ceta_eq: termination proof not accepted 1: error below switch to dependency pairs 1.1: error below the dependency graph processor 1.1.1: error below the reduction pair processor 1.1.1.1: error below the reduction pair processor 1.1.1.1.1: error below the reduction pair processor 1.1.1.1.1.1: error when applying the reduction pair processor to remove from the DP problem pairs: active#(U61(tt, V)) -> mark#(U62(isQid(V))) active#(isNePal(V)) -> mark#(U61(isPalListKind(V), V)) mark#(__(X1, X2)) -> active#(__(mark(X1), mark(X2))) mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)) mark#(U12(X)) -> active#(U12(mark(X))) mark#(U12(X)) -> mark#(X) mark#(isNeList(X)) -> active#(isNeList(X)) mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)) mark#(U22(X1, X2)) -> active#(U22(mark(X1), X2)) mark#(isList(X)) -> active#(isList(X)) mark#(U23(X)) -> active#(U23(mark(X))) mark#(U31(X1, X2)) -> active#(U31(mark(X1), X2)) mark#(U32(X)) -> active#(U32(mark(X))) mark#(isQid(X)) -> active#(isQid(X)) mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)) mark#(U42(X1, X2)) -> active#(U42(mark(X1), X2)) mark#(U43(X)) -> active#(U43(mark(X))) mark#(U51(X1, X2, X3)) -> active#(U51(mark(X1), X2, X3)) mark#(U52(X1, X2)) -> active#(U52(mark(X1), X2)) mark#(U53(X)) -> active#(U53(mark(X))) mark#(U53(X)) -> mark#(X) mark#(U61(X1, X2)) -> active#(U61(mark(X1), X2)) mark#(U61(X1, X2)) -> mark#(X1) mark#(U62(X)) -> active#(U62(mark(X))) mark#(U62(X)) -> mark#(X) mark#(U71(X1, X2)) -> active#(U71(mark(X1), X2)) mark#(U72(X)) -> active#(U72(mark(X))) mark#(isNePal(X)) -> active#(isNePal(X)) mark#(isPalListKind(X)) -> active#(isPalListKind(X)) mark#(isPal(X)) -> active#(isPal(X)) rules: U11(mark(X1), X2) -> U11(X1, X2) U11(X1, mark(X2)) -> U11(X1, X2) U11(active(X1), X2) -> U11(X1, X2) U11(X1, active(X2)) -> U11(X1, X2) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) U21(mark(X1), X2, X3) -> U21(X1, X2, X3) U21(X1, mark(X2), X3) -> U21(X1, X2, X3) U21(X1, X2, mark(X3)) -> U21(X1, X2, X3) U21(active(X1), X2, X3) -> U21(X1, X2, X3) U21(X1, active(X2), X3) -> U21(X1, X2, X3) U21(X1, X2, active(X3)) -> U21(X1, X2, X3) U22(mark(X1), X2) -> U22(X1, X2) U22(X1, mark(X2)) -> U22(X1, X2) U22(active(X1), X2) -> U22(X1, X2) U22(X1, active(X2)) -> U22(X1, X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1), X2) -> U31(X1, X2) U31(X1, mark(X2)) -> U31(X1, X2) U31(active(X1), X2) -> U31(X1, X2) U31(X1, active(X2)) -> U31(X1, X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) U41(mark(X1), X2, X3) -> U41(X1, X2, X3) U41(X1, mark(X2), X3) -> U41(X1, X2, X3) U41(X1, X2, mark(X3)) -> U41(X1, X2, X3) U41(active(X1), X2, X3) -> U41(X1, X2, X3) U41(X1, active(X2), X3) -> U41(X1, X2, X3) U41(X1, X2, active(X3)) -> U41(X1, X2, X3) U42(mark(X1), X2) -> U42(X1, X2) U42(X1, mark(X2)) -> U42(X1, X2) U42(active(X1), X2) -> U42(X1, X2) U42(X1, active(X2)) -> U42(X1, X2) U43(mark(X)) -> U43(X) U43(active(X)) -> U43(X) U51(mark(X1), X2, X3) -> U51(X1, X2, X3) U51(X1, mark(X2), X3) -> U51(X1, X2, X3) U51(X1, X2, mark(X3)) -> U51(X1, X2, X3) U51(active(X1), X2, X3) -> U51(X1, X2, X3) U51(X1, active(X2), X3) -> U51(X1, X2, X3) U51(X1, X2, active(X3)) -> U51(X1, X2, X3) U52(mark(X1), X2) -> U52(X1, X2) U52(X1, mark(X2)) -> U52(X1, X2) U52(active(X1), X2) -> U52(X1, X2) U52(X1, active(X2)) -> U52(X1, X2) U53(mark(X)) -> U53(X) U53(active(X)) -> U53(X) U61(mark(X1), X2) -> U61(X1, X2) U61(X1, mark(X2)) -> U61(X1, X2) U61(active(X1), X2) -> U61(X1, X2) U61(X1, active(X2)) -> U61(X1, X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1), X2) -> U71(X1, X2) U71(X1, mark(X2)) -> U71(X1, X2) U71(active(X1), X2) -> U71(X1, X2) U71(X1, active(X2)) -> U71(X1, X2) U72(mark(X)) -> U72(X) U72(active(X)) -> U72(X) __(mark(X1), X2) -> __(X1, X2) __(X1, mark(X2)) -> __(X1, X2) __(active(X1), X2) -> __(X1, X2) __(X1, active(X2)) -> __(X1, X2) active(__(__(X, Y), Z)) -> mark(__(X, __(Y, Z))) active(__(X, nil)) -> mark(X) active(__(nil, X)) -> mark(X) active(U11(tt, V)) -> mark(U12(isNeList(V))) active(U12(tt)) -> mark(tt) active(U21(tt, V1, V2)) -> mark(U22(isList(V1), V2)) active(U22(tt, V2)) -> mark(U23(isList(V2))) active(U23(tt)) -> mark(tt) active(U31(tt, V)) -> mark(U32(isQid(V))) active(U32(tt)) -> mark(tt) active(U41(tt, V1, V2)) -> mark(U42(isList(V1), V2)) active(U42(tt, V2)) -> mark(U43(isNeList(V2))) active(U43(tt)) -> mark(tt) active(U51(tt, V1, V2)) -> mark(U52(isNeList(V1), V2)) active(U52(tt, V2)) -> mark(U53(isList(V2))) active(U53(tt)) -> mark(tt) active(U61(tt, V)) -> mark(U62(isQid(V))) active(U62(tt)) -> mark(tt) active(U71(tt, V)) -> mark(U72(isNePal(V))) active(U72(tt)) -> mark(tt) active(and(tt, X)) -> mark(X) active(isList(V)) -> mark(U11(isPalListKind(V), V)) active(isList(nil)) -> mark(tt) active(isList(__(V1, V2))) -> mark(U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)) active(isNeList(V)) -> mark(U31(isPalListKind(V), V)) active(isNeList(__(V1, V2))) -> mark(U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)) active(isNeList(__(V1, V2))) -> mark(U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)) active(isNePal(V)) -> mark(U61(isPalListKind(V), V)) active(isNePal(__(I, __(P, I)))) -> mark(and(and(isQid(I), isPalListKind(I)), and(isPal(P), isPalListKind(P)))) active(isPal(V)) -> mark(U71(isPalListKind(V), V)) active(isPal(nil)) -> mark(tt) active(isPalListKind(a)) -> mark(tt) active(isPalListKind(e)) -> mark(tt) active(isPalListKind(i)) -> mark(tt) active(isPalListKind(nil)) -> mark(tt) active(isPalListKind(o)) -> mark(tt) active(isPalListKind(u)) -> mark(tt) active(isPalListKind(__(V1, V2))) -> mark(and(isPalListKind(V1), isPalListKind(V2))) 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) and(mark(X1), X2) -> and(X1, X2) and(X1, mark(X2)) -> and(X1, X2) and(active(X1), X2) -> and(X1, X2) and(X1, active(X2)) -> and(X1, X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) isPalListKind(mark(X)) -> isPalListKind(X) isPalListKind(active(X)) -> isPalListKind(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) mark(__(X1, X2)) -> active(__(mark(X1), mark(X2))) mark(nil) -> active(nil) mark(U11(X1, X2)) -> active(U11(mark(X1), X2)) mark(tt) -> active(tt) mark(U12(X)) -> active(U12(mark(X))) mark(isNeList(X)) -> active(isNeList(X)) mark(U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)) mark(U22(X1, X2)) -> active(U22(mark(X1), X2)) mark(isList(X)) -> active(isList(X)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1, X2)) -> active(U31(mark(X1), X2)) mark(U32(X)) -> active(U32(mark(X))) mark(isQid(X)) -> active(isQid(X)) mark(U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3)) mark(U42(X1, X2)) -> active(U42(mark(X1), X2)) mark(U43(X)) -> active(U43(mark(X))) mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)) mark(U52(X1, X2)) -> active(U52(mark(X1), X2)) mark(U53(X)) -> active(U53(mark(X))) mark(U61(X1, X2)) -> active(U61(mark(X1), X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1, X2)) -> active(U71(mark(X1), X2)) mark(U72(X)) -> active(U72(mark(X))) mark(isNePal(X)) -> active(isNePal(X)) mark(and(X1, X2)) -> active(and(mark(X1), X2)) mark(isPalListKind(X)) -> active(isPalListKind(X)) mark(isPal(X)) -> active(isPal(X)) mark(a) -> active(a) mark(e) -> active(e) mark(i) -> active(i) mark(o) -> active(o) mark(u) -> active(u) the pairs active#(isNePal(V)) -> mark#(U61(isPalListKind(V), V)) could not apply the generic reduction pair processor with the following Argument Filter: pi(mark#/1) = [1] pi(__/2) = [1,2] pi(active#/1) = [1] pi(mark/1) = 1 pi(U11/2) = [2] pi(U12/1) = 1 pi(isNeList/1) = [1] pi(U21/3) = [1,2,3] pi(U22/2) = [2] pi(isList/1) = [1] pi(U23/1) = [] pi(U31/2) = [2] pi(U32/1) = [] pi(isQid/1) = [] pi(U41/3) = [2] pi(U61/2) = 1 pi(tt/0) = [] pi(U62/1) = 1 pi(U42/2) = 1 pi(U43/1) = [] pi(U51/3) = [3] pi(U52/2) = [2] pi(U53/1) = 1 pi(U71/2) = [] pi(isNePal/1) = [] pi(isPalListKind/1) = [] pi(U72/1) = 1 pi(isPal/1) = [] pi(active/1) = 1 pi(nil/0) = [] pi(and/2) = 2 pi(a/0) = [] pi(e/0) = [] pi(i/0) = [] pi(o/0) = [] pi(u/0) = [] RPO with the following precedence precedence(mark#[1]) = 2 precedence(__[2]) = 0 precedence(active#[1]) = 2 precedence(U11[2]) = 6 precedence(isNeList[1]) = 6 precedence(U21[3]) = 4 precedence(U22[2]) = 4 precedence(isList[1]) = 6 precedence(U23[1]) = 3 precedence(U31[2]) = 5 precedence(U32[1]) = 5 precedence(isQid[1]) = 1 precedence(U41[3]) = 6 precedence(tt[0]) = 1 precedence(U43[1]) = 1 precedence(U51[3]) = 6 precedence(U52[2]) = 6 precedence(U71[2]) = 7 precedence(isNePal[1]) = 7 precedence(isPalListKind[1]) = 1 precedence(isPal[1]) = 7 precedence(nil[0]) = 8 precedence(a[0]) = 9 precedence(e[0]) = 10 precedence(i[0]) = 11 precedence(o[0]) = 1 precedence(u[0]) = 12 precedence(_) = 0 and the following status status(mark#[1]) = mul status(__[2]) = lex status(active#[1]) = mul status(U11[2]) = mul status(isNeList[1]) = mul status(U21[3]) = mul status(U22[2]) = mul status(isList[1]) = mul status(U23[1]) = lex status(U31[2]) = lex status(U32[1]) = lex status(isQid[1]) = mul status(U41[3]) = mul status(tt[0]) = mul status(U43[1]) = mul status(U51[3]) = mul status(U52[2]) = mul status(U71[2]) = lex status(isNePal[1]) = lex status(isPalListKind[1]) = mul status(isPal[1]) = lex status(nil[0]) = mul status(a[0]) = mul status(e[0]) = mul status(i[0]) = mul status(o[0]) = mul status(u[0]) = mul status(_) = lex problem when orienting DPs could not orient active#(U61(tt, V)) >= mark#(U62(isQid(V))) pi( active#(U61(tt, V)) ) = active#(tt) pi( mark#(U62(isQid(V))) ) = mark#(isQid) could not orient active#(tt) >=RPO mark#(isQid)