11.35/7.05 YES 11.48/7.08 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 11.48/7.08 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 11.48/7.08 11.48/7.08 11.48/7.08 Termination w.r.t. Q of the given QTRS could be proven: 11.48/7.08 11.48/7.08 (0) QTRS 11.48/7.08 (1) QTRSRRRProof [EQUIVALENT, 1427 ms] 11.48/7.08 (2) QTRS 11.48/7.08 (3) QTRSRRRProof [EQUIVALENT, 145 ms] 11.48/7.08 (4) QTRS 11.48/7.08 (5) QTRSRRRProof [EQUIVALENT, 74 ms] 11.48/7.08 (6) QTRS 11.48/7.08 (7) QTRSRRRProof [EQUIVALENT, 7 ms] 11.48/7.08 (8) QTRS 11.48/7.08 (9) QTRSRRRProof [EQUIVALENT, 0 ms] 11.48/7.08 (10) QTRS 11.48/7.08 (11) RisEmptyProof [EQUIVALENT, 0 ms] 11.48/7.08 (12) YES 11.48/7.08 11.48/7.08 11.48/7.08 ---------------------------------------- 11.48/7.08 11.48/7.08 (0) 11.48/7.08 Obligation: 11.48/7.08 Q restricted rewrite system: 11.48/7.08 The TRS R consists of the following rules: 11.48/7.08 11.48/7.08 a____(__(X, Y), Z) -> a____(mark(X), a____(mark(Y), mark(Z))) 11.48/7.08 a____(X, nil) -> mark(X) 11.48/7.08 a____(nil, X) -> mark(X) 11.48/7.08 a__U11(tt, V) -> a__U12(a__isPalListKind(V), V) 11.48/7.08 a__U12(tt, V) -> a__U13(a__isNeList(V)) 11.48/7.08 a__U13(tt) -> tt 11.48/7.08 a__U21(tt, V1, V2) -> a__U22(a__isPalListKind(V1), V1, V2) 11.48/7.08 a__U22(tt, V1, V2) -> a__U23(a__isPalListKind(V2), V1, V2) 11.48/7.08 a__U23(tt, V1, V2) -> a__U24(a__isPalListKind(V2), V1, V2) 11.48/7.08 a__U24(tt, V1, V2) -> a__U25(a__isList(V1), V2) 11.48/7.08 a__U25(tt, V2) -> a__U26(a__isList(V2)) 11.48/7.08 a__U26(tt) -> tt 11.48/7.08 a__U31(tt, V) -> a__U32(a__isPalListKind(V), V) 11.48/7.08 a__U32(tt, V) -> a__U33(a__isQid(V)) 11.48/7.08 a__U33(tt) -> tt 11.48/7.08 a__U41(tt, V1, V2) -> a__U42(a__isPalListKind(V1), V1, V2) 11.48/7.08 a__U42(tt, V1, V2) -> a__U43(a__isPalListKind(V2), V1, V2) 11.48/7.08 a__U43(tt, V1, V2) -> a__U44(a__isPalListKind(V2), V1, V2) 11.48/7.08 a__U44(tt, V1, V2) -> a__U45(a__isList(V1), V2) 11.48/7.08 a__U45(tt, V2) -> a__U46(a__isNeList(V2)) 11.48/7.08 a__U46(tt) -> tt 11.48/7.08 a__U51(tt, V1, V2) -> a__U52(a__isPalListKind(V1), V1, V2) 11.48/7.08 a__U52(tt, V1, V2) -> a__U53(a__isPalListKind(V2), V1, V2) 11.48/7.08 a__U53(tt, V1, V2) -> a__U54(a__isPalListKind(V2), V1, V2) 11.48/7.08 a__U54(tt, V1, V2) -> a__U55(a__isNeList(V1), V2) 11.48/7.08 a__U55(tt, V2) -> a__U56(a__isList(V2)) 11.48/7.08 a__U56(tt) -> tt 11.48/7.08 a__U61(tt, V) -> a__U62(a__isPalListKind(V), V) 11.48/7.08 a__U62(tt, V) -> a__U63(a__isQid(V)) 11.48/7.08 a__U63(tt) -> tt 11.48/7.08 a__U71(tt, I, P) -> a__U72(a__isPalListKind(I), P) 11.48/7.08 a__U72(tt, P) -> a__U73(a__isPal(P), P) 11.48/7.08 a__U73(tt, P) -> a__U74(a__isPalListKind(P)) 11.48/7.08 a__U74(tt) -> tt 11.48/7.08 a__U81(tt, V) -> a__U82(a__isPalListKind(V), V) 11.48/7.08 a__U82(tt, V) -> a__U83(a__isNePal(V)) 11.48/7.08 a__U83(tt) -> tt 11.48/7.08 a__U91(tt, V2) -> a__U92(a__isPalListKind(V2)) 11.48/7.08 a__U92(tt) -> tt 11.48/7.08 a__isList(V) -> a__U11(a__isPalListKind(V), V) 11.48/7.08 a__isList(nil) -> tt 11.48/7.08 a__isList(__(V1, V2)) -> a__U21(a__isPalListKind(V1), V1, V2) 11.48/7.08 a__isNeList(V) -> a__U31(a__isPalListKind(V), V) 11.48/7.08 a__isNeList(__(V1, V2)) -> a__U41(a__isPalListKind(V1), V1, V2) 11.48/7.08 a__isNeList(__(V1, V2)) -> a__U51(a__isPalListKind(V1), V1, V2) 11.48/7.08 a__isNePal(V) -> a__U61(a__isPalListKind(V), V) 11.48/7.08 a__isNePal(__(I, __(P, I))) -> a__U71(a__isQid(I), I, P) 11.48/7.08 a__isPal(V) -> a__U81(a__isPalListKind(V), V) 11.48/7.08 a__isPal(nil) -> tt 11.48/7.08 a__isPalListKind(a) -> tt 11.48/7.08 a__isPalListKind(e) -> tt 11.48/7.08 a__isPalListKind(i) -> tt 11.48/7.08 a__isPalListKind(nil) -> tt 11.48/7.08 a__isPalListKind(o) -> tt 11.48/7.08 a__isPalListKind(u) -> tt 11.48/7.08 a__isPalListKind(__(V1, V2)) -> a__U91(a__isPalListKind(V1), V2) 11.48/7.08 a__isQid(a) -> tt 11.48/7.08 a__isQid(e) -> tt 11.48/7.08 a__isQid(i) -> tt 11.48/7.08 a__isQid(o) -> tt 11.48/7.08 a__isQid(u) -> tt 11.48/7.08 mark(__(X1, X2)) -> a____(mark(X1), mark(X2)) 11.48/7.08 mark(U11(X1, X2)) -> a__U11(mark(X1), X2) 11.48/7.08 mark(U12(X1, X2)) -> a__U12(mark(X1), X2) 11.48/7.08 mark(isPalListKind(X)) -> a__isPalListKind(X) 11.48/7.08 mark(U13(X)) -> a__U13(mark(X)) 11.48/7.08 mark(isNeList(X)) -> a__isNeList(X) 11.48/7.08 mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3) 11.48/7.08 mark(U22(X1, X2, X3)) -> a__U22(mark(X1), X2, X3) 11.48/7.08 mark(U23(X1, X2, X3)) -> a__U23(mark(X1), X2, X3) 11.48/7.08 mark(U24(X1, X2, X3)) -> a__U24(mark(X1), X2, X3) 11.48/7.08 mark(U25(X1, X2)) -> a__U25(mark(X1), X2) 11.48/7.08 mark(isList(X)) -> a__isList(X) 11.48/7.08 mark(U26(X)) -> a__U26(mark(X)) 11.48/7.08 mark(U31(X1, X2)) -> a__U31(mark(X1), X2) 11.48/7.08 mark(U32(X1, X2)) -> a__U32(mark(X1), X2) 11.48/7.08 mark(U33(X)) -> a__U33(mark(X)) 11.48/7.08 mark(isQid(X)) -> a__isQid(X) 11.48/7.08 mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) 11.48/7.08 mark(U42(X1, X2, X3)) -> a__U42(mark(X1), X2, X3) 11.48/7.08 mark(U43(X1, X2, X3)) -> a__U43(mark(X1), X2, X3) 11.48/7.08 mark(U44(X1, X2, X3)) -> a__U44(mark(X1), X2, X3) 11.48/7.08 mark(U45(X1, X2)) -> a__U45(mark(X1), X2) 11.48/7.08 mark(U46(X)) -> a__U46(mark(X)) 11.48/7.08 mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3) 11.48/7.08 mark(U52(X1, X2, X3)) -> a__U52(mark(X1), X2, X3) 11.48/7.08 mark(U53(X1, X2, X3)) -> a__U53(mark(X1), X2, X3) 11.48/7.08 mark(U54(X1, X2, X3)) -> a__U54(mark(X1), X2, X3) 11.48/7.08 mark(U55(X1, X2)) -> a__U55(mark(X1), X2) 11.48/7.08 mark(U56(X)) -> a__U56(mark(X)) 11.48/7.08 mark(U61(X1, X2)) -> a__U61(mark(X1), X2) 11.48/7.08 mark(U62(X1, X2)) -> a__U62(mark(X1), X2) 11.48/7.08 mark(U63(X)) -> a__U63(mark(X)) 11.48/7.08 mark(U71(X1, X2, X3)) -> a__U71(mark(X1), X2, X3) 11.48/7.08 mark(U72(X1, X2)) -> a__U72(mark(X1), X2) 11.48/7.08 mark(U73(X1, X2)) -> a__U73(mark(X1), X2) 11.48/7.08 mark(isPal(X)) -> a__isPal(X) 11.48/7.08 mark(U74(X)) -> a__U74(mark(X)) 11.48/7.08 mark(U81(X1, X2)) -> a__U81(mark(X1), X2) 11.48/7.08 mark(U82(X1, X2)) -> a__U82(mark(X1), X2) 11.48/7.08 mark(U83(X)) -> a__U83(mark(X)) 11.48/7.08 mark(isNePal(X)) -> a__isNePal(X) 11.48/7.08 mark(U91(X1, X2)) -> a__U91(mark(X1), X2) 11.48/7.08 mark(U92(X)) -> a__U92(mark(X)) 11.48/7.08 mark(nil) -> nil 11.48/7.08 mark(tt) -> tt 11.48/7.08 mark(a) -> a 11.48/7.08 mark(e) -> e 11.48/7.08 mark(i) -> i 11.48/7.08 mark(o) -> o 11.48/7.08 mark(u) -> u 11.48/7.08 a____(X1, X2) -> __(X1, X2) 11.48/7.08 a__U11(X1, X2) -> U11(X1, X2) 11.48/7.08 a__U12(X1, X2) -> U12(X1, X2) 11.48/7.08 a__isPalListKind(X) -> isPalListKind(X) 11.48/7.08 a__U13(X) -> U13(X) 11.48/7.08 a__isNeList(X) -> isNeList(X) 11.48/7.08 a__U21(X1, X2, X3) -> U21(X1, X2, X3) 11.48/7.08 a__U22(X1, X2, X3) -> U22(X1, X2, X3) 11.48/7.08 a__U23(X1, X2, X3) -> U23(X1, X2, X3) 11.48/7.08 a__U24(X1, X2, X3) -> U24(X1, X2, X3) 11.48/7.08 a__U25(X1, X2) -> U25(X1, X2) 11.48/7.08 a__isList(X) -> isList(X) 11.48/7.08 a__U26(X) -> U26(X) 11.48/7.08 a__U31(X1, X2) -> U31(X1, X2) 11.48/7.08 a__U32(X1, X2) -> U32(X1, X2) 11.48/7.08 a__U33(X) -> U33(X) 11.48/7.08 a__isQid(X) -> isQid(X) 11.48/7.08 a__U41(X1, X2, X3) -> U41(X1, X2, X3) 11.48/7.08 a__U42(X1, X2, X3) -> U42(X1, X2, X3) 11.48/7.08 a__U43(X1, X2, X3) -> U43(X1, X2, X3) 11.48/7.08 a__U44(X1, X2, X3) -> U44(X1, X2, X3) 11.48/7.08 a__U45(X1, X2) -> U45(X1, X2) 11.48/7.08 a__U46(X) -> U46(X) 11.48/7.08 a__U51(X1, X2, X3) -> U51(X1, X2, X3) 11.48/7.08 a__U52(X1, X2, X3) -> U52(X1, X2, X3) 11.48/7.08 a__U53(X1, X2, X3) -> U53(X1, X2, X3) 11.48/7.08 a__U54(X1, X2, X3) -> U54(X1, X2, X3) 11.48/7.08 a__U55(X1, X2) -> U55(X1, X2) 11.48/7.08 a__U56(X) -> U56(X) 11.48/7.08 a__U61(X1, X2) -> U61(X1, X2) 11.48/7.08 a__U62(X1, X2) -> U62(X1, X2) 11.48/7.08 a__U63(X) -> U63(X) 11.48/7.08 a__U71(X1, X2, X3) -> U71(X1, X2, X3) 11.48/7.08 a__U72(X1, X2) -> U72(X1, X2) 11.48/7.08 a__U73(X1, X2) -> U73(X1, X2) 11.48/7.08 a__isPal(X) -> isPal(X) 11.48/7.08 a__U74(X) -> U74(X) 11.48/7.08 a__U81(X1, X2) -> U81(X1, X2) 11.48/7.08 a__U82(X1, X2) -> U82(X1, X2) 11.48/7.08 a__U83(X) -> U83(X) 11.48/7.08 a__isNePal(X) -> isNePal(X) 11.48/7.08 a__U91(X1, X2) -> U91(X1, X2) 11.48/7.08 a__U92(X) -> U92(X) 11.48/7.08 11.48/7.08 The set Q consists of the following terms: 11.48/7.08 11.48/7.08 a__isList(x0) 11.48/7.08 a__isNeList(x0) 11.48/7.08 a__isNePal(x0) 11.48/7.08 a__isPal(x0) 11.48/7.08 mark(__(x0, x1)) 11.48/7.08 mark(U11(x0, x1)) 11.48/7.08 mark(U12(x0, x1)) 11.48/7.08 mark(isPalListKind(x0)) 11.48/7.08 mark(U13(x0)) 11.48/7.08 mark(isNeList(x0)) 11.48/7.08 mark(U21(x0, x1, x2)) 11.48/7.08 mark(U22(x0, x1, x2)) 11.48/7.08 mark(U23(x0, x1, x2)) 11.48/7.08 mark(U24(x0, x1, x2)) 11.48/7.08 mark(U25(x0, x1)) 11.48/7.08 mark(isList(x0)) 11.48/7.08 mark(U26(x0)) 11.48/7.08 mark(U31(x0, x1)) 11.48/7.08 mark(U32(x0, x1)) 11.48/7.08 mark(U33(x0)) 11.48/7.08 mark(isQid(x0)) 11.48/7.08 mark(U41(x0, x1, x2)) 11.48/7.08 mark(U42(x0, x1, x2)) 11.48/7.08 mark(U43(x0, x1, x2)) 11.48/7.08 mark(U44(x0, x1, x2)) 11.48/7.08 mark(U45(x0, x1)) 11.48/7.08 mark(U46(x0)) 11.48/7.08 mark(U51(x0, x1, x2)) 11.48/7.08 mark(U52(x0, x1, x2)) 11.48/7.08 mark(U53(x0, x1, x2)) 11.48/7.08 mark(U54(x0, x1, x2)) 11.48/7.08 mark(U55(x0, x1)) 11.48/7.08 mark(U56(x0)) 11.48/7.08 mark(U61(x0, x1)) 11.48/7.08 mark(U62(x0, x1)) 11.48/7.08 mark(U63(x0)) 11.48/7.08 mark(U71(x0, x1, x2)) 11.48/7.08 mark(U72(x0, x1)) 11.48/7.08 mark(U73(x0, x1)) 11.48/7.08 mark(isPal(x0)) 11.48/7.08 mark(U74(x0)) 11.48/7.08 mark(U81(x0, x1)) 11.48/7.08 mark(U82(x0, x1)) 11.48/7.08 mark(U83(x0)) 11.48/7.08 mark(isNePal(x0)) 11.48/7.08 mark(U91(x0, x1)) 11.48/7.08 mark(U92(x0)) 11.48/7.08 mark(nil) 11.48/7.08 mark(tt) 11.48/7.08 mark(a) 11.48/7.08 mark(e) 11.48/7.08 mark(i) 11.48/7.08 mark(o) 11.48/7.08 mark(u) 11.48/7.08 a____(x0, x1) 11.48/7.08 a__U11(x0, x1) 11.48/7.08 a__U12(x0, x1) 11.48/7.08 a__isPalListKind(x0) 11.48/7.08 a__U13(x0) 11.48/7.08 a__U21(x0, x1, x2) 11.48/7.08 a__U22(x0, x1, x2) 11.48/7.08 a__U23(x0, x1, x2) 11.48/7.08 a__U24(x0, x1, x2) 11.48/7.08 a__U25(x0, x1) 11.48/7.08 a__U26(x0) 11.48/7.08 a__U31(x0, x1) 11.48/7.08 a__U32(x0, x1) 11.48/7.08 a__U33(x0) 11.48/7.08 a__isQid(x0) 11.48/7.08 a__U41(x0, x1, x2) 11.48/7.08 a__U42(x0, x1, x2) 11.48/7.08 a__U43(x0, x1, x2) 11.48/7.08 a__U44(x0, x1, x2) 11.48/7.08 a__U45(x0, x1) 11.48/7.08 a__U46(x0) 11.48/7.08 a__U51(x0, x1, x2) 11.48/7.08 a__U52(x0, x1, x2) 11.48/7.08 a__U53(x0, x1, x2) 11.48/7.08 a__U54(x0, x1, x2) 11.48/7.08 a__U55(x0, x1) 11.48/7.08 a__U56(x0) 11.48/7.08 a__U61(x0, x1) 11.48/7.08 a__U62(x0, x1) 11.48/7.08 a__U63(x0) 11.48/7.08 a__U71(x0, x1, x2) 11.48/7.08 a__U72(x0, x1) 11.48/7.08 a__U73(x0, x1) 11.48/7.08 a__U74(x0) 11.48/7.08 a__U81(x0, x1) 11.48/7.08 a__U82(x0, x1) 11.48/7.08 a__U83(x0) 11.48/7.08 a__U91(x0, x1) 11.48/7.08 a__U92(x0) 11.48/7.08 11.48/7.08 11.48/7.08 ---------------------------------------- 11.48/7.08 11.48/7.08 (1) QTRSRRRProof (EQUIVALENT) 11.48/7.08 Used ordering: 11.48/7.08 a____/2(YES,YES) 11.48/7.08 __/2(YES,YES) 11.48/7.08 mark/1)YES( 11.48/7.08 nil/0) 11.48/7.08 a__U11/2(YES,YES) 11.48/7.08 tt/0) 11.48/7.08 a__U12/2(YES,YES) 11.48/7.08 a__isPalListKind/1)YES( 11.48/7.08 a__U13/1)YES( 11.48/7.08 a__isNeList/1(YES) 11.48/7.08 a__U21/3(YES,YES,YES) 11.48/7.08 a__U22/3(YES,YES,YES) 11.48/7.08 a__U23/3(YES,YES,YES) 11.48/7.08 a__U24/3(YES,YES,YES) 11.48/7.08 a__U25/2(YES,YES) 11.48/7.08 a__isList/1(YES) 11.48/7.08 a__U26/1)YES( 11.48/7.08 a__U31/2(YES,YES) 11.48/7.08 a__U32/2(YES,YES) 11.48/7.08 a__U33/1)YES( 11.48/7.08 a__isQid/1(YES) 11.48/7.08 a__U41/3(YES,YES,YES) 11.48/7.08 a__U42/3(YES,YES,YES) 11.48/7.08 a__U43/3(YES,YES,YES) 11.48/7.08 a__U44/3(YES,YES,YES) 11.48/7.08 a__U45/2(YES,YES) 11.48/7.08 a__U46/1(YES) 11.48/7.08 a__U51/3(YES,YES,YES) 11.48/7.08 a__U52/3(YES,YES,YES) 11.48/7.08 a__U53/3(YES,YES,YES) 11.48/7.08 a__U54/3(YES,YES,YES) 11.48/7.08 a__U55/2(YES,YES) 11.48/7.08 a__U56/1(YES) 11.48/7.08 a__U61/2(YES,YES) 11.48/7.08 a__U62/2(YES,YES) 11.48/7.08 a__U63/1)YES( 11.48/7.08 a__U71/3(YES,YES,YES) 11.48/7.08 a__U72/2(YES,YES) 11.48/7.08 a__U73/2(YES,YES) 11.48/7.08 a__isPal/1(YES) 11.48/7.08 a__U74/1)YES( 11.48/7.08 a__U81/2(YES,YES) 11.48/7.08 a__U82/2(YES,YES) 11.48/7.08 a__U83/1)YES( 11.48/7.08 a__isNePal/1(YES) 11.48/7.08 a__U91/2(YES,YES) 11.48/7.08 a__U92/1)YES( 11.48/7.08 a/0) 11.48/7.08 e/0) 11.48/7.08 i/0) 11.48/7.08 o/0) 11.48/7.08 u/0) 11.48/7.08 U11/2(YES,YES) 11.48/7.08 U12/2(YES,YES) 11.48/7.08 isPalListKind/1)YES( 11.48/7.08 U13/1)YES( 11.48/7.08 isNeList/1(YES) 11.48/7.08 U21/3(YES,YES,YES) 11.48/7.08 U22/3(YES,YES,YES) 11.48/7.08 U23/3(YES,YES,YES) 11.48/7.08 U24/3(YES,YES,YES) 11.48/7.08 U25/2(YES,YES) 11.48/7.08 isList/1(YES) 11.48/7.08 U26/1)YES( 11.48/7.08 U31/2(YES,YES) 11.48/7.08 U32/2(YES,YES) 11.48/7.08 U33/1)YES( 11.48/7.08 isQid/1(YES) 11.48/7.08 U41/3(YES,YES,YES) 11.48/7.08 U42/3(YES,YES,YES) 11.48/7.08 U43/3(YES,YES,YES) 11.48/7.08 U44/3(YES,YES,YES) 11.48/7.08 U45/2(YES,YES) 11.48/7.08 U46/1(YES) 11.48/7.08 U51/3(YES,YES,YES) 11.48/7.08 U52/3(YES,YES,YES) 11.48/7.08 U53/3(YES,YES,YES) 11.48/7.08 U54/3(YES,YES,YES) 11.48/7.08 U55/2(YES,YES) 11.48/7.08 U56/1(YES) 11.48/7.08 U61/2(YES,YES) 11.48/7.08 U62/2(YES,YES) 11.48/7.08 U63/1)YES( 11.48/7.08 U71/3(YES,YES,YES) 11.48/7.08 U72/2(YES,YES) 11.48/7.08 U73/2(YES,YES) 11.48/7.08 isPal/1(YES) 11.48/7.08 U74/1)YES( 11.48/7.08 U81/2(YES,YES) 11.48/7.08 U82/2(YES,YES) 11.48/7.08 U83/1)YES( 11.48/7.08 isNePal/1(YES) 11.48/7.08 U91/2(YES,YES) 11.48/7.08 U92/1)YES( 11.48/7.08 11.48/7.08 Quasi precedence: 11.48/7.08 [a_____2, ___2] > [a__U21_3, U21_3] > [a__U22_3, U22_3] > [a__U23_3, U23_3] > [a__U24_3, U24_3] > [a__U25_2, a__isList_1, a__U55_2, U25_2, isList_1, U55_2] > [a__U11_2, U11_2] > [a__U12_2, a__isNeList_1, U12_2, isNeList_1] > [a__U31_2, U31_2] > [a__U32_2, U32_2] > [a__isQid_1, a__U62_2, isQid_1, U62_2] 11.48/7.08 [a_____2, ___2] > [a__U21_3, U21_3] > [a__U22_3, U22_3] > [a__U23_3, U23_3] > [a__U24_3, U24_3] > [a__U25_2, a__isList_1, a__U55_2, U25_2, isList_1, U55_2] > [a__U56_1, U56_1] 11.48/7.08 [a_____2, ___2] > [a__U41_3, U41_3] > [a__U42_3, U42_3] > [a__U43_3, U43_3] > [a__U44_3, U44_3] > [a__U45_2, U45_2] > [a__U46_1, U46_1] > [nil, tt, a__U54_3, o, U54_3] > [a__U25_2, a__isList_1, a__U55_2, U25_2, isList_1, U55_2] > [a__U11_2, U11_2] > [a__U12_2, a__isNeList_1, U12_2, isNeList_1] > [a__U31_2, U31_2] > [a__U32_2, U32_2] > [a__isQid_1, a__U62_2, isQid_1, U62_2] 11.48/7.08 [a_____2, ___2] > [a__U41_3, U41_3] > [a__U42_3, U42_3] > [a__U43_3, U43_3] > [a__U44_3, U44_3] > [a__U45_2, U45_2] > [a__U46_1, U46_1] > [nil, tt, a__U54_3, o, U54_3] > [a__U25_2, a__isList_1, a__U55_2, U25_2, isList_1, U55_2] > [a__U56_1, U56_1] 11.48/7.08 [a_____2, ___2] > [a__U41_3, U41_3] > [a__U42_3, U42_3] > [a__U43_3, U43_3] > [a__U44_3, U44_3] > [a__U45_2, U45_2] > [a__U46_1, U46_1] > [nil, tt, a__U54_3, o, U54_3] > [a__U72_2, U72_2] > [a__U73_2, U73_2] 11.48/7.08 [a_____2, ___2] > [a__U41_3, U41_3] > [a__U42_3, U42_3] > [a__U43_3, U43_3] > [a__U44_3, U44_3] > [a__U45_2, U45_2] > [a__U46_1, U46_1] > [nil, tt, a__U54_3, o, U54_3] > [a__U72_2, U72_2] > [a__isPal_1, isPal_1] > [a__U81_2, U81_2] > [a__U82_2, U82_2] > [a__isNePal_1, isNePal_1] > [a__U61_2, U61_2] > [a__isQid_1, a__U62_2, isQid_1, U62_2] 11.48/7.08 [a_____2, ___2] > [a__U51_3, U51_3] > [a__U52_3, U52_3] > [a__U53_3, U53_3] > [nil, tt, a__U54_3, o, U54_3] > [a__U25_2, a__isList_1, a__U55_2, U25_2, isList_1, U55_2] > [a__U11_2, U11_2] > [a__U12_2, a__isNeList_1, U12_2, isNeList_1] > [a__U31_2, U31_2] > [a__U32_2, U32_2] > [a__isQid_1, a__U62_2, isQid_1, U62_2] 11.48/7.08 [a_____2, ___2] > [a__U51_3, U51_3] > [a__U52_3, U52_3] > [a__U53_3, U53_3] > [nil, tt, a__U54_3, o, U54_3] > [a__U25_2, a__isList_1, a__U55_2, U25_2, isList_1, U55_2] > [a__U56_1, U56_1] 11.48/7.08 [a_____2, ___2] > [a__U51_3, U51_3] > [a__U52_3, U52_3] > [a__U53_3, U53_3] > [nil, tt, a__U54_3, o, U54_3] > [a__U72_2, U72_2] > [a__U73_2, U73_2] 11.48/7.08 [a_____2, ___2] > [a__U51_3, U51_3] > [a__U52_3, U52_3] > [a__U53_3, U53_3] > [nil, tt, a__U54_3, o, U54_3] > [a__U72_2, U72_2] > [a__isPal_1, isPal_1] > [a__U81_2, U81_2] > [a__U82_2, U82_2] > [a__isNePal_1, isNePal_1] > [a__U61_2, U61_2] > [a__isQid_1, a__U62_2, isQid_1, U62_2] 11.48/7.08 [a_____2, ___2] > [a__U71_3, U71_3] > [a__U72_2, U72_2] > [a__U73_2, U73_2] 11.48/7.08 [a_____2, ___2] > [a__U71_3, U71_3] > [a__U72_2, U72_2] > [a__isPal_1, isPal_1] > [a__U81_2, U81_2] > [a__U82_2, U82_2] > [a__isNePal_1, isNePal_1] > [a__U61_2, U61_2] > [a__isQid_1, a__U62_2, isQid_1, U62_2] 11.48/7.08 [a_____2, ___2] > [a__U91_2, U91_2] 11.48/7.08 a > [nil, tt, a__U54_3, o, U54_3] > [a__U25_2, a__isList_1, a__U55_2, U25_2, isList_1, U55_2] > [a__U11_2, U11_2] > [a__U12_2, a__isNeList_1, U12_2, isNeList_1] > [a__U31_2, U31_2] > [a__U32_2, U32_2] > [a__isQid_1, a__U62_2, isQid_1, U62_2] 11.48/7.08 a > [nil, tt, a__U54_3, o, U54_3] > [a__U25_2, a__isList_1, a__U55_2, U25_2, isList_1, U55_2] > [a__U56_1, U56_1] 11.48/7.08 a > [nil, tt, a__U54_3, o, U54_3] > [a__U72_2, U72_2] > [a__U73_2, U73_2] 11.48/7.08 a > [nil, tt, a__U54_3, o, U54_3] > [a__U72_2, U72_2] > [a__isPal_1, isPal_1] > [a__U81_2, U81_2] > [a__U82_2, U82_2] > [a__isNePal_1, isNePal_1] > [a__U61_2, U61_2] > [a__isQid_1, a__U62_2, isQid_1, U62_2] 11.48/7.08 e > [nil, tt, a__U54_3, o, U54_3] > [a__U25_2, a__isList_1, a__U55_2, U25_2, isList_1, U55_2] > [a__U11_2, U11_2] > [a__U12_2, a__isNeList_1, U12_2, isNeList_1] > [a__U31_2, U31_2] > [a__U32_2, U32_2] > [a__isQid_1, a__U62_2, isQid_1, U62_2] 11.48/7.08 e > [nil, tt, a__U54_3, o, U54_3] > [a__U25_2, a__isList_1, a__U55_2, U25_2, isList_1, U55_2] > [a__U56_1, U56_1] 11.48/7.08 e > [nil, tt, a__U54_3, o, U54_3] > [a__U72_2, U72_2] > [a__U73_2, U73_2] 11.48/7.08 e > [nil, tt, a__U54_3, o, U54_3] > [a__U72_2, U72_2] > [a__isPal_1, isPal_1] > [a__U81_2, U81_2] > [a__U82_2, U82_2] > [a__isNePal_1, isNePal_1] > [a__U61_2, U61_2] > [a__isQid_1, a__U62_2, isQid_1, U62_2] 11.48/7.08 i > [nil, tt, a__U54_3, o, U54_3] > [a__U25_2, a__isList_1, a__U55_2, U25_2, isList_1, U55_2] > [a__U11_2, U11_2] > [a__U12_2, a__isNeList_1, U12_2, isNeList_1] > [a__U31_2, U31_2] > [a__U32_2, U32_2] > [a__isQid_1, a__U62_2, isQid_1, U62_2] 11.48/7.08 i > [nil, tt, a__U54_3, o, U54_3] > [a__U25_2, a__isList_1, a__U55_2, U25_2, isList_1, U55_2] > [a__U56_1, U56_1] 11.48/7.08 i > [nil, tt, a__U54_3, o, U54_3] > [a__U72_2, U72_2] > [a__U73_2, U73_2] 11.48/7.08 i > [nil, tt, a__U54_3, o, U54_3] > [a__U72_2, U72_2] > [a__isPal_1, isPal_1] > [a__U81_2, U81_2] > [a__U82_2, U82_2] > [a__isNePal_1, isNePal_1] > [a__U61_2, U61_2] > [a__isQid_1, a__U62_2, isQid_1, U62_2] 11.48/7.08 u > [nil, tt, a__U54_3, o, U54_3] > [a__U25_2, a__isList_1, a__U55_2, U25_2, isList_1, U55_2] > [a__U11_2, U11_2] > [a__U12_2, a__isNeList_1, U12_2, isNeList_1] > [a__U31_2, U31_2] > [a__U32_2, U32_2] > [a__isQid_1, a__U62_2, isQid_1, U62_2] 11.48/7.08 u > [nil, tt, a__U54_3, o, U54_3] > [a__U25_2, a__isList_1, a__U55_2, U25_2, isList_1, U55_2] > [a__U56_1, U56_1] 11.48/7.08 u > [nil, tt, a__U54_3, o, U54_3] > [a__U72_2, U72_2] > [a__U73_2, U73_2] 11.48/7.08 u > [nil, tt, a__U54_3, o, U54_3] > [a__U72_2, U72_2] > [a__isPal_1, isPal_1] > [a__U81_2, U81_2] > [a__U82_2, U82_2] > [a__isNePal_1, isNePal_1] > [a__U61_2, U61_2] > [a__isQid_1, a__U62_2, isQid_1, U62_2] 11.48/7.08 11.48/7.08 11.48/7.08 Status: 11.48/7.08 a_____2: [1,2] 11.48/7.08 ___2: [1,2] 11.48/7.08 nil: multiset status 11.48/7.08 a__U11_2: multiset status 11.48/7.08 tt: multiset status 11.48/7.08 a__U12_2: multiset status 11.48/7.08 a__isNeList_1: multiset status 11.48/7.08 a__U21_3: multiset status 11.48/7.08 a__U22_3: multiset status 11.48/7.08 a__U23_3: multiset status 11.48/7.08 a__U24_3: multiset status 11.48/7.08 a__U25_2: multiset status 11.48/7.08 a__isList_1: multiset status 11.48/7.08 a__U31_2: multiset status 11.48/7.08 a__U32_2: multiset status 11.48/7.08 a__isQid_1: multiset status 11.48/7.08 a__U41_3: multiset status 11.48/7.08 a__U42_3: multiset status 11.48/7.08 a__U43_3: multiset status 11.48/7.08 a__U44_3: multiset status 11.48/7.08 a__U45_2: multiset status 11.48/7.08 a__U46_1: multiset status 11.48/7.08 a__U51_3: multiset status 11.48/7.08 a__U52_3: multiset status 11.48/7.08 a__U53_3: multiset status 11.48/7.08 a__U54_3: multiset status 11.48/7.08 a__U55_2: multiset status 11.48/7.08 a__U56_1: multiset status 11.48/7.08 a__U61_2: multiset status 11.48/7.08 a__U62_2: multiset status 11.48/7.08 a__U71_3: multiset status 11.48/7.08 a__U72_2: multiset status 11.48/7.08 a__U73_2: multiset status 11.48/7.08 a__isPal_1: multiset status 11.48/7.08 a__U81_2: multiset status 11.48/7.08 a__U82_2: multiset status 11.48/7.08 a__isNePal_1: multiset status 11.48/7.08 a__U91_2: multiset status 11.48/7.08 a: multiset status 11.48/7.08 e: multiset status 11.48/7.08 i: multiset status 11.48/7.08 o: multiset status 11.48/7.08 u: multiset status 11.48/7.08 U11_2: multiset status 11.48/7.08 U12_2: multiset status 11.48/7.08 isNeList_1: multiset status 11.48/7.08 U21_3: multiset status 11.48/7.08 U22_3: multiset status 11.48/7.08 U23_3: multiset status 11.48/7.08 U24_3: multiset status 11.48/7.08 U25_2: multiset status 11.48/7.08 isList_1: multiset status 11.48/7.08 U31_2: multiset status 11.48/7.08 U32_2: multiset status 11.48/7.08 isQid_1: multiset status 11.48/7.08 U41_3: multiset status 11.48/7.08 U42_3: multiset status 11.48/7.08 U43_3: multiset status 11.48/7.08 U44_3: multiset status 11.48/7.08 U45_2: multiset status 11.48/7.08 U46_1: multiset status 11.48/7.08 U51_3: multiset status 11.48/7.08 U52_3: multiset status 11.48/7.08 U53_3: multiset status 11.48/7.08 U54_3: multiset status 11.48/7.08 U55_2: multiset status 11.48/7.08 U56_1: multiset status 11.48/7.08 U61_2: multiset status 11.48/7.08 U62_2: multiset status 11.48/7.08 U71_3: multiset status 11.48/7.08 U72_2: multiset status 11.48/7.08 U73_2: multiset status 11.48/7.08 isPal_1: multiset status 11.48/7.08 U81_2: multiset status 11.48/7.08 U82_2: multiset status 11.48/7.08 isNePal_1: multiset status 11.48/7.08 U91_2: multiset status 11.48/7.08 11.48/7.08 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 11.48/7.08 11.48/7.08 a____(__(X, Y), Z) -> a____(mark(X), a____(mark(Y), mark(Z))) 11.48/7.08 a____(X, nil) -> mark(X) 11.48/7.08 a____(nil, X) -> mark(X) 11.48/7.08 a__U11(tt, V) -> a__U12(a__isPalListKind(V), V) 11.48/7.08 a__U12(tt, V) -> a__U13(a__isNeList(V)) 11.48/7.08 a__U21(tt, V1, V2) -> a__U22(a__isPalListKind(V1), V1, V2) 11.48/7.08 a__U22(tt, V1, V2) -> a__U23(a__isPalListKind(V2), V1, V2) 11.48/7.08 a__U23(tt, V1, V2) -> a__U24(a__isPalListKind(V2), V1, V2) 11.48/7.08 a__U24(tt, V1, V2) -> a__U25(a__isList(V1), V2) 11.48/7.08 a__U25(tt, V2) -> a__U26(a__isList(V2)) 11.48/7.08 a__U31(tt, V) -> a__U32(a__isPalListKind(V), V) 11.48/7.08 a__U32(tt, V) -> a__U33(a__isQid(V)) 11.48/7.08 a__U41(tt, V1, V2) -> a__U42(a__isPalListKind(V1), V1, V2) 11.48/7.08 a__U42(tt, V1, V2) -> a__U43(a__isPalListKind(V2), V1, V2) 11.48/7.08 a__U43(tt, V1, V2) -> a__U44(a__isPalListKind(V2), V1, V2) 11.48/7.08 a__U44(tt, V1, V2) -> a__U45(a__isList(V1), V2) 11.48/7.08 a__U45(tt, V2) -> a__U46(a__isNeList(V2)) 11.48/7.08 a__U46(tt) -> tt 11.48/7.08 a__U51(tt, V1, V2) -> a__U52(a__isPalListKind(V1), V1, V2) 11.48/7.08 a__U52(tt, V1, V2) -> a__U53(a__isPalListKind(V2), V1, V2) 11.48/7.08 a__U53(tt, V1, V2) -> a__U54(a__isPalListKind(V2), V1, V2) 11.48/7.08 a__U54(tt, V1, V2) -> a__U55(a__isNeList(V1), V2) 11.48/7.08 a__U55(tt, V2) -> a__U56(a__isList(V2)) 11.48/7.08 a__U56(tt) -> tt 11.48/7.08 a__U61(tt, V) -> a__U62(a__isPalListKind(V), V) 11.48/7.08 a__U62(tt, V) -> a__U63(a__isQid(V)) 11.48/7.08 a__U71(tt, I, P) -> a__U72(a__isPalListKind(I), P) 11.48/7.08 a__U72(tt, P) -> a__U73(a__isPal(P), P) 11.48/7.08 a__U73(tt, P) -> a__U74(a__isPalListKind(P)) 11.48/7.08 a__U81(tt, V) -> a__U82(a__isPalListKind(V), V) 11.48/7.08 a__U82(tt, V) -> a__U83(a__isNePal(V)) 11.48/7.08 a__U91(tt, V2) -> a__U92(a__isPalListKind(V2)) 11.48/7.08 a__isList(V) -> a__U11(a__isPalListKind(V), V) 11.48/7.08 a__isList(nil) -> tt 11.48/7.08 a__isList(__(V1, V2)) -> a__U21(a__isPalListKind(V1), V1, V2) 11.48/7.08 a__isNeList(V) -> a__U31(a__isPalListKind(V), V) 11.48/7.08 a__isNeList(__(V1, V2)) -> a__U41(a__isPalListKind(V1), V1, V2) 11.48/7.08 a__isNeList(__(V1, V2)) -> a__U51(a__isPalListKind(V1), V1, V2) 11.48/7.08 a__isNePal(V) -> a__U61(a__isPalListKind(V), V) 11.48/7.08 a__isNePal(__(I, __(P, I))) -> a__U71(a__isQid(I), I, P) 11.48/7.08 a__isPal(V) -> a__U81(a__isPalListKind(V), V) 11.48/7.08 a__isPal(nil) -> tt 11.48/7.08 a__isPalListKind(a) -> tt 11.48/7.08 a__isPalListKind(e) -> tt 11.48/7.08 a__isPalListKind(i) -> tt 11.48/7.08 a__isPalListKind(u) -> tt 11.48/7.08 a__isPalListKind(__(V1, V2)) -> a__U91(a__isPalListKind(V1), V2) 11.48/7.08 a__isQid(a) -> tt 11.48/7.08 a__isQid(e) -> tt 11.48/7.08 a__isQid(i) -> tt 11.48/7.08 a__isQid(o) -> tt 11.48/7.08 a__isQid(u) -> tt 11.48/7.08 11.48/7.08 11.48/7.08 11.48/7.08 11.48/7.08 ---------------------------------------- 11.48/7.08 11.48/7.08 (2) 11.48/7.08 Obligation: 11.48/7.08 Q restricted rewrite system: 11.48/7.08 The TRS R consists of the following rules: 11.48/7.08 11.48/7.08 a__U13(tt) -> tt 11.48/7.08 a__U26(tt) -> tt 11.48/7.08 a__U33(tt) -> tt 11.48/7.08 a__U63(tt) -> tt 11.48/7.08 a__U74(tt) -> tt 11.48/7.08 a__U83(tt) -> tt 11.48/7.08 a__U92(tt) -> tt 11.48/7.08 a__isPalListKind(nil) -> tt 11.48/7.08 a__isPalListKind(o) -> tt 11.48/7.08 mark(__(X1, X2)) -> a____(mark(X1), mark(X2)) 11.48/7.08 mark(U11(X1, X2)) -> a__U11(mark(X1), X2) 11.48/7.08 mark(U12(X1, X2)) -> a__U12(mark(X1), X2) 11.48/7.08 mark(isPalListKind(X)) -> a__isPalListKind(X) 11.48/7.08 mark(U13(X)) -> a__U13(mark(X)) 11.48/7.08 mark(isNeList(X)) -> a__isNeList(X) 11.48/7.08 mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3) 11.48/7.08 mark(U22(X1, X2, X3)) -> a__U22(mark(X1), X2, X3) 11.48/7.08 mark(U23(X1, X2, X3)) -> a__U23(mark(X1), X2, X3) 11.48/7.08 mark(U24(X1, X2, X3)) -> a__U24(mark(X1), X2, X3) 11.48/7.08 mark(U25(X1, X2)) -> a__U25(mark(X1), X2) 11.48/7.08 mark(isList(X)) -> a__isList(X) 11.48/7.08 mark(U26(X)) -> a__U26(mark(X)) 11.48/7.08 mark(U31(X1, X2)) -> a__U31(mark(X1), X2) 11.48/7.08 mark(U32(X1, X2)) -> a__U32(mark(X1), X2) 11.48/7.08 mark(U33(X)) -> a__U33(mark(X)) 11.48/7.08 mark(isQid(X)) -> a__isQid(X) 11.48/7.08 mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) 11.48/7.08 mark(U42(X1, X2, X3)) -> a__U42(mark(X1), X2, X3) 11.48/7.08 mark(U43(X1, X2, X3)) -> a__U43(mark(X1), X2, X3) 11.48/7.08 mark(U44(X1, X2, X3)) -> a__U44(mark(X1), X2, X3) 11.48/7.08 mark(U45(X1, X2)) -> a__U45(mark(X1), X2) 11.48/7.08 mark(U46(X)) -> a__U46(mark(X)) 11.48/7.08 mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3) 11.48/7.08 mark(U52(X1, X2, X3)) -> a__U52(mark(X1), X2, X3) 11.48/7.08 mark(U53(X1, X2, X3)) -> a__U53(mark(X1), X2, X3) 11.48/7.08 mark(U54(X1, X2, X3)) -> a__U54(mark(X1), X2, X3) 11.48/7.08 mark(U55(X1, X2)) -> a__U55(mark(X1), X2) 11.48/7.08 mark(U56(X)) -> a__U56(mark(X)) 11.48/7.08 mark(U61(X1, X2)) -> a__U61(mark(X1), X2) 11.48/7.08 mark(U62(X1, X2)) -> a__U62(mark(X1), X2) 11.48/7.08 mark(U63(X)) -> a__U63(mark(X)) 11.48/7.08 mark(U71(X1, X2, X3)) -> a__U71(mark(X1), X2, X3) 11.48/7.08 mark(U72(X1, X2)) -> a__U72(mark(X1), X2) 11.48/7.08 mark(U73(X1, X2)) -> a__U73(mark(X1), X2) 11.48/7.08 mark(isPal(X)) -> a__isPal(X) 11.48/7.08 mark(U74(X)) -> a__U74(mark(X)) 11.48/7.08 mark(U81(X1, X2)) -> a__U81(mark(X1), X2) 11.48/7.08 mark(U82(X1, X2)) -> a__U82(mark(X1), X2) 11.48/7.08 mark(U83(X)) -> a__U83(mark(X)) 11.48/7.08 mark(isNePal(X)) -> a__isNePal(X) 11.48/7.08 mark(U91(X1, X2)) -> a__U91(mark(X1), X2) 11.48/7.08 mark(U92(X)) -> a__U92(mark(X)) 11.48/7.08 mark(nil) -> nil 11.48/7.08 mark(tt) -> tt 11.48/7.08 mark(a) -> a 11.48/7.08 mark(e) -> e 11.48/7.08 mark(i) -> i 11.48/7.08 mark(o) -> o 11.48/7.08 mark(u) -> u 11.48/7.08 a____(X1, X2) -> __(X1, X2) 11.48/7.08 a__U11(X1, X2) -> U11(X1, X2) 11.48/7.08 a__U12(X1, X2) -> U12(X1, X2) 11.48/7.08 a__isPalListKind(X) -> isPalListKind(X) 11.48/7.08 a__U13(X) -> U13(X) 11.48/7.08 a__isNeList(X) -> isNeList(X) 11.48/7.08 a__U21(X1, X2, X3) -> U21(X1, X2, X3) 11.48/7.08 a__U22(X1, X2, X3) -> U22(X1, X2, X3) 11.48/7.08 a__U23(X1, X2, X3) -> U23(X1, X2, X3) 11.48/7.08 a__U24(X1, X2, X3) -> U24(X1, X2, X3) 11.48/7.08 a__U25(X1, X2) -> U25(X1, X2) 11.48/7.08 a__isList(X) -> isList(X) 11.48/7.08 a__U26(X) -> U26(X) 11.48/7.08 a__U31(X1, X2) -> U31(X1, X2) 11.48/7.08 a__U32(X1, X2) -> U32(X1, X2) 11.48/7.08 a__U33(X) -> U33(X) 11.48/7.08 a__isQid(X) -> isQid(X) 11.48/7.08 a__U41(X1, X2, X3) -> U41(X1, X2, X3) 11.48/7.08 a__U42(X1, X2, X3) -> U42(X1, X2, X3) 11.48/7.08 a__U43(X1, X2, X3) -> U43(X1, X2, X3) 11.48/7.08 a__U44(X1, X2, X3) -> U44(X1, X2, X3) 11.48/7.08 a__U45(X1, X2) -> U45(X1, X2) 11.48/7.08 a__U46(X) -> U46(X) 11.48/7.08 a__U51(X1, X2, X3) -> U51(X1, X2, X3) 11.48/7.08 a__U52(X1, X2, X3) -> U52(X1, X2, X3) 11.48/7.08 a__U53(X1, X2, X3) -> U53(X1, X2, X3) 11.48/7.08 a__U54(X1, X2, X3) -> U54(X1, X2, X3) 11.48/7.08 a__U55(X1, X2) -> U55(X1, X2) 11.48/7.08 a__U56(X) -> U56(X) 11.48/7.08 a__U61(X1, X2) -> U61(X1, X2) 11.48/7.08 a__U62(X1, X2) -> U62(X1, X2) 11.48/7.08 a__U63(X) -> U63(X) 11.48/7.08 a__U71(X1, X2, X3) -> U71(X1, X2, X3) 11.48/7.08 a__U72(X1, X2) -> U72(X1, X2) 11.48/7.08 a__U73(X1, X2) -> U73(X1, X2) 11.48/7.08 a__isPal(X) -> isPal(X) 11.48/7.08 a__U74(X) -> U74(X) 11.48/7.08 a__U81(X1, X2) -> U81(X1, X2) 11.48/7.08 a__U82(X1, X2) -> U82(X1, X2) 11.48/7.08 a__U83(X) -> U83(X) 11.48/7.08 a__isNePal(X) -> isNePal(X) 11.48/7.08 a__U91(X1, X2) -> U91(X1, X2) 11.48/7.08 a__U92(X) -> U92(X) 11.48/7.08 11.48/7.08 The set Q consists of the following terms: 11.48/7.08 11.48/7.08 a__isList(x0) 11.48/7.08 a__isNeList(x0) 11.48/7.08 a__isNePal(x0) 11.48/7.08 a__isPal(x0) 11.48/7.08 mark(__(x0, x1)) 11.48/7.08 mark(U11(x0, x1)) 11.48/7.08 mark(U12(x0, x1)) 11.48/7.08 mark(isPalListKind(x0)) 11.48/7.08 mark(U13(x0)) 11.48/7.08 mark(isNeList(x0)) 11.48/7.08 mark(U21(x0, x1, x2)) 11.48/7.08 mark(U22(x0, x1, x2)) 11.48/7.08 mark(U23(x0, x1, x2)) 11.48/7.08 mark(U24(x0, x1, x2)) 11.48/7.08 mark(U25(x0, x1)) 11.48/7.08 mark(isList(x0)) 11.48/7.08 mark(U26(x0)) 11.48/7.08 mark(U31(x0, x1)) 11.48/7.08 mark(U32(x0, x1)) 11.48/7.08 mark(U33(x0)) 11.48/7.08 mark(isQid(x0)) 11.48/7.08 mark(U41(x0, x1, x2)) 11.48/7.08 mark(U42(x0, x1, x2)) 11.48/7.08 mark(U43(x0, x1, x2)) 11.48/7.08 mark(U44(x0, x1, x2)) 11.48/7.08 mark(U45(x0, x1)) 11.48/7.08 mark(U46(x0)) 11.48/7.08 mark(U51(x0, x1, x2)) 11.48/7.08 mark(U52(x0, x1, x2)) 11.48/7.08 mark(U53(x0, x1, x2)) 11.48/7.08 mark(U54(x0, x1, x2)) 11.48/7.08 mark(U55(x0, x1)) 11.48/7.08 mark(U56(x0)) 11.48/7.08 mark(U61(x0, x1)) 11.48/7.08 mark(U62(x0, x1)) 11.48/7.08 mark(U63(x0)) 11.48/7.08 mark(U71(x0, x1, x2)) 11.48/7.08 mark(U72(x0, x1)) 11.48/7.08 mark(U73(x0, x1)) 11.48/7.08 mark(isPal(x0)) 11.48/7.08 mark(U74(x0)) 11.48/7.08 mark(U81(x0, x1)) 11.48/7.08 mark(U82(x0, x1)) 11.48/7.08 mark(U83(x0)) 11.48/7.08 mark(isNePal(x0)) 11.48/7.08 mark(U91(x0, x1)) 11.48/7.08 mark(U92(x0)) 11.48/7.08 mark(nil) 11.48/7.08 mark(tt) 11.48/7.08 mark(a) 11.48/7.08 mark(e) 11.48/7.08 mark(i) 11.48/7.08 mark(o) 11.48/7.08 mark(u) 11.48/7.08 a____(x0, x1) 11.48/7.08 a__U11(x0, x1) 11.48/7.08 a__U12(x0, x1) 11.48/7.08 a__isPalListKind(x0) 11.48/7.08 a__U13(x0) 11.48/7.08 a__U21(x0, x1, x2) 11.48/7.08 a__U22(x0, x1, x2) 11.48/7.08 a__U23(x0, x1, x2) 11.48/7.08 a__U24(x0, x1, x2) 11.48/7.08 a__U25(x0, x1) 11.48/7.08 a__U26(x0) 11.48/7.08 a__U31(x0, x1) 11.48/7.08 a__U32(x0, x1) 11.48/7.08 a__U33(x0) 11.48/7.08 a__isQid(x0) 11.48/7.08 a__U41(x0, x1, x2) 11.48/7.08 a__U42(x0, x1, x2) 11.48/7.08 a__U43(x0, x1, x2) 11.48/7.08 a__U44(x0, x1, x2) 11.48/7.08 a__U45(x0, x1) 11.48/7.08 a__U46(x0) 11.48/7.08 a__U51(x0, x1, x2) 11.48/7.08 a__U52(x0, x1, x2) 11.48/7.08 a__U53(x0, x1, x2) 11.48/7.08 a__U54(x0, x1, x2) 11.48/7.08 a__U55(x0, x1) 11.48/7.08 a__U56(x0) 11.48/7.08 a__U61(x0, x1) 11.48/7.08 a__U62(x0, x1) 11.48/7.08 a__U63(x0) 11.48/7.08 a__U71(x0, x1, x2) 11.48/7.08 a__U72(x0, x1) 11.48/7.08 a__U73(x0, x1) 11.48/7.08 a__U74(x0) 11.48/7.08 a__U81(x0, x1) 11.48/7.08 a__U82(x0, x1) 11.48/7.08 a__U83(x0) 11.48/7.08 a__U91(x0, x1) 11.48/7.08 a__U92(x0) 11.48/7.08 11.48/7.08 11.48/7.08 ---------------------------------------- 11.48/7.08 11.48/7.08 (3) QTRSRRRProof (EQUIVALENT) 11.48/7.08 Used ordering: 11.48/7.08 Polynomial interpretation [POLO]: 11.48/7.08 11.48/7.08 POL(U11(x_1, x_2)) = 1 + x_1 + 2*x_2 11.48/7.08 POL(U12(x_1, x_2)) = 1 + x_1 + 2*x_2 11.48/7.08 POL(U13(x_1)) = 1 + 2*x_1 11.48/7.08 POL(U21(x_1, x_2, x_3)) = 1 + x_1 + 2*x_2 + 2*x_3 11.48/7.08 POL(U22(x_1, x_2, x_3)) = 1 + x_1 + 2*x_2 + 2*x_3 11.48/7.08 POL(U23(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3 11.48/7.08 POL(U24(x_1, x_2, x_3)) = 1 + x_1 + 2*x_2 + 2*x_3 11.48/7.08 POL(U25(x_1, x_2)) = 1 + x_1 + 2*x_2 11.48/7.08 POL(U26(x_1)) = 1 + 2*x_1 11.48/7.08 POL(U31(x_1, x_2)) = 1 + x_1 + 2*x_2 11.48/7.08 POL(U32(x_1, x_2)) = 1 + x_1 + 2*x_2 11.48/7.08 POL(U33(x_1)) = 1 + 2*x_1 11.48/7.08 POL(U41(x_1, x_2, x_3)) = 1 + x_1 + 2*x_2 + 2*x_3 11.48/7.08 POL(U42(x_1, x_2, x_3)) = 1 + x_1 + 2*x_2 + 2*x_3 11.48/7.08 POL(U43(x_1, x_2, x_3)) = 1 + x_1 + 2*x_2 + 2*x_3 11.48/7.08 POL(U44(x_1, x_2, x_3)) = 1 + x_1 + 2*x_2 + 2*x_3 11.48/7.08 POL(U45(x_1, x_2)) = 1 + x_1 + 2*x_2 11.48/7.08 POL(U46(x_1)) = 1 + x_1 11.48/7.08 POL(U51(x_1, x_2, x_3)) = 1 + x_1 + 2*x_2 + 2*x_3 11.48/7.08 POL(U52(x_1, x_2, x_3)) = 1 + x_1 + 2*x_2 + 2*x_3 11.48/7.08 POL(U53(x_1, x_2, x_3)) = 1 + x_1 + 2*x_2 + 2*x_3 11.48/7.08 POL(U54(x_1, x_2, x_3)) = 1 + x_1 + 2*x_2 + 2*x_3 11.48/7.08 POL(U55(x_1, x_2)) = 1 + x_1 + 2*x_2 11.48/7.08 POL(U56(x_1)) = 1 + x_1 11.48/7.08 POL(U61(x_1, x_2)) = 1 + x_1 + 2*x_2 11.48/7.08 POL(U62(x_1, x_2)) = 1 + x_1 + 2*x_2 11.48/7.08 POL(U63(x_1)) = 1 + 2*x_1 11.48/7.08 POL(U71(x_1, x_2, x_3)) = 1 + x_1 + 2*x_2 + 2*x_3 11.48/7.08 POL(U72(x_1, x_2)) = 1 + x_1 + 2*x_2 11.48/7.08 POL(U73(x_1, x_2)) = 1 + x_1 + 2*x_2 11.48/7.08 POL(U74(x_1)) = 1 + 2*x_1 11.48/7.08 POL(U81(x_1, x_2)) = 1 + x_1 + 2*x_2 11.48/7.08 POL(U82(x_1, x_2)) = 1 + x_1 + 2*x_2 11.48/7.08 POL(U83(x_1)) = 1 + 2*x_1 11.48/7.08 POL(U91(x_1, x_2)) = 1 + x_1 + x_2 11.48/7.08 POL(U92(x_1)) = 1 + 2*x_1 11.48/7.08 POL(__(x_1, x_2)) = 1 + x_1 + 2*x_2 11.48/7.08 POL(a) = 1 11.48/7.08 POL(a__U11(x_1, x_2)) = 2 + x_1 + 2*x_2 11.48/7.08 POL(a__U12(x_1, x_2)) = 2 + x_1 + 2*x_2 11.48/7.08 POL(a__U13(x_1)) = 2 + 2*x_1 11.48/7.08 POL(a__U21(x_1, x_2, x_3)) = 2 + x_1 + 2*x_2 + 2*x_3 11.48/7.08 POL(a__U22(x_1, x_2, x_3)) = 2 + x_1 + 2*x_2 + 2*x_3 11.48/7.08 POL(a__U23(x_1, x_2, x_3)) = 2 + x_1 + 2*x_2 + 2*x_3 11.48/7.08 POL(a__U24(x_1, x_2, x_3)) = 2 + x_1 + 2*x_2 + 2*x_3 11.48/7.08 POL(a__U25(x_1, x_2)) = 2 + x_1 + 2*x_2 11.48/7.08 POL(a__U26(x_1)) = 2 + 2*x_1 11.48/7.08 POL(a__U31(x_1, x_2)) = 2 + x_1 + 2*x_2 11.48/7.08 POL(a__U32(x_1, x_2)) = 2 + x_1 + 2*x_2 11.48/7.08 POL(a__U33(x_1)) = 2 + 2*x_1 11.48/7.08 POL(a__U41(x_1, x_2, x_3)) = 2 + x_1 + 2*x_2 + 2*x_3 11.48/7.08 POL(a__U42(x_1, x_2, x_3)) = 2 + x_1 + 2*x_2 + 2*x_3 11.48/7.08 POL(a__U43(x_1, x_2, x_3)) = 2 + x_1 + 2*x_2 + 2*x_3 11.48/7.08 POL(a__U44(x_1, x_2, x_3)) = 2 + x_1 + 2*x_2 + 2*x_3 11.48/7.08 POL(a__U45(x_1, x_2)) = 2 + x_1 + 2*x_2 11.48/7.08 POL(a__U46(x_1)) = 2 + x_1 11.48/7.08 POL(a__U51(x_1, x_2, x_3)) = 2 + x_1 + 2*x_2 + 2*x_3 11.48/7.08 POL(a__U52(x_1, x_2, x_3)) = 2 + x_1 + 2*x_2 + 2*x_3 11.48/7.08 POL(a__U53(x_1, x_2, x_3)) = 2 + x_1 + 2*x_2 + 2*x_3 11.48/7.08 POL(a__U54(x_1, x_2, x_3)) = 2 + x_1 + 2*x_2 + 2*x_3 11.48/7.08 POL(a__U55(x_1, x_2)) = 2 + x_1 + 2*x_2 11.48/7.08 POL(a__U56(x_1)) = 2 + x_1 11.48/7.08 POL(a__U61(x_1, x_2)) = 2 + x_1 + 2*x_2 11.48/7.08 POL(a__U62(x_1, x_2)) = 2 + x_1 + 2*x_2 11.48/7.08 POL(a__U63(x_1)) = 2 + 2*x_1 11.48/7.08 POL(a__U71(x_1, x_2, x_3)) = 2 + x_1 + 2*x_2 + 2*x_3 11.48/7.08 POL(a__U72(x_1, x_2)) = 2 + x_1 + 2*x_2 11.48/7.08 POL(a__U73(x_1, x_2)) = 2 + x_1 + 2*x_2 11.48/7.08 POL(a__U74(x_1)) = 2 + 2*x_1 11.48/7.08 POL(a__U81(x_1, x_2)) = 2 + x_1 + 2*x_2 11.48/7.08 POL(a__U82(x_1, x_2)) = 2 + x_1 + 2*x_2 11.48/7.08 POL(a__U83(x_1)) = 2 + 2*x_1 11.48/7.08 POL(a__U91(x_1, x_2)) = 2 + x_1 + 2*x_2 11.48/7.08 POL(a__U92(x_1)) = 2 + 2*x_1 11.48/7.08 POL(a____(x_1, x_2)) = 2 + x_1 + 2*x_2 11.48/7.08 POL(a__isList(x_1)) = 2 + 2*x_1 11.48/7.08 POL(a__isNeList(x_1)) = 2 + 2*x_1 11.48/7.08 POL(a__isNePal(x_1)) = 2 + 2*x_1 11.48/7.08 POL(a__isPal(x_1)) = 2 + 2*x_1 11.48/7.08 POL(a__isPalListKind(x_1)) = 2 + 2*x_1 11.48/7.08 POL(a__isQid(x_1)) = 2 + 2*x_1 11.48/7.08 POL(e) = 1 11.48/7.08 POL(i) = 1 11.48/7.08 POL(isList(x_1)) = 1 + 2*x_1 11.48/7.08 POL(isNeList(x_1)) = 1 + 2*x_1 11.48/7.08 POL(isNePal(x_1)) = 1 + 2*x_1 11.48/7.08 POL(isPal(x_1)) = 1 + 2*x_1 11.48/7.08 POL(isPalListKind(x_1)) = 1 + 2*x_1 11.48/7.08 POL(isQid(x_1)) = 1 + 2*x_1 11.48/7.08 POL(mark(x_1)) = 2*x_1 11.48/7.08 POL(nil) = 1 11.48/7.08 POL(o) = 1 11.48/7.08 POL(tt) = 1 11.48/7.08 POL(u) = 1 11.48/7.08 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 11.48/7.08 11.48/7.08 a__U13(tt) -> tt 11.48/7.08 a__U26(tt) -> tt 11.48/7.08 a__U33(tt) -> tt 11.48/7.08 a__U63(tt) -> tt 11.48/7.08 a__U74(tt) -> tt 11.48/7.08 a__U83(tt) -> tt 11.48/7.08 a__U92(tt) -> tt 11.48/7.08 a__isPalListKind(nil) -> tt 11.48/7.08 a__isPalListKind(o) -> tt 11.48/7.08 mark(nil) -> nil 11.48/7.08 mark(tt) -> tt 11.48/7.08 mark(a) -> a 11.48/7.08 mark(e) -> e 11.48/7.08 mark(i) -> i 11.48/7.08 mark(o) -> o 11.48/7.08 mark(u) -> u 11.48/7.08 a____(X1, X2) -> __(X1, X2) 11.48/7.08 a__U11(X1, X2) -> U11(X1, X2) 11.48/7.08 a__U12(X1, X2) -> U12(X1, X2) 11.48/7.08 a__isPalListKind(X) -> isPalListKind(X) 11.48/7.08 a__U13(X) -> U13(X) 11.48/7.08 a__isNeList(X) -> isNeList(X) 11.48/7.08 a__U21(X1, X2, X3) -> U21(X1, X2, X3) 11.48/7.08 a__U22(X1, X2, X3) -> U22(X1, X2, X3) 11.48/7.08 a__U23(X1, X2, X3) -> U23(X1, X2, X3) 11.48/7.08 a__U24(X1, X2, X3) -> U24(X1, X2, X3) 11.48/7.08 a__U25(X1, X2) -> U25(X1, X2) 11.48/7.08 a__isList(X) -> isList(X) 11.48/7.08 a__U26(X) -> U26(X) 11.48/7.08 a__U31(X1, X2) -> U31(X1, X2) 11.48/7.08 a__U32(X1, X2) -> U32(X1, X2) 11.48/7.08 a__U33(X) -> U33(X) 11.48/7.08 a__isQid(X) -> isQid(X) 11.48/7.08 a__U41(X1, X2, X3) -> U41(X1, X2, X3) 11.48/7.08 a__U42(X1, X2, X3) -> U42(X1, X2, X3) 11.48/7.08 a__U43(X1, X2, X3) -> U43(X1, X2, X3) 11.48/7.08 a__U44(X1, X2, X3) -> U44(X1, X2, X3) 11.48/7.08 a__U45(X1, X2) -> U45(X1, X2) 11.48/7.08 a__U46(X) -> U46(X) 11.48/7.08 a__U51(X1, X2, X3) -> U51(X1, X2, X3) 11.48/7.08 a__U52(X1, X2, X3) -> U52(X1, X2, X3) 11.48/7.08 a__U53(X1, X2, X3) -> U53(X1, X2, X3) 11.48/7.08 a__U54(X1, X2, X3) -> U54(X1, X2, X3) 11.48/7.08 a__U55(X1, X2) -> U55(X1, X2) 11.48/7.08 a__U56(X) -> U56(X) 11.48/7.08 a__U61(X1, X2) -> U61(X1, X2) 11.48/7.08 a__U62(X1, X2) -> U62(X1, X2) 11.48/7.08 a__U63(X) -> U63(X) 11.48/7.08 a__U71(X1, X2, X3) -> U71(X1, X2, X3) 11.48/7.08 a__U72(X1, X2) -> U72(X1, X2) 11.48/7.08 a__U73(X1, X2) -> U73(X1, X2) 11.48/7.08 a__isPal(X) -> isPal(X) 11.48/7.08 a__U74(X) -> U74(X) 11.48/7.08 a__U81(X1, X2) -> U81(X1, X2) 11.48/7.08 a__U82(X1, X2) -> U82(X1, X2) 11.48/7.08 a__U83(X) -> U83(X) 11.48/7.08 a__isNePal(X) -> isNePal(X) 11.48/7.08 a__U91(X1, X2) -> U91(X1, X2) 11.48/7.08 a__U92(X) -> U92(X) 11.48/7.08 11.48/7.08 11.48/7.08 11.48/7.08 11.48/7.08 ---------------------------------------- 11.48/7.08 11.48/7.08 (4) 11.48/7.08 Obligation: 11.48/7.08 Q restricted rewrite system: 11.48/7.08 The TRS R consists of the following rules: 11.48/7.08 11.48/7.08 mark(__(X1, X2)) -> a____(mark(X1), mark(X2)) 11.48/7.08 mark(U11(X1, X2)) -> a__U11(mark(X1), X2) 11.48/7.08 mark(U12(X1, X2)) -> a__U12(mark(X1), X2) 11.48/7.08 mark(isPalListKind(X)) -> a__isPalListKind(X) 11.48/7.08 mark(U13(X)) -> a__U13(mark(X)) 11.48/7.08 mark(isNeList(X)) -> a__isNeList(X) 11.48/7.08 mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3) 11.48/7.08 mark(U22(X1, X2, X3)) -> a__U22(mark(X1), X2, X3) 11.48/7.08 mark(U23(X1, X2, X3)) -> a__U23(mark(X1), X2, X3) 11.48/7.08 mark(U24(X1, X2, X3)) -> a__U24(mark(X1), X2, X3) 11.48/7.08 mark(U25(X1, X2)) -> a__U25(mark(X1), X2) 11.48/7.08 mark(isList(X)) -> a__isList(X) 11.48/7.08 mark(U26(X)) -> a__U26(mark(X)) 11.48/7.08 mark(U31(X1, X2)) -> a__U31(mark(X1), X2) 11.48/7.08 mark(U32(X1, X2)) -> a__U32(mark(X1), X2) 11.48/7.08 mark(U33(X)) -> a__U33(mark(X)) 11.48/7.08 mark(isQid(X)) -> a__isQid(X) 11.48/7.08 mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) 11.48/7.08 mark(U42(X1, X2, X3)) -> a__U42(mark(X1), X2, X3) 11.48/7.08 mark(U43(X1, X2, X3)) -> a__U43(mark(X1), X2, X3) 11.48/7.08 mark(U44(X1, X2, X3)) -> a__U44(mark(X1), X2, X3) 11.48/7.08 mark(U45(X1, X2)) -> a__U45(mark(X1), X2) 11.48/7.08 mark(U46(X)) -> a__U46(mark(X)) 11.48/7.08 mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3) 11.48/7.08 mark(U52(X1, X2, X3)) -> a__U52(mark(X1), X2, X3) 11.48/7.08 mark(U53(X1, X2, X3)) -> a__U53(mark(X1), X2, X3) 11.48/7.08 mark(U54(X1, X2, X3)) -> a__U54(mark(X1), X2, X3) 11.48/7.08 mark(U55(X1, X2)) -> a__U55(mark(X1), X2) 11.48/7.08 mark(U56(X)) -> a__U56(mark(X)) 11.48/7.08 mark(U61(X1, X2)) -> a__U61(mark(X1), X2) 11.48/7.08 mark(U62(X1, X2)) -> a__U62(mark(X1), X2) 11.48/7.08 mark(U63(X)) -> a__U63(mark(X)) 11.48/7.08 mark(U71(X1, X2, X3)) -> a__U71(mark(X1), X2, X3) 11.48/7.08 mark(U72(X1, X2)) -> a__U72(mark(X1), X2) 11.48/7.08 mark(U73(X1, X2)) -> a__U73(mark(X1), X2) 11.48/7.08 mark(isPal(X)) -> a__isPal(X) 11.48/7.08 mark(U74(X)) -> a__U74(mark(X)) 11.48/7.08 mark(U81(X1, X2)) -> a__U81(mark(X1), X2) 11.48/7.08 mark(U82(X1, X2)) -> a__U82(mark(X1), X2) 11.48/7.08 mark(U83(X)) -> a__U83(mark(X)) 11.48/7.08 mark(isNePal(X)) -> a__isNePal(X) 11.48/7.08 mark(U91(X1, X2)) -> a__U91(mark(X1), X2) 11.48/7.08 mark(U92(X)) -> a__U92(mark(X)) 11.48/7.08 11.48/7.08 The set Q consists of the following terms: 11.48/7.08 11.48/7.08 a__isList(x0) 11.48/7.08 a__isNeList(x0) 11.48/7.08 a__isNePal(x0) 11.48/7.08 a__isPal(x0) 11.48/7.08 mark(__(x0, x1)) 11.48/7.08 mark(U11(x0, x1)) 11.48/7.08 mark(U12(x0, x1)) 11.48/7.08 mark(isPalListKind(x0)) 11.48/7.08 mark(U13(x0)) 11.48/7.08 mark(isNeList(x0)) 11.48/7.08 mark(U21(x0, x1, x2)) 11.48/7.08 mark(U22(x0, x1, x2)) 11.48/7.08 mark(U23(x0, x1, x2)) 11.48/7.08 mark(U24(x0, x1, x2)) 11.48/7.08 mark(U25(x0, x1)) 11.48/7.08 mark(isList(x0)) 11.48/7.08 mark(U26(x0)) 11.48/7.08 mark(U31(x0, x1)) 11.48/7.08 mark(U32(x0, x1)) 11.48/7.08 mark(U33(x0)) 11.48/7.08 mark(isQid(x0)) 11.48/7.08 mark(U41(x0, x1, x2)) 11.48/7.08 mark(U42(x0, x1, x2)) 11.48/7.08 mark(U43(x0, x1, x2)) 11.48/7.08 mark(U44(x0, x1, x2)) 11.48/7.08 mark(U45(x0, x1)) 11.48/7.08 mark(U46(x0)) 11.48/7.08 mark(U51(x0, x1, x2)) 11.48/7.08 mark(U52(x0, x1, x2)) 11.48/7.08 mark(U53(x0, x1, x2)) 11.48/7.08 mark(U54(x0, x1, x2)) 11.48/7.08 mark(U55(x0, x1)) 11.48/7.08 mark(U56(x0)) 11.48/7.08 mark(U61(x0, x1)) 11.48/7.08 mark(U62(x0, x1)) 11.48/7.08 mark(U63(x0)) 11.48/7.08 mark(U71(x0, x1, x2)) 11.48/7.08 mark(U72(x0, x1)) 11.48/7.08 mark(U73(x0, x1)) 11.48/7.08 mark(isPal(x0)) 11.48/7.08 mark(U74(x0)) 11.48/7.08 mark(U81(x0, x1)) 11.48/7.08 mark(U82(x0, x1)) 11.48/7.08 mark(U83(x0)) 11.48/7.08 mark(isNePal(x0)) 11.48/7.08 mark(U91(x0, x1)) 11.48/7.08 mark(U92(x0)) 11.48/7.08 mark(nil) 11.48/7.08 mark(tt) 11.48/7.08 mark(a) 11.48/7.08 mark(e) 11.48/7.08 mark(i) 11.48/7.08 mark(o) 11.48/7.08 mark(u) 11.48/7.08 a____(x0, x1) 11.48/7.08 a__U11(x0, x1) 11.48/7.08 a__U12(x0, x1) 11.48/7.08 a__isPalListKind(x0) 11.48/7.08 a__U13(x0) 11.48/7.08 a__U21(x0, x1, x2) 11.48/7.08 a__U22(x0, x1, x2) 11.48/7.08 a__U23(x0, x1, x2) 11.48/7.08 a__U24(x0, x1, x2) 11.48/7.08 a__U25(x0, x1) 11.48/7.08 a__U26(x0) 11.48/7.08 a__U31(x0, x1) 11.48/7.08 a__U32(x0, x1) 11.48/7.08 a__U33(x0) 11.48/7.08 a__isQid(x0) 11.48/7.08 a__U41(x0, x1, x2) 11.48/7.08 a__U42(x0, x1, x2) 11.48/7.08 a__U43(x0, x1, x2) 11.48/7.08 a__U44(x0, x1, x2) 11.48/7.08 a__U45(x0, x1) 11.48/7.08 a__U46(x0) 11.48/7.08 a__U51(x0, x1, x2) 11.48/7.08 a__U52(x0, x1, x2) 11.48/7.08 a__U53(x0, x1, x2) 11.48/7.08 a__U54(x0, x1, x2) 11.48/7.08 a__U55(x0, x1) 11.48/7.08 a__U56(x0) 11.48/7.08 a__U61(x0, x1) 11.48/7.08 a__U62(x0, x1) 11.48/7.08 a__U63(x0) 11.48/7.08 a__U71(x0, x1, x2) 11.48/7.08 a__U72(x0, x1) 11.48/7.08 a__U73(x0, x1) 11.48/7.08 a__U74(x0) 11.48/7.08 a__U81(x0, x1) 11.48/7.08 a__U82(x0, x1) 11.48/7.08 a__U83(x0) 11.48/7.08 a__U91(x0, x1) 11.48/7.08 a__U92(x0) 11.48/7.08 11.48/7.08 11.48/7.08 ---------------------------------------- 11.48/7.08 11.48/7.08 (5) QTRSRRRProof (EQUIVALENT) 11.48/7.08 Used ordering: 11.48/7.08 Polynomial interpretation [POLO]: 11.48/7.08 11.48/7.08 POL(U11(x_1, x_2)) = 2 + 2*x_1 + 2*x_2 11.48/7.08 POL(U12(x_1, x_2)) = 2 + 2*x_1 + x_2 11.48/7.08 POL(U13(x_1)) = 2 + 2*x_1 11.48/7.08 POL(U21(x_1, x_2, x_3)) = 1 + 2*x_1 + 2*x_2 + x_3 11.48/7.08 POL(U22(x_1, x_2, x_3)) = 2 + 2*x_1 + x_2 + x_3 11.48/7.08 POL(U23(x_1, x_2, x_3)) = 1 + 2*x_1 + 2*x_2 + 2*x_3 11.48/7.08 POL(U24(x_1, x_2, x_3)) = 2 + 2*x_1 + x_2 + x_3 11.48/7.08 POL(U25(x_1, x_2)) = 1 + 2*x_1 + 2*x_2 11.48/7.08 POL(U26(x_1)) = 2*x_1 11.48/7.08 POL(U31(x_1, x_2)) = 2*x_1 + x_2 11.48/7.08 POL(U32(x_1, x_2)) = 2 + 2*x_1 + x_2 11.48/7.08 POL(U33(x_1)) = 2 + 2*x_1 11.48/7.08 POL(U41(x_1, x_2, x_3)) = 2 + 2*x_1 + x_2 + 2*x_3 11.48/7.08 POL(U42(x_1, x_2, x_3)) = 2 + 2*x_1 + 2*x_2 + 2*x_3 11.48/7.08 POL(U43(x_1, x_2, x_3)) = 2 + 2*x_1 + 2*x_2 + 2*x_3 11.48/7.08 POL(U44(x_1, x_2, x_3)) = 2 + 2*x_1 + x_2 + x_3 11.48/7.08 POL(U45(x_1, x_2)) = 2 + 2*x_1 + 2*x_2 11.48/7.08 POL(U46(x_1)) = 2 + 2*x_1 11.48/7.08 POL(U51(x_1, x_2, x_3)) = 2 + 2*x_1 + 2*x_2 + 2*x_3 11.48/7.08 POL(U52(x_1, x_2, x_3)) = 1 + 2*x_1 + 2*x_2 + 2*x_3 11.48/7.08 POL(U53(x_1, x_2, x_3)) = 2 + 2*x_1 + 2*x_2 + 2*x_3 11.48/7.08 POL(U54(x_1, x_2, x_3)) = 1 + 2*x_1 + 2*x_2 + x_3 11.48/7.08 POL(U55(x_1, x_2)) = 2 + 2*x_1 + x_2 11.48/7.08 POL(U56(x_1)) = 2 + 2*x_1 11.48/7.08 POL(U61(x_1, x_2)) = 1 + 2*x_1 + x_2 11.48/7.08 POL(U62(x_1, x_2)) = 2 + 2*x_1 + x_2 11.48/7.08 POL(U63(x_1)) = 2 + 2*x_1 11.48/7.08 POL(U71(x_1, x_2, x_3)) = 2 + 2*x_1 + x_2 + 2*x_3 11.48/7.08 POL(U72(x_1, x_2)) = 2 + 2*x_1 + 2*x_2 11.48/7.08 POL(U73(x_1, x_2)) = 2 + 2*x_1 + 2*x_2 11.48/7.08 POL(U74(x_1)) = 2 + 2*x_1 11.48/7.08 POL(U81(x_1, x_2)) = 2 + 2*x_1 + x_2 11.48/7.08 POL(U82(x_1, x_2)) = 2 + 2*x_1 + 2*x_2 11.48/7.08 POL(U83(x_1)) = 2 + 2*x_1 11.48/7.08 POL(U91(x_1, x_2)) = 2 + 2*x_1 + 2*x_2 11.48/7.08 POL(U92(x_1)) = 2 + 2*x_1 11.48/7.08 POL(__(x_1, x_2)) = 2 + 2*x_1 + 2*x_2 11.48/7.08 POL(a__U11(x_1, x_2)) = 1 + x_1 + 2*x_2 11.48/7.08 POL(a__U12(x_1, x_2)) = 2*x_1 + 2*x_2 11.48/7.08 POL(a__U13(x_1)) = 1 + x_1 11.48/7.08 POL(a__U21(x_1, x_2, x_3)) = x_1 + 2*x_2 + 2*x_3 11.48/7.08 POL(a__U22(x_1, x_2, x_3)) = x_1 + 2*x_2 + 2*x_3 11.48/7.08 POL(a__U23(x_1, x_2, x_3)) = 1 + x_1 + 2*x_2 + 2*x_3 11.48/7.08 POL(a__U24(x_1, x_2, x_3)) = 2*x_1 + 2*x_2 + 2*x_3 11.48/7.08 POL(a__U25(x_1, x_2)) = x_1 + 2*x_2 11.48/7.08 POL(a__U26(x_1)) = x_1 11.48/7.08 POL(a__U31(x_1, x_2)) = x_1 + 2*x_2 11.48/7.08 POL(a__U32(x_1, x_2)) = 2*x_1 + 2*x_2 11.48/7.08 POL(a__U33(x_1)) = 2*x_1 11.48/7.08 POL(a__U41(x_1, x_2, x_3)) = 1 + x_1 + 2*x_2 + 2*x_3 11.48/7.08 POL(a__U42(x_1, x_2, x_3)) = 1 + x_1 + 2*x_2 + 2*x_3 11.48/7.08 POL(a__U43(x_1, x_2, x_3)) = 1 + x_1 + 2*x_2 + 2*x_3 11.48/7.08 POL(a__U44(x_1, x_2, x_3)) = 1 + x_1 + 2*x_2 + 2*x_3 11.48/7.08 POL(a__U45(x_1, x_2)) = 1 + x_1 + 2*x_2 11.48/7.08 POL(a__U46(x_1)) = 1 + x_1 11.48/7.08 POL(a__U51(x_1, x_2, x_3)) = 1 + x_1 + 2*x_2 + 2*x_3 11.48/7.08 POL(a__U52(x_1, x_2, x_3)) = x_1 + 2*x_2 + 2*x_3 11.48/7.08 POL(a__U53(x_1, x_2, x_3)) = 1 + x_1 + 2*x_2 + 2*x_3 11.48/7.08 POL(a__U54(x_1, x_2, x_3)) = x_1 + 2*x_2 + 2*x_3 11.48/7.08 POL(a__U55(x_1, x_2)) = 1 + x_1 + 2*x_2 11.48/7.08 POL(a__U56(x_1)) = 1 + x_1 11.48/7.08 POL(a__U61(x_1, x_2)) = x_1 + 2*x_2 11.48/7.08 POL(a__U62(x_1, x_2)) = 1 + x_1 + 2*x_2 11.48/7.08 POL(a__U63(x_1)) = 1 + x_1 11.48/7.08 POL(a__U71(x_1, x_2, x_3)) = 1 + x_1 + 2*x_2 + 2*x_3 11.48/7.08 POL(a__U72(x_1, x_2)) = 1 + x_1 + 2*x_2 11.48/7.08 POL(a__U73(x_1, x_2)) = 1 + x_1 + 2*x_2 11.48/7.08 POL(a__U74(x_1)) = 1 + x_1 11.48/7.08 POL(a__U81(x_1, x_2)) = 1 + x_1 + 2*x_2 11.48/7.08 POL(a__U82(x_1, x_2)) = 1 + x_1 + 2*x_2 11.48/7.08 POL(a__U83(x_1)) = 1 + x_1 11.48/7.08 POL(a__U91(x_1, x_2)) = 1 + x_1 + 2*x_2 11.48/7.08 POL(a__U92(x_1)) = 2*x_1 11.48/7.08 POL(a____(x_1, x_2)) = x_1 + x_2 11.48/7.08 POL(a__isList(x_1)) = 2*x_1 11.48/7.08 POL(a__isNeList(x_1)) = 2 + 2*x_1 11.48/7.08 POL(a__isNePal(x_1)) = 1 + 2*x_1 11.48/7.08 POL(a__isPal(x_1)) = 1 + 2*x_1 11.48/7.08 POL(a__isPalListKind(x_1)) = 2*x_1 11.48/7.08 POL(a__isQid(x_1)) = 2*x_1 11.48/7.08 POL(isList(x_1)) = x_1 11.48/7.08 POL(isNeList(x_1)) = 2 + x_1 11.48/7.08 POL(isNePal(x_1)) = 2*x_1 11.48/7.08 POL(isPal(x_1)) = x_1 11.48/7.08 POL(isPalListKind(x_1)) = 2*x_1 11.48/7.08 POL(isQid(x_1)) = 2*x_1 11.48/7.08 POL(mark(x_1)) = 1 + 2*x_1 11.48/7.08 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 11.48/7.08 11.48/7.08 mark(__(X1, X2)) -> a____(mark(X1), mark(X2)) 11.48/7.08 mark(U11(X1, X2)) -> a__U11(mark(X1), X2) 11.48/7.08 mark(U12(X1, X2)) -> a__U12(mark(X1), X2) 11.48/7.08 mark(isPalListKind(X)) -> a__isPalListKind(X) 11.48/7.08 mark(U13(X)) -> a__U13(mark(X)) 11.48/7.08 mark(isNeList(X)) -> a__isNeList(X) 11.48/7.08 mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3) 11.48/7.08 mark(U22(X1, X2, X3)) -> a__U22(mark(X1), X2, X3) 11.48/7.08 mark(U23(X1, X2, X3)) -> a__U23(mark(X1), X2, X3) 11.48/7.08 mark(U24(X1, X2, X3)) -> a__U24(mark(X1), X2, X3) 11.48/7.08 mark(U25(X1, X2)) -> a__U25(mark(X1), X2) 11.48/7.08 mark(isList(X)) -> a__isList(X) 11.48/7.08 mark(U32(X1, X2)) -> a__U32(mark(X1), X2) 11.48/7.08 mark(U33(X)) -> a__U33(mark(X)) 11.48/7.08 mark(isQid(X)) -> a__isQid(X) 11.48/7.08 mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) 11.48/7.08 mark(U42(X1, X2, X3)) -> a__U42(mark(X1), X2, X3) 11.48/7.08 mark(U43(X1, X2, X3)) -> a__U43(mark(X1), X2, X3) 11.48/7.08 mark(U44(X1, X2, X3)) -> a__U44(mark(X1), X2, X3) 11.48/7.08 mark(U45(X1, X2)) -> a__U45(mark(X1), X2) 11.48/7.08 mark(U46(X)) -> a__U46(mark(X)) 11.48/7.08 mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3) 11.48/7.08 mark(U52(X1, X2, X3)) -> a__U52(mark(X1), X2, X3) 11.48/7.08 mark(U53(X1, X2, X3)) -> a__U53(mark(X1), X2, X3) 11.48/7.08 mark(U54(X1, X2, X3)) -> a__U54(mark(X1), X2, X3) 11.48/7.08 mark(U55(X1, X2)) -> a__U55(mark(X1), X2) 11.48/7.08 mark(U56(X)) -> a__U56(mark(X)) 11.48/7.08 mark(U61(X1, X2)) -> a__U61(mark(X1), X2) 11.48/7.08 mark(U62(X1, X2)) -> a__U62(mark(X1), X2) 11.48/7.08 mark(U63(X)) -> a__U63(mark(X)) 11.48/7.08 mark(U71(X1, X2, X3)) -> a__U71(mark(X1), X2, X3) 11.48/7.08 mark(U72(X1, X2)) -> a__U72(mark(X1), X2) 11.48/7.08 mark(U73(X1, X2)) -> a__U73(mark(X1), X2) 11.48/7.08 mark(U74(X)) -> a__U74(mark(X)) 11.48/7.08 mark(U81(X1, X2)) -> a__U81(mark(X1), X2) 11.48/7.08 mark(U82(X1, X2)) -> a__U82(mark(X1), X2) 11.48/7.08 mark(U83(X)) -> a__U83(mark(X)) 11.48/7.08 mark(U91(X1, X2)) -> a__U91(mark(X1), X2) 11.48/7.08 mark(U92(X)) -> a__U92(mark(X)) 11.48/7.08 11.48/7.08 11.48/7.08 11.48/7.08 11.48/7.08 ---------------------------------------- 11.48/7.08 11.48/7.08 (6) 11.48/7.08 Obligation: 11.48/7.08 Q restricted rewrite system: 11.48/7.08 The TRS R consists of the following rules: 11.48/7.08 11.48/7.08 mark(U26(X)) -> a__U26(mark(X)) 11.48/7.08 mark(U31(X1, X2)) -> a__U31(mark(X1), X2) 11.48/7.08 mark(isPal(X)) -> a__isPal(X) 11.48/7.09 mark(isNePal(X)) -> a__isNePal(X) 11.48/7.09 11.48/7.09 The set Q consists of the following terms: 11.48/7.09 11.48/7.09 a__isList(x0) 11.48/7.09 a__isNeList(x0) 11.48/7.09 a__isNePal(x0) 11.48/7.09 a__isPal(x0) 11.48/7.09 mark(__(x0, x1)) 11.48/7.09 mark(U11(x0, x1)) 11.48/7.09 mark(U12(x0, x1)) 11.48/7.09 mark(isPalListKind(x0)) 11.48/7.09 mark(U13(x0)) 11.48/7.09 mark(isNeList(x0)) 11.48/7.09 mark(U21(x0, x1, x2)) 11.48/7.09 mark(U22(x0, x1, x2)) 11.48/7.09 mark(U23(x0, x1, x2)) 11.48/7.09 mark(U24(x0, x1, x2)) 11.48/7.09 mark(U25(x0, x1)) 11.48/7.09 mark(isList(x0)) 11.48/7.09 mark(U26(x0)) 11.48/7.09 mark(U31(x0, x1)) 11.48/7.09 mark(U32(x0, x1)) 11.48/7.09 mark(U33(x0)) 11.48/7.09 mark(isQid(x0)) 11.48/7.09 mark(U41(x0, x1, x2)) 11.48/7.09 mark(U42(x0, x1, x2)) 11.48/7.09 mark(U43(x0, x1, x2)) 11.48/7.09 mark(U44(x0, x1, x2)) 11.48/7.09 mark(U45(x0, x1)) 11.48/7.09 mark(U46(x0)) 11.48/7.09 mark(U51(x0, x1, x2)) 11.48/7.09 mark(U52(x0, x1, x2)) 11.48/7.09 mark(U53(x0, x1, x2)) 11.48/7.09 mark(U54(x0, x1, x2)) 11.48/7.09 mark(U55(x0, x1)) 11.48/7.09 mark(U56(x0)) 11.48/7.09 mark(U61(x0, x1)) 11.48/7.09 mark(U62(x0, x1)) 11.48/7.09 mark(U63(x0)) 11.48/7.09 mark(U71(x0, x1, x2)) 11.48/7.09 mark(U72(x0, x1)) 11.48/7.09 mark(U73(x0, x1)) 11.48/7.09 mark(isPal(x0)) 11.48/7.09 mark(U74(x0)) 11.48/7.09 mark(U81(x0, x1)) 11.48/7.09 mark(U82(x0, x1)) 11.48/7.09 mark(U83(x0)) 11.48/7.09 mark(isNePal(x0)) 11.48/7.09 mark(U91(x0, x1)) 11.48/7.09 mark(U92(x0)) 11.48/7.09 mark(nil) 11.48/7.09 mark(tt) 11.48/7.09 mark(a) 11.48/7.09 mark(e) 11.48/7.09 mark(i) 11.48/7.09 mark(o) 11.48/7.09 mark(u) 11.48/7.09 a____(x0, x1) 11.48/7.09 a__U11(x0, x1) 11.48/7.09 a__U12(x0, x1) 11.48/7.09 a__isPalListKind(x0) 11.48/7.09 a__U13(x0) 11.48/7.09 a__U21(x0, x1, x2) 11.48/7.09 a__U22(x0, x1, x2) 11.48/7.09 a__U23(x0, x1, x2) 11.48/7.09 a__U24(x0, x1, x2) 11.48/7.09 a__U25(x0, x1) 11.48/7.09 a__U26(x0) 11.48/7.09 a__U31(x0, x1) 11.48/7.09 a__U32(x0, x1) 11.48/7.09 a__U33(x0) 11.48/7.09 a__isQid(x0) 11.48/7.09 a__U41(x0, x1, x2) 11.48/7.09 a__U42(x0, x1, x2) 11.48/7.09 a__U43(x0, x1, x2) 11.48/7.09 a__U44(x0, x1, x2) 11.48/7.09 a__U45(x0, x1) 11.48/7.09 a__U46(x0) 11.48/7.09 a__U51(x0, x1, x2) 11.48/7.09 a__U52(x0, x1, x2) 11.48/7.09 a__U53(x0, x1, x2) 11.48/7.09 a__U54(x0, x1, x2) 11.48/7.09 a__U55(x0, x1) 11.48/7.09 a__U56(x0) 11.48/7.09 a__U61(x0, x1) 11.48/7.09 a__U62(x0, x1) 11.48/7.09 a__U63(x0) 11.48/7.09 a__U71(x0, x1, x2) 11.48/7.09 a__U72(x0, x1) 11.48/7.09 a__U73(x0, x1) 11.48/7.09 a__U74(x0) 11.48/7.09 a__U81(x0, x1) 11.48/7.09 a__U82(x0, x1) 11.48/7.09 a__U83(x0) 11.48/7.09 a__U91(x0, x1) 11.48/7.09 a__U92(x0) 11.48/7.09 11.48/7.09 11.48/7.09 ---------------------------------------- 11.48/7.09 11.48/7.09 (7) QTRSRRRProof (EQUIVALENT) 11.48/7.09 Used ordering: 11.48/7.09 mark/1)YES( 11.48/7.09 U26/1(YES) 11.48/7.09 a__U26/1(YES) 11.48/7.09 U31/2(YES,YES) 11.48/7.09 a__U31/2(YES,YES) 11.48/7.09 isPal/1(YES) 11.48/7.09 a__isPal/1(YES) 11.48/7.09 isNePal/1)YES( 11.48/7.09 a__isNePal/1)YES( 11.48/7.09 11.48/7.09 Quasi precedence: 11.48/7.09 [U26_1, a__U26_1] 11.48/7.09 U31_2 > a__U31_2 11.48/7.09 [isPal_1, a__isPal_1] 11.48/7.09 11.48/7.09 11.48/7.09 Status: 11.48/7.09 U26_1: multiset status 11.48/7.09 a__U26_1: multiset status 11.48/7.09 U31_2: multiset status 11.48/7.09 a__U31_2: multiset status 11.48/7.09 isPal_1: [1] 11.48/7.09 a__isPal_1: [1] 11.48/7.09 11.48/7.09 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 11.48/7.09 11.48/7.09 mark(U31(X1, X2)) -> a__U31(mark(X1), X2) 11.48/7.09 11.48/7.09 11.48/7.09 11.48/7.09 11.48/7.09 ---------------------------------------- 11.48/7.09 11.48/7.09 (8) 11.48/7.09 Obligation: 11.48/7.09 Q restricted rewrite system: 11.48/7.09 The TRS R consists of the following rules: 11.48/7.09 11.48/7.09 mark(U26(X)) -> a__U26(mark(X)) 11.48/7.09 mark(isPal(X)) -> a__isPal(X) 11.48/7.09 mark(isNePal(X)) -> a__isNePal(X) 11.48/7.09 11.48/7.09 The set Q consists of the following terms: 11.48/7.09 11.48/7.09 a__isList(x0) 11.48/7.09 a__isNeList(x0) 11.48/7.09 a__isNePal(x0) 11.48/7.09 a__isPal(x0) 11.48/7.09 mark(__(x0, x1)) 11.48/7.09 mark(U11(x0, x1)) 11.48/7.09 mark(U12(x0, x1)) 11.48/7.09 mark(isPalListKind(x0)) 11.48/7.09 mark(U13(x0)) 11.48/7.09 mark(isNeList(x0)) 11.48/7.09 mark(U21(x0, x1, x2)) 11.48/7.09 mark(U22(x0, x1, x2)) 11.48/7.09 mark(U23(x0, x1, x2)) 11.48/7.09 mark(U24(x0, x1, x2)) 11.48/7.09 mark(U25(x0, x1)) 11.48/7.09 mark(isList(x0)) 11.48/7.09 mark(U26(x0)) 11.48/7.09 mark(U31(x0, x1)) 11.48/7.09 mark(U32(x0, x1)) 11.48/7.09 mark(U33(x0)) 11.48/7.09 mark(isQid(x0)) 11.48/7.09 mark(U41(x0, x1, x2)) 11.48/7.09 mark(U42(x0, x1, x2)) 11.48/7.09 mark(U43(x0, x1, x2)) 11.48/7.09 mark(U44(x0, x1, x2)) 11.48/7.09 mark(U45(x0, x1)) 11.48/7.09 mark(U46(x0)) 11.48/7.09 mark(U51(x0, x1, x2)) 11.48/7.09 mark(U52(x0, x1, x2)) 11.48/7.09 mark(U53(x0, x1, x2)) 11.48/7.09 mark(U54(x0, x1, x2)) 11.48/7.09 mark(U55(x0, x1)) 11.48/7.09 mark(U56(x0)) 11.48/7.09 mark(U61(x0, x1)) 11.48/7.09 mark(U62(x0, x1)) 11.48/7.09 mark(U63(x0)) 11.48/7.09 mark(U71(x0, x1, x2)) 11.48/7.09 mark(U72(x0, x1)) 11.48/7.09 mark(U73(x0, x1)) 11.48/7.09 mark(isPal(x0)) 11.48/7.09 mark(U74(x0)) 11.48/7.09 mark(U81(x0, x1)) 11.48/7.09 mark(U82(x0, x1)) 11.48/7.09 mark(U83(x0)) 11.48/7.09 mark(isNePal(x0)) 11.48/7.09 mark(U91(x0, x1)) 11.48/7.09 mark(U92(x0)) 11.48/7.09 mark(nil) 11.48/7.09 mark(tt) 11.48/7.09 mark(a) 11.48/7.09 mark(e) 11.48/7.09 mark(i) 11.48/7.09 mark(o) 11.48/7.09 mark(u) 11.48/7.09 a____(x0, x1) 11.48/7.09 a__U11(x0, x1) 11.48/7.09 a__U12(x0, x1) 11.48/7.09 a__isPalListKind(x0) 11.48/7.09 a__U13(x0) 11.48/7.09 a__U21(x0, x1, x2) 11.48/7.09 a__U22(x0, x1, x2) 11.48/7.09 a__U23(x0, x1, x2) 11.48/7.09 a__U24(x0, x1, x2) 11.48/7.09 a__U25(x0, x1) 11.48/7.09 a__U26(x0) 11.48/7.09 a__U31(x0, x1) 11.48/7.09 a__U32(x0, x1) 11.48/7.09 a__U33(x0) 11.48/7.09 a__isQid(x0) 11.48/7.09 a__U41(x0, x1, x2) 11.48/7.09 a__U42(x0, x1, x2) 11.48/7.09 a__U43(x0, x1, x2) 11.48/7.09 a__U44(x0, x1, x2) 11.48/7.09 a__U45(x0, x1) 11.48/7.09 a__U46(x0) 11.48/7.09 a__U51(x0, x1, x2) 11.48/7.09 a__U52(x0, x1, x2) 11.48/7.09 a__U53(x0, x1, x2) 11.48/7.09 a__U54(x0, x1, x2) 11.48/7.09 a__U55(x0, x1) 11.48/7.09 a__U56(x0) 11.48/7.09 a__U61(x0, x1) 11.48/7.09 a__U62(x0, x1) 11.48/7.09 a__U63(x0) 11.48/7.09 a__U71(x0, x1, x2) 11.48/7.09 a__U72(x0, x1) 11.48/7.09 a__U73(x0, x1) 11.48/7.09 a__U74(x0) 11.48/7.09 a__U81(x0, x1) 11.48/7.09 a__U82(x0, x1) 11.48/7.09 a__U83(x0) 11.48/7.09 a__U91(x0, x1) 11.48/7.09 a__U92(x0) 11.48/7.09 11.48/7.09 11.48/7.09 ---------------------------------------- 11.48/7.09 11.48/7.09 (9) QTRSRRRProof (EQUIVALENT) 11.48/7.09 Used ordering: 11.48/7.09 Knuth-Bendix order [KBO] with precedence:mark_1 > U26_1 > a__isPal_1 > isNePal_1 > a__isNePal_1 > isPal_1 > a__U26_1 11.48/7.09 11.48/7.09 and weight map: 11.48/7.09 11.48/7.09 mark_1=3 11.48/7.09 U26_1=2 11.48/7.09 a__U26_1=1 11.48/7.09 isPal_1=1 11.48/7.09 a__isPal_1=4 11.48/7.09 isNePal_1=1 11.48/7.09 a__isNePal_1=2 11.48/7.09 11.48/7.09 The variable weight is 1With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 11.48/7.09 11.48/7.09 mark(U26(X)) -> a__U26(mark(X)) 11.48/7.09 mark(isPal(X)) -> a__isPal(X) 11.48/7.09 mark(isNePal(X)) -> a__isNePal(X) 11.48/7.09 11.48/7.09 11.48/7.09 11.48/7.09 11.48/7.09 ---------------------------------------- 11.48/7.09 11.48/7.09 (10) 11.48/7.09 Obligation: 11.48/7.09 Q restricted rewrite system: 11.48/7.09 R is empty. 11.48/7.09 The set Q consists of the following terms: 11.48/7.09 11.48/7.09 a__isList(x0) 11.48/7.09 a__isNeList(x0) 11.48/7.09 a__isNePal(x0) 11.48/7.09 a__isPal(x0) 11.48/7.09 mark(__(x0, x1)) 11.48/7.09 mark(U11(x0, x1)) 11.48/7.09 mark(U12(x0, x1)) 11.48/7.09 mark(isPalListKind(x0)) 11.48/7.09 mark(U13(x0)) 11.48/7.09 mark(isNeList(x0)) 11.48/7.09 mark(U21(x0, x1, x2)) 11.48/7.09 mark(U22(x0, x1, x2)) 11.48/7.09 mark(U23(x0, x1, x2)) 11.48/7.09 mark(U24(x0, x1, x2)) 11.48/7.09 mark(U25(x0, x1)) 11.48/7.09 mark(isList(x0)) 11.48/7.09 mark(U26(x0)) 11.48/7.09 mark(U31(x0, x1)) 11.48/7.09 mark(U32(x0, x1)) 11.48/7.09 mark(U33(x0)) 11.48/7.09 mark(isQid(x0)) 11.48/7.09 mark(U41(x0, x1, x2)) 11.48/7.09 mark(U42(x0, x1, x2)) 11.48/7.09 mark(U43(x0, x1, x2)) 11.48/7.09 mark(U44(x0, x1, x2)) 11.48/7.09 mark(U45(x0, x1)) 11.48/7.09 mark(U46(x0)) 11.48/7.09 mark(U51(x0, x1, x2)) 11.48/7.09 mark(U52(x0, x1, x2)) 11.48/7.09 mark(U53(x0, x1, x2)) 11.48/7.09 mark(U54(x0, x1, x2)) 11.48/7.09 mark(U55(x0, x1)) 11.48/7.09 mark(U56(x0)) 11.48/7.09 mark(U61(x0, x1)) 11.48/7.09 mark(U62(x0, x1)) 11.48/7.09 mark(U63(x0)) 11.48/7.09 mark(U71(x0, x1, x2)) 11.48/7.09 mark(U72(x0, x1)) 11.48/7.09 mark(U73(x0, x1)) 11.48/7.09 mark(isPal(x0)) 11.48/7.09 mark(U74(x0)) 11.48/7.09 mark(U81(x0, x1)) 11.48/7.09 mark(U82(x0, x1)) 11.48/7.09 mark(U83(x0)) 11.48/7.09 mark(isNePal(x0)) 11.48/7.09 mark(U91(x0, x1)) 11.48/7.09 mark(U92(x0)) 11.48/7.09 mark(nil) 11.48/7.09 mark(tt) 11.48/7.09 mark(a) 11.48/7.09 mark(e) 11.48/7.09 mark(i) 11.48/7.09 mark(o) 11.48/7.09 mark(u) 11.48/7.09 a____(x0, x1) 11.48/7.09 a__U11(x0, x1) 11.48/7.09 a__U12(x0, x1) 11.48/7.09 a__isPalListKind(x0) 11.48/7.09 a__U13(x0) 11.48/7.09 a__U21(x0, x1, x2) 11.48/7.09 a__U22(x0, x1, x2) 11.48/7.09 a__U23(x0, x1, x2) 11.48/7.09 a__U24(x0, x1, x2) 11.48/7.09 a__U25(x0, x1) 11.48/7.09 a__U26(x0) 11.48/7.09 a__U31(x0, x1) 11.48/7.09 a__U32(x0, x1) 11.48/7.09 a__U33(x0) 11.48/7.09 a__isQid(x0) 11.48/7.09 a__U41(x0, x1, x2) 11.48/7.09 a__U42(x0, x1, x2) 11.48/7.09 a__U43(x0, x1, x2) 11.48/7.09 a__U44(x0, x1, x2) 11.48/7.09 a__U45(x0, x1) 11.48/7.09 a__U46(x0) 11.48/7.09 a__U51(x0, x1, x2) 11.48/7.09 a__U52(x0, x1, x2) 11.48/7.09 a__U53(x0, x1, x2) 11.48/7.09 a__U54(x0, x1, x2) 11.48/7.09 a__U55(x0, x1) 11.48/7.09 a__U56(x0) 11.48/7.09 a__U61(x0, x1) 11.48/7.09 a__U62(x0, x1) 11.48/7.09 a__U63(x0) 11.48/7.09 a__U71(x0, x1, x2) 11.48/7.09 a__U72(x0, x1) 11.48/7.09 a__U73(x0, x1) 11.48/7.09 a__U74(x0) 11.48/7.09 a__U81(x0, x1) 11.48/7.09 a__U82(x0, x1) 11.48/7.09 a__U83(x0) 11.48/7.09 a__U91(x0, x1) 11.48/7.09 a__U92(x0) 11.48/7.09 11.48/7.09 11.48/7.09 ---------------------------------------- 11.48/7.09 11.48/7.09 (11) RisEmptyProof (EQUIVALENT) 11.48/7.09 The TRS R is empty. Hence, termination is trivially proven. 11.48/7.09 ---------------------------------------- 11.48/7.09 11.48/7.09 (12) 11.48/7.09 YES 11.67/7.22 EOF