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 dependency graph processor 1.1.1.1.1.1: error below the reduction pair processor 1.1.1.1.1.1.1: error below the dependency graph processor 1.1.1.1.1.1.1.1: error below the reduction pair processor 1.1.1.1.1.1.1.1.1: error below the reduction pair processor 1.1.1.1.1.1.1.1.1.1: error below the reduction pair processor 1.1.1.1.1.1.1.1.1.1.1: error below the reduction pair processor 1.1.1.1.1.1.1.1.1.1.1.1: error below the reduction pair processor 1.1.1.1.1.1.1.1.1.1.1.1.1: error when applying the reduction pair processor with usable rules to remove from the DP problem pairs: mark#(U32(X)) -> mark#(X) mark#(U53(X)) -> mark#(X) mark#(U72(X)) -> mark#(X) rules: a__U11(tt, V) -> a__U12(a__isNeList(V)) a__U11(X1, X2) -> U11(X1, X2) a__U12(tt) -> tt a__U12(X) -> U12(X) a__U21(tt, V1, V2) -> a__U22(a__isList(V1), V2) a__U21(X1, X2, X3) -> U21(X1, X2, X3) a__U22(tt, V2) -> a__U23(a__isList(V2)) a__U22(X1, X2) -> U22(X1, X2) a__U23(tt) -> tt a__U23(X) -> U23(X) a__U31(tt, V) -> a__U32(a__isQid(V)) a__U31(X1, X2) -> U31(X1, X2) a__U32(tt) -> tt a__U32(X) -> U32(X) a__U41(tt, V1, V2) -> a__U42(a__isList(V1), V2) a__U41(X1, X2, X3) -> U41(X1, X2, X3) a__U42(tt, V2) -> a__U43(a__isNeList(V2)) a__U42(X1, X2) -> U42(X1, X2) a__U43(tt) -> tt a__U43(X) -> U43(X) a__U51(tt, V1, V2) -> a__U52(a__isNeList(V1), V2) a__U51(X1, X2, X3) -> U51(X1, X2, X3) a__U52(tt, V2) -> a__U53(a__isList(V2)) a__U52(X1, X2) -> U52(X1, X2) a__U53(tt) -> tt a__U53(X) -> U53(X) a__U61(tt, V) -> a__U62(a__isQid(V)) a__U61(X1, X2) -> U61(X1, X2) a__U62(tt) -> tt a__U62(X) -> U62(X) a__U71(tt, V) -> a__U72(a__isNePal(V)) a__U71(X1, X2) -> U71(X1, X2) a__U72(tt) -> tt a__U72(X) -> U72(X) a____(__(X, Y), Z) -> a____(mark(X), a____(mark(Y), mark(Z))) a____(X, nil) -> mark(X) a____(nil, X) -> mark(X) a____(X1, X2) -> __(X1, X2) a__and(tt, X) -> mark(X) a__and(X1, X2) -> and(X1, X2) a__isList(V) -> a__U11(a__isPalListKind(V), V) a__isList(nil) -> tt a__isList(__(V1, V2)) -> a__U21(a__and(a__isPalListKind(V1), isPalListKind(V2)), V1, V2) a__isList(X) -> isList(X) a__isNeList(V) -> a__U31(a__isPalListKind(V), V) a__isNeList(__(V1, V2)) -> a__U41(a__and(a__isPalListKind(V1), isPalListKind(V2)), V1, V2) a__isNeList(__(V1, V2)) -> a__U51(a__and(a__isPalListKind(V1), isPalListKind(V2)), V1, V2) a__isNeList(X) -> isNeList(X) a__isNePal(V) -> a__U61(a__isPalListKind(V), V) a__isNePal(__(I, __(P, I))) -> a__and(a__and(a__isQid(I), isPalListKind(I)), and(isPal(P), isPalListKind(P))) a__isNePal(X) -> isNePal(X) a__isPal(V) -> a__U71(a__isPalListKind(V), V) a__isPal(nil) -> tt a__isPal(X) -> isPal(X) a__isPalListKind(a) -> tt a__isPalListKind(e) -> tt a__isPalListKind(i) -> tt a__isPalListKind(nil) -> tt a__isPalListKind(o) -> tt a__isPalListKind(u) -> tt a__isPalListKind(__(V1, V2)) -> a__and(a__isPalListKind(V1), isPalListKind(V2)) a__isPalListKind(X) -> isPalListKind(X) a__isQid(a) -> tt a__isQid(e) -> tt a__isQid(i) -> tt a__isQid(o) -> tt a__isQid(u) -> tt a__isQid(X) -> isQid(X) mark(__(X1, X2)) -> a____(mark(X1), mark(X2)) mark(U11(X1, X2)) -> a__U11(mark(X1), X2) mark(U12(X)) -> a__U12(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3) mark(U22(X1, X2)) -> a__U22(mark(X1), X2) mark(isList(X)) -> a__isList(X) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1, X2)) -> a__U31(mark(X1), X2) mark(U32(X)) -> a__U32(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) mark(U42(X1, X2)) -> a__U42(mark(X1), X2) mark(U43(X)) -> a__U43(mark(X)) mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3) mark(U52(X1, X2)) -> a__U52(mark(X1), X2) mark(U53(X)) -> a__U53(mark(X)) mark(U61(X1, X2)) -> a__U61(mark(X1), X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X1, X2)) -> a__U71(mark(X1), X2) mark(U72(X)) -> a__U72(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(and(X1, X2)) -> a__and(mark(X1), X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(isPal(X)) -> a__isPal(X) mark(nil) -> nil mark(tt) -> tt mark(a) -> a mark(e) -> e mark(i) -> i mark(o) -> o mark(u) -> u the pairs mark#(U53(X)) -> mark#(X) could not apply the generic root reduction pair processor with the following SCNP-version with mu = MS and the level mapping defined by pi(mark#) = [(epsilon,0),(1,0)] Argument Filter: pi(mark#/1) = [] pi(U32/1) = 1 pi(U53/1) = [1] pi(U72/1) = 1 RPO with the following precedence precedence(mark#[1]) = 0 precedence(U53[1]) = 1 precedence(_) = 0 and the following status status(mark#[1]) = lex status(U53[1]) = lex status(_) = lex problem when orienting DPs cannot orient pair mark#(U32(X)) -> mark#(X) weakly: [(mark#(U32(X)),0),(U32(X),0)] >=mu [(mark#(X),0),(X,0)] could not be ensured