21.08/8.98 YES 21.38/9.08 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 21.38/9.08 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 21.38/9.08 21.38/9.08 21.38/9.08 Termination w.r.t. Q of the given QTRS could be proven: 21.38/9.08 21.38/9.08 (0) QTRS 21.38/9.08 (1) QTRSRRRProof [EQUIVALENT, 2041 ms] 21.38/9.08 (2) QTRS 21.38/9.08 (3) QTRSRRRProof [EQUIVALENT, 1103 ms] 21.38/9.08 (4) QTRS 21.38/9.08 (5) QTRSRRRProof [EQUIVALENT, 206 ms] 21.38/9.08 (6) QTRS 21.38/9.08 (7) QTRSRRRProof [EQUIVALENT, 354 ms] 21.38/9.08 (8) QTRS 21.38/9.08 (9) QTRSRRRProof [EQUIVALENT, 51 ms] 21.38/9.08 (10) QTRS 21.38/9.08 (11) RisEmptyProof [EQUIVALENT, 0 ms] 21.38/9.08 (12) YES 21.38/9.08 21.38/9.08 21.38/9.08 ---------------------------------------- 21.38/9.08 21.38/9.08 (0) 21.38/9.08 Obligation: 21.38/9.08 Q restricted rewrite system: 21.38/9.08 The TRS R consists of the following rules: 21.38/9.08 21.38/9.08 active(__(__(X, Y), Z)) -> mark(__(X, __(Y, Z))) 21.38/9.08 active(__(X, nil)) -> mark(X) 21.38/9.08 active(__(nil, X)) -> mark(X) 21.38/9.08 active(U11(tt, V)) -> mark(U12(isPalListKind(V), V)) 21.38/9.08 active(U12(tt, V)) -> mark(U13(isNeList(V))) 21.38/9.08 active(U13(tt)) -> mark(tt) 21.38/9.08 active(U21(tt, V1, V2)) -> mark(U22(isPalListKind(V1), V1, V2)) 21.38/9.08 active(U22(tt, V1, V2)) -> mark(U23(isPalListKind(V2), V1, V2)) 21.38/9.08 active(U23(tt, V1, V2)) -> mark(U24(isPalListKind(V2), V1, V2)) 21.38/9.08 active(U24(tt, V1, V2)) -> mark(U25(isList(V1), V2)) 21.38/9.08 active(U25(tt, V2)) -> mark(U26(isList(V2))) 21.38/9.08 active(U26(tt)) -> mark(tt) 21.38/9.08 active(U31(tt, V)) -> mark(U32(isPalListKind(V), V)) 21.38/9.08 active(U32(tt, V)) -> mark(U33(isQid(V))) 21.38/9.08 active(U33(tt)) -> mark(tt) 21.38/9.08 active(U41(tt, V1, V2)) -> mark(U42(isPalListKind(V1), V1, V2)) 21.38/9.08 active(U42(tt, V1, V2)) -> mark(U43(isPalListKind(V2), V1, V2)) 21.38/9.08 active(U43(tt, V1, V2)) -> mark(U44(isPalListKind(V2), V1, V2)) 21.38/9.08 active(U44(tt, V1, V2)) -> mark(U45(isList(V1), V2)) 21.38/9.08 active(U45(tt, V2)) -> mark(U46(isNeList(V2))) 21.38/9.08 active(U46(tt)) -> mark(tt) 21.38/9.08 active(U51(tt, V1, V2)) -> mark(U52(isPalListKind(V1), V1, V2)) 21.38/9.08 active(U52(tt, V1, V2)) -> mark(U53(isPalListKind(V2), V1, V2)) 21.38/9.08 active(U53(tt, V1, V2)) -> mark(U54(isPalListKind(V2), V1, V2)) 21.38/9.08 active(U54(tt, V1, V2)) -> mark(U55(isNeList(V1), V2)) 21.38/9.08 active(U55(tt, V2)) -> mark(U56(isList(V2))) 21.38/9.08 active(U56(tt)) -> mark(tt) 21.38/9.08 active(U61(tt, V)) -> mark(U62(isPalListKind(V), V)) 21.38/9.08 active(U62(tt, V)) -> mark(U63(isQid(V))) 21.38/9.08 active(U63(tt)) -> mark(tt) 21.38/9.08 active(U71(tt, I, P)) -> mark(U72(isPalListKind(I), P)) 21.38/9.08 active(U72(tt, P)) -> mark(U73(isPal(P), P)) 21.38/9.08 active(U73(tt, P)) -> mark(U74(isPalListKind(P))) 21.38/9.08 active(U74(tt)) -> mark(tt) 21.38/9.08 active(U81(tt, V)) -> mark(U82(isPalListKind(V), V)) 21.38/9.08 active(U82(tt, V)) -> mark(U83(isNePal(V))) 21.38/9.08 active(U83(tt)) -> mark(tt) 21.38/9.08 active(U91(tt, V2)) -> mark(U92(isPalListKind(V2))) 21.38/9.08 active(U92(tt)) -> mark(tt) 21.38/9.08 active(isList(V)) -> mark(U11(isPalListKind(V), V)) 21.38/9.08 active(isList(nil)) -> mark(tt) 21.38/9.08 active(isList(__(V1, V2))) -> mark(U21(isPalListKind(V1), V1, V2)) 21.38/9.08 active(isNeList(V)) -> mark(U31(isPalListKind(V), V)) 21.38/9.08 active(isNeList(__(V1, V2))) -> mark(U41(isPalListKind(V1), V1, V2)) 21.38/9.08 active(isNeList(__(V1, V2))) -> mark(U51(isPalListKind(V1), V1, V2)) 21.38/9.08 active(isNePal(V)) -> mark(U61(isPalListKind(V), V)) 21.38/9.08 active(isNePal(__(I, __(P, I)))) -> mark(U71(isQid(I), I, P)) 21.38/9.08 active(isPal(V)) -> mark(U81(isPalListKind(V), V)) 21.38/9.08 active(isPal(nil)) -> mark(tt) 21.38/9.08 active(isPalListKind(a)) -> mark(tt) 21.38/9.08 active(isPalListKind(e)) -> mark(tt) 21.38/9.08 active(isPalListKind(i)) -> mark(tt) 21.38/9.08 active(isPalListKind(nil)) -> mark(tt) 21.38/9.08 active(isPalListKind(o)) -> mark(tt) 21.38/9.08 active(isPalListKind(u)) -> mark(tt) 21.38/9.08 active(isPalListKind(__(V1, V2))) -> mark(U91(isPalListKind(V1), V2)) 21.38/9.08 active(isQid(a)) -> mark(tt) 21.38/9.08 active(isQid(e)) -> mark(tt) 21.38/9.08 active(isQid(i)) -> mark(tt) 21.38/9.08 active(isQid(o)) -> mark(tt) 21.38/9.08 active(isQid(u)) -> mark(tt) 21.38/9.08 mark(__(X1, X2)) -> active(__(mark(X1), mark(X2))) 21.38/9.08 mark(nil) -> active(nil) 21.38/9.08 mark(U11(X1, X2)) -> active(U11(mark(X1), X2)) 21.38/9.08 mark(tt) -> active(tt) 21.38/9.08 mark(U12(X1, X2)) -> active(U12(mark(X1), X2)) 21.38/9.08 mark(isPalListKind(X)) -> active(isPalListKind(X)) 21.38/9.08 mark(U13(X)) -> active(U13(mark(X))) 21.38/9.08 mark(isNeList(X)) -> active(isNeList(X)) 21.38/9.08 mark(U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)) 21.38/9.08 mark(U22(X1, X2, X3)) -> active(U22(mark(X1), X2, X3)) 21.38/9.08 mark(U23(X1, X2, X3)) -> active(U23(mark(X1), X2, X3)) 21.38/9.08 mark(U24(X1, X2, X3)) -> active(U24(mark(X1), X2, X3)) 21.38/9.08 mark(U25(X1, X2)) -> active(U25(mark(X1), X2)) 21.38/9.08 mark(isList(X)) -> active(isList(X)) 21.38/9.08 mark(U26(X)) -> active(U26(mark(X))) 21.38/9.08 mark(U31(X1, X2)) -> active(U31(mark(X1), X2)) 21.38/9.08 mark(U32(X1, X2)) -> active(U32(mark(X1), X2)) 21.38/9.08 mark(U33(X)) -> active(U33(mark(X))) 21.38/9.08 mark(isQid(X)) -> active(isQid(X)) 21.38/9.08 mark(U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3)) 21.38/9.08 mark(U42(X1, X2, X3)) -> active(U42(mark(X1), X2, X3)) 21.38/9.08 mark(U43(X1, X2, X3)) -> active(U43(mark(X1), X2, X3)) 21.38/9.08 mark(U44(X1, X2, X3)) -> active(U44(mark(X1), X2, X3)) 21.38/9.08 mark(U45(X1, X2)) -> active(U45(mark(X1), X2)) 21.38/9.08 mark(U46(X)) -> active(U46(mark(X))) 21.38/9.08 mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)) 21.38/9.08 mark(U52(X1, X2, X3)) -> active(U52(mark(X1), X2, X3)) 21.38/9.08 mark(U53(X1, X2, X3)) -> active(U53(mark(X1), X2, X3)) 21.38/9.08 mark(U54(X1, X2, X3)) -> active(U54(mark(X1), X2, X3)) 21.38/9.08 mark(U55(X1, X2)) -> active(U55(mark(X1), X2)) 21.38/9.08 mark(U56(X)) -> active(U56(mark(X))) 21.38/9.08 mark(U61(X1, X2)) -> active(U61(mark(X1), X2)) 21.38/9.08 mark(U62(X1, X2)) -> active(U62(mark(X1), X2)) 21.38/9.08 mark(U63(X)) -> active(U63(mark(X))) 21.38/9.08 mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)) 21.38/9.08 mark(U72(X1, X2)) -> active(U72(mark(X1), X2)) 21.38/9.08 mark(U73(X1, X2)) -> active(U73(mark(X1), X2)) 21.38/9.08 mark(isPal(X)) -> active(isPal(X)) 21.38/9.08 mark(U74(X)) -> active(U74(mark(X))) 21.38/9.08 mark(U81(X1, X2)) -> active(U81(mark(X1), X2)) 21.38/9.08 mark(U82(X1, X2)) -> active(U82(mark(X1), X2)) 21.38/9.08 mark(U83(X)) -> active(U83(mark(X))) 21.38/9.08 mark(isNePal(X)) -> active(isNePal(X)) 21.38/9.08 mark(U91(X1, X2)) -> active(U91(mark(X1), X2)) 21.38/9.08 mark(U92(X)) -> active(U92(mark(X))) 21.38/9.08 mark(a) -> active(a) 21.38/9.08 mark(e) -> active(e) 21.38/9.08 mark(i) -> active(i) 21.38/9.08 mark(o) -> active(o) 21.38/9.08 mark(u) -> active(u) 21.38/9.08 __(mark(X1), X2) -> __(X1, X2) 21.38/9.08 __(X1, mark(X2)) -> __(X1, X2) 21.38/9.08 __(active(X1), X2) -> __(X1, X2) 21.38/9.08 __(X1, active(X2)) -> __(X1, X2) 21.38/9.08 U11(mark(X1), X2) -> U11(X1, X2) 21.38/9.08 U11(X1, mark(X2)) -> U11(X1, X2) 21.38/9.08 U11(active(X1), X2) -> U11(X1, X2) 21.38/9.08 U11(X1, active(X2)) -> U11(X1, X2) 21.38/9.08 U12(mark(X1), X2) -> U12(X1, X2) 21.38/9.08 U12(X1, mark(X2)) -> U12(X1, X2) 21.38/9.08 U12(active(X1), X2) -> U12(X1, X2) 21.38/9.08 U12(X1, active(X2)) -> U12(X1, X2) 21.38/9.08 isPalListKind(mark(X)) -> isPalListKind(X) 21.38/9.08 isPalListKind(active(X)) -> isPalListKind(X) 21.38/9.08 U13(mark(X)) -> U13(X) 21.38/9.08 U13(active(X)) -> U13(X) 21.38/9.08 isNeList(mark(X)) -> isNeList(X) 21.38/9.08 isNeList(active(X)) -> isNeList(X) 21.38/9.08 U21(mark(X1), X2, X3) -> U21(X1, X2, X3) 21.38/9.08 U21(X1, mark(X2), X3) -> U21(X1, X2, X3) 21.38/9.08 U21(X1, X2, mark(X3)) -> U21(X1, X2, X3) 21.38/9.08 U21(active(X1), X2, X3) -> U21(X1, X2, X3) 21.38/9.08 U21(X1, active(X2), X3) -> U21(X1, X2, X3) 21.38/9.08 U21(X1, X2, active(X3)) -> U21(X1, X2, X3) 21.38/9.08 U22(mark(X1), X2, X3) -> U22(X1, X2, X3) 21.38/9.08 U22(X1, mark(X2), X3) -> U22(X1, X2, X3) 21.38/9.08 U22(X1, X2, mark(X3)) -> U22(X1, X2, X3) 21.38/9.08 U22(active(X1), X2, X3) -> U22(X1, X2, X3) 21.38/9.08 U22(X1, active(X2), X3) -> U22(X1, X2, X3) 21.38/9.08 U22(X1, X2, active(X3)) -> U22(X1, X2, X3) 21.38/9.08 U23(mark(X1), X2, X3) -> U23(X1, X2, X3) 21.38/9.08 U23(X1, mark(X2), X3) -> U23(X1, X2, X3) 21.38/9.08 U23(X1, X2, mark(X3)) -> U23(X1, X2, X3) 21.38/9.08 U23(active(X1), X2, X3) -> U23(X1, X2, X3) 21.38/9.08 U23(X1, active(X2), X3) -> U23(X1, X2, X3) 21.38/9.08 U23(X1, X2, active(X3)) -> U23(X1, X2, X3) 21.38/9.08 U24(mark(X1), X2, X3) -> U24(X1, X2, X3) 21.38/9.08 U24(X1, mark(X2), X3) -> U24(X1, X2, X3) 21.38/9.08 U24(X1, X2, mark(X3)) -> U24(X1, X2, X3) 21.38/9.08 U24(active(X1), X2, X3) -> U24(X1, X2, X3) 21.38/9.08 U24(X1, active(X2), X3) -> U24(X1, X2, X3) 21.38/9.08 U24(X1, X2, active(X3)) -> U24(X1, X2, X3) 21.38/9.08 U25(mark(X1), X2) -> U25(X1, X2) 21.38/9.08 U25(X1, mark(X2)) -> U25(X1, X2) 21.38/9.08 U25(active(X1), X2) -> U25(X1, X2) 21.38/9.08 U25(X1, active(X2)) -> U25(X1, X2) 21.38/9.08 isList(mark(X)) -> isList(X) 21.38/9.08 isList(active(X)) -> isList(X) 21.38/9.08 U26(mark(X)) -> U26(X) 21.38/9.08 U26(active(X)) -> U26(X) 21.38/9.08 U31(mark(X1), X2) -> U31(X1, X2) 21.38/9.08 U31(X1, mark(X2)) -> U31(X1, X2) 21.38/9.08 U31(active(X1), X2) -> U31(X1, X2) 21.38/9.08 U31(X1, active(X2)) -> U31(X1, X2) 21.38/9.08 U32(mark(X1), X2) -> U32(X1, X2) 21.38/9.08 U32(X1, mark(X2)) -> U32(X1, X2) 21.38/9.08 U32(active(X1), X2) -> U32(X1, X2) 21.38/9.08 U32(X1, active(X2)) -> U32(X1, X2) 21.38/9.08 U33(mark(X)) -> U33(X) 21.38/9.08 U33(active(X)) -> U33(X) 21.38/9.08 isQid(mark(X)) -> isQid(X) 21.38/9.08 isQid(active(X)) -> isQid(X) 21.38/9.08 U41(mark(X1), X2, X3) -> U41(X1, X2, X3) 21.38/9.08 U41(X1, mark(X2), X3) -> U41(X1, X2, X3) 21.38/9.08 U41(X1, X2, mark(X3)) -> U41(X1, X2, X3) 21.38/9.08 U41(active(X1), X2, X3) -> U41(X1, X2, X3) 21.38/9.08 U41(X1, active(X2), X3) -> U41(X1, X2, X3) 21.38/9.08 U41(X1, X2, active(X3)) -> U41(X1, X2, X3) 21.38/9.08 U42(mark(X1), X2, X3) -> U42(X1, X2, X3) 21.38/9.08 U42(X1, mark(X2), X3) -> U42(X1, X2, X3) 21.38/9.08 U42(X1, X2, mark(X3)) -> U42(X1, X2, X3) 21.38/9.08 U42(active(X1), X2, X3) -> U42(X1, X2, X3) 21.38/9.08 U42(X1, active(X2), X3) -> U42(X1, X2, X3) 21.38/9.08 U42(X1, X2, active(X3)) -> U42(X1, X2, X3) 21.38/9.08 U43(mark(X1), X2, X3) -> U43(X1, X2, X3) 21.38/9.08 U43(X1, mark(X2), X3) -> U43(X1, X2, X3) 21.38/9.08 U43(X1, X2, mark(X3)) -> U43(X1, X2, X3) 21.38/9.08 U43(active(X1), X2, X3) -> U43(X1, X2, X3) 21.38/9.08 U43(X1, active(X2), X3) -> U43(X1, X2, X3) 21.38/9.08 U43(X1, X2, active(X3)) -> U43(X1, X2, X3) 21.38/9.08 U44(mark(X1), X2, X3) -> U44(X1, X2, X3) 21.38/9.08 U44(X1, mark(X2), X3) -> U44(X1, X2, X3) 21.38/9.08 U44(X1, X2, mark(X3)) -> U44(X1, X2, X3) 21.38/9.08 U44(active(X1), X2, X3) -> U44(X1, X2, X3) 21.38/9.08 U44(X1, active(X2), X3) -> U44(X1, X2, X3) 21.38/9.08 U44(X1, X2, active(X3)) -> U44(X1, X2, X3) 21.38/9.08 U45(mark(X1), X2) -> U45(X1, X2) 21.38/9.08 U45(X1, mark(X2)) -> U45(X1, X2) 21.38/9.08 U45(active(X1), X2) -> U45(X1, X2) 21.38/9.08 U45(X1, active(X2)) -> U45(X1, X2) 21.38/9.08 U46(mark(X)) -> U46(X) 21.38/9.08 U46(active(X)) -> U46(X) 21.38/9.08 U51(mark(X1), X2, X3) -> U51(X1, X2, X3) 21.38/9.08 U51(X1, mark(X2), X3) -> U51(X1, X2, X3) 21.38/9.08 U51(X1, X2, mark(X3)) -> U51(X1, X2, X3) 21.38/9.08 U51(active(X1), X2, X3) -> U51(X1, X2, X3) 21.38/9.08 U51(X1, active(X2), X3) -> U51(X1, X2, X3) 21.38/9.08 U51(X1, X2, active(X3)) -> U51(X1, X2, X3) 21.38/9.08 U52(mark(X1), X2, X3) -> U52(X1, X2, X3) 21.38/9.08 U52(X1, mark(X2), X3) -> U52(X1, X2, X3) 21.38/9.08 U52(X1, X2, mark(X3)) -> U52(X1, X2, X3) 21.38/9.08 U52(active(X1), X2, X3) -> U52(X1, X2, X3) 21.38/9.08 U52(X1, active(X2), X3) -> U52(X1, X2, X3) 21.38/9.08 U52(X1, X2, active(X3)) -> U52(X1, X2, X3) 21.38/9.08 U53(mark(X1), X2, X3) -> U53(X1, X2, X3) 21.38/9.08 U53(X1, mark(X2), X3) -> U53(X1, X2, X3) 21.38/9.08 U53(X1, X2, mark(X3)) -> U53(X1, X2, X3) 21.38/9.08 U53(active(X1), X2, X3) -> U53(X1, X2, X3) 21.38/9.08 U53(X1, active(X2), X3) -> U53(X1, X2, X3) 21.38/9.08 U53(X1, X2, active(X3)) -> U53(X1, X2, X3) 21.38/9.08 U54(mark(X1), X2, X3) -> U54(X1, X2, X3) 21.38/9.08 U54(X1, mark(X2), X3) -> U54(X1, X2, X3) 21.38/9.08 U54(X1, X2, mark(X3)) -> U54(X1, X2, X3) 21.38/9.08 U54(active(X1), X2, X3) -> U54(X1, X2, X3) 21.38/9.08 U54(X1, active(X2), X3) -> U54(X1, X2, X3) 21.38/9.08 U54(X1, X2, active(X3)) -> U54(X1, X2, X3) 21.38/9.08 U55(mark(X1), X2) -> U55(X1, X2) 21.38/9.08 U55(X1, mark(X2)) -> U55(X1, X2) 21.38/9.08 U55(active(X1), X2) -> U55(X1, X2) 21.38/9.08 U55(X1, active(X2)) -> U55(X1, X2) 21.38/9.08 U56(mark(X)) -> U56(X) 21.38/9.08 U56(active(X)) -> U56(X) 21.38/9.08 U61(mark(X1), X2) -> U61(X1, X2) 21.38/9.08 U61(X1, mark(X2)) -> U61(X1, X2) 21.38/9.08 U61(active(X1), X2) -> U61(X1, X2) 21.38/9.08 U61(X1, active(X2)) -> U61(X1, X2) 21.38/9.08 U62(mark(X1), X2) -> U62(X1, X2) 21.38/9.08 U62(X1, mark(X2)) -> U62(X1, X2) 21.38/9.08 U62(active(X1), X2) -> U62(X1, X2) 21.38/9.08 U62(X1, active(X2)) -> U62(X1, X2) 21.38/9.08 U63(mark(X)) -> U63(X) 21.38/9.08 U63(active(X)) -> U63(X) 21.38/9.08 U71(mark(X1), X2, X3) -> U71(X1, X2, X3) 21.38/9.08 U71(X1, mark(X2), X3) -> U71(X1, X2, X3) 21.38/9.08 U71(X1, X2, mark(X3)) -> U71(X1, X2, X3) 21.38/9.08 U71(active(X1), X2, X3) -> U71(X1, X2, X3) 21.38/9.08 U71(X1, active(X2), X3) -> U71(X1, X2, X3) 21.38/9.08 U71(X1, X2, active(X3)) -> U71(X1, X2, X3) 21.38/9.08 U72(mark(X1), X2) -> U72(X1, X2) 21.38/9.08 U72(X1, mark(X2)) -> U72(X1, X2) 21.38/9.08 U72(active(X1), X2) -> U72(X1, X2) 21.38/9.08 U72(X1, active(X2)) -> U72(X1, X2) 21.38/9.08 U73(mark(X1), X2) -> U73(X1, X2) 21.38/9.08 U73(X1, mark(X2)) -> U73(X1, X2) 21.38/9.08 U73(active(X1), X2) -> U73(X1, X2) 21.38/9.08 U73(X1, active(X2)) -> U73(X1, X2) 21.38/9.08 isPal(mark(X)) -> isPal(X) 21.38/9.08 isPal(active(X)) -> isPal(X) 21.38/9.08 U74(mark(X)) -> U74(X) 21.38/9.08 U74(active(X)) -> U74(X) 21.38/9.08 U81(mark(X1), X2) -> U81(X1, X2) 21.38/9.08 U81(X1, mark(X2)) -> U81(X1, X2) 21.38/9.08 U81(active(X1), X2) -> U81(X1, X2) 21.38/9.08 U81(X1, active(X2)) -> U81(X1, X2) 21.38/9.08 U82(mark(X1), X2) -> U82(X1, X2) 21.38/9.08 U82(X1, mark(X2)) -> U82(X1, X2) 21.38/9.08 U82(active(X1), X2) -> U82(X1, X2) 21.38/9.08 U82(X1, active(X2)) -> U82(X1, X2) 21.38/9.08 U83(mark(X)) -> U83(X) 21.38/9.08 U83(active(X)) -> U83(X) 21.38/9.08 isNePal(mark(X)) -> isNePal(X) 21.38/9.08 isNePal(active(X)) -> isNePal(X) 21.38/9.08 U91(mark(X1), X2) -> U91(X1, X2) 21.38/9.08 U91(X1, mark(X2)) -> U91(X1, X2) 21.38/9.08 U91(active(X1), X2) -> U91(X1, X2) 21.38/9.08 U91(X1, active(X2)) -> U91(X1, X2) 21.38/9.08 U92(mark(X)) -> U92(X) 21.38/9.08 U92(active(X)) -> U92(X) 21.38/9.08 21.38/9.08 The set Q consists of the following terms: 21.38/9.08 21.38/9.08 active(__(__(x0, x1), x2)) 21.38/9.08 active(__(x0, nil)) 21.38/9.08 active(__(nil, x0)) 21.38/9.08 active(U11(tt, x0)) 21.38/9.08 active(U12(tt, x0)) 21.38/9.08 active(U13(tt)) 21.38/9.08 active(U21(tt, x0, x1)) 21.38/9.08 active(U22(tt, x0, x1)) 21.38/9.08 active(U23(tt, x0, x1)) 21.38/9.08 active(U24(tt, x0, x1)) 21.38/9.08 active(U25(tt, x0)) 21.38/9.08 active(U26(tt)) 21.38/9.08 active(U31(tt, x0)) 21.38/9.08 active(U32(tt, x0)) 21.38/9.08 active(U33(tt)) 21.38/9.08 active(U41(tt, x0, x1)) 21.38/9.08 active(U42(tt, x0, x1)) 21.38/9.08 active(U43(tt, x0, x1)) 21.38/9.08 active(U44(tt, x0, x1)) 21.38/9.08 active(U45(tt, x0)) 21.38/9.08 active(U46(tt)) 21.38/9.08 active(U51(tt, x0, x1)) 21.38/9.08 active(U52(tt, x0, x1)) 21.38/9.08 active(U53(tt, x0, x1)) 21.38/9.08 active(U54(tt, x0, x1)) 21.38/9.08 active(U55(tt, x0)) 21.38/9.08 active(U56(tt)) 21.38/9.08 active(U61(tt, x0)) 21.38/9.08 active(U62(tt, x0)) 21.38/9.08 active(U63(tt)) 21.38/9.08 active(U71(tt, x0, x1)) 21.38/9.08 active(U72(tt, x0)) 21.38/9.08 active(U73(tt, x0)) 21.38/9.08 active(U74(tt)) 21.38/9.08 active(U81(tt, x0)) 21.38/9.08 active(U82(tt, x0)) 21.38/9.08 active(U83(tt)) 21.38/9.08 active(U91(tt, x0)) 21.38/9.08 active(U92(tt)) 21.38/9.08 active(isList(x0)) 21.38/9.08 active(isNeList(x0)) 21.38/9.08 active(isNePal(x0)) 21.38/9.08 active(isPal(x0)) 21.38/9.08 active(isPalListKind(a)) 21.38/9.08 active(isPalListKind(e)) 21.38/9.08 active(isPalListKind(i)) 21.38/9.08 active(isPalListKind(nil)) 21.38/9.08 active(isPalListKind(o)) 21.38/9.08 active(isPalListKind(u)) 21.38/9.08 active(isPalListKind(__(x0, x1))) 21.38/9.08 active(isQid(a)) 21.38/9.08 active(isQid(e)) 21.38/9.08 active(isQid(i)) 21.38/9.08 active(isQid(o)) 21.38/9.08 active(isQid(u)) 21.38/9.08 mark(__(x0, x1)) 21.38/9.08 mark(nil) 21.38/9.08 mark(U11(x0, x1)) 21.38/9.08 mark(tt) 21.38/9.08 mark(U12(x0, x1)) 21.38/9.08 mark(isPalListKind(x0)) 21.38/9.08 mark(U13(x0)) 21.38/9.08 mark(isNeList(x0)) 21.38/9.08 mark(U21(x0, x1, x2)) 21.38/9.08 mark(U22(x0, x1, x2)) 21.38/9.08 mark(U23(x0, x1, x2)) 21.38/9.08 mark(U24(x0, x1, x2)) 21.38/9.08 mark(U25(x0, x1)) 21.38/9.08 mark(isList(x0)) 21.38/9.08 mark(U26(x0)) 21.38/9.08 mark(U31(x0, x1)) 21.38/9.08 mark(U32(x0, x1)) 21.38/9.08 mark(U33(x0)) 21.38/9.08 mark(isQid(x0)) 21.38/9.08 mark(U41(x0, x1, x2)) 21.38/9.08 mark(U42(x0, x1, x2)) 21.38/9.08 mark(U43(x0, x1, x2)) 21.38/9.08 mark(U44(x0, x1, x2)) 21.38/9.08 mark(U45(x0, x1)) 21.38/9.08 mark(U46(x0)) 21.38/9.08 mark(U51(x0, x1, x2)) 21.38/9.08 mark(U52(x0, x1, x2)) 21.38/9.08 mark(U53(x0, x1, x2)) 21.38/9.08 mark(U54(x0, x1, x2)) 21.38/9.08 mark(U55(x0, x1)) 21.38/9.08 mark(U56(x0)) 21.38/9.08 mark(U61(x0, x1)) 21.38/9.08 mark(U62(x0, x1)) 21.38/9.08 mark(U63(x0)) 21.38/9.08 mark(U71(x0, x1, x2)) 21.38/9.08 mark(U72(x0, x1)) 21.38/9.08 mark(U73(x0, x1)) 21.38/9.08 mark(isPal(x0)) 21.38/9.08 mark(U74(x0)) 21.38/9.08 mark(U81(x0, x1)) 21.38/9.08 mark(U82(x0, x1)) 21.38/9.08 mark(U83(x0)) 21.38/9.08 mark(isNePal(x0)) 21.38/9.08 mark(U91(x0, x1)) 21.38/9.08 mark(U92(x0)) 21.38/9.08 mark(a) 21.38/9.08 mark(e) 21.38/9.08 mark(i) 21.38/9.08 mark(o) 21.38/9.08 mark(u) 21.38/9.08 __(mark(x0), x1) 21.38/9.08 __(x0, mark(x1)) 21.38/9.08 __(active(x0), x1) 21.38/9.08 __(x0, active(x1)) 21.38/9.08 U11(mark(x0), x1) 21.38/9.08 U11(x0, mark(x1)) 21.38/9.08 U11(active(x0), x1) 21.38/9.08 U11(x0, active(x1)) 21.38/9.08 U12(mark(x0), x1) 21.38/9.08 U12(x0, mark(x1)) 21.38/9.08 U12(active(x0), x1) 21.38/9.08 U12(x0, active(x1)) 21.38/9.08 isPalListKind(mark(x0)) 21.38/9.08 isPalListKind(active(x0)) 21.38/9.08 U13(mark(x0)) 21.38/9.08 U13(active(x0)) 21.38/9.08 isNeList(mark(x0)) 21.38/9.08 isNeList(active(x0)) 21.38/9.08 U21(mark(x0), x1, x2) 21.38/9.08 U21(x0, mark(x1), x2) 21.38/9.08 U21(x0, x1, mark(x2)) 21.38/9.08 U21(active(x0), x1, x2) 21.38/9.08 U21(x0, active(x1), x2) 21.38/9.08 U21(x0, x1, active(x2)) 21.38/9.08 U22(mark(x0), x1, x2) 21.38/9.08 U22(x0, mark(x1), x2) 21.38/9.08 U22(x0, x1, mark(x2)) 21.38/9.08 U22(active(x0), x1, x2) 21.38/9.08 U22(x0, active(x1), x2) 21.38/9.08 U22(x0, x1, active(x2)) 21.38/9.08 U23(mark(x0), x1, x2) 21.38/9.08 U23(x0, mark(x1), x2) 21.38/9.08 U23(x0, x1, mark(x2)) 21.38/9.08 U23(active(x0), x1, x2) 21.38/9.08 U23(x0, active(x1), x2) 21.38/9.08 U23(x0, x1, active(x2)) 21.38/9.08 U24(mark(x0), x1, x2) 21.38/9.08 U24(x0, mark(x1), x2) 21.38/9.08 U24(x0, x1, mark(x2)) 21.38/9.08 U24(active(x0), x1, x2) 21.38/9.08 U24(x0, active(x1), x2) 21.38/9.08 U24(x0, x1, active(x2)) 21.38/9.08 U25(mark(x0), x1) 21.38/9.08 U25(x0, mark(x1)) 21.38/9.08 U25(active(x0), x1) 21.38/9.08 U25(x0, active(x1)) 21.38/9.08 isList(mark(x0)) 21.38/9.08 isList(active(x0)) 21.38/9.08 U26(mark(x0)) 21.38/9.08 U26(active(x0)) 21.38/9.08 U31(mark(x0), x1) 21.38/9.08 U31(x0, mark(x1)) 21.38/9.08 U31(active(x0), x1) 21.38/9.08 U31(x0, active(x1)) 21.38/9.08 U32(mark(x0), x1) 21.38/9.08 U32(x0, mark(x1)) 21.38/9.08 U32(active(x0), x1) 21.38/9.08 U32(x0, active(x1)) 21.38/9.08 U33(mark(x0)) 21.38/9.08 U33(active(x0)) 21.38/9.08 isQid(mark(x0)) 21.38/9.08 isQid(active(x0)) 21.38/9.08 U41(mark(x0), x1, x2) 21.38/9.08 U41(x0, mark(x1), x2) 21.38/9.08 U41(x0, x1, mark(x2)) 21.38/9.08 U41(active(x0), x1, x2) 21.38/9.08 U41(x0, active(x1), x2) 21.38/9.08 U41(x0, x1, active(x2)) 21.38/9.08 U42(mark(x0), x1, x2) 21.38/9.08 U42(x0, mark(x1), x2) 21.38/9.08 U42(x0, x1, mark(x2)) 21.38/9.08 U42(active(x0), x1, x2) 21.38/9.08 U42(x0, active(x1), x2) 21.38/9.08 U42(x0, x1, active(x2)) 21.38/9.08 U43(mark(x0), x1, x2) 21.38/9.08 U43(x0, mark(x1), x2) 21.38/9.08 U43(x0, x1, mark(x2)) 21.38/9.08 U43(active(x0), x1, x2) 21.38/9.08 U43(x0, active(x1), x2) 21.38/9.08 U43(x0, x1, active(x2)) 21.38/9.08 U44(mark(x0), x1, x2) 21.38/9.08 U44(x0, mark(x1), x2) 21.38/9.08 U44(x0, x1, mark(x2)) 21.38/9.08 U44(active(x0), x1, x2) 21.38/9.08 U44(x0, active(x1), x2) 21.38/9.08 U44(x0, x1, active(x2)) 21.38/9.08 U45(mark(x0), x1) 21.38/9.08 U45(x0, mark(x1)) 21.38/9.08 U45(active(x0), x1) 21.38/9.08 U45(x0, active(x1)) 21.38/9.08 U46(mark(x0)) 21.38/9.08 U46(active(x0)) 21.38/9.08 U51(mark(x0), x1, x2) 21.38/9.08 U51(x0, mark(x1), x2) 21.38/9.08 U51(x0, x1, mark(x2)) 21.38/9.08 U51(active(x0), x1, x2) 21.38/9.08 U51(x0, active(x1), x2) 21.38/9.08 U51(x0, x1, active(x2)) 21.38/9.08 U52(mark(x0), x1, x2) 21.38/9.08 U52(x0, mark(x1), x2) 21.38/9.08 U52(x0, x1, mark(x2)) 21.38/9.08 U52(active(x0), x1, x2) 21.38/9.08 U52(x0, active(x1), x2) 21.38/9.08 U52(x0, x1, active(x2)) 21.38/9.08 U53(mark(x0), x1, x2) 21.38/9.08 U53(x0, mark(x1), x2) 21.38/9.08 U53(x0, x1, mark(x2)) 21.38/9.08 U53(active(x0), x1, x2) 21.38/9.08 U53(x0, active(x1), x2) 21.38/9.08 U53(x0, x1, active(x2)) 21.38/9.08 U54(mark(x0), x1, x2) 21.38/9.08 U54(x0, mark(x1), x2) 21.38/9.08 U54(x0, x1, mark(x2)) 21.38/9.08 U54(active(x0), x1, x2) 21.38/9.08 U54(x0, active(x1), x2) 21.38/9.08 U54(x0, x1, active(x2)) 21.38/9.08 U55(mark(x0), x1) 21.38/9.08 U55(x0, mark(x1)) 21.38/9.08 U55(active(x0), x1) 21.38/9.08 U55(x0, active(x1)) 21.38/9.08 U56(mark(x0)) 21.38/9.08 U56(active(x0)) 21.38/9.08 U61(mark(x0), x1) 21.38/9.08 U61(x0, mark(x1)) 21.38/9.08 U61(active(x0), x1) 21.38/9.08 U61(x0, active(x1)) 21.38/9.08 U62(mark(x0), x1) 21.38/9.08 U62(x0, mark(x1)) 21.38/9.08 U62(active(x0), x1) 21.38/9.08 U62(x0, active(x1)) 21.38/9.08 U63(mark(x0)) 21.38/9.08 U63(active(x0)) 21.38/9.08 U71(mark(x0), x1, x2) 21.38/9.08 U71(x0, mark(x1), x2) 21.38/9.08 U71(x0, x1, mark(x2)) 21.38/9.08 U71(active(x0), x1, x2) 21.38/9.08 U71(x0, active(x1), x2) 21.38/9.08 U71(x0, x1, active(x2)) 21.38/9.08 U72(mark(x0), x1) 21.38/9.08 U72(x0, mark(x1)) 21.38/9.08 U72(active(x0), x1) 21.38/9.08 U72(x0, active(x1)) 21.38/9.08 U73(mark(x0), x1) 21.38/9.08 U73(x0, mark(x1)) 21.38/9.08 U73(active(x0), x1) 21.38/9.08 U73(x0, active(x1)) 21.38/9.08 isPal(mark(x0)) 21.38/9.08 isPal(active(x0)) 21.38/9.08 U74(mark(x0)) 21.38/9.08 U74(active(x0)) 21.38/9.08 U81(mark(x0), x1) 21.38/9.08 U81(x0, mark(x1)) 21.38/9.08 U81(active(x0), x1) 21.38/9.08 U81(x0, active(x1)) 21.38/9.08 U82(mark(x0), x1) 21.38/9.08 U82(x0, mark(x1)) 21.38/9.08 U82(active(x0), x1) 21.38/9.08 U82(x0, active(x1)) 21.38/9.08 U83(mark(x0)) 21.38/9.08 U83(active(x0)) 21.38/9.08 isNePal(mark(x0)) 21.38/9.08 isNePal(active(x0)) 21.38/9.08 U91(mark(x0), x1) 21.38/9.08 U91(x0, mark(x1)) 21.38/9.08 U91(active(x0), x1) 21.38/9.08 U91(x0, active(x1)) 21.38/9.08 U92(mark(x0)) 21.38/9.08 U92(active(x0)) 21.38/9.08 21.38/9.08 21.38/9.08 ---------------------------------------- 21.38/9.08 21.38/9.08 (1) QTRSRRRProof (EQUIVALENT) 21.38/9.08 Used ordering: 21.38/9.08 active/1)YES( 21.38/9.08 __/2(YES,YES) 21.38/9.08 mark/1)YES( 21.38/9.08 nil/0) 21.38/9.08 U11/2(YES,YES) 21.38/9.08 tt/0) 21.38/9.08 U12/2(YES,YES) 21.38/9.08 isPalListKind/1)YES( 21.38/9.08 U13/1)YES( 21.38/9.08 isNeList/1(YES) 21.38/9.08 U21/3(YES,YES,YES) 21.38/9.08 U22/3(YES,YES,YES) 21.38/9.08 U23/3(YES,YES,YES) 21.38/9.08 U24/3(YES,YES,YES) 21.38/9.08 U25/2(YES,YES) 21.38/9.08 isList/1(YES) 21.38/9.08 U26/1)YES( 21.38/9.08 U31/2(YES,YES) 21.38/9.08 U32/2(YES,YES) 21.38/9.08 U33/1)YES( 21.38/9.08 isQid/1(YES) 21.38/9.08 U41/3(YES,YES,YES) 21.38/9.08 U42/3(YES,YES,YES) 21.38/9.08 U43/3(YES,YES,YES) 21.38/9.08 U44/3(YES,YES,YES) 21.38/9.08 U45/2(YES,YES) 21.38/9.08 U46/1)YES( 21.38/9.08 U51/3(YES,YES,YES) 21.38/9.08 U52/3(YES,YES,YES) 21.38/9.08 U53/3(YES,YES,YES) 21.38/9.08 U54/3(YES,YES,YES) 21.38/9.08 U55/2(YES,YES) 21.38/9.08 U56/1(YES) 21.38/9.08 U61/2(YES,YES) 21.38/9.08 U62/2(YES,YES) 21.38/9.08 U63/1)YES( 21.38/9.08 U71/3(YES,YES,YES) 21.38/9.08 U72/2(YES,YES) 21.38/9.08 U73/2(YES,YES) 21.38/9.08 isPal/1(YES) 21.38/9.08 U74/1(YES) 21.38/9.08 U81/2(YES,YES) 21.38/9.08 U82/2(YES,YES) 21.38/9.08 U83/1)YES( 21.38/9.08 isNePal/1(YES) 21.38/9.08 U91/2(YES,YES) 21.38/9.08 U92/1)YES( 21.38/9.08 a/0) 21.38/9.08 e/0) 21.38/9.08 i/0) 21.38/9.08 o/0) 21.38/9.08 u/0) 21.38/9.08 21.38/9.08 Quasi precedence: 21.38/9.08 ___2 > U21_3 > U22_3 > U23_3 > U24_3 > [U25_2, isList_1, U44_3] > U11_2 > [U12_2, isNeList_1, U45_2] > U31_2 > [U32_2, isQid_1, U62_2] 21.38/9.08 ___2 > U41_3 > U42_3 > U43_3 > [U25_2, isList_1, U44_3] > U11_2 > [U12_2, isNeList_1, U45_2] > U31_2 > [U32_2, isQid_1, U62_2] 21.38/9.08 ___2 > U51_3 > U52_3 > U53_3 > U54_3 > U55_2 > [U25_2, isList_1, U44_3] > U11_2 > [U12_2, isNeList_1, U45_2] > U31_2 > [U32_2, isQid_1, U62_2] 21.38/9.08 ___2 > U51_3 > U52_3 > U53_3 > U54_3 > U55_2 > U56_1 21.38/9.08 ___2 > [U71_3, U72_2, isPal_1] > [tt, a, i, u] > U24_3 > [U25_2, isList_1, U44_3] > U11_2 > [U12_2, isNeList_1, U45_2] > U31_2 > [U32_2, isQid_1, U62_2] 21.38/9.08 ___2 > [U71_3, U72_2, isPal_1] > [tt, a, i, u] > U55_2 > [U25_2, isList_1, U44_3] > U11_2 > [U12_2, isNeList_1, U45_2] > U31_2 > [U32_2, isQid_1, U62_2] 21.38/9.08 ___2 > [U71_3, U72_2, isPal_1] > [tt, a, i, u] > U55_2 > U56_1 21.38/9.08 ___2 > [U71_3, U72_2, isPal_1] > [tt, a, i, u] > U74_1 21.38/9.08 ___2 > [U71_3, U72_2, isPal_1] > U73_2 > U74_1 21.38/9.08 ___2 > [U71_3, U72_2, isPal_1] > U81_2 > [U82_2, isNePal_1] > U61_2 > [U32_2, isQid_1, U62_2] 21.38/9.08 ___2 > U91_2 21.38/9.08 nil > [tt, a, i, u] > U24_3 > [U25_2, isList_1, U44_3] > U11_2 > [U12_2, isNeList_1, U45_2] > U31_2 > [U32_2, isQid_1, U62_2] 21.38/9.08 nil > [tt, a, i, u] > U55_2 > [U25_2, isList_1, U44_3] > U11_2 > [U12_2, isNeList_1, U45_2] > U31_2 > [U32_2, isQid_1, U62_2] 21.38/9.08 nil > [tt, a, i, u] > U55_2 > U56_1 21.38/9.08 nil > [tt, a, i, u] > U74_1 21.38/9.08 e > [tt, a, i, u] > U24_3 > [U25_2, isList_1, U44_3] > U11_2 > [U12_2, isNeList_1, U45_2] > U31_2 > [U32_2, isQid_1, U62_2] 21.38/9.08 e > [tt, a, i, u] > U55_2 > [U25_2, isList_1, U44_3] > U11_2 > [U12_2, isNeList_1, U45_2] > U31_2 > [U32_2, isQid_1, U62_2] 21.38/9.08 e > [tt, a, i, u] > U55_2 > U56_1 21.38/9.08 e > [tt, a, i, u] > U74_1 21.38/9.08 o > [tt, a, i, u] > U24_3 > [U25_2, isList_1, U44_3] > U11_2 > [U12_2, isNeList_1, U45_2] > U31_2 > [U32_2, isQid_1, U62_2] 21.38/9.08 o > [tt, a, i, u] > U55_2 > [U25_2, isList_1, U44_3] > U11_2 > [U12_2, isNeList_1, U45_2] > U31_2 > [U32_2, isQid_1, U62_2] 21.38/9.08 o > [tt, a, i, u] > U55_2 > U56_1 21.38/9.08 o > [tt, a, i, u] > U74_1 21.38/9.08 21.38/9.08 21.38/9.08 Status: 21.38/9.08 ___2: [1,2] 21.38/9.08 nil: multiset status 21.38/9.08 U11_2: multiset status 21.38/9.08 tt: multiset status 21.38/9.08 U12_2: multiset status 21.38/9.08 isNeList_1: multiset status 21.38/9.08 U21_3: [1,3,2] 21.38/9.08 U22_3: multiset status 21.38/9.08 U23_3: multiset status 21.38/9.08 U24_3: [3,2,1] 21.38/9.08 U25_2: [2,1] 21.38/9.08 isList_1: [1] 21.38/9.08 U31_2: multiset status 21.38/9.08 U32_2: multiset status 21.38/9.08 isQid_1: multiset status 21.38/9.08 U41_3: [1,2,3] 21.38/9.08 U42_3: [3,2,1] 21.38/9.08 U43_3: multiset status 21.38/9.08 U44_3: [2,3,1] 21.38/9.08 U45_2: multiset status 21.38/9.08 U51_3: multiset status 21.38/9.08 U52_3: multiset status 21.38/9.08 U53_3: multiset status 21.38/9.08 U54_3: [2,1,3] 21.38/9.08 U55_2: multiset status 21.38/9.08 U56_1: multiset status 21.38/9.08 U61_2: multiset status 21.38/9.08 U62_2: multiset status 21.38/9.08 U71_3: multiset status 21.38/9.08 U72_2: multiset status 21.38/9.08 U73_2: multiset status 21.38/9.08 isPal_1: multiset status 21.38/9.08 U74_1: multiset status 21.38/9.08 U81_2: multiset status 21.38/9.08 U82_2: multiset status 21.38/9.08 isNePal_1: multiset status 21.38/9.08 U91_2: multiset status 21.38/9.08 a: multiset status 21.38/9.08 e: multiset status 21.38/9.08 i: multiset status 21.38/9.08 o: multiset status 21.38/9.08 u: multiset status 21.38/9.09 21.38/9.09 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 21.38/9.09 21.38/9.09 active(__(__(X, Y), Z)) -> mark(__(X, __(Y, Z))) 21.38/9.09 active(__(X, nil)) -> mark(X) 21.38/9.09 active(__(nil, X)) -> mark(X) 21.38/9.09 active(U11(tt, V)) -> mark(U12(isPalListKind(V), V)) 21.38/9.09 active(U12(tt, V)) -> mark(U13(isNeList(V))) 21.38/9.09 active(U21(tt, V1, V2)) -> mark(U22(isPalListKind(V1), V1, V2)) 21.38/9.09 active(U22(tt, V1, V2)) -> mark(U23(isPalListKind(V2), V1, V2)) 21.38/9.09 active(U23(tt, V1, V2)) -> mark(U24(isPalListKind(V2), V1, V2)) 21.38/9.09 active(U24(tt, V1, V2)) -> mark(U25(isList(V1), V2)) 21.38/9.09 active(U25(tt, V2)) -> mark(U26(isList(V2))) 21.38/9.09 active(U31(tt, V)) -> mark(U32(isPalListKind(V), V)) 21.38/9.09 active(U32(tt, V)) -> mark(U33(isQid(V))) 21.38/9.09 active(U41(tt, V1, V2)) -> mark(U42(isPalListKind(V1), V1, V2)) 21.38/9.09 active(U42(tt, V1, V2)) -> mark(U43(isPalListKind(V2), V1, V2)) 21.38/9.09 active(U43(tt, V1, V2)) -> mark(U44(isPalListKind(V2), V1, V2)) 21.38/9.09 active(U44(tt, V1, V2)) -> mark(U45(isList(V1), V2)) 21.38/9.09 active(U45(tt, V2)) -> mark(U46(isNeList(V2))) 21.38/9.09 active(U51(tt, V1, V2)) -> mark(U52(isPalListKind(V1), V1, V2)) 21.38/9.09 active(U52(tt, V1, V2)) -> mark(U53(isPalListKind(V2), V1, V2)) 21.38/9.09 active(U53(tt, V1, V2)) -> mark(U54(isPalListKind(V2), V1, V2)) 21.38/9.09 active(U54(tt, V1, V2)) -> mark(U55(isNeList(V1), V2)) 21.38/9.09 active(U55(tt, V2)) -> mark(U56(isList(V2))) 21.38/9.09 active(U56(tt)) -> mark(tt) 21.38/9.09 active(U61(tt, V)) -> mark(U62(isPalListKind(V), V)) 21.38/9.09 active(U62(tt, V)) -> mark(U63(isQid(V))) 21.38/9.09 active(U71(tt, I, P)) -> mark(U72(isPalListKind(I), P)) 21.38/9.09 active(U72(tt, P)) -> mark(U73(isPal(P), P)) 21.38/9.09 active(U73(tt, P)) -> mark(U74(isPalListKind(P))) 21.38/9.09 active(U74(tt)) -> mark(tt) 21.38/9.09 active(U81(tt, V)) -> mark(U82(isPalListKind(V), V)) 21.38/9.09 active(U82(tt, V)) -> mark(U83(isNePal(V))) 21.38/9.09 active(U91(tt, V2)) -> mark(U92(isPalListKind(V2))) 21.38/9.09 active(isList(V)) -> mark(U11(isPalListKind(V), V)) 21.38/9.09 active(isList(nil)) -> mark(tt) 21.38/9.09 active(isList(__(V1, V2))) -> mark(U21(isPalListKind(V1), V1, V2)) 21.38/9.09 active(isNeList(V)) -> mark(U31(isPalListKind(V), V)) 21.38/9.09 active(isNeList(__(V1, V2))) -> mark(U41(isPalListKind(V1), V1, V2)) 21.38/9.09 active(isNeList(__(V1, V2))) -> mark(U51(isPalListKind(V1), V1, V2)) 21.38/9.09 active(isNePal(V)) -> mark(U61(isPalListKind(V), V)) 21.38/9.09 active(isNePal(__(I, __(P, I)))) -> mark(U71(isQid(I), I, P)) 21.38/9.09 active(isPal(V)) -> mark(U81(isPalListKind(V), V)) 21.38/9.09 active(isPal(nil)) -> mark(tt) 21.38/9.09 active(isPalListKind(e)) -> mark(tt) 21.38/9.09 active(isPalListKind(nil)) -> mark(tt) 21.38/9.09 active(isPalListKind(o)) -> mark(tt) 21.38/9.09 active(isPalListKind(__(V1, V2))) -> mark(U91(isPalListKind(V1), V2)) 21.38/9.09 active(isQid(a)) -> mark(tt) 21.38/9.09 active(isQid(e)) -> mark(tt) 21.38/9.09 active(isQid(i)) -> mark(tt) 21.38/9.09 active(isQid(o)) -> mark(tt) 21.38/9.09 active(isQid(u)) -> mark(tt) 21.38/9.09 21.38/9.09 21.38/9.09 21.38/9.09 21.38/9.09 ---------------------------------------- 21.38/9.09 21.38/9.09 (2) 21.38/9.09 Obligation: 21.38/9.09 Q restricted rewrite system: 21.38/9.09 The TRS R consists of the following rules: 21.38/9.09 21.38/9.09 active(U13(tt)) -> mark(tt) 21.38/9.09 active(U26(tt)) -> mark(tt) 21.38/9.09 active(U33(tt)) -> mark(tt) 21.38/9.09 active(U46(tt)) -> mark(tt) 21.38/9.09 active(U63(tt)) -> mark(tt) 21.38/9.09 active(U83(tt)) -> mark(tt) 21.38/9.09 active(U92(tt)) -> mark(tt) 21.38/9.09 active(isPalListKind(a)) -> mark(tt) 21.38/9.09 active(isPalListKind(i)) -> mark(tt) 21.38/9.09 active(isPalListKind(u)) -> mark(tt) 21.38/9.09 mark(__(X1, X2)) -> active(__(mark(X1), mark(X2))) 21.38/9.09 mark(nil) -> active(nil) 21.38/9.09 mark(U11(X1, X2)) -> active(U11(mark(X1), X2)) 21.38/9.09 mark(tt) -> active(tt) 21.38/9.09 mark(U12(X1, X2)) -> active(U12(mark(X1), X2)) 21.38/9.09 mark(isPalListKind(X)) -> active(isPalListKind(X)) 21.38/9.09 mark(U13(X)) -> active(U13(mark(X))) 21.38/9.09 mark(isNeList(X)) -> active(isNeList(X)) 21.38/9.09 mark(U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)) 21.38/9.09 mark(U22(X1, X2, X3)) -> active(U22(mark(X1), X2, X3)) 21.38/9.09 mark(U23(X1, X2, X3)) -> active(U23(mark(X1), X2, X3)) 21.38/9.09 mark(U24(X1, X2, X3)) -> active(U24(mark(X1), X2, X3)) 21.38/9.09 mark(U25(X1, X2)) -> active(U25(mark(X1), X2)) 21.38/9.09 mark(isList(X)) -> active(isList(X)) 21.38/9.09 mark(U26(X)) -> active(U26(mark(X))) 21.38/9.09 mark(U31(X1, X2)) -> active(U31(mark(X1), X2)) 21.38/9.09 mark(U32(X1, X2)) -> active(U32(mark(X1), X2)) 21.38/9.09 mark(U33(X)) -> active(U33(mark(X))) 21.38/9.09 mark(isQid(X)) -> active(isQid(X)) 21.38/9.09 mark(U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3)) 21.38/9.09 mark(U42(X1, X2, X3)) -> active(U42(mark(X1), X2, X3)) 21.38/9.09 mark(U43(X1, X2, X3)) -> active(U43(mark(X1), X2, X3)) 21.38/9.09 mark(U44(X1, X2, X3)) -> active(U44(mark(X1), X2, X3)) 21.38/9.09 mark(U45(X1, X2)) -> active(U45(mark(X1), X2)) 21.38/9.09 mark(U46(X)) -> active(U46(mark(X))) 21.38/9.09 mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)) 21.38/9.09 mark(U52(X1, X2, X3)) -> active(U52(mark(X1), X2, X3)) 21.38/9.09 mark(U53(X1, X2, X3)) -> active(U53(mark(X1), X2, X3)) 21.38/9.09 mark(U54(X1, X2, X3)) -> active(U54(mark(X1), X2, X3)) 21.38/9.09 mark(U55(X1, X2)) -> active(U55(mark(X1), X2)) 21.38/9.09 mark(U56(X)) -> active(U56(mark(X))) 21.38/9.09 mark(U61(X1, X2)) -> active(U61(mark(X1), X2)) 21.38/9.09 mark(U62(X1, X2)) -> active(U62(mark(X1), X2)) 21.38/9.09 mark(U63(X)) -> active(U63(mark(X))) 21.38/9.09 mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)) 21.38/9.09 mark(U72(X1, X2)) -> active(U72(mark(X1), X2)) 21.38/9.09 mark(U73(X1, X2)) -> active(U73(mark(X1), X2)) 21.38/9.09 mark(isPal(X)) -> active(isPal(X)) 21.38/9.09 mark(U74(X)) -> active(U74(mark(X))) 21.38/9.09 mark(U81(X1, X2)) -> active(U81(mark(X1), X2)) 21.38/9.09 mark(U82(X1, X2)) -> active(U82(mark(X1), X2)) 21.38/9.09 mark(U83(X)) -> active(U83(mark(X))) 21.38/9.09 mark(isNePal(X)) -> active(isNePal(X)) 21.38/9.09 mark(U91(X1, X2)) -> active(U91(mark(X1), X2)) 21.38/9.09 mark(U92(X)) -> active(U92(mark(X))) 21.38/9.09 mark(a) -> active(a) 21.38/9.09 mark(e) -> active(e) 21.38/9.09 mark(i) -> active(i) 21.38/9.09 mark(o) -> active(o) 21.38/9.09 mark(u) -> active(u) 21.38/9.09 __(mark(X1), X2) -> __(X1, X2) 21.38/9.09 __(X1, mark(X2)) -> __(X1, X2) 21.38/9.09 __(active(X1), X2) -> __(X1, X2) 21.38/9.09 __(X1, active(X2)) -> __(X1, X2) 21.38/9.09 U11(mark(X1), X2) -> U11(X1, X2) 21.38/9.09 U11(X1, mark(X2)) -> U11(X1, X2) 21.38/9.09 U11(active(X1), X2) -> U11(X1, X2) 21.38/9.09 U11(X1, active(X2)) -> U11(X1, X2) 21.38/9.09 U12(mark(X1), X2) -> U12(X1, X2) 21.38/9.09 U12(X1, mark(X2)) -> U12(X1, X2) 21.38/9.09 U12(active(X1), X2) -> U12(X1, X2) 21.38/9.09 U12(X1, active(X2)) -> U12(X1, X2) 21.38/9.09 isPalListKind(mark(X)) -> isPalListKind(X) 21.38/9.09 isPalListKind(active(X)) -> isPalListKind(X) 21.38/9.09 U13(mark(X)) -> U13(X) 21.38/9.09 U13(active(X)) -> U13(X) 21.38/9.09 isNeList(mark(X)) -> isNeList(X) 21.38/9.09 isNeList(active(X)) -> isNeList(X) 21.38/9.09 U21(mark(X1), X2, X3) -> U21(X1, X2, X3) 21.38/9.09 U21(X1, mark(X2), X3) -> U21(X1, X2, X3) 21.38/9.09 U21(X1, X2, mark(X3)) -> U21(X1, X2, X3) 21.38/9.09 U21(active(X1), X2, X3) -> U21(X1, X2, X3) 21.38/9.09 U21(X1, active(X2), X3) -> U21(X1, X2, X3) 21.38/9.09 U21(X1, X2, active(X3)) -> U21(X1, X2, X3) 21.38/9.09 U22(mark(X1), X2, X3) -> U22(X1, X2, X3) 21.38/9.09 U22(X1, mark(X2), X3) -> U22(X1, X2, X3) 21.38/9.09 U22(X1, X2, mark(X3)) -> U22(X1, X2, X3) 21.38/9.09 U22(active(X1), X2, X3) -> U22(X1, X2, X3) 21.38/9.09 U22(X1, active(X2), X3) -> U22(X1, X2, X3) 21.38/9.09 U22(X1, X2, active(X3)) -> U22(X1, X2, X3) 21.38/9.09 U23(mark(X1), X2, X3) -> U23(X1, X2, X3) 21.38/9.09 U23(X1, mark(X2), X3) -> U23(X1, X2, X3) 21.38/9.09 U23(X1, X2, mark(X3)) -> U23(X1, X2, X3) 21.38/9.09 U23(active(X1), X2, X3) -> U23(X1, X2, X3) 21.38/9.09 U23(X1, active(X2), X3) -> U23(X1, X2, X3) 21.38/9.09 U23(X1, X2, active(X3)) -> U23(X1, X2, X3) 21.38/9.09 U24(mark(X1), X2, X3) -> U24(X1, X2, X3) 21.38/9.09 U24(X1, mark(X2), X3) -> U24(X1, X2, X3) 21.38/9.09 U24(X1, X2, mark(X3)) -> U24(X1, X2, X3) 21.38/9.09 U24(active(X1), X2, X3) -> U24(X1, X2, X3) 21.38/9.09 U24(X1, active(X2), X3) -> U24(X1, X2, X3) 21.38/9.09 U24(X1, X2, active(X3)) -> U24(X1, X2, X3) 21.38/9.09 U25(mark(X1), X2) -> U25(X1, X2) 21.38/9.09 U25(X1, mark(X2)) -> U25(X1, X2) 21.38/9.09 U25(active(X1), X2) -> U25(X1, X2) 21.38/9.09 U25(X1, active(X2)) -> U25(X1, X2) 21.38/9.09 isList(mark(X)) -> isList(X) 21.38/9.09 isList(active(X)) -> isList(X) 21.38/9.09 U26(mark(X)) -> U26(X) 21.38/9.09 U26(active(X)) -> U26(X) 21.38/9.09 U31(mark(X1), X2) -> U31(X1, X2) 21.38/9.09 U31(X1, mark(X2)) -> U31(X1, X2) 21.38/9.09 U31(active(X1), X2) -> U31(X1, X2) 21.38/9.09 U31(X1, active(X2)) -> U31(X1, X2) 21.38/9.09 U32(mark(X1), X2) -> U32(X1, X2) 21.38/9.09 U32(X1, mark(X2)) -> U32(X1, X2) 21.38/9.09 U32(active(X1), X2) -> U32(X1, X2) 21.38/9.09 U32(X1, active(X2)) -> U32(X1, X2) 21.38/9.09 U33(mark(X)) -> U33(X) 21.38/9.09 U33(active(X)) -> U33(X) 21.38/9.09 isQid(mark(X)) -> isQid(X) 21.38/9.09 isQid(active(X)) -> isQid(X) 21.38/9.09 U41(mark(X1), X2, X3) -> U41(X1, X2, X3) 21.38/9.09 U41(X1, mark(X2), X3) -> U41(X1, X2, X3) 21.38/9.09 U41(X1, X2, mark(X3)) -> U41(X1, X2, X3) 21.38/9.09 U41(active(X1), X2, X3) -> U41(X1, X2, X3) 21.38/9.09 U41(X1, active(X2), X3) -> U41(X1, X2, X3) 21.38/9.09 U41(X1, X2, active(X3)) -> U41(X1, X2, X3) 21.38/9.09 U42(mark(X1), X2, X3) -> U42(X1, X2, X3) 21.38/9.09 U42(X1, mark(X2), X3) -> U42(X1, X2, X3) 21.38/9.09 U42(X1, X2, mark(X3)) -> U42(X1, X2, X3) 21.38/9.09 U42(active(X1), X2, X3) -> U42(X1, X2, X3) 21.38/9.09 U42(X1, active(X2), X3) -> U42(X1, X2, X3) 21.38/9.09 U42(X1, X2, active(X3)) -> U42(X1, X2, X3) 21.38/9.09 U43(mark(X1), X2, X3) -> U43(X1, X2, X3) 21.38/9.09 U43(X1, mark(X2), X3) -> U43(X1, X2, X3) 21.38/9.09 U43(X1, X2, mark(X3)) -> U43(X1, X2, X3) 21.38/9.09 U43(active(X1), X2, X3) -> U43(X1, X2, X3) 21.38/9.09 U43(X1, active(X2), X3) -> U43(X1, X2, X3) 21.38/9.09 U43(X1, X2, active(X3)) -> U43(X1, X2, X3) 21.38/9.09 U44(mark(X1), X2, X3) -> U44(X1, X2, X3) 21.38/9.09 U44(X1, mark(X2), X3) -> U44(X1, X2, X3) 21.38/9.09 U44(X1, X2, mark(X3)) -> U44(X1, X2, X3) 21.38/9.09 U44(active(X1), X2, X3) -> U44(X1, X2, X3) 21.38/9.09 U44(X1, active(X2), X3) -> U44(X1, X2, X3) 21.38/9.09 U44(X1, X2, active(X3)) -> U44(X1, X2, X3) 21.38/9.09 U45(mark(X1), X2) -> U45(X1, X2) 21.38/9.09 U45(X1, mark(X2)) -> U45(X1, X2) 21.38/9.09 U45(active(X1), X2) -> U45(X1, X2) 21.38/9.09 U45(X1, active(X2)) -> U45(X1, X2) 21.38/9.09 U46(mark(X)) -> U46(X) 21.38/9.09 U46(active(X)) -> U46(X) 21.38/9.09 U51(mark(X1), X2, X3) -> U51(X1, X2, X3) 21.38/9.09 U51(X1, mark(X2), X3) -> U51(X1, X2, X3) 21.38/9.09 U51(X1, X2, mark(X3)) -> U51(X1, X2, X3) 21.38/9.09 U51(active(X1), X2, X3) -> U51(X1, X2, X3) 21.38/9.09 U51(X1, active(X2), X3) -> U51(X1, X2, X3) 21.38/9.09 U51(X1, X2, active(X3)) -> U51(X1, X2, X3) 21.38/9.09 U52(mark(X1), X2, X3) -> U52(X1, X2, X3) 21.38/9.09 U52(X1, mark(X2), X3) -> U52(X1, X2, X3) 21.38/9.09 U52(X1, X2, mark(X3)) -> U52(X1, X2, X3) 21.38/9.09 U52(active(X1), X2, X3) -> U52(X1, X2, X3) 21.38/9.09 U52(X1, active(X2), X3) -> U52(X1, X2, X3) 21.38/9.09 U52(X1, X2, active(X3)) -> U52(X1, X2, X3) 21.38/9.09 U53(mark(X1), X2, X3) -> U53(X1, X2, X3) 21.38/9.09 U53(X1, mark(X2), X3) -> U53(X1, X2, X3) 21.38/9.09 U53(X1, X2, mark(X3)) -> U53(X1, X2, X3) 21.38/9.09 U53(active(X1), X2, X3) -> U53(X1, X2, X3) 21.38/9.09 U53(X1, active(X2), X3) -> U53(X1, X2, X3) 21.38/9.09 U53(X1, X2, active(X3)) -> U53(X1, X2, X3) 21.38/9.09 U54(mark(X1), X2, X3) -> U54(X1, X2, X3) 21.38/9.09 U54(X1, mark(X2), X3) -> U54(X1, X2, X3) 21.38/9.09 U54(X1, X2, mark(X3)) -> U54(X1, X2, X3) 21.38/9.09 U54(active(X1), X2, X3) -> U54(X1, X2, X3) 21.38/9.09 U54(X1, active(X2), X3) -> U54(X1, X2, X3) 21.38/9.09 U54(X1, X2, active(X3)) -> U54(X1, X2, X3) 21.38/9.09 U55(mark(X1), X2) -> U55(X1, X2) 21.38/9.09 U55(X1, mark(X2)) -> U55(X1, X2) 21.38/9.09 U55(active(X1), X2) -> U55(X1, X2) 21.38/9.09 U55(X1, active(X2)) -> U55(X1, X2) 21.38/9.09 U56(mark(X)) -> U56(X) 21.38/9.09 U56(active(X)) -> U56(X) 21.38/9.09 U61(mark(X1), X2) -> U61(X1, X2) 21.38/9.09 U61(X1, mark(X2)) -> U61(X1, X2) 21.38/9.09 U61(active(X1), X2) -> U61(X1, X2) 21.38/9.09 U61(X1, active(X2)) -> U61(X1, X2) 21.38/9.09 U62(mark(X1), X2) -> U62(X1, X2) 21.38/9.09 U62(X1, mark(X2)) -> U62(X1, X2) 21.38/9.09 U62(active(X1), X2) -> U62(X1, X2) 21.38/9.09 U62(X1, active(X2)) -> U62(X1, X2) 21.38/9.09 U63(mark(X)) -> U63(X) 21.38/9.09 U63(active(X)) -> U63(X) 21.38/9.09 U71(mark(X1), X2, X3) -> U71(X1, X2, X3) 21.38/9.09 U71(X1, mark(X2), X3) -> U71(X1, X2, X3) 21.38/9.09 U71(X1, X2, mark(X3)) -> U71(X1, X2, X3) 21.38/9.09 U71(active(X1), X2, X3) -> U71(X1, X2, X3) 21.38/9.09 U71(X1, active(X2), X3) -> U71(X1, X2, X3) 21.38/9.09 U71(X1, X2, active(X3)) -> U71(X1, X2, X3) 21.38/9.09 U72(mark(X1), X2) -> U72(X1, X2) 21.38/9.09 U72(X1, mark(X2)) -> U72(X1, X2) 21.38/9.09 U72(active(X1), X2) -> U72(X1, X2) 21.38/9.09 U72(X1, active(X2)) -> U72(X1, X2) 21.38/9.09 U73(mark(X1), X2) -> U73(X1, X2) 21.38/9.09 U73(X1, mark(X2)) -> U73(X1, X2) 21.38/9.09 U73(active(X1), X2) -> U73(X1, X2) 21.38/9.09 U73(X1, active(X2)) -> U73(X1, X2) 21.38/9.09 isPal(mark(X)) -> isPal(X) 21.38/9.09 isPal(active(X)) -> isPal(X) 21.38/9.09 U74(mark(X)) -> U74(X) 21.38/9.09 U74(active(X)) -> U74(X) 21.38/9.09 U81(mark(X1), X2) -> U81(X1, X2) 21.38/9.09 U81(X1, mark(X2)) -> U81(X1, X2) 21.38/9.09 U81(active(X1), X2) -> U81(X1, X2) 21.38/9.09 U81(X1, active(X2)) -> U81(X1, X2) 21.38/9.09 U82(mark(X1), X2) -> U82(X1, X2) 21.38/9.09 U82(X1, mark(X2)) -> U82(X1, X2) 21.38/9.09 U82(active(X1), X2) -> U82(X1, X2) 21.38/9.09 U82(X1, active(X2)) -> U82(X1, X2) 21.38/9.09 U83(mark(X)) -> U83(X) 21.38/9.09 U83(active(X)) -> U83(X) 21.38/9.09 isNePal(mark(X)) -> isNePal(X) 21.38/9.09 isNePal(active(X)) -> isNePal(X) 21.38/9.09 U91(mark(X1), X2) -> U91(X1, X2) 21.38/9.09 U91(X1, mark(X2)) -> U91(X1, X2) 21.38/9.09 U91(active(X1), X2) -> U91(X1, X2) 21.38/9.09 U91(X1, active(X2)) -> U91(X1, X2) 21.38/9.09 U92(mark(X)) -> U92(X) 21.38/9.09 U92(active(X)) -> U92(X) 21.38/9.09 21.38/9.09 The set Q consists of the following terms: 21.38/9.09 21.38/9.09 active(__(__(x0, x1), x2)) 21.38/9.09 active(__(x0, nil)) 21.38/9.09 active(__(nil, x0)) 21.38/9.09 active(U11(tt, x0)) 21.38/9.09 active(U12(tt, x0)) 21.38/9.09 active(U13(tt)) 21.38/9.09 active(U21(tt, x0, x1)) 21.38/9.09 active(U22(tt, x0, x1)) 21.38/9.09 active(U23(tt, x0, x1)) 21.38/9.09 active(U24(tt, x0, x1)) 21.38/9.09 active(U25(tt, x0)) 21.38/9.09 active(U26(tt)) 21.38/9.09 active(U31(tt, x0)) 21.38/9.09 active(U32(tt, x0)) 21.38/9.09 active(U33(tt)) 21.38/9.09 active(U41(tt, x0, x1)) 21.38/9.09 active(U42(tt, x0, x1)) 21.38/9.09 active(U43(tt, x0, x1)) 21.38/9.09 active(U44(tt, x0, x1)) 21.38/9.09 active(U45(tt, x0)) 21.38/9.09 active(U46(tt)) 21.38/9.09 active(U51(tt, x0, x1)) 21.38/9.09 active(U52(tt, x0, x1)) 21.38/9.09 active(U53(tt, x0, x1)) 21.38/9.09 active(U54(tt, x0, x1)) 21.38/9.09 active(U55(tt, x0)) 21.38/9.09 active(U56(tt)) 21.38/9.09 active(U61(tt, x0)) 21.38/9.09 active(U62(tt, x0)) 21.38/9.09 active(U63(tt)) 21.38/9.09 active(U71(tt, x0, x1)) 21.38/9.09 active(U72(tt, x0)) 21.38/9.09 active(U73(tt, x0)) 21.38/9.09 active(U74(tt)) 21.38/9.09 active(U81(tt, x0)) 21.38/9.09 active(U82(tt, x0)) 21.38/9.09 active(U83(tt)) 21.38/9.09 active(U91(tt, x0)) 21.38/9.09 active(U92(tt)) 21.38/9.09 active(isList(x0)) 21.38/9.09 active(isNeList(x0)) 21.38/9.09 active(isNePal(x0)) 21.38/9.09 active(isPal(x0)) 21.38/9.09 active(isPalListKind(a)) 21.38/9.09 active(isPalListKind(e)) 21.38/9.09 active(isPalListKind(i)) 21.38/9.09 active(isPalListKind(nil)) 21.38/9.09 active(isPalListKind(o)) 21.38/9.09 active(isPalListKind(u)) 21.38/9.09 active(isPalListKind(__(x0, x1))) 21.38/9.09 active(isQid(a)) 21.38/9.09 active(isQid(e)) 21.38/9.09 active(isQid(i)) 21.38/9.09 active(isQid(o)) 21.38/9.09 active(isQid(u)) 21.38/9.09 mark(__(x0, x1)) 21.38/9.09 mark(nil) 21.38/9.09 mark(U11(x0, x1)) 21.38/9.09 mark(tt) 21.38/9.09 mark(U12(x0, x1)) 21.38/9.09 mark(isPalListKind(x0)) 21.38/9.09 mark(U13(x0)) 21.38/9.09 mark(isNeList(x0)) 21.38/9.09 mark(U21(x0, x1, x2)) 21.38/9.09 mark(U22(x0, x1, x2)) 21.38/9.09 mark(U23(x0, x1, x2)) 21.38/9.09 mark(U24(x0, x1, x2)) 21.38/9.09 mark(U25(x0, x1)) 21.38/9.09 mark(isList(x0)) 21.38/9.09 mark(U26(x0)) 21.38/9.09 mark(U31(x0, x1)) 21.38/9.09 mark(U32(x0, x1)) 21.38/9.09 mark(U33(x0)) 21.38/9.09 mark(isQid(x0)) 21.38/9.09 mark(U41(x0, x1, x2)) 21.38/9.09 mark(U42(x0, x1, x2)) 21.38/9.09 mark(U43(x0, x1, x2)) 21.38/9.09 mark(U44(x0, x1, x2)) 21.38/9.09 mark(U45(x0, x1)) 21.38/9.09 mark(U46(x0)) 21.38/9.09 mark(U51(x0, x1, x2)) 21.38/9.09 mark(U52(x0, x1, x2)) 21.38/9.09 mark(U53(x0, x1, x2)) 21.38/9.09 mark(U54(x0, x1, x2)) 21.38/9.09 mark(U55(x0, x1)) 21.38/9.09 mark(U56(x0)) 21.38/9.09 mark(U61(x0, x1)) 21.38/9.09 mark(U62(x0, x1)) 21.38/9.09 mark(U63(x0)) 21.38/9.09 mark(U71(x0, x1, x2)) 21.38/9.09 mark(U72(x0, x1)) 21.38/9.09 mark(U73(x0, x1)) 21.38/9.09 mark(isPal(x0)) 21.38/9.09 mark(U74(x0)) 21.38/9.09 mark(U81(x0, x1)) 21.38/9.09 mark(U82(x0, x1)) 21.38/9.09 mark(U83(x0)) 21.38/9.09 mark(isNePal(x0)) 21.38/9.09 mark(U91(x0, x1)) 21.38/9.09 mark(U92(x0)) 21.38/9.09 mark(a) 21.38/9.09 mark(e) 21.38/9.09 mark(i) 21.38/9.09 mark(o) 21.38/9.09 mark(u) 21.38/9.09 __(mark(x0), x1) 21.38/9.09 __(x0, mark(x1)) 21.38/9.09 __(active(x0), x1) 21.38/9.09 __(x0, active(x1)) 21.38/9.09 U11(mark(x0), x1) 21.38/9.09 U11(x0, mark(x1)) 21.38/9.09 U11(active(x0), x1) 21.38/9.09 U11(x0, active(x1)) 21.38/9.09 U12(mark(x0), x1) 21.38/9.09 U12(x0, mark(x1)) 21.38/9.09 U12(active(x0), x1) 21.38/9.09 U12(x0, active(x1)) 21.38/9.09 isPalListKind(mark(x0)) 21.38/9.09 isPalListKind(active(x0)) 21.38/9.09 U13(mark(x0)) 21.38/9.09 U13(active(x0)) 21.38/9.09 isNeList(mark(x0)) 21.38/9.09 isNeList(active(x0)) 21.38/9.09 U21(mark(x0), x1, x2) 21.38/9.09 U21(x0, mark(x1), x2) 21.38/9.09 U21(x0, x1, mark(x2)) 21.38/9.09 U21(active(x0), x1, x2) 21.38/9.09 U21(x0, active(x1), x2) 21.38/9.09 U21(x0, x1, active(x2)) 21.38/9.09 U22(mark(x0), x1, x2) 21.38/9.09 U22(x0, mark(x1), x2) 21.38/9.09 U22(x0, x1, mark(x2)) 21.38/9.09 U22(active(x0), x1, x2) 21.38/9.09 U22(x0, active(x1), x2) 21.38/9.09 U22(x0, x1, active(x2)) 21.38/9.09 U23(mark(x0), x1, x2) 21.38/9.09 U23(x0, mark(x1), x2) 21.38/9.09 U23(x0, x1, mark(x2)) 21.38/9.09 U23(active(x0), x1, x2) 21.38/9.09 U23(x0, active(x1), x2) 21.38/9.09 U23(x0, x1, active(x2)) 21.38/9.09 U24(mark(x0), x1, x2) 21.38/9.09 U24(x0, mark(x1), x2) 21.38/9.09 U24(x0, x1, mark(x2)) 21.38/9.09 U24(active(x0), x1, x2) 21.38/9.09 U24(x0, active(x1), x2) 21.38/9.09 U24(x0, x1, active(x2)) 21.38/9.09 U25(mark(x0), x1) 21.38/9.09 U25(x0, mark(x1)) 21.38/9.09 U25(active(x0), x1) 21.38/9.09 U25(x0, active(x1)) 21.38/9.09 isList(mark(x0)) 21.38/9.09 isList(active(x0)) 21.38/9.09 U26(mark(x0)) 21.38/9.09 U26(active(x0)) 21.38/9.09 U31(mark(x0), x1) 21.38/9.09 U31(x0, mark(x1)) 21.38/9.09 U31(active(x0), x1) 21.38/9.09 U31(x0, active(x1)) 21.38/9.09 U32(mark(x0), x1) 21.38/9.09 U32(x0, mark(x1)) 21.38/9.09 U32(active(x0), x1) 21.38/9.09 U32(x0, active(x1)) 21.38/9.09 U33(mark(x0)) 21.38/9.09 U33(active(x0)) 21.38/9.09 isQid(mark(x0)) 21.38/9.09 isQid(active(x0)) 21.38/9.09 U41(mark(x0), x1, x2) 21.38/9.09 U41(x0, mark(x1), x2) 21.38/9.09 U41(x0, x1, mark(x2)) 21.38/9.09 U41(active(x0), x1, x2) 21.38/9.09 U41(x0, active(x1), x2) 21.38/9.09 U41(x0, x1, active(x2)) 21.38/9.09 U42(mark(x0), x1, x2) 21.38/9.09 U42(x0, mark(x1), x2) 21.38/9.09 U42(x0, x1, mark(x2)) 21.38/9.09 U42(active(x0), x1, x2) 21.38/9.09 U42(x0, active(x1), x2) 21.38/9.09 U42(x0, x1, active(x2)) 21.38/9.09 U43(mark(x0), x1, x2) 21.38/9.09 U43(x0, mark(x1), x2) 21.38/9.09 U43(x0, x1, mark(x2)) 21.38/9.09 U43(active(x0), x1, x2) 21.38/9.09 U43(x0, active(x1), x2) 21.38/9.09 U43(x0, x1, active(x2)) 21.38/9.09 U44(mark(x0), x1, x2) 21.38/9.09 U44(x0, mark(x1), x2) 21.38/9.09 U44(x0, x1, mark(x2)) 21.38/9.09 U44(active(x0), x1, x2) 21.38/9.09 U44(x0, active(x1), x2) 21.38/9.09 U44(x0, x1, active(x2)) 21.38/9.09 U45(mark(x0), x1) 21.38/9.09 U45(x0, mark(x1)) 21.38/9.09 U45(active(x0), x1) 21.38/9.09 U45(x0, active(x1)) 21.38/9.09 U46(mark(x0)) 21.38/9.09 U46(active(x0)) 21.38/9.09 U51(mark(x0), x1, x2) 21.38/9.09 U51(x0, mark(x1), x2) 21.38/9.09 U51(x0, x1, mark(x2)) 21.38/9.09 U51(active(x0), x1, x2) 21.38/9.09 U51(x0, active(x1), x2) 21.38/9.09 U51(x0, x1, active(x2)) 21.38/9.09 U52(mark(x0), x1, x2) 21.38/9.09 U52(x0, mark(x1), x2) 21.38/9.09 U52(x0, x1, mark(x2)) 21.38/9.09 U52(active(x0), x1, x2) 21.38/9.09 U52(x0, active(x1), x2) 21.38/9.09 U52(x0, x1, active(x2)) 21.38/9.09 U53(mark(x0), x1, x2) 21.38/9.09 U53(x0, mark(x1), x2) 21.38/9.09 U53(x0, x1, mark(x2)) 21.38/9.09 U53(active(x0), x1, x2) 21.38/9.09 U53(x0, active(x1), x2) 21.38/9.09 U53(x0, x1, active(x2)) 21.38/9.09 U54(mark(x0), x1, x2) 21.38/9.09 U54(x0, mark(x1), x2) 21.38/9.09 U54(x0, x1, mark(x2)) 21.38/9.09 U54(active(x0), x1, x2) 21.38/9.09 U54(x0, active(x1), x2) 21.38/9.09 U54(x0, x1, active(x2)) 21.38/9.09 U55(mark(x0), x1) 21.38/9.09 U55(x0, mark(x1)) 21.38/9.09 U55(active(x0), x1) 21.38/9.09 U55(x0, active(x1)) 21.38/9.09 U56(mark(x0)) 21.38/9.09 U56(active(x0)) 21.38/9.09 U61(mark(x0), x1) 21.38/9.09 U61(x0, mark(x1)) 21.38/9.09 U61(active(x0), x1) 21.38/9.09 U61(x0, active(x1)) 21.38/9.09 U62(mark(x0), x1) 21.38/9.09 U62(x0, mark(x1)) 21.38/9.09 U62(active(x0), x1) 21.38/9.09 U62(x0, active(x1)) 21.38/9.09 U63(mark(x0)) 21.38/9.09 U63(active(x0)) 21.38/9.09 U71(mark(x0), x1, x2) 21.38/9.09 U71(x0, mark(x1), x2) 21.38/9.09 U71(x0, x1, mark(x2)) 21.38/9.09 U71(active(x0), x1, x2) 21.38/9.09 U71(x0, active(x1), x2) 21.38/9.09 U71(x0, x1, active(x2)) 21.38/9.09 U72(mark(x0), x1) 21.38/9.09 U72(x0, mark(x1)) 21.38/9.09 U72(active(x0), x1) 21.38/9.09 U72(x0, active(x1)) 21.38/9.09 U73(mark(x0), x1) 21.38/9.09 U73(x0, mark(x1)) 21.38/9.09 U73(active(x0), x1) 21.38/9.09 U73(x0, active(x1)) 21.38/9.09 isPal(mark(x0)) 21.38/9.09 isPal(active(x0)) 21.38/9.09 U74(mark(x0)) 21.38/9.09 U74(active(x0)) 21.38/9.09 U81(mark(x0), x1) 21.38/9.09 U81(x0, mark(x1)) 21.38/9.09 U81(active(x0), x1) 21.38/9.09 U81(x0, active(x1)) 21.38/9.09 U82(mark(x0), x1) 21.38/9.09 U82(x0, mark(x1)) 21.38/9.09 U82(active(x0), x1) 21.38/9.09 U82(x0, active(x1)) 21.38/9.09 U83(mark(x0)) 21.38/9.09 U83(active(x0)) 21.38/9.09 isNePal(mark(x0)) 21.38/9.09 isNePal(active(x0)) 21.38/9.09 U91(mark(x0), x1) 21.38/9.09 U91(x0, mark(x1)) 21.38/9.09 U91(active(x0), x1) 21.38/9.09 U91(x0, active(x1)) 21.38/9.09 U92(mark(x0)) 21.38/9.09 U92(active(x0)) 21.38/9.09 21.38/9.09 21.38/9.09 ---------------------------------------- 21.38/9.09 21.38/9.09 (3) QTRSRRRProof (EQUIVALENT) 21.38/9.09 Used ordering: 21.38/9.09 active/1)YES( 21.38/9.09 U13/1(YES) 21.38/9.09 tt/0) 21.38/9.09 mark/1(YES) 21.38/9.09 U26/1(YES) 21.38/9.09 U33/1(YES) 21.38/9.09 U46/1(YES) 21.38/9.09 U63/1(YES) 21.38/9.09 U83/1(YES) 21.38/9.09 U92/1(YES) 21.38/9.09 isPalListKind/1(YES) 21.38/9.09 a/0) 21.38/9.09 i/0) 21.38/9.09 u/0) 21.38/9.09 __/2(YES,YES) 21.38/9.09 nil/0) 21.38/9.09 U11/2(YES,YES) 21.38/9.09 U12/2(YES,YES) 21.38/9.09 isNeList/1(YES) 21.38/9.09 U21/3(YES,YES,YES) 21.38/9.09 U22/3(YES,YES,YES) 21.38/9.09 U23/3(YES,YES,YES) 21.38/9.09 U24/3(YES,YES,YES) 21.38/9.09 U25/2(YES,YES) 21.38/9.09 isList/1(YES) 21.38/9.09 U31/2(YES,YES) 21.38/9.09 U32/2(YES,YES) 21.38/9.09 isQid/1(YES) 21.38/9.09 U41/3(YES,YES,YES) 21.38/9.09 U42/3(YES,YES,YES) 21.38/9.09 U43/3(YES,YES,YES) 21.38/9.09 U44/3(YES,YES,YES) 21.38/9.09 U45/2(YES,YES) 21.38/9.09 U51/3(YES,YES,YES) 21.38/9.09 U52/3(YES,YES,YES) 21.38/9.09 U53/3(YES,YES,YES) 21.38/9.09 U54/3(YES,YES,YES) 21.38/9.09 U55/2(YES,YES) 21.38/9.09 U56/1)YES( 21.38/9.09 U61/2(YES,YES) 21.38/9.09 U62/2(YES,YES) 21.38/9.09 U71/3(YES,YES,YES) 21.38/9.09 U72/2(YES,YES) 21.38/9.09 U73/2(YES,YES) 21.38/9.09 isPal/1(YES) 21.38/9.09 U74/1(YES) 21.38/9.09 U81/2(YES,YES) 21.38/9.09 U82/2(YES,YES) 21.38/9.09 isNePal/1(YES) 21.38/9.09 U91/2(YES,YES) 21.38/9.09 e/0) 21.38/9.09 o/0) 21.38/9.09 21.38/9.09 Quasi precedence: 21.38/9.09 a > [U13_1, tt, mark_1, U26_1, U33_1, U46_1, U63_1, U83_1, U92_1, isPalListKind_1, u, isList_1, isQid_1, U45_2, U61_2, U62_2, U73_2, isPal_1, U74_1, U91_2] > ___2 21.38/9.09 a > [U13_1, tt, mark_1, U26_1, U33_1, U46_1, U63_1, U83_1, U92_1, isPalListKind_1, u, isList_1, isQid_1, U45_2, U61_2, U62_2, U73_2, isPal_1, U74_1, U91_2] > nil 21.38/9.09 a > [U13_1, tt, mark_1, U26_1, U33_1, U46_1, U63_1, U83_1, U92_1, isPalListKind_1, u, isList_1, isQid_1, U45_2, U61_2, U62_2, U73_2, isPal_1, U74_1, U91_2] > U11_2 21.38/9.09 a > [U13_1, tt, mark_1, U26_1, U33_1, U46_1, U63_1, U83_1, U92_1, isPalListKind_1, u, isList_1, isQid_1, U45_2, U61_2, U62_2, U73_2, isPal_1, U74_1, U91_2] > U12_2 21.38/9.09 a > [U13_1, tt, mark_1, U26_1, U33_1, U46_1, U63_1, U83_1, U92_1, isPalListKind_1, u, isList_1, isQid_1, U45_2, U61_2, U62_2, U73_2, isPal_1, U74_1, U91_2] > isNeList_1 21.38/9.09 a > [U13_1, tt, mark_1, U26_1, U33_1, U46_1, U63_1, U83_1, U92_1, isPalListKind_1, u, isList_1, isQid_1, U45_2, U61_2, U62_2, U73_2, isPal_1, U74_1, U91_2] > U21_3 21.38/9.09 a > [U13_1, tt, mark_1, U26_1, U33_1, U46_1, U63_1, U83_1, U92_1, isPalListKind_1, u, isList_1, isQid_1, U45_2, U61_2, U62_2, U73_2, isPal_1, U74_1, U91_2] > U22_3 21.38/9.09 a > [U13_1, tt, mark_1, U26_1, U33_1, U46_1, U63_1, U83_1, U92_1, isPalListKind_1, u, isList_1, isQid_1, U45_2, U61_2, U62_2, U73_2, isPal_1, U74_1, U91_2] > U23_3 21.38/9.09 a > [U13_1, tt, mark_1, U26_1, U33_1, U46_1, U63_1, U83_1, U92_1, isPalListKind_1, u, isList_1, isQid_1, U45_2, U61_2, U62_2, U73_2, isPal_1, U74_1, U91_2] > U24_3 21.38/9.09 a > [U13_1, tt, mark_1, U26_1, U33_1, U46_1, U63_1, U83_1, U92_1, isPalListKind_1, u, isList_1, isQid_1, U45_2, U61_2, U62_2, U73_2, isPal_1, U74_1, U91_2] > U25_2 21.38/9.09 a > [U13_1, tt, mark_1, U26_1, U33_1, U46_1, U63_1, U83_1, U92_1, isPalListKind_1, u, isList_1, isQid_1, U45_2, U61_2, U62_2, U73_2, isPal_1, U74_1, U91_2] > U31_2 21.38/9.09 a > [U13_1, tt, mark_1, U26_1, U33_1, U46_1, U63_1, U83_1, U92_1, isPalListKind_1, u, isList_1, isQid_1, U45_2, U61_2, U62_2, U73_2, isPal_1, U74_1, U91_2] > U32_2 21.38/9.09 a > [U13_1, tt, mark_1, U26_1, U33_1, U46_1, U63_1, U83_1, U92_1, isPalListKind_1, u, isList_1, isQid_1, U45_2, U61_2, U62_2, U73_2, isPal_1, U74_1, U91_2] > U41_3 21.38/9.09 a > [U13_1, tt, mark_1, U26_1, U33_1, U46_1, U63_1, U83_1, U92_1, isPalListKind_1, u, isList_1, isQid_1, U45_2, U61_2, U62_2, U73_2, isPal_1, U74_1, U91_2] > U42_3 21.38/9.09 a > [U13_1, tt, mark_1, U26_1, U33_1, U46_1, U63_1, U83_1, U92_1, isPalListKind_1, u, isList_1, isQid_1, U45_2, U61_2, U62_2, U73_2, isPal_1, U74_1, U91_2] > U43_3 21.38/9.09 a > [U13_1, tt, mark_1, U26_1, U33_1, U46_1, U63_1, U83_1, U92_1, isPalListKind_1, u, isList_1, isQid_1, U45_2, U61_2, U62_2, U73_2, isPal_1, U74_1, U91_2] > U44_3 21.38/9.09 a > [U13_1, tt, mark_1, U26_1, U33_1, U46_1, U63_1, U83_1, U92_1, isPalListKind_1, u, isList_1, isQid_1, U45_2, U61_2, U62_2, U73_2, isPal_1, U74_1, U91_2] > U51_3 21.38/9.09 a > [U13_1, tt, mark_1, U26_1, U33_1, U46_1, U63_1, U83_1, U92_1, isPalListKind_1, u, isList_1, isQid_1, U45_2, U61_2, U62_2, U73_2, isPal_1, U74_1, U91_2] > U52_3 21.38/9.09 a > [U13_1, tt, mark_1, U26_1, U33_1, U46_1, U63_1, U83_1, U92_1, isPalListKind_1, u, isList_1, isQid_1, U45_2, U61_2, U62_2, U73_2, isPal_1, U74_1, U91_2] > U53_3 21.38/9.09 a > [U13_1, tt, mark_1, U26_1, U33_1, U46_1, U63_1, U83_1, U92_1, isPalListKind_1, u, isList_1, isQid_1, U45_2, U61_2, U62_2, U73_2, isPal_1, U74_1, U91_2] > U54_3 21.38/9.09 a > [U13_1, tt, mark_1, U26_1, U33_1, U46_1, U63_1, U83_1, U92_1, isPalListKind_1, u, isList_1, isQid_1, U45_2, U61_2, U62_2, U73_2, isPal_1, U74_1, U91_2] > U55_2 21.38/9.09 a > [U13_1, tt, mark_1, U26_1, U33_1, U46_1, U63_1, U83_1, U92_1, isPalListKind_1, u, isList_1, isQid_1, U45_2, U61_2, U62_2, U73_2, isPal_1, U74_1, U91_2] > U71_3 21.38/9.09 a > [U13_1, tt, mark_1, U26_1, U33_1, U46_1, U63_1, U83_1, U92_1, isPalListKind_1, u, isList_1, isQid_1, U45_2, U61_2, U62_2, U73_2, isPal_1, U74_1, U91_2] > U72_2 21.38/9.09 a > [U13_1, tt, mark_1, U26_1, U33_1, U46_1, U63_1, U83_1, U92_1, isPalListKind_1, u, isList_1, isQid_1, U45_2, U61_2, U62_2, U73_2, isPal_1, U74_1, U91_2] > U81_2 21.38/9.09 a > [U13_1, tt, mark_1, U26_1, U33_1, U46_1, U63_1, U83_1, U92_1, isPalListKind_1, u, isList_1, isQid_1, U45_2, U61_2, U62_2, U73_2, isPal_1, U74_1, U91_2] > U82_2 21.38/9.09 a > [U13_1, tt, mark_1, U26_1, U33_1, U46_1, U63_1, U83_1, U92_1, isPalListKind_1, u, isList_1, isQid_1, U45_2, U61_2, U62_2, U73_2, isPal_1, U74_1, U91_2] > isNePal_1 21.38/9.09 a > [U13_1, tt, mark_1, U26_1, U33_1, U46_1, U63_1, U83_1, U92_1, isPalListKind_1, u, isList_1, isQid_1, U45_2, U61_2, U62_2, U73_2, isPal_1, U74_1, U91_2] > e 21.38/9.09 a > [U13_1, tt, mark_1, U26_1, U33_1, U46_1, U63_1, U83_1, U92_1, isPalListKind_1, u, isList_1, isQid_1, U45_2, U61_2, U62_2, U73_2, isPal_1, U74_1, U91_2] > o 21.38/9.09 i > [U13_1, tt, mark_1, U26_1, U33_1, U46_1, U63_1, U83_1, U92_1, isPalListKind_1, u, isList_1, isQid_1, U45_2, U61_2, U62_2, U73_2, isPal_1, U74_1, U91_2] > ___2 21.38/9.09 i > [U13_1, tt, mark_1, U26_1, U33_1, U46_1, U63_1, U83_1, U92_1, isPalListKind_1, u, isList_1, isQid_1, U45_2, U61_2, U62_2, U73_2, isPal_1, U74_1, U91_2] > nil 21.38/9.09 i > [U13_1, tt, mark_1, U26_1, U33_1, U46_1, U63_1, U83_1, U92_1, isPalListKind_1, u, isList_1, isQid_1, U45_2, U61_2, U62_2, U73_2, isPal_1, U74_1, U91_2] > U11_2 21.38/9.09 i > [U13_1, tt, mark_1, U26_1, U33_1, U46_1, U63_1, U83_1, U92_1, isPalListKind_1, u, isList_1, isQid_1, U45_2, U61_2, U62_2, U73_2, isPal_1, U74_1, U91_2] > U12_2 21.38/9.09 i > [U13_1, tt, mark_1, U26_1, U33_1, U46_1, U63_1, U83_1, U92_1, isPalListKind_1, u, isList_1, isQid_1, U45_2, U61_2, U62_2, U73_2, isPal_1, U74_1, U91_2] > isNeList_1 21.38/9.09 i > [U13_1, tt, mark_1, U26_1, U33_1, U46_1, U63_1, U83_1, U92_1, isPalListKind_1, u, isList_1, isQid_1, U45_2, U61_2, U62_2, U73_2, isPal_1, U74_1, U91_2] > U21_3 21.38/9.09 i > [U13_1, tt, mark_1, U26_1, U33_1, U46_1, U63_1, U83_1, U92_1, isPalListKind_1, u, isList_1, isQid_1, U45_2, U61_2, U62_2, U73_2, isPal_1, U74_1, U91_2] > U22_3 21.38/9.09 i > [U13_1, tt, mark_1, U26_1, U33_1, U46_1, U63_1, U83_1, U92_1, isPalListKind_1, u, isList_1, isQid_1, U45_2, U61_2, U62_2, U73_2, isPal_1, U74_1, U91_2] > U23_3 21.38/9.09 i > [U13_1, tt, mark_1, U26_1, U33_1, U46_1, U63_1, U83_1, U92_1, isPalListKind_1, u, isList_1, isQid_1, U45_2, U61_2, U62_2, U73_2, isPal_1, U74_1, U91_2] > U24_3 21.38/9.09 i > [U13_1, tt, mark_1, U26_1, U33_1, U46_1, U63_1, U83_1, U92_1, isPalListKind_1, u, isList_1, isQid_1, U45_2, U61_2, U62_2, U73_2, isPal_1, U74_1, U91_2] > U25_2 21.38/9.09 i > [U13_1, tt, mark_1, U26_1, U33_1, U46_1, U63_1, U83_1, U92_1, isPalListKind_1, u, isList_1, isQid_1, U45_2, U61_2, U62_2, U73_2, isPal_1, U74_1, U91_2] > U31_2 21.38/9.09 i > [U13_1, tt, mark_1, U26_1, U33_1, U46_1, U63_1, U83_1, U92_1, isPalListKind_1, u, isList_1, isQid_1, U45_2, U61_2, U62_2, U73_2, isPal_1, U74_1, U91_2] > U32_2 21.38/9.09 i > [U13_1, tt, mark_1, U26_1, U33_1, U46_1, U63_1, U83_1, U92_1, isPalListKind_1, u, isList_1, isQid_1, U45_2, U61_2, U62_2, U73_2, isPal_1, U74_1, U91_2] > U41_3 21.38/9.09 i > [U13_1, tt, mark_1, U26_1, U33_1, U46_1, U63_1, U83_1, U92_1, isPalListKind_1, u, isList_1, isQid_1, U45_2, U61_2, U62_2, U73_2, isPal_1, U74_1, U91_2] > U42_3 21.38/9.09 i > [U13_1, tt, mark_1, U26_1, U33_1, U46_1, U63_1, U83_1, U92_1, isPalListKind_1, u, isList_1, isQid_1, U45_2, U61_2, U62_2, U73_2, isPal_1, U74_1, U91_2] > U43_3 21.38/9.09 i > [U13_1, tt, mark_1, U26_1, U33_1, U46_1, U63_1, U83_1, U92_1, isPalListKind_1, u, isList_1, isQid_1, U45_2, U61_2, U62_2, U73_2, isPal_1, U74_1, U91_2] > U44_3 21.38/9.09 i > [U13_1, tt, mark_1, U26_1, U33_1, U46_1, U63_1, U83_1, U92_1, isPalListKind_1, u, isList_1, isQid_1, U45_2, U61_2, U62_2, U73_2, isPal_1, U74_1, U91_2] > U51_3 21.38/9.09 i > [U13_1, tt, mark_1, U26_1, U33_1, U46_1, U63_1, U83_1, U92_1, isPalListKind_1, u, isList_1, isQid_1, U45_2, U61_2, U62_2, U73_2, isPal_1, U74_1, U91_2] > U52_3 21.38/9.09 i > [U13_1, tt, mark_1, U26_1, U33_1, U46_1, U63_1, U83_1, U92_1, isPalListKind_1, u, isList_1, isQid_1, U45_2, U61_2, U62_2, U73_2, isPal_1, U74_1, U91_2] > U53_3 21.38/9.09 i > [U13_1, tt, mark_1, U26_1, U33_1, U46_1, U63_1, U83_1, U92_1, isPalListKind_1, u, isList_1, isQid_1, U45_2, U61_2, U62_2, U73_2, isPal_1, U74_1, U91_2] > U54_3 21.38/9.09 i > [U13_1, tt, mark_1, U26_1, U33_1, U46_1, U63_1, U83_1, U92_1, isPalListKind_1, u, isList_1, isQid_1, U45_2, U61_2, U62_2, U73_2, isPal_1, U74_1, U91_2] > U55_2 21.38/9.09 i > [U13_1, tt, mark_1, U26_1, U33_1, U46_1, U63_1, U83_1, U92_1, isPalListKind_1, u, isList_1, isQid_1, U45_2, U61_2, U62_2, U73_2, isPal_1, U74_1, U91_2] > U71_3 21.38/9.09 i > [U13_1, tt, mark_1, U26_1, U33_1, U46_1, U63_1, U83_1, U92_1, isPalListKind_1, u, isList_1, isQid_1, U45_2, U61_2, U62_2, U73_2, isPal_1, U74_1, U91_2] > U72_2 21.38/9.09 i > [U13_1, tt, mark_1, U26_1, U33_1, U46_1, U63_1, U83_1, U92_1, isPalListKind_1, u, isList_1, isQid_1, U45_2, U61_2, U62_2, U73_2, isPal_1, U74_1, U91_2] > U81_2 21.38/9.09 i > [U13_1, tt, mark_1, U26_1, U33_1, U46_1, U63_1, U83_1, U92_1, isPalListKind_1, u, isList_1, isQid_1, U45_2, U61_2, U62_2, U73_2, isPal_1, U74_1, U91_2] > U82_2 21.38/9.09 i > [U13_1, tt, mark_1, U26_1, U33_1, U46_1, U63_1, U83_1, U92_1, isPalListKind_1, u, isList_1, isQid_1, U45_2, U61_2, U62_2, U73_2, isPal_1, U74_1, U91_2] > isNePal_1 21.38/9.09 i > [U13_1, tt, mark_1, U26_1, U33_1, U46_1, U63_1, U83_1, U92_1, isPalListKind_1, u, isList_1, isQid_1, U45_2, U61_2, U62_2, U73_2, isPal_1, U74_1, U91_2] > e 21.38/9.09 i > [U13_1, tt, mark_1, U26_1, U33_1, U46_1, U63_1, U83_1, U92_1, isPalListKind_1, u, isList_1, isQid_1, U45_2, U61_2, U62_2, U73_2, isPal_1, U74_1, U91_2] > o 21.38/9.09 21.38/9.09 21.38/9.09 Status: 21.38/9.09 U13_1: multiset status 21.38/9.09 tt: multiset status 21.38/9.09 mark_1: multiset status 21.38/9.09 U26_1: multiset status 21.38/9.09 U33_1: multiset status 21.38/9.09 U46_1: multiset status 21.38/9.09 U63_1: multiset status 21.38/9.09 U83_1: multiset status 21.38/9.09 U92_1: multiset status 21.38/9.09 isPalListKind_1: multiset status 21.38/9.09 a: multiset status 21.38/9.09 i: multiset status 21.38/9.09 u: multiset status 21.38/9.09 ___2: multiset status 21.38/9.09 nil: multiset status 21.38/9.09 U11_2: multiset status 21.38/9.09 U12_2: multiset status 21.38/9.09 isNeList_1: multiset status 21.38/9.09 U21_3: [3,1,2] 21.38/9.09 U22_3: multiset status 21.38/9.09 U23_3: [2,3,1] 21.38/9.09 U24_3: [3,2,1] 21.38/9.09 U25_2: multiset status 21.38/9.09 isList_1: multiset status 21.38/9.09 U31_2: multiset status 21.38/9.09 U32_2: multiset status 21.38/9.09 isQid_1: multiset status 21.38/9.09 U41_3: [3,1,2] 21.38/9.09 U42_3: [1,3,2] 21.38/9.09 U43_3: [2,3,1] 21.38/9.09 U44_3: [3,1,2] 21.38/9.09 U45_2: multiset status 21.38/9.09 U51_3: [2,1,3] 21.38/9.09 U52_3: [1,3,2] 21.38/9.09 U53_3: [3,1,2] 21.38/9.09 U54_3: [3,2,1] 21.38/9.09 U55_2: multiset status 21.38/9.09 U61_2: multiset status 21.38/9.09 U62_2: multiset status 21.38/9.09 U71_3: [3,1,2] 21.38/9.09 U72_2: multiset status 21.38/9.09 U73_2: multiset status 21.38/9.09 isPal_1: multiset status 21.38/9.09 U74_1: multiset status 21.38/9.09 U81_2: multiset status 21.38/9.09 U82_2: multiset status 21.38/9.09 isNePal_1: multiset status 21.38/9.09 U91_2: multiset status 21.38/9.09 e: multiset status 21.38/9.09 o: multiset status 21.38/9.09 21.38/9.09 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 21.38/9.09 21.38/9.09 active(isPalListKind(a)) -> mark(tt) 21.38/9.09 active(isPalListKind(i)) -> mark(tt) 21.38/9.09 mark(__(X1, X2)) -> active(__(mark(X1), mark(X2))) 21.38/9.09 mark(nil) -> active(nil) 21.38/9.09 mark(U11(X1, X2)) -> active(U11(mark(X1), X2)) 21.38/9.09 mark(tt) -> active(tt) 21.38/9.09 mark(U12(X1, X2)) -> active(U12(mark(X1), X2)) 21.38/9.09 mark(isPalListKind(X)) -> active(isPalListKind(X)) 21.38/9.09 mark(isNeList(X)) -> active(isNeList(X)) 21.38/9.09 mark(U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)) 21.38/9.09 mark(U22(X1, X2, X3)) -> active(U22(mark(X1), X2, X3)) 21.38/9.09 mark(U23(X1, X2, X3)) -> active(U23(mark(X1), X2, X3)) 21.38/9.09 mark(U24(X1, X2, X3)) -> active(U24(mark(X1), X2, X3)) 21.38/9.09 mark(U25(X1, X2)) -> active(U25(mark(X1), X2)) 21.38/9.09 mark(isList(X)) -> active(isList(X)) 21.38/9.09 mark(U31(X1, X2)) -> active(U31(mark(X1), X2)) 21.38/9.09 mark(U32(X1, X2)) -> active(U32(mark(X1), X2)) 21.38/9.09 mark(isQid(X)) -> active(isQid(X)) 21.38/9.09 mark(U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3)) 21.38/9.09 mark(U42(X1, X2, X3)) -> active(U42(mark(X1), X2, X3)) 21.38/9.09 mark(U43(X1, X2, X3)) -> active(U43(mark(X1), X2, X3)) 21.38/9.09 mark(U44(X1, X2, X3)) -> active(U44(mark(X1), X2, X3)) 21.38/9.09 mark(U45(X1, X2)) -> active(U45(mark(X1), X2)) 21.38/9.09 mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)) 21.38/9.09 mark(U52(X1, X2, X3)) -> active(U52(mark(X1), X2, X3)) 21.38/9.09 mark(U53(X1, X2, X3)) -> active(U53(mark(X1), X2, X3)) 21.38/9.09 mark(U54(X1, X2, X3)) -> active(U54(mark(X1), X2, X3)) 21.38/9.09 mark(U55(X1, X2)) -> active(U55(mark(X1), X2)) 21.38/9.09 mark(U61(X1, X2)) -> active(U61(mark(X1), X2)) 21.38/9.09 mark(U62(X1, X2)) -> active(U62(mark(X1), X2)) 21.38/9.09 mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)) 21.38/9.09 mark(U72(X1, X2)) -> active(U72(mark(X1), X2)) 21.38/9.09 mark(U73(X1, X2)) -> active(U73(mark(X1), X2)) 21.38/9.09 mark(isPal(X)) -> active(isPal(X)) 21.38/9.09 mark(U81(X1, X2)) -> active(U81(mark(X1), X2)) 21.38/9.09 mark(U82(X1, X2)) -> active(U82(mark(X1), X2)) 21.38/9.09 mark(isNePal(X)) -> active(isNePal(X)) 21.38/9.09 mark(U91(X1, X2)) -> active(U91(mark(X1), X2)) 21.38/9.09 mark(a) -> active(a) 21.38/9.09 mark(e) -> active(e) 21.38/9.09 mark(i) -> active(i) 21.38/9.09 mark(o) -> active(o) 21.38/9.09 mark(u) -> active(u) 21.38/9.09 __(mark(X1), X2) -> __(X1, X2) 21.38/9.09 __(X1, mark(X2)) -> __(X1, X2) 21.38/9.09 U11(mark(X1), X2) -> U11(X1, X2) 21.38/9.09 U11(X1, mark(X2)) -> U11(X1, X2) 21.38/9.09 U12(mark(X1), X2) -> U12(X1, X2) 21.38/9.09 U12(X1, mark(X2)) -> U12(X1, X2) 21.38/9.09 isPalListKind(mark(X)) -> isPalListKind(X) 21.38/9.09 U13(mark(X)) -> U13(X) 21.38/9.09 isNeList(mark(X)) -> isNeList(X) 21.38/9.09 U21(mark(X1), X2, X3) -> U21(X1, X2, X3) 21.38/9.09 U21(X1, mark(X2), X3) -> U21(X1, X2, X3) 21.38/9.09 U21(X1, X2, mark(X3)) -> U21(X1, X2, X3) 21.38/9.09 U22(mark(X1), X2, X3) -> U22(X1, X2, X3) 21.38/9.09 U22(X1, mark(X2), X3) -> U22(X1, X2, X3) 21.38/9.09 U22(X1, X2, mark(X3)) -> U22(X1, X2, X3) 21.38/9.09 U23(mark(X1), X2, X3) -> U23(X1, X2, X3) 21.38/9.09 U23(X1, mark(X2), X3) -> U23(X1, X2, X3) 21.38/9.09 U23(X1, X2, mark(X3)) -> U23(X1, X2, X3) 21.38/9.09 U24(mark(X1), X2, X3) -> U24(X1, X2, X3) 21.38/9.09 U24(X1, mark(X2), X3) -> U24(X1, X2, X3) 21.38/9.09 U24(X1, X2, mark(X3)) -> U24(X1, X2, X3) 21.38/9.09 U25(mark(X1), X2) -> U25(X1, X2) 21.38/9.09 U25(X1, mark(X2)) -> U25(X1, X2) 21.38/9.09 isList(mark(X)) -> isList(X) 21.38/9.09 U26(mark(X)) -> U26(X) 21.38/9.09 U31(mark(X1), X2) -> U31(X1, X2) 21.38/9.09 U31(X1, mark(X2)) -> U31(X1, X2) 21.38/9.09 U32(mark(X1), X2) -> U32(X1, X2) 21.38/9.09 U32(X1, mark(X2)) -> U32(X1, X2) 21.38/9.09 U33(mark(X)) -> U33(X) 21.38/9.09 isQid(mark(X)) -> isQid(X) 21.38/9.09 U41(mark(X1), X2, X3) -> U41(X1, X2, X3) 21.38/9.09 U41(X1, mark(X2), X3) -> U41(X1, X2, X3) 21.38/9.09 U41(X1, X2, mark(X3)) -> U41(X1, X2, X3) 21.38/9.09 U42(mark(X1), X2, X3) -> U42(X1, X2, X3) 21.38/9.09 U42(X1, mark(X2), X3) -> U42(X1, X2, X3) 21.38/9.09 U42(X1, X2, mark(X3)) -> U42(X1, X2, X3) 21.38/9.09 U43(mark(X1), X2, X3) -> U43(X1, X2, X3) 21.38/9.09 U43(X1, mark(X2), X3) -> U43(X1, X2, X3) 21.38/9.09 U43(X1, X2, mark(X3)) -> U43(X1, X2, X3) 21.38/9.09 U44(mark(X1), X2, X3) -> U44(X1, X2, X3) 21.38/9.09 U44(X1, mark(X2), X3) -> U44(X1, X2, X3) 21.38/9.09 U44(X1, X2, mark(X3)) -> U44(X1, X2, X3) 21.38/9.09 U45(mark(X1), X2) -> U45(X1, X2) 21.38/9.09 U45(X1, mark(X2)) -> U45(X1, X2) 21.38/9.09 U46(mark(X)) -> U46(X) 21.38/9.09 U51(mark(X1), X2, X3) -> U51(X1, X2, X3) 21.38/9.09 U51(X1, mark(X2), X3) -> U51(X1, X2, X3) 21.38/9.09 U51(X1, X2, mark(X3)) -> U51(X1, X2, X3) 21.38/9.09 U52(mark(X1), X2, X3) -> U52(X1, X2, X3) 21.38/9.09 U52(X1, mark(X2), X3) -> U52(X1, X2, X3) 21.38/9.09 U52(X1, X2, mark(X3)) -> U52(X1, X2, X3) 21.38/9.09 U53(mark(X1), X2, X3) -> U53(X1, X2, X3) 21.38/9.09 U53(X1, mark(X2), X3) -> U53(X1, X2, X3) 21.38/9.09 U53(X1, X2, mark(X3)) -> U53(X1, X2, X3) 21.38/9.09 U54(mark(X1), X2, X3) -> U54(X1, X2, X3) 21.38/9.09 U54(X1, mark(X2), X3) -> U54(X1, X2, X3) 21.38/9.09 U54(X1, X2, mark(X3)) -> U54(X1, X2, X3) 21.38/9.09 U55(mark(X1), X2) -> U55(X1, X2) 21.38/9.09 U55(X1, mark(X2)) -> U55(X1, X2) 21.38/9.09 U56(mark(X)) -> U56(X) 21.38/9.09 U61(mark(X1), X2) -> U61(X1, X2) 21.38/9.09 U61(X1, mark(X2)) -> U61(X1, X2) 21.38/9.09 U62(mark(X1), X2) -> U62(X1, X2) 21.38/9.09 U62(X1, mark(X2)) -> U62(X1, X2) 21.38/9.09 U63(mark(X)) -> U63(X) 21.38/9.09 U71(mark(X1), X2, X3) -> U71(X1, X2, X3) 21.38/9.09 U71(X1, mark(X2), X3) -> U71(X1, X2, X3) 21.38/9.09 U71(X1, X2, mark(X3)) -> U71(X1, X2, X3) 21.38/9.09 U72(mark(X1), X2) -> U72(X1, X2) 21.38/9.09 U72(X1, mark(X2)) -> U72(X1, X2) 21.38/9.09 U73(mark(X1), X2) -> U73(X1, X2) 21.38/9.09 U73(X1, mark(X2)) -> U73(X1, X2) 21.38/9.09 isPal(mark(X)) -> isPal(X) 21.38/9.09 U74(mark(X)) -> U74(X) 21.38/9.09 U81(mark(X1), X2) -> U81(X1, X2) 21.38/9.09 U81(X1, mark(X2)) -> U81(X1, X2) 21.38/9.09 U82(mark(X1), X2) -> U82(X1, X2) 21.38/9.09 U82(X1, mark(X2)) -> U82(X1, X2) 21.38/9.09 U83(mark(X)) -> U83(X) 21.38/9.09 isNePal(mark(X)) -> isNePal(X) 21.38/9.09 U91(mark(X1), X2) -> U91(X1, X2) 21.38/9.09 U91(X1, mark(X2)) -> U91(X1, X2) 21.38/9.09 U92(mark(X)) -> U92(X) 21.38/9.09 21.38/9.09 21.38/9.09 21.38/9.09 21.38/9.09 ---------------------------------------- 21.38/9.09 21.38/9.09 (4) 21.38/9.09 Obligation: 21.38/9.09 Q restricted rewrite system: 21.38/9.09 The TRS R consists of the following rules: 21.38/9.09 21.38/9.09 active(U13(tt)) -> mark(tt) 21.38/9.09 active(U26(tt)) -> mark(tt) 21.38/9.09 active(U33(tt)) -> mark(tt) 21.38/9.09 active(U46(tt)) -> mark(tt) 21.38/9.09 active(U63(tt)) -> mark(tt) 21.38/9.09 active(U83(tt)) -> mark(tt) 21.38/9.09 active(U92(tt)) -> mark(tt) 21.38/9.09 active(isPalListKind(u)) -> mark(tt) 21.38/9.09 mark(U13(X)) -> active(U13(mark(X))) 21.38/9.09 mark(U26(X)) -> active(U26(mark(X))) 21.38/9.09 mark(U33(X)) -> active(U33(mark(X))) 21.38/9.09 mark(U46(X)) -> active(U46(mark(X))) 21.38/9.09 mark(U56(X)) -> active(U56(mark(X))) 21.38/9.09 mark(U63(X)) -> active(U63(mark(X))) 21.38/9.09 mark(U74(X)) -> active(U74(mark(X))) 21.38/9.09 mark(U83(X)) -> active(U83(mark(X))) 21.38/9.09 mark(U92(X)) -> active(U92(mark(X))) 21.38/9.09 __(active(X1), X2) -> __(X1, X2) 21.38/9.09 __(X1, active(X2)) -> __(X1, X2) 21.38/9.09 U11(active(X1), X2) -> U11(X1, X2) 21.38/9.09 U11(X1, active(X2)) -> U11(X1, X2) 21.38/9.09 U12(active(X1), X2) -> U12(X1, X2) 21.38/9.09 U12(X1, active(X2)) -> U12(X1, X2) 21.38/9.09 isPalListKind(active(X)) -> isPalListKind(X) 21.38/9.09 U13(active(X)) -> U13(X) 21.38/9.09 isNeList(active(X)) -> isNeList(X) 21.38/9.09 U21(active(X1), X2, X3) -> U21(X1, X2, X3) 21.38/9.09 U21(X1, active(X2), X3) -> U21(X1, X2, X3) 21.38/9.09 U21(X1, X2, active(X3)) -> U21(X1, X2, X3) 21.38/9.09 U22(active(X1), X2, X3) -> U22(X1, X2, X3) 21.38/9.09 U22(X1, active(X2), X3) -> U22(X1, X2, X3) 21.38/9.09 U22(X1, X2, active(X3)) -> U22(X1, X2, X3) 21.38/9.09 U23(active(X1), X2, X3) -> U23(X1, X2, X3) 21.38/9.09 U23(X1, active(X2), X3) -> U23(X1, X2, X3) 21.38/9.09 U23(X1, X2, active(X3)) -> U23(X1, X2, X3) 21.38/9.09 U24(active(X1), X2, X3) -> U24(X1, X2, X3) 21.38/9.09 U24(X1, active(X2), X3) -> U24(X1, X2, X3) 21.38/9.09 U24(X1, X2, active(X3)) -> U24(X1, X2, X3) 21.38/9.09 U25(active(X1), X2) -> U25(X1, X2) 21.38/9.09 U25(X1, active(X2)) -> U25(X1, X2) 21.38/9.09 isList(active(X)) -> isList(X) 21.38/9.09 U26(active(X)) -> U26(X) 21.38/9.09 U31(active(X1), X2) -> U31(X1, X2) 21.38/9.09 U31(X1, active(X2)) -> U31(X1, X2) 21.38/9.09 U32(active(X1), X2) -> U32(X1, X2) 21.38/9.09 U32(X1, active(X2)) -> U32(X1, X2) 21.38/9.09 U33(active(X)) -> U33(X) 21.38/9.09 isQid(active(X)) -> isQid(X) 21.38/9.09 U41(active(X1), X2, X3) -> U41(X1, X2, X3) 21.38/9.09 U41(X1, active(X2), X3) -> U41(X1, X2, X3) 21.38/9.09 U41(X1, X2, active(X3)) -> U41(X1, X2, X3) 21.38/9.09 U42(active(X1), X2, X3) -> U42(X1, X2, X3) 21.38/9.09 U42(X1, active(X2), X3) -> U42(X1, X2, X3) 21.38/9.09 U42(X1, X2, active(X3)) -> U42(X1, X2, X3) 21.38/9.09 U43(active(X1), X2, X3) -> U43(X1, X2, X3) 21.38/9.09 U43(X1, active(X2), X3) -> U43(X1, X2, X3) 21.38/9.09 U43(X1, X2, active(X3)) -> U43(X1, X2, X3) 21.38/9.09 U44(active(X1), X2, X3) -> U44(X1, X2, X3) 21.38/9.09 U44(X1, active(X2), X3) -> U44(X1, X2, X3) 21.38/9.09 U44(X1, X2, active(X3)) -> U44(X1, X2, X3) 21.38/9.09 U45(active(X1), X2) -> U45(X1, X2) 21.38/9.09 U45(X1, active(X2)) -> U45(X1, X2) 21.38/9.09 U46(active(X)) -> U46(X) 21.38/9.09 U51(active(X1), X2, X3) -> U51(X1, X2, X3) 21.38/9.09 U51(X1, active(X2), X3) -> U51(X1, X2, X3) 21.38/9.09 U51(X1, X2, active(X3)) -> U51(X1, X2, X3) 21.38/9.09 U52(active(X1), X2, X3) -> U52(X1, X2, X3) 21.38/9.09 U52(X1, active(X2), X3) -> U52(X1, X2, X3) 21.38/9.09 U52(X1, X2, active(X3)) -> U52(X1, X2, X3) 21.38/9.09 U53(active(X1), X2, X3) -> U53(X1, X2, X3) 21.38/9.09 U53(X1, active(X2), X3) -> U53(X1, X2, X3) 21.38/9.09 U53(X1, X2, active(X3)) -> U53(X1, X2, X3) 21.38/9.09 U54(active(X1), X2, X3) -> U54(X1, X2, X3) 21.38/9.09 U54(X1, active(X2), X3) -> U54(X1, X2, X3) 21.38/9.09 U54(X1, X2, active(X3)) -> U54(X1, X2, X3) 21.38/9.09 U55(active(X1), X2) -> U55(X1, X2) 21.38/9.09 U55(X1, active(X2)) -> U55(X1, X2) 21.38/9.09 U56(active(X)) -> U56(X) 21.38/9.09 U61(active(X1), X2) -> U61(X1, X2) 21.38/9.09 U61(X1, active(X2)) -> U61(X1, X2) 21.38/9.09 U62(active(X1), X2) -> U62(X1, X2) 21.38/9.09 U62(X1, active(X2)) -> U62(X1, X2) 21.38/9.09 U63(active(X)) -> U63(X) 21.38/9.09 U71(active(X1), X2, X3) -> U71(X1, X2, X3) 21.38/9.09 U71(X1, active(X2), X3) -> U71(X1, X2, X3) 21.38/9.09 U71(X1, X2, active(X3)) -> U71(X1, X2, X3) 21.38/9.09 U72(active(X1), X2) -> U72(X1, X2) 21.38/9.09 U72(X1, active(X2)) -> U72(X1, X2) 21.38/9.09 U73(active(X1), X2) -> U73(X1, X2) 21.38/9.09 U73(X1, active(X2)) -> U73(X1, X2) 21.38/9.09 isPal(active(X)) -> isPal(X) 21.38/9.09 U74(active(X)) -> U74(X) 21.38/9.09 U81(active(X1), X2) -> U81(X1, X2) 21.38/9.09 U81(X1, active(X2)) -> U81(X1, X2) 21.38/9.09 U82(active(X1), X2) -> U82(X1, X2) 21.38/9.09 U82(X1, active(X2)) -> U82(X1, X2) 21.38/9.09 U83(active(X)) -> U83(X) 21.38/9.09 isNePal(active(X)) -> isNePal(X) 21.38/9.09 U91(active(X1), X2) -> U91(X1, X2) 21.38/9.09 U91(X1, active(X2)) -> U91(X1, X2) 21.38/9.09 U92(active(X)) -> U92(X) 21.38/9.09 21.38/9.09 The set Q consists of the following terms: 21.38/9.09 21.38/9.09 active(__(__(x0, x1), x2)) 21.38/9.09 active(__(x0, nil)) 21.38/9.09 active(__(nil, x0)) 21.38/9.09 active(U11(tt, x0)) 21.38/9.09 active(U12(tt, x0)) 21.38/9.09 active(U13(tt)) 21.38/9.09 active(U21(tt, x0, x1)) 21.38/9.09 active(U22(tt, x0, x1)) 21.38/9.09 active(U23(tt, x0, x1)) 21.38/9.09 active(U24(tt, x0, x1)) 21.38/9.09 active(U25(tt, x0)) 21.38/9.09 active(U26(tt)) 21.38/9.09 active(U31(tt, x0)) 21.38/9.09 active(U32(tt, x0)) 21.38/9.09 active(U33(tt)) 21.38/9.09 active(U41(tt, x0, x1)) 21.38/9.09 active(U42(tt, x0, x1)) 21.38/9.09 active(U43(tt, x0, x1)) 21.38/9.09 active(U44(tt, x0, x1)) 21.38/9.09 active(U45(tt, x0)) 21.38/9.09 active(U46(tt)) 21.38/9.09 active(U51(tt, x0, x1)) 21.38/9.09 active(U52(tt, x0, x1)) 21.38/9.09 active(U53(tt, x0, x1)) 21.38/9.09 active(U54(tt, x0, x1)) 21.38/9.09 active(U55(tt, x0)) 21.38/9.09 active(U56(tt)) 21.38/9.09 active(U61(tt, x0)) 21.38/9.09 active(U62(tt, x0)) 21.38/9.09 active(U63(tt)) 21.38/9.09 active(U71(tt, x0, x1)) 21.38/9.09 active(U72(tt, x0)) 21.38/9.09 active(U73(tt, x0)) 21.38/9.09 active(U74(tt)) 21.38/9.09 active(U81(tt, x0)) 21.38/9.09 active(U82(tt, x0)) 21.38/9.09 active(U83(tt)) 21.38/9.09 active(U91(tt, x0)) 21.38/9.09 active(U92(tt)) 21.38/9.09 active(isList(x0)) 21.38/9.09 active(isNeList(x0)) 21.38/9.09 active(isNePal(x0)) 21.38/9.09 active(isPal(x0)) 21.38/9.09 active(isPalListKind(a)) 21.38/9.09 active(isPalListKind(e)) 21.38/9.09 active(isPalListKind(i)) 21.38/9.09 active(isPalListKind(nil)) 21.38/9.09 active(isPalListKind(o)) 21.38/9.09 active(isPalListKind(u)) 21.38/9.09 active(isPalListKind(__(x0, x1))) 21.38/9.09 active(isQid(a)) 21.38/9.09 active(isQid(e)) 21.38/9.09 active(isQid(i)) 21.38/9.09 active(isQid(o)) 21.38/9.09 active(isQid(u)) 21.38/9.09 mark(__(x0, x1)) 21.38/9.09 mark(nil) 21.38/9.09 mark(U11(x0, x1)) 21.38/9.09 mark(tt) 21.38/9.09 mark(U12(x0, x1)) 21.38/9.09 mark(isPalListKind(x0)) 21.38/9.09 mark(U13(x0)) 21.38/9.09 mark(isNeList(x0)) 21.38/9.09 mark(U21(x0, x1, x2)) 21.38/9.09 mark(U22(x0, x1, x2)) 21.38/9.09 mark(U23(x0, x1, x2)) 21.38/9.09 mark(U24(x0, x1, x2)) 21.38/9.09 mark(U25(x0, x1)) 21.38/9.09 mark(isList(x0)) 21.38/9.09 mark(U26(x0)) 21.38/9.09 mark(U31(x0, x1)) 21.38/9.09 mark(U32(x0, x1)) 21.38/9.09 mark(U33(x0)) 21.38/9.09 mark(isQid(x0)) 21.38/9.09 mark(U41(x0, x1, x2)) 21.38/9.09 mark(U42(x0, x1, x2)) 21.38/9.09 mark(U43(x0, x1, x2)) 21.38/9.09 mark(U44(x0, x1, x2)) 21.38/9.09 mark(U45(x0, x1)) 21.38/9.09 mark(U46(x0)) 21.38/9.09 mark(U51(x0, x1, x2)) 21.38/9.09 mark(U52(x0, x1, x2)) 21.38/9.09 mark(U53(x0, x1, x2)) 21.38/9.09 mark(U54(x0, x1, x2)) 21.38/9.09 mark(U55(x0, x1)) 21.38/9.09 mark(U56(x0)) 21.38/9.09 mark(U61(x0, x1)) 21.38/9.09 mark(U62(x0, x1)) 21.38/9.09 mark(U63(x0)) 21.38/9.09 mark(U71(x0, x1, x2)) 21.38/9.09 mark(U72(x0, x1)) 21.38/9.09 mark(U73(x0, x1)) 21.38/9.09 mark(isPal(x0)) 21.38/9.09 mark(U74(x0)) 21.38/9.09 mark(U81(x0, x1)) 21.38/9.09 mark(U82(x0, x1)) 21.38/9.09 mark(U83(x0)) 21.38/9.09 mark(isNePal(x0)) 21.38/9.09 mark(U91(x0, x1)) 21.38/9.09 mark(U92(x0)) 21.38/9.09 mark(a) 21.38/9.09 mark(e) 21.38/9.09 mark(i) 21.38/9.09 mark(o) 21.38/9.09 mark(u) 21.38/9.09 __(mark(x0), x1) 21.38/9.09 __(x0, mark(x1)) 21.38/9.09 __(active(x0), x1) 21.38/9.09 __(x0, active(x1)) 21.38/9.09 U11(mark(x0), x1) 21.38/9.09 U11(x0, mark(x1)) 21.38/9.09 U11(active(x0), x1) 21.38/9.09 U11(x0, active(x1)) 21.38/9.09 U12(mark(x0), x1) 21.38/9.09 U12(x0, mark(x1)) 21.38/9.09 U12(active(x0), x1) 21.38/9.09 U12(x0, active(x1)) 21.38/9.09 isPalListKind(mark(x0)) 21.38/9.09 isPalListKind(active(x0)) 21.38/9.09 U13(mark(x0)) 21.38/9.09 U13(active(x0)) 21.38/9.09 isNeList(mark(x0)) 21.38/9.09 isNeList(active(x0)) 21.38/9.09 U21(mark(x0), x1, x2) 21.38/9.09 U21(x0, mark(x1), x2) 21.38/9.09 U21(x0, x1, mark(x2)) 21.38/9.09 U21(active(x0), x1, x2) 21.38/9.09 U21(x0, active(x1), x2) 21.38/9.09 U21(x0, x1, active(x2)) 21.38/9.09 U22(mark(x0), x1, x2) 21.38/9.09 U22(x0, mark(x1), x2) 21.38/9.09 U22(x0, x1, mark(x2)) 21.38/9.09 U22(active(x0), x1, x2) 21.38/9.09 U22(x0, active(x1), x2) 21.38/9.09 U22(x0, x1, active(x2)) 21.38/9.09 U23(mark(x0), x1, x2) 21.38/9.09 U23(x0, mark(x1), x2) 21.38/9.09 U23(x0, x1, mark(x2)) 21.38/9.09 U23(active(x0), x1, x2) 21.38/9.09 U23(x0, active(x1), x2) 21.38/9.09 U23(x0, x1, active(x2)) 21.38/9.09 U24(mark(x0), x1, x2) 21.38/9.09 U24(x0, mark(x1), x2) 21.38/9.09 U24(x0, x1, mark(x2)) 21.38/9.09 U24(active(x0), x1, x2) 21.38/9.09 U24(x0, active(x1), x2) 21.38/9.09 U24(x0, x1, active(x2)) 21.38/9.09 U25(mark(x0), x1) 21.38/9.09 U25(x0, mark(x1)) 21.38/9.09 U25(active(x0), x1) 21.38/9.09 U25(x0, active(x1)) 21.38/9.09 isList(mark(x0)) 21.38/9.09 isList(active(x0)) 21.38/9.09 U26(mark(x0)) 21.38/9.09 U26(active(x0)) 21.38/9.09 U31(mark(x0), x1) 21.38/9.09 U31(x0, mark(x1)) 21.38/9.09 U31(active(x0), x1) 21.38/9.09 U31(x0, active(x1)) 21.38/9.09 U32(mark(x0), x1) 21.38/9.09 U32(x0, mark(x1)) 21.38/9.09 U32(active(x0), x1) 21.38/9.09 U32(x0, active(x1)) 21.38/9.09 U33(mark(x0)) 21.38/9.09 U33(active(x0)) 21.38/9.09 isQid(mark(x0)) 21.38/9.09 isQid(active(x0)) 21.38/9.09 U41(mark(x0), x1, x2) 21.38/9.09 U41(x0, mark(x1), x2) 21.38/9.09 U41(x0, x1, mark(x2)) 21.38/9.09 U41(active(x0), x1, x2) 21.38/9.10 U41(x0, active(x1), x2) 21.38/9.10 U41(x0, x1, active(x2)) 21.38/9.10 U42(mark(x0), x1, x2) 21.38/9.10 U42(x0, mark(x1), x2) 21.38/9.10 U42(x0, x1, mark(x2)) 21.38/9.10 U42(active(x0), x1, x2) 21.38/9.10 U42(x0, active(x1), x2) 21.38/9.10 U42(x0, x1, active(x2)) 21.38/9.10 U43(mark(x0), x1, x2) 21.38/9.10 U43(x0, mark(x1), x2) 21.38/9.10 U43(x0, x1, mark(x2)) 21.38/9.10 U43(active(x0), x1, x2) 21.38/9.10 U43(x0, active(x1), x2) 21.38/9.10 U43(x0, x1, active(x2)) 21.38/9.10 U44(mark(x0), x1, x2) 21.38/9.10 U44(x0, mark(x1), x2) 21.38/9.10 U44(x0, x1, mark(x2)) 21.38/9.10 U44(active(x0), x1, x2) 21.38/9.10 U44(x0, active(x1), x2) 21.38/9.10 U44(x0, x1, active(x2)) 21.38/9.10 U45(mark(x0), x1) 21.38/9.10 U45(x0, mark(x1)) 21.38/9.10 U45(active(x0), x1) 21.38/9.10 U45(x0, active(x1)) 21.38/9.10 U46(mark(x0)) 21.38/9.10 U46(active(x0)) 21.38/9.10 U51(mark(x0), x1, x2) 21.38/9.10 U51(x0, mark(x1), x2) 21.38/9.10 U51(x0, x1, mark(x2)) 21.38/9.10 U51(active(x0), x1, x2) 21.38/9.10 U51(x0, active(x1), x2) 21.38/9.10 U51(x0, x1, active(x2)) 21.38/9.10 U52(mark(x0), x1, x2) 21.38/9.10 U52(x0, mark(x1), x2) 21.38/9.10 U52(x0, x1, mark(x2)) 21.38/9.10 U52(active(x0), x1, x2) 21.38/9.10 U52(x0, active(x1), x2) 21.38/9.10 U52(x0, x1, active(x2)) 21.38/9.10 U53(mark(x0), x1, x2) 21.38/9.10 U53(x0, mark(x1), x2) 21.38/9.10 U53(x0, x1, mark(x2)) 21.38/9.10 U53(active(x0), x1, x2) 21.38/9.10 U53(x0, active(x1), x2) 21.38/9.10 U53(x0, x1, active(x2)) 21.38/9.10 U54(mark(x0), x1, x2) 21.38/9.10 U54(x0, mark(x1), x2) 21.38/9.10 U54(x0, x1, mark(x2)) 21.38/9.10 U54(active(x0), x1, x2) 21.38/9.10 U54(x0, active(x1), x2) 21.38/9.10 U54(x0, x1, active(x2)) 21.38/9.10 U55(mark(x0), x1) 21.38/9.10 U55(x0, mark(x1)) 21.38/9.10 U55(active(x0), x1) 21.38/9.10 U55(x0, active(x1)) 21.38/9.10 U56(mark(x0)) 21.38/9.10 U56(active(x0)) 21.38/9.10 U61(mark(x0), x1) 21.38/9.10 U61(x0, mark(x1)) 21.38/9.10 U61(active(x0), x1) 21.38/9.10 U61(x0, active(x1)) 21.38/9.10 U62(mark(x0), x1) 21.38/9.10 U62(x0, mark(x1)) 21.38/9.10 U62(active(x0), x1) 21.38/9.10 U62(x0, active(x1)) 21.38/9.10 U63(mark(x0)) 21.38/9.10 U63(active(x0)) 21.38/9.10 U71(mark(x0), x1, x2) 21.38/9.10 U71(x0, mark(x1), x2) 21.38/9.10 U71(x0, x1, mark(x2)) 21.38/9.10 U71(active(x0), x1, x2) 21.38/9.10 U71(x0, active(x1), x2) 21.38/9.10 U71(x0, x1, active(x2)) 21.38/9.10 U72(mark(x0), x1) 21.38/9.10 U72(x0, mark(x1)) 21.38/9.10 U72(active(x0), x1) 21.38/9.10 U72(x0, active(x1)) 21.38/9.10 U73(mark(x0), x1) 21.38/9.10 U73(x0, mark(x1)) 21.38/9.10 U73(active(x0), x1) 21.38/9.10 U73(x0, active(x1)) 21.38/9.10 isPal(mark(x0)) 21.38/9.10 isPal(active(x0)) 21.38/9.10 U74(mark(x0)) 21.38/9.10 U74(active(x0)) 21.38/9.10 U81(mark(x0), x1) 21.38/9.10 U81(x0, mark(x1)) 21.38/9.10 U81(active(x0), x1) 21.38/9.10 U81(x0, active(x1)) 21.38/9.10 U82(mark(x0), x1) 21.38/9.10 U82(x0, mark(x1)) 21.38/9.10 U82(active(x0), x1) 21.38/9.10 U82(x0, active(x1)) 21.38/9.10 U83(mark(x0)) 21.38/9.10 U83(active(x0)) 21.38/9.10 isNePal(mark(x0)) 21.38/9.10 isNePal(active(x0)) 21.38/9.10 U91(mark(x0), x1) 21.38/9.10 U91(x0, mark(x1)) 21.38/9.10 U91(active(x0), x1) 21.38/9.10 U91(x0, active(x1)) 21.38/9.10 U92(mark(x0)) 21.38/9.10 U92(active(x0)) 21.38/9.10 21.38/9.10 21.38/9.10 ---------------------------------------- 21.38/9.10 21.38/9.10 (5) QTRSRRRProof (EQUIVALENT) 21.38/9.10 Used ordering: 21.38/9.10 Polynomial interpretation [POLO]: 21.38/9.10 21.38/9.10 POL(U11(x_1, x_2)) = 2*x_1 + 2*x_2 21.38/9.10 POL(U12(x_1, x_2)) = 2*x_1 + 2*x_2 21.38/9.10 POL(U13(x_1)) = 1 + 2*x_1 21.38/9.10 POL(U21(x_1, x_2, x_3)) = 2*x_1 + 2*x_2 + 2*x_3 21.38/9.10 POL(U22(x_1, x_2, x_3)) = 2*x_1 + 2*x_2 + 2*x_3 21.38/9.10 POL(U23(x_1, x_2, x_3)) = 2*x_1 + 2*x_2 + 2*x_3 21.38/9.10 POL(U24(x_1, x_2, x_3)) = 2*x_1 + x_2 + 2*x_3 21.38/9.10 POL(U25(x_1, x_2)) = 2*x_1 + 2*x_2 21.38/9.10 POL(U26(x_1)) = 1 + x_1 21.38/9.10 POL(U31(x_1, x_2)) = 2*x_1 + 2*x_2 21.38/9.10 POL(U32(x_1, x_2)) = 2*x_1 + 2*x_2 21.38/9.10 POL(U33(x_1)) = 1 + x_1 21.38/9.10 POL(U41(x_1, x_2, x_3)) = 2*x_1 + 2*x_2 + 2*x_3 21.38/9.10 POL(U42(x_1, x_2, x_3)) = 2*x_1 + 2*x_2 + 2*x_3 21.38/9.10 POL(U43(x_1, x_2, x_3)) = 2*x_1 + 2*x_2 + 2*x_3 21.38/9.10 POL(U44(x_1, x_2, x_3)) = 2*x_1 + 2*x_2 + 2*x_3 21.38/9.10 POL(U45(x_1, x_2)) = 2*x_1 + 2*x_2 21.38/9.10 POL(U46(x_1)) = 2 + x_1 21.38/9.10 POL(U51(x_1, x_2, x_3)) = 2*x_1 + 2*x_2 + 2*x_3 21.38/9.10 POL(U52(x_1, x_2, x_3)) = 2*x_1 + 2*x_2 + 2*x_3 21.38/9.10 POL(U53(x_1, x_2, x_3)) = 2*x_1 + 2*x_2 + 2*x_3 21.38/9.10 POL(U54(x_1, x_2, x_3)) = 2*x_1 + 2*x_2 + 2*x_3 21.38/9.10 POL(U55(x_1, x_2)) = 2*x_1 + 2*x_2 21.38/9.10 POL(U56(x_1)) = 2*x_1 21.38/9.10 POL(U61(x_1, x_2)) = 2*x_1 + 2*x_2 21.38/9.10 POL(U62(x_1, x_2)) = 2*x_1 + 2*x_2 21.38/9.10 POL(U63(x_1)) = 1 + 2*x_1 21.38/9.10 POL(U71(x_1, x_2, x_3)) = 2*x_1 + 2*x_2 + 2*x_3 21.38/9.10 POL(U72(x_1, x_2)) = x_1 + 2*x_2 21.38/9.10 POL(U73(x_1, x_2)) = 2*x_1 + 2*x_2 21.38/9.10 POL(U74(x_1)) = x_1 21.38/9.10 POL(U81(x_1, x_2)) = 2*x_1 + 2*x_2 21.38/9.10 POL(U82(x_1, x_2)) = 2*x_1 + x_2 21.38/9.10 POL(U83(x_1)) = 2*x_1 21.38/9.10 POL(U91(x_1, x_2)) = 2*x_1 + 2*x_2 21.38/9.10 POL(U92(x_1)) = x_1 21.38/9.10 POL(__(x_1, x_2)) = 2*x_1 + 2*x_2 21.38/9.10 POL(active(x_1)) = x_1 21.38/9.10 POL(isList(x_1)) = 2*x_1 21.38/9.10 POL(isNeList(x_1)) = 2*x_1 21.38/9.10 POL(isNePal(x_1)) = 2*x_1 21.38/9.10 POL(isPal(x_1)) = 2*x_1 21.38/9.10 POL(isPalListKind(x_1)) = 1 + x_1 21.38/9.10 POL(isQid(x_1)) = 2*x_1 21.38/9.10 POL(mark(x_1)) = 2*x_1 21.38/9.10 POL(tt) = 0 21.38/9.10 POL(u) = 0 21.38/9.10 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 21.38/9.10 21.38/9.10 active(U13(tt)) -> mark(tt) 21.38/9.10 active(U26(tt)) -> mark(tt) 21.38/9.10 active(U33(tt)) -> mark(tt) 21.38/9.10 active(U46(tt)) -> mark(tt) 21.38/9.10 active(U63(tt)) -> mark(tt) 21.38/9.10 active(isPalListKind(u)) -> mark(tt) 21.38/9.10 mark(U13(X)) -> active(U13(mark(X))) 21.38/9.10 mark(U26(X)) -> active(U26(mark(X))) 21.38/9.10 mark(U33(X)) -> active(U33(mark(X))) 21.38/9.10 mark(U46(X)) -> active(U46(mark(X))) 21.38/9.10 mark(U63(X)) -> active(U63(mark(X))) 21.38/9.10 21.38/9.10 21.38/9.10 21.38/9.10 21.38/9.10 ---------------------------------------- 21.38/9.10 21.38/9.10 (6) 21.38/9.10 Obligation: 21.38/9.10 Q restricted rewrite system: 21.38/9.10 The TRS R consists of the following rules: 21.38/9.10 21.38/9.10 active(U83(tt)) -> mark(tt) 21.38/9.10 active(U92(tt)) -> mark(tt) 21.38/9.10 mark(U56(X)) -> active(U56(mark(X))) 21.38/9.10 mark(U74(X)) -> active(U74(mark(X))) 21.38/9.10 mark(U83(X)) -> active(U83(mark(X))) 21.38/9.10 mark(U92(X)) -> active(U92(mark(X))) 21.38/9.10 __(active(X1), X2) -> __(X1, X2) 21.38/9.10 __(X1, active(X2)) -> __(X1, X2) 21.38/9.10 U11(active(X1), X2) -> U11(X1, X2) 21.38/9.10 U11(X1, active(X2)) -> U11(X1, X2) 21.38/9.10 U12(active(X1), X2) -> U12(X1, X2) 21.38/9.10 U12(X1, active(X2)) -> U12(X1, X2) 21.38/9.10 isPalListKind(active(X)) -> isPalListKind(X) 21.38/9.10 U13(active(X)) -> U13(X) 21.38/9.10 isNeList(active(X)) -> isNeList(X) 21.38/9.10 U21(active(X1), X2, X3) -> U21(X1, X2, X3) 21.38/9.10 U21(X1, active(X2), X3) -> U21(X1, X2, X3) 21.38/9.10 U21(X1, X2, active(X3)) -> U21(X1, X2, X3) 21.38/9.10 U22(active(X1), X2, X3) -> U22(X1, X2, X3) 21.38/9.10 U22(X1, active(X2), X3) -> U22(X1, X2, X3) 21.38/9.10 U22(X1, X2, active(X3)) -> U22(X1, X2, X3) 21.38/9.10 U23(active(X1), X2, X3) -> U23(X1, X2, X3) 21.38/9.10 U23(X1, active(X2), X3) -> U23(X1, X2, X3) 21.38/9.10 U23(X1, X2, active(X3)) -> U23(X1, X2, X3) 21.38/9.10 U24(active(X1), X2, X3) -> U24(X1, X2, X3) 21.38/9.10 U24(X1, active(X2), X3) -> U24(X1, X2, X3) 21.38/9.10 U24(X1, X2, active(X3)) -> U24(X1, X2, X3) 21.38/9.10 U25(active(X1), X2) -> U25(X1, X2) 21.38/9.10 U25(X1, active(X2)) -> U25(X1, X2) 21.38/9.10 isList(active(X)) -> isList(X) 21.38/9.10 U26(active(X)) -> U26(X) 21.38/9.10 U31(active(X1), X2) -> U31(X1, X2) 21.38/9.10 U31(X1, active(X2)) -> U31(X1, X2) 21.38/9.10 U32(active(X1), X2) -> U32(X1, X2) 21.38/9.10 U32(X1, active(X2)) -> U32(X1, X2) 21.38/9.10 U33(active(X)) -> U33(X) 21.38/9.10 isQid(active(X)) -> isQid(X) 21.38/9.10 U41(active(X1), X2, X3) -> U41(X1, X2, X3) 21.38/9.10 U41(X1, active(X2), X3) -> U41(X1, X2, X3) 21.38/9.10 U41(X1, X2, active(X3)) -> U41(X1, X2, X3) 21.38/9.10 U42(active(X1), X2, X3) -> U42(X1, X2, X3) 21.38/9.10 U42(X1, active(X2), X3) -> U42(X1, X2, X3) 21.38/9.10 U42(X1, X2, active(X3)) -> U42(X1, X2, X3) 21.38/9.10 U43(active(X1), X2, X3) -> U43(X1, X2, X3) 21.38/9.10 U43(X1, active(X2), X3) -> U43(X1, X2, X3) 21.38/9.10 U43(X1, X2, active(X3)) -> U43(X1, X2, X3) 21.38/9.10 U44(active(X1), X2, X3) -> U44(X1, X2, X3) 21.38/9.10 U44(X1, active(X2), X3) -> U44(X1, X2, X3) 21.38/9.10 U44(X1, X2, active(X3)) -> U44(X1, X2, X3) 21.38/9.10 U45(active(X1), X2) -> U45(X1, X2) 21.38/9.10 U45(X1, active(X2)) -> U45(X1, X2) 21.38/9.10 U46(active(X)) -> U46(X) 21.38/9.10 U51(active(X1), X2, X3) -> U51(X1, X2, X3) 21.38/9.10 U51(X1, active(X2), X3) -> U51(X1, X2, X3) 21.38/9.10 U51(X1, X2, active(X3)) -> U51(X1, X2, X3) 21.38/9.10 U52(active(X1), X2, X3) -> U52(X1, X2, X3) 21.38/9.10 U52(X1, active(X2), X3) -> U52(X1, X2, X3) 21.38/9.10 U52(X1, X2, active(X3)) -> U52(X1, X2, X3) 21.38/9.10 U53(active(X1), X2, X3) -> U53(X1, X2, X3) 21.38/9.10 U53(X1, active(X2), X3) -> U53(X1, X2, X3) 21.38/9.10 U53(X1, X2, active(X3)) -> U53(X1, X2, X3) 21.38/9.10 U54(active(X1), X2, X3) -> U54(X1, X2, X3) 21.38/9.10 U54(X1, active(X2), X3) -> U54(X1, X2, X3) 21.38/9.10 U54(X1, X2, active(X3)) -> U54(X1, X2, X3) 21.38/9.10 U55(active(X1), X2) -> U55(X1, X2) 21.38/9.10 U55(X1, active(X2)) -> U55(X1, X2) 21.38/9.10 U56(active(X)) -> U56(X) 21.38/9.10 U61(active(X1), X2) -> U61(X1, X2) 21.38/9.10 U61(X1, active(X2)) -> U61(X1, X2) 21.38/9.10 U62(active(X1), X2) -> U62(X1, X2) 21.38/9.10 U62(X1, active(X2)) -> U62(X1, X2) 21.38/9.10 U63(active(X)) -> U63(X) 21.38/9.10 U71(active(X1), X2, X3) -> U71(X1, X2, X3) 21.38/9.10 U71(X1, active(X2), X3) -> U71(X1, X2, X3) 21.38/9.10 U71(X1, X2, active(X3)) -> U71(X1, X2, X3) 21.38/9.10 U72(active(X1), X2) -> U72(X1, X2) 21.38/9.10 U72(X1, active(X2)) -> U72(X1, X2) 21.38/9.10 U73(active(X1), X2) -> U73(X1, X2) 21.38/9.10 U73(X1, active(X2)) -> U73(X1, X2) 21.38/9.10 isPal(active(X)) -> isPal(X) 21.38/9.10 U74(active(X)) -> U74(X) 21.38/9.10 U81(active(X1), X2) -> U81(X1, X2) 21.38/9.10 U81(X1, active(X2)) -> U81(X1, X2) 21.38/9.10 U82(active(X1), X2) -> U82(X1, X2) 21.38/9.10 U82(X1, active(X2)) -> U82(X1, X2) 21.38/9.10 U83(active(X)) -> U83(X) 21.38/9.10 isNePal(active(X)) -> isNePal(X) 21.38/9.10 U91(active(X1), X2) -> U91(X1, X2) 21.38/9.10 U91(X1, active(X2)) -> U91(X1, X2) 21.38/9.10 U92(active(X)) -> U92(X) 21.38/9.10 21.38/9.10 The set Q consists of the following terms: 21.38/9.10 21.38/9.10 active(__(__(x0, x1), x2)) 21.38/9.10 active(__(x0, nil)) 21.38/9.10 active(__(nil, x0)) 21.38/9.10 active(U11(tt, x0)) 21.38/9.10 active(U12(tt, x0)) 21.38/9.10 active(U13(tt)) 21.38/9.10 active(U21(tt, x0, x1)) 21.38/9.10 active(U22(tt, x0, x1)) 21.38/9.10 active(U23(tt, x0, x1)) 21.38/9.10 active(U24(tt, x0, x1)) 21.38/9.10 active(U25(tt, x0)) 21.38/9.10 active(U26(tt)) 21.38/9.10 active(U31(tt, x0)) 21.38/9.10 active(U32(tt, x0)) 21.38/9.10 active(U33(tt)) 21.38/9.10 active(U41(tt, x0, x1)) 21.38/9.10 active(U42(tt, x0, x1)) 21.38/9.10 active(U43(tt, x0, x1)) 21.38/9.10 active(U44(tt, x0, x1)) 21.38/9.10 active(U45(tt, x0)) 21.38/9.10 active(U46(tt)) 21.38/9.10 active(U51(tt, x0, x1)) 21.38/9.10 active(U52(tt, x0, x1)) 21.38/9.10 active(U53(tt, x0, x1)) 21.38/9.10 active(U54(tt, x0, x1)) 21.38/9.10 active(U55(tt, x0)) 21.38/9.10 active(U56(tt)) 21.38/9.10 active(U61(tt, x0)) 21.38/9.10 active(U62(tt, x0)) 21.38/9.10 active(U63(tt)) 21.38/9.10 active(U71(tt, x0, x1)) 21.38/9.10 active(U72(tt, x0)) 21.38/9.10 active(U73(tt, x0)) 21.38/9.10 active(U74(tt)) 21.38/9.10 active(U81(tt, x0)) 21.38/9.10 active(U82(tt, x0)) 21.38/9.10 active(U83(tt)) 21.38/9.10 active(U91(tt, x0)) 21.38/9.10 active(U92(tt)) 21.38/9.10 active(isList(x0)) 21.38/9.10 active(isNeList(x0)) 21.38/9.10 active(isNePal(x0)) 21.38/9.10 active(isPal(x0)) 21.38/9.10 active(isPalListKind(a)) 21.38/9.10 active(isPalListKind(e)) 21.38/9.10 active(isPalListKind(i)) 21.38/9.10 active(isPalListKind(nil)) 21.38/9.10 active(isPalListKind(o)) 21.38/9.10 active(isPalListKind(u)) 21.38/9.10 active(isPalListKind(__(x0, x1))) 21.38/9.10 active(isQid(a)) 21.38/9.10 active(isQid(e)) 21.38/9.10 active(isQid(i)) 21.38/9.10 active(isQid(o)) 21.38/9.10 active(isQid(u)) 21.38/9.10 mark(__(x0, x1)) 21.38/9.10 mark(nil) 21.38/9.10 mark(U11(x0, x1)) 21.38/9.10 mark(tt) 21.38/9.10 mark(U12(x0, x1)) 21.38/9.10 mark(isPalListKind(x0)) 21.38/9.10 mark(U13(x0)) 21.38/9.10 mark(isNeList(x0)) 21.38/9.10 mark(U21(x0, x1, x2)) 21.38/9.10 mark(U22(x0, x1, x2)) 21.38/9.10 mark(U23(x0, x1, x2)) 21.38/9.10 mark(U24(x0, x1, x2)) 21.38/9.10 mark(U25(x0, x1)) 21.38/9.10 mark(isList(x0)) 21.38/9.10 mark(U26(x0)) 21.38/9.10 mark(U31(x0, x1)) 21.38/9.10 mark(U32(x0, x1)) 21.38/9.10 mark(U33(x0)) 21.38/9.10 mark(isQid(x0)) 21.38/9.10 mark(U41(x0, x1, x2)) 21.38/9.10 mark(U42(x0, x1, x2)) 21.38/9.10 mark(U43(x0, x1, x2)) 21.38/9.10 mark(U44(x0, x1, x2)) 21.38/9.10 mark(U45(x0, x1)) 21.38/9.10 mark(U46(x0)) 21.38/9.10 mark(U51(x0, x1, x2)) 21.38/9.10 mark(U52(x0, x1, x2)) 21.38/9.10 mark(U53(x0, x1, x2)) 21.38/9.10 mark(U54(x0, x1, x2)) 21.38/9.10 mark(U55(x0, x1)) 21.38/9.10 mark(U56(x0)) 21.38/9.10 mark(U61(x0, x1)) 21.38/9.10 mark(U62(x0, x1)) 21.38/9.10 mark(U63(x0)) 21.38/9.10 mark(U71(x0, x1, x2)) 21.38/9.10 mark(U72(x0, x1)) 21.38/9.10 mark(U73(x0, x1)) 21.38/9.10 mark(isPal(x0)) 21.38/9.10 mark(U74(x0)) 21.38/9.10 mark(U81(x0, x1)) 21.38/9.10 mark(U82(x0, x1)) 21.38/9.10 mark(U83(x0)) 21.38/9.10 mark(isNePal(x0)) 21.38/9.10 mark(U91(x0, x1)) 21.38/9.10 mark(U92(x0)) 21.38/9.10 mark(a) 21.38/9.10 mark(e) 21.38/9.10 mark(i) 21.38/9.10 mark(o) 21.38/9.10 mark(u) 21.38/9.10 __(mark(x0), x1) 21.38/9.10 __(x0, mark(x1)) 21.38/9.10 __(active(x0), x1) 21.38/9.10 __(x0, active(x1)) 21.38/9.10 U11(mark(x0), x1) 21.38/9.10 U11(x0, mark(x1)) 21.38/9.10 U11(active(x0), x1) 21.38/9.10 U11(x0, active(x1)) 21.38/9.10 U12(mark(x0), x1) 21.38/9.10 U12(x0, mark(x1)) 21.38/9.10 U12(active(x0), x1) 21.38/9.10 U12(x0, active(x1)) 21.38/9.10 isPalListKind(mark(x0)) 21.38/9.10 isPalListKind(active(x0)) 21.38/9.10 U13(mark(x0)) 21.38/9.10 U13(active(x0)) 21.38/9.10 isNeList(mark(x0)) 21.38/9.10 isNeList(active(x0)) 21.38/9.10 U21(mark(x0), x1, x2) 21.38/9.10 U21(x0, mark(x1), x2) 21.38/9.10 U21(x0, x1, mark(x2)) 21.38/9.10 U21(active(x0), x1, x2) 21.38/9.10 U21(x0, active(x1), x2) 21.38/9.10 U21(x0, x1, active(x2)) 21.38/9.10 U22(mark(x0), x1, x2) 21.38/9.10 U22(x0, mark(x1), x2) 21.38/9.10 U22(x0, x1, mark(x2)) 21.38/9.10 U22(active(x0), x1, x2) 21.38/9.10 U22(x0, active(x1), x2) 21.38/9.10 U22(x0, x1, active(x2)) 21.38/9.10 U23(mark(x0), x1, x2) 21.38/9.10 U23(x0, mark(x1), x2) 21.38/9.10 U23(x0, x1, mark(x2)) 21.38/9.10 U23(active(x0), x1, x2) 21.38/9.10 U23(x0, active(x1), x2) 21.38/9.10 U23(x0, x1, active(x2)) 21.38/9.10 U24(mark(x0), x1, x2) 21.38/9.10 U24(x0, mark(x1), x2) 21.38/9.10 U24(x0, x1, mark(x2)) 21.38/9.10 U24(active(x0), x1, x2) 21.38/9.10 U24(x0, active(x1), x2) 21.38/9.10 U24(x0, x1, active(x2)) 21.38/9.10 U25(mark(x0), x1) 21.38/9.10 U25(x0, mark(x1)) 21.38/9.10 U25(active(x0), x1) 21.38/9.10 U25(x0, active(x1)) 21.38/9.10 isList(mark(x0)) 21.38/9.10 isList(active(x0)) 21.38/9.10 U26(mark(x0)) 21.38/9.10 U26(active(x0)) 21.38/9.10 U31(mark(x0), x1) 21.38/9.10 U31(x0, mark(x1)) 21.38/9.10 U31(active(x0), x1) 21.38/9.10 U31(x0, active(x1)) 21.38/9.10 U32(mark(x0), x1) 21.38/9.10 U32(x0, mark(x1)) 21.38/9.10 U32(active(x0), x1) 21.38/9.10 U32(x0, active(x1)) 21.38/9.10 U33(mark(x0)) 21.38/9.10 U33(active(x0)) 21.38/9.10 isQid(mark(x0)) 21.38/9.10 isQid(active(x0)) 21.38/9.10 U41(mark(x0), x1, x2) 21.38/9.10 U41(x0, mark(x1), x2) 21.38/9.10 U41(x0, x1, mark(x2)) 21.38/9.10 U41(active(x0), x1, x2) 21.38/9.10 U41(x0, active(x1), x2) 21.38/9.10 U41(x0, x1, active(x2)) 21.38/9.10 U42(mark(x0), x1, x2) 21.38/9.10 U42(x0, mark(x1), x2) 21.38/9.10 U42(x0, x1, mark(x2)) 21.38/9.10 U42(active(x0), x1, x2) 21.38/9.10 U42(x0, active(x1), x2) 21.38/9.10 U42(x0, x1, active(x2)) 21.38/9.10 U43(mark(x0), x1, x2) 21.38/9.10 U43(x0, mark(x1), x2) 21.38/9.10 U43(x0, x1, mark(x2)) 21.38/9.10 U43(active(x0), x1, x2) 21.38/9.10 U43(x0, active(x1), x2) 21.38/9.10 U43(x0, x1, active(x2)) 21.38/9.10 U44(mark(x0), x1, x2) 21.38/9.10 U44(x0, mark(x1), x2) 21.38/9.10 U44(x0, x1, mark(x2)) 21.38/9.10 U44(active(x0), x1, x2) 21.38/9.10 U44(x0, active(x1), x2) 21.38/9.10 U44(x0, x1, active(x2)) 21.38/9.10 U45(mark(x0), x1) 21.38/9.10 U45(x0, mark(x1)) 21.38/9.10 U45(active(x0), x1) 21.38/9.10 U45(x0, active(x1)) 21.38/9.10 U46(mark(x0)) 21.38/9.10 U46(active(x0)) 21.38/9.10 U51(mark(x0), x1, x2) 21.38/9.10 U51(x0, mark(x1), x2) 21.38/9.10 U51(x0, x1, mark(x2)) 21.38/9.10 U51(active(x0), x1, x2) 21.38/9.10 U51(x0, active(x1), x2) 21.38/9.10 U51(x0, x1, active(x2)) 21.38/9.10 U52(mark(x0), x1, x2) 21.38/9.10 U52(x0, mark(x1), x2) 21.38/9.10 U52(x0, x1, mark(x2)) 21.38/9.10 U52(active(x0), x1, x2) 21.38/9.10 U52(x0, active(x1), x2) 21.38/9.10 U52(x0, x1, active(x2)) 21.38/9.10 U53(mark(x0), x1, x2) 21.38/9.10 U53(x0, mark(x1), x2) 21.38/9.10 U53(x0, x1, mark(x2)) 21.38/9.10 U53(active(x0), x1, x2) 21.38/9.10 U53(x0, active(x1), x2) 21.38/9.10 U53(x0, x1, active(x2)) 21.38/9.10 U54(mark(x0), x1, x2) 21.38/9.10 U54(x0, mark(x1), x2) 21.38/9.10 U54(x0, x1, mark(x2)) 21.38/9.10 U54(active(x0), x1, x2) 21.38/9.10 U54(x0, active(x1), x2) 21.38/9.10 U54(x0, x1, active(x2)) 21.38/9.10 U55(mark(x0), x1) 21.38/9.10 U55(x0, mark(x1)) 21.38/9.10 U55(active(x0), x1) 21.38/9.10 U55(x0, active(x1)) 21.38/9.10 U56(mark(x0)) 21.38/9.10 U56(active(x0)) 21.38/9.10 U61(mark(x0), x1) 21.38/9.10 U61(x0, mark(x1)) 21.38/9.10 U61(active(x0), x1) 21.38/9.10 U61(x0, active(x1)) 21.38/9.10 U62(mark(x0), x1) 21.38/9.10 U62(x0, mark(x1)) 21.38/9.10 U62(active(x0), x1) 21.38/9.10 U62(x0, active(x1)) 21.38/9.10 U63(mark(x0)) 21.38/9.10 U63(active(x0)) 21.38/9.10 U71(mark(x0), x1, x2) 21.38/9.10 U71(x0, mark(x1), x2) 21.38/9.10 U71(x0, x1, mark(x2)) 21.38/9.10 U71(active(x0), x1, x2) 21.38/9.10 U71(x0, active(x1), x2) 21.38/9.10 U71(x0, x1, active(x2)) 21.38/9.10 U72(mark(x0), x1) 21.38/9.10 U72(x0, mark(x1)) 21.38/9.10 U72(active(x0), x1) 21.38/9.10 U72(x0, active(x1)) 21.38/9.10 U73(mark(x0), x1) 21.38/9.10 U73(x0, mark(x1)) 21.38/9.10 U73(active(x0), x1) 21.38/9.10 U73(x0, active(x1)) 21.38/9.10 isPal(mark(x0)) 21.38/9.10 isPal(active(x0)) 21.38/9.10 U74(mark(x0)) 21.38/9.10 U74(active(x0)) 21.38/9.10 U81(mark(x0), x1) 21.38/9.10 U81(x0, mark(x1)) 21.38/9.10 U81(active(x0), x1) 21.38/9.10 U81(x0, active(x1)) 21.38/9.10 U82(mark(x0), x1) 21.38/9.10 U82(x0, mark(x1)) 21.38/9.10 U82(active(x0), x1) 21.38/9.10 U82(x0, active(x1)) 21.38/9.10 U83(mark(x0)) 21.38/9.10 U83(active(x0)) 21.38/9.10 isNePal(mark(x0)) 21.38/9.10 isNePal(active(x0)) 21.38/9.10 U91(mark(x0), x1) 21.38/9.10 U91(x0, mark(x1)) 21.38/9.10 U91(active(x0), x1) 21.38/9.10 U91(x0, active(x1)) 21.38/9.10 U92(mark(x0)) 21.38/9.10 U92(active(x0)) 21.38/9.10 21.38/9.10 21.38/9.10 ---------------------------------------- 21.38/9.10 21.38/9.10 (7) QTRSRRRProof (EQUIVALENT) 21.38/9.10 Used ordering: 21.38/9.10 active/1)YES( 21.38/9.10 U83/1(YES) 21.38/9.10 tt/0) 21.38/9.10 mark/1(YES) 21.38/9.10 U92/1(YES) 21.38/9.10 U56/1(YES) 21.38/9.10 U74/1(YES) 21.38/9.10 __/2(YES,YES) 21.38/9.10 U11/2(YES,YES) 21.38/9.10 U12/2(YES,YES) 21.38/9.10 isPalListKind/1(YES) 21.38/9.10 U13/1)YES( 21.38/9.10 isNeList/1)YES( 21.38/9.10 U21/3(YES,YES,YES) 21.38/9.10 U22/3(YES,YES,YES) 21.38/9.10 U23/3(YES,YES,YES) 21.38/9.10 U24/3(YES,YES,YES) 21.38/9.10 U25/2(YES,YES) 21.38/9.10 isList/1)YES( 21.38/9.10 U26/1)YES( 21.38/9.10 U31/2(YES,YES) 21.38/9.10 U32/2(YES,YES) 21.38/9.10 U33/1(YES) 21.38/9.10 isQid/1(YES) 21.38/9.10 U41/3(YES,YES,YES) 21.38/9.10 U42/3(YES,YES,YES) 21.38/9.10 U43/3(YES,YES,YES) 21.38/9.10 U44/3(YES,YES,YES) 21.38/9.10 U45/2(YES,YES) 21.38/9.10 U46/1)YES( 21.38/9.10 U51/3(YES,YES,YES) 21.38/9.10 U52/3(YES,YES,YES) 21.38/9.10 U53/3(YES,YES,YES) 21.38/9.10 U54/3(YES,YES,YES) 21.38/9.10 U55/2(YES,YES) 21.38/9.10 U61/2(YES,YES) 21.38/9.10 U62/2(YES,YES) 21.38/9.10 U63/1(YES) 21.38/9.10 U71/3(YES,YES,YES) 21.38/9.10 U72/2(YES,YES) 21.38/9.10 U73/2(YES,YES) 21.38/9.10 isPal/1(YES) 21.38/9.10 U81/2(YES,YES) 21.38/9.10 U82/2(YES,YES) 21.38/9.10 isNePal/1(YES) 21.38/9.10 U91/2(YES,YES) 21.38/9.10 21.38/9.10 Quasi precedence: 21.38/9.10 tt > [U83_1, mark_1, U92_1] > U56_1 > isQid_1 21.38/9.10 tt > [U83_1, mark_1, U92_1] > U74_1 > isQid_1 21.38/9.10 ___2 > isQid_1 21.38/9.10 U11_2 > isQid_1 21.38/9.10 U12_2 > isQid_1 21.38/9.10 isPalListKind_1 > isQid_1 21.38/9.10 U21_3 > isQid_1 21.38/9.10 U22_3 > isQid_1 21.38/9.10 U23_3 > isQid_1 21.38/9.10 U24_3 > isQid_1 21.38/9.10 U25_2 > isQid_1 21.38/9.10 U31_2 > isQid_1 21.38/9.10 U32_2 > isQid_1 21.38/9.10 U33_1 > isQid_1 21.38/9.10 U41_3 > isQid_1 21.38/9.10 U42_3 > isQid_1 21.38/9.10 U43_3 > isQid_1 21.38/9.10 U44_3 > isQid_1 21.38/9.10 U45_2 > isQid_1 21.38/9.10 U51_3 > isQid_1 21.38/9.10 U52_3 > isQid_1 21.38/9.10 U53_3 > isQid_1 21.38/9.10 U54_3 > isQid_1 21.38/9.10 U55_2 > isQid_1 21.38/9.10 U61_2 > isQid_1 21.38/9.10 U62_2 > isQid_1 21.38/9.10 U63_1 > isQid_1 21.38/9.10 U71_3 > isQid_1 21.38/9.10 U72_2 > isQid_1 21.38/9.10 U73_2 > isQid_1 21.38/9.10 isPal_1 > isQid_1 21.38/9.10 U81_2 > isQid_1 21.38/9.10 U82_2 > isQid_1 21.38/9.10 isNePal_1 > isQid_1 21.38/9.10 U91_2 > isQid_1 21.38/9.10 21.38/9.10 21.38/9.10 Status: 21.38/9.10 U83_1: [1] 21.38/9.10 tt: multiset status 21.38/9.10 mark_1: [1] 21.38/9.10 U92_1: [1] 21.38/9.10 U56_1: multiset status 21.38/9.10 U74_1: multiset status 21.38/9.10 ___2: [2,1] 21.38/9.10 U11_2: [2,1] 21.38/9.10 U12_2: [2,1] 21.38/9.10 isPalListKind_1: [1] 21.38/9.10 U21_3: [2,1,3] 21.38/9.10 U22_3: [3,1,2] 21.38/9.10 U23_3: [1,2,3] 21.38/9.10 U24_3: [3,1,2] 21.38/9.10 U25_2: [2,1] 21.38/9.10 U31_2: [2,1] 21.38/9.10 U32_2: [2,1] 21.38/9.10 U33_1: [1] 21.38/9.10 isQid_1: [1] 21.38/9.10 U41_3: [3,1,2] 21.38/9.10 U42_3: [2,1,3] 21.38/9.10 U43_3: [1,2,3] 21.38/9.10 U44_3: [2,1,3] 21.38/9.10 U45_2: [2,1] 21.38/9.10 U51_3: [3,2,1] 21.38/9.10 U52_3: [1,2,3] 21.38/9.10 U53_3: [3,1,2] 21.38/9.10 U54_3: [3,1,2] 21.38/9.10 U55_2: [1,2] 21.38/9.10 U61_2: [1,2] 21.38/9.10 U62_2: [2,1] 21.38/9.10 U63_1: [1] 21.38/9.10 U71_3: [2,1,3] 21.38/9.10 U72_2: [2,1] 21.38/9.10 U73_2: [2,1] 21.38/9.10 isPal_1: [1] 21.38/9.10 U81_2: [2,1] 21.38/9.10 U82_2: [2,1] 21.38/9.10 isNePal_1: [1] 21.38/9.10 U91_2: [2,1] 21.38/9.10 21.38/9.10 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 21.38/9.10 21.38/9.10 mark(U56(X)) -> active(U56(mark(X))) 21.38/9.10 mark(U74(X)) -> active(U74(mark(X))) 21.38/9.10 21.38/9.10 21.38/9.10 21.38/9.10 21.38/9.10 ---------------------------------------- 21.38/9.10 21.38/9.10 (8) 21.38/9.10 Obligation: 21.38/9.10 Q restricted rewrite system: 21.38/9.10 The TRS R consists of the following rules: 21.38/9.10 21.38/9.10 active(U83(tt)) -> mark(tt) 21.38/9.10 active(U92(tt)) -> mark(tt) 21.38/9.10 mark(U83(X)) -> active(U83(mark(X))) 21.38/9.10 mark(U92(X)) -> active(U92(mark(X))) 21.38/9.10 __(active(X1), X2) -> __(X1, X2) 21.38/9.10 __(X1, active(X2)) -> __(X1, X2) 21.38/9.10 U11(active(X1), X2) -> U11(X1, X2) 21.38/9.10 U11(X1, active(X2)) -> U11(X1, X2) 21.38/9.10 U12(active(X1), X2) -> U12(X1, X2) 21.38/9.10 U12(X1, active(X2)) -> U12(X1, X2) 21.38/9.10 isPalListKind(active(X)) -> isPalListKind(X) 21.38/9.10 U13(active(X)) -> U13(X) 21.38/9.10 isNeList(active(X)) -> isNeList(X) 21.38/9.10 U21(active(X1), X2, X3) -> U21(X1, X2, X3) 21.38/9.10 U21(X1, active(X2), X3) -> U21(X1, X2, X3) 21.38/9.10 U21(X1, X2, active(X3)) -> U21(X1, X2, X3) 21.38/9.10 U22(active(X1), X2, X3) -> U22(X1, X2, X3) 21.38/9.10 U22(X1, active(X2), X3) -> U22(X1, X2, X3) 21.38/9.10 U22(X1, X2, active(X3)) -> U22(X1, X2, X3) 21.38/9.10 U23(active(X1), X2, X3) -> U23(X1, X2, X3) 21.38/9.10 U23(X1, active(X2), X3) -> U23(X1, X2, X3) 21.38/9.10 U23(X1, X2, active(X3)) -> U23(X1, X2, X3) 21.38/9.10 U24(active(X1), X2, X3) -> U24(X1, X2, X3) 21.38/9.10 U24(X1, active(X2), X3) -> U24(X1, X2, X3) 21.38/9.10 U24(X1, X2, active(X3)) -> U24(X1, X2, X3) 21.38/9.10 U25(active(X1), X2) -> U25(X1, X2) 21.38/9.10 U25(X1, active(X2)) -> U25(X1, X2) 21.38/9.10 isList(active(X)) -> isList(X) 21.38/9.10 U26(active(X)) -> U26(X) 21.38/9.10 U31(active(X1), X2) -> U31(X1, X2) 21.38/9.10 U31(X1, active(X2)) -> U31(X1, X2) 21.38/9.10 U32(active(X1), X2) -> U32(X1, X2) 21.38/9.10 U32(X1, active(X2)) -> U32(X1, X2) 21.38/9.10 U33(active(X)) -> U33(X) 21.38/9.10 isQid(active(X)) -> isQid(X) 21.38/9.10 U41(active(X1), X2, X3) -> U41(X1, X2, X3) 21.38/9.10 U41(X1, active(X2), X3) -> U41(X1, X2, X3) 21.38/9.10 U41(X1, X2, active(X3)) -> U41(X1, X2, X3) 21.38/9.10 U42(active(X1), X2, X3) -> U42(X1, X2, X3) 21.38/9.10 U42(X1, active(X2), X3) -> U42(X1, X2, X3) 21.38/9.10 U42(X1, X2, active(X3)) -> U42(X1, X2, X3) 21.38/9.10 U43(active(X1), X2, X3) -> U43(X1, X2, X3) 21.38/9.10 U43(X1, active(X2), X3) -> U43(X1, X2, X3) 21.38/9.10 U43(X1, X2, active(X3)) -> U43(X1, X2, X3) 21.38/9.10 U44(active(X1), X2, X3) -> U44(X1, X2, X3) 21.38/9.10 U44(X1, active(X2), X3) -> U44(X1, X2, X3) 21.38/9.10 U44(X1, X2, active(X3)) -> U44(X1, X2, X3) 21.38/9.10 U45(active(X1), X2) -> U45(X1, X2) 21.38/9.10 U45(X1, active(X2)) -> U45(X1, X2) 21.38/9.10 U46(active(X)) -> U46(X) 21.38/9.10 U51(active(X1), X2, X3) -> U51(X1, X2, X3) 21.38/9.10 U51(X1, active(X2), X3) -> U51(X1, X2, X3) 21.38/9.10 U51(X1, X2, active(X3)) -> U51(X1, X2, X3) 21.38/9.10 U52(active(X1), X2, X3) -> U52(X1, X2, X3) 21.38/9.10 U52(X1, active(X2), X3) -> U52(X1, X2, X3) 21.38/9.10 U52(X1, X2, active(X3)) -> U52(X1, X2, X3) 21.38/9.10 U53(active(X1), X2, X3) -> U53(X1, X2, X3) 21.38/9.10 U53(X1, active(X2), X3) -> U53(X1, X2, X3) 21.38/9.10 U53(X1, X2, active(X3)) -> U53(X1, X2, X3) 21.38/9.10 U54(active(X1), X2, X3) -> U54(X1, X2, X3) 21.38/9.10 U54(X1, active(X2), X3) -> U54(X1, X2, X3) 21.38/9.10 U54(X1, X2, active(X3)) -> U54(X1, X2, X3) 21.38/9.10 U55(active(X1), X2) -> U55(X1, X2) 21.38/9.10 U55(X1, active(X2)) -> U55(X1, X2) 21.38/9.10 U56(active(X)) -> U56(X) 21.38/9.10 U61(active(X1), X2) -> U61(X1, X2) 21.38/9.10 U61(X1, active(X2)) -> U61(X1, X2) 21.38/9.10 U62(active(X1), X2) -> U62(X1, X2) 21.38/9.10 U62(X1, active(X2)) -> U62(X1, X2) 21.38/9.10 U63(active(X)) -> U63(X) 21.38/9.10 U71(active(X1), X2, X3) -> U71(X1, X2, X3) 21.38/9.10 U71(X1, active(X2), X3) -> U71(X1, X2, X3) 21.38/9.10 U71(X1, X2, active(X3)) -> U71(X1, X2, X3) 21.38/9.10 U72(active(X1), X2) -> U72(X1, X2) 21.38/9.10 U72(X1, active(X2)) -> U72(X1, X2) 21.38/9.10 U73(active(X1), X2) -> U73(X1, X2) 21.38/9.10 U73(X1, active(X2)) -> U73(X1, X2) 21.38/9.10 isPal(active(X)) -> isPal(X) 21.38/9.10 U74(active(X)) -> U74(X) 21.38/9.10 U81(active(X1), X2) -> U81(X1, X2) 21.38/9.10 U81(X1, active(X2)) -> U81(X1, X2) 21.38/9.10 U82(active(X1), X2) -> U82(X1, X2) 21.38/9.10 U82(X1, active(X2)) -> U82(X1, X2) 21.38/9.10 U83(active(X)) -> U83(X) 21.38/9.10 isNePal(active(X)) -> isNePal(X) 21.38/9.10 U91(active(X1), X2) -> U91(X1, X2) 21.38/9.10 U91(X1, active(X2)) -> U91(X1, X2) 21.38/9.10 U92(active(X)) -> U92(X) 21.38/9.10 21.38/9.10 The set Q consists of the following terms: 21.38/9.10 21.38/9.10 active(__(__(x0, x1), x2)) 21.38/9.10 active(__(x0, nil)) 21.38/9.10 active(__(nil, x0)) 21.38/9.10 active(U11(tt, x0)) 21.38/9.10 active(U12(tt, x0)) 21.38/9.10 active(U13(tt)) 21.38/9.10 active(U21(tt, x0, x1)) 21.38/9.10 active(U22(tt, x0, x1)) 21.38/9.10 active(U23(tt, x0, x1)) 21.38/9.10 active(U24(tt, x0, x1)) 21.38/9.10 active(U25(tt, x0)) 21.38/9.10 active(U26(tt)) 21.38/9.10 active(U31(tt, x0)) 21.38/9.10 active(U32(tt, x0)) 21.38/9.10 active(U33(tt)) 21.38/9.10 active(U41(tt, x0, x1)) 21.38/9.10 active(U42(tt, x0, x1)) 21.38/9.10 active(U43(tt, x0, x1)) 21.38/9.10 active(U44(tt, x0, x1)) 21.38/9.10 active(U45(tt, x0)) 21.38/9.10 active(U46(tt)) 21.38/9.10 active(U51(tt, x0, x1)) 21.38/9.10 active(U52(tt, x0, x1)) 21.38/9.10 active(U53(tt, x0, x1)) 21.38/9.10 active(U54(tt, x0, x1)) 21.38/9.10 active(U55(tt, x0)) 21.38/9.10 active(U56(tt)) 21.38/9.10 active(U61(tt, x0)) 21.38/9.10 active(U62(tt, x0)) 21.38/9.10 active(U63(tt)) 21.38/9.10 active(U71(tt, x0, x1)) 21.38/9.10 active(U72(tt, x0)) 21.38/9.10 active(U73(tt, x0)) 21.38/9.10 active(U74(tt)) 21.38/9.10 active(U81(tt, x0)) 21.38/9.10 active(U82(tt, x0)) 21.38/9.10 active(U83(tt)) 21.38/9.10 active(U91(tt, x0)) 21.38/9.10 active(U92(tt)) 21.38/9.10 active(isList(x0)) 21.38/9.10 active(isNeList(x0)) 21.38/9.10 active(isNePal(x0)) 21.38/9.10 active(isPal(x0)) 21.38/9.10 active(isPalListKind(a)) 21.38/9.10 active(isPalListKind(e)) 21.38/9.10 active(isPalListKind(i)) 21.38/9.10 active(isPalListKind(nil)) 21.38/9.10 active(isPalListKind(o)) 21.38/9.10 active(isPalListKind(u)) 21.38/9.10 active(isPalListKind(__(x0, x1))) 21.38/9.10 active(isQid(a)) 21.38/9.10 active(isQid(e)) 21.38/9.10 active(isQid(i)) 21.38/9.10 active(isQid(o)) 21.38/9.10 active(isQid(u)) 21.38/9.10 mark(__(x0, x1)) 21.38/9.10 mark(nil) 21.38/9.10 mark(U11(x0, x1)) 21.38/9.10 mark(tt) 21.38/9.10 mark(U12(x0, x1)) 21.38/9.10 mark(isPalListKind(x0)) 21.38/9.10 mark(U13(x0)) 21.38/9.10 mark(isNeList(x0)) 21.38/9.10 mark(U21(x0, x1, x2)) 21.38/9.10 mark(U22(x0, x1, x2)) 21.38/9.10 mark(U23(x0, x1, x2)) 21.38/9.10 mark(U24(x0, x1, x2)) 21.38/9.10 mark(U25(x0, x1)) 21.38/9.10 mark(isList(x0)) 21.38/9.10 mark(U26(x0)) 21.38/9.10 mark(U31(x0, x1)) 21.38/9.10 mark(U32(x0, x1)) 21.38/9.10 mark(U33(x0)) 21.38/9.10 mark(isQid(x0)) 21.38/9.10 mark(U41(x0, x1, x2)) 21.38/9.10 mark(U42(x0, x1, x2)) 21.38/9.10 mark(U43(x0, x1, x2)) 21.38/9.10 mark(U44(x0, x1, x2)) 21.38/9.10 mark(U45(x0, x1)) 21.38/9.10 mark(U46(x0)) 21.38/9.10 mark(U51(x0, x1, x2)) 21.38/9.10 mark(U52(x0, x1, x2)) 21.38/9.10 mark(U53(x0, x1, x2)) 21.38/9.10 mark(U54(x0, x1, x2)) 21.38/9.10 mark(U55(x0, x1)) 21.38/9.10 mark(U56(x0)) 21.38/9.10 mark(U61(x0, x1)) 21.38/9.10 mark(U62(x0, x1)) 21.38/9.10 mark(U63(x0)) 21.38/9.10 mark(U71(x0, x1, x2)) 21.38/9.10 mark(U72(x0, x1)) 21.38/9.10 mark(U73(x0, x1)) 21.38/9.10 mark(isPal(x0)) 21.38/9.10 mark(U74(x0)) 21.38/9.10 mark(U81(x0, x1)) 21.38/9.10 mark(U82(x0, x1)) 21.38/9.10 mark(U83(x0)) 21.38/9.10 mark(isNePal(x0)) 21.38/9.10 mark(U91(x0, x1)) 21.38/9.10 mark(U92(x0)) 21.38/9.10 mark(a) 21.38/9.10 mark(e) 21.38/9.10 mark(i) 21.38/9.10 mark(o) 21.38/9.10 mark(u) 21.38/9.10 __(mark(x0), x1) 21.38/9.10 __(x0, mark(x1)) 21.38/9.10 __(active(x0), x1) 21.38/9.10 __(x0, active(x1)) 21.38/9.10 U11(mark(x0), x1) 21.38/9.10 U11(x0, mark(x1)) 21.38/9.10 U11(active(x0), x1) 21.38/9.10 U11(x0, active(x1)) 21.38/9.10 U12(mark(x0), x1) 21.38/9.10 U12(x0, mark(x1)) 21.38/9.10 U12(active(x0), x1) 21.38/9.10 U12(x0, active(x1)) 21.38/9.10 isPalListKind(mark(x0)) 21.38/9.10 isPalListKind(active(x0)) 21.38/9.10 U13(mark(x0)) 21.38/9.10 U13(active(x0)) 21.38/9.10 isNeList(mark(x0)) 21.38/9.10 isNeList(active(x0)) 21.38/9.10 U21(mark(x0), x1, x2) 21.38/9.10 U21(x0, mark(x1), x2) 21.38/9.10 U21(x0, x1, mark(x2)) 21.38/9.10 U21(active(x0), x1, x2) 21.38/9.10 U21(x0, active(x1), x2) 21.38/9.10 U21(x0, x1, active(x2)) 21.38/9.10 U22(mark(x0), x1, x2) 21.38/9.10 U22(x0, mark(x1), x2) 21.38/9.10 U22(x0, x1, mark(x2)) 21.38/9.10 U22(active(x0), x1, x2) 21.38/9.10 U22(x0, active(x1), x2) 21.38/9.10 U22(x0, x1, active(x2)) 21.38/9.10 U23(mark(x0), x1, x2) 21.38/9.10 U23(x0, mark(x1), x2) 21.38/9.10 U23(x0, x1, mark(x2)) 21.38/9.10 U23(active(x0), x1, x2) 21.38/9.10 U23(x0, active(x1), x2) 21.38/9.10 U23(x0, x1, active(x2)) 21.38/9.10 U24(mark(x0), x1, x2) 21.38/9.10 U24(x0, mark(x1), x2) 21.38/9.10 U24(x0, x1, mark(x2)) 21.38/9.10 U24(active(x0), x1, x2) 21.38/9.10 U24(x0, active(x1), x2) 21.38/9.10 U24(x0, x1, active(x2)) 21.38/9.10 U25(mark(x0), x1) 21.38/9.10 U25(x0, mark(x1)) 21.38/9.10 U25(active(x0), x1) 21.38/9.10 U25(x0, active(x1)) 21.38/9.10 isList(mark(x0)) 21.38/9.10 isList(active(x0)) 21.38/9.10 U26(mark(x0)) 21.38/9.10 U26(active(x0)) 21.38/9.10 U31(mark(x0), x1) 21.38/9.10 U31(x0, mark(x1)) 21.38/9.10 U31(active(x0), x1) 21.38/9.10 U31(x0, active(x1)) 21.38/9.10 U32(mark(x0), x1) 21.38/9.10 U32(x0, mark(x1)) 21.38/9.10 U32(active(x0), x1) 21.38/9.10 U32(x0, active(x1)) 21.38/9.10 U33(mark(x0)) 21.38/9.10 U33(active(x0)) 21.38/9.10 isQid(mark(x0)) 21.38/9.10 isQid(active(x0)) 21.38/9.10 U41(mark(x0), x1, x2) 21.38/9.10 U41(x0, mark(x1), x2) 21.38/9.10 U41(x0, x1, mark(x2)) 21.38/9.10 U41(active(x0), x1, x2) 21.38/9.10 U41(x0, active(x1), x2) 21.38/9.10 U41(x0, x1, active(x2)) 21.38/9.10 U42(mark(x0), x1, x2) 21.38/9.10 U42(x0, mark(x1), x2) 21.38/9.10 U42(x0, x1, mark(x2)) 21.38/9.10 U42(active(x0), x1, x2) 21.38/9.10 U42(x0, active(x1), x2) 21.38/9.10 U42(x0, x1, active(x2)) 21.38/9.10 U43(mark(x0), x1, x2) 21.38/9.10 U43(x0, mark(x1), x2) 21.38/9.10 U43(x0, x1, mark(x2)) 21.38/9.10 U43(active(x0), x1, x2) 21.38/9.10 U43(x0, active(x1), x2) 21.38/9.10 U43(x0, x1, active(x2)) 21.38/9.10 U44(mark(x0), x1, x2) 21.38/9.10 U44(x0, mark(x1), x2) 21.38/9.10 U44(x0, x1, mark(x2)) 21.38/9.10 U44(active(x0), x1, x2) 21.38/9.10 U44(x0, active(x1), x2) 21.38/9.10 U44(x0, x1, active(x2)) 21.38/9.10 U45(mark(x0), x1) 21.38/9.10 U45(x0, mark(x1)) 21.38/9.10 U45(active(x0), x1) 21.38/9.10 U45(x0, active(x1)) 21.38/9.10 U46(mark(x0)) 21.38/9.10 U46(active(x0)) 21.38/9.10 U51(mark(x0), x1, x2) 21.38/9.10 U51(x0, mark(x1), x2) 21.38/9.10 U51(x0, x1, mark(x2)) 21.38/9.10 U51(active(x0), x1, x2) 21.38/9.10 U51(x0, active(x1), x2) 21.38/9.10 U51(x0, x1, active(x2)) 21.38/9.10 U52(mark(x0), x1, x2) 21.38/9.10 U52(x0, mark(x1), x2) 21.38/9.10 U52(x0, x1, mark(x2)) 21.38/9.10 U52(active(x0), x1, x2) 21.38/9.10 U52(x0, active(x1), x2) 21.38/9.10 U52(x0, x1, active(x2)) 21.38/9.10 U53(mark(x0), x1, x2) 21.38/9.10 U53(x0, mark(x1), x2) 21.38/9.10 U53(x0, x1, mark(x2)) 21.38/9.10 U53(active(x0), x1, x2) 21.38/9.10 U53(x0, active(x1), x2) 21.38/9.10 U53(x0, x1, active(x2)) 21.38/9.10 U54(mark(x0), x1, x2) 21.38/9.10 U54(x0, mark(x1), x2) 21.38/9.10 U54(x0, x1, mark(x2)) 21.38/9.10 U54(active(x0), x1, x2) 21.38/9.10 U54(x0, active(x1), x2) 21.38/9.10 U54(x0, x1, active(x2)) 21.38/9.10 U55(mark(x0), x1) 21.38/9.10 U55(x0, mark(x1)) 21.38/9.10 U55(active(x0), x1) 21.38/9.10 U55(x0, active(x1)) 21.38/9.10 U56(mark(x0)) 21.38/9.10 U56(active(x0)) 21.38/9.10 U61(mark(x0), x1) 21.38/9.10 U61(x0, mark(x1)) 21.38/9.10 U61(active(x0), x1) 21.38/9.10 U61(x0, active(x1)) 21.38/9.10 U62(mark(x0), x1) 21.38/9.10 U62(x0, mark(x1)) 21.38/9.10 U62(active(x0), x1) 21.38/9.10 U62(x0, active(x1)) 21.38/9.10 U63(mark(x0)) 21.38/9.10 U63(active(x0)) 21.38/9.10 U71(mark(x0), x1, x2) 21.38/9.10 U71(x0, mark(x1), x2) 21.38/9.10 U71(x0, x1, mark(x2)) 21.38/9.10 U71(active(x0), x1, x2) 21.38/9.10 U71(x0, active(x1), x2) 21.38/9.10 U71(x0, x1, active(x2)) 21.38/9.10 U72(mark(x0), x1) 21.38/9.10 U72(x0, mark(x1)) 21.38/9.10 U72(active(x0), x1) 21.38/9.10 U72(x0, active(x1)) 21.38/9.10 U73(mark(x0), x1) 21.38/9.10 U73(x0, mark(x1)) 21.38/9.10 U73(active(x0), x1) 21.38/9.10 U73(x0, active(x1)) 21.38/9.10 isPal(mark(x0)) 21.38/9.10 isPal(active(x0)) 21.38/9.10 U74(mark(x0)) 21.38/9.10 U74(active(x0)) 21.38/9.10 U81(mark(x0), x1) 21.38/9.10 U81(x0, mark(x1)) 21.38/9.10 U81(active(x0), x1) 21.38/9.10 U81(x0, active(x1)) 21.38/9.10 U82(mark(x0), x1) 21.38/9.10 U82(x0, mark(x1)) 21.38/9.10 U82(active(x0), x1) 21.38/9.10 U82(x0, active(x1)) 21.38/9.10 U83(mark(x0)) 21.38/9.10 U83(active(x0)) 21.38/9.10 isNePal(mark(x0)) 21.38/9.10 isNePal(active(x0)) 21.38/9.10 U91(mark(x0), x1) 21.38/9.10 U91(x0, mark(x1)) 21.38/9.10 U91(active(x0), x1) 21.38/9.10 U91(x0, active(x1)) 21.38/9.10 U92(mark(x0)) 21.38/9.10 U92(active(x0)) 21.38/9.10 21.38/9.10 21.38/9.10 ---------------------------------------- 21.38/9.10 21.38/9.10 (9) QTRSRRRProof (EQUIVALENT) 21.38/9.10 Used ordering: 21.38/9.10 Polynomial interpretation [POLO]: 21.38/9.10 21.38/9.10 POL(U11(x_1, x_2)) = 2*x_1 + 2*x_2 21.38/9.10 POL(U12(x_1, x_2)) = 2*x_1 + 2*x_2 21.38/9.10 POL(U13(x_1)) = 2*x_1 21.38/9.10 POL(U21(x_1, x_2, x_3)) = 2*x_1 + 2*x_2 + 2*x_3 21.38/9.10 POL(U22(x_1, x_2, x_3)) = 2*x_1 + 2*x_2 + 2*x_3 21.38/9.10 POL(U23(x_1, x_2, x_3)) = 2*x_1 + 2*x_2 + 2*x_3 21.38/9.10 POL(U24(x_1, x_2, x_3)) = 2*x_1 + 2*x_2 + 2*x_3 21.38/9.10 POL(U25(x_1, x_2)) = 2*x_1 + 2*x_2 21.38/9.10 POL(U26(x_1)) = 2*x_1 21.38/9.10 POL(U31(x_1, x_2)) = 2*x_1 + 2*x_2 21.38/9.10 POL(U32(x_1, x_2)) = 2*x_1 + 2*x_2 21.38/9.10 POL(U33(x_1)) = 2*x_1 21.38/9.10 POL(U41(x_1, x_2, x_3)) = 2*x_1 + 2*x_2 + 2*x_3 21.38/9.10 POL(U42(x_1, x_2, x_3)) = 2*x_1 + 2*x_2 + 2*x_3 21.38/9.10 POL(U43(x_1, x_2, x_3)) = 2*x_1 + 2*x_2 + 2*x_3 21.38/9.10 POL(U44(x_1, x_2, x_3)) = 2*x_1 + 2*x_2 + 2*x_3 21.38/9.10 POL(U45(x_1, x_2)) = 2*x_1 + 2*x_2 21.38/9.10 POL(U46(x_1)) = 2*x_1 21.38/9.10 POL(U51(x_1, x_2, x_3)) = 2*x_1 + 2*x_2 + 2*x_3 21.38/9.10 POL(U52(x_1, x_2, x_3)) = 2*x_1 + 2*x_2 + 2*x_3 21.38/9.10 POL(U53(x_1, x_2, x_3)) = 2*x_1 + 2*x_2 + 2*x_3 21.38/9.10 POL(U54(x_1, x_2, x_3)) = 2*x_1 + 2*x_2 + 2*x_3 21.38/9.10 POL(U55(x_1, x_2)) = 2*x_1 + 2*x_2 21.38/9.10 POL(U56(x_1)) = 2*x_1 21.38/9.10 POL(U61(x_1, x_2)) = 2*x_1 + 2*x_2 21.38/9.10 POL(U62(x_1, x_2)) = 2*x_1 + 2*x_2 21.38/9.10 POL(U63(x_1)) = 2*x_1 21.38/9.10 POL(U71(x_1, x_2, x_3)) = 2*x_1 + 2*x_2 + 2*x_3 21.38/9.10 POL(U72(x_1, x_2)) = 2*x_1 + 2*x_2 21.38/9.10 POL(U73(x_1, x_2)) = 2*x_1 + 2*x_2 21.38/9.10 POL(U74(x_1)) = 2*x_1 21.38/9.10 POL(U81(x_1, x_2)) = 2*x_1 + 2*x_2 21.38/9.10 POL(U82(x_1, x_2)) = 2*x_1 + 2*x_2 21.38/9.10 POL(U83(x_1)) = 2 + 2*x_1 21.38/9.10 POL(U91(x_1, x_2)) = 2*x_1 + 2*x_2 21.38/9.10 POL(U92(x_1)) = 2 + 2*x_1 21.38/9.10 POL(__(x_1, x_2)) = 2*x_1 + 2*x_2 21.38/9.10 POL(active(x_1)) = 1 + x_1 21.38/9.10 POL(isList(x_1)) = 2*x_1 21.38/9.10 POL(isNeList(x_1)) = 2*x_1 21.38/9.10 POL(isNePal(x_1)) = 2*x_1 21.38/9.10 POL(isPal(x_1)) = 2*x_1 21.38/9.10 POL(isPalListKind(x_1)) = 2*x_1 21.38/9.10 POL(isQid(x_1)) = 2*x_1 21.38/9.10 POL(mark(x_1)) = 2*x_1 21.38/9.10 POL(tt) = 1 21.38/9.10 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 21.38/9.10 21.38/9.10 active(U83(tt)) -> mark(tt) 21.38/9.10 active(U92(tt)) -> mark(tt) 21.38/9.10 mark(U83(X)) -> active(U83(mark(X))) 21.38/9.10 mark(U92(X)) -> active(U92(mark(X))) 21.38/9.10 __(active(X1), X2) -> __(X1, X2) 21.38/9.10 __(X1, active(X2)) -> __(X1, X2) 21.38/9.10 U11(active(X1), X2) -> U11(X1, X2) 21.38/9.10 U11(X1, active(X2)) -> U11(X1, X2) 21.38/9.10 U12(active(X1), X2) -> U12(X1, X2) 21.38/9.10 U12(X1, active(X2)) -> U12(X1, X2) 21.38/9.10 isPalListKind(active(X)) -> isPalListKind(X) 21.38/9.10 U13(active(X)) -> U13(X) 21.38/9.10 isNeList(active(X)) -> isNeList(X) 21.38/9.10 U21(active(X1), X2, X3) -> U21(X1, X2, X3) 21.38/9.10 U21(X1, active(X2), X3) -> U21(X1, X2, X3) 21.38/9.10 U21(X1, X2, active(X3)) -> U21(X1, X2, X3) 21.38/9.10 U22(active(X1), X2, X3) -> U22(X1, X2, X3) 21.38/9.10 U22(X1, active(X2), X3) -> U22(X1, X2, X3) 21.38/9.10 U22(X1, X2, active(X3)) -> U22(X1, X2, X3) 21.38/9.10 U23(active(X1), X2, X3) -> U23(X1, X2, X3) 21.38/9.10 U23(X1, active(X2), X3) -> U23(X1, X2, X3) 21.38/9.10 U23(X1, X2, active(X3)) -> U23(X1, X2, X3) 21.38/9.10 U24(active(X1), X2, X3) -> U24(X1, X2, X3) 21.38/9.10 U24(X1, active(X2), X3) -> U24(X1, X2, X3) 21.38/9.10 U24(X1, X2, active(X3)) -> U24(X1, X2, X3) 21.38/9.10 U25(active(X1), X2) -> U25(X1, X2) 21.38/9.10 U25(X1, active(X2)) -> U25(X1, X2) 21.38/9.10 isList(active(X)) -> isList(X) 21.38/9.10 U26(active(X)) -> U26(X) 21.38/9.10 U31(active(X1), X2) -> U31(X1, X2) 21.38/9.10 U31(X1, active(X2)) -> U31(X1, X2) 21.38/9.10 U32(active(X1), X2) -> U32(X1, X2) 21.38/9.10 U32(X1, active(X2)) -> U32(X1, X2) 21.38/9.10 U33(active(X)) -> U33(X) 21.38/9.10 isQid(active(X)) -> isQid(X) 21.38/9.10 U41(active(X1), X2, X3) -> U41(X1, X2, X3) 21.38/9.10 U41(X1, active(X2), X3) -> U41(X1, X2, X3) 21.38/9.10 U41(X1, X2, active(X3)) -> U41(X1, X2, X3) 21.38/9.10 U42(active(X1), X2, X3) -> U42(X1, X2, X3) 21.38/9.10 U42(X1, active(X2), X3) -> U42(X1, X2, X3) 21.38/9.10 U42(X1, X2, active(X3)) -> U42(X1, X2, X3) 21.38/9.10 U43(active(X1), X2, X3) -> U43(X1, X2, X3) 21.38/9.10 U43(X1, active(X2), X3) -> U43(X1, X2, X3) 21.38/9.10 U43(X1, X2, active(X3)) -> U43(X1, X2, X3) 21.38/9.10 U44(active(X1), X2, X3) -> U44(X1, X2, X3) 21.38/9.10 U44(X1, active(X2), X3) -> U44(X1, X2, X3) 21.38/9.10 U44(X1, X2, active(X3)) -> U44(X1, X2, X3) 21.38/9.10 U45(active(X1), X2) -> U45(X1, X2) 21.38/9.10 U45(X1, active(X2)) -> U45(X1, X2) 21.38/9.10 U46(active(X)) -> U46(X) 21.38/9.10 U51(active(X1), X2, X3) -> U51(X1, X2, X3) 21.38/9.10 U51(X1, active(X2), X3) -> U51(X1, X2, X3) 21.38/9.10 U51(X1, X2, active(X3)) -> U51(X1, X2, X3) 21.38/9.10 U52(active(X1), X2, X3) -> U52(X1, X2, X3) 21.38/9.10 U52(X1, active(X2), X3) -> U52(X1, X2, X3) 21.38/9.10 U52(X1, X2, active(X3)) -> U52(X1, X2, X3) 21.38/9.10 U53(active(X1), X2, X3) -> U53(X1, X2, X3) 21.38/9.10 U53(X1, active(X2), X3) -> U53(X1, X2, X3) 21.38/9.10 U53(X1, X2, active(X3)) -> U53(X1, X2, X3) 21.38/9.10 U54(active(X1), X2, X3) -> U54(X1, X2, X3) 21.38/9.10 U54(X1, active(X2), X3) -> U54(X1, X2, X3) 21.38/9.10 U54(X1, X2, active(X3)) -> U54(X1, X2, X3) 21.38/9.10 U55(active(X1), X2) -> U55(X1, X2) 21.38/9.10 U55(X1, active(X2)) -> U55(X1, X2) 21.38/9.10 U56(active(X)) -> U56(X) 21.38/9.10 U61(active(X1), X2) -> U61(X1, X2) 21.38/9.10 U61(X1, active(X2)) -> U61(X1, X2) 21.38/9.10 U62(active(X1), X2) -> U62(X1, X2) 21.38/9.10 U62(X1, active(X2)) -> U62(X1, X2) 21.38/9.10 U63(active(X)) -> U63(X) 21.38/9.10 U71(active(X1), X2, X3) -> U71(X1, X2, X3) 21.38/9.10 U71(X1, active(X2), X3) -> U71(X1, X2, X3) 21.38/9.10 U71(X1, X2, active(X3)) -> U71(X1, X2, X3) 21.38/9.10 U72(active(X1), X2) -> U72(X1, X2) 21.38/9.10 U72(X1, active(X2)) -> U72(X1, X2) 21.38/9.10 U73(active(X1), X2) -> U73(X1, X2) 21.38/9.10 U73(X1, active(X2)) -> U73(X1, X2) 21.38/9.10 isPal(active(X)) -> isPal(X) 21.38/9.10 U74(active(X)) -> U74(X) 21.38/9.10 U81(active(X1), X2) -> U81(X1, X2) 21.38/9.10 U81(X1, active(X2)) -> U81(X1, X2) 21.38/9.10 U82(active(X1), X2) -> U82(X1, X2) 21.38/9.10 U82(X1, active(X2)) -> U82(X1, X2) 21.38/9.10 U83(active(X)) -> U83(X) 21.38/9.10 isNePal(active(X)) -> isNePal(X) 21.38/9.10 U91(active(X1), X2) -> U91(X1, X2) 21.38/9.10 U91(X1, active(X2)) -> U91(X1, X2) 21.38/9.10 U92(active(X)) -> U92(X) 21.38/9.10 21.38/9.10 21.38/9.10 21.38/9.10 21.38/9.10 ---------------------------------------- 21.38/9.10 21.38/9.10 (10) 21.38/9.10 Obligation: 21.38/9.10 Q restricted rewrite system: 21.38/9.10 R is empty. 21.38/9.10 The set Q consists of the following terms: 21.38/9.10 21.38/9.10 active(__(__(x0, x1), x2)) 21.38/9.10 active(__(x0, nil)) 21.38/9.10 active(__(nil, x0)) 21.65/9.10 active(U11(tt, x0)) 21.65/9.10 active(U12(tt, x0)) 21.65/9.10 active(U13(tt)) 21.65/9.10 active(U21(tt, x0, x1)) 21.65/9.10 active(U22(tt, x0, x1)) 21.65/9.10 active(U23(tt, x0, x1)) 21.65/9.10 active(U24(tt, x0, x1)) 21.65/9.10 active(U25(tt, x0)) 21.65/9.10 active(U26(tt)) 21.65/9.10 active(U31(tt, x0)) 21.65/9.10 active(U32(tt, x0)) 21.65/9.10 active(U33(tt)) 21.65/9.10 active(U41(tt, x0, x1)) 21.65/9.10 active(U42(tt, x0, x1)) 21.65/9.10 active(U43(tt, x0, x1)) 21.65/9.10 active(U44(tt, x0, x1)) 21.65/9.10 active(U45(tt, x0)) 21.65/9.10 active(U46(tt)) 21.65/9.10 active(U51(tt, x0, x1)) 21.65/9.10 active(U52(tt, x0, x1)) 21.65/9.10 active(U53(tt, x0, x1)) 21.65/9.10 active(U54(tt, x0, x1)) 21.65/9.10 active(U55(tt, x0)) 21.65/9.10 active(U56(tt)) 21.65/9.10 active(U61(tt, x0)) 21.65/9.10 active(U62(tt, x0)) 21.65/9.10 active(U63(tt)) 21.65/9.10 active(U71(tt, x0, x1)) 21.65/9.10 active(U72(tt, x0)) 21.65/9.10 active(U73(tt, x0)) 21.65/9.10 active(U74(tt)) 21.65/9.10 active(U81(tt, x0)) 21.65/9.10 active(U82(tt, x0)) 21.65/9.10 active(U83(tt)) 21.65/9.10 active(U91(tt, x0)) 21.65/9.10 active(U92(tt)) 21.65/9.10 active(isList(x0)) 21.65/9.10 active(isNeList(x0)) 21.65/9.10 active(isNePal(x0)) 21.65/9.10 active(isPal(x0)) 21.65/9.10 active(isPalListKind(a)) 21.65/9.10 active(isPalListKind(e)) 21.65/9.10 active(isPalListKind(i)) 21.65/9.10 active(isPalListKind(nil)) 21.65/9.10 active(isPalListKind(o)) 21.65/9.10 active(isPalListKind(u)) 21.65/9.10 active(isPalListKind(__(x0, x1))) 21.65/9.10 active(isQid(a)) 21.65/9.10 active(isQid(e)) 21.65/9.10 active(isQid(i)) 21.65/9.10 active(isQid(o)) 21.65/9.10 active(isQid(u)) 21.65/9.10 mark(__(x0, x1)) 21.65/9.10 mark(nil) 21.65/9.10 mark(U11(x0, x1)) 21.65/9.10 mark(tt) 21.65/9.10 mark(U12(x0, x1)) 21.65/9.10 mark(isPalListKind(x0)) 21.65/9.10 mark(U13(x0)) 21.65/9.10 mark(isNeList(x0)) 21.65/9.10 mark(U21(x0, x1, x2)) 21.65/9.10 mark(U22(x0, x1, x2)) 21.65/9.10 mark(U23(x0, x1, x2)) 21.65/9.10 mark(U24(x0, x1, x2)) 21.65/9.10 mark(U25(x0, x1)) 21.65/9.10 mark(isList(x0)) 21.65/9.10 mark(U26(x0)) 21.65/9.10 mark(U31(x0, x1)) 21.65/9.10 mark(U32(x0, x1)) 21.65/9.10 mark(U33(x0)) 21.65/9.10 mark(isQid(x0)) 21.65/9.10 mark(U41(x0, x1, x2)) 21.65/9.10 mark(U42(x0, x1, x2)) 21.65/9.10 mark(U43(x0, x1, x2)) 21.65/9.10 mark(U44(x0, x1, x2)) 21.65/9.10 mark(U45(x0, x1)) 21.65/9.10 mark(U46(x0)) 21.65/9.10 mark(U51(x0, x1, x2)) 21.65/9.10 mark(U52(x0, x1, x2)) 21.65/9.10 mark(U53(x0, x1, x2)) 21.65/9.10 mark(U54(x0, x1, x2)) 21.65/9.10 mark(U55(x0, x1)) 21.65/9.10 mark(U56(x0)) 21.65/9.10 mark(U61(x0, x1)) 21.65/9.10 mark(U62(x0, x1)) 21.65/9.10 mark(U63(x0)) 21.65/9.10 mark(U71(x0, x1, x2)) 21.65/9.10 mark(U72(x0, x1)) 21.65/9.10 mark(U73(x0, x1)) 21.65/9.10 mark(isPal(x0)) 21.65/9.10 mark(U74(x0)) 21.65/9.10 mark(U81(x0, x1)) 21.65/9.10 mark(U82(x0, x1)) 21.65/9.10 mark(U83(x0)) 21.65/9.10 mark(isNePal(x0)) 21.65/9.10 mark(U91(x0, x1)) 21.65/9.10 mark(U92(x0)) 21.65/9.10 mark(a) 21.65/9.10 mark(e) 21.65/9.10 mark(i) 21.65/9.10 mark(o) 21.65/9.10 mark(u) 21.65/9.10 __(mark(x0), x1) 21.65/9.10 __(x0, mark(x1)) 21.65/9.10 __(active(x0), x1) 21.65/9.10 __(x0, active(x1)) 21.65/9.10 U11(mark(x0), x1) 21.65/9.10 U11(x0, mark(x1)) 21.65/9.10 U11(active(x0), x1) 21.65/9.10 U11(x0, active(x1)) 21.65/9.10 U12(mark(x0), x1) 21.65/9.10 U12(x0, mark(x1)) 21.65/9.10 U12(active(x0), x1) 21.65/9.10 U12(x0, active(x1)) 21.65/9.10 isPalListKind(mark(x0)) 21.65/9.10 isPalListKind(active(x0)) 21.65/9.10 U13(mark(x0)) 21.65/9.10 U13(active(x0)) 21.65/9.10 isNeList(mark(x0)) 21.65/9.10 isNeList(active(x0)) 21.65/9.10 U21(mark(x0), x1, x2) 21.65/9.10 U21(x0, mark(x1), x2) 21.65/9.10 U21(x0, x1, mark(x2)) 21.65/9.10 U21(active(x0), x1, x2) 21.65/9.10 U21(x0, active(x1), x2) 21.65/9.10 U21(x0, x1, active(x2)) 21.65/9.10 U22(mark(x0), x1, x2) 21.65/9.10 U22(x0, mark(x1), x2) 21.65/9.10 U22(x0, x1, mark(x2)) 21.65/9.10 U22(active(x0), x1, x2) 21.65/9.10 U22(x0, active(x1), x2) 21.65/9.10 U22(x0, x1, active(x2)) 21.65/9.10 U23(mark(x0), x1, x2) 21.65/9.10 U23(x0, mark(x1), x2) 21.65/9.10 U23(x0, x1, mark(x2)) 21.65/9.10 U23(active(x0), x1, x2) 21.65/9.10 U23(x0, active(x1), x2) 21.65/9.10 U23(x0, x1, active(x2)) 21.65/9.10 U24(mark(x0), x1, x2) 21.65/9.10 U24(x0, mark(x1), x2) 21.65/9.10 U24(x0, x1, mark(x2)) 21.65/9.10 U24(active(x0), x1, x2) 21.65/9.10 U24(x0, active(x1), x2) 21.65/9.10 U24(x0, x1, active(x2)) 21.65/9.10 U25(mark(x0), x1) 21.65/9.10 U25(x0, mark(x1)) 21.65/9.10 U25(active(x0), x1) 21.65/9.10 U25(x0, active(x1)) 21.65/9.10 isList(mark(x0)) 21.65/9.10 isList(active(x0)) 21.65/9.10 U26(mark(x0)) 21.65/9.10 U26(active(x0)) 21.65/9.10 U31(mark(x0), x1) 21.65/9.10 U31(x0, mark(x1)) 21.65/9.10 U31(active(x0), x1) 21.65/9.10 U31(x0, active(x1)) 21.65/9.10 U32(mark(x0), x1) 21.65/9.10 U32(x0, mark(x1)) 21.65/9.10 U32(active(x0), x1) 21.65/9.10 U32(x0, active(x1)) 21.65/9.10 U33(mark(x0)) 21.65/9.10 U33(active(x0)) 21.65/9.10 isQid(mark(x0)) 21.65/9.10 isQid(active(x0)) 21.65/9.10 U41(mark(x0), x1, x2) 21.65/9.10 U41(x0, mark(x1), x2) 21.65/9.10 U41(x0, x1, mark(x2)) 21.65/9.10 U41(active(x0), x1, x2) 21.65/9.10 U41(x0, active(x1), x2) 21.65/9.10 U41(x0, x1, active(x2)) 21.65/9.10 U42(mark(x0), x1, x2) 21.65/9.10 U42(x0, mark(x1), x2) 21.65/9.10 U42(x0, x1, mark(x2)) 21.65/9.10 U42(active(x0), x1, x2) 21.65/9.10 U42(x0, active(x1), x2) 21.65/9.10 U42(x0, x1, active(x2)) 21.65/9.10 U43(mark(x0), x1, x2) 21.65/9.10 U43(x0, mark(x1), x2) 21.65/9.10 U43(x0, x1, mark(x2)) 21.65/9.10 U43(active(x0), x1, x2) 21.65/9.10 U43(x0, active(x1), x2) 21.65/9.10 U43(x0, x1, active(x2)) 21.65/9.10 U44(mark(x0), x1, x2) 21.65/9.10 U44(x0, mark(x1), x2) 21.65/9.10 U44(x0, x1, mark(x2)) 21.65/9.10 U44(active(x0), x1, x2) 21.65/9.10 U44(x0, active(x1), x2) 21.65/9.10 U44(x0, x1, active(x2)) 21.65/9.10 U45(mark(x0), x1) 21.65/9.10 U45(x0, mark(x1)) 21.65/9.10 U45(active(x0), x1) 21.65/9.10 U45(x0, active(x1)) 21.65/9.10 U46(mark(x0)) 21.65/9.10 U46(active(x0)) 21.65/9.10 U51(mark(x0), x1, x2) 21.65/9.10 U51(x0, mark(x1), x2) 21.65/9.10 U51(x0, x1, mark(x2)) 21.65/9.10 U51(active(x0), x1, x2) 21.65/9.10 U51(x0, active(x1), x2) 21.65/9.10 U51(x0, x1, active(x2)) 21.65/9.10 U52(mark(x0), x1, x2) 21.65/9.10 U52(x0, mark(x1), x2) 21.65/9.10 U52(x0, x1, mark(x2)) 21.65/9.10 U52(active(x0), x1, x2) 21.65/9.10 U52(x0, active(x1), x2) 21.65/9.10 U52(x0, x1, active(x2)) 21.65/9.10 U53(mark(x0), x1, x2) 21.65/9.10 U53(x0, mark(x1), x2) 21.65/9.10 U53(x0, x1, mark(x2)) 21.65/9.10 U53(active(x0), x1, x2) 21.65/9.10 U53(x0, active(x1), x2) 21.65/9.10 U53(x0, x1, active(x2)) 21.65/9.10 U54(mark(x0), x1, x2) 21.65/9.10 U54(x0, mark(x1), x2) 21.65/9.10 U54(x0, x1, mark(x2)) 21.65/9.10 U54(active(x0), x1, x2) 21.65/9.10 U54(x0, active(x1), x2) 21.65/9.10 U54(x0, x1, active(x2)) 21.65/9.10 U55(mark(x0), x1) 21.65/9.10 U55(x0, mark(x1)) 21.65/9.10 U55(active(x0), x1) 21.65/9.10 U55(x0, active(x1)) 21.65/9.10 U56(mark(x0)) 21.65/9.10 U56(active(x0)) 21.65/9.10 U61(mark(x0), x1) 21.65/9.10 U61(x0, mark(x1)) 21.65/9.10 U61(active(x0), x1) 21.65/9.10 U61(x0, active(x1)) 21.65/9.10 U62(mark(x0), x1) 21.65/9.10 U62(x0, mark(x1)) 21.65/9.10 U62(active(x0), x1) 21.65/9.10 U62(x0, active(x1)) 21.65/9.10 U63(mark(x0)) 21.65/9.10 U63(active(x0)) 21.65/9.10 U71(mark(x0), x1, x2) 21.65/9.10 U71(x0, mark(x1), x2) 21.65/9.10 U71(x0, x1, mark(x2)) 21.65/9.10 U71(active(x0), x1, x2) 21.65/9.10 U71(x0, active(x1), x2) 21.65/9.10 U71(x0, x1, active(x2)) 21.65/9.10 U72(mark(x0), x1) 21.65/9.10 U72(x0, mark(x1)) 21.65/9.10 U72(active(x0), x1) 21.65/9.10 U72(x0, active(x1)) 21.65/9.10 U73(mark(x0), x1) 21.65/9.10 U73(x0, mark(x1)) 21.65/9.10 U73(active(x0), x1) 21.65/9.10 U73(x0, active(x1)) 21.65/9.10 isPal(mark(x0)) 21.65/9.10 isPal(active(x0)) 21.65/9.10 U74(mark(x0)) 21.65/9.10 U74(active(x0)) 21.65/9.10 U81(mark(x0), x1) 21.65/9.10 U81(x0, mark(x1)) 21.65/9.10 U81(active(x0), x1) 21.65/9.10 U81(x0, active(x1)) 21.65/9.10 U82(mark(x0), x1) 21.65/9.10 U82(x0, mark(x1)) 21.65/9.10 U82(active(x0), x1) 21.65/9.10 U82(x0, active(x1)) 21.65/9.10 U83(mark(x0)) 21.65/9.10 U83(active(x0)) 21.65/9.10 isNePal(mark(x0)) 21.65/9.10 isNePal(active(x0)) 21.65/9.10 U91(mark(x0), x1) 21.65/9.10 U91(x0, mark(x1)) 21.65/9.10 U91(active(x0), x1) 21.65/9.10 U91(x0, active(x1)) 21.65/9.10 U92(mark(x0)) 21.65/9.10 U92(active(x0)) 21.65/9.10 21.65/9.10 21.65/9.10 ---------------------------------------- 21.65/9.10 21.65/9.10 (11) RisEmptyProof (EQUIVALENT) 21.65/9.10 The TRS R is empty. Hence, termination is trivially proven. 21.65/9.10 ---------------------------------------- 21.65/9.10 21.65/9.10 (12) 21.65/9.10 YES 21.65/9.14 EOF