10.01/3.46 YES 10.01/3.48 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 10.01/3.48 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 10.01/3.48 10.01/3.48 10.01/3.48 Termination w.r.t. Q of the given QTRS could be proven: 10.01/3.48 10.01/3.48 (0) QTRS 10.01/3.48 (1) QTRSRRRProof [EQUIVALENT, 1134 ms] 10.01/3.48 (2) QTRS 10.01/3.48 (3) QTRSRRRProof [EQUIVALENT, 223 ms] 10.01/3.48 (4) QTRS 10.01/3.48 (5) QTRSRRRProof [EQUIVALENT, 19 ms] 10.01/3.48 (6) QTRS 10.01/3.48 (7) RisEmptyProof [EQUIVALENT, 0 ms] 10.01/3.48 (8) YES 10.01/3.48 10.01/3.48 10.01/3.48 ---------------------------------------- 10.01/3.48 10.01/3.48 (0) 10.01/3.48 Obligation: 10.01/3.48 Q restricted rewrite system: 10.01/3.48 The TRS R consists of the following rules: 10.01/3.48 10.01/3.48 active(__(__(X, Y), Z)) -> mark(__(X, __(Y, Z))) 10.01/3.48 active(__(X, nil)) -> mark(X) 10.01/3.48 active(__(nil, X)) -> mark(X) 10.01/3.48 active(U11(tt, V)) -> mark(U12(isNeList(V))) 10.01/3.48 active(U12(tt)) -> mark(tt) 10.01/3.48 active(U21(tt, V1, V2)) -> mark(U22(isList(V1), V2)) 10.01/3.48 active(U22(tt, V2)) -> mark(U23(isList(V2))) 10.01/3.48 active(U23(tt)) -> mark(tt) 10.01/3.48 active(U31(tt, V)) -> mark(U32(isQid(V))) 10.01/3.48 active(U32(tt)) -> mark(tt) 10.01/3.48 active(U41(tt, V1, V2)) -> mark(U42(isList(V1), V2)) 10.01/3.48 active(U42(tt, V2)) -> mark(U43(isNeList(V2))) 10.01/3.48 active(U43(tt)) -> mark(tt) 10.01/3.48 active(U51(tt, V1, V2)) -> mark(U52(isNeList(V1), V2)) 10.01/3.48 active(U52(tt, V2)) -> mark(U53(isList(V2))) 10.01/3.48 active(U53(tt)) -> mark(tt) 10.01/3.48 active(U61(tt, V)) -> mark(U62(isQid(V))) 10.01/3.48 active(U62(tt)) -> mark(tt) 10.01/3.48 active(U71(tt, V)) -> mark(U72(isNePal(V))) 10.01/3.48 active(U72(tt)) -> mark(tt) 10.01/3.48 active(and(tt, X)) -> mark(X) 10.01/3.48 active(isList(V)) -> mark(U11(isPalListKind(V), V)) 10.01/3.48 active(isList(nil)) -> mark(tt) 10.01/3.48 active(isList(__(V1, V2))) -> mark(U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)) 10.01/3.48 active(isNeList(V)) -> mark(U31(isPalListKind(V), V)) 10.01/3.48 active(isNeList(__(V1, V2))) -> mark(U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)) 10.01/3.48 active(isNeList(__(V1, V2))) -> mark(U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)) 10.01/3.48 active(isNePal(V)) -> mark(U61(isPalListKind(V), V)) 10.01/3.48 active(isNePal(__(I, __(P, I)))) -> mark(and(and(isQid(I), isPalListKind(I)), and(isPal(P), isPalListKind(P)))) 10.01/3.48 active(isPal(V)) -> mark(U71(isPalListKind(V), V)) 10.01/3.48 active(isPal(nil)) -> mark(tt) 10.01/3.48 active(isPalListKind(a)) -> mark(tt) 10.01/3.48 active(isPalListKind(e)) -> mark(tt) 10.01/3.48 active(isPalListKind(i)) -> mark(tt) 10.01/3.48 active(isPalListKind(nil)) -> mark(tt) 10.01/3.48 active(isPalListKind(o)) -> mark(tt) 10.01/3.48 active(isPalListKind(u)) -> mark(tt) 10.01/3.48 active(isPalListKind(__(V1, V2))) -> mark(and(isPalListKind(V1), isPalListKind(V2))) 10.01/3.48 active(isQid(a)) -> mark(tt) 10.01/3.48 active(isQid(e)) -> mark(tt) 10.01/3.48 active(isQid(i)) -> mark(tt) 10.01/3.48 active(isQid(o)) -> mark(tt) 10.01/3.48 active(isQid(u)) -> mark(tt) 10.01/3.48 mark(__(X1, X2)) -> active(__(mark(X1), mark(X2))) 10.01/3.48 mark(nil) -> active(nil) 10.01/3.48 mark(U11(X1, X2)) -> active(U11(mark(X1), X2)) 10.01/3.48 mark(tt) -> active(tt) 10.01/3.48 mark(U12(X)) -> active(U12(mark(X))) 10.01/3.48 mark(isNeList(X)) -> active(isNeList(X)) 10.01/3.48 mark(U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)) 10.01/3.48 mark(U22(X1, X2)) -> active(U22(mark(X1), X2)) 10.01/3.48 mark(isList(X)) -> active(isList(X)) 10.01/3.48 mark(U23(X)) -> active(U23(mark(X))) 10.01/3.48 mark(U31(X1, X2)) -> active(U31(mark(X1), X2)) 10.01/3.48 mark(U32(X)) -> active(U32(mark(X))) 10.01/3.48 mark(isQid(X)) -> active(isQid(X)) 10.01/3.48 mark(U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3)) 10.01/3.48 mark(U42(X1, X2)) -> active(U42(mark(X1), X2)) 10.01/3.48 mark(U43(X)) -> active(U43(mark(X))) 10.01/3.48 mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)) 10.01/3.48 mark(U52(X1, X2)) -> active(U52(mark(X1), X2)) 10.01/3.48 mark(U53(X)) -> active(U53(mark(X))) 10.01/3.48 mark(U61(X1, X2)) -> active(U61(mark(X1), X2)) 10.01/3.48 mark(U62(X)) -> active(U62(mark(X))) 10.01/3.48 mark(U71(X1, X2)) -> active(U71(mark(X1), X2)) 10.01/3.48 mark(U72(X)) -> active(U72(mark(X))) 10.01/3.48 mark(isNePal(X)) -> active(isNePal(X)) 10.01/3.48 mark(and(X1, X2)) -> active(and(mark(X1), X2)) 10.01/3.48 mark(isPalListKind(X)) -> active(isPalListKind(X)) 10.01/3.48 mark(isPal(X)) -> active(isPal(X)) 10.01/3.48 mark(a) -> active(a) 10.01/3.48 mark(e) -> active(e) 10.01/3.48 mark(i) -> active(i) 10.01/3.48 mark(o) -> active(o) 10.01/3.48 mark(u) -> active(u) 10.01/3.48 __(mark(X1), X2) -> __(X1, X2) 10.01/3.48 __(X1, mark(X2)) -> __(X1, X2) 10.01/3.48 __(active(X1), X2) -> __(X1, X2) 10.01/3.48 __(X1, active(X2)) -> __(X1, X2) 10.01/3.48 U11(mark(X1), X2) -> U11(X1, X2) 10.01/3.48 U11(X1, mark(X2)) -> U11(X1, X2) 10.01/3.48 U11(active(X1), X2) -> U11(X1, X2) 10.01/3.48 U11(X1, active(X2)) -> U11(X1, X2) 10.01/3.48 U12(mark(X)) -> U12(X) 10.01/3.48 U12(active(X)) -> U12(X) 10.01/3.48 isNeList(mark(X)) -> isNeList(X) 10.01/3.48 isNeList(active(X)) -> isNeList(X) 10.01/3.48 U21(mark(X1), X2, X3) -> U21(X1, X2, X3) 10.01/3.48 U21(X1, mark(X2), X3) -> U21(X1, X2, X3) 10.01/3.48 U21(X1, X2, mark(X3)) -> U21(X1, X2, X3) 10.01/3.48 U21(active(X1), X2, X3) -> U21(X1, X2, X3) 10.01/3.48 U21(X1, active(X2), X3) -> U21(X1, X2, X3) 10.01/3.48 U21(X1, X2, active(X3)) -> U21(X1, X2, X3) 10.01/3.48 U22(mark(X1), X2) -> U22(X1, X2) 10.01/3.48 U22(X1, mark(X2)) -> U22(X1, X2) 10.01/3.48 U22(active(X1), X2) -> U22(X1, X2) 10.01/3.48 U22(X1, active(X2)) -> U22(X1, X2) 10.01/3.48 isList(mark(X)) -> isList(X) 10.01/3.48 isList(active(X)) -> isList(X) 10.01/3.48 U23(mark(X)) -> U23(X) 10.01/3.48 U23(active(X)) -> U23(X) 10.01/3.48 U31(mark(X1), X2) -> U31(X1, X2) 10.01/3.48 U31(X1, mark(X2)) -> U31(X1, X2) 10.01/3.48 U31(active(X1), X2) -> U31(X1, X2) 10.01/3.48 U31(X1, active(X2)) -> U31(X1, X2) 10.01/3.48 U32(mark(X)) -> U32(X) 10.01/3.48 U32(active(X)) -> U32(X) 10.01/3.48 isQid(mark(X)) -> isQid(X) 10.01/3.48 isQid(active(X)) -> isQid(X) 10.01/3.48 U41(mark(X1), X2, X3) -> U41(X1, X2, X3) 10.01/3.48 U41(X1, mark(X2), X3) -> U41(X1, X2, X3) 10.01/3.48 U41(X1, X2, mark(X3)) -> U41(X1, X2, X3) 10.01/3.48 U41(active(X1), X2, X3) -> U41(X1, X2, X3) 10.01/3.48 U41(X1, active(X2), X3) -> U41(X1, X2, X3) 10.01/3.48 U41(X1, X2, active(X3)) -> U41(X1, X2, X3) 10.01/3.48 U42(mark(X1), X2) -> U42(X1, X2) 10.01/3.48 U42(X1, mark(X2)) -> U42(X1, X2) 10.01/3.48 U42(active(X1), X2) -> U42(X1, X2) 10.01/3.48 U42(X1, active(X2)) -> U42(X1, X2) 10.01/3.48 U43(mark(X)) -> U43(X) 10.01/3.48 U43(active(X)) -> U43(X) 10.01/3.48 U51(mark(X1), X2, X3) -> U51(X1, X2, X3) 10.01/3.48 U51(X1, mark(X2), X3) -> U51(X1, X2, X3) 10.01/3.48 U51(X1, X2, mark(X3)) -> U51(X1, X2, X3) 10.01/3.48 U51(active(X1), X2, X3) -> U51(X1, X2, X3) 10.01/3.48 U51(X1, active(X2), X3) -> U51(X1, X2, X3) 10.01/3.48 U51(X1, X2, active(X3)) -> U51(X1, X2, X3) 10.01/3.48 U52(mark(X1), X2) -> U52(X1, X2) 10.01/3.48 U52(X1, mark(X2)) -> U52(X1, X2) 10.01/3.48 U52(active(X1), X2) -> U52(X1, X2) 10.01/3.48 U52(X1, active(X2)) -> U52(X1, X2) 10.01/3.48 U53(mark(X)) -> U53(X) 10.01/3.48 U53(active(X)) -> U53(X) 10.01/3.48 U61(mark(X1), X2) -> U61(X1, X2) 10.01/3.48 U61(X1, mark(X2)) -> U61(X1, X2) 10.01/3.48 U61(active(X1), X2) -> U61(X1, X2) 10.01/3.48 U61(X1, active(X2)) -> U61(X1, X2) 10.01/3.48 U62(mark(X)) -> U62(X) 10.01/3.48 U62(active(X)) -> U62(X) 10.01/3.48 U71(mark(X1), X2) -> U71(X1, X2) 10.01/3.48 U71(X1, mark(X2)) -> U71(X1, X2) 10.01/3.48 U71(active(X1), X2) -> U71(X1, X2) 10.01/3.48 U71(X1, active(X2)) -> U71(X1, X2) 10.01/3.48 U72(mark(X)) -> U72(X) 10.01/3.48 U72(active(X)) -> U72(X) 10.01/3.48 isNePal(mark(X)) -> isNePal(X) 10.01/3.48 isNePal(active(X)) -> isNePal(X) 10.01/3.48 and(mark(X1), X2) -> and(X1, X2) 10.01/3.48 and(X1, mark(X2)) -> and(X1, X2) 10.01/3.48 and(active(X1), X2) -> and(X1, X2) 10.01/3.48 and(X1, active(X2)) -> and(X1, X2) 10.01/3.48 isPalListKind(mark(X)) -> isPalListKind(X) 10.01/3.48 isPalListKind(active(X)) -> isPalListKind(X) 10.01/3.48 isPal(mark(X)) -> isPal(X) 10.01/3.48 isPal(active(X)) -> isPal(X) 10.01/3.48 10.01/3.48 The set Q consists of the following terms: 10.01/3.48 10.01/3.48 active(__(__(x0, x1), x2)) 10.01/3.48 active(__(x0, nil)) 10.01/3.48 active(__(nil, x0)) 10.01/3.48 active(U11(tt, x0)) 10.01/3.48 active(U12(tt)) 10.01/3.48 active(U21(tt, x0, x1)) 10.01/3.48 active(U22(tt, x0)) 10.01/3.48 active(U23(tt)) 10.01/3.48 active(U31(tt, x0)) 10.01/3.48 active(U32(tt)) 10.01/3.48 active(U41(tt, x0, x1)) 10.01/3.48 active(U42(tt, x0)) 10.01/3.48 active(U43(tt)) 10.01/3.48 active(U51(tt, x0, x1)) 10.01/3.48 active(U52(tt, x0)) 10.01/3.48 active(U53(tt)) 10.01/3.48 active(U61(tt, x0)) 10.01/3.48 active(U62(tt)) 10.01/3.48 active(U71(tt, x0)) 10.01/3.48 active(U72(tt)) 10.01/3.48 active(and(tt, x0)) 10.01/3.48 active(isList(x0)) 10.01/3.48 active(isNeList(x0)) 10.01/3.48 active(isNePal(x0)) 10.01/3.48 active(isPal(x0)) 10.01/3.48 active(isPalListKind(a)) 10.01/3.48 active(isPalListKind(e)) 10.01/3.48 active(isPalListKind(i)) 10.01/3.48 active(isPalListKind(nil)) 10.01/3.48 active(isPalListKind(o)) 10.01/3.48 active(isPalListKind(u)) 10.01/3.48 active(isPalListKind(__(x0, x1))) 10.01/3.48 active(isQid(a)) 10.01/3.48 active(isQid(e)) 10.01/3.48 active(isQid(i)) 10.01/3.48 active(isQid(o)) 10.01/3.48 active(isQid(u)) 10.01/3.48 mark(__(x0, x1)) 10.01/3.48 mark(nil) 10.01/3.48 mark(U11(x0, x1)) 10.01/3.48 mark(tt) 10.01/3.48 mark(U12(x0)) 10.01/3.48 mark(isNeList(x0)) 10.01/3.48 mark(U21(x0, x1, x2)) 10.01/3.48 mark(U22(x0, x1)) 10.01/3.48 mark(isList(x0)) 10.01/3.48 mark(U23(x0)) 10.01/3.48 mark(U31(x0, x1)) 10.01/3.48 mark(U32(x0)) 10.01/3.48 mark(isQid(x0)) 10.01/3.48 mark(U41(x0, x1, x2)) 10.01/3.48 mark(U42(x0, x1)) 10.01/3.48 mark(U43(x0)) 10.01/3.48 mark(U51(x0, x1, x2)) 10.01/3.48 mark(U52(x0, x1)) 10.01/3.48 mark(U53(x0)) 10.01/3.48 mark(U61(x0, x1)) 10.01/3.48 mark(U62(x0)) 10.01/3.48 mark(U71(x0, x1)) 10.01/3.48 mark(U72(x0)) 10.01/3.48 mark(isNePal(x0)) 10.01/3.48 mark(and(x0, x1)) 10.01/3.48 mark(isPalListKind(x0)) 10.01/3.48 mark(isPal(x0)) 10.01/3.48 mark(a) 10.01/3.48 mark(e) 10.01/3.48 mark(i) 10.01/3.48 mark(o) 10.01/3.48 mark(u) 10.01/3.48 __(mark(x0), x1) 10.01/3.48 __(x0, mark(x1)) 10.01/3.48 __(active(x0), x1) 10.01/3.48 __(x0, active(x1)) 10.01/3.48 U11(mark(x0), x1) 10.01/3.48 U11(x0, mark(x1)) 10.01/3.48 U11(active(x0), x1) 10.01/3.48 U11(x0, active(x1)) 10.01/3.48 U12(mark(x0)) 10.01/3.48 U12(active(x0)) 10.01/3.48 isNeList(mark(x0)) 10.01/3.48 isNeList(active(x0)) 10.01/3.48 U21(mark(x0), x1, x2) 10.01/3.48 U21(x0, mark(x1), x2) 10.01/3.48 U21(x0, x1, mark(x2)) 10.01/3.48 U21(active(x0), x1, x2) 10.01/3.48 U21(x0, active(x1), x2) 10.01/3.48 U21(x0, x1, active(x2)) 10.01/3.48 U22(mark(x0), x1) 10.01/3.48 U22(x0, mark(x1)) 10.01/3.48 U22(active(x0), x1) 10.01/3.48 U22(x0, active(x1)) 10.01/3.48 isList(mark(x0)) 10.01/3.48 isList(active(x0)) 10.01/3.48 U23(mark(x0)) 10.01/3.48 U23(active(x0)) 10.01/3.48 U31(mark(x0), x1) 10.01/3.48 U31(x0, mark(x1)) 10.01/3.48 U31(active(x0), x1) 10.01/3.48 U31(x0, active(x1)) 10.01/3.48 U32(mark(x0)) 10.01/3.48 U32(active(x0)) 10.01/3.48 isQid(mark(x0)) 10.01/3.48 isQid(active(x0)) 10.01/3.48 U41(mark(x0), x1, x2) 10.01/3.48 U41(x0, mark(x1), x2) 10.01/3.48 U41(x0, x1, mark(x2)) 10.01/3.48 U41(active(x0), x1, x2) 10.01/3.48 U41(x0, active(x1), x2) 10.01/3.48 U41(x0, x1, active(x2)) 10.01/3.48 U42(mark(x0), x1) 10.01/3.48 U42(x0, mark(x1)) 10.01/3.48 U42(active(x0), x1) 10.01/3.48 U42(x0, active(x1)) 10.01/3.48 U43(mark(x0)) 10.01/3.48 U43(active(x0)) 10.01/3.48 U51(mark(x0), x1, x2) 10.01/3.48 U51(x0, mark(x1), x2) 10.01/3.48 U51(x0, x1, mark(x2)) 10.01/3.48 U51(active(x0), x1, x2) 10.01/3.48 U51(x0, active(x1), x2) 10.01/3.48 U51(x0, x1, active(x2)) 10.01/3.48 U52(mark(x0), x1) 10.01/3.48 U52(x0, mark(x1)) 10.01/3.48 U52(active(x0), x1) 10.01/3.48 U52(x0, active(x1)) 10.01/3.48 U53(mark(x0)) 10.01/3.48 U53(active(x0)) 10.01/3.48 U61(mark(x0), x1) 10.01/3.48 U61(x0, mark(x1)) 10.01/3.48 U61(active(x0), x1) 10.01/3.48 U61(x0, active(x1)) 10.01/3.48 U62(mark(x0)) 10.01/3.48 U62(active(x0)) 10.01/3.48 U71(mark(x0), x1) 10.01/3.48 U71(x0, mark(x1)) 10.01/3.48 U71(active(x0), x1) 10.01/3.48 U71(x0, active(x1)) 10.01/3.48 U72(mark(x0)) 10.01/3.48 U72(active(x0)) 10.01/3.48 isNePal(mark(x0)) 10.01/3.48 isNePal(active(x0)) 10.01/3.48 and(mark(x0), x1) 10.01/3.48 and(x0, mark(x1)) 10.01/3.48 and(active(x0), x1) 10.01/3.48 and(x0, active(x1)) 10.01/3.48 isPalListKind(mark(x0)) 10.01/3.48 isPalListKind(active(x0)) 10.01/3.48 isPal(mark(x0)) 10.01/3.48 isPal(active(x0)) 10.01/3.48 10.01/3.48 10.01/3.48 ---------------------------------------- 10.01/3.48 10.01/3.48 (1) QTRSRRRProof (EQUIVALENT) 10.01/3.48 Used ordering: 10.01/3.48 active/1)YES( 10.01/3.48 __/2(YES,YES) 10.01/3.48 mark/1)YES( 10.01/3.48 nil/0) 10.01/3.48 U11/2(YES,YES) 10.01/3.48 tt/0) 10.01/3.48 U12/1)YES( 10.01/3.48 isNeList/1(YES) 10.01/3.48 U21/3(YES,YES,YES) 10.01/3.48 U22/2(YES,YES) 10.01/3.48 isList/1(YES) 10.01/3.48 U23/1)YES( 10.01/3.48 U31/2(YES,YES) 10.01/3.48 U32/1)YES( 10.01/3.48 isQid/1)YES( 10.01/3.48 U41/3(YES,YES,YES) 10.01/3.48 U42/2(YES,YES) 10.01/3.48 U43/1)YES( 10.01/3.48 U51/3(YES,YES,YES) 10.01/3.48 U52/2(YES,YES) 10.01/3.48 U53/1)YES( 10.01/3.48 U61/2(YES,YES) 10.01/3.48 U62/1)YES( 10.01/3.48 U71/2(YES,YES) 10.01/3.48 U72/1)YES( 10.01/3.48 isNePal/1(YES) 10.01/3.48 and/2(YES,YES) 10.01/3.48 isPalListKind/1)YES( 10.01/3.48 isPal/1(YES) 10.01/3.48 a/0) 10.01/3.48 e/0) 10.01/3.48 i/0) 10.01/3.48 o/0) 10.01/3.48 u/0) 10.01/3.48 10.01/3.48 Quasi precedence: 10.01/3.48 ___2 > U21_3 > U22_2 > [isList_1, U52_2] > [U11_2, isNeList_1, U42_2] > U31_2 10.01/3.48 ___2 > U41_3 > [isList_1, U52_2] > [U11_2, isNeList_1, U42_2] > U31_2 10.01/3.48 ___2 > U51_3 > [isList_1, U52_2] > [U11_2, isNeList_1, U42_2] > U31_2 10.01/3.48 ___2 > and_2 10.01/3.48 ___2 > isPal_1 > U71_2 > isNePal_1 > U61_2 10.01/3.48 nil > [tt, e, i, u] > U22_2 > [isList_1, U52_2] > [U11_2, isNeList_1, U42_2] > U31_2 10.01/3.48 nil > [tt, e, i, u] > isNePal_1 > U61_2 10.01/3.48 a > [tt, e, i, u] > U22_2 > [isList_1, U52_2] > [U11_2, isNeList_1, U42_2] > U31_2 10.01/3.48 a > [tt, e, i, u] > isNePal_1 > U61_2 10.01/3.48 o > [tt, e, i, u] > U22_2 > [isList_1, U52_2] > [U11_2, isNeList_1, U42_2] > U31_2 10.01/3.48 o > [tt, e, i, u] > isNePal_1 > U61_2 10.01/3.48 10.01/3.48 10.01/3.48 Status: 10.01/3.48 ___2: [1,2] 10.01/3.48 nil: multiset status 10.01/3.48 U11_2: multiset status 10.01/3.48 tt: multiset status 10.01/3.48 isNeList_1: multiset status 10.01/3.48 U21_3: [1,2,3] 10.01/3.48 U22_2: multiset status 10.01/3.48 isList_1: multiset status 10.01/3.48 U31_2: multiset status 10.01/3.48 U41_3: [1,3,2] 10.01/3.48 U42_2: multiset status 10.01/3.48 U51_3: [1,2,3] 10.01/3.48 U52_2: multiset status 10.01/3.48 U61_2: multiset status 10.01/3.48 U71_2: multiset status 10.01/3.48 isNePal_1: multiset status 10.01/3.48 and_2: [2,1] 10.01/3.48 isPal_1: multiset status 10.01/3.48 a: multiset status 10.01/3.48 e: multiset status 10.01/3.48 i: multiset status 10.01/3.48 o: multiset status 10.01/3.48 u: multiset status 10.01/3.48 10.01/3.48 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 10.01/3.48 10.01/3.48 active(__(__(X, Y), Z)) -> mark(__(X, __(Y, Z))) 10.01/3.48 active(__(X, nil)) -> mark(X) 10.01/3.48 active(__(nil, X)) -> mark(X) 10.01/3.48 active(U11(tt, V)) -> mark(U12(isNeList(V))) 10.01/3.48 active(U21(tt, V1, V2)) -> mark(U22(isList(V1), V2)) 10.01/3.48 active(U22(tt, V2)) -> mark(U23(isList(V2))) 10.01/3.48 active(U31(tt, V)) -> mark(U32(isQid(V))) 10.01/3.48 active(U41(tt, V1, V2)) -> mark(U42(isList(V1), V2)) 10.01/3.48 active(U42(tt, V2)) -> mark(U43(isNeList(V2))) 10.01/3.48 active(U51(tt, V1, V2)) -> mark(U52(isNeList(V1), V2)) 10.01/3.48 active(U52(tt, V2)) -> mark(U53(isList(V2))) 10.01/3.48 active(U61(tt, V)) -> mark(U62(isQid(V))) 10.01/3.48 active(U71(tt, V)) -> mark(U72(isNePal(V))) 10.01/3.48 active(and(tt, X)) -> mark(X) 10.01/3.48 active(isList(V)) -> mark(U11(isPalListKind(V), V)) 10.01/3.48 active(isList(nil)) -> mark(tt) 10.01/3.48 active(isList(__(V1, V2))) -> mark(U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)) 10.01/3.48 active(isNeList(V)) -> mark(U31(isPalListKind(V), V)) 10.01/3.48 active(isNeList(__(V1, V2))) -> mark(U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)) 10.01/3.48 active(isNeList(__(V1, V2))) -> mark(U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)) 10.01/3.48 active(isNePal(V)) -> mark(U61(isPalListKind(V), V)) 10.01/3.48 active(isNePal(__(I, __(P, I)))) -> mark(and(and(isQid(I), isPalListKind(I)), and(isPal(P), isPalListKind(P)))) 10.01/3.48 active(isPal(V)) -> mark(U71(isPalListKind(V), V)) 10.01/3.48 active(isPal(nil)) -> mark(tt) 10.01/3.48 active(isPalListKind(a)) -> mark(tt) 10.01/3.48 active(isPalListKind(nil)) -> mark(tt) 10.01/3.48 active(isPalListKind(o)) -> mark(tt) 10.01/3.48 active(isPalListKind(__(V1, V2))) -> mark(and(isPalListKind(V1), isPalListKind(V2))) 10.01/3.48 active(isQid(a)) -> mark(tt) 10.01/3.48 active(isQid(o)) -> mark(tt) 10.01/3.48 10.01/3.48 10.01/3.48 10.01/3.48 10.01/3.48 ---------------------------------------- 10.01/3.48 10.01/3.48 (2) 10.01/3.48 Obligation: 10.01/3.48 Q restricted rewrite system: 10.01/3.48 The TRS R consists of the following rules: 10.01/3.48 10.01/3.48 active(U12(tt)) -> mark(tt) 10.01/3.48 active(U23(tt)) -> mark(tt) 10.01/3.48 active(U32(tt)) -> mark(tt) 10.01/3.48 active(U43(tt)) -> mark(tt) 10.01/3.48 active(U53(tt)) -> mark(tt) 10.01/3.48 active(U62(tt)) -> mark(tt) 10.01/3.48 active(U72(tt)) -> mark(tt) 10.01/3.48 active(isPalListKind(e)) -> mark(tt) 10.01/3.48 active(isPalListKind(i)) -> mark(tt) 10.01/3.48 active(isPalListKind(u)) -> mark(tt) 10.01/3.48 active(isQid(e)) -> mark(tt) 10.01/3.48 active(isQid(i)) -> mark(tt) 10.01/3.48 active(isQid(u)) -> mark(tt) 10.01/3.48 mark(__(X1, X2)) -> active(__(mark(X1), mark(X2))) 10.01/3.48 mark(nil) -> active(nil) 10.01/3.48 mark(U11(X1, X2)) -> active(U11(mark(X1), X2)) 10.01/3.48 mark(tt) -> active(tt) 10.01/3.48 mark(U12(X)) -> active(U12(mark(X))) 10.01/3.48 mark(isNeList(X)) -> active(isNeList(X)) 10.01/3.48 mark(U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)) 10.01/3.48 mark(U22(X1, X2)) -> active(U22(mark(X1), X2)) 10.01/3.48 mark(isList(X)) -> active(isList(X)) 10.01/3.48 mark(U23(X)) -> active(U23(mark(X))) 10.01/3.48 mark(U31(X1, X2)) -> active(U31(mark(X1), X2)) 10.01/3.48 mark(U32(X)) -> active(U32(mark(X))) 10.01/3.48 mark(isQid(X)) -> active(isQid(X)) 10.01/3.48 mark(U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3)) 10.01/3.48 mark(U42(X1, X2)) -> active(U42(mark(X1), X2)) 10.01/3.48 mark(U43(X)) -> active(U43(mark(X))) 10.01/3.48 mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)) 10.01/3.48 mark(U52(X1, X2)) -> active(U52(mark(X1), X2)) 10.01/3.48 mark(U53(X)) -> active(U53(mark(X))) 10.01/3.48 mark(U61(X1, X2)) -> active(U61(mark(X1), X2)) 10.01/3.48 mark(U62(X)) -> active(U62(mark(X))) 10.01/3.48 mark(U71(X1, X2)) -> active(U71(mark(X1), X2)) 10.01/3.48 mark(U72(X)) -> active(U72(mark(X))) 10.01/3.48 mark(isNePal(X)) -> active(isNePal(X)) 10.01/3.48 mark(and(X1, X2)) -> active(and(mark(X1), X2)) 10.01/3.48 mark(isPalListKind(X)) -> active(isPalListKind(X)) 10.01/3.48 mark(isPal(X)) -> active(isPal(X)) 10.01/3.48 mark(a) -> active(a) 10.01/3.48 mark(e) -> active(e) 10.01/3.48 mark(i) -> active(i) 10.01/3.48 mark(o) -> active(o) 10.01/3.48 mark(u) -> active(u) 10.01/3.48 __(mark(X1), X2) -> __(X1, X2) 10.01/3.48 __(X1, mark(X2)) -> __(X1, X2) 10.01/3.48 __(active(X1), X2) -> __(X1, X2) 10.01/3.48 __(X1, active(X2)) -> __(X1, X2) 10.01/3.48 U11(mark(X1), X2) -> U11(X1, X2) 10.01/3.48 U11(X1, mark(X2)) -> U11(X1, X2) 10.01/3.48 U11(active(X1), X2) -> U11(X1, X2) 10.01/3.48 U11(X1, active(X2)) -> U11(X1, X2) 10.01/3.48 U12(mark(X)) -> U12(X) 10.01/3.48 U12(active(X)) -> U12(X) 10.01/3.48 isNeList(mark(X)) -> isNeList(X) 10.01/3.48 isNeList(active(X)) -> isNeList(X) 10.01/3.48 U21(mark(X1), X2, X3) -> U21(X1, X2, X3) 10.01/3.48 U21(X1, mark(X2), X3) -> U21(X1, X2, X3) 10.01/3.48 U21(X1, X2, mark(X3)) -> U21(X1, X2, X3) 10.01/3.48 U21(active(X1), X2, X3) -> U21(X1, X2, X3) 10.01/3.48 U21(X1, active(X2), X3) -> U21(X1, X2, X3) 10.01/3.48 U21(X1, X2, active(X3)) -> U21(X1, X2, X3) 10.01/3.48 U22(mark(X1), X2) -> U22(X1, X2) 10.01/3.48 U22(X1, mark(X2)) -> U22(X1, X2) 10.01/3.48 U22(active(X1), X2) -> U22(X1, X2) 10.01/3.48 U22(X1, active(X2)) -> U22(X1, X2) 10.01/3.48 isList(mark(X)) -> isList(X) 10.01/3.48 isList(active(X)) -> isList(X) 10.01/3.48 U23(mark(X)) -> U23(X) 10.01/3.48 U23(active(X)) -> U23(X) 10.01/3.48 U31(mark(X1), X2) -> U31(X1, X2) 10.01/3.48 U31(X1, mark(X2)) -> U31(X1, X2) 10.01/3.48 U31(active(X1), X2) -> U31(X1, X2) 10.01/3.48 U31(X1, active(X2)) -> U31(X1, X2) 10.01/3.48 U32(mark(X)) -> U32(X) 10.01/3.48 U32(active(X)) -> U32(X) 10.01/3.48 isQid(mark(X)) -> isQid(X) 10.01/3.48 isQid(active(X)) -> isQid(X) 10.01/3.48 U41(mark(X1), X2, X3) -> U41(X1, X2, X3) 10.01/3.48 U41(X1, mark(X2), X3) -> U41(X1, X2, X3) 10.01/3.48 U41(X1, X2, mark(X3)) -> U41(X1, X2, X3) 10.01/3.48 U41(active(X1), X2, X3) -> U41(X1, X2, X3) 10.01/3.48 U41(X1, active(X2), X3) -> U41(X1, X2, X3) 10.01/3.48 U41(X1, X2, active(X3)) -> U41(X1, X2, X3) 10.01/3.48 U42(mark(X1), X2) -> U42(X1, X2) 10.01/3.48 U42(X1, mark(X2)) -> U42(X1, X2) 10.01/3.48 U42(active(X1), X2) -> U42(X1, X2) 10.01/3.48 U42(X1, active(X2)) -> U42(X1, X2) 10.01/3.48 U43(mark(X)) -> U43(X) 10.01/3.48 U43(active(X)) -> U43(X) 10.01/3.48 U51(mark(X1), X2, X3) -> U51(X1, X2, X3) 10.01/3.48 U51(X1, mark(X2), X3) -> U51(X1, X2, X3) 10.01/3.48 U51(X1, X2, mark(X3)) -> U51(X1, X2, X3) 10.01/3.48 U51(active(X1), X2, X3) -> U51(X1, X2, X3) 10.01/3.48 U51(X1, active(X2), X3) -> U51(X1, X2, X3) 10.01/3.48 U51(X1, X2, active(X3)) -> U51(X1, X2, X3) 10.01/3.48 U52(mark(X1), X2) -> U52(X1, X2) 10.01/3.48 U52(X1, mark(X2)) -> U52(X1, X2) 10.01/3.48 U52(active(X1), X2) -> U52(X1, X2) 10.01/3.48 U52(X1, active(X2)) -> U52(X1, X2) 10.01/3.48 U53(mark(X)) -> U53(X) 10.01/3.48 U53(active(X)) -> U53(X) 10.01/3.48 U61(mark(X1), X2) -> U61(X1, X2) 10.01/3.48 U61(X1, mark(X2)) -> U61(X1, X2) 10.01/3.48 U61(active(X1), X2) -> U61(X1, X2) 10.01/3.48 U61(X1, active(X2)) -> U61(X1, X2) 10.01/3.48 U62(mark(X)) -> U62(X) 10.01/3.48 U62(active(X)) -> U62(X) 10.01/3.48 U71(mark(X1), X2) -> U71(X1, X2) 10.01/3.48 U71(X1, mark(X2)) -> U71(X1, X2) 10.01/3.48 U71(active(X1), X2) -> U71(X1, X2) 10.01/3.48 U71(X1, active(X2)) -> U71(X1, X2) 10.01/3.48 U72(mark(X)) -> U72(X) 10.01/3.48 U72(active(X)) -> U72(X) 10.01/3.48 isNePal(mark(X)) -> isNePal(X) 10.01/3.48 isNePal(active(X)) -> isNePal(X) 10.01/3.48 and(mark(X1), X2) -> and(X1, X2) 10.01/3.48 and(X1, mark(X2)) -> and(X1, X2) 10.01/3.48 and(active(X1), X2) -> and(X1, X2) 10.01/3.48 and(X1, active(X2)) -> and(X1, X2) 10.01/3.48 isPalListKind(mark(X)) -> isPalListKind(X) 10.01/3.48 isPalListKind(active(X)) -> isPalListKind(X) 10.01/3.48 isPal(mark(X)) -> isPal(X) 10.01/3.48 isPal(active(X)) -> isPal(X) 10.01/3.48 10.01/3.48 The set Q consists of the following terms: 10.01/3.48 10.01/3.48 active(__(__(x0, x1), x2)) 10.01/3.48 active(__(x0, nil)) 10.01/3.48 active(__(nil, x0)) 10.01/3.48 active(U11(tt, x0)) 10.01/3.48 active(U12(tt)) 10.01/3.48 active(U21(tt, x0, x1)) 10.01/3.48 active(U22(tt, x0)) 10.01/3.48 active(U23(tt)) 10.01/3.48 active(U31(tt, x0)) 10.01/3.48 active(U32(tt)) 10.01/3.48 active(U41(tt, x0, x1)) 10.01/3.48 active(U42(tt, x0)) 10.01/3.48 active(U43(tt)) 10.01/3.48 active(U51(tt, x0, x1)) 10.01/3.48 active(U52(tt, x0)) 10.01/3.48 active(U53(tt)) 10.01/3.48 active(U61(tt, x0)) 10.01/3.48 active(U62(tt)) 10.01/3.48 active(U71(tt, x0)) 10.01/3.48 active(U72(tt)) 10.01/3.48 active(and(tt, x0)) 10.01/3.48 active(isList(x0)) 10.01/3.48 active(isNeList(x0)) 10.01/3.48 active(isNePal(x0)) 10.01/3.48 active(isPal(x0)) 10.01/3.48 active(isPalListKind(a)) 10.01/3.48 active(isPalListKind(e)) 10.01/3.48 active(isPalListKind(i)) 10.01/3.48 active(isPalListKind(nil)) 10.01/3.48 active(isPalListKind(o)) 10.01/3.48 active(isPalListKind(u)) 10.01/3.48 active(isPalListKind(__(x0, x1))) 10.01/3.48 active(isQid(a)) 10.01/3.48 active(isQid(e)) 10.01/3.48 active(isQid(i)) 10.01/3.48 active(isQid(o)) 10.01/3.48 active(isQid(u)) 10.01/3.48 mark(__(x0, x1)) 10.01/3.48 mark(nil) 10.01/3.48 mark(U11(x0, x1)) 10.01/3.48 mark(tt) 10.01/3.48 mark(U12(x0)) 10.01/3.48 mark(isNeList(x0)) 10.01/3.48 mark(U21(x0, x1, x2)) 10.01/3.48 mark(U22(x0, x1)) 10.01/3.48 mark(isList(x0)) 10.01/3.48 mark(U23(x0)) 10.01/3.48 mark(U31(x0, x1)) 10.01/3.48 mark(U32(x0)) 10.01/3.48 mark(isQid(x0)) 10.01/3.48 mark(U41(x0, x1, x2)) 10.01/3.48 mark(U42(x0, x1)) 10.01/3.48 mark(U43(x0)) 10.01/3.48 mark(U51(x0, x1, x2)) 10.01/3.48 mark(U52(x0, x1)) 10.01/3.48 mark(U53(x0)) 10.01/3.48 mark(U61(x0, x1)) 10.01/3.48 mark(U62(x0)) 10.01/3.48 mark(U71(x0, x1)) 10.01/3.48 mark(U72(x0)) 10.01/3.48 mark(isNePal(x0)) 10.01/3.48 mark(and(x0, x1)) 10.01/3.48 mark(isPalListKind(x0)) 10.01/3.48 mark(isPal(x0)) 10.01/3.48 mark(a) 10.01/3.48 mark(e) 10.01/3.48 mark(i) 10.01/3.48 mark(o) 10.01/3.48 mark(u) 10.01/3.48 __(mark(x0), x1) 10.01/3.48 __(x0, mark(x1)) 10.01/3.48 __(active(x0), x1) 10.01/3.48 __(x0, active(x1)) 10.01/3.48 U11(mark(x0), x1) 10.01/3.48 U11(x0, mark(x1)) 10.01/3.48 U11(active(x0), x1) 10.01/3.48 U11(x0, active(x1)) 10.01/3.48 U12(mark(x0)) 10.01/3.48 U12(active(x0)) 10.01/3.48 isNeList(mark(x0)) 10.01/3.48 isNeList(active(x0)) 10.01/3.48 U21(mark(x0), x1, x2) 10.01/3.48 U21(x0, mark(x1), x2) 10.01/3.48 U21(x0, x1, mark(x2)) 10.01/3.48 U21(active(x0), x1, x2) 10.01/3.48 U21(x0, active(x1), x2) 10.01/3.48 U21(x0, x1, active(x2)) 10.01/3.48 U22(mark(x0), x1) 10.01/3.48 U22(x0, mark(x1)) 10.01/3.48 U22(active(x0), x1) 10.01/3.48 U22(x0, active(x1)) 10.01/3.48 isList(mark(x0)) 10.01/3.48 isList(active(x0)) 10.01/3.48 U23(mark(x0)) 10.01/3.48 U23(active(x0)) 10.01/3.49 U31(mark(x0), x1) 10.01/3.49 U31(x0, mark(x1)) 10.01/3.49 U31(active(x0), x1) 10.01/3.49 U31(x0, active(x1)) 10.01/3.49 U32(mark(x0)) 10.01/3.49 U32(active(x0)) 10.01/3.49 isQid(mark(x0)) 10.01/3.49 isQid(active(x0)) 10.01/3.49 U41(mark(x0), x1, x2) 10.01/3.49 U41(x0, mark(x1), x2) 10.01/3.49 U41(x0, x1, mark(x2)) 10.01/3.49 U41(active(x0), x1, x2) 10.01/3.49 U41(x0, active(x1), x2) 10.01/3.49 U41(x0, x1, active(x2)) 10.01/3.49 U42(mark(x0), x1) 10.01/3.49 U42(x0, mark(x1)) 10.01/3.49 U42(active(x0), x1) 10.01/3.49 U42(x0, active(x1)) 10.01/3.49 U43(mark(x0)) 10.01/3.49 U43(active(x0)) 10.01/3.49 U51(mark(x0), x1, x2) 10.01/3.49 U51(x0, mark(x1), x2) 10.01/3.49 U51(x0, x1, mark(x2)) 10.01/3.49 U51(active(x0), x1, x2) 10.01/3.49 U51(x0, active(x1), x2) 10.01/3.49 U51(x0, x1, active(x2)) 10.01/3.49 U52(mark(x0), x1) 10.01/3.49 U52(x0, mark(x1)) 10.01/3.49 U52(active(x0), x1) 10.01/3.49 U52(x0, active(x1)) 10.01/3.49 U53(mark(x0)) 10.01/3.49 U53(active(x0)) 10.01/3.49 U61(mark(x0), x1) 10.01/3.49 U61(x0, mark(x1)) 10.01/3.49 U61(active(x0), x1) 10.01/3.49 U61(x0, active(x1)) 10.01/3.49 U62(mark(x0)) 10.01/3.49 U62(active(x0)) 10.01/3.49 U71(mark(x0), x1) 10.01/3.49 U71(x0, mark(x1)) 10.01/3.49 U71(active(x0), x1) 10.01/3.49 U71(x0, active(x1)) 10.01/3.49 U72(mark(x0)) 10.01/3.49 U72(active(x0)) 10.01/3.49 isNePal(mark(x0)) 10.01/3.49 isNePal(active(x0)) 10.01/3.49 and(mark(x0), x1) 10.01/3.49 and(x0, mark(x1)) 10.01/3.49 and(active(x0), x1) 10.01/3.49 and(x0, active(x1)) 10.01/3.49 isPalListKind(mark(x0)) 10.01/3.49 isPalListKind(active(x0)) 10.01/3.49 isPal(mark(x0)) 10.01/3.49 isPal(active(x0)) 10.01/3.49 10.01/3.49 10.01/3.49 ---------------------------------------- 10.01/3.49 10.01/3.49 (3) QTRSRRRProof (EQUIVALENT) 10.01/3.49 Used ordering: 10.01/3.49 Polynomial interpretation [POLO]: 10.01/3.49 10.01/3.49 POL(U11(x_1, x_2)) = 1 + x_1 + x_2 10.01/3.49 POL(U12(x_1)) = 1 + x_1 10.01/3.49 POL(U21(x_1, x_2, x_3)) = 1 + 2*x_1 + 2*x_2 + 2*x_3 10.01/3.49 POL(U22(x_1, x_2)) = 1 + 2*x_1 + 2*x_2 10.01/3.49 POL(U23(x_1)) = 1 + 2*x_1 10.01/3.49 POL(U31(x_1, x_2)) = 1 + 2*x_1 + 2*x_2 10.01/3.49 POL(U32(x_1)) = 1 + 2*x_1 10.01/3.49 POL(U41(x_1, x_2, x_3)) = 1 + 2*x_1 + 2*x_2 + 2*x_3 10.01/3.49 POL(U42(x_1, x_2)) = 1 + 2*x_1 + 2*x_2 10.01/3.49 POL(U43(x_1)) = 1 + x_1 10.01/3.49 POL(U51(x_1, x_2, x_3)) = 1 + 2*x_1 + 2*x_2 + 2*x_3 10.01/3.49 POL(U52(x_1, x_2)) = 2 + x_1 + 2*x_2 10.01/3.49 POL(U53(x_1)) = 1 + 2*x_1 10.01/3.49 POL(U61(x_1, x_2)) = 1 + 2*x_1 + 2*x_2 10.01/3.49 POL(U62(x_1)) = 1 + 2*x_1 10.01/3.49 POL(U71(x_1, x_2)) = 1 + x_1 + 2*x_2 10.01/3.49 POL(U72(x_1)) = 1 + 2*x_1 10.01/3.49 POL(__(x_1, x_2)) = 1 + 2*x_1 + 2*x_2 10.01/3.49 POL(a) = 1 10.01/3.49 POL(active(x_1)) = x_1 10.01/3.49 POL(and(x_1, x_2)) = 1 + 2*x_1 + 2*x_2 10.01/3.49 POL(e) = 1 10.01/3.49 POL(i) = 1 10.01/3.49 POL(isList(x_1)) = 1 + 2*x_1 10.01/3.49 POL(isNeList(x_1)) = 1 + 2*x_1 10.01/3.49 POL(isNePal(x_1)) = 1 + 2*x_1 10.01/3.49 POL(isPal(x_1)) = 1 + 2*x_1 10.01/3.49 POL(isPalListKind(x_1)) = 1 + 2*x_1 10.01/3.49 POL(isQid(x_1)) = 1 + 2*x_1 10.01/3.49 POL(mark(x_1)) = 2*x_1 10.01/3.49 POL(nil) = 2 10.01/3.49 POL(o) = 1 10.01/3.49 POL(tt) = 1 10.01/3.49 POL(u) = 1 10.01/3.49 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 10.01/3.49 10.01/3.49 active(U23(tt)) -> mark(tt) 10.01/3.49 active(U32(tt)) -> mark(tt) 10.01/3.49 active(U53(tt)) -> mark(tt) 10.01/3.49 active(U62(tt)) -> mark(tt) 10.01/3.49 active(U72(tt)) -> mark(tt) 10.01/3.49 active(isPalListKind(e)) -> mark(tt) 10.01/3.49 active(isPalListKind(i)) -> mark(tt) 10.01/3.49 active(isPalListKind(u)) -> mark(tt) 10.01/3.49 active(isQid(e)) -> mark(tt) 10.01/3.49 active(isQid(i)) -> mark(tt) 10.01/3.49 active(isQid(u)) -> mark(tt) 10.01/3.49 mark(__(X1, X2)) -> active(__(mark(X1), mark(X2))) 10.01/3.49 mark(nil) -> active(nil) 10.01/3.49 mark(U11(X1, X2)) -> active(U11(mark(X1), X2)) 10.01/3.49 mark(tt) -> active(tt) 10.01/3.49 mark(U12(X)) -> active(U12(mark(X))) 10.01/3.49 mark(isNeList(X)) -> active(isNeList(X)) 10.01/3.49 mark(U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)) 10.01/3.49 mark(U22(X1, X2)) -> active(U22(mark(X1), X2)) 10.01/3.49 mark(isList(X)) -> active(isList(X)) 10.01/3.49 mark(U23(X)) -> active(U23(mark(X))) 10.01/3.49 mark(U31(X1, X2)) -> active(U31(mark(X1), X2)) 10.01/3.49 mark(U32(X)) -> active(U32(mark(X))) 10.01/3.49 mark(isQid(X)) -> active(isQid(X)) 10.01/3.49 mark(U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3)) 10.01/3.49 mark(U42(X1, X2)) -> active(U42(mark(X1), X2)) 10.01/3.49 mark(U43(X)) -> active(U43(mark(X))) 10.01/3.49 mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)) 10.01/3.49 mark(U52(X1, X2)) -> active(U52(mark(X1), X2)) 10.01/3.49 mark(U53(X)) -> active(U53(mark(X))) 10.01/3.49 mark(U61(X1, X2)) -> active(U61(mark(X1), X2)) 10.01/3.49 mark(U62(X)) -> active(U62(mark(X))) 10.01/3.49 mark(U71(X1, X2)) -> active(U71(mark(X1), X2)) 10.01/3.49 mark(U72(X)) -> active(U72(mark(X))) 10.01/3.49 mark(isNePal(X)) -> active(isNePal(X)) 10.01/3.49 mark(and(X1, X2)) -> active(and(mark(X1), X2)) 10.01/3.49 mark(isPalListKind(X)) -> active(isPalListKind(X)) 10.01/3.49 mark(isPal(X)) -> active(isPal(X)) 10.01/3.49 mark(a) -> active(a) 10.01/3.49 mark(e) -> active(e) 10.01/3.49 mark(i) -> active(i) 10.01/3.49 mark(o) -> active(o) 10.01/3.49 mark(u) -> active(u) 10.01/3.49 10.01/3.49 10.01/3.49 10.01/3.49 10.01/3.49 ---------------------------------------- 10.01/3.49 10.01/3.49 (4) 10.01/3.49 Obligation: 10.01/3.49 Q restricted rewrite system: 10.01/3.49 The TRS R consists of the following rules: 10.01/3.49 10.01/3.49 active(U12(tt)) -> mark(tt) 10.01/3.49 active(U43(tt)) -> mark(tt) 10.01/3.49 __(mark(X1), X2) -> __(X1, X2) 10.01/3.49 __(X1, mark(X2)) -> __(X1, X2) 10.01/3.49 __(active(X1), X2) -> __(X1, X2) 10.01/3.49 __(X1, active(X2)) -> __(X1, X2) 10.01/3.49 U11(mark(X1), X2) -> U11(X1, X2) 10.01/3.49 U11(X1, mark(X2)) -> U11(X1, X2) 10.01/3.49 U11(active(X1), X2) -> U11(X1, X2) 10.01/3.49 U11(X1, active(X2)) -> U11(X1, X2) 10.01/3.49 U12(mark(X)) -> U12(X) 10.01/3.49 U12(active(X)) -> U12(X) 10.01/3.49 isNeList(mark(X)) -> isNeList(X) 10.01/3.49 isNeList(active(X)) -> isNeList(X) 10.01/3.49 U21(mark(X1), X2, X3) -> U21(X1, X2, X3) 10.01/3.49 U21(X1, mark(X2), X3) -> U21(X1, X2, X3) 10.01/3.49 U21(X1, X2, mark(X3)) -> U21(X1, X2, X3) 10.01/3.49 U21(active(X1), X2, X3) -> U21(X1, X2, X3) 10.01/3.49 U21(X1, active(X2), X3) -> U21(X1, X2, X3) 10.01/3.49 U21(X1, X2, active(X3)) -> U21(X1, X2, X3) 10.01/3.49 U22(mark(X1), X2) -> U22(X1, X2) 10.01/3.49 U22(X1, mark(X2)) -> U22(X1, X2) 10.01/3.49 U22(active(X1), X2) -> U22(X1, X2) 10.01/3.49 U22(X1, active(X2)) -> U22(X1, X2) 10.01/3.49 isList(mark(X)) -> isList(X) 10.01/3.49 isList(active(X)) -> isList(X) 10.01/3.49 U23(mark(X)) -> U23(X) 10.01/3.49 U23(active(X)) -> U23(X) 10.01/3.49 U31(mark(X1), X2) -> U31(X1, X2) 10.01/3.49 U31(X1, mark(X2)) -> U31(X1, X2) 10.01/3.49 U31(active(X1), X2) -> U31(X1, X2) 10.01/3.49 U31(X1, active(X2)) -> U31(X1, X2) 10.01/3.49 U32(mark(X)) -> U32(X) 10.01/3.49 U32(active(X)) -> U32(X) 10.01/3.49 isQid(mark(X)) -> isQid(X) 10.01/3.49 isQid(active(X)) -> isQid(X) 10.01/3.49 U41(mark(X1), X2, X3) -> U41(X1, X2, X3) 10.01/3.49 U41(X1, mark(X2), X3) -> U41(X1, X2, X3) 10.01/3.49 U41(X1, X2, mark(X3)) -> U41(X1, X2, X3) 10.01/3.49 U41(active(X1), X2, X3) -> U41(X1, X2, X3) 10.01/3.49 U41(X1, active(X2), X3) -> U41(X1, X2, X3) 10.01/3.49 U41(X1, X2, active(X3)) -> U41(X1, X2, X3) 10.01/3.49 U42(mark(X1), X2) -> U42(X1, X2) 10.01/3.49 U42(X1, mark(X2)) -> U42(X1, X2) 10.01/3.49 U42(active(X1), X2) -> U42(X1, X2) 10.01/3.49 U42(X1, active(X2)) -> U42(X1, X2) 10.01/3.49 U43(mark(X)) -> U43(X) 10.01/3.49 U43(active(X)) -> U43(X) 10.01/3.49 U51(mark(X1), X2, X3) -> U51(X1, X2, X3) 10.01/3.49 U51(X1, mark(X2), X3) -> U51(X1, X2, X3) 10.01/3.49 U51(X1, X2, mark(X3)) -> U51(X1, X2, X3) 10.01/3.49 U51(active(X1), X2, X3) -> U51(X1, X2, X3) 10.01/3.49 U51(X1, active(X2), X3) -> U51(X1, X2, X3) 10.01/3.49 U51(X1, X2, active(X3)) -> U51(X1, X2, X3) 10.01/3.49 U52(mark(X1), X2) -> U52(X1, X2) 10.01/3.49 U52(X1, mark(X2)) -> U52(X1, X2) 10.01/3.49 U52(active(X1), X2) -> U52(X1, X2) 10.01/3.49 U52(X1, active(X2)) -> U52(X1, X2) 10.01/3.49 U53(mark(X)) -> U53(X) 10.01/3.49 U53(active(X)) -> U53(X) 10.01/3.49 U61(mark(X1), X2) -> U61(X1, X2) 10.01/3.49 U61(X1, mark(X2)) -> U61(X1, X2) 10.01/3.49 U61(active(X1), X2) -> U61(X1, X2) 10.01/3.49 U61(X1, active(X2)) -> U61(X1, X2) 10.01/3.49 U62(mark(X)) -> U62(X) 10.01/3.49 U62(active(X)) -> U62(X) 10.01/3.49 U71(mark(X1), X2) -> U71(X1, X2) 10.01/3.49 U71(X1, mark(X2)) -> U71(X1, X2) 10.01/3.49 U71(active(X1), X2) -> U71(X1, X2) 10.01/3.49 U71(X1, active(X2)) -> U71(X1, X2) 10.01/3.49 U72(mark(X)) -> U72(X) 10.01/3.49 U72(active(X)) -> U72(X) 10.01/3.49 isNePal(mark(X)) -> isNePal(X) 10.01/3.49 isNePal(active(X)) -> isNePal(X) 10.01/3.49 and(mark(X1), X2) -> and(X1, X2) 10.01/3.49 and(X1, mark(X2)) -> and(X1, X2) 10.01/3.49 and(active(X1), X2) -> and(X1, X2) 10.01/3.49 and(X1, active(X2)) -> and(X1, X2) 10.01/3.49 isPalListKind(mark(X)) -> isPalListKind(X) 10.01/3.49 isPalListKind(active(X)) -> isPalListKind(X) 10.01/3.49 isPal(mark(X)) -> isPal(X) 10.01/3.49 isPal(active(X)) -> isPal(X) 10.01/3.49 10.01/3.49 The set Q consists of the following terms: 10.01/3.49 10.01/3.49 active(__(__(x0, x1), x2)) 10.01/3.49 active(__(x0, nil)) 10.01/3.49 active(__(nil, x0)) 10.01/3.49 active(U11(tt, x0)) 10.01/3.49 active(U12(tt)) 10.01/3.49 active(U21(tt, x0, x1)) 10.01/3.49 active(U22(tt, x0)) 10.01/3.49 active(U23(tt)) 10.01/3.49 active(U31(tt, x0)) 10.01/3.49 active(U32(tt)) 10.01/3.49 active(U41(tt, x0, x1)) 10.01/3.49 active(U42(tt, x0)) 10.01/3.49 active(U43(tt)) 10.01/3.49 active(U51(tt, x0, x1)) 10.01/3.49 active(U52(tt, x0)) 10.01/3.49 active(U53(tt)) 10.01/3.49 active(U61(tt, x0)) 10.01/3.49 active(U62(tt)) 10.01/3.49 active(U71(tt, x0)) 10.01/3.49 active(U72(tt)) 10.01/3.49 active(and(tt, x0)) 10.01/3.49 active(isList(x0)) 10.01/3.49 active(isNeList(x0)) 10.01/3.49 active(isNePal(x0)) 10.01/3.49 active(isPal(x0)) 10.01/3.49 active(isPalListKind(a)) 10.01/3.49 active(isPalListKind(e)) 10.01/3.49 active(isPalListKind(i)) 10.01/3.49 active(isPalListKind(nil)) 10.01/3.49 active(isPalListKind(o)) 10.01/3.49 active(isPalListKind(u)) 10.01/3.49 active(isPalListKind(__(x0, x1))) 10.01/3.49 active(isQid(a)) 10.01/3.49 active(isQid(e)) 10.01/3.49 active(isQid(i)) 10.01/3.49 active(isQid(o)) 10.01/3.49 active(isQid(u)) 10.01/3.49 mark(__(x0, x1)) 10.01/3.49 mark(nil) 10.01/3.49 mark(U11(x0, x1)) 10.01/3.49 mark(tt) 10.01/3.49 mark(U12(x0)) 10.01/3.49 mark(isNeList(x0)) 10.01/3.49 mark(U21(x0, x1, x2)) 10.01/3.49 mark(U22(x0, x1)) 10.01/3.49 mark(isList(x0)) 10.01/3.49 mark(U23(x0)) 10.01/3.49 mark(U31(x0, x1)) 10.01/3.49 mark(U32(x0)) 10.01/3.49 mark(isQid(x0)) 10.01/3.49 mark(U41(x0, x1, x2)) 10.01/3.49 mark(U42(x0, x1)) 10.01/3.49 mark(U43(x0)) 10.01/3.49 mark(U51(x0, x1, x2)) 10.01/3.49 mark(U52(x0, x1)) 10.01/3.49 mark(U53(x0)) 10.01/3.49 mark(U61(x0, x1)) 10.01/3.49 mark(U62(x0)) 10.01/3.49 mark(U71(x0, x1)) 10.01/3.49 mark(U72(x0)) 10.01/3.49 mark(isNePal(x0)) 10.01/3.49 mark(and(x0, x1)) 10.01/3.49 mark(isPalListKind(x0)) 10.01/3.49 mark(isPal(x0)) 10.01/3.49 mark(a) 10.01/3.49 mark(e) 10.01/3.49 mark(i) 10.01/3.49 mark(o) 10.01/3.49 mark(u) 10.01/3.49 __(mark(x0), x1) 10.01/3.49 __(x0, mark(x1)) 10.01/3.49 __(active(x0), x1) 10.01/3.49 __(x0, active(x1)) 10.01/3.49 U11(mark(x0), x1) 10.01/3.49 U11(x0, mark(x1)) 10.01/3.49 U11(active(x0), x1) 10.01/3.49 U11(x0, active(x1)) 10.01/3.49 U12(mark(x0)) 10.01/3.49 U12(active(x0)) 10.01/3.49 isNeList(mark(x0)) 10.01/3.49 isNeList(active(x0)) 10.01/3.49 U21(mark(x0), x1, x2) 10.01/3.49 U21(x0, mark(x1), x2) 10.01/3.49 U21(x0, x1, mark(x2)) 10.01/3.49 U21(active(x0), x1, x2) 10.01/3.49 U21(x0, active(x1), x2) 10.01/3.49 U21(x0, x1, active(x2)) 10.01/3.49 U22(mark(x0), x1) 10.01/3.49 U22(x0, mark(x1)) 10.01/3.49 U22(active(x0), x1) 10.01/3.49 U22(x0, active(x1)) 10.01/3.49 isList(mark(x0)) 10.01/3.49 isList(active(x0)) 10.01/3.49 U23(mark(x0)) 10.01/3.49 U23(active(x0)) 10.01/3.49 U31(mark(x0), x1) 10.01/3.49 U31(x0, mark(x1)) 10.01/3.49 U31(active(x0), x1) 10.01/3.49 U31(x0, active(x1)) 10.01/3.49 U32(mark(x0)) 10.01/3.49 U32(active(x0)) 10.01/3.49 isQid(mark(x0)) 10.01/3.49 isQid(active(x0)) 10.01/3.49 U41(mark(x0), x1, x2) 10.01/3.49 U41(x0, mark(x1), x2) 10.01/3.49 U41(x0, x1, mark(x2)) 10.01/3.49 U41(active(x0), x1, x2) 10.01/3.49 U41(x0, active(x1), x2) 10.01/3.49 U41(x0, x1, active(x2)) 10.01/3.49 U42(mark(x0), x1) 10.01/3.49 U42(x0, mark(x1)) 10.01/3.49 U42(active(x0), x1) 10.01/3.49 U42(x0, active(x1)) 10.01/3.49 U43(mark(x0)) 10.01/3.49 U43(active(x0)) 10.01/3.49 U51(mark(x0), x1, x2) 10.01/3.49 U51(x0, mark(x1), x2) 10.01/3.49 U51(x0, x1, mark(x2)) 10.01/3.49 U51(active(x0), x1, x2) 10.01/3.49 U51(x0, active(x1), x2) 10.01/3.49 U51(x0, x1, active(x2)) 10.01/3.49 U52(mark(x0), x1) 10.01/3.49 U52(x0, mark(x1)) 10.01/3.49 U52(active(x0), x1) 10.01/3.49 U52(x0, active(x1)) 10.01/3.49 U53(mark(x0)) 10.01/3.49 U53(active(x0)) 10.01/3.49 U61(mark(x0), x1) 10.01/3.49 U61(x0, mark(x1)) 10.01/3.49 U61(active(x0), x1) 10.01/3.49 U61(x0, active(x1)) 10.01/3.49 U62(mark(x0)) 10.01/3.49 U62(active(x0)) 10.01/3.49 U71(mark(x0), x1) 10.01/3.49 U71(x0, mark(x1)) 10.01/3.49 U71(active(x0), x1) 10.01/3.49 U71(x0, active(x1)) 10.01/3.49 U72(mark(x0)) 10.01/3.49 U72(active(x0)) 10.01/3.49 isNePal(mark(x0)) 10.01/3.49 isNePal(active(x0)) 10.01/3.49 and(mark(x0), x1) 10.01/3.49 and(x0, mark(x1)) 10.01/3.49 and(active(x0), x1) 10.01/3.49 and(x0, active(x1)) 10.01/3.49 isPalListKind(mark(x0)) 10.01/3.49 isPalListKind(active(x0)) 10.01/3.49 isPal(mark(x0)) 10.01/3.49 isPal(active(x0)) 10.01/3.49 10.01/3.49 10.01/3.49 ---------------------------------------- 10.01/3.49 10.01/3.49 (5) QTRSRRRProof (EQUIVALENT) 10.01/3.49 Used ordering: 10.01/3.49 Knuth-Bendix order [KBO] with precedence:active_1 > isPal_1 > isPalListKind_1 > and_2 > isNePal_1 > U72_1 > U71_2 > U62_1 > U61_2 > U53_1 > U52_2 > U51_3 > U42_2 > U41_3 > isQid_1 > U32_1 > U31_2 > U23_1 > isList_1 > U22_2 > U21_3 > isNeList_1 > U11_2 > ___2 > U43_1 > mark_1 > tt > U12_1 10.01/3.49 10.01/3.49 and weight map: 10.01/3.49 10.01/3.49 tt=1 10.01/3.49 active_1=0 10.01/3.49 U12_1=1 10.01/3.49 mark_1=1 10.01/3.49 U43_1=1 10.01/3.49 isNeList_1=1 10.01/3.49 isList_1=1 10.01/3.49 U23_1=1 10.01/3.49 U32_1=1 10.01/3.49 isQid_1=1 10.01/3.49 U53_1=1 10.01/3.49 U62_1=1 10.01/3.49 U72_1=1 10.01/3.49 isNePal_1=1 10.01/3.49 isPalListKind_1=1 10.01/3.49 isPal_1=1 10.01/3.49 ___2=0 10.01/3.49 U11_2=0 10.01/3.49 U21_3=0 10.01/3.49 U22_2=0 10.01/3.49 U31_2=0 10.01/3.49 U41_3=0 10.01/3.49 U42_2=0 10.01/3.49 U51_3=0 10.01/3.49 U52_2=0 10.01/3.49 U61_2=0 10.01/3.49 U71_2=0 10.01/3.49 and_2=0 10.01/3.49 10.01/3.49 The variable weight is 1With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 10.01/3.49 10.01/3.49 active(U12(tt)) -> mark(tt) 10.01/3.49 active(U43(tt)) -> mark(tt) 10.01/3.49 __(mark(X1), X2) -> __(X1, X2) 10.01/3.49 __(X1, mark(X2)) -> __(X1, X2) 10.01/3.49 __(active(X1), X2) -> __(X1, X2) 10.01/3.49 __(X1, active(X2)) -> __(X1, X2) 10.01/3.49 U11(mark(X1), X2) -> U11(X1, X2) 10.01/3.49 U11(X1, mark(X2)) -> U11(X1, X2) 10.01/3.49 U11(active(X1), X2) -> U11(X1, X2) 10.01/3.49 U11(X1, active(X2)) -> U11(X1, X2) 10.01/3.49 U12(mark(X)) -> U12(X) 10.01/3.49 U12(active(X)) -> U12(X) 10.01/3.49 isNeList(mark(X)) -> isNeList(X) 10.01/3.49 isNeList(active(X)) -> isNeList(X) 10.01/3.49 U21(mark(X1), X2, X3) -> U21(X1, X2, X3) 10.01/3.49 U21(X1, mark(X2), X3) -> U21(X1, X2, X3) 10.01/3.49 U21(X1, X2, mark(X3)) -> U21(X1, X2, X3) 10.01/3.49 U21(active(X1), X2, X3) -> U21(X1, X2, X3) 10.01/3.49 U21(X1, active(X2), X3) -> U21(X1, X2, X3) 10.01/3.49 U21(X1, X2, active(X3)) -> U21(X1, X2, X3) 10.01/3.49 U22(mark(X1), X2) -> U22(X1, X2) 10.01/3.49 U22(X1, mark(X2)) -> U22(X1, X2) 10.01/3.49 U22(active(X1), X2) -> U22(X1, X2) 10.01/3.49 U22(X1, active(X2)) -> U22(X1, X2) 10.01/3.49 isList(mark(X)) -> isList(X) 10.01/3.49 isList(active(X)) -> isList(X) 10.01/3.49 U23(mark(X)) -> U23(X) 10.01/3.49 U23(active(X)) -> U23(X) 10.01/3.49 U31(mark(X1), X2) -> U31(X1, X2) 10.01/3.49 U31(X1, mark(X2)) -> U31(X1, X2) 10.01/3.49 U31(active(X1), X2) -> U31(X1, X2) 10.01/3.49 U31(X1, active(X2)) -> U31(X1, X2) 10.01/3.49 U32(mark(X)) -> U32(X) 10.01/3.49 U32(active(X)) -> U32(X) 10.01/3.49 isQid(mark(X)) -> isQid(X) 10.01/3.49 isQid(active(X)) -> isQid(X) 10.01/3.49 U41(mark(X1), X2, X3) -> U41(X1, X2, X3) 10.01/3.49 U41(X1, mark(X2), X3) -> U41(X1, X2, X3) 10.01/3.49 U41(X1, X2, mark(X3)) -> U41(X1, X2, X3) 10.01/3.49 U41(active(X1), X2, X3) -> U41(X1, X2, X3) 10.01/3.49 U41(X1, active(X2), X3) -> U41(X1, X2, X3) 10.01/3.49 U41(X1, X2, active(X3)) -> U41(X1, X2, X3) 10.01/3.49 U42(mark(X1), X2) -> U42(X1, X2) 10.01/3.49 U42(X1, mark(X2)) -> U42(X1, X2) 10.01/3.49 U42(active(X1), X2) -> U42(X1, X2) 10.01/3.49 U42(X1, active(X2)) -> U42(X1, X2) 10.01/3.49 U43(mark(X)) -> U43(X) 10.01/3.49 U43(active(X)) -> U43(X) 10.01/3.49 U51(mark(X1), X2, X3) -> U51(X1, X2, X3) 10.01/3.49 U51(X1, mark(X2), X3) -> U51(X1, X2, X3) 10.01/3.49 U51(X1, X2, mark(X3)) -> U51(X1, X2, X3) 10.01/3.49 U51(active(X1), X2, X3) -> U51(X1, X2, X3) 10.01/3.49 U51(X1, active(X2), X3) -> U51(X1, X2, X3) 10.01/3.49 U51(X1, X2, active(X3)) -> U51(X1, X2, X3) 10.01/3.49 U52(mark(X1), X2) -> U52(X1, X2) 10.01/3.49 U52(X1, mark(X2)) -> U52(X1, X2) 10.01/3.49 U52(active(X1), X2) -> U52(X1, X2) 10.01/3.49 U52(X1, active(X2)) -> U52(X1, X2) 10.01/3.49 U53(mark(X)) -> U53(X) 10.01/3.49 U53(active(X)) -> U53(X) 10.01/3.49 U61(mark(X1), X2) -> U61(X1, X2) 10.01/3.49 U61(X1, mark(X2)) -> U61(X1, X2) 10.01/3.49 U61(active(X1), X2) -> U61(X1, X2) 10.01/3.49 U61(X1, active(X2)) -> U61(X1, X2) 10.01/3.49 U62(mark(X)) -> U62(X) 10.01/3.49 U62(active(X)) -> U62(X) 10.01/3.49 U71(mark(X1), X2) -> U71(X1, X2) 10.01/3.49 U71(X1, mark(X2)) -> U71(X1, X2) 10.01/3.49 U71(active(X1), X2) -> U71(X1, X2) 10.01/3.49 U71(X1, active(X2)) -> U71(X1, X2) 10.01/3.49 U72(mark(X)) -> U72(X) 10.01/3.49 U72(active(X)) -> U72(X) 10.01/3.49 isNePal(mark(X)) -> isNePal(X) 10.01/3.49 isNePal(active(X)) -> isNePal(X) 10.01/3.49 and(mark(X1), X2) -> and(X1, X2) 10.01/3.49 and(X1, mark(X2)) -> and(X1, X2) 10.01/3.49 and(active(X1), X2) -> and(X1, X2) 10.01/3.49 and(X1, active(X2)) -> and(X1, X2) 10.01/3.49 isPalListKind(mark(X)) -> isPalListKind(X) 10.01/3.49 isPalListKind(active(X)) -> isPalListKind(X) 10.01/3.49 isPal(mark(X)) -> isPal(X) 10.01/3.49 isPal(active(X)) -> isPal(X) 10.01/3.49 10.01/3.49 10.01/3.49 10.01/3.49 10.01/3.49 ---------------------------------------- 10.01/3.49 10.01/3.49 (6) 10.01/3.49 Obligation: 10.01/3.49 Q restricted rewrite system: 10.01/3.49 R is empty. 10.01/3.49 The set Q consists of the following terms: 10.01/3.49 10.01/3.49 active(__(__(x0, x1), x2)) 10.01/3.49 active(__(x0, nil)) 10.01/3.49 active(__(nil, x0)) 10.01/3.49 active(U11(tt, x0)) 10.01/3.49 active(U12(tt)) 10.01/3.49 active(U21(tt, x0, x1)) 10.01/3.49 active(U22(tt, x0)) 10.01/3.49 active(U23(tt)) 10.01/3.49 active(U31(tt, x0)) 10.01/3.49 active(U32(tt)) 10.01/3.49 active(U41(tt, x0, x1)) 10.01/3.49 active(U42(tt, x0)) 10.01/3.49 active(U43(tt)) 10.01/3.49 active(U51(tt, x0, x1)) 10.01/3.49 active(U52(tt, x0)) 10.01/3.49 active(U53(tt)) 10.01/3.49 active(U61(tt, x0)) 10.01/3.49 active(U62(tt)) 10.01/3.49 active(U71(tt, x0)) 10.01/3.49 active(U72(tt)) 10.01/3.49 active(and(tt, x0)) 10.01/3.49 active(isList(x0)) 10.01/3.49 active(isNeList(x0)) 10.01/3.49 active(isNePal(x0)) 10.01/3.49 active(isPal(x0)) 10.01/3.49 active(isPalListKind(a)) 10.01/3.49 active(isPalListKind(e)) 10.01/3.49 active(isPalListKind(i)) 10.01/3.49 active(isPalListKind(nil)) 10.01/3.49 active(isPalListKind(o)) 10.01/3.49 active(isPalListKind(u)) 10.01/3.49 active(isPalListKind(__(x0, x1))) 10.01/3.49 active(isQid(a)) 10.01/3.49 active(isQid(e)) 10.01/3.49 active(isQid(i)) 10.01/3.49 active(isQid(o)) 10.01/3.49 active(isQid(u)) 10.01/3.49 mark(__(x0, x1)) 10.01/3.49 mark(nil) 10.01/3.49 mark(U11(x0, x1)) 10.01/3.49 mark(tt) 10.01/3.49 mark(U12(x0)) 10.01/3.49 mark(isNeList(x0)) 10.01/3.49 mark(U21(x0, x1, x2)) 10.01/3.49 mark(U22(x0, x1)) 10.01/3.49 mark(isList(x0)) 10.01/3.49 mark(U23(x0)) 10.01/3.49 mark(U31(x0, x1)) 10.01/3.49 mark(U32(x0)) 10.01/3.49 mark(isQid(x0)) 10.01/3.49 mark(U41(x0, x1, x2)) 10.01/3.49 mark(U42(x0, x1)) 10.01/3.49 mark(U43(x0)) 10.01/3.49 mark(U51(x0, x1, x2)) 10.01/3.49 mark(U52(x0, x1)) 10.01/3.49 mark(U53(x0)) 10.01/3.49 mark(U61(x0, x1)) 10.01/3.49 mark(U62(x0)) 10.01/3.49 mark(U71(x0, x1)) 10.01/3.49 mark(U72(x0)) 10.01/3.49 mark(isNePal(x0)) 10.01/3.49 mark(and(x0, x1)) 10.01/3.49 mark(isPalListKind(x0)) 10.01/3.49 mark(isPal(x0)) 10.01/3.49 mark(a) 10.01/3.49 mark(e) 10.01/3.49 mark(i) 10.01/3.49 mark(o) 10.01/3.49 mark(u) 10.01/3.49 __(mark(x0), x1) 10.01/3.49 __(x0, mark(x1)) 10.01/3.49 __(active(x0), x1) 10.01/3.49 __(x0, active(x1)) 10.01/3.49 U11(mark(x0), x1) 10.01/3.49 U11(x0, mark(x1)) 10.01/3.49 U11(active(x0), x1) 10.01/3.49 U11(x0, active(x1)) 10.01/3.49 U12(mark(x0)) 10.01/3.49 U12(active(x0)) 10.01/3.49 isNeList(mark(x0)) 10.01/3.49 isNeList(active(x0)) 10.01/3.49 U21(mark(x0), x1, x2) 10.01/3.49 U21(x0, mark(x1), x2) 10.01/3.49 U21(x0, x1, mark(x2)) 10.01/3.49 U21(active(x0), x1, x2) 10.01/3.49 U21(x0, active(x1), x2) 10.01/3.49 U21(x0, x1, active(x2)) 10.01/3.49 U22(mark(x0), x1) 10.01/3.49 U22(x0, mark(x1)) 10.01/3.49 U22(active(x0), x1) 10.01/3.49 U22(x0, active(x1)) 10.01/3.49 isList(mark(x0)) 10.01/3.49 isList(active(x0)) 10.01/3.49 U23(mark(x0)) 10.01/3.49 U23(active(x0)) 10.01/3.49 U31(mark(x0), x1) 10.01/3.49 U31(x0, mark(x1)) 10.01/3.49 U31(active(x0), x1) 10.01/3.49 U31(x0, active(x1)) 10.01/3.49 U32(mark(x0)) 10.01/3.49 U32(active(x0)) 10.01/3.49 isQid(mark(x0)) 10.01/3.49 isQid(active(x0)) 10.01/3.49 U41(mark(x0), x1, x2) 10.01/3.49 U41(x0, mark(x1), x2) 10.01/3.49 U41(x0, x1, mark(x2)) 10.01/3.49 U41(active(x0), x1, x2) 10.01/3.49 U41(x0, active(x1), x2) 10.01/3.49 U41(x0, x1, active(x2)) 10.01/3.49 U42(mark(x0), x1) 10.01/3.49 U42(x0, mark(x1)) 10.01/3.49 U42(active(x0), x1) 10.01/3.49 U42(x0, active(x1)) 10.01/3.49 U43(mark(x0)) 10.01/3.49 U43(active(x0)) 10.01/3.49 U51(mark(x0), x1, x2) 10.01/3.49 U51(x0, mark(x1), x2) 10.01/3.49 U51(x0, x1, mark(x2)) 10.01/3.49 U51(active(x0), x1, x2) 10.01/3.49 U51(x0, active(x1), x2) 10.01/3.49 U51(x0, x1, active(x2)) 10.01/3.49 U52(mark(x0), x1) 10.01/3.49 U52(x0, mark(x1)) 10.01/3.49 U52(active(x0), x1) 10.01/3.49 U52(x0, active(x1)) 10.01/3.49 U53(mark(x0)) 10.01/3.49 U53(active(x0)) 10.01/3.49 U61(mark(x0), x1) 10.01/3.49 U61(x0, mark(x1)) 10.01/3.49 U61(active(x0), x1) 10.01/3.49 U61(x0, active(x1)) 10.01/3.49 U62(mark(x0)) 10.01/3.49 U62(active(x0)) 10.01/3.49 U71(mark(x0), x1) 10.01/3.49 U71(x0, mark(x1)) 10.01/3.49 U71(active(x0), x1) 10.01/3.49 U71(x0, active(x1)) 10.01/3.49 U72(mark(x0)) 10.01/3.49 U72(active(x0)) 10.01/3.49 isNePal(mark(x0)) 10.01/3.49 isNePal(active(x0)) 10.01/3.49 and(mark(x0), x1) 10.01/3.49 and(x0, mark(x1)) 10.01/3.49 and(active(x0), x1) 10.01/3.49 and(x0, active(x1)) 10.01/3.49 isPalListKind(mark(x0)) 10.01/3.49 isPalListKind(active(x0)) 10.01/3.49 isPal(mark(x0)) 10.01/3.49 isPal(active(x0)) 10.01/3.49 10.01/3.49 10.01/3.49 ---------------------------------------- 10.01/3.49 10.01/3.49 (7) RisEmptyProof (EQUIVALENT) 10.01/3.49 The TRS R is empty. Hence, termination is trivially proven. 10.01/3.49 ---------------------------------------- 10.01/3.49 10.01/3.49 (8) 10.01/3.49 YES 10.35/3.55 EOF