNeList](x0) = [1 0 0]x0 + [1] [0 0 0] [0], [1 0 0] [U31](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [U51](x0, x1) = [1 0 1]x0 + [0 0 0]x1 [1 0 0] [0 0 0] , [1 0 0] [1 0 0] [U21](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 1] [0] [mark](x0) = [1 0 1]x0 + [0] [0 0 0] [1] orientation: [1 0 1] [1] [1 0 1] [1] mark(U22(X)) = [1 0 1]X + [1] >= [1 0 1]X + [1] = active(U22(mark(X))) [0 0 0] [1] [0 0 0] [1] [1 0 1] [1] [1 0 1] [1] mark(U42(X)) = [1 0 1]X + [1] >= [1 0 1]X + [1] = active(U42(mark(X))) [0 0 0] [1] [0 0 0] [1] [1] [0] mark(a()) = [1] >= [0] = active(a()) [1] [1] [1] [1] mark(e()) = [1] >= [0] = active(e()) [1] [1] [1] [1] mark(i()) = [1] >= [0] = active(i()) [1] [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 + [0] >= [0 0 0]X1 + [0 0 0]X2 = __(X1,X2) [1 0 1] [0 0 0] [0] [1 0 0] [0 0 0] [1 0 1] [1 0 1] [1 0 1] [1 0 0] __(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = __(X1,X2) [1 0 0] [0 0 0] [1 0 0] [0 0 0] [1 1 1] [1 0 0] [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 = __(X1,X2) [1 1 0] [0 0 0] [1 0 0] [0 0 0] [1 0 1] [1 1 0] [1 0 1] [1 0 0] __(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = __(X1,X2) [1 0 0] [0 0 0] [1 0 0] [0 0 0] [1 0 1] [1] [1 0 1] [0] U11(mark(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = U11(X) [0 0 0] [0] [0 0 0] [0] [1 1 1] [0] [1 0 1] [0] U11(active(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = U11(X) [0 0 0] [0] [0 0 0] [0] [1 0 1] [1 0 0] [1 0 0] [1 0 0] U21(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = U21(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 1] [1 0 0] [1 0 0] U21(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = U21(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [1 0 0] [1 0 0] [1 0 0] U21(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = U21(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 1 0] [1 0 0] [1 0 0] U21(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = U21(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 1] [1] [1 0 1] [0] U22(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = U22(X) [0 0 0] [1] [0 0 0] [1] [1 1 1] [0] [1 0 1] [0] U22(active(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = U22(X) [0 0 0] [1] [0 0 0] [1] [1 0 1] [1 0 0] isList(mark(X)) = [0 0 0]X >= [0 0 0]X = isList(X) [0 0 0] [0 0 0] [1 1 0] [1 0 0] isList(active(X)) = [0 0 0]X >= [0 0 0]X = isList(X) [0 0 0] [0 0 0] [1 0 1] [1 0 0] U31(mark(X)) = [0 0 0]X >= [0 0 0]X = U31(X) [0 0 0] [0 0 0] [1 1 0] [1 0 0] U31(active(X)) = [0 0 0]X >= [0 0 0]X = U31(X) [0 0 0] [0 0 0] [1 0 1] [1 0 0] [1 0 0] [1 0 0] U41(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = U41(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 1] [1 0 0] [1 0 0] U41(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = U41(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [1 0 0] [1 0 0] [1 0 0] U41(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = U41(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 1 0] [1 0 0] [1 0 0] U41(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = U41(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 1] [1] [1 0 1] [0] U42(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = U42(X) [0 0 0] [1] [0 0 0] [1] [1 1 1] [0] [1 0 1] [0] U42(active(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = U42(X) [0 0 0] [1] [0 0 0] [1] [1 0 1] [1] [1 0 1] [0] isNeList(mark(X)) = [1 0 1]X + [1] >= [1 0 0]X + [1] = isNeList(X) [0 0 0] [0] [0 0 0] [0] [1 1 1] [0] [1 0 1] [0] isNeList(active(X)) = [1 1 0]X + [1] >= [1 0 0]X + [1] = isNeList(X) [0 0 0] [0] [0 0 0] [0] [1 0 1] [1 0 0] [0] [1 0 0] [1 0 0] U51(mark(X1),X2) = [1 0 1]X1 + [0 0 0]X2 + [1] >= [1 0 1]X1 + [0 0 0]X2 = U51(X1,X2) [1 0 1] [0 0 0] [0] [1 0 0] [0 0 0] [1 0 0] [1 0 1] [1 0 0] [1 0 0] U51(X1,mark(X2)) = [1 0 1]X1 + [0 0 0]X2 >= [1 0 1]X1 + [0 0 0]X2 = U51(X1,X2) [1 0 0] [0 0 0] [1 0 0] [0 0 0] [1 1 0] [1 0 0] [1 0 0] [1 0 0] U51(active(X1),X2) = [1 1 1]X1 + [0 0 0]X2 >= [1 0 1]X1 + [0 0 0]X2 = U51(X1,X2) [1 1 0] [0 0 0] [1 0 0] [0 0 0] [1 0 0] [1 1 0] [1 0 0] [1 0 0] U51(X1,active(X2)) = [1 0 1]X1 + [0 0 0]X2 >= [1 0 1]X1 + [0 0 0]X2 = U51(X1,X2) [1 0 0] [0 0 0] [1 0 0] [0 0 0] [1 0 1] [0] [1 0 0] [0] U52(mark(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = U52(X) [0 0 0] [0] [0 0 0] [0] [1 1 0] [0] [1 0 0] [0] U52(active(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = U52(X) [0 0 0] [0] [0 0 0] [0] [1 0 1] [1] [1 0 0] [1] U61(mark(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = U61(X) [0 0 0] [0] [0 0 0] [0] [1 1 0] [1] [1 0 0] [1] U61(active(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = U61(X) [0 0 0] [0] [0 0 0] [0] [1 0 1] [1 0 0] [1 0 0] [1 0 0] U71(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = U71(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 1] [1 0 0] [1 0 0] U71(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = U71(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [1 0 0] [1 0 0] [1 0 0] U71(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = U71(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 1 0] [1 0 0] [1 0 0] U71(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = U71(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 1] [1] [1 0 1] U72(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X = U72(X) [1 0 1] [1] [1 0 1] [1 1 1] [1 0 1] U72(active(X)) = [0 0 0]X >= [0 0 0]X = U72(X) [1 1 1] [1 0 1] [1 0 1] [1 0 0] isPal(mark(X)) = [0 0 0]X >= [0 0 0]X = isPal(X) [1 0 1] [1 0 0] [1 1 0] [1 0 0] isPal(active(X)) = [0 0 0]X >= [0 0 0]X = isPal(X) [1 1 0] [1 0 0] [1 0 1] [0] [1 0 0] U81(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X = U81(X) [1 0 1] [1] [1 0 1] [1 1 0] [1 0 0] U81(active(X)) = [0 0 0]X >= [0 0 0]X = U81(X) [1 1 1] [1 0 1] [1 0 1] [1] [1 0 1] isQid(mark(X)) = [1 0 1]X + [1] >= [1 0 1]X = isQid(X) [0 0 0] [0] [0 0 0] [1 1 1] [1 0 1] isQid(active(X)) = [1 1 1]X >= [1 0 1]X = isQid(X) [0 0 0] [0 0 0] [1 0 1] [0] [1 0 0] [0] isNePal(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = isNePal(X) [0 0 0] [1] [0 0 0] [1] [1 1 0] [0] [1 0 0] [0] isNePal(active(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = isNePal(X) [0 0 0] [1] [0 0 0] [1] problem: mark(U22(X)) -> active(U22(mark(X))) mark(U42(X)) -> active(U42(mark(X))) mark(e()) -> active(e()) mark(i()) -> active(i()) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(active(X)) -> U11(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(active(X)) -> U22(X) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) U31(mark(X)) -> U31(X) U31(active(X)) -> U31(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(active(X)) -> U42(X) isNeList(active(X)) -> isNeList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(active(X)) -> U72(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) isQid(active(X)) -> isQid(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) Matrix Interpretation Processor: dim=1 interpretation: [U72](x0) = 4x0, [U61](x0) = x0, [U22](x0) = x0 + 6, [active](x0) = x0, [U71](x0, x1) = 2x0 + 3x1, [isNePal](x0) = 2x0, [U81](x0) = x0, [isPal](x0) = x0 + 6, [U11](x0) = 2x0 + 6, [U41](x0, x1) = x0 + 4x1, [__](x0, x1) = 2x0 + 4x1 + 1, [isList](x0) = x0, [isQid](x0) = 4x0, [U52](x0) = 2x0 + 2, [U42](x0) = 4x0 + 2, [e] = 6, [i] = 1, [isNeList](x0) = 4x0 + 6, [U31](x0) = x0 + 2, [U51](x0, x1) = 5x0 + 4x1, [U21](x0, x1) = 3x0 + 4x1, [mark](x0) = 4x0 + 2 orientation: mark(U22(X)) = 4X + 26 >= 4X + 8 = active(U22(mark(X))) mark(U42(X)) = 16X + 10 >= 16X + 10 = active(U42(mark(X))) mark(e()) = 26 >= 6 = active(e()) mark(i()) = 6 >= 1 = active(i()) __(X1,mark(X2)) = 2X1 + 16X2 + 9 >= 2X1 + 4X2 + 1 = __(X1,X2) __(active(X1),X2) = 2X1 + 4X2 + 1 >= 2X1 + 4X2 + 1 = __(X1,X2) __(X1,active(X2)) = 2X1 + 4X2 + 1 >= 2X1 + 4X2 + 1 = __(X1,X2) U11(active(X)) = 2X + 6 >= 2X + 6 = U11(X) U21(mark(X1),X2) = 12X1 + 4X2 + 6 >= 3X1 + 4X2 = U21(X1,X2) U21(X1,mark(X2)) = 3X1 + 16X2 + 8 >= 3X1 + 4X2 = U21(X1,X2) U21(active(X1),X2) = 3X1 + 4X2 >= 3X1 + 4X2 = U21(X1,X2) U21(X1,active(X2)) = 3X1 + 4X2 >= 3X1 + 4X2 = U21(X1,X2) U22(active(X)) = X + 6 >= X + 6 = U22(X) isList(mark(X)) = 4X + 2 >= X = isList(X) isList(active(X)) = X >= X = isList(X) U31(mark(X)) = 4X + 4 >= X + 2 = U31(X) U31(active(X)) = X + 2 >= X + 2 = U31(X) U41(mark(X1),X2) = 4X1 + 4X2 + 2 >= X1 + 4X2 = U41(X1,X2) U41(X1,mark(X2)) = X1 + 16X2 + 8 >= X1 + 4X2 = U41(X1,X2) U41(active(X1),X2) = X1 + 4X2 >= X1 + 4X2 = U41(X1,X2) U41(X1,active(X2)) = X1 + 4X2 >= X1 + 4X2 = U41(X1,X2) U42(active(X)) = 4X + 2 >= 4X + 2 = U42(X) isNeList(active(X)) = 4X + 6 >= 4X + 6 = isNeList(X) U51(mark(X1),X2) = 20X1 + 4X2 + 10 >= 5X1 + 4X2 = U51(X1,X2) U51(X1,mark(X2)) = 5X1 + 16X2 + 8 >= 5X1 + 4X2 = U51(X1,X2) U51(active(X1),X2) = 5X1 + 4X2 >= 5X1 + 4X2 = U51(X1,X2) U51(X1,active(X2)) = 5X1 + 4X2 >= 5X1 + 4X2 = U51(X1,X2) U52(mark(X)) = 8X + 6 >= 2X + 2 = U52(X) U52(active(X)) = 2X + 2 >= 2X + 2 = U52(X) U61(mark(X)) = 4X + 2 >= X = U61(X) U61(active(X)) = X >= X = U61(X) U71(mark(X1),X2) = 8X1 + 3X2 + 4 >= 2X1 + 3X2 = U71(X1,X2) U71(X1,mark(X2)) = 2X1 + 12X2 + 6 >= 2X1 + 3X2 = U71(X1,X2) U71(active(X1),X2) = 2X1 + 3X2 >= 2X1 + 3X2 = U71(X1,X2) U71(X1,active(X2)) = 2X1 + 3X2 >= 2X1 + 3X2 = U71(X1,X2) U72(active(X)) = 4X >= 4X = U72(X) isPal(mark(X)) = 4X + 8 >= X + 6 = isPal(X) isPal(active(X)) = X + 6 >= X + 6 = isPal(X) U81(mark(X)) = 4X + 2 >= X = U81(X) U81(active(X)) = X >= X = U81(X) isQid(active(X)) = 4X >= 4X = isQid(X) isNePal(mark(X)) = 8X + 4 >= 2X = isNePal(X) isNePal(active(X)) = 2X >= 2X = isNePal(X) problem: mark(U42(X)) -> active(U42(mark(X))) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(active(X)) -> U11(X) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(active(X)) -> U22(X) isList(active(X)) -> isList(X) U31(active(X)) -> U31(X) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(active(X)) -> U42(X) isNeList(active(X)) -> isNeList(X) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(active(X)) -> U52(X) U61(active(X)) -> U61(X) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(active(X)) -> U72(X) isPal(active(X)) -> isPal(X) U81(active(X)) -> U81(X) isQid(active(X)) -> isQid(X) isNePal(active(X)) -> isNePal(X) Matrix Interpretation Processor: dim=1 interpretation: [U72](x0) = 2x0, [U61](x0) = 7x0, [U22](x0) = 7x0 + 2, [active](x0) = x0 + 1, [U71](x0, x1) = 6x0 + 2x1 + 5, [isNePal](x0) = 4x0 + 2, [U81](x0) = 2x0 + 6, [isPal](x0) = 2x0 + 2, [U11](x0) = 2x0, [U41](x0, x1) = 2x0 + 6x1 + 4, [__](x0, x1) = 3x0 + 3x1 + 1, [isList](x0) = 2x0, [isQid](x0) = 3x0, [U52](x0) = 4x0 + 4, [U42](x0) = 4x0 + 1, [isNeList](x0) = 2x0 + 2, [U31](x0) = 7x0 + 1, [U51](x0, x1) = x0 + 6x1 + 2, [U21](x0, x1) = 4x0 + x1, [mark](x0) = 2x0 orientation: mark(U42(X)) = 8X + 2 >= 8X + 2 = active(U42(mark(X))) __(active(X1),X2) = 3X1 + 3X2 + 4 >= 3X1 + 3X2 + 1 = __(X1,X2) __(X1,active(X2)) = 3X1 + 3X2 + 4 >= 3X1 + 3X2 + 1 = __(X1,X2) U11(active(X)) = 2X + 2 >= 2X = U11(X) U21(active(X1),X2) = 4X1 + X2 + 4 >= 4X1 + X2 = U21(X1,X2) U21(X1,active(X2)) = 4X1 + X2 + 1 >= 4X1 + X2 = U21(X1,X2) U22(active(X)) = 7X + 9 >= 7X + 2 = U22(X) isList(active(X)) = 2X + 2 >= 2X = isList(X) U31(active(X)) = 7X + 8 >= 7X + 1 = U31(X) U41(active(X1),X2) = 2X1 + 6X2 + 6 >= 2X1 + 6X2 + 4 = U41(X1,X2) U41(X1,active(X2)) = 2X1 + 6X2 + 10 >= 2X1 + 6X2 + 4 = U41(X1,X2) U42(active(X)) = 4X + 5 >= 4X + 1 = U42(X) isNeList(active(X)) = 2X + 4 >= 2X + 2 = isNeList(X) U51(active(X1),X2) = X1 + 6X2 + 3 >= X1 + 6X2 + 2 = U51(X1,X2) U51(X1,active(X2)) = X1 + 6X2 + 8 >= X1 + 6X2 + 2 = U51(X1,X2) U52(active(X)) = 4X + 8 >= 4X + 4 = U52(X) U61(active(X)) = 7X + 7 >= 7X = U61(X) U71(active(X1),X2) = 6X1 + 2X2 + 11 >= 6X1 + 2X2 + 5 = U71(X1,X2) U71(X1,active(X2)) = 6X1 + 2X2 + 7 >= 6X1 + 2X2 + 5 = U71(X1,X2) U72(active(X)) = 2X + 2 >= 2X = U72(X) isPal(active(X)) = 2X + 4 >= 2X + 2 = isPal(X) U81(active(X)) = 2X + 8 >= 2X + 6 = U81(X) isQid(active(X)) = 3X + 3 >= 3X = isQid(X) isNePal(active(X)) = 4X + 6 >= 4X + 2 = isNePal(X) problem: mark(U42(X)) -> active(U42(mark(X))) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [active](x0) = [0 0 0]x0 [1 0 0] , [1 1 0] [0] [U42](x0) = [0 0 1]x0 + [0] [0 0 0] [1], [1 1 1] [mark](x0) = [0 0 0]x0 [1 1 0] orientation: [1 1 1] [1] [1 1 1] mark(U42(X)) = [0 0 0]X + [0] >= [0 0 0]X = active(U42(mark(X))) [1 1 1] [0] [1 1 1] problem: Qed