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 below the reduction pair processor 1.1.1.1.1.1.1: error below the reduction pair 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 below the reduction pair processor 1.1.1.1.1.1.1.1.1.1.1.1.1.1: error below the reduction pair processor 1.1.1.1.1.1.1.1.1.1.1.1.1.1.1: error below the reduction pair processor 1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1: error below the reduction pair processor 1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1: error below the reduction pair processor 1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1: error below the reduction pair processor 1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1: error below the reduction pair processor 1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1: error below the reduction pair processor 1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1: error when applying the reduction pair processor with usable rules to remove from the DP problem pairs: mark#(U33(X)) -> mark#(X) mark#(U83(X)) -> mark#(X) mark#(U92(X)) -> mark#(X) rules: a__U11(tt, V) -> a__U12(a__isPalListKind(V), V) a__U11(X1, X2) -> U11(X1, X2) a__U12(tt, V) -> a__U13(a__isNeList(V)) a__U12(X1, X2) -> U12(X1, X2) a__U13(tt) -> tt a__U13(X) -> U13(X) a__U21(tt, V1, V2) -> a__U22(a__isPalListKind(V1), V1, V2) a__U21(X1, X2, X3) -> U21(X1, X2, X3) a__U22(tt, V1, V2) -> a__U23(a__isPalListKind(V2), V1, V2) a__U22(X1, X2, X3) -> U22(X1, X2, X3) a__U23(tt, V1, V2) -> a__U24(a__isPalListKind(V2), V1, V2) a__U23(X1, X2, X3) -> U23(X1, X2, X3) a__U24(tt, V1, V2) -> a__U25(a__isList(V1), V2) a__U24(X1, X2, X3) -> U24(X1, X2, X3) a__U25(tt, V2) -> a__U26(a__isList(V2)) a__U25(X1, X2) -> U25(X1, X2) a__U26(tt) -> tt a__U26(X) -> U26(X) a__U31(tt, V) -> a__U32(a__isPalListKind(V), V) a__U31(X1, X2) -> U31(X1, X2) a__U32(tt, V) -> a__U33(a__isQid(V)) a__U32(X1, X2) -> U32(X1, X2) a__U33(tt) -> tt a__U33(X) -> U33(X) a__U41(tt, V1, V2) -> a__U42(a__isPalListKind(V1), V1, V2) a__U41(X1, X2, X3) -> U41(X1, X2, X3) a__U42(tt, V1, V2) -> a__U43(a__isPalListKind(V2), V1, V2) a__U42(X1, X2, X3) -> U42(X1, X2, X3) a__U43(tt, V1, V2) -> a__U44(a__isPalListKind(V2), V1, V2) a__U43(X1, X2, X3) -> U43(X1, X2, X3) a__U44(tt, V1, V2) -> a__U45(a__isList(V1), V2) a__U44(X1, X2, X3) -> U44(X1, X2, X3) a__U45(tt, V2) -> a__U46(a__isNeList(V2)) a__U45(X1, X2) -> U45(X1, X2) a__U46(tt) -> tt a__U46(X) -> U46(X) a__U51(tt, V1, V2) -> a__U52(a__isPalListKind(V1), V1, V2) a__U51(X1, X2, X3) -> U51(X1, X2, X3) a__U52(tt, V1, V2) -> a__U53(a__isPalListKind(V2), V1, V2) a__U52(X1, X2, X3) -> U52(X1, X2, X3) a__U53(tt, V1, V2) -> a__U54(a__isPalListKind(V2), V1, V2) a__U53(X1, X2, X3) -> U53(X1, X2, X3) a__U54(tt, V1, V2) -> a__U55(a__isNeList(V1), V2) a__U54(X1, X2, X3) -> U54(X1, X2, X3) a__U55(tt, V2) -> a__U56(a__isList(V2)) a__U55(X1, X2) -> U55(X1, X2) a__U56(tt) -> tt a__U56(X) -> U56(X) a__U61(tt, V) -> a__U62(a__isPalListKind(V), V) a__U61(X1, X2) -> U61(X1, X2) a__U62(tt, V) -> a__U63(a__isQid(V)) a__U62(X1, X2) -> U62(X1, X2) a__U63(tt) -> tt a__U63(X) -> U63(X) a__U71(tt, I, P) -> a__U72(a__isPalListKind(I), P) a__U71(X1, X2, X3) -> U71(X1, X2, X3) a__U72(tt, P) -> a__U73(a__isPal(P), P) a__U72(X1, X2) -> U72(X1, X2) a__U73(tt, P) -> a__U74(a__isPalListKind(P)) a__U73(X1, X2) -> U73(X1, X2) a__U74(tt) -> tt a__U74(X) -> U74(X) a__U81(tt, V) -> a__U82(a__isPalListKind(V), V) a__U81(X1, X2) -> U81(X1, X2) a__U82(tt, V) -> a__U83(a__isNePal(V)) a__U82(X1, X2) -> U82(X1, X2) a__U83(tt) -> tt a__U83(X) -> U83(X) a__U91(tt, V2) -> a__U92(a__isPalListKind(V2)) a__U91(X1, X2) -> U91(X1, X2) a__U92(tt) -> tt a__U92(X) -> U92(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__isList(V) -> a__U11(a__isPalListKind(V), V) a__isList(nil) -> tt a__isList(__(V1, V2)) -> a__U21(a__isPalListKind(V1), V1, V2) a__isList(X) -> isList(X) a__isNeList(V) -> a__U31(a__isPalListKind(V), V) a__isNeList(__(V1, V2)) -> a__U41(a__isPalListKind(V1), V1, V2) a__isNeList(__(V1, V2)) -> a__U51(a__isPalListKind(V1), V1, V2) a__isNeList(X) -> isNeList(X) a__isNePal(V) -> a__U61(a__isPalListKind(V), V) a__isNePal(__(I, __(P, I))) -> a__U71(a__isQid(I), I, P) a__isNePal(X) -> isNePal(X) a__isPal(V) -> a__U81(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__U91(a__isPalListKind(V1), 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(X1, X2)) -> a__U12(mark(X1), X2) mark(isPalListKind(X)) -> a__isPalListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3) mark(U22(X1, X2, X3)) -> a__U22(mark(X1), X2, X3) mark(U23(X1, X2, X3)) -> a__U23(mark(X1), X2, X3) mark(U24(X1, X2, X3)) -> a__U24(mark(X1), X2, X3) mark(U25(X1, X2)) -> a__U25(mark(X1), X2) mark(isList(X)) -> a__isList(X) mark(U26(X)) -> a__U26(mark(X)) mark(U31(X1, X2)) -> a__U31(mark(X1), X2) mark(U32(X1, X2)) -> a__U32(mark(X1), X2) mark(U33(X)) -> a__U33(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) mark(U42(X1, X2, X3)) -> a__U42(mark(X1), X2, X3) mark(U43(X1, X2, X3)) -> a__U43(mark(X1), X2, X3) mark(U44(X1, X2, X3)) -> a__U44(mark(X1), X2, X3) mark(U45(X1, X2)) -> a__U45(mark(X1), X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3) mark(U52(X1, X2, X3)) -> a__U52(mark(X1), X2, X3) mark(U53(X1, X2, X3)) -> a__U53(mark(X1), X2, X3) mark(U54(X1, X2, X3)) -> a__U54(mark(X1), X2, X3) mark(U55(X1, X2)) -> a__U55(mark(X1), X2) mark(U56(X)) -> a__U56(mark(X)) mark(U61(X1, X2)) -> a__U61(mark(X1), X2) mark(U62(X1, X2)) -> a__U62(mark(X1), X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1, X2, X3)) -> a__U71(mark(X1), X2, X3) mark(U72(X1, X2)) -> a__U72(mark(X1), X2) mark(U73(X1, X2)) -> a__U73(mark(X1), X2) mark(isPal(X)) -> a__isPal(X) mark(U74(X)) -> a__U74(mark(X)) mark(U81(X1, X2)) -> a__U81(mark(X1), X2) mark(U82(X1, X2)) -> a__U82(mark(X1), X2) mark(U83(X)) -> a__U83(mark(X)) mark(isNePal(X)) -> a__isNePal(X) mark(U91(X1, X2)) -> a__U91(mark(X1), X2) mark(U92(X)) -> a__U92(mark(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#(U83(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(U33/1) = 1 pi(U83/1) = [1] pi(U92/1) = 1 RPO with the following precedence precedence(mark#[1]) = 0 precedence(U83[1]) = 1 precedence(_) = 0 and the following status status(mark#[1]) = lex status(U83[1]) = lex status(_) = lex problem when orienting DPs cannot orient pair mark#(U33(X)) -> mark#(X) weakly: [(mark#(U33(X)),0),(U33(X),0)] >=mu [(mark#(X),0),(X,0)] could not be ensured