/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/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()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U61(mark(X)) -> mark(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U81(mark(X)) -> mark(U81(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(ok(X)) -> ok(U22(X)) isList(ok(X)) -> ok(isList(X)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(ok(X)) -> ok(U42(X)) isNeList(ok(X)) -> ok(isNeList(X)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(ok(X)) -> ok(U52(X)) U61(ok(X)) -> ok(U61(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isPal(ok(X)) -> ok(isPal(X)) U81(ok(X)) -> ok(U81(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Proof: Matrix Interpretation Processor: dim=1 interpretation: [top](x0) = 4x0, [ok](x0) = x0, [proper](x0) = x0, [u] = 0, [o] = 0, [i] = 1, [e] = 0, [a] = 0, [isNePal](x0) = 3x0, [isQid](x0) = x0, [U81](x0) = x0, [U72](x0) = x0, [isPal](x0) = 3x0, [U71](x0, x1) = 4x0 + 3x1, [U61](x0) = 3x0, [U52](x0) = x0, [U51](x0, x1) = 2x0 + x1, [U42](x0) = x0, [isNeList](x0) = x0, [U41](x0, x1) = x0 + x1, [U31](x0) = x0, [U22](x0) = x0, [isList](x0) = x0, [U21](x0, x1) = 2x0 + x1, [U11](x0) = x0, [tt] = 0, [nil] = 0, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = 4x0 + x1 orientation: active(__(__(X,Y),Z)) = 16X + 4Y + Z >= 4X + 4Y + Z = mark(__(X,__(Y,Z))) active(__(X,nil())) = 4X >= X = mark(X) active(__(nil(),X)) = X >= X = mark(X) active(U11(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V2)) = V2 >= V2 = mark(U22(isList(V2))) active(U22(tt())) = 0 >= 0 = mark(tt()) active(U31(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V2)) = V2 >= V2 = mark(U42(isNeList(V2))) active(U42(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V2)) = V2 >= V2 = mark(U52(isList(V2))) active(U52(tt())) = 0 >= 0 = mark(tt()) active(U61(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),P)) = 3P >= 3P = mark(U72(isPal(P))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(U81(tt())) = 0 >= 0 = mark(tt()) active(isList(V)) = V >= V = mark(U11(isNeList(V))) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = 4V1 + V2 >= 2V1 + V2 = mark(U21(isList(V1),V2)) active(isNeList(V)) = V >= V = mark(U31(isQid(V))) active(isNeList(__(V1,V2))) = 4V1 + V2 >= V1 + V2 = mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) = 4V1 + V2 >= 2V1 + V2 = mark(U51(isNeList(V1),V2)) active(isNePal(V)) = 3V >= 3V = mark(U61(isQid(V))) active(isNePal(__(I,__(P,I)))) = 15I + 12P >= 4I + 3P = mark(U71(isQid(I),P)) active(isPal(V)) = 3V >= 3V = mark(U81(isNePal(V))) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 1 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = 4X1 + X2 >= 4X1 + X2 = __(active(X1),X2) active(__(X1,X2)) = 4X1 + X2 >= 4X1 + X2 = __(X1,active(X2)) active(U11(X)) = X >= X = U11(active(X)) active(U21(X1,X2)) = 2X1 + X2 >= 2X1 + X2 = U21(active(X1),X2) active(U22(X)) = X >= X = U22(active(X)) active(U31(X)) = X >= X = U31(active(X)) active(U41(X1,X2)) = X1 + X2 >= X1 + X2 = U41(active(X1),X2) active(U42(X)) = X >= X = U42(active(X)) active(U51(X1,X2)) = 2X1 + X2 >= 2X1 + X2 = U51(active(X1),X2) active(U52(X)) = X >= X = U52(active(X)) active(U61(X)) = 3X >= 3X = U61(active(X)) active(U71(X1,X2)) = 4X1 + 3X2 >= 4X1 + 3X2 = U71(active(X1),X2) active(U72(X)) = X >= X = U72(active(X)) active(U81(X)) = X >= X = U81(active(X)) __(mark(X1),X2) = 4X1 + X2 >= 4X1 + X2 = mark(__(X1,X2)) __(X1,mark(X2)) = 4X1 + X2 >= 4X1 + X2 = mark(__(X1,X2)) U11(mark(X)) = X >= X = mark(U11(X)) U21(mark(X1),X2) = 2X1 + X2 >= 2X1 + X2 = mark(U21(X1,X2)) U22(mark(X)) = X >= X = mark(U22(X)) U31(mark(X)) = X >= X = mark(U31(X)) U41(mark(X1),X2) = X1 + X2 >= X1 + X2 = mark(U41(X1,X2)) U42(mark(X)) = X >= X = mark(U42(X)) U51(mark(X1),X2) = 2X1 + X2 >= 2X1 + X2 = mark(U51(X1,X2)) U52(mark(X)) = X >= X = mark(U52(X)) U61(mark(X)) = 3X >= 3X = mark(U61(X)) U71(mark(X1),X2) = 4X1 + 3X2 >= 4X1 + 3X2 = mark(U71(X1,X2)) U72(mark(X)) = X >= X = mark(U72(X)) U81(mark(X)) = X >= X = mark(U81(X)) proper(__(X1,X2)) = 4X1 + X2 >= 4X1 + X2 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X)) = X >= X = U11(proper(X)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U21(X1,X2)) = 2X1 + X2 >= 2X1 + X2 = U21(proper(X1),proper(X2)) proper(U22(X)) = X >= X = U22(proper(X)) proper(isList(X)) = X >= X = isList(proper(X)) proper(U31(X)) = X >= X = U31(proper(X)) proper(U41(X1,X2)) = X1 + X2 >= X1 + X2 = U41(proper(X1),proper(X2)) proper(U42(X)) = X >= X = U42(proper(X)) proper(isNeList(X)) = X >= X = isNeList(proper(X)) proper(U51(X1,X2)) = 2X1 + X2 >= 2X1 + X2 = U51(proper(X1),proper(X2)) proper(U52(X)) = X >= X = U52(proper(X)) proper(U61(X)) = 3X >= 3X = U61(proper(X)) proper(U71(X1,X2)) = 4X1 + 3X2 >= 4X1 + 3X2 = U71(proper(X1),proper(X2)) proper(U72(X)) = X >= X = U72(proper(X)) proper(isPal(X)) = 3X >= 3X = isPal(proper(X)) proper(U81(X)) = X >= X = U81(proper(X)) proper(isQid(X)) = X >= X = isQid(proper(X)) proper(isNePal(X)) = 3X >= 3X = isNePal(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = 4X1 + X2 >= 4X1 + X2 = ok(__(X1,X2)) U11(ok(X)) = X >= X = ok(U11(X)) U21(ok(X1),ok(X2)) = 2X1 + X2 >= 2X1 + X2 = ok(U21(X1,X2)) U22(ok(X)) = X >= X = ok(U22(X)) isList(ok(X)) = X >= X = ok(isList(X)) U31(ok(X)) = X >= X = ok(U31(X)) U41(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(U41(X1,X2)) U42(ok(X)) = X >= X = ok(U42(X)) isNeList(ok(X)) = X >= X = ok(isNeList(X)) U51(ok(X1),ok(X2)) = 2X1 + X2 >= 2X1 + X2 = ok(U51(X1,X2)) U52(ok(X)) = X >= X = ok(U52(X)) U61(ok(X)) = 3X >= 3X = ok(U61(X)) U71(ok(X1),ok(X2)) = 4X1 + 3X2 >= 4X1 + 3X2 = ok(U71(X1,X2)) U72(ok(X)) = X >= X = ok(U72(X)) isPal(ok(X)) = 3X >= 3X = ok(isPal(X)) U81(ok(X)) = X >= X = ok(U81(X)) isQid(ok(X)) = X >= X = ok(isQid(X)) isNePal(ok(X)) = 3X >= 3X = ok(isNePal(X)) top(mark(X)) = 4X >= 4X = top(proper(X)) top(ok(X)) = 4X >= 4X = top(active(X)) problem: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt())) -> mark(tt()) active(U21(tt(),V2)) -> mark(U22(isList(V2))) active(U22(tt())) -> mark(tt()) active(U31(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNeList(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(U52(tt())) -> mark(tt()) active(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(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U61(mark(X)) -> mark(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U81(mark(X)) -> mark(U81(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(ok(X)) -> ok(U22(X)) isList(ok(X)) -> ok(isList(X)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(ok(X)) -> ok(U42(X)) isNeList(ok(X)) -> ok(isNeList(X)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(ok(X)) -> ok(U52(X)) U61(ok(X)) -> ok(U61(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isPal(ok(X)) -> ok(isPal(X)) U81(ok(X)) -> ok(U81(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dim=1 interpretation: [top](x0) = x0, [ok](x0) = x0, [proper](x0) = x0, [u] = 0, [o] = 0, [i] = 2, [e] = 0, [a] = 1, [isNePal](x0) = x0, [isQid](x0) = x0, [U81](x0) = x0, [U72](x0) = 2x0, [isPal](x0) = x0, [U71](x0, x1) = x0 + 3x1, [U61](x0) = x0, [U52](x0) = x0, [U51](x0, x1) = x0 + x1 + 1, [U42](x0) = x0, [isNeList](x0) = x0, [U41](x0, x1) = 4x0 + x1, [U31](x0) = x0, [U22](x0) = x0, [isList](x0) = x0 + 1, [U21](x0, x1) = 4x0 + x1 + 1, [U11](x0) = x0, [tt] = 0, [nil] = 4, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = 4x0 + x1 + 4 orientation: active(__(__(X,Y),Z)) = 16X + 4Y + Z + 20 >= 4X + 4Y + Z + 8 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 4X + 8 >= X = mark(X) active(__(nil(),X)) = X + 20 >= X = mark(X) active(U11(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V2)) = V2 + 1 >= V2 + 1 = mark(U22(isList(V2))) active(U22(tt())) = 0 >= 0 = mark(tt()) active(U31(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V2)) = V2 >= V2 = mark(U42(isNeList(V2))) active(U42(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V2)) = V2 + 1 >= V2 + 1 = mark(U52(isList(V2))) active(U52(tt())) = 0 >= 0 = mark(tt()) active(U61(tt())) = 0 >= 0 = mark(tt()) active(U71(tt(),P)) = 3P >= 2P = mark(U72(isPal(P))) active(U72(tt())) = 0 >= 0 = mark(tt()) active(U81(tt())) = 0 >= 0 = mark(tt()) active(isList(V)) = V + 1 >= V = mark(U11(isNeList(V))) active(isList(nil())) = 5 >= 0 = mark(tt()) active(isList(__(V1,V2))) = 4V1 + V2 + 5 >= 4V1 + V2 + 5 = mark(U21(isList(V1),V2)) active(isNeList(V)) = V >= V = mark(U31(isQid(V))) active(isNeList(__(V1,V2))) = 4V1 + V2 + 4 >= 4V1 + V2 + 4 = mark(U41(isList(V1),V2)) active(isNeList(__(V1,V2))) = 4V1 + V2 + 4 >= V1 + V2 + 1 = mark(U51(isNeList(V1),V2)) active(isNePal(V)) = V >= V = mark(U61(isQid(V))) active(isNePal(__(I,__(P,I)))) = 5I + 4P + 8 >= I + 3P = mark(U71(isQid(I),P)) active(isPal(V)) = V >= V = mark(U81(isNePal(V))) active(isPal(nil())) = 4 >= 0 = mark(tt()) active(isQid(a())) = 1 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = 4X1 + X2 + 4 >= 4X1 + X2 + 4 = __(active(X1),X2) active(__(X1,X2)) = 4X1 + X2 + 4 >= 4X1 + X2 + 4 = __(X1,active(X2)) active(U11(X)) = X >= X = U11(active(X)) active(U21(X1,X2)) = 4X1 + X2 + 1 >= 4X1 + X2 + 1 = U21(active(X1),X2) active(U22(X)) = X >= X = U22(active(X)) active(U31(X)) = X >= X = U31(active(X)) active(U41(X1,X2)) = 4X1 + X2 >= 4X1 + X2 = U41(active(X1),X2) active(U42(X)) = X >= X = U42(active(X)) active(U51(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U51(active(X1),X2) active(U52(X)) = X >= X = U52(active(X)) active(U61(X)) = X >= X = U61(active(X)) active(U71(X1,X2)) = X1 + 3X2 >= X1 + 3X2 = U71(active(X1),X2) active(U72(X)) = 2X >= 2X = U72(active(X)) active(U81(X)) = X >= X = U81(active(X)) __(mark(X1),X2) = 4X1 + X2 + 4 >= 4X1 + X2 + 4 = mark(__(X1,X2)) __(X1,mark(X2)) = 4X1 + X2 + 4 >= 4X1 + X2 + 4 = mark(__(X1,X2)) U11(mark(X)) = X >= X = mark(U11(X)) U21(mark(X1),X2) = 4X1 + X2 + 1 >= 4X1 + X2 + 1 = mark(U21(X1,X2)) U22(mark(X)) = X >= X = mark(U22(X)) U31(mark(X)) = X >= X = mark(U31(X)) U41(mark(X1),X2) = 4X1 + X2 >= 4X1 + X2 = mark(U41(X1,X2)) U42(mark(X)) = X >= X = mark(U42(X)) U51(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(U51(X1,X2)) U52(mark(X)) = X >= X = mark(U52(X)) U61(mark(X)) = X >= X = mark(U61(X)) U71(mark(X1),X2) = X1 + 3X2 >= X1 + 3X2 = mark(U71(X1,X2)) U72(mark(X)) = 2X >= 2X = mark(U72(X)) U81(mark(X)) = X >= X = mark(U81(X)) proper(__(X1,X2)) = 4X1 + X2 + 4 >= 4X1 + X2 + 4 = __(proper(X1),proper(X2)) proper(nil()) = 4 >= 4 = ok(nil()) proper(U11(X)) = X >= X = U11(proper(X)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U21(X1,X2)) = 4X1 + X2 + 1 >= 4X1 + X2 + 1 = U21(proper(X1),proper(X2)) proper(U22(X)) = X >= X = U22(proper(X)) proper(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(U31(X)) = X >= X = U31(proper(X)) proper(U41(X1,X2)) = 4X1 + X2 >= 4X1 + X2 = U41(proper(X1),proper(X2)) proper(U42(X)) = X >= X = U42(proper(X)) proper(isNeList(X)) = X >= X = isNeList(proper(X)) proper(U51(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U51(proper(X1),proper(X2)) proper(U52(X)) = X >= X = U52(proper(X)) proper(U61(X)) = X >= X = U61(proper(X)) proper(U71(X1,X2)) = X1 + 3X2 >= X1 + 3X2 = U71(proper(X1),proper(X2)) proper(U72(X)) = 2X >= 2X = U72(proper(X)) proper(isPal(X)) = X >= X = isPal(proper(X)) proper(U81(X)) = X >= X = U81(proper(X)) proper(isQid(X)) = X >= X = isQid(proper(X)) proper(isNePal(X)) = X >= X = isNePal(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 2 >= 2 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = 4X1 + X2 + 4 >= 4X1 + X2 + 4 = ok(__(X1,X2)) U11(ok(X)) = X >= X = ok(U11(X)) U21(ok(X1),ok(X2)) = 4X1 + X2 + 1 >= 4X1 + X2 + 1 = ok(U21(X1,X2)) U22(ok(X)) = X >= X = ok(U22(X)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) U31(ok(X)) = X >= X = ok(U31(X)) U41(ok(X1),ok(X2)) = 4X1 + X2 >= 4X1 + X2 = ok(U41(X1,X2)) U42(ok(X)) = X >= X = ok(U42(X)) isNeList(ok(X)) = X >= X = ok(isNeList(X)) U51(ok(X1),ok(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = ok(U51(X1,X2)) U52(ok(X)) = X >= X = ok(U52(X)) U61(ok(X)) = X >= X = ok(U61(X)) U71(ok(X1),ok(X2)) = X1 + 3X2 >= X1 + 3X2 = ok(U71(X1,X2)) U72(ok(X)) = 2X >= 2X = ok(U72(X)) isPal(ok(X)) = X >= X = ok(isPal(X)) U81(ok(X)) = X >= X = ok(U81(X)) isQid(ok(X)) = X >= X = ok(isQid(X)) isNePal(ok(X)) = X >= X = ok(isNePal(X)) top(mark(X)) = X >= X = top(proper(X)) top(ok(X)) = X >= X = top(active(X)) problem: 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(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isNeList(V)) -> mark(U31(isQid(V))) active(isNeList(__(V1,V2))) -> mark(U41(isList(V1),V2)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(V)) -> mark(U81(isNePal(V))) active(isQid(e())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U61(mark(X)) -> mark(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U81(mark(X)) -> mark(U81(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(ok(X)) -> ok(U22(X)) isList(ok(X)) -> ok(isList(X)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(ok(X)) -> ok(U42(X)) isNeList(ok(X)) -> ok(isNeList(X)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(ok(X)) -> ok(U52(X)) U61(ok(X)) -> ok(U61(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isPal(ok(X)) -> ok(isPal(X)) U81(ok(X)) -> ok(U81(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dim=1 interpretation: [top](x0) = 2x0, [ok](x0) = x0, [proper](x0) = x0, [u] = 3, [o] = 3, [i] = 0, [e] = 6, [a] = 0, [isNePal](x0) = x0, [isQid](x0) = x0, [U81](x0) = 6x0, [U72](x0) = x0, [isPal](x0) = 7x0, [U71](x0, x1) = 2x0 + 7x1, [U61](x0) = x0, [U52](x0) = 2x0 + 7, [U51](x0, x1) = x0 + 2x1 + 4, [U42](x0) = 2x0, [isNeList](x0) = x0 + 4, [U41](x0, x1) = 4x0 + 2x1 + 1, [U31](x0) = x0 + 3, [U22](x0) = 4x0, [isList](x0) = x0, [U21](x0, x1) = x0 + 4x1, [U11](x0) = x0, [tt] = 3, [nil] = 2, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = 4x0 + 4x1 orientation: active(U11(tt())) = 3 >= 3 = mark(tt()) active(U21(tt(),V2)) = 4V2 + 3 >= 4V2 = mark(U22(isList(V2))) active(U22(tt())) = 12 >= 3 = mark(tt()) active(U31(tt())) = 6 >= 3 = mark(tt()) active(U41(tt(),V2)) = 2V2 + 13 >= 2V2 + 8 = mark(U42(isNeList(V2))) active(U42(tt())) = 6 >= 3 = mark(tt()) active(U51(tt(),V2)) = 2V2 + 7 >= 2V2 + 7 = mark(U52(isList(V2))) active(U52(tt())) = 13 >= 3 = mark(tt()) active(U61(tt())) = 3 >= 3 = mark(tt()) active(U71(tt(),P)) = 7P + 6 >= 7P = mark(U72(isPal(P))) active(U72(tt())) = 3 >= 3 = mark(tt()) active(U81(tt())) = 18 >= 3 = mark(tt()) active(isList(__(V1,V2))) = 4V1 + 4V2 >= V1 + 4V2 = mark(U21(isList(V1),V2)) active(isNeList(V)) = V + 4 >= V + 3 = mark(U31(isQid(V))) active(isNeList(__(V1,V2))) = 4V1 + 4V2 + 4 >= 4V1 + 2V2 + 1 = mark(U41(isList(V1),V2)) active(isNePal(V)) = V >= V = mark(U61(isQid(V))) active(isPal(V)) = 7V >= 6V = mark(U81(isNePal(V))) active(isQid(e())) = 6 >= 3 = mark(tt()) active(isQid(o())) = 3 >= 3 = mark(tt()) active(isQid(u())) = 3 >= 3 = mark(tt()) active(__(X1,X2)) = 4X1 + 4X2 >= 4X1 + 4X2 = __(active(X1),X2) active(__(X1,X2)) = 4X1 + 4X2 >= 4X1 + 4X2 = __(X1,active(X2)) active(U11(X)) = X >= X = U11(active(X)) active(U21(X1,X2)) = X1 + 4X2 >= X1 + 4X2 = U21(active(X1),X2) active(U22(X)) = 4X >= 4X = U22(active(X)) active(U31(X)) = X + 3 >= X + 3 = U31(active(X)) active(U41(X1,X2)) = 4X1 + 2X2 + 1 >= 4X1 + 2X2 + 1 = U41(active(X1),X2) active(U42(X)) = 2X >= 2X = U42(active(X)) active(U51(X1,X2)) = X1 + 2X2 + 4 >= X1 + 2X2 + 4 = U51(active(X1),X2) active(U52(X)) = 2X + 7 >= 2X + 7 = U52(active(X)) active(U61(X)) = X >= X = U61(active(X)) active(U71(X1,X2)) = 2X1 + 7X2 >= 2X1 + 7X2 = U71(active(X1),X2) active(U72(X)) = X >= X = U72(active(X)) active(U81(X)) = 6X >= 6X = U81(active(X)) __(mark(X1),X2) = 4X1 + 4X2 >= 4X1 + 4X2 = mark(__(X1,X2)) __(X1,mark(X2)) = 4X1 + 4X2 >= 4X1 + 4X2 = mark(__(X1,X2)) U11(mark(X)) = X >= X = mark(U11(X)) U21(mark(X1),X2) = X1 + 4X2 >= X1 + 4X2 = mark(U21(X1,X2)) U22(mark(X)) = 4X >= 4X = mark(U22(X)) U31(mark(X)) = X + 3 >= X + 3 = mark(U31(X)) U41(mark(X1),X2) = 4X1 + 2X2 + 1 >= 4X1 + 2X2 + 1 = mark(U41(X1,X2)) U42(mark(X)) = 2X >= 2X = mark(U42(X)) U51(mark(X1),X2) = X1 + 2X2 + 4 >= X1 + 2X2 + 4 = mark(U51(X1,X2)) U52(mark(X)) = 2X + 7 >= 2X + 7 = mark(U52(X)) U61(mark(X)) = X >= X = mark(U61(X)) U71(mark(X1),X2) = 2X1 + 7X2 >= 2X1 + 7X2 = mark(U71(X1,X2)) U72(mark(X)) = X >= X = mark(U72(X)) U81(mark(X)) = 6X >= 6X = mark(U81(X)) proper(__(X1,X2)) = 4X1 + 4X2 >= 4X1 + 4X2 = __(proper(X1),proper(X2)) proper(nil()) = 2 >= 2 = ok(nil()) proper(U11(X)) = X >= X = U11(proper(X)) proper(tt()) = 3 >= 3 = ok(tt()) proper(U21(X1,X2)) = X1 + 4X2 >= X1 + 4X2 = U21(proper(X1),proper(X2)) proper(U22(X)) = 4X >= 4X = U22(proper(X)) proper(isList(X)) = X >= X = isList(proper(X)) proper(U31(X)) = X + 3 >= X + 3 = U31(proper(X)) proper(U41(X1,X2)) = 4X1 + 2X2 + 1 >= 4X1 + 2X2 + 1 = U41(proper(X1),proper(X2)) proper(U42(X)) = 2X >= 2X = U42(proper(X)) proper(isNeList(X)) = X + 4 >= X + 4 = isNeList(proper(X)) proper(U51(X1,X2)) = X1 + 2X2 + 4 >= X1 + 2X2 + 4 = U51(proper(X1),proper(X2)) proper(U52(X)) = 2X + 7 >= 2X + 7 = U52(proper(X)) proper(U61(X)) = X >= X = U61(proper(X)) proper(U71(X1,X2)) = 2X1 + 7X2 >= 2X1 + 7X2 = U71(proper(X1),proper(X2)) proper(U72(X)) = X >= X = U72(proper(X)) proper(isPal(X)) = 7X >= 7X = isPal(proper(X)) proper(U81(X)) = 6X >= 6X = U81(proper(X)) proper(isQid(X)) = X >= X = isQid(proper(X)) proper(isNePal(X)) = X >= X = isNePal(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 6 >= 6 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 3 >= 3 = ok(o()) proper(u()) = 3 >= 3 = ok(u()) __(ok(X1),ok(X2)) = 4X1 + 4X2 >= 4X1 + 4X2 = ok(__(X1,X2)) U11(ok(X)) = X >= X = ok(U11(X)) U21(ok(X1),ok(X2)) = X1 + 4X2 >= X1 + 4X2 = ok(U21(X1,X2)) U22(ok(X)) = 4X >= 4X = ok(U22(X)) isList(ok(X)) = X >= X = ok(isList(X)) U31(ok(X)) = X + 3 >= X + 3 = ok(U31(X)) U41(ok(X1),ok(X2)) = 4X1 + 2X2 + 1 >= 4X1 + 2X2 + 1 = ok(U41(X1,X2)) U42(ok(X)) = 2X >= 2X = ok(U42(X)) isNeList(ok(X)) = X + 4 >= X + 4 = ok(isNeList(X)) U51(ok(X1),ok(X2)) = X1 + 2X2 + 4 >= X1 + 2X2 + 4 = ok(U51(X1,X2)) U52(ok(X)) = 2X + 7 >= 2X + 7 = ok(U52(X)) U61(ok(X)) = X >= X = ok(U61(X)) U71(ok(X1),ok(X2)) = 2X1 + 7X2 >= 2X1 + 7X2 = ok(U71(X1,X2)) U72(ok(X)) = X >= X = ok(U72(X)) isPal(ok(X)) = 7X >= 7X = ok(isPal(X)) U81(ok(X)) = 6X >= 6X = ok(U81(X)) isQid(ok(X)) = X >= X = ok(isQid(X)) isNePal(ok(X)) = X >= X = ok(isNePal(X)) top(mark(X)) = 2X >= 2X = top(proper(X)) top(ok(X)) = 2X >= 2X = top(active(X)) problem: active(U11(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(U61(tt())) -> mark(tt()) active(U72(tt())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(V)) -> mark(U81(isNePal(V))) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U61(mark(X)) -> mark(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U81(mark(X)) -> mark(U81(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(ok(X)) -> ok(U22(X)) isList(ok(X)) -> ok(isList(X)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(ok(X)) -> ok(U42(X)) isNeList(ok(X)) -> ok(isNeList(X)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(ok(X)) -> ok(U52(X)) U61(ok(X)) -> ok(U61(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isPal(ok(X)) -> ok(isPal(X)) U81(ok(X)) -> ok(U81(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) DP Processor: DPs: active#(U51(tt(),V2)) -> isList#(V2) active#(U51(tt(),V2)) -> U52#(isList(V2)) active#(isList(__(V1,V2))) -> isList#(V1) active#(isList(__(V1,V2))) -> U21#(isList(V1),V2) active#(isNePal(V)) -> isQid#(V) active#(isNePal(V)) -> U61#(isQid(V)) active#(isPal(V)) -> isNePal#(V) active#(isPal(V)) -> U81#(isNePal(V)) active#(__(X1,X2)) -> active#(X1) active#(__(X1,X2)) -> __#(active(X1),X2) active#(__(X1,X2)) -> active#(X2) active#(__(X1,X2)) -> __#(X1,active(X2)) active#(U11(X)) -> active#(X) active#(U11(X)) -> U11#(active(X)) active#(U21(X1,X2)) -> active#(X1) active#(U21(X1,X2)) -> U21#(active(X1),X2) active#(U22(X)) -> active#(X) active#(U22(X)) -> U22#(active(X)) active#(U31(X)) -> active#(X) active#(U31(X)) -> U31#(active(X)) active#(U41(X1,X2)) -> active#(X1) active#(U41(X1,X2)) -> U41#(active(X1),X2) active#(U42(X)) -> active#(X) active#(U42(X)) -> U42#(active(X)) active#(U51(X1,X2)) -> active#(X1) active#(U51(X1,X2)) -> U51#(active(X1),X2) active#(U52(X)) -> active#(X) active#(U52(X)) -> U52#(active(X)) active#(U61(X)) -> active#(X) active#(U61(X)) -> U61#(active(X)) active#(U71(X1,X2)) -> active#(X1) active#(U71(X1,X2)) -> U71#(active(X1),X2) active#(U72(X)) -> active#(X) active#(U72(X)) -> U72#(active(X)) active#(U81(X)) -> active#(X) active#(U81(X)) -> U81#(active(X)) __#(mark(X1),X2) -> __#(X1,X2) __#(X1,mark(X2)) -> __#(X1,X2) U11#(mark(X)) -> U11#(X) U21#(mark(X1),X2) -> U21#(X1,X2) U22#(mark(X)) -> U22#(X) U31#(mark(X)) -> U31#(X) U41#(mark(X1),X2) -> U41#(X1,X2) U42#(mark(X)) -> U42#(X) U51#(mark(X1),X2) -> U51#(X1,X2) U52#(mark(X)) -> U52#(X) U61#(mark(X)) -> U61#(X) U71#(mark(X1),X2) -> U71#(X1,X2) U72#(mark(X)) -> U72#(X) U81#(mark(X)) -> U81#(X) proper#(__(X1,X2)) -> proper#(X2) proper#(__(X1,X2)) -> proper#(X1) proper#(__(X1,X2)) -> __#(proper(X1),proper(X2)) proper#(U11(X)) -> proper#(X) proper#(U11(X)) -> U11#(proper(X)) proper#(U21(X1,X2)) -> proper#(X2) proper#(U21(X1,X2)) -> proper#(X1) proper#(U21(X1,X2)) -> U21#(proper(X1),proper(X2)) proper#(U22(X)) -> proper#(X) proper#(U22(X)) -> U22#(proper(X)) proper#(isList(X)) -> proper#(X) proper#(isList(X)) -> isList#(proper(X)) proper#(U31(X)) -> proper#(X) proper#(U31(X)) -> U31#(proper(X)) proper#(U41(X1,X2)) -> proper#(X2) proper#(U41(X1,X2)) -> proper#(X1) proper#(U41(X1,X2)) -> U41#(proper(X1),proper(X2)) proper#(U42(X)) -> proper#(X) proper#(U42(X)) -> U42#(proper(X)) proper#(isNeList(X)) -> proper#(X) proper#(isNeList(X)) -> isNeList#(proper(X)) proper#(U51(X1,X2)) -> proper#(X2) proper#(U51(X1,X2)) -> proper#(X1) proper#(U51(X1,X2)) -> U51#(proper(X1),proper(X2)) proper#(U52(X)) -> proper#(X) proper#(U52(X)) -> U52#(proper(X)) proper#(U61(X)) -> proper#(X) proper#(U61(X)) -> U61#(proper(X)) proper#(U71(X1,X2)) -> proper#(X2) proper#(U71(X1,X2)) -> proper#(X1) proper#(U71(X1,X2)) -> U71#(proper(X1),proper(X2)) proper#(U72(X)) -> proper#(X) proper#(U72(X)) -> U72#(proper(X)) proper#(isPal(X)) -> proper#(X) proper#(isPal(X)) -> isPal#(proper(X)) proper#(U81(X)) -> proper#(X) proper#(U81(X)) -> U81#(proper(X)) proper#(isQid(X)) -> proper#(X) proper#(isQid(X)) -> isQid#(proper(X)) proper#(isNePal(X)) -> proper#(X) proper#(isNePal(X)) -> isNePal#(proper(X)) __#(ok(X1),ok(X2)) -> __#(X1,X2) U11#(ok(X)) -> U11#(X) U21#(ok(X1),ok(X2)) -> U21#(X1,X2) U22#(ok(X)) -> U22#(X) isList#(ok(X)) -> isList#(X) U31#(ok(X)) -> U31#(X) U41#(ok(X1),ok(X2)) -> U41#(X1,X2) U42#(ok(X)) -> U42#(X) isNeList#(ok(X)) -> isNeList#(X) U51#(ok(X1),ok(X2)) -> U51#(X1,X2) U52#(ok(X)) -> U52#(X) U61#(ok(X)) -> U61#(X) U71#(ok(X1),ok(X2)) -> U71#(X1,X2) U72#(ok(X)) -> U72#(X) isPal#(ok(X)) -> isPal#(X) U81#(ok(X)) -> U81#(X) isQid#(ok(X)) -> isQid#(X) isNePal#(ok(X)) -> isNePal#(X) top#(mark(X)) -> proper#(X) top#(mark(X)) -> top#(proper(X)) top#(ok(X)) -> active#(X) top#(ok(X)) -> top#(active(X)) TRS: active(U11(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(U61(tt())) -> mark(tt()) active(U72(tt())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(V)) -> mark(U81(isNePal(V))) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U61(mark(X)) -> mark(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U81(mark(X)) -> mark(U81(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(ok(X)) -> ok(U22(X)) isList(ok(X)) -> ok(isList(X)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(ok(X)) -> ok(U42(X)) isNeList(ok(X)) -> ok(isNeList(X)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(ok(X)) -> ok(U52(X)) U61(ok(X)) -> ok(U61(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isPal(ok(X)) -> ok(isPal(X)) U81(ok(X)) -> ok(U81(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) TDG Processor: DPs: active#(U51(tt(),V2)) -> isList#(V2) active#(U51(tt(),V2)) -> U52#(isList(V2)) active#(isList(__(V1,V2))) -> isList#(V1) active#(isList(__(V1,V2))) -> U21#(isList(V1),V2) active#(isNePal(V)) -> isQid#(V) active#(isNePal(V)) -> U61#(isQid(V)) active#(isPal(V)) -> isNePal#(V) active#(isPal(V)) -> U81#(isNePal(V)) active#(__(X1,X2)) -> active#(X1) active#(__(X1,X2)) -> __#(active(X1),X2) active#(__(X1,X2)) -> active#(X2) active#(__(X1,X2)) -> __#(X1,active(X2)) active#(U11(X)) -> active#(X) active#(U11(X)) -> U11#(active(X)) active#(U21(X1,X2)) -> active#(X1) active#(U21(X1,X2)) -> U21#(active(X1),X2) active#(U22(X)) -> active#(X) active#(U22(X)) -> U22#(active(X)) active#(U31(X)) -> active#(X) active#(U31(X)) -> U31#(active(X)) active#(U41(X1,X2)) -> active#(X1) active#(U41(X1,X2)) -> U41#(active(X1),X2) active#(U42(X)) -> active#(X) active#(U42(X)) -> U42#(active(X)) active#(U51(X1,X2)) -> active#(X1) active#(U51(X1,X2)) -> U51#(active(X1),X2) active#(U52(X)) -> active#(X) active#(U52(X)) -> U52#(active(X)) active#(U61(X)) -> active#(X) active#(U61(X)) -> U61#(active(X)) active#(U71(X1,X2)) -> active#(X1) active#(U71(X1,X2)) -> U71#(active(X1),X2) active#(U72(X)) -> active#(X) active#(U72(X)) -> U72#(active(X)) active#(U81(X)) -> active#(X) active#(U81(X)) -> U81#(active(X)) __#(mark(X1),X2) -> __#(X1,X2) __#(X1,mark(X2)) -> __#(X1,X2) U11#(mark(X)) -> U11#(X) U21#(mark(X1),X2) -> U21#(X1,X2) U22#(mark(X)) -> U22#(X) U31#(mark(X)) -> U31#(X) U41#(mark(X1),X2) -> U41#(X1,X2) U42#(mark(X)) -> U42#(X) U51#(mark(X1),X2) -> U51#(X1,X2) U52#(mark(X)) -> U52#(X) U61#(mark(X)) -> U61#(X) U71#(mark(X1),X2) -> U71#(X1,X2) U72#(mark(X)) -> U72#(X) U81#(mark(X)) -> U81#(X) proper#(__(X1,X2)) -> proper#(X2) proper#(__(X1,X2)) -> proper#(X1) proper#(__(X1,X2)) -> __#(proper(X1),proper(X2)) proper#(U11(X)) -> proper#(X) proper#(U11(X)) -> U11#(proper(X)) proper#(U21(X1,X2)) -> proper#(X2) proper#(U21(X1,X2)) -> proper#(X1) proper#(U21(X1,X2)) -> U21#(proper(X1),proper(X2)) proper#(U22(X)) -> proper#(X) proper#(U22(X)) -> U22#(proper(X)) proper#(isList(X)) -> proper#(X) proper#(isList(X)) -> isList#(proper(X)) proper#(U31(X)) -> proper#(X) proper#(U31(X)) -> U31#(proper(X)) proper#(U41(X1,X2)) -> proper#(X2) proper#(U41(X1,X2)) -> proper#(X1) proper#(U41(X1,X2)) -> U41#(proper(X1),proper(X2)) proper#(U42(X)) -> proper#(X) proper#(U42(X)) -> U42#(proper(X)) proper#(isNeList(X)) -> proper#(X) proper#(isNeList(X)) -> isNeList#(proper(X)) proper#(U51(X1,X2)) -> proper#(X2) proper#(U51(X1,X2)) -> proper#(X1) proper#(U51(X1,X2)) -> U51#(proper(X1),proper(X2)) proper#(U52(X)) -> proper#(X) proper#(U52(X)) -> U52#(proper(X)) proper#(U61(X)) -> proper#(X) proper#(U61(X)) -> U61#(proper(X)) proper#(U71(X1,X2)) -> proper#(X2) proper#(U71(X1,X2)) -> proper#(X1) proper#(U71(X1,X2)) -> U71#(proper(X1),proper(X2)) proper#(U72(X)) -> proper#(X) proper#(U72(X)) -> U72#(proper(X)) proper#(isPal(X)) -> proper#(X) proper#(isPal(X)) -> isPal#(proper(X)) proper#(U81(X)) -> proper#(X) proper#(U81(X)) -> U81#(proper(X)) proper#(isQid(X)) -> proper#(X) proper#(isQid(X)) -> isQid#(proper(X)) proper#(isNePal(X)) -> proper#(X) proper#(isNePal(X)) -> isNePal#(proper(X)) __#(ok(X1),ok(X2)) -> __#(X1,X2) U11#(ok(X)) -> U11#(X) U21#(ok(X1),ok(X2)) -> U21#(X1,X2) U22#(ok(X)) -> U22#(X) isList#(ok(X)) -> isList#(X) U31#(ok(X)) -> U31#(X) U41#(ok(X1),ok(X2)) -> U41#(X1,X2) U42#(ok(X)) -> U42#(X) isNeList#(ok(X)) -> isNeList#(X) U51#(ok(X1),ok(X2)) -> U51#(X1,X2) U52#(ok(X)) -> U52#(X) U61#(ok(X)) -> U61#(X) U71#(ok(X1),ok(X2)) -> U71#(X1,X2) U72#(ok(X)) -> U72#(X) isPal#(ok(X)) -> isPal#(X) U81#(ok(X)) -> U81#(X) isQid#(ok(X)) -> isQid#(X) isNePal#(ok(X)) -> isNePal#(X) top#(mark(X)) -> proper#(X) top#(mark(X)) -> top#(proper(X)) top#(ok(X)) -> active#(X) top#(ok(X)) -> top#(active(X)) TRS: active(U11(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(U61(tt())) -> mark(tt()) active(U72(tt())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(V)) -> mark(U81(isNePal(V))) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U61(mark(X)) -> mark(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U81(mark(X)) -> mark(U81(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(ok(X)) -> ok(U22(X)) isList(ok(X)) -> ok(isList(X)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(ok(X)) -> ok(U42(X)) isNeList(ok(X)) -> ok(isNeList(X)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(ok(X)) -> ok(U52(X)) U61(ok(X)) -> ok(U61(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isPal(ok(X)) -> ok(isPal(X)) U81(ok(X)) -> ok(U81(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) graph: ... SCC Processor: #sccs: 21 #rules: 71 #arcs: 1668/12769 DPs: top#(ok(X)) -> top#(active(X)) top#(mark(X)) -> top#(proper(X)) TRS: active(U11(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(U61(tt())) -> mark(tt()) active(U72(tt())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(V)) -> mark(U81(isNePal(V))) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U61(mark(X)) -> mark(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U81(mark(X)) -> mark(U81(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(ok(X)) -> ok(U22(X)) isList(ok(X)) -> ok(isList(X)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(ok(X)) -> ok(U42(X)) isNeList(ok(X)) -> ok(isNeList(X)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(ok(X)) -> ok(U52(X)) U61(ok(X)) -> ok(U61(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isPal(ok(X)) -> ok(isPal(X)) U81(ok(X)) -> ok(U81(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Usable Rule Processor: DPs: top#(ok(X)) -> top#(active(X)) top#(mark(X)) -> top#(proper(X)) TRS: active(U11(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(U61(tt())) -> mark(tt()) active(U72(tt())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(V)) -> mark(U81(isNePal(V))) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) isList(ok(X)) -> ok(isList(X)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) isQid(ok(X)) -> ok(isQid(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) isNePal(ok(X)) -> ok(isNePal(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) isNeList(ok(X)) -> ok(isNeList(X)) isPal(ok(X)) -> ok(isPal(X)) LPO Processor: argument filtering: pi(__) = [0,1] pi(active) = 0 pi(mark) = [0] pi(nil) = [] pi(tt) = [] pi(U11) = [0] pi(U21) = 0 pi(isList) = 0 pi(U22) = 0 pi(U31) = 0 pi(U41) = [0] pi(isNeList) = [] pi(U42) = 0 pi(U51) = [0,1] pi(U52) = 0 pi(U61) = [0] pi(U71) = 0 pi(isPal) = [] pi(U72) = [0] pi(U81) = 0 pi(isQid) = [] pi(isNePal) = [] pi(a) = [] pi(e) = [] pi(i) = [] pi(o) = [] pi(u) = [] pi(proper) = 0 pi(ok) = 0 pi(top#) = 0 usable rules: active(U11(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(U61(tt())) -> mark(tt()) active(U72(tt())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(V)) -> mark(U81(isNePal(V))) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) isList(ok(X)) -> ok(isList(X)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) isQid(ok(X)) -> ok(isQid(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) isNePal(ok(X)) -> ok(isNePal(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) isNeList(ok(X)) -> ok(isNeList(X)) isPal(ok(X)) -> ok(isPal(X)) precedence: isPal > isNePal > isQid ~ U41 > U72 ~ U61 ~ U51 ~ U11 ~ __ > top# ~ ok ~ proper ~ u ~ o ~ i ~ e ~ a ~ U81 ~ U71 ~ U52 ~ U42 ~ isNeList ~ U31 ~ U22 ~ isList ~ U21 ~ tt ~ nil ~ mark ~ active problem: DPs: top#(ok(X)) -> top#(active(X)) TRS: active(U11(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(U61(tt())) -> mark(tt()) active(U72(tt())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(V)) -> mark(U81(isNePal(V))) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) isList(ok(X)) -> ok(isList(X)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) isQid(ok(X)) -> ok(isQid(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) isNePal(ok(X)) -> ok(isNePal(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) isNeList(ok(X)) -> ok(isNeList(X)) isPal(ok(X)) -> ok(isPal(X)) Restore Modifier: DPs: top#(ok(X)) -> top#(active(X)) TRS: active(U11(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(U61(tt())) -> mark(tt()) active(U72(tt())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(V)) -> mark(U81(isNePal(V))) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U61(mark(X)) -> mark(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U81(mark(X)) -> mark(U81(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(ok(X)) -> ok(U22(X)) isList(ok(X)) -> ok(isList(X)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(ok(X)) -> ok(U42(X)) isNeList(ok(X)) -> ok(isNeList(X)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(ok(X)) -> ok(U52(X)) U61(ok(X)) -> ok(U61(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isPal(ok(X)) -> ok(isPal(X)) U81(ok(X)) -> ok(U81(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Usable Rule Processor: DPs: top#(ok(X)) -> top#(active(X)) TRS: active(U11(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(U61(tt())) -> mark(tt()) active(U72(tt())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(V)) -> mark(U81(isNePal(V))) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) isList(ok(X)) -> ok(isList(X)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) isQid(ok(X)) -> ok(isQid(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) isNePal(ok(X)) -> ok(isNePal(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) KBO Processor: argument filtering: pi(__) = 0 pi(active) = 0 pi(mark) = 0 pi(tt) = [] pi(U11) = 0 pi(U21) = 0 pi(isList) = 0 pi(U22) = 0 pi(U31) = 0 pi(U41) = 1 pi(U42) = 0 pi(U51) = 1 pi(U52) = 0 pi(U61) = 0 pi(U71) = 0 pi(isPal) = 0 pi(U72) = 0 pi(U81) = 0 pi(isQid) = 0 pi(isNePal) = 0 pi(o) = [] pi(u) = [] pi(ok) = [0] pi(top#) = 0 usable rules: active(U11(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(U61(tt())) -> mark(tt()) active(U72(tt())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(V)) -> mark(U81(isNePal(V))) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) isList(ok(X)) -> ok(isList(X)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) isQid(ok(X)) -> ok(isQid(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) isNePal(ok(X)) -> ok(isNePal(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) weight function: w0 = 1 w(top#) = w(ok) = w(u) = w(o) = w(U72) = w(tt) = 1 w(isNePal) = w(isQid) = w(U81) = w(isPal) = w(U71) = w(U61) = w( U52) = w(U51) = w(U42) = w(U41) = w(U31) = w(U22) = w(isList) = w( U21) = w(U11) = w(mark) = w(active) = w(__) = 0 precedence: u ~ o > top# ~ ok ~ isNePal ~ isQid ~ U81 ~ U72 ~ isPal ~ U71 ~ U61 ~ U52 ~ U51 ~ U42 ~ U41 ~ U31 ~ U22 ~ isList ~ U21 ~ U11 ~ tt ~ mark ~ active ~ __ problem: DPs: TRS: active(U11(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(U61(tt())) -> mark(tt()) active(U72(tt())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(V)) -> mark(U81(isNePal(V))) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) isList(ok(X)) -> ok(isList(X)) U52(mark(X)) -> mark(U52(X)) U52(ok(X)) -> ok(U52(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) isQid(ok(X)) -> ok(isQid(X)) U61(mark(X)) -> mark(U61(X)) U61(ok(X)) -> ok(U61(X)) isNePal(ok(X)) -> ok(isNePal(X)) U81(mark(X)) -> mark(U81(X)) U81(ok(X)) -> ok(U81(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U11(ok(X)) -> ok(U11(X)) U22(mark(X)) -> mark(U22(X)) U22(ok(X)) -> ok(U22(X)) U31(mark(X)) -> mark(U31(X)) U31(ok(X)) -> ok(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U42(ok(X)) -> ok(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U72(ok(X)) -> ok(U72(X)) Qed DPs: active#(__(X1,X2)) -> active#(X1) active#(__(X1,X2)) -> active#(X2) active#(U11(X)) -> active#(X) active#(U21(X1,X2)) -> active#(X1) active#(U22(X)) -> active#(X) active#(U31(X)) -> active#(X) active#(U41(X1,X2)) -> active#(X1) active#(U42(X)) -> active#(X) active#(U51(X1,X2)) -> active#(X1) active#(U52(X)) -> active#(X) active#(U61(X)) -> active#(X) active#(U71(X1,X2)) -> active#(X1) active#(U72(X)) -> active#(X) active#(U81(X)) -> active#(X) TRS: active(U11(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(U61(tt())) -> mark(tt()) active(U72(tt())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(V)) -> mark(U81(isNePal(V))) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U61(mark(X)) -> mark(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U81(mark(X)) -> mark(U81(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(ok(X)) -> ok(U22(X)) isList(ok(X)) -> ok(isList(X)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(ok(X)) -> ok(U42(X)) isNeList(ok(X)) -> ok(isNeList(X)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(ok(X)) -> ok(U52(X)) U61(ok(X)) -> ok(U61(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isPal(ok(X)) -> ok(isPal(X)) U81(ok(X)) -> ok(U81(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(active#) = 0 problem: DPs: TRS: active(U11(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(U61(tt())) -> mark(tt()) active(U72(tt())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(V)) -> mark(U81(isNePal(V))) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U61(mark(X)) -> mark(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U81(mark(X)) -> mark(U81(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(ok(X)) -> ok(U22(X)) isList(ok(X)) -> ok(isList(X)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(ok(X)) -> ok(U42(X)) isNeList(ok(X)) -> ok(isNeList(X)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(ok(X)) -> ok(U52(X)) U61(ok(X)) -> ok(U61(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isPal(ok(X)) -> ok(isPal(X)) U81(ok(X)) -> ok(U81(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: proper#(__(X1,X2)) -> proper#(X2) proper#(__(X1,X2)) -> proper#(X1) proper#(U11(X)) -> proper#(X) proper#(U21(X1,X2)) -> proper#(X2) proper#(U21(X1,X2)) -> proper#(X1) proper#(U22(X)) -> proper#(X) proper#(isList(X)) -> proper#(X) proper#(U31(X)) -> proper#(X) proper#(U41(X1,X2)) -> proper#(X2) proper#(U41(X1,X2)) -> proper#(X1) proper#(U42(X)) -> proper#(X) proper#(isNeList(X)) -> proper#(X) proper#(U51(X1,X2)) -> proper#(X2) proper#(U51(X1,X2)) -> proper#(X1) proper#(U52(X)) -> proper#(X) proper#(U61(X)) -> proper#(X) proper#(U71(X1,X2)) -> proper#(X2) proper#(U71(X1,X2)) -> proper#(X1) proper#(U72(X)) -> proper#(X) proper#(isPal(X)) -> proper#(X) proper#(U81(X)) -> proper#(X) proper#(isQid(X)) -> proper#(X) proper#(isNePal(X)) -> proper#(X) TRS: active(U11(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(U61(tt())) -> mark(tt()) active(U72(tt())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(V)) -> mark(U81(isNePal(V))) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U61(mark(X)) -> mark(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U81(mark(X)) -> mark(U81(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(ok(X)) -> ok(U22(X)) isList(ok(X)) -> ok(isList(X)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(ok(X)) -> ok(U42(X)) isNeList(ok(X)) -> ok(isNeList(X)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(ok(X)) -> ok(U52(X)) U61(ok(X)) -> ok(U61(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isPal(ok(X)) -> ok(isPal(X)) U81(ok(X)) -> ok(U81(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(proper#) = 0 problem: DPs: TRS: active(U11(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(U61(tt())) -> mark(tt()) active(U72(tt())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(V)) -> mark(U81(isNePal(V))) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U61(mark(X)) -> mark(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U81(mark(X)) -> mark(U81(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(ok(X)) -> ok(U22(X)) isList(ok(X)) -> ok(isList(X)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(ok(X)) -> ok(U42(X)) isNeList(ok(X)) -> ok(isNeList(X)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(ok(X)) -> ok(U52(X)) U61(ok(X)) -> ok(U61(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isPal(ok(X)) -> ok(isPal(X)) U81(ok(X)) -> ok(U81(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: isNePal#(ok(X)) -> isNePal#(X) TRS: active(U11(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(U61(tt())) -> mark(tt()) active(U72(tt())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(V)) -> mark(U81(isNePal(V))) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U61(mark(X)) -> mark(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U81(mark(X)) -> mark(U81(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(ok(X)) -> ok(U22(X)) isList(ok(X)) -> ok(isList(X)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(ok(X)) -> ok(U42(X)) isNeList(ok(X)) -> ok(isNeList(X)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(ok(X)) -> ok(U52(X)) U61(ok(X)) -> ok(U61(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isPal(ok(X)) -> ok(isPal(X)) U81(ok(X)) -> ok(U81(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(isNePal#) = 0 problem: DPs: TRS: active(U11(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(U61(tt())) -> mark(tt()) active(U72(tt())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(V)) -> mark(U81(isNePal(V))) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U61(mark(X)) -> mark(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U81(mark(X)) -> mark(U81(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(ok(X)) -> ok(U22(X)) isList(ok(X)) -> ok(isList(X)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(ok(X)) -> ok(U42(X)) isNeList(ok(X)) -> ok(isNeList(X)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(ok(X)) -> ok(U52(X)) U61(ok(X)) -> ok(U61(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isPal(ok(X)) -> ok(isPal(X)) U81(ok(X)) -> ok(U81(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: isQid#(ok(X)) -> isQid#(X) TRS: active(U11(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(U61(tt())) -> mark(tt()) active(U72(tt())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(V)) -> mark(U81(isNePal(V))) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U61(mark(X)) -> mark(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U81(mark(X)) -> mark(U81(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(ok(X)) -> ok(U22(X)) isList(ok(X)) -> ok(isList(X)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(ok(X)) -> ok(U42(X)) isNeList(ok(X)) -> ok(isNeList(X)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(ok(X)) -> ok(U52(X)) U61(ok(X)) -> ok(U61(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isPal(ok(X)) -> ok(isPal(X)) U81(ok(X)) -> ok(U81(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(isQid#) = 0 problem: DPs: TRS: active(U11(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(U61(tt())) -> mark(tt()) active(U72(tt())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(V)) -> mark(U81(isNePal(V))) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U61(mark(X)) -> mark(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U81(mark(X)) -> mark(U81(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(ok(X)) -> ok(U22(X)) isList(ok(X)) -> ok(isList(X)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(ok(X)) -> ok(U42(X)) isNeList(ok(X)) -> ok(isNeList(X)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(ok(X)) -> ok(U52(X)) U61(ok(X)) -> ok(U61(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isPal(ok(X)) -> ok(isPal(X)) U81(ok(X)) -> ok(U81(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U81#(mark(X)) -> U81#(X) U81#(ok(X)) -> U81#(X) TRS: active(U11(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(U61(tt())) -> mark(tt()) active(U72(tt())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(V)) -> mark(U81(isNePal(V))) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U61(mark(X)) -> mark(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U81(mark(X)) -> mark(U81(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(ok(X)) -> ok(U22(X)) isList(ok(X)) -> ok(isList(X)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(ok(X)) -> ok(U42(X)) isNeList(ok(X)) -> ok(isNeList(X)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(ok(X)) -> ok(U52(X)) U61(ok(X)) -> ok(U61(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isPal(ok(X)) -> ok(isPal(X)) U81(ok(X)) -> ok(U81(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(U81#) = 0 problem: DPs: TRS: active(U11(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(U61(tt())) -> mark(tt()) active(U72(tt())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(V)) -> mark(U81(isNePal(V))) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U61(mark(X)) -> mark(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U81(mark(X)) -> mark(U81(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(ok(X)) -> ok(U22(X)) isList(ok(X)) -> ok(isList(X)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(ok(X)) -> ok(U42(X)) isNeList(ok(X)) -> ok(isNeList(X)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(ok(X)) -> ok(U52(X)) U61(ok(X)) -> ok(U61(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isPal(ok(X)) -> ok(isPal(X)) U81(ok(X)) -> ok(U81(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: isPal#(ok(X)) -> isPal#(X) TRS: active(U11(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(U61(tt())) -> mark(tt()) active(U72(tt())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(V)) -> mark(U81(isNePal(V))) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U61(mark(X)) -> mark(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U81(mark(X)) -> mark(U81(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(ok(X)) -> ok(U22(X)) isList(ok(X)) -> ok(isList(X)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(ok(X)) -> ok(U42(X)) isNeList(ok(X)) -> ok(isNeList(X)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(ok(X)) -> ok(U52(X)) U61(ok(X)) -> ok(U61(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isPal(ok(X)) -> ok(isPal(X)) U81(ok(X)) -> ok(U81(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(isPal#) = 0 problem: DPs: TRS: active(U11(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(U61(tt())) -> mark(tt()) active(U72(tt())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(V)) -> mark(U81(isNePal(V))) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U61(mark(X)) -> mark(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U81(mark(X)) -> mark(U81(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(ok(X)) -> ok(U22(X)) isList(ok(X)) -> ok(isList(X)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(ok(X)) -> ok(U42(X)) isNeList(ok(X)) -> ok(isNeList(X)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(ok(X)) -> ok(U52(X)) U61(ok(X)) -> ok(U61(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isPal(ok(X)) -> ok(isPal(X)) U81(ok(X)) -> ok(U81(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U72#(mark(X)) -> U72#(X) U72#(ok(X)) -> U72#(X) TRS: active(U11(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(U61(tt())) -> mark(tt()) active(U72(tt())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(V)) -> mark(U81(isNePal(V))) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U61(mark(X)) -> mark(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U81(mark(X)) -> mark(U81(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(ok(X)) -> ok(U22(X)) isList(ok(X)) -> ok(isList(X)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(ok(X)) -> ok(U42(X)) isNeList(ok(X)) -> ok(isNeList(X)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(ok(X)) -> ok(U52(X)) U61(ok(X)) -> ok(U61(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isPal(ok(X)) -> ok(isPal(X)) U81(ok(X)) -> ok(U81(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(U72#) = 0 problem: DPs: TRS: active(U11(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(U61(tt())) -> mark(tt()) active(U72(tt())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(V)) -> mark(U81(isNePal(V))) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U61(mark(X)) -> mark(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U81(mark(X)) -> mark(U81(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(ok(X)) -> ok(U22(X)) isList(ok(X)) -> ok(isList(X)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(ok(X)) -> ok(U42(X)) isNeList(ok(X)) -> ok(isNeList(X)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(ok(X)) -> ok(U52(X)) U61(ok(X)) -> ok(U61(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isPal(ok(X)) -> ok(isPal(X)) U81(ok(X)) -> ok(U81(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U71#(mark(X1),X2) -> U71#(X1,X2) U71#(ok(X1),ok(X2)) -> U71#(X1,X2) TRS: active(U11(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(U61(tt())) -> mark(tt()) active(U72(tt())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(V)) -> mark(U81(isNePal(V))) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U61(mark(X)) -> mark(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U81(mark(X)) -> mark(U81(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(ok(X)) -> ok(U22(X)) isList(ok(X)) -> ok(isList(X)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(ok(X)) -> ok(U42(X)) isNeList(ok(X)) -> ok(isNeList(X)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(ok(X)) -> ok(U52(X)) U61(ok(X)) -> ok(U61(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isPal(ok(X)) -> ok(isPal(X)) U81(ok(X)) -> ok(U81(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(U71#) = 0 problem: DPs: TRS: active(U11(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(U61(tt())) -> mark(tt()) active(U72(tt())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(V)) -> mark(U81(isNePal(V))) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U61(mark(X)) -> mark(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U81(mark(X)) -> mark(U81(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(ok(X)) -> ok(U22(X)) isList(ok(X)) -> ok(isList(X)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(ok(X)) -> ok(U42(X)) isNeList(ok(X)) -> ok(isNeList(X)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(ok(X)) -> ok(U52(X)) U61(ok(X)) -> ok(U61(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isPal(ok(X)) -> ok(isPal(X)) U81(ok(X)) -> ok(U81(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U61#(mark(X)) -> U61#(X) U61#(ok(X)) -> U61#(X) TRS: active(U11(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(U61(tt())) -> mark(tt()) active(U72(tt())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(V)) -> mark(U81(isNePal(V))) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U61(mark(X)) -> mark(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U81(mark(X)) -> mark(U81(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(ok(X)) -> ok(U22(X)) isList(ok(X)) -> ok(isList(X)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(ok(X)) -> ok(U42(X)) isNeList(ok(X)) -> ok(isNeList(X)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(ok(X)) -> ok(U52(X)) U61(ok(X)) -> ok(U61(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isPal(ok(X)) -> ok(isPal(X)) U81(ok(X)) -> ok(U81(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(U61#) = 0 problem: DPs: TRS: active(U11(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(U61(tt())) -> mark(tt()) active(U72(tt())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(V)) -> mark(U81(isNePal(V))) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U61(mark(X)) -> mark(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U81(mark(X)) -> mark(U81(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(ok(X)) -> ok(U22(X)) isList(ok(X)) -> ok(isList(X)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(ok(X)) -> ok(U42(X)) isNeList(ok(X)) -> ok(isNeList(X)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(ok(X)) -> ok(U52(X)) U61(ok(X)) -> ok(U61(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isPal(ok(X)) -> ok(isPal(X)) U81(ok(X)) -> ok(U81(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U52#(mark(X)) -> U52#(X) U52#(ok(X)) -> U52#(X) TRS: active(U11(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(U61(tt())) -> mark(tt()) active(U72(tt())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(V)) -> mark(U81(isNePal(V))) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U61(mark(X)) -> mark(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U81(mark(X)) -> mark(U81(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(ok(X)) -> ok(U22(X)) isList(ok(X)) -> ok(isList(X)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(ok(X)) -> ok(U42(X)) isNeList(ok(X)) -> ok(isNeList(X)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(ok(X)) -> ok(U52(X)) U61(ok(X)) -> ok(U61(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isPal(ok(X)) -> ok(isPal(X)) U81(ok(X)) -> ok(U81(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(U52#) = 0 problem: DPs: TRS: active(U11(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(U61(tt())) -> mark(tt()) active(U72(tt())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(V)) -> mark(U81(isNePal(V))) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U61(mark(X)) -> mark(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U81(mark(X)) -> mark(U81(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(ok(X)) -> ok(U22(X)) isList(ok(X)) -> ok(isList(X)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(ok(X)) -> ok(U42(X)) isNeList(ok(X)) -> ok(isNeList(X)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(ok(X)) -> ok(U52(X)) U61(ok(X)) -> ok(U61(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isPal(ok(X)) -> ok(isPal(X)) U81(ok(X)) -> ok(U81(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U51#(mark(X1),X2) -> U51#(X1,X2) U51#(ok(X1),ok(X2)) -> U51#(X1,X2) TRS: active(U11(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(U61(tt())) -> mark(tt()) active(U72(tt())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(V)) -> mark(U81(isNePal(V))) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U61(mark(X)) -> mark(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U81(mark(X)) -> mark(U81(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(ok(X)) -> ok(U22(X)) isList(ok(X)) -> ok(isList(X)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(ok(X)) -> ok(U42(X)) isNeList(ok(X)) -> ok(isNeList(X)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(ok(X)) -> ok(U52(X)) U61(ok(X)) -> ok(U61(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isPal(ok(X)) -> ok(isPal(X)) U81(ok(X)) -> ok(U81(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(U51#) = 0 problem: DPs: TRS: active(U11(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(U61(tt())) -> mark(tt()) active(U72(tt())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(V)) -> mark(U81(isNePal(V))) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U61(mark(X)) -> mark(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U81(mark(X)) -> mark(U81(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(ok(X)) -> ok(U22(X)) isList(ok(X)) -> ok(isList(X)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(ok(X)) -> ok(U42(X)) isNeList(ok(X)) -> ok(isNeList(X)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(ok(X)) -> ok(U52(X)) U61(ok(X)) -> ok(U61(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isPal(ok(X)) -> ok(isPal(X)) U81(ok(X)) -> ok(U81(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: isNeList#(ok(X)) -> isNeList#(X) TRS: active(U11(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(U61(tt())) -> mark(tt()) active(U72(tt())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(V)) -> mark(U81(isNePal(V))) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U61(mark(X)) -> mark(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U81(mark(X)) -> mark(U81(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(ok(X)) -> ok(U22(X)) isList(ok(X)) -> ok(isList(X)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(ok(X)) -> ok(U42(X)) isNeList(ok(X)) -> ok(isNeList(X)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(ok(X)) -> ok(U52(X)) U61(ok(X)) -> ok(U61(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isPal(ok(X)) -> ok(isPal(X)) U81(ok(X)) -> ok(U81(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(isNeList#) = 0 problem: DPs: TRS: active(U11(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(U61(tt())) -> mark(tt()) active(U72(tt())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(V)) -> mark(U81(isNePal(V))) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U61(mark(X)) -> mark(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U81(mark(X)) -> mark(U81(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(ok(X)) -> ok(U22(X)) isList(ok(X)) -> ok(isList(X)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(ok(X)) -> ok(U42(X)) isNeList(ok(X)) -> ok(isNeList(X)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(ok(X)) -> ok(U52(X)) U61(ok(X)) -> ok(U61(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isPal(ok(X)) -> ok(isPal(X)) U81(ok(X)) -> ok(U81(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U42#(mark(X)) -> U42#(X) U42#(ok(X)) -> U42#(X) TRS: active(U11(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(U61(tt())) -> mark(tt()) active(U72(tt())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(V)) -> mark(U81(isNePal(V))) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U61(mark(X)) -> mark(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U81(mark(X)) -> mark(U81(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(ok(X)) -> ok(U22(X)) isList(ok(X)) -> ok(isList(X)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(ok(X)) -> ok(U42(X)) isNeList(ok(X)) -> ok(isNeList(X)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(ok(X)) -> ok(U52(X)) U61(ok(X)) -> ok(U61(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isPal(ok(X)) -> ok(isPal(X)) U81(ok(X)) -> ok(U81(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(U42#) = 0 problem: DPs: TRS: active(U11(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(U61(tt())) -> mark(tt()) active(U72(tt())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(V)) -> mark(U81(isNePal(V))) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U61(mark(X)) -> mark(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U81(mark(X)) -> mark(U81(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(ok(X)) -> ok(U22(X)) isList(ok(X)) -> ok(isList(X)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(ok(X)) -> ok(U42(X)) isNeList(ok(X)) -> ok(isNeList(X)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(ok(X)) -> ok(U52(X)) U61(ok(X)) -> ok(U61(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isPal(ok(X)) -> ok(isPal(X)) U81(ok(X)) -> ok(U81(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U41#(mark(X1),X2) -> U41#(X1,X2) U41#(ok(X1),ok(X2)) -> U41#(X1,X2) TRS: active(U11(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(U61(tt())) -> mark(tt()) active(U72(tt())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(V)) -> mark(U81(isNePal(V))) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U61(mark(X)) -> mark(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U81(mark(X)) -> mark(U81(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(ok(X)) -> ok(U22(X)) isList(ok(X)) -> ok(isList(X)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(ok(X)) -> ok(U42(X)) isNeList(ok(X)) -> ok(isNeList(X)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(ok(X)) -> ok(U52(X)) U61(ok(X)) -> ok(U61(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isPal(ok(X)) -> ok(isPal(X)) U81(ok(X)) -> ok(U81(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(U41#) = 0 problem: DPs: TRS: active(U11(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(U61(tt())) -> mark(tt()) active(U72(tt())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(V)) -> mark(U81(isNePal(V))) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U61(mark(X)) -> mark(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U81(mark(X)) -> mark(U81(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(ok(X)) -> ok(U22(X)) isList(ok(X)) -> ok(isList(X)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(ok(X)) -> ok(U42(X)) isNeList(ok(X)) -> ok(isNeList(X)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(ok(X)) -> ok(U52(X)) U61(ok(X)) -> ok(U61(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isPal(ok(X)) -> ok(isPal(X)) U81(ok(X)) -> ok(U81(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U31#(mark(X)) -> U31#(X) U31#(ok(X)) -> U31#(X) TRS: active(U11(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(U61(tt())) -> mark(tt()) active(U72(tt())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(V)) -> mark(U81(isNePal(V))) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U61(mark(X)) -> mark(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U81(mark(X)) -> mark(U81(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(ok(X)) -> ok(U22(X)) isList(ok(X)) -> ok(isList(X)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(ok(X)) -> ok(U42(X)) isNeList(ok(X)) -> ok(isNeList(X)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(ok(X)) -> ok(U52(X)) U61(ok(X)) -> ok(U61(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isPal(ok(X)) -> ok(isPal(X)) U81(ok(X)) -> ok(U81(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(U31#) = 0 problem: DPs: TRS: active(U11(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(U61(tt())) -> mark(tt()) active(U72(tt())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(V)) -> mark(U81(isNePal(V))) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U61(mark(X)) -> mark(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U81(mark(X)) -> mark(U81(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(ok(X)) -> ok(U22(X)) isList(ok(X)) -> ok(isList(X)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(ok(X)) -> ok(U42(X)) isNeList(ok(X)) -> ok(isNeList(X)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(ok(X)) -> ok(U52(X)) U61(ok(X)) -> ok(U61(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isPal(ok(X)) -> ok(isPal(X)) U81(ok(X)) -> ok(U81(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: isList#(ok(X)) -> isList#(X) TRS: active(U11(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(U61(tt())) -> mark(tt()) active(U72(tt())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(V)) -> mark(U81(isNePal(V))) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U61(mark(X)) -> mark(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U81(mark(X)) -> mark(U81(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(ok(X)) -> ok(U22(X)) isList(ok(X)) -> ok(isList(X)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(ok(X)) -> ok(U42(X)) isNeList(ok(X)) -> ok(isNeList(X)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(ok(X)) -> ok(U52(X)) U61(ok(X)) -> ok(U61(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isPal(ok(X)) -> ok(isPal(X)) U81(ok(X)) -> ok(U81(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(isList#) = 0 problem: DPs: TRS: active(U11(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(U61(tt())) -> mark(tt()) active(U72(tt())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(V)) -> mark(U81(isNePal(V))) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U61(mark(X)) -> mark(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U81(mark(X)) -> mark(U81(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(ok(X)) -> ok(U22(X)) isList(ok(X)) -> ok(isList(X)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(ok(X)) -> ok(U42(X)) isNeList(ok(X)) -> ok(isNeList(X)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(ok(X)) -> ok(U52(X)) U61(ok(X)) -> ok(U61(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isPal(ok(X)) -> ok(isPal(X)) U81(ok(X)) -> ok(U81(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U22#(mark(X)) -> U22#(X) U22#(ok(X)) -> U22#(X) TRS: active(U11(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(U61(tt())) -> mark(tt()) active(U72(tt())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(V)) -> mark(U81(isNePal(V))) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U61(mark(X)) -> mark(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U81(mark(X)) -> mark(U81(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(ok(X)) -> ok(U22(X)) isList(ok(X)) -> ok(isList(X)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(ok(X)) -> ok(U42(X)) isNeList(ok(X)) -> ok(isNeList(X)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(ok(X)) -> ok(U52(X)) U61(ok(X)) -> ok(U61(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isPal(ok(X)) -> ok(isPal(X)) U81(ok(X)) -> ok(U81(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(U22#) = 0 problem: DPs: TRS: active(U11(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(U61(tt())) -> mark(tt()) active(U72(tt())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(V)) -> mark(U81(isNePal(V))) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U61(mark(X)) -> mark(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U81(mark(X)) -> mark(U81(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(ok(X)) -> ok(U22(X)) isList(ok(X)) -> ok(isList(X)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(ok(X)) -> ok(U42(X)) isNeList(ok(X)) -> ok(isNeList(X)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(ok(X)) -> ok(U52(X)) U61(ok(X)) -> ok(U61(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isPal(ok(X)) -> ok(isPal(X)) U81(ok(X)) -> ok(U81(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U21#(mark(X1),X2) -> U21#(X1,X2) U21#(ok(X1),ok(X2)) -> U21#(X1,X2) TRS: active(U11(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(U61(tt())) -> mark(tt()) active(U72(tt())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(V)) -> mark(U81(isNePal(V))) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U61(mark(X)) -> mark(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U81(mark(X)) -> mark(U81(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(ok(X)) -> ok(U22(X)) isList(ok(X)) -> ok(isList(X)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(ok(X)) -> ok(U42(X)) isNeList(ok(X)) -> ok(isNeList(X)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(ok(X)) -> ok(U52(X)) U61(ok(X)) -> ok(U61(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isPal(ok(X)) -> ok(isPal(X)) U81(ok(X)) -> ok(U81(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(U21#) = 0 problem: DPs: TRS: active(U11(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(U61(tt())) -> mark(tt()) active(U72(tt())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(V)) -> mark(U81(isNePal(V))) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U61(mark(X)) -> mark(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U81(mark(X)) -> mark(U81(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(ok(X)) -> ok(U22(X)) isList(ok(X)) -> ok(isList(X)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(ok(X)) -> ok(U42(X)) isNeList(ok(X)) -> ok(isNeList(X)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(ok(X)) -> ok(U52(X)) U61(ok(X)) -> ok(U61(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isPal(ok(X)) -> ok(isPal(X)) U81(ok(X)) -> ok(U81(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U11#(mark(X)) -> U11#(X) U11#(ok(X)) -> U11#(X) TRS: active(U11(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(U61(tt())) -> mark(tt()) active(U72(tt())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(V)) -> mark(U81(isNePal(V))) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U61(mark(X)) -> mark(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U81(mark(X)) -> mark(U81(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(ok(X)) -> ok(U22(X)) isList(ok(X)) -> ok(isList(X)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(ok(X)) -> ok(U42(X)) isNeList(ok(X)) -> ok(isNeList(X)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(ok(X)) -> ok(U52(X)) U61(ok(X)) -> ok(U61(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isPal(ok(X)) -> ok(isPal(X)) U81(ok(X)) -> ok(U81(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(U11#) = 0 problem: DPs: TRS: active(U11(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(U61(tt())) -> mark(tt()) active(U72(tt())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(V)) -> mark(U81(isNePal(V))) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U61(mark(X)) -> mark(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U81(mark(X)) -> mark(U81(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(ok(X)) -> ok(U22(X)) isList(ok(X)) -> ok(isList(X)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(ok(X)) -> ok(U42(X)) isNeList(ok(X)) -> ok(isNeList(X)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(ok(X)) -> ok(U52(X)) U61(ok(X)) -> ok(U61(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isPal(ok(X)) -> ok(isPal(X)) U81(ok(X)) -> ok(U81(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: __#(mark(X1),X2) -> __#(X1,X2) __#(X1,mark(X2)) -> __#(X1,X2) __#(ok(X1),ok(X2)) -> __#(X1,X2) TRS: active(U11(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(U61(tt())) -> mark(tt()) active(U72(tt())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(V)) -> mark(U81(isNePal(V))) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U61(mark(X)) -> mark(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U81(mark(X)) -> mark(U81(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(ok(X)) -> ok(U22(X)) isList(ok(X)) -> ok(isList(X)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(ok(X)) -> ok(U42(X)) isNeList(ok(X)) -> ok(isNeList(X)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(ok(X)) -> ok(U52(X)) U61(ok(X)) -> ok(U61(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isPal(ok(X)) -> ok(isPal(X)) U81(ok(X)) -> ok(U81(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(__#) = 0 problem: DPs: __#(X1,mark(X2)) -> __#(X1,X2) TRS: active(U11(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(U61(tt())) -> mark(tt()) active(U72(tt())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(V)) -> mark(U81(isNePal(V))) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U61(mark(X)) -> mark(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U81(mark(X)) -> mark(U81(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(ok(X)) -> ok(U22(X)) isList(ok(X)) -> ok(isList(X)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(ok(X)) -> ok(U42(X)) isNeList(ok(X)) -> ok(isNeList(X)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(ok(X)) -> ok(U52(X)) U61(ok(X)) -> ok(U61(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isPal(ok(X)) -> ok(isPal(X)) U81(ok(X)) -> ok(U81(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(__#) = 1 problem: DPs: TRS: active(U11(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isList(V2))) active(U61(tt())) -> mark(tt()) active(U72(tt())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(U21(isList(V1),V2)) active(isNePal(V)) -> mark(U61(isQid(V))) active(isPal(V)) -> mark(U81(isNePal(V))) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U21(X1,X2)) -> U21(active(X1),X2) active(U22(X)) -> U22(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X)) -> U61(active(X)) active(U71(X1,X2)) -> U71(active(X1),X2) active(U72(X)) -> U72(active(X)) active(U81(X)) -> U81(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U21(mark(X1),X2) -> mark(U21(X1,X2)) U22(mark(X)) -> mark(U22(X)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U61(mark(X)) -> mark(U61(X)) U71(mark(X1),X2) -> mark(U71(X1,X2)) U72(mark(X)) -> mark(U72(X)) U81(mark(X)) -> mark(U81(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) proper(U22(X)) -> U22(proper(X)) proper(isList(X)) -> isList(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(U61(X)) -> U61(proper(X)) proper(U71(X1,X2)) -> U71(proper(X1),proper(X2)) proper(U72(X)) -> U72(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(U81(X)) -> U81(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) U22(ok(X)) -> ok(U22(X)) isList(ok(X)) -> ok(isList(X)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(ok(X)) -> ok(U42(X)) isNeList(ok(X)) -> ok(isNeList(X)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(ok(X)) -> ok(U52(X)) U61(ok(X)) -> ok(U61(X)) U71(ok(X1),ok(X2)) -> ok(U71(X1,X2)) U72(ok(X)) -> ok(U72(X)) isPal(ok(X)) -> ok(isPal(X)) U81(ok(X)) -> ok(U81(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed