20.51/20.84 YES 20.51/20.84 20.51/20.84 Problem 1: 20.51/20.84 20.51/20.84 (VAR v_NonEmpty:S I:S P:S V:S V1:S V2:S X:S X1:S X2:S X3:S Y:S Z:S) 20.51/20.84 (RULES 20.51/20.84 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.51/20.84 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.51/20.84 a__U12(tt) -> tt 20.51/20.84 a__U12(X:S) -> U12(X:S) 20.51/20.84 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.51/20.84 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.51/20.84 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.51/20.84 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.51/20.84 a__U23(tt) -> tt 20.51/20.84 a__U23(X:S) -> U23(X:S) 20.51/20.84 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.51/20.84 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.51/20.84 a__U32(tt) -> tt 20.51/20.84 a__U32(X:S) -> U32(X:S) 20.51/20.84 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.51/20.84 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.51/20.84 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.51/20.84 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.51/20.84 a__U43(tt) -> tt 20.51/20.84 a__U43(X:S) -> U43(X:S) 20.51/20.84 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.51/20.84 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.51/20.84 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.51/20.84 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.51/20.84 a__U53(tt) -> tt 20.51/20.84 a__U53(X:S) -> U53(X:S) 20.51/20.84 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.51/20.84 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.51/20.84 a__U62(tt) -> tt 20.51/20.84 a__U62(X:S) -> U62(X:S) 20.51/20.84 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.51/20.84 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.51/20.84 a__U72(tt) -> tt 20.51/20.84 a__U72(X:S) -> U72(X:S) 20.51/20.84 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.51/20.84 a____(nil,X:S) -> mark(X:S) 20.51/20.84 a____(X:S,nil) -> mark(X:S) 20.51/20.84 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.51/20.84 a__and(tt,X:S) -> mark(X:S) 20.51/20.84 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.51/20.84 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.84 a__isList(nil) -> tt 20.51/20.84 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.51/20.84 a__isList(X:S) -> isList(X:S) 20.51/20.84 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.84 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.84 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.51/20.84 a__isNeList(X:S) -> isNeList(X:S) 20.51/20.84 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.51/20.84 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.51/20.84 a__isNePal(X:S) -> isNePal(X:S) 20.51/20.84 a__isPal(nil) -> tt 20.51/20.84 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.51/20.84 a__isPal(X:S) -> isPal(X:S) 20.51/20.84 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.84 a__isPalListKind(a) -> tt 20.51/20.84 a__isPalListKind(e) -> tt 20.51/20.84 a__isPalListKind(i) -> tt 20.51/20.84 a__isPalListKind(nil) -> tt 20.51/20.84 a__isPalListKind(o) -> tt 20.51/20.84 a__isPalListKind(u) -> tt 20.51/20.84 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.51/20.84 a__isQid(a) -> tt 20.51/20.84 a__isQid(e) -> tt 20.51/20.84 a__isQid(i) -> tt 20.51/20.84 a__isQid(o) -> tt 20.51/20.84 a__isQid(u) -> tt 20.51/20.84 a__isQid(X:S) -> isQid(X:S) 20.51/20.84 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.51/20.84 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.51/20.84 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.51/20.84 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.51/20.84 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.51/20.84 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.51/20.84 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.51/20.84 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.51/20.84 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.51/20.84 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.51/20.84 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.51/20.84 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.51/20.84 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.51/20.84 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.51/20.84 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.51/20.84 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.51/20.84 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.51/20.84 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.51/20.84 mark(a) -> a 20.51/20.84 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.51/20.84 mark(e) -> e 20.51/20.84 mark(i) -> i 20.51/20.84 mark(isList(X:S)) -> a__isList(X:S) 20.51/20.84 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.51/20.84 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.51/20.84 mark(isPal(X:S)) -> a__isPal(X:S) 20.51/20.84 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.51/20.84 mark(isQid(X:S)) -> a__isQid(X:S) 20.51/20.84 mark(nil) -> nil 20.51/20.84 mark(o) -> o 20.51/20.84 mark(tt) -> tt 20.51/20.84 mark(u) -> u 20.51/20.84 ) 20.51/20.84 (STRATEGY INNERMOST) 20.51/20.84 20.51/20.84 Problem 1: 20.51/20.84 20.51/20.84 Dependency Pairs Processor: 20.51/20.84 -> Pairs: 20.51/20.84 A__U11(tt,V:S) -> A__U12(a__isNeList(V:S)) 20.51/20.84 A__U11(tt,V:S) -> A__ISNELIST(V:S) 20.51/20.84 A__U21(tt,V1:S,V2:S) -> A__U22(a__isList(V1:S),V2:S) 20.51/20.84 A__U21(tt,V1:S,V2:S) -> A__ISLIST(V1:S) 20.51/20.84 A__U22(tt,V2:S) -> A__U23(a__isList(V2:S)) 20.51/20.84 A__U22(tt,V2:S) -> A__ISLIST(V2:S) 20.51/20.84 A__U31(tt,V:S) -> A__U32(a__isQid(V:S)) 20.51/20.84 A__U31(tt,V:S) -> A__ISQID(V:S) 20.51/20.84 A__U41(tt,V1:S,V2:S) -> A__U42(a__isList(V1:S),V2:S) 20.51/20.84 A__U41(tt,V1:S,V2:S) -> A__ISLIST(V1:S) 20.51/20.84 A__U42(tt,V2:S) -> A__U43(a__isNeList(V2:S)) 20.51/20.84 A__U42(tt,V2:S) -> A__ISNELIST(V2:S) 20.51/20.84 A__U51(tt,V1:S,V2:S) -> A__U52(a__isNeList(V1:S),V2:S) 20.51/20.84 A__U51(tt,V1:S,V2:S) -> A__ISNELIST(V1:S) 20.51/20.84 A__U52(tt,V2:S) -> A__U53(a__isList(V2:S)) 20.51/20.84 A__U52(tt,V2:S) -> A__ISLIST(V2:S) 20.51/20.84 A__U61(tt,V:S) -> A__U62(a__isQid(V:S)) 20.51/20.84 A__U61(tt,V:S) -> A__ISQID(V:S) 20.51/20.84 A__U71(tt,V:S) -> A__U72(a__isNePal(V:S)) 20.51/20.84 A__U71(tt,V:S) -> A__ISNEPAL(V:S) 20.51/20.84 A____(__(X:S,Y:S),Z:S) -> A____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.51/20.84 A____(__(X:S,Y:S),Z:S) -> A____(mark(Y:S),mark(Z:S)) 20.51/20.84 A____(__(X:S,Y:S),Z:S) -> MARK(X:S) 20.51/20.84 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S) 20.51/20.84 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 20.51/20.84 A____(nil,X:S) -> MARK(X:S) 20.51/20.84 A____(X:S,nil) -> MARK(X:S) 20.51/20.84 A__AND(tt,X:S) -> MARK(X:S) 20.51/20.84 A__ISLIST(__(V1:S,V2:S)) -> A__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.84 A__ISLIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.84 A__ISLIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.51/20.84 A__ISLIST(V:S) -> A__U11(a__isPalListKind(V:S),V:S) 20.51/20.84 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.84 A__ISNELIST(__(V1:S,V2:S)) -> A__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.84 A__ISNELIST(__(V1:S,V2:S)) -> A__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.84 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.84 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.51/20.84 A__ISNELIST(V:S) -> A__U31(a__isPalListKind(V:S),V:S) 20.51/20.84 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.84 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.51/20.84 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.51/20.84 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__ISQID(I:S) 20.51/20.84 A__ISNEPAL(V:S) -> A__U61(a__isPalListKind(V:S),V:S) 20.51/20.84 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.84 A__ISPAL(V:S) -> A__U71(a__isPalListKind(V:S),V:S) 20.51/20.84 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.84 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.84 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.51/20.84 MARK(U11(X1:S,X2:S)) -> A__U11(mark(X1:S),X2:S) 20.51/20.84 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(U12(X:S)) -> A__U12(mark(X:S)) 20.51/20.84 MARK(U12(X:S)) -> MARK(X:S) 20.51/20.84 MARK(U21(X1:S,X2:S,X3:S)) -> A__U21(mark(X1:S),X2:S,X3:S) 20.51/20.84 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.51/20.84 MARK(U22(X1:S,X2:S)) -> A__U22(mark(X1:S),X2:S) 20.51/20.84 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(U23(X:S)) -> A__U23(mark(X:S)) 20.51/20.84 MARK(U23(X:S)) -> MARK(X:S) 20.51/20.84 MARK(U31(X1:S,X2:S)) -> A__U31(mark(X1:S),X2:S) 20.51/20.84 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(U32(X:S)) -> A__U32(mark(X:S)) 20.51/20.84 MARK(U32(X:S)) -> MARK(X:S) 20.51/20.84 MARK(U41(X1:S,X2:S,X3:S)) -> A__U41(mark(X1:S),X2:S,X3:S) 20.51/20.84 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.51/20.84 MARK(U42(X1:S,X2:S)) -> A__U42(mark(X1:S),X2:S) 20.51/20.84 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(U43(X:S)) -> A__U43(mark(X:S)) 20.51/20.84 MARK(U43(X:S)) -> MARK(X:S) 20.51/20.84 MARK(U51(X1:S,X2:S,X3:S)) -> A__U51(mark(X1:S),X2:S,X3:S) 20.51/20.84 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.51/20.84 MARK(U52(X1:S,X2:S)) -> A__U52(mark(X1:S),X2:S) 20.51/20.84 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(U53(X:S)) -> A__U53(mark(X:S)) 20.51/20.84 MARK(U53(X:S)) -> MARK(X:S) 20.51/20.84 MARK(U61(X1:S,X2:S)) -> A__U61(mark(X1:S),X2:S) 20.51/20.84 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(U62(X:S)) -> A__U62(mark(X:S)) 20.51/20.84 MARK(U62(X:S)) -> MARK(X:S) 20.51/20.84 MARK(U71(X1:S,X2:S)) -> A__U71(mark(X1:S),X2:S) 20.51/20.84 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(U72(X:S)) -> A__U72(mark(X:S)) 20.51/20.84 MARK(U72(X:S)) -> MARK(X:S) 20.51/20.84 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 20.51/20.84 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.51/20.84 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.51/20.84 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.51/20.84 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.51/20.84 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.51/20.84 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.51/20.84 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.51/20.84 MARK(isQid(X:S)) -> A__ISQID(X:S) 20.51/20.84 -> Rules: 20.51/20.84 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.51/20.84 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.51/20.84 a__U12(tt) -> tt 20.51/20.84 a__U12(X:S) -> U12(X:S) 20.51/20.84 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.51/20.84 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.51/20.84 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.51/20.84 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.51/20.84 a__U23(tt) -> tt 20.51/20.84 a__U23(X:S) -> U23(X:S) 20.51/20.84 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.51/20.84 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.51/20.84 a__U32(tt) -> tt 20.51/20.84 a__U32(X:S) -> U32(X:S) 20.51/20.84 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.51/20.84 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.51/20.84 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.51/20.84 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.51/20.84 a__U43(tt) -> tt 20.51/20.84 a__U43(X:S) -> U43(X:S) 20.51/20.84 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.51/20.84 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.51/20.84 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.51/20.84 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.51/20.84 a__U53(tt) -> tt 20.51/20.84 a__U53(X:S) -> U53(X:S) 20.51/20.84 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.51/20.84 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.51/20.84 a__U62(tt) -> tt 20.51/20.84 a__U62(X:S) -> U62(X:S) 20.51/20.84 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.51/20.84 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.51/20.84 a__U72(tt) -> tt 20.51/20.84 a__U72(X:S) -> U72(X:S) 20.51/20.84 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.51/20.84 a____(nil,X:S) -> mark(X:S) 20.51/20.84 a____(X:S,nil) -> mark(X:S) 20.51/20.84 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.51/20.84 a__and(tt,X:S) -> mark(X:S) 20.51/20.84 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.51/20.84 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.84 a__isList(nil) -> tt 20.51/20.84 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.51/20.84 a__isList(X:S) -> isList(X:S) 20.51/20.84 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.84 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.84 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.51/20.84 a__isNeList(X:S) -> isNeList(X:S) 20.51/20.84 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.51/20.84 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.51/20.84 a__isNePal(X:S) -> isNePal(X:S) 20.51/20.84 a__isPal(nil) -> tt 20.51/20.84 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.51/20.84 a__isPal(X:S) -> isPal(X:S) 20.51/20.84 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.84 a__isPalListKind(a) -> tt 20.51/20.84 a__isPalListKind(e) -> tt 20.51/20.84 a__isPalListKind(i) -> tt 20.51/20.84 a__isPalListKind(nil) -> tt 20.51/20.84 a__isPalListKind(o) -> tt 20.51/20.84 a__isPalListKind(u) -> tt 20.51/20.84 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.51/20.84 a__isQid(a) -> tt 20.51/20.84 a__isQid(e) -> tt 20.51/20.84 a__isQid(i) -> tt 20.51/20.84 a__isQid(o) -> tt 20.51/20.84 a__isQid(u) -> tt 20.51/20.84 a__isQid(X:S) -> isQid(X:S) 20.51/20.84 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.51/20.84 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.51/20.84 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.51/20.84 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.51/20.84 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.51/20.84 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.51/20.84 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.51/20.84 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.51/20.84 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.51/20.84 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.51/20.84 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.51/20.84 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.51/20.84 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.51/20.84 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.51/20.84 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.51/20.84 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.51/20.84 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.51/20.84 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.51/20.84 mark(a) -> a 20.51/20.84 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.51/20.84 mark(e) -> e 20.51/20.84 mark(i) -> i 20.51/20.84 mark(isList(X:S)) -> a__isList(X:S) 20.51/20.84 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.51/20.84 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.51/20.84 mark(isPal(X:S)) -> a__isPal(X:S) 20.51/20.84 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.51/20.84 mark(isQid(X:S)) -> a__isQid(X:S) 20.51/20.84 mark(nil) -> nil 20.51/20.84 mark(o) -> o 20.51/20.84 mark(tt) -> tt 20.51/20.84 mark(u) -> u 20.51/20.84 20.51/20.84 Problem 1: 20.51/20.84 20.51/20.84 SCC Processor: 20.51/20.84 -> Pairs: 20.51/20.84 A__U11(tt,V:S) -> A__U12(a__isNeList(V:S)) 20.51/20.84 A__U11(tt,V:S) -> A__ISNELIST(V:S) 20.51/20.84 A__U21(tt,V1:S,V2:S) -> A__U22(a__isList(V1:S),V2:S) 20.51/20.84 A__U21(tt,V1:S,V2:S) -> A__ISLIST(V1:S) 20.51/20.84 A__U22(tt,V2:S) -> A__U23(a__isList(V2:S)) 20.51/20.84 A__U22(tt,V2:S) -> A__ISLIST(V2:S) 20.51/20.84 A__U31(tt,V:S) -> A__U32(a__isQid(V:S)) 20.51/20.84 A__U31(tt,V:S) -> A__ISQID(V:S) 20.51/20.84 A__U41(tt,V1:S,V2:S) -> A__U42(a__isList(V1:S),V2:S) 20.51/20.84 A__U41(tt,V1:S,V2:S) -> A__ISLIST(V1:S) 20.51/20.84 A__U42(tt,V2:S) -> A__U43(a__isNeList(V2:S)) 20.51/20.84 A__U42(tt,V2:S) -> A__ISNELIST(V2:S) 20.51/20.84 A__U51(tt,V1:S,V2:S) -> A__U52(a__isNeList(V1:S),V2:S) 20.51/20.84 A__U51(tt,V1:S,V2:S) -> A__ISNELIST(V1:S) 20.51/20.84 A__U52(tt,V2:S) -> A__U53(a__isList(V2:S)) 20.51/20.84 A__U52(tt,V2:S) -> A__ISLIST(V2:S) 20.51/20.84 A__U61(tt,V:S) -> A__U62(a__isQid(V:S)) 20.51/20.84 A__U61(tt,V:S) -> A__ISQID(V:S) 20.51/20.84 A__U71(tt,V:S) -> A__U72(a__isNePal(V:S)) 20.51/20.84 A__U71(tt,V:S) -> A__ISNEPAL(V:S) 20.51/20.84 A____(__(X:S,Y:S),Z:S) -> A____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.51/20.84 A____(__(X:S,Y:S),Z:S) -> A____(mark(Y:S),mark(Z:S)) 20.51/20.84 A____(__(X:S,Y:S),Z:S) -> MARK(X:S) 20.51/20.84 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S) 20.51/20.84 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 20.51/20.84 A____(nil,X:S) -> MARK(X:S) 20.51/20.84 A____(X:S,nil) -> MARK(X:S) 20.51/20.84 A__AND(tt,X:S) -> MARK(X:S) 20.51/20.84 A__ISLIST(__(V1:S,V2:S)) -> A__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.84 A__ISLIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.84 A__ISLIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.51/20.84 A__ISLIST(V:S) -> A__U11(a__isPalListKind(V:S),V:S) 20.51/20.84 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.84 A__ISNELIST(__(V1:S,V2:S)) -> A__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.84 A__ISNELIST(__(V1:S,V2:S)) -> A__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.84 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.84 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.51/20.84 A__ISNELIST(V:S) -> A__U31(a__isPalListKind(V:S),V:S) 20.51/20.84 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.84 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.51/20.84 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.51/20.84 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__ISQID(I:S) 20.51/20.84 A__ISNEPAL(V:S) -> A__U61(a__isPalListKind(V:S),V:S) 20.51/20.84 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.84 A__ISPAL(V:S) -> A__U71(a__isPalListKind(V:S),V:S) 20.51/20.84 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.84 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.84 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.51/20.84 MARK(U11(X1:S,X2:S)) -> A__U11(mark(X1:S),X2:S) 20.51/20.84 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(U12(X:S)) -> A__U12(mark(X:S)) 20.51/20.84 MARK(U12(X:S)) -> MARK(X:S) 20.51/20.84 MARK(U21(X1:S,X2:S,X3:S)) -> A__U21(mark(X1:S),X2:S,X3:S) 20.51/20.84 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.51/20.84 MARK(U22(X1:S,X2:S)) -> A__U22(mark(X1:S),X2:S) 20.51/20.84 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(U23(X:S)) -> A__U23(mark(X:S)) 20.51/20.84 MARK(U23(X:S)) -> MARK(X:S) 20.51/20.84 MARK(U31(X1:S,X2:S)) -> A__U31(mark(X1:S),X2:S) 20.51/20.84 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(U32(X:S)) -> A__U32(mark(X:S)) 20.51/20.84 MARK(U32(X:S)) -> MARK(X:S) 20.51/20.84 MARK(U41(X1:S,X2:S,X3:S)) -> A__U41(mark(X1:S),X2:S,X3:S) 20.51/20.84 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.51/20.84 MARK(U42(X1:S,X2:S)) -> A__U42(mark(X1:S),X2:S) 20.51/20.84 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(U43(X:S)) -> A__U43(mark(X:S)) 20.51/20.84 MARK(U43(X:S)) -> MARK(X:S) 20.51/20.84 MARK(U51(X1:S,X2:S,X3:S)) -> A__U51(mark(X1:S),X2:S,X3:S) 20.51/20.84 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.51/20.84 MARK(U52(X1:S,X2:S)) -> A__U52(mark(X1:S),X2:S) 20.51/20.84 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(U53(X:S)) -> A__U53(mark(X:S)) 20.51/20.84 MARK(U53(X:S)) -> MARK(X:S) 20.51/20.84 MARK(U61(X1:S,X2:S)) -> A__U61(mark(X1:S),X2:S) 20.51/20.84 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(U62(X:S)) -> A__U62(mark(X:S)) 20.51/20.84 MARK(U62(X:S)) -> MARK(X:S) 20.51/20.84 MARK(U71(X1:S,X2:S)) -> A__U71(mark(X1:S),X2:S) 20.51/20.84 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(U72(X:S)) -> A__U72(mark(X:S)) 20.51/20.84 MARK(U72(X:S)) -> MARK(X:S) 20.51/20.84 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 20.51/20.84 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.51/20.84 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.51/20.84 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.51/20.84 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.51/20.84 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.51/20.84 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.51/20.84 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.51/20.84 MARK(isQid(X:S)) -> A__ISQID(X:S) 20.51/20.84 -> Rules: 20.51/20.84 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.51/20.84 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.51/20.84 a__U12(tt) -> tt 20.51/20.84 a__U12(X:S) -> U12(X:S) 20.51/20.84 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.51/20.84 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.51/20.84 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.51/20.84 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.51/20.84 a__U23(tt) -> tt 20.51/20.84 a__U23(X:S) -> U23(X:S) 20.51/20.84 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.51/20.84 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.51/20.84 a__U32(tt) -> tt 20.51/20.84 a__U32(X:S) -> U32(X:S) 20.51/20.84 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.51/20.84 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.51/20.84 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.51/20.84 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.51/20.84 a__U43(tt) -> tt 20.51/20.84 a__U43(X:S) -> U43(X:S) 20.51/20.84 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.51/20.84 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.51/20.84 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.51/20.84 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.51/20.84 a__U53(tt) -> tt 20.51/20.84 a__U53(X:S) -> U53(X:S) 20.51/20.84 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.51/20.84 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.51/20.84 a__U62(tt) -> tt 20.51/20.84 a__U62(X:S) -> U62(X:S) 20.51/20.84 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.51/20.84 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.51/20.84 a__U72(tt) -> tt 20.51/20.84 a__U72(X:S) -> U72(X:S) 20.51/20.84 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.51/20.84 a____(nil,X:S) -> mark(X:S) 20.51/20.84 a____(X:S,nil) -> mark(X:S) 20.51/20.84 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.51/20.84 a__and(tt,X:S) -> mark(X:S) 20.51/20.84 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.51/20.84 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.84 a__isList(nil) -> tt 20.51/20.84 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.51/20.84 a__isList(X:S) -> isList(X:S) 20.51/20.84 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.84 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.84 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.51/20.84 a__isNeList(X:S) -> isNeList(X:S) 20.51/20.84 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.51/20.84 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.51/20.84 a__isNePal(X:S) -> isNePal(X:S) 20.51/20.84 a__isPal(nil) -> tt 20.51/20.84 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.51/20.84 a__isPal(X:S) -> isPal(X:S) 20.51/20.84 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.84 a__isPalListKind(a) -> tt 20.51/20.84 a__isPalListKind(e) -> tt 20.51/20.84 a__isPalListKind(i) -> tt 20.51/20.84 a__isPalListKind(nil) -> tt 20.51/20.84 a__isPalListKind(o) -> tt 20.51/20.84 a__isPalListKind(u) -> tt 20.51/20.84 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.51/20.84 a__isQid(a) -> tt 20.51/20.84 a__isQid(e) -> tt 20.51/20.84 a__isQid(i) -> tt 20.51/20.84 a__isQid(o) -> tt 20.51/20.84 a__isQid(u) -> tt 20.51/20.84 a__isQid(X:S) -> isQid(X:S) 20.51/20.84 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.51/20.84 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.51/20.84 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.51/20.84 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.51/20.84 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.51/20.84 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.51/20.84 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.51/20.84 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.51/20.84 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.51/20.84 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.51/20.84 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.51/20.84 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.51/20.84 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.51/20.84 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.51/20.84 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.51/20.84 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.51/20.84 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.51/20.84 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.51/20.84 mark(a) -> a 20.51/20.84 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.51/20.84 mark(e) -> e 20.51/20.84 mark(i) -> i 20.51/20.84 mark(isList(X:S)) -> a__isList(X:S) 20.51/20.84 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.51/20.84 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.51/20.84 mark(isPal(X:S)) -> a__isPal(X:S) 20.51/20.84 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.51/20.84 mark(isQid(X:S)) -> a__isQid(X:S) 20.51/20.84 mark(nil) -> nil 20.51/20.84 mark(o) -> o 20.51/20.84 mark(tt) -> tt 20.51/20.84 mark(u) -> u 20.51/20.84 ->Strongly Connected Components: 20.51/20.84 ->->Cycle: 20.51/20.84 ->->-> Pairs: 20.51/20.84 A__U11(tt,V:S) -> A__ISNELIST(V:S) 20.51/20.84 A__U21(tt,V1:S,V2:S) -> A__U22(a__isList(V1:S),V2:S) 20.51/20.84 A__U21(tt,V1:S,V2:S) -> A__ISLIST(V1:S) 20.51/20.84 A__U22(tt,V2:S) -> A__ISLIST(V2:S) 20.51/20.84 A__U41(tt,V1:S,V2:S) -> A__U42(a__isList(V1:S),V2:S) 20.51/20.84 A__U41(tt,V1:S,V2:S) -> A__ISLIST(V1:S) 20.51/20.84 A__U42(tt,V2:S) -> A__ISNELIST(V2:S) 20.51/20.84 A__U51(tt,V1:S,V2:S) -> A__U52(a__isNeList(V1:S),V2:S) 20.51/20.84 A__U51(tt,V1:S,V2:S) -> A__ISNELIST(V1:S) 20.51/20.84 A__U52(tt,V2:S) -> A__ISLIST(V2:S) 20.51/20.84 A__U71(tt,V:S) -> A__ISNEPAL(V:S) 20.51/20.84 A____(__(X:S,Y:S),Z:S) -> A____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.51/20.84 A____(__(X:S,Y:S),Z:S) -> A____(mark(Y:S),mark(Z:S)) 20.51/20.84 A____(__(X:S,Y:S),Z:S) -> MARK(X:S) 20.51/20.84 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S) 20.51/20.84 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 20.51/20.84 A____(nil,X:S) -> MARK(X:S) 20.51/20.84 A____(X:S,nil) -> MARK(X:S) 20.51/20.84 A__AND(tt,X:S) -> MARK(X:S) 20.51/20.84 A__ISLIST(__(V1:S,V2:S)) -> A__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.84 A__ISLIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.84 A__ISLIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.51/20.84 A__ISLIST(V:S) -> A__U11(a__isPalListKind(V:S),V:S) 20.51/20.84 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.84 A__ISNELIST(__(V1:S,V2:S)) -> A__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.84 A__ISNELIST(__(V1:S,V2:S)) -> A__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.84 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.84 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.51/20.84 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.84 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.51/20.84 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.51/20.84 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.84 A__ISPAL(V:S) -> A__U71(a__isPalListKind(V:S),V:S) 20.51/20.84 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.84 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.84 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.51/20.84 MARK(U11(X1:S,X2:S)) -> A__U11(mark(X1:S),X2:S) 20.51/20.84 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(U12(X:S)) -> MARK(X:S) 20.51/20.84 MARK(U21(X1:S,X2:S,X3:S)) -> A__U21(mark(X1:S),X2:S,X3:S) 20.51/20.84 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.51/20.84 MARK(U22(X1:S,X2:S)) -> A__U22(mark(X1:S),X2:S) 20.51/20.84 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(U23(X:S)) -> MARK(X:S) 20.51/20.84 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(U32(X:S)) -> MARK(X:S) 20.51/20.84 MARK(U41(X1:S,X2:S,X3:S)) -> A__U41(mark(X1:S),X2:S,X3:S) 20.51/20.84 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.51/20.84 MARK(U42(X1:S,X2:S)) -> A__U42(mark(X1:S),X2:S) 20.51/20.84 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(U43(X:S)) -> MARK(X:S) 20.51/20.84 MARK(U51(X1:S,X2:S,X3:S)) -> A__U51(mark(X1:S),X2:S,X3:S) 20.51/20.84 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.51/20.84 MARK(U52(X1:S,X2:S)) -> A__U52(mark(X1:S),X2:S) 20.51/20.84 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(U53(X:S)) -> MARK(X:S) 20.51/20.84 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(U62(X:S)) -> MARK(X:S) 20.51/20.84 MARK(U71(X1:S,X2:S)) -> A__U71(mark(X1:S),X2:S) 20.51/20.84 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(U72(X:S)) -> MARK(X:S) 20.51/20.84 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 20.51/20.84 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.51/20.84 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.51/20.84 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.51/20.84 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.51/20.84 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.51/20.84 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.51/20.84 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.51/20.84 ->->-> Rules: 20.51/20.84 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.51/20.84 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.51/20.84 a__U12(tt) -> tt 20.51/20.84 a__U12(X:S) -> U12(X:S) 20.51/20.84 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.51/20.84 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.51/20.84 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.51/20.84 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.51/20.84 a__U23(tt) -> tt 20.51/20.84 a__U23(X:S) -> U23(X:S) 20.51/20.84 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.51/20.84 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.51/20.84 a__U32(tt) -> tt 20.51/20.84 a__U32(X:S) -> U32(X:S) 20.51/20.84 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.51/20.84 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.51/20.84 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.51/20.84 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.51/20.84 a__U43(tt) -> tt 20.51/20.84 a__U43(X:S) -> U43(X:S) 20.51/20.84 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.51/20.84 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.51/20.84 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.51/20.84 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.51/20.84 a__U53(tt) -> tt 20.51/20.84 a__U53(X:S) -> U53(X:S) 20.51/20.84 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.51/20.84 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.51/20.84 a__U62(tt) -> tt 20.51/20.84 a__U62(X:S) -> U62(X:S) 20.51/20.84 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.51/20.84 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.51/20.84 a__U72(tt) -> tt 20.51/20.84 a__U72(X:S) -> U72(X:S) 20.51/20.84 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.51/20.84 a____(nil,X:S) -> mark(X:S) 20.51/20.84 a____(X:S,nil) -> mark(X:S) 20.51/20.84 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.51/20.84 a__and(tt,X:S) -> mark(X:S) 20.51/20.84 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.51/20.84 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.84 a__isList(nil) -> tt 20.51/20.84 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.51/20.84 a__isList(X:S) -> isList(X:S) 20.51/20.84 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.84 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.84 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.51/20.84 a__isNeList(X:S) -> isNeList(X:S) 20.51/20.84 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.51/20.84 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.51/20.84 a__isNePal(X:S) -> isNePal(X:S) 20.51/20.84 a__isPal(nil) -> tt 20.51/20.84 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.51/20.84 a__isPal(X:S) -> isPal(X:S) 20.51/20.84 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.84 a__isPalListKind(a) -> tt 20.51/20.84 a__isPalListKind(e) -> tt 20.51/20.84 a__isPalListKind(i) -> tt 20.51/20.84 a__isPalListKind(nil) -> tt 20.51/20.84 a__isPalListKind(o) -> tt 20.51/20.84 a__isPalListKind(u) -> tt 20.51/20.84 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.51/20.84 a__isQid(a) -> tt 20.51/20.84 a__isQid(e) -> tt 20.51/20.84 a__isQid(i) -> tt 20.51/20.84 a__isQid(o) -> tt 20.51/20.84 a__isQid(u) -> tt 20.51/20.84 a__isQid(X:S) -> isQid(X:S) 20.51/20.84 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.51/20.84 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.51/20.84 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.51/20.84 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.51/20.84 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.51/20.84 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.51/20.84 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.51/20.84 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.51/20.84 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.51/20.84 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.51/20.84 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.51/20.84 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.51/20.84 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.51/20.84 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.51/20.84 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.51/20.84 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.51/20.84 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.51/20.84 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.51/20.84 mark(a) -> a 20.51/20.84 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.51/20.84 mark(e) -> e 20.51/20.84 mark(i) -> i 20.51/20.84 mark(isList(X:S)) -> a__isList(X:S) 20.51/20.84 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.51/20.84 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.51/20.84 mark(isPal(X:S)) -> a__isPal(X:S) 20.51/20.84 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.51/20.84 mark(isQid(X:S)) -> a__isQid(X:S) 20.51/20.84 mark(nil) -> nil 20.51/20.84 mark(o) -> o 20.51/20.84 mark(tt) -> tt 20.51/20.84 mark(u) -> u 20.51/20.84 20.51/20.84 Problem 1: 20.51/20.84 20.51/20.84 Reduction Pairs Processor: 20.51/20.84 -> Pairs: 20.51/20.84 A__U11(tt,V:S) -> A__ISNELIST(V:S) 20.51/20.84 A__U21(tt,V1:S,V2:S) -> A__U22(a__isList(V1:S),V2:S) 20.51/20.84 A__U21(tt,V1:S,V2:S) -> A__ISLIST(V1:S) 20.51/20.84 A__U22(tt,V2:S) -> A__ISLIST(V2:S) 20.51/20.84 A__U41(tt,V1:S,V2:S) -> A__U42(a__isList(V1:S),V2:S) 20.51/20.84 A__U41(tt,V1:S,V2:S) -> A__ISLIST(V1:S) 20.51/20.84 A__U42(tt,V2:S) -> A__ISNELIST(V2:S) 20.51/20.84 A__U51(tt,V1:S,V2:S) -> A__U52(a__isNeList(V1:S),V2:S) 20.51/20.84 A__U51(tt,V1:S,V2:S) -> A__ISNELIST(V1:S) 20.51/20.84 A__U52(tt,V2:S) -> A__ISLIST(V2:S) 20.51/20.84 A__U71(tt,V:S) -> A__ISNEPAL(V:S) 20.51/20.84 A____(__(X:S,Y:S),Z:S) -> A____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.51/20.84 A____(__(X:S,Y:S),Z:S) -> A____(mark(Y:S),mark(Z:S)) 20.51/20.84 A____(__(X:S,Y:S),Z:S) -> MARK(X:S) 20.51/20.84 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S) 20.51/20.84 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 20.51/20.84 A____(nil,X:S) -> MARK(X:S) 20.51/20.84 A____(X:S,nil) -> MARK(X:S) 20.51/20.84 A__AND(tt,X:S) -> MARK(X:S) 20.51/20.84 A__ISLIST(__(V1:S,V2:S)) -> A__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.84 A__ISLIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.84 A__ISLIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.51/20.84 A__ISLIST(V:S) -> A__U11(a__isPalListKind(V:S),V:S) 20.51/20.84 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.84 A__ISNELIST(__(V1:S,V2:S)) -> A__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.84 A__ISNELIST(__(V1:S,V2:S)) -> A__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.84 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.84 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.51/20.84 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.84 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.51/20.84 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.51/20.84 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.84 A__ISPAL(V:S) -> A__U71(a__isPalListKind(V:S),V:S) 20.51/20.84 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.84 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.84 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.51/20.84 MARK(U11(X1:S,X2:S)) -> A__U11(mark(X1:S),X2:S) 20.51/20.84 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(U12(X:S)) -> MARK(X:S) 20.51/20.84 MARK(U21(X1:S,X2:S,X3:S)) -> A__U21(mark(X1:S),X2:S,X3:S) 20.51/20.84 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.51/20.84 MARK(U22(X1:S,X2:S)) -> A__U22(mark(X1:S),X2:S) 20.51/20.84 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(U23(X:S)) -> MARK(X:S) 20.51/20.84 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(U32(X:S)) -> MARK(X:S) 20.51/20.84 MARK(U41(X1:S,X2:S,X3:S)) -> A__U41(mark(X1:S),X2:S,X3:S) 20.51/20.84 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.51/20.84 MARK(U42(X1:S,X2:S)) -> A__U42(mark(X1:S),X2:S) 20.51/20.84 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(U43(X:S)) -> MARK(X:S) 20.51/20.84 MARK(U51(X1:S,X2:S,X3:S)) -> A__U51(mark(X1:S),X2:S,X3:S) 20.51/20.84 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.51/20.84 MARK(U52(X1:S,X2:S)) -> A__U52(mark(X1:S),X2:S) 20.51/20.84 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(U53(X:S)) -> MARK(X:S) 20.51/20.84 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(U62(X:S)) -> MARK(X:S) 20.51/20.84 MARK(U71(X1:S,X2:S)) -> A__U71(mark(X1:S),X2:S) 20.51/20.84 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(U72(X:S)) -> MARK(X:S) 20.51/20.84 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 20.51/20.84 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.51/20.84 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.51/20.84 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.51/20.84 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.51/20.84 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.51/20.84 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.51/20.84 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.51/20.84 -> Rules: 20.51/20.84 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.51/20.84 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.51/20.84 a__U12(tt) -> tt 20.51/20.84 a__U12(X:S) -> U12(X:S) 20.51/20.84 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.51/20.84 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.51/20.84 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.51/20.84 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.51/20.84 a__U23(tt) -> tt 20.51/20.84 a__U23(X:S) -> U23(X:S) 20.51/20.84 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.51/20.84 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.51/20.84 a__U32(tt) -> tt 20.51/20.84 a__U32(X:S) -> U32(X:S) 20.51/20.84 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.51/20.84 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.51/20.84 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.51/20.84 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.51/20.84 a__U43(tt) -> tt 20.51/20.84 a__U43(X:S) -> U43(X:S) 20.51/20.84 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.51/20.84 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.51/20.84 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.51/20.84 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.51/20.84 a__U53(tt) -> tt 20.51/20.84 a__U53(X:S) -> U53(X:S) 20.51/20.84 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.51/20.84 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.51/20.84 a__U62(tt) -> tt 20.51/20.84 a__U62(X:S) -> U62(X:S) 20.51/20.84 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.51/20.84 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.51/20.84 a__U72(tt) -> tt 20.51/20.84 a__U72(X:S) -> U72(X:S) 20.51/20.84 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.51/20.84 a____(nil,X:S) -> mark(X:S) 20.51/20.84 a____(X:S,nil) -> mark(X:S) 20.51/20.84 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.51/20.84 a__and(tt,X:S) -> mark(X:S) 20.51/20.84 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.51/20.84 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.84 a__isList(nil) -> tt 20.51/20.84 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.51/20.84 a__isList(X:S) -> isList(X:S) 20.51/20.84 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.84 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.84 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.51/20.84 a__isNeList(X:S) -> isNeList(X:S) 20.51/20.84 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.51/20.84 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.51/20.84 a__isNePal(X:S) -> isNePal(X:S) 20.51/20.84 a__isPal(nil) -> tt 20.51/20.84 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.51/20.84 a__isPal(X:S) -> isPal(X:S) 20.51/20.84 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.84 a__isPalListKind(a) -> tt 20.51/20.84 a__isPalListKind(e) -> tt 20.51/20.84 a__isPalListKind(i) -> tt 20.51/20.84 a__isPalListKind(nil) -> tt 20.51/20.84 a__isPalListKind(o) -> tt 20.51/20.84 a__isPalListKind(u) -> tt 20.51/20.84 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.51/20.84 a__isQid(a) -> tt 20.51/20.84 a__isQid(e) -> tt 20.51/20.84 a__isQid(i) -> tt 20.51/20.84 a__isQid(o) -> tt 20.51/20.84 a__isQid(u) -> tt 20.51/20.84 a__isQid(X:S) -> isQid(X:S) 20.51/20.84 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.51/20.84 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.51/20.84 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.51/20.84 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.51/20.84 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.51/20.84 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.51/20.84 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.51/20.84 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.51/20.84 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.51/20.84 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.51/20.84 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.51/20.84 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.51/20.84 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.51/20.84 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.51/20.84 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.51/20.84 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.51/20.84 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.51/20.84 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.51/20.84 mark(a) -> a 20.51/20.84 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.51/20.84 mark(e) -> e 20.51/20.84 mark(i) -> i 20.51/20.84 mark(isList(X:S)) -> a__isList(X:S) 20.51/20.84 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.51/20.84 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.51/20.84 mark(isPal(X:S)) -> a__isPal(X:S) 20.51/20.84 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.51/20.84 mark(isQid(X:S)) -> a__isQid(X:S) 20.51/20.84 mark(nil) -> nil 20.51/20.84 mark(o) -> o 20.51/20.84 mark(tt) -> tt 20.51/20.84 mark(u) -> u 20.51/20.84 -> Usable rules: 20.51/20.84 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.51/20.84 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.51/20.84 a__U12(tt) -> tt 20.51/20.84 a__U12(X:S) -> U12(X:S) 20.51/20.84 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.51/20.84 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.51/20.84 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.51/20.84 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.51/20.84 a__U23(tt) -> tt 20.51/20.84 a__U23(X:S) -> U23(X:S) 20.51/20.84 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.51/20.84 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.51/20.84 a__U32(tt) -> tt 20.51/20.84 a__U32(X:S) -> U32(X:S) 20.51/20.84 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.51/20.84 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.51/20.84 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.51/20.84 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.51/20.84 a__U43(tt) -> tt 20.51/20.84 a__U43(X:S) -> U43(X:S) 20.51/20.84 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.51/20.84 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.51/20.84 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.51/20.84 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.51/20.84 a__U53(tt) -> tt 20.51/20.84 a__U53(X:S) -> U53(X:S) 20.51/20.84 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.51/20.84 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.51/20.84 a__U62(tt) -> tt 20.51/20.84 a__U62(X:S) -> U62(X:S) 20.51/20.84 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.51/20.84 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.51/20.84 a__U72(tt) -> tt 20.51/20.84 a__U72(X:S) -> U72(X:S) 20.51/20.84 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.51/20.84 a____(nil,X:S) -> mark(X:S) 20.51/20.84 a____(X:S,nil) -> mark(X:S) 20.51/20.84 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.51/20.84 a__and(tt,X:S) -> mark(X:S) 20.51/20.84 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.51/20.84 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.84 a__isList(nil) -> tt 20.51/20.84 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.51/20.84 a__isList(X:S) -> isList(X:S) 20.51/20.84 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.84 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.84 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.51/20.84 a__isNeList(X:S) -> isNeList(X:S) 20.51/20.84 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.51/20.84 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.51/20.84 a__isNePal(X:S) -> isNePal(X:S) 20.51/20.84 a__isPal(nil) -> tt 20.51/20.84 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.51/20.84 a__isPal(X:S) -> isPal(X:S) 20.51/20.84 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.84 a__isPalListKind(a) -> tt 20.51/20.84 a__isPalListKind(e) -> tt 20.51/20.84 a__isPalListKind(i) -> tt 20.51/20.84 a__isPalListKind(nil) -> tt 20.51/20.84 a__isPalListKind(o) -> tt 20.51/20.84 a__isPalListKind(u) -> tt 20.51/20.84 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.51/20.84 a__isQid(a) -> tt 20.51/20.84 a__isQid(e) -> tt 20.51/20.84 a__isQid(i) -> tt 20.51/20.84 a__isQid(o) -> tt 20.51/20.84 a__isQid(u) -> tt 20.51/20.84 a__isQid(X:S) -> isQid(X:S) 20.51/20.84 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.51/20.84 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.51/20.84 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.51/20.84 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.51/20.84 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.51/20.84 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.51/20.84 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.51/20.84 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.51/20.84 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.51/20.84 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.51/20.84 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.51/20.84 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.51/20.84 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.51/20.84 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.51/20.84 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.51/20.84 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.51/20.84 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.51/20.84 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.51/20.84 mark(a) -> a 20.51/20.84 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.51/20.84 mark(e) -> e 20.51/20.84 mark(i) -> i 20.51/20.84 mark(isList(X:S)) -> a__isList(X:S) 20.51/20.84 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.51/20.84 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.51/20.84 mark(isPal(X:S)) -> a__isPal(X:S) 20.51/20.84 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.51/20.84 mark(isQid(X:S)) -> a__isQid(X:S) 20.51/20.84 mark(nil) -> nil 20.51/20.84 mark(o) -> o 20.51/20.84 mark(tt) -> tt 20.51/20.84 mark(u) -> u 20.51/20.84 ->Interpretation type: 20.51/20.84 Linear 20.51/20.84 ->Coefficients: 20.51/20.84 Natural Numbers 20.51/20.84 ->Dimension: 20.51/20.84 1 20.51/20.84 ->Bound: 20.51/20.84 2 20.51/20.84 ->Interpretation: 20.51/20.84 20.51/20.84 [a__U11](X1,X2) = 2.X1 + 2.X2 + 1 20.51/20.84 [a__U12](X) = X + 1 20.51/20.84 [a__U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.51/20.84 [a__U22](X1,X2) = X1 + 2.X2 + 1 20.51/20.84 [a__U23](X) = X 20.51/20.84 [a__U31](X1,X2) = 2.X1 + 2.X2 20.51/20.84 [a__U32](X) = 2.X 20.51/20.84 [a__U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.51/20.84 [a__U42](X1,X2) = X1 + 2.X2 + 1 20.51/20.84 [a__U43](X) = X + 1 20.51/20.84 [a__U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.51/20.84 [a__U52](X1,X2) = X1 + 2.X2 + 2 20.51/20.84 [a__U53](X) = X + 1 20.51/20.84 [a__U61](X1,X2) = 2.X1 20.51/20.84 [a__U62](X) = 2.X 20.51/20.84 [a__U71](X1,X2) = 2.X1 20.51/20.84 [a__U72](X) = 2.X 20.51/20.84 [a____](X1,X2) = X1 + X2 + 2 20.51/20.84 [a__and](X1,X2) = 2.X1 + 2.X2 20.51/20.84 [a__isList](X) = 2.X + 1 20.51/20.84 [a__isNeList](X) = 2.X 20.51/20.84 [a__isNePal](X) = 0 20.51/20.84 [a__isPal](X) = 0 20.51/20.84 [a__isPalListKind](X) = 0 20.51/20.84 [a__isQid](X) = 0 20.51/20.84 [mark](X) = X 20.51/20.84 [U11](X1,X2) = 2.X1 + 2.X2 + 1 20.51/20.84 [U12](X) = X + 1 20.51/20.84 [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.51/20.84 [U22](X1,X2) = X1 + 2.X2 + 1 20.51/20.84 [U23](X) = X 20.51/20.84 [U31](X1,X2) = 2.X1 + 2.X2 20.51/20.84 [U32](X) = 2.X 20.51/20.84 [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.51/20.84 [U42](X1,X2) = X1 + 2.X2 + 1 20.51/20.84 [U43](X) = X + 1 20.51/20.84 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.51/20.84 [U52](X1,X2) = X1 + 2.X2 + 2 20.51/20.84 [U53](X) = X + 1 20.51/20.84 [U61](X1,X2) = 2.X1 20.51/20.84 [U62](X) = 2.X 20.51/20.84 [U71](X1,X2) = 2.X1 20.51/20.84 [U72](X) = 2.X 20.51/20.84 [__](X1,X2) = X1 + X2 + 2 20.51/20.84 [a] = 2 20.51/20.84 [and](X1,X2) = 2.X1 + 2.X2 20.51/20.84 [e] = 2 20.51/20.84 [fSNonEmpty] = 0 20.51/20.84 [i] = 2 20.51/20.84 [isList](X) = 2.X + 1 20.51/20.84 [isNeList](X) = 2.X 20.51/20.84 [isNePal](X) = 0 20.51/20.84 [isPal](X) = 0 20.51/20.84 [isPalListKind](X) = 0 20.51/20.84 [isQid](X) = 0 20.51/20.84 [nil] = 1 20.51/20.84 [o] = 2 20.51/20.84 [tt] = 0 20.51/20.84 [u] = 0 20.51/20.84 [A__U11](X1,X2) = 2.X1 + 2.X2 + 1 20.51/20.84 [A__U12](X) = 0 20.51/20.84 [A__U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.51/20.84 [A__U22](X1,X2) = X1 + 2.X2 + 1 20.51/20.84 [A__U23](X) = 0 20.51/20.84 [A__U31](X1,X2) = 0 20.51/20.84 [A__U32](X) = 0 20.51/20.84 [A__U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.51/20.84 [A__U42](X1,X2) = 2.X2 + 2 20.51/20.84 [A__U43](X) = 0 20.51/20.84 [A__U51](X1,X2,X3) = 2.X2 + 2.X3 + 2 20.51/20.84 [A__U52](X1,X2) = X1 + 2.X2 + 2 20.51/20.84 [A__U53](X) = 0 20.51/20.84 [A__U61](X1,X2) = 0 20.51/20.84 [A__U62](X) = 0 20.51/20.84 [A__U71](X1,X2) = X1 20.51/20.84 [A__U72](X) = 0 20.51/20.84 [A____](X1,X2) = 2.X1 + 2.X2 + 2 20.51/20.84 [A__AND](X1,X2) = 2.X2 20.51/20.84 [A__ISLIST](X) = 2.X + 1 20.51/20.84 [A__ISNELIST](X) = 2.X 20.51/20.84 [A__ISNEPAL](X) = 0 20.51/20.84 [A__ISPAL](X) = 0 20.51/20.84 [A__ISPALLISTKIND](X) = 0 20.51/20.84 [A__ISQID](X) = 0 20.51/20.84 [MARK](X) = 2.X 20.51/20.84 20.51/20.84 Problem 1: 20.51/20.84 20.51/20.84 SCC Processor: 20.51/20.84 -> Pairs: 20.51/20.84 A__U21(tt,V1:S,V2:S) -> A__U22(a__isList(V1:S),V2:S) 20.51/20.84 A__U21(tt,V1:S,V2:S) -> A__ISLIST(V1:S) 20.51/20.84 A__U22(tt,V2:S) -> A__ISLIST(V2:S) 20.51/20.84 A__U41(tt,V1:S,V2:S) -> A__U42(a__isList(V1:S),V2:S) 20.51/20.84 A__U41(tt,V1:S,V2:S) -> A__ISLIST(V1:S) 20.51/20.84 A__U42(tt,V2:S) -> A__ISNELIST(V2:S) 20.51/20.84 A__U51(tt,V1:S,V2:S) -> A__U52(a__isNeList(V1:S),V2:S) 20.51/20.84 A__U51(tt,V1:S,V2:S) -> A__ISNELIST(V1:S) 20.51/20.84 A__U52(tt,V2:S) -> A__ISLIST(V2:S) 20.51/20.84 A__U71(tt,V:S) -> A__ISNEPAL(V:S) 20.51/20.84 A____(__(X:S,Y:S),Z:S) -> A____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.51/20.84 A____(__(X:S,Y:S),Z:S) -> A____(mark(Y:S),mark(Z:S)) 20.51/20.84 A____(__(X:S,Y:S),Z:S) -> MARK(X:S) 20.51/20.84 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S) 20.51/20.84 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 20.51/20.84 A____(nil,X:S) -> MARK(X:S) 20.51/20.84 A____(X:S,nil) -> MARK(X:S) 20.51/20.84 A__AND(tt,X:S) -> MARK(X:S) 20.51/20.84 A__ISLIST(__(V1:S,V2:S)) -> A__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.84 A__ISLIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.84 A__ISLIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.51/20.84 A__ISLIST(V:S) -> A__U11(a__isPalListKind(V:S),V:S) 20.51/20.84 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.84 A__ISNELIST(__(V1:S,V2:S)) -> A__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.84 A__ISNELIST(__(V1:S,V2:S)) -> A__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.84 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.84 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.51/20.84 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.84 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.51/20.84 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.51/20.84 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.84 A__ISPAL(V:S) -> A__U71(a__isPalListKind(V:S),V:S) 20.51/20.84 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.84 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.84 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.51/20.84 MARK(U11(X1:S,X2:S)) -> A__U11(mark(X1:S),X2:S) 20.51/20.84 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(U12(X:S)) -> MARK(X:S) 20.51/20.84 MARK(U21(X1:S,X2:S,X3:S)) -> A__U21(mark(X1:S),X2:S,X3:S) 20.51/20.84 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.51/20.84 MARK(U22(X1:S,X2:S)) -> A__U22(mark(X1:S),X2:S) 20.51/20.84 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(U23(X:S)) -> MARK(X:S) 20.51/20.84 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(U32(X:S)) -> MARK(X:S) 20.51/20.84 MARK(U41(X1:S,X2:S,X3:S)) -> A__U41(mark(X1:S),X2:S,X3:S) 20.51/20.84 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.51/20.84 MARK(U42(X1:S,X2:S)) -> A__U42(mark(X1:S),X2:S) 20.51/20.84 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(U43(X:S)) -> MARK(X:S) 20.51/20.84 MARK(U51(X1:S,X2:S,X3:S)) -> A__U51(mark(X1:S),X2:S,X3:S) 20.51/20.84 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.51/20.84 MARK(U52(X1:S,X2:S)) -> A__U52(mark(X1:S),X2:S) 20.51/20.84 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(U53(X:S)) -> MARK(X:S) 20.51/20.84 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(U62(X:S)) -> MARK(X:S) 20.51/20.84 MARK(U71(X1:S,X2:S)) -> A__U71(mark(X1:S),X2:S) 20.51/20.84 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(U72(X:S)) -> MARK(X:S) 20.51/20.84 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 20.51/20.84 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.51/20.84 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.51/20.84 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.51/20.84 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.51/20.84 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.51/20.84 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.51/20.84 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.51/20.84 -> Rules: 20.51/20.84 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.51/20.84 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.51/20.84 a__U12(tt) -> tt 20.51/20.84 a__U12(X:S) -> U12(X:S) 20.51/20.84 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.51/20.84 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.51/20.84 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.51/20.84 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.51/20.84 a__U23(tt) -> tt 20.51/20.84 a__U23(X:S) -> U23(X:S) 20.51/20.84 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.51/20.84 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.51/20.84 a__U32(tt) -> tt 20.51/20.84 a__U32(X:S) -> U32(X:S) 20.51/20.84 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.51/20.84 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.51/20.84 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.51/20.84 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.51/20.84 a__U43(tt) -> tt 20.51/20.84 a__U43(X:S) -> U43(X:S) 20.51/20.84 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.51/20.84 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.51/20.84 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.51/20.84 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.51/20.84 a__U53(tt) -> tt 20.51/20.84 a__U53(X:S) -> U53(X:S) 20.51/20.84 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.51/20.84 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.51/20.84 a__U62(tt) -> tt 20.51/20.84 a__U62(X:S) -> U62(X:S) 20.51/20.84 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.51/20.84 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.51/20.84 a__U72(tt) -> tt 20.51/20.84 a__U72(X:S) -> U72(X:S) 20.51/20.84 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.51/20.84 a____(nil,X:S) -> mark(X:S) 20.51/20.84 a____(X:S,nil) -> mark(X:S) 20.51/20.84 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.51/20.84 a__and(tt,X:S) -> mark(X:S) 20.51/20.84 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.51/20.84 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.84 a__isList(nil) -> tt 20.51/20.84 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.51/20.84 a__isList(X:S) -> isList(X:S) 20.51/20.84 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.84 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.84 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.51/20.84 a__isNeList(X:S) -> isNeList(X:S) 20.51/20.84 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.51/20.84 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.51/20.84 a__isNePal(X:S) -> isNePal(X:S) 20.51/20.84 a__isPal(nil) -> tt 20.51/20.84 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.51/20.84 a__isPal(X:S) -> isPal(X:S) 20.51/20.84 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.84 a__isPalListKind(a) -> tt 20.51/20.84 a__isPalListKind(e) -> tt 20.51/20.84 a__isPalListKind(i) -> tt 20.51/20.84 a__isPalListKind(nil) -> tt 20.51/20.84 a__isPalListKind(o) -> tt 20.51/20.84 a__isPalListKind(u) -> tt 20.51/20.84 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.51/20.84 a__isQid(a) -> tt 20.51/20.84 a__isQid(e) -> tt 20.51/20.84 a__isQid(i) -> tt 20.51/20.84 a__isQid(o) -> tt 20.51/20.84 a__isQid(u) -> tt 20.51/20.84 a__isQid(X:S) -> isQid(X:S) 20.51/20.84 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.51/20.84 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.51/20.84 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.51/20.84 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.51/20.84 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.51/20.84 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.51/20.84 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.51/20.84 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.51/20.84 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.51/20.84 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.51/20.84 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.51/20.84 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.51/20.84 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.51/20.84 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.51/20.84 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.51/20.84 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.51/20.84 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.51/20.84 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.51/20.84 mark(a) -> a 20.51/20.84 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.51/20.84 mark(e) -> e 20.51/20.84 mark(i) -> i 20.51/20.84 mark(isList(X:S)) -> a__isList(X:S) 20.51/20.84 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.51/20.84 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.51/20.84 mark(isPal(X:S)) -> a__isPal(X:S) 20.51/20.84 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.51/20.84 mark(isQid(X:S)) -> a__isQid(X:S) 20.51/20.84 mark(nil) -> nil 20.51/20.84 mark(o) -> o 20.51/20.84 mark(tt) -> tt 20.51/20.84 mark(u) -> u 20.51/20.84 ->Strongly Connected Components: 20.51/20.84 ->->Cycle: 20.51/20.84 ->->-> Pairs: 20.51/20.84 A__U21(tt,V1:S,V2:S) -> A__U22(a__isList(V1:S),V2:S) 20.51/20.84 A__U21(tt,V1:S,V2:S) -> A__ISLIST(V1:S) 20.51/20.84 A__U22(tt,V2:S) -> A__ISLIST(V2:S) 20.51/20.84 A__U41(tt,V1:S,V2:S) -> A__U42(a__isList(V1:S),V2:S) 20.51/20.84 A__U41(tt,V1:S,V2:S) -> A__ISLIST(V1:S) 20.51/20.84 A__U42(tt,V2:S) -> A__ISNELIST(V2:S) 20.51/20.84 A__U51(tt,V1:S,V2:S) -> A__U52(a__isNeList(V1:S),V2:S) 20.51/20.84 A__U51(tt,V1:S,V2:S) -> A__ISNELIST(V1:S) 20.51/20.84 A__U52(tt,V2:S) -> A__ISLIST(V2:S) 20.51/20.84 A__U71(tt,V:S) -> A__ISNEPAL(V:S) 20.51/20.84 A____(__(X:S,Y:S),Z:S) -> A____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.51/20.84 A____(__(X:S,Y:S),Z:S) -> A____(mark(Y:S),mark(Z:S)) 20.51/20.84 A____(__(X:S,Y:S),Z:S) -> MARK(X:S) 20.51/20.84 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S) 20.51/20.84 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 20.51/20.84 A____(nil,X:S) -> MARK(X:S) 20.51/20.84 A____(X:S,nil) -> MARK(X:S) 20.51/20.84 A__AND(tt,X:S) -> MARK(X:S) 20.51/20.84 A__ISLIST(__(V1:S,V2:S)) -> A__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.84 A__ISLIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.84 A__ISLIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.51/20.84 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.84 A__ISNELIST(__(V1:S,V2:S)) -> A__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.84 A__ISNELIST(__(V1:S,V2:S)) -> A__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.84 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.84 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.51/20.84 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.84 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.51/20.84 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.51/20.84 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.84 A__ISPAL(V:S) -> A__U71(a__isPalListKind(V:S),V:S) 20.51/20.84 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.84 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.84 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.51/20.84 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(U12(X:S)) -> MARK(X:S) 20.51/20.84 MARK(U21(X1:S,X2:S,X3:S)) -> A__U21(mark(X1:S),X2:S,X3:S) 20.51/20.84 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.51/20.84 MARK(U22(X1:S,X2:S)) -> A__U22(mark(X1:S),X2:S) 20.51/20.84 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(U23(X:S)) -> MARK(X:S) 20.51/20.84 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(U32(X:S)) -> MARK(X:S) 20.51/20.84 MARK(U41(X1:S,X2:S,X3:S)) -> A__U41(mark(X1:S),X2:S,X3:S) 20.51/20.84 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.51/20.84 MARK(U42(X1:S,X2:S)) -> A__U42(mark(X1:S),X2:S) 20.51/20.84 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(U43(X:S)) -> MARK(X:S) 20.51/20.84 MARK(U51(X1:S,X2:S,X3:S)) -> A__U51(mark(X1:S),X2:S,X3:S) 20.51/20.84 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.51/20.84 MARK(U52(X1:S,X2:S)) -> A__U52(mark(X1:S),X2:S) 20.51/20.84 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(U53(X:S)) -> MARK(X:S) 20.51/20.84 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(U62(X:S)) -> MARK(X:S) 20.51/20.84 MARK(U71(X1:S,X2:S)) -> A__U71(mark(X1:S),X2:S) 20.51/20.84 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(U72(X:S)) -> MARK(X:S) 20.51/20.84 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 20.51/20.84 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.51/20.84 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.51/20.84 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.51/20.84 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.51/20.84 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.51/20.84 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.51/20.84 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.51/20.84 ->->-> Rules: 20.51/20.84 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.51/20.84 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.51/20.84 a__U12(tt) -> tt 20.51/20.84 a__U12(X:S) -> U12(X:S) 20.51/20.84 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.51/20.84 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.51/20.84 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.51/20.84 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.51/20.84 a__U23(tt) -> tt 20.51/20.84 a__U23(X:S) -> U23(X:S) 20.51/20.84 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.51/20.84 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.51/20.84 a__U32(tt) -> tt 20.51/20.84 a__U32(X:S) -> U32(X:S) 20.51/20.84 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.51/20.84 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.51/20.84 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.51/20.84 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.51/20.84 a__U43(tt) -> tt 20.51/20.84 a__U43(X:S) -> U43(X:S) 20.51/20.84 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.51/20.84 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.51/20.84 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.51/20.84 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.51/20.84 a__U53(tt) -> tt 20.51/20.84 a__U53(X:S) -> U53(X:S) 20.51/20.84 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.51/20.84 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.51/20.84 a__U62(tt) -> tt 20.51/20.84 a__U62(X:S) -> U62(X:S) 20.51/20.84 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.51/20.84 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.51/20.84 a__U72(tt) -> tt 20.51/20.84 a__U72(X:S) -> U72(X:S) 20.51/20.84 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.51/20.84 a____(nil,X:S) -> mark(X:S) 20.51/20.84 a____(X:S,nil) -> mark(X:S) 20.51/20.84 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.51/20.84 a__and(tt,X:S) -> mark(X:S) 20.51/20.84 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.51/20.84 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.84 a__isList(nil) -> tt 20.51/20.84 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.51/20.84 a__isList(X:S) -> isList(X:S) 20.51/20.84 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.84 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.84 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.51/20.84 a__isNeList(X:S) -> isNeList(X:S) 20.51/20.84 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.51/20.84 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.51/20.84 a__isNePal(X:S) -> isNePal(X:S) 20.51/20.84 a__isPal(nil) -> tt 20.51/20.84 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.51/20.84 a__isPal(X:S) -> isPal(X:S) 20.51/20.84 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.84 a__isPalListKind(a) -> tt 20.51/20.84 a__isPalListKind(e) -> tt 20.51/20.84 a__isPalListKind(i) -> tt 20.51/20.84 a__isPalListKind(nil) -> tt 20.51/20.84 a__isPalListKind(o) -> tt 20.51/20.84 a__isPalListKind(u) -> tt 20.51/20.84 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.51/20.84 a__isQid(a) -> tt 20.51/20.84 a__isQid(e) -> tt 20.51/20.84 a__isQid(i) -> tt 20.51/20.84 a__isQid(o) -> tt 20.51/20.84 a__isQid(u) -> tt 20.51/20.84 a__isQid(X:S) -> isQid(X:S) 20.51/20.84 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.51/20.84 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.51/20.84 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.51/20.84 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.51/20.84 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.51/20.84 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.51/20.84 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.51/20.84 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.51/20.84 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.51/20.84 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.51/20.84 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.51/20.84 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.51/20.84 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.51/20.84 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.51/20.84 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.51/20.84 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.51/20.84 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.51/20.84 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.51/20.84 mark(a) -> a 20.51/20.84 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.51/20.84 mark(e) -> e 20.51/20.84 mark(i) -> i 20.51/20.84 mark(isList(X:S)) -> a__isList(X:S) 20.51/20.84 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.51/20.84 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.51/20.84 mark(isPal(X:S)) -> a__isPal(X:S) 20.51/20.84 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.51/20.84 mark(isQid(X:S)) -> a__isQid(X:S) 20.51/20.84 mark(nil) -> nil 20.51/20.84 mark(o) -> o 20.51/20.84 mark(tt) -> tt 20.51/20.84 mark(u) -> u 20.51/20.84 20.51/20.84 Problem 1: 20.51/20.84 20.51/20.84 Reduction Pairs Processor: 20.51/20.84 -> Pairs: 20.51/20.84 A__U21(tt,V1:S,V2:S) -> A__U22(a__isList(V1:S),V2:S) 20.51/20.84 A__U21(tt,V1:S,V2:S) -> A__ISLIST(V1:S) 20.51/20.84 A__U22(tt,V2:S) -> A__ISLIST(V2:S) 20.51/20.84 A__U41(tt,V1:S,V2:S) -> A__U42(a__isList(V1:S),V2:S) 20.51/20.84 A__U41(tt,V1:S,V2:S) -> A__ISLIST(V1:S) 20.51/20.84 A__U42(tt,V2:S) -> A__ISNELIST(V2:S) 20.51/20.84 A__U51(tt,V1:S,V2:S) -> A__U52(a__isNeList(V1:S),V2:S) 20.51/20.84 A__U51(tt,V1:S,V2:S) -> A__ISNELIST(V1:S) 20.51/20.84 A__U52(tt,V2:S) -> A__ISLIST(V2:S) 20.51/20.84 A__U71(tt,V:S) -> A__ISNEPAL(V:S) 20.51/20.84 A____(__(X:S,Y:S),Z:S) -> A____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.51/20.84 A____(__(X:S,Y:S),Z:S) -> A____(mark(Y:S),mark(Z:S)) 20.51/20.84 A____(__(X:S,Y:S),Z:S) -> MARK(X:S) 20.51/20.84 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S) 20.51/20.84 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 20.51/20.84 A____(nil,X:S) -> MARK(X:S) 20.51/20.84 A____(X:S,nil) -> MARK(X:S) 20.51/20.84 A__AND(tt,X:S) -> MARK(X:S) 20.51/20.84 A__ISLIST(__(V1:S,V2:S)) -> A__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.84 A__ISLIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.84 A__ISLIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.51/20.84 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.84 A__ISNELIST(__(V1:S,V2:S)) -> A__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.84 A__ISNELIST(__(V1:S,V2:S)) -> A__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.84 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.84 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.51/20.84 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.84 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.51/20.84 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.51/20.84 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.84 A__ISPAL(V:S) -> A__U71(a__isPalListKind(V:S),V:S) 20.51/20.84 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.84 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.84 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.51/20.84 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(U12(X:S)) -> MARK(X:S) 20.51/20.84 MARK(U21(X1:S,X2:S,X3:S)) -> A__U21(mark(X1:S),X2:S,X3:S) 20.51/20.84 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.51/20.84 MARK(U22(X1:S,X2:S)) -> A__U22(mark(X1:S),X2:S) 20.51/20.84 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(U23(X:S)) -> MARK(X:S) 20.51/20.84 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(U32(X:S)) -> MARK(X:S) 20.51/20.84 MARK(U41(X1:S,X2:S,X3:S)) -> A__U41(mark(X1:S),X2:S,X3:S) 20.51/20.84 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.51/20.84 MARK(U42(X1:S,X2:S)) -> A__U42(mark(X1:S),X2:S) 20.51/20.84 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(U43(X:S)) -> MARK(X:S) 20.51/20.84 MARK(U51(X1:S,X2:S,X3:S)) -> A__U51(mark(X1:S),X2:S,X3:S) 20.51/20.84 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.51/20.84 MARK(U52(X1:S,X2:S)) -> A__U52(mark(X1:S),X2:S) 20.51/20.84 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(U53(X:S)) -> MARK(X:S) 20.51/20.84 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(U62(X:S)) -> MARK(X:S) 20.51/20.84 MARK(U71(X1:S,X2:S)) -> A__U71(mark(X1:S),X2:S) 20.51/20.84 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(U72(X:S)) -> MARK(X:S) 20.51/20.84 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 20.51/20.84 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.51/20.84 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.51/20.84 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.84 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.51/20.84 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.51/20.84 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.51/20.84 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.51/20.84 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.51/20.84 -> Rules: 20.51/20.84 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.51/20.84 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.51/20.84 a__U12(tt) -> tt 20.51/20.84 a__U12(X:S) -> U12(X:S) 20.51/20.84 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.51/20.84 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.51/20.84 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.51/20.84 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.51/20.84 a__U23(tt) -> tt 20.51/20.84 a__U23(X:S) -> U23(X:S) 20.51/20.84 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.51/20.84 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.51/20.84 a__U32(tt) -> tt 20.51/20.84 a__U32(X:S) -> U32(X:S) 20.51/20.84 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.51/20.84 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.51/20.84 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.51/20.84 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.51/20.84 a__U43(tt) -> tt 20.51/20.84 a__U43(X:S) -> U43(X:S) 20.51/20.84 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.51/20.84 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.51/20.84 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.51/20.84 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.51/20.84 a__U53(tt) -> tt 20.51/20.84 a__U53(X:S) -> U53(X:S) 20.51/20.84 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.51/20.84 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.51/20.84 a__U62(tt) -> tt 20.51/20.84 a__U62(X:S) -> U62(X:S) 20.51/20.84 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.51/20.84 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.51/20.84 a__U72(tt) -> tt 20.51/20.84 a__U72(X:S) -> U72(X:S) 20.51/20.84 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.51/20.84 a____(nil,X:S) -> mark(X:S) 20.51/20.84 a____(X:S,nil) -> mark(X:S) 20.51/20.84 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.51/20.84 a__and(tt,X:S) -> mark(X:S) 20.51/20.84 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.51/20.84 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.84 a__isList(nil) -> tt 20.51/20.84 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.51/20.84 a__isList(X:S) -> isList(X:S) 20.51/20.84 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.84 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.84 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.51/20.84 a__isNeList(X:S) -> isNeList(X:S) 20.51/20.84 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.51/20.84 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.51/20.84 a__isNePal(X:S) -> isNePal(X:S) 20.51/20.84 a__isPal(nil) -> tt 20.51/20.84 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.51/20.84 a__isPal(X:S) -> isPal(X:S) 20.51/20.84 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.84 a__isPalListKind(a) -> tt 20.51/20.84 a__isPalListKind(e) -> tt 20.51/20.84 a__isPalListKind(i) -> tt 20.51/20.84 a__isPalListKind(nil) -> tt 20.51/20.84 a__isPalListKind(o) -> tt 20.51/20.84 a__isPalListKind(u) -> tt 20.51/20.84 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.51/20.84 a__isQid(a) -> tt 20.51/20.84 a__isQid(e) -> tt 20.51/20.84 a__isQid(i) -> tt 20.51/20.84 a__isQid(o) -> tt 20.51/20.84 a__isQid(u) -> tt 20.51/20.84 a__isQid(X:S) -> isQid(X:S) 20.51/20.84 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.51/20.84 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.51/20.84 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.51/20.84 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.51/20.84 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.51/20.84 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.51/20.84 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.51/20.84 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.51/20.84 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.51/20.84 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.51/20.84 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.51/20.84 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.51/20.84 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.51/20.84 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.51/20.84 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.51/20.84 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.51/20.84 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.51/20.84 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.51/20.84 mark(a) -> a 20.51/20.84 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.51/20.84 mark(e) -> e 20.51/20.84 mark(i) -> i 20.51/20.84 mark(isList(X:S)) -> a__isList(X:S) 20.51/20.84 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.51/20.84 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.51/20.84 mark(isPal(X:S)) -> a__isPal(X:S) 20.51/20.84 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.51/20.84 mark(isQid(X:S)) -> a__isQid(X:S) 20.51/20.84 mark(nil) -> nil 20.51/20.84 mark(o) -> o 20.51/20.84 mark(tt) -> tt 20.51/20.84 mark(u) -> u 20.51/20.84 -> Usable rules: 20.51/20.84 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.51/20.84 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.51/20.84 a__U12(tt) -> tt 20.51/20.84 a__U12(X:S) -> U12(X:S) 20.51/20.84 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.51/20.84 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.51/20.84 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.51/20.84 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.51/20.84 a__U23(tt) -> tt 20.51/20.84 a__U23(X:S) -> U23(X:S) 20.51/20.84 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.51/20.84 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.51/20.84 a__U32(tt) -> tt 20.51/20.84 a__U32(X:S) -> U32(X:S) 20.51/20.84 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.51/20.84 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.51/20.84 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.51/20.84 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.51/20.84 a__U43(tt) -> tt 20.51/20.84 a__U43(X:S) -> U43(X:S) 20.51/20.84 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.51/20.84 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.51/20.84 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.51/20.84 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.51/20.84 a__U53(tt) -> tt 20.51/20.84 a__U53(X:S) -> U53(X:S) 20.51/20.84 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.51/20.84 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.51/20.84 a__U62(tt) -> tt 20.51/20.84 a__U62(X:S) -> U62(X:S) 20.51/20.84 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.51/20.84 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.51/20.84 a__U72(tt) -> tt 20.51/20.84 a__U72(X:S) -> U72(X:S) 20.51/20.84 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.51/20.84 a____(nil,X:S) -> mark(X:S) 20.51/20.84 a____(X:S,nil) -> mark(X:S) 20.51/20.84 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.51/20.84 a__and(tt,X:S) -> mark(X:S) 20.51/20.84 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.51/20.84 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.84 a__isList(nil) -> tt 20.51/20.84 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.51/20.84 a__isList(X:S) -> isList(X:S) 20.51/20.84 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.84 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.84 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.51/20.84 a__isNeList(X:S) -> isNeList(X:S) 20.51/20.84 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.51/20.84 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.51/20.84 a__isNePal(X:S) -> isNePal(X:S) 20.51/20.84 a__isPal(nil) -> tt 20.51/20.84 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.51/20.84 a__isPal(X:S) -> isPal(X:S) 20.51/20.84 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.84 a__isPalListKind(a) -> tt 20.51/20.84 a__isPalListKind(e) -> tt 20.51/20.84 a__isPalListKind(i) -> tt 20.51/20.84 a__isPalListKind(nil) -> tt 20.51/20.84 a__isPalListKind(o) -> tt 20.51/20.84 a__isPalListKind(u) -> tt 20.51/20.84 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.51/20.84 a__isQid(a) -> tt 20.51/20.84 a__isQid(e) -> tt 20.51/20.84 a__isQid(i) -> tt 20.51/20.84 a__isQid(o) -> tt 20.51/20.84 a__isQid(u) -> tt 20.51/20.84 a__isQid(X:S) -> isQid(X:S) 20.51/20.84 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.51/20.84 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.51/20.84 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.51/20.84 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.51/20.84 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.51/20.84 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.51/20.84 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.51/20.84 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.51/20.84 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.51/20.84 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.51/20.84 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.51/20.84 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.51/20.84 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.51/20.84 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.51/20.84 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.51/20.84 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.51/20.84 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.51/20.84 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.51/20.84 mark(a) -> a 20.51/20.84 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.51/20.84 mark(e) -> e 20.51/20.84 mark(i) -> i 20.51/20.84 mark(isList(X:S)) -> a__isList(X:S) 20.51/20.84 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.51/20.84 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.51/20.84 mark(isPal(X:S)) -> a__isPal(X:S) 20.51/20.84 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.51/20.84 mark(isQid(X:S)) -> a__isQid(X:S) 20.51/20.84 mark(nil) -> nil 20.51/20.84 mark(o) -> o 20.51/20.84 mark(tt) -> tt 20.51/20.84 mark(u) -> u 20.51/20.84 ->Interpretation type: 20.51/20.84 Linear 20.51/20.84 ->Coefficients: 20.51/20.84 Natural Numbers 20.51/20.84 ->Dimension: 20.51/20.84 1 20.51/20.84 ->Bound: 20.51/20.84 2 20.51/20.84 ->Interpretation: 20.51/20.84 20.51/20.84 [a__U11](X1,X2) = X1 + 2.X2 + 1 20.51/20.84 [a__U12](X) = X 20.51/20.84 [a__U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.51/20.84 [a__U22](X1,X2) = X1 + 2.X2 + 1 20.51/20.84 [a__U23](X) = X 20.51/20.84 [a__U31](X1,X2) = X1 + 2.X2 + 1 20.51/20.84 [a__U32](X) = X 20.51/20.84 [a__U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.51/20.84 [a__U42](X1,X2) = X1 + 2.X2 + 1 20.51/20.84 [a__U43](X) = X 20.51/20.84 [a__U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.51/20.84 [a__U52](X1,X2) = X1 + 2.X2 + 1 20.51/20.84 [a__U53](X) = X 20.51/20.84 [a__U61](X1,X2) = 2.X1 + X2 + 2 20.51/20.84 [a__U62](X) = X + 1 20.51/20.84 [a__U71](X1,X2) = 2.X1 + X2 + 2 20.51/20.84 [a__U72](X) = X 20.51/20.84 [a____](X1,X2) = X1 + X2 + 2 20.51/20.84 [a__and](X1,X2) = X1 + X2 20.51/20.84 [a__isList](X) = 2.X + 1 20.51/20.84 [a__isNeList](X) = 2.X + 1 20.51/20.84 [a__isNePal](X) = X + 2 20.51/20.84 [a__isPal](X) = X + 2 20.51/20.84 [a__isPalListKind](X) = 0 20.51/20.84 [a__isQid](X) = X + 1 20.51/20.84 [mark](X) = X 20.51/20.84 [U11](X1,X2) = X1 + 2.X2 + 1 20.51/20.84 [U12](X) = X 20.51/20.84 [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.51/20.84 [U22](X1,X2) = X1 + 2.X2 + 1 20.51/20.84 [U23](X) = X 20.51/20.84 [U31](X1,X2) = X1 + 2.X2 + 1 20.51/20.84 [U32](X) = X 20.51/20.84 [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.51/20.84 [U42](X1,X2) = X1 + 2.X2 + 1 20.51/20.84 [U43](X) = X 20.51/20.84 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.51/20.84 [U52](X1,X2) = X1 + 2.X2 + 1 20.51/20.84 [U53](X) = X 20.51/20.84 [U61](X1,X2) = 2.X1 + X2 + 2 20.51/20.84 [U62](X) = X + 1 20.51/20.84 [U71](X1,X2) = 2.X1 + X2 + 2 20.51/20.84 [U72](X) = X 20.51/20.84 [__](X1,X2) = X1 + X2 + 2 20.51/20.84 [a] = 1 20.51/20.84 [and](X1,X2) = X1 + X2 20.51/20.84 [e] = 2 20.51/20.84 [fSNonEmpty] = 0 20.51/20.84 [i] = 2 20.51/20.84 [isList](X) = 2.X + 1 20.51/20.84 [isNeList](X) = 2.X + 1 20.51/20.84 [isNePal](X) = X + 2 20.51/20.84 [isPal](X) = X + 2 20.51/20.84 [isPalListKind](X) = 0 20.51/20.84 [isQid](X) = X + 1 20.51/20.84 [nil] = 2 20.51/20.84 [o] = 2 20.51/20.84 [tt] = 0 20.51/20.84 [u] = 2 20.51/20.84 [A__U11](X1,X2) = 0 20.51/20.84 [A__U12](X) = 0 20.51/20.84 [A__U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.51/20.84 [A__U22](X1,X2) = 2.X2 + 1 20.51/20.84 [A__U23](X) = 0 20.51/20.84 [A__U31](X1,X2) = 0 20.51/20.84 [A__U32](X) = 0 20.51/20.84 [A__U41](X1,X2,X3) = 2.X2 + 2.X3 + 2 20.51/20.84 [A__U42](X1,X2) = X1 + 2.X2 + 1 20.51/20.84 [A__U43](X) = 0 20.51/20.84 [A__U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.51/20.84 [A__U52](X1,X2) = X1 + 2.X2 + 1 20.51/20.84 [A__U53](X) = 0 20.51/20.84 [A__U61](X1,X2) = 0 20.51/20.84 [A__U62](X) = 0 20.51/20.84 [A__U71](X1,X2) = 2.X2 + 2 20.51/20.84 [A__U72](X) = 0 20.51/20.84 [A____](X1,X2) = 2.X1 + 2.X2 20.51/20.84 [A__AND](X1,X2) = 2.X2 + 1 20.51/20.84 [A__ISLIST](X) = 2.X + 1 20.51/20.84 [A__ISNELIST](X) = 2.X + 1 20.51/20.84 [A__ISNEPAL](X) = 2.X + 2 20.51/20.84 [A__ISPAL](X) = 2.X + 2 20.51/20.84 [A__ISPALLISTKIND](X) = 1 20.51/20.84 [A__ISQID](X) = 0 20.51/20.84 [MARK](X) = 2.X + 1 20.51/20.84 20.51/20.84 Problem 1: 20.51/20.84 20.51/20.84 SCC Processor: 20.51/20.84 -> Pairs: 20.51/20.84 A__U21(tt,V1:S,V2:S) -> A__ISLIST(V1:S) 20.51/20.84 A__U22(tt,V2:S) -> A__ISLIST(V2:S) 20.51/20.84 A__U41(tt,V1:S,V2:S) -> A__U42(a__isList(V1:S),V2:S) 20.51/20.84 A__U41(tt,V1:S,V2:S) -> A__ISLIST(V1:S) 20.51/20.84 A__U42(tt,V2:S) -> A__ISNELIST(V2:S) 20.51/20.84 A__U51(tt,V1:S,V2:S) -> A__U52(a__isNeList(V1:S),V2:S) 20.51/20.85 A__U51(tt,V1:S,V2:S) -> A__ISNELIST(V1:S) 20.51/20.85 A__U52(tt,V2:S) -> A__ISLIST(V2:S) 20.51/20.85 A__U71(tt,V:S) -> A__ISNEPAL(V:S) 20.51/20.85 A____(__(X:S,Y:S),Z:S) -> A____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.51/20.85 A____(__(X:S,Y:S),Z:S) -> A____(mark(Y:S),mark(Z:S)) 20.51/20.85 A____(__(X:S,Y:S),Z:S) -> MARK(X:S) 20.51/20.85 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S) 20.51/20.85 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 20.51/20.85 A____(nil,X:S) -> MARK(X:S) 20.51/20.85 A____(X:S,nil) -> MARK(X:S) 20.51/20.85 A__AND(tt,X:S) -> MARK(X:S) 20.51/20.85 A__ISLIST(__(V1:S,V2:S)) -> A__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.85 A__ISLIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.85 A__ISLIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.51/20.85 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.85 A__ISNELIST(__(V1:S,V2:S)) -> A__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.85 A__ISNELIST(__(V1:S,V2:S)) -> A__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.85 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.85 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.51/20.85 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.85 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.51/20.85 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.51/20.85 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.85 A__ISPAL(V:S) -> A__U71(a__isPalListKind(V:S),V:S) 20.51/20.85 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.85 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.85 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.51/20.85 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U12(X:S)) -> MARK(X:S) 20.51/20.85 MARK(U21(X1:S,X2:S,X3:S)) -> A__U21(mark(X1:S),X2:S,X3:S) 20.51/20.85 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.51/20.85 MARK(U22(X1:S,X2:S)) -> A__U22(mark(X1:S),X2:S) 20.51/20.85 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U23(X:S)) -> MARK(X:S) 20.51/20.85 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U32(X:S)) -> MARK(X:S) 20.51/20.85 MARK(U41(X1:S,X2:S,X3:S)) -> A__U41(mark(X1:S),X2:S,X3:S) 20.51/20.85 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.51/20.85 MARK(U42(X1:S,X2:S)) -> A__U42(mark(X1:S),X2:S) 20.51/20.85 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U43(X:S)) -> MARK(X:S) 20.51/20.85 MARK(U51(X1:S,X2:S,X3:S)) -> A__U51(mark(X1:S),X2:S,X3:S) 20.51/20.85 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.51/20.85 MARK(U52(X1:S,X2:S)) -> A__U52(mark(X1:S),X2:S) 20.51/20.85 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U53(X:S)) -> MARK(X:S) 20.51/20.85 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U62(X:S)) -> MARK(X:S) 20.51/20.85 MARK(U71(X1:S,X2:S)) -> A__U71(mark(X1:S),X2:S) 20.51/20.85 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U72(X:S)) -> MARK(X:S) 20.51/20.85 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 20.51/20.85 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.51/20.85 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.51/20.85 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.51/20.85 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.51/20.85 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.51/20.85 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.51/20.85 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.51/20.85 -> Rules: 20.51/20.85 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.51/20.85 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.51/20.85 a__U12(tt) -> tt 20.51/20.85 a__U12(X:S) -> U12(X:S) 20.51/20.85 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.51/20.85 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.51/20.85 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.51/20.85 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.51/20.85 a__U23(tt) -> tt 20.51/20.85 a__U23(X:S) -> U23(X:S) 20.51/20.85 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.51/20.85 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.51/20.85 a__U32(tt) -> tt 20.51/20.85 a__U32(X:S) -> U32(X:S) 20.51/20.85 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.51/20.85 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.51/20.85 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.51/20.85 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.51/20.85 a__U43(tt) -> tt 20.51/20.85 a__U43(X:S) -> U43(X:S) 20.51/20.85 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.51/20.85 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.51/20.85 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.51/20.85 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.51/20.85 a__U53(tt) -> tt 20.51/20.85 a__U53(X:S) -> U53(X:S) 20.51/20.85 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.51/20.85 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.51/20.85 a__U62(tt) -> tt 20.51/20.85 a__U62(X:S) -> U62(X:S) 20.51/20.85 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.51/20.85 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.51/20.85 a__U72(tt) -> tt 20.51/20.85 a__U72(X:S) -> U72(X:S) 20.51/20.85 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.51/20.85 a____(nil,X:S) -> mark(X:S) 20.51/20.85 a____(X:S,nil) -> mark(X:S) 20.51/20.85 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.51/20.85 a__and(tt,X:S) -> mark(X:S) 20.51/20.85 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.51/20.85 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.85 a__isList(nil) -> tt 20.51/20.85 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.51/20.85 a__isList(X:S) -> isList(X:S) 20.51/20.85 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.85 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.85 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.51/20.85 a__isNeList(X:S) -> isNeList(X:S) 20.51/20.85 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.51/20.85 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.51/20.85 a__isNePal(X:S) -> isNePal(X:S) 20.51/20.85 a__isPal(nil) -> tt 20.51/20.85 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.51/20.85 a__isPal(X:S) -> isPal(X:S) 20.51/20.85 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.85 a__isPalListKind(a) -> tt 20.51/20.85 a__isPalListKind(e) -> tt 20.51/20.85 a__isPalListKind(i) -> tt 20.51/20.85 a__isPalListKind(nil) -> tt 20.51/20.85 a__isPalListKind(o) -> tt 20.51/20.85 a__isPalListKind(u) -> tt 20.51/20.85 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.51/20.85 a__isQid(a) -> tt 20.51/20.85 a__isQid(e) -> tt 20.51/20.85 a__isQid(i) -> tt 20.51/20.85 a__isQid(o) -> tt 20.51/20.85 a__isQid(u) -> tt 20.51/20.85 a__isQid(X:S) -> isQid(X:S) 20.51/20.85 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.51/20.85 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.51/20.85 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.51/20.85 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.51/20.85 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.51/20.85 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.51/20.85 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.51/20.85 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.51/20.85 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.51/20.85 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.51/20.85 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.51/20.85 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.51/20.85 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.51/20.85 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.51/20.85 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.51/20.85 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.51/20.85 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.51/20.85 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.51/20.85 mark(a) -> a 20.51/20.85 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.51/20.85 mark(e) -> e 20.51/20.85 mark(i) -> i 20.51/20.85 mark(isList(X:S)) -> a__isList(X:S) 20.51/20.85 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.51/20.85 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.51/20.85 mark(isPal(X:S)) -> a__isPal(X:S) 20.51/20.85 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.51/20.85 mark(isQid(X:S)) -> a__isQid(X:S) 20.51/20.85 mark(nil) -> nil 20.51/20.85 mark(o) -> o 20.51/20.85 mark(tt) -> tt 20.51/20.85 mark(u) -> u 20.51/20.85 ->Strongly Connected Components: 20.51/20.85 ->->Cycle: 20.51/20.85 ->->-> Pairs: 20.51/20.85 A__U21(tt,V1:S,V2:S) -> A__ISLIST(V1:S) 20.51/20.85 A__U22(tt,V2:S) -> A__ISLIST(V2:S) 20.51/20.85 A__U41(tt,V1:S,V2:S) -> A__U42(a__isList(V1:S),V2:S) 20.51/20.85 A__U41(tt,V1:S,V2:S) -> A__ISLIST(V1:S) 20.51/20.85 A__U42(tt,V2:S) -> A__ISNELIST(V2:S) 20.51/20.85 A__U51(tt,V1:S,V2:S) -> A__U52(a__isNeList(V1:S),V2:S) 20.51/20.85 A__U51(tt,V1:S,V2:S) -> A__ISNELIST(V1:S) 20.51/20.85 A__U52(tt,V2:S) -> A__ISLIST(V2:S) 20.51/20.85 A__U71(tt,V:S) -> A__ISNEPAL(V:S) 20.51/20.85 A____(__(X:S,Y:S),Z:S) -> A____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.51/20.85 A____(__(X:S,Y:S),Z:S) -> A____(mark(Y:S),mark(Z:S)) 20.51/20.85 A____(__(X:S,Y:S),Z:S) -> MARK(X:S) 20.51/20.85 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S) 20.51/20.85 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 20.51/20.85 A____(nil,X:S) -> MARK(X:S) 20.51/20.85 A____(X:S,nil) -> MARK(X:S) 20.51/20.85 A__AND(tt,X:S) -> MARK(X:S) 20.51/20.85 A__ISLIST(__(V1:S,V2:S)) -> A__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.85 A__ISLIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.85 A__ISLIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.51/20.85 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.85 A__ISNELIST(__(V1:S,V2:S)) -> A__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.85 A__ISNELIST(__(V1:S,V2:S)) -> A__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.85 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.85 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.51/20.85 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.85 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.51/20.85 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.51/20.85 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.85 A__ISPAL(V:S) -> A__U71(a__isPalListKind(V:S),V:S) 20.51/20.85 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.85 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.85 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.51/20.85 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U12(X:S)) -> MARK(X:S) 20.51/20.85 MARK(U21(X1:S,X2:S,X3:S)) -> A__U21(mark(X1:S),X2:S,X3:S) 20.51/20.85 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.51/20.85 MARK(U22(X1:S,X2:S)) -> A__U22(mark(X1:S),X2:S) 20.51/20.85 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U23(X:S)) -> MARK(X:S) 20.51/20.85 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U32(X:S)) -> MARK(X:S) 20.51/20.85 MARK(U41(X1:S,X2:S,X3:S)) -> A__U41(mark(X1:S),X2:S,X3:S) 20.51/20.85 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.51/20.85 MARK(U42(X1:S,X2:S)) -> A__U42(mark(X1:S),X2:S) 20.51/20.85 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U43(X:S)) -> MARK(X:S) 20.51/20.85 MARK(U51(X1:S,X2:S,X3:S)) -> A__U51(mark(X1:S),X2:S,X3:S) 20.51/20.85 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.51/20.85 MARK(U52(X1:S,X2:S)) -> A__U52(mark(X1:S),X2:S) 20.51/20.85 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U53(X:S)) -> MARK(X:S) 20.51/20.85 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U62(X:S)) -> MARK(X:S) 20.51/20.85 MARK(U71(X1:S,X2:S)) -> A__U71(mark(X1:S),X2:S) 20.51/20.85 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U72(X:S)) -> MARK(X:S) 20.51/20.85 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 20.51/20.85 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.51/20.85 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.51/20.85 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.51/20.85 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.51/20.85 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.51/20.85 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.51/20.85 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.51/20.85 ->->-> Rules: 20.51/20.85 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.51/20.85 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.51/20.85 a__U12(tt) -> tt 20.51/20.85 a__U12(X:S) -> U12(X:S) 20.51/20.85 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.51/20.85 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.51/20.85 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.51/20.85 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.51/20.85 a__U23(tt) -> tt 20.51/20.85 a__U23(X:S) -> U23(X:S) 20.51/20.85 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.51/20.85 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.51/20.85 a__U32(tt) -> tt 20.51/20.85 a__U32(X:S) -> U32(X:S) 20.51/20.85 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.51/20.85 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.51/20.85 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.51/20.85 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.51/20.85 a__U43(tt) -> tt 20.51/20.85 a__U43(X:S) -> U43(X:S) 20.51/20.85 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.51/20.85 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.51/20.85 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.51/20.85 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.51/20.85 a__U53(tt) -> tt 20.51/20.85 a__U53(X:S) -> U53(X:S) 20.51/20.85 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.51/20.85 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.51/20.85 a__U62(tt) -> tt 20.51/20.85 a__U62(X:S) -> U62(X:S) 20.51/20.85 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.51/20.85 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.51/20.85 a__U72(tt) -> tt 20.51/20.85 a__U72(X:S) -> U72(X:S) 20.51/20.85 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.51/20.85 a____(nil,X:S) -> mark(X:S) 20.51/20.85 a____(X:S,nil) -> mark(X:S) 20.51/20.85 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.51/20.85 a__and(tt,X:S) -> mark(X:S) 20.51/20.85 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.51/20.85 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.85 a__isList(nil) -> tt 20.51/20.85 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.51/20.85 a__isList(X:S) -> isList(X:S) 20.51/20.85 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.85 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.85 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.51/20.85 a__isNeList(X:S) -> isNeList(X:S) 20.51/20.85 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.51/20.85 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.51/20.85 a__isNePal(X:S) -> isNePal(X:S) 20.51/20.85 a__isPal(nil) -> tt 20.51/20.85 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.51/20.85 a__isPal(X:S) -> isPal(X:S) 20.51/20.85 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.85 a__isPalListKind(a) -> tt 20.51/20.85 a__isPalListKind(e) -> tt 20.51/20.85 a__isPalListKind(i) -> tt 20.51/20.85 a__isPalListKind(nil) -> tt 20.51/20.85 a__isPalListKind(o) -> tt 20.51/20.85 a__isPalListKind(u) -> tt 20.51/20.85 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.51/20.85 a__isQid(a) -> tt 20.51/20.85 a__isQid(e) -> tt 20.51/20.85 a__isQid(i) -> tt 20.51/20.85 a__isQid(o) -> tt 20.51/20.85 a__isQid(u) -> tt 20.51/20.85 a__isQid(X:S) -> isQid(X:S) 20.51/20.85 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.51/20.85 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.51/20.85 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.51/20.85 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.51/20.85 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.51/20.85 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.51/20.85 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.51/20.85 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.51/20.85 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.51/20.85 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.51/20.85 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.51/20.85 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.51/20.85 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.51/20.85 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.51/20.85 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.51/20.85 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.51/20.85 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.51/20.85 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.51/20.85 mark(a) -> a 20.51/20.85 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.51/20.85 mark(e) -> e 20.51/20.85 mark(i) -> i 20.51/20.85 mark(isList(X:S)) -> a__isList(X:S) 20.51/20.85 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.51/20.85 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.51/20.85 mark(isPal(X:S)) -> a__isPal(X:S) 20.51/20.85 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.51/20.85 mark(isQid(X:S)) -> a__isQid(X:S) 20.51/20.85 mark(nil) -> nil 20.51/20.85 mark(o) -> o 20.51/20.85 mark(tt) -> tt 20.51/20.85 mark(u) -> u 20.51/20.85 20.51/20.85 Problem 1: 20.51/20.85 20.51/20.85 Reduction Pairs Processor: 20.51/20.85 -> Pairs: 20.51/20.85 A__U21(tt,V1:S,V2:S) -> A__ISLIST(V1:S) 20.51/20.85 A__U22(tt,V2:S) -> A__ISLIST(V2:S) 20.51/20.85 A__U41(tt,V1:S,V2:S) -> A__U42(a__isList(V1:S),V2:S) 20.51/20.85 A__U41(tt,V1:S,V2:S) -> A__ISLIST(V1:S) 20.51/20.85 A__U42(tt,V2:S) -> A__ISNELIST(V2:S) 20.51/20.85 A__U51(tt,V1:S,V2:S) -> A__U52(a__isNeList(V1:S),V2:S) 20.51/20.85 A__U51(tt,V1:S,V2:S) -> A__ISNELIST(V1:S) 20.51/20.85 A__U52(tt,V2:S) -> A__ISLIST(V2:S) 20.51/20.85 A__U71(tt,V:S) -> A__ISNEPAL(V:S) 20.51/20.85 A____(__(X:S,Y:S),Z:S) -> A____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.51/20.85 A____(__(X:S,Y:S),Z:S) -> A____(mark(Y:S),mark(Z:S)) 20.51/20.85 A____(__(X:S,Y:S),Z:S) -> MARK(X:S) 20.51/20.85 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S) 20.51/20.85 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 20.51/20.85 A____(nil,X:S) -> MARK(X:S) 20.51/20.85 A____(X:S,nil) -> MARK(X:S) 20.51/20.85 A__AND(tt,X:S) -> MARK(X:S) 20.51/20.85 A__ISLIST(__(V1:S,V2:S)) -> A__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.85 A__ISLIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.85 A__ISLIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.51/20.85 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.85 A__ISNELIST(__(V1:S,V2:S)) -> A__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.85 A__ISNELIST(__(V1:S,V2:S)) -> A__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.85 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.85 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.51/20.85 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.85 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.51/20.85 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.51/20.85 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.85 A__ISPAL(V:S) -> A__U71(a__isPalListKind(V:S),V:S) 20.51/20.85 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.85 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.85 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.51/20.85 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U12(X:S)) -> MARK(X:S) 20.51/20.85 MARK(U21(X1:S,X2:S,X3:S)) -> A__U21(mark(X1:S),X2:S,X3:S) 20.51/20.85 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.51/20.85 MARK(U22(X1:S,X2:S)) -> A__U22(mark(X1:S),X2:S) 20.51/20.85 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U23(X:S)) -> MARK(X:S) 20.51/20.85 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U32(X:S)) -> MARK(X:S) 20.51/20.85 MARK(U41(X1:S,X2:S,X3:S)) -> A__U41(mark(X1:S),X2:S,X3:S) 20.51/20.85 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.51/20.85 MARK(U42(X1:S,X2:S)) -> A__U42(mark(X1:S),X2:S) 20.51/20.85 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U43(X:S)) -> MARK(X:S) 20.51/20.85 MARK(U51(X1:S,X2:S,X3:S)) -> A__U51(mark(X1:S),X2:S,X3:S) 20.51/20.85 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.51/20.85 MARK(U52(X1:S,X2:S)) -> A__U52(mark(X1:S),X2:S) 20.51/20.85 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U53(X:S)) -> MARK(X:S) 20.51/20.85 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U62(X:S)) -> MARK(X:S) 20.51/20.85 MARK(U71(X1:S,X2:S)) -> A__U71(mark(X1:S),X2:S) 20.51/20.85 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U72(X:S)) -> MARK(X:S) 20.51/20.85 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 20.51/20.85 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.51/20.85 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.51/20.85 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.51/20.85 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.51/20.85 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.51/20.85 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.51/20.85 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.51/20.85 -> Rules: 20.51/20.85 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.51/20.85 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.51/20.85 a__U12(tt) -> tt 20.51/20.85 a__U12(X:S) -> U12(X:S) 20.51/20.85 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.51/20.85 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.51/20.85 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.51/20.85 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.51/20.85 a__U23(tt) -> tt 20.51/20.85 a__U23(X:S) -> U23(X:S) 20.51/20.85 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.51/20.85 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.51/20.85 a__U32(tt) -> tt 20.51/20.85 a__U32(X:S) -> U32(X:S) 20.51/20.85 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.51/20.85 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.51/20.85 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.51/20.85 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.51/20.85 a__U43(tt) -> tt 20.51/20.85 a__U43(X:S) -> U43(X:S) 20.51/20.85 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.51/20.85 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.51/20.85 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.51/20.85 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.51/20.85 a__U53(tt) -> tt 20.51/20.85 a__U53(X:S) -> U53(X:S) 20.51/20.85 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.51/20.85 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.51/20.85 a__U62(tt) -> tt 20.51/20.85 a__U62(X:S) -> U62(X:S) 20.51/20.85 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.51/20.85 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.51/20.85 a__U72(tt) -> tt 20.51/20.85 a__U72(X:S) -> U72(X:S) 20.51/20.85 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.51/20.85 a____(nil,X:S) -> mark(X:S) 20.51/20.85 a____(X:S,nil) -> mark(X:S) 20.51/20.85 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.51/20.85 a__and(tt,X:S) -> mark(X:S) 20.51/20.85 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.51/20.85 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.85 a__isList(nil) -> tt 20.51/20.85 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.51/20.85 a__isList(X:S) -> isList(X:S) 20.51/20.85 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.85 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.85 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.51/20.85 a__isNeList(X:S) -> isNeList(X:S) 20.51/20.85 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.51/20.85 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.51/20.85 a__isNePal(X:S) -> isNePal(X:S) 20.51/20.85 a__isPal(nil) -> tt 20.51/20.85 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.51/20.85 a__isPal(X:S) -> isPal(X:S) 20.51/20.85 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.85 a__isPalListKind(a) -> tt 20.51/20.85 a__isPalListKind(e) -> tt 20.51/20.85 a__isPalListKind(i) -> tt 20.51/20.85 a__isPalListKind(nil) -> tt 20.51/20.85 a__isPalListKind(o) -> tt 20.51/20.85 a__isPalListKind(u) -> tt 20.51/20.85 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.51/20.85 a__isQid(a) -> tt 20.51/20.85 a__isQid(e) -> tt 20.51/20.85 a__isQid(i) -> tt 20.51/20.85 a__isQid(o) -> tt 20.51/20.85 a__isQid(u) -> tt 20.51/20.85 a__isQid(X:S) -> isQid(X:S) 20.51/20.85 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.51/20.85 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.51/20.85 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.51/20.85 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.51/20.85 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.51/20.85 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.51/20.85 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.51/20.85 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.51/20.85 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.51/20.85 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.51/20.85 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.51/20.85 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.51/20.85 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.51/20.85 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.51/20.85 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.51/20.85 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.51/20.85 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.51/20.85 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.51/20.85 mark(a) -> a 20.51/20.85 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.51/20.85 mark(e) -> e 20.51/20.85 mark(i) -> i 20.51/20.85 mark(isList(X:S)) -> a__isList(X:S) 20.51/20.85 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.51/20.85 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.51/20.85 mark(isPal(X:S)) -> a__isPal(X:S) 20.51/20.85 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.51/20.85 mark(isQid(X:S)) -> a__isQid(X:S) 20.51/20.85 mark(nil) -> nil 20.51/20.85 mark(o) -> o 20.51/20.85 mark(tt) -> tt 20.51/20.85 mark(u) -> u 20.51/20.85 -> Usable rules: 20.51/20.85 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.51/20.85 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.51/20.85 a__U12(tt) -> tt 20.51/20.85 a__U12(X:S) -> U12(X:S) 20.51/20.85 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.51/20.85 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.51/20.85 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.51/20.85 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.51/20.85 a__U23(tt) -> tt 20.51/20.85 a__U23(X:S) -> U23(X:S) 20.51/20.85 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.51/20.85 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.51/20.85 a__U32(tt) -> tt 20.51/20.85 a__U32(X:S) -> U32(X:S) 20.51/20.85 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.51/20.85 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.51/20.85 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.51/20.85 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.51/20.85 a__U43(tt) -> tt 20.51/20.85 a__U43(X:S) -> U43(X:S) 20.51/20.85 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.51/20.85 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.51/20.85 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.51/20.85 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.51/20.85 a__U53(tt) -> tt 20.51/20.85 a__U53(X:S) -> U53(X:S) 20.51/20.85 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.51/20.85 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.51/20.85 a__U62(tt) -> tt 20.51/20.85 a__U62(X:S) -> U62(X:S) 20.51/20.85 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.51/20.85 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.51/20.85 a__U72(tt) -> tt 20.51/20.85 a__U72(X:S) -> U72(X:S) 20.51/20.85 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.51/20.85 a____(nil,X:S) -> mark(X:S) 20.51/20.85 a____(X:S,nil) -> mark(X:S) 20.51/20.85 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.51/20.85 a__and(tt,X:S) -> mark(X:S) 20.51/20.85 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.51/20.85 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.85 a__isList(nil) -> tt 20.51/20.85 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.51/20.85 a__isList(X:S) -> isList(X:S) 20.51/20.85 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.85 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.85 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.51/20.85 a__isNeList(X:S) -> isNeList(X:S) 20.51/20.85 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.51/20.85 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.51/20.85 a__isNePal(X:S) -> isNePal(X:S) 20.51/20.85 a__isPal(nil) -> tt 20.51/20.85 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.51/20.85 a__isPal(X:S) -> isPal(X:S) 20.51/20.85 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.85 a__isPalListKind(a) -> tt 20.51/20.85 a__isPalListKind(e) -> tt 20.51/20.85 a__isPalListKind(i) -> tt 20.51/20.85 a__isPalListKind(nil) -> tt 20.51/20.85 a__isPalListKind(o) -> tt 20.51/20.85 a__isPalListKind(u) -> tt 20.51/20.85 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.51/20.85 a__isQid(a) -> tt 20.51/20.85 a__isQid(e) -> tt 20.51/20.85 a__isQid(i) -> tt 20.51/20.85 a__isQid(o) -> tt 20.51/20.85 a__isQid(u) -> tt 20.51/20.85 a__isQid(X:S) -> isQid(X:S) 20.51/20.85 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.51/20.85 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.51/20.85 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.51/20.85 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.51/20.85 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.51/20.85 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.51/20.85 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.51/20.85 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.51/20.85 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.51/20.85 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.51/20.85 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.51/20.85 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.51/20.85 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.51/20.85 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.51/20.85 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.51/20.85 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.51/20.85 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.51/20.85 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.51/20.85 mark(a) -> a 20.51/20.85 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.51/20.85 mark(e) -> e 20.51/20.85 mark(i) -> i 20.51/20.85 mark(isList(X:S)) -> a__isList(X:S) 20.51/20.85 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.51/20.85 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.51/20.85 mark(isPal(X:S)) -> a__isPal(X:S) 20.51/20.85 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.51/20.85 mark(isQid(X:S)) -> a__isQid(X:S) 20.51/20.85 mark(nil) -> nil 20.51/20.85 mark(o) -> o 20.51/20.85 mark(tt) -> tt 20.51/20.85 mark(u) -> u 20.51/20.85 ->Interpretation type: 20.51/20.85 Linear 20.51/20.85 ->Coefficients: 20.51/20.85 Natural Numbers 20.51/20.85 ->Dimension: 20.51/20.85 1 20.51/20.85 ->Bound: 20.51/20.85 2 20.51/20.85 ->Interpretation: 20.51/20.85 20.51/20.85 [a__U11](X1,X2) = X1 + 2.X2 + 1 20.51/20.85 [a__U12](X) = X 20.51/20.85 [a__U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.51/20.85 [a__U22](X1,X2) = X1 + 2.X2 + 1 20.51/20.85 [a__U23](X) = X 20.51/20.85 [a__U31](X1,X2) = 2.X1 + 2.X2 + 1 20.51/20.85 [a__U32](X) = X 20.51/20.85 [a__U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.51/20.85 [a__U42](X1,X2) = X1 + 2.X2 + 1 20.51/20.85 [a__U43](X) = X 20.51/20.85 [a__U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.51/20.85 [a__U52](X1,X2) = X1 + 2.X2 + 1 20.51/20.85 [a__U53](X) = X 20.51/20.85 [a__U61](X1,X2) = 2.X1 + 2.X2 + 2 20.51/20.85 [a__U62](X) = X + 2 20.51/20.85 [a__U71](X1,X2) = 2.X1 + 2.X2 + 2 20.51/20.85 [a__U72](X) = X 20.51/20.85 [a____](X1,X2) = 2.X1 + X2 + 2 20.51/20.85 [a__and](X1,X2) = X1 + 2.X2 20.51/20.85 [a__isList](X) = 2.X + 1 20.51/20.85 [a__isNeList](X) = 2.X + 1 20.51/20.85 [a__isNePal](X) = 2.X + 2 20.51/20.85 [a__isPal](X) = 2.X + 2 20.51/20.85 [a__isPalListKind](X) = 0 20.51/20.85 [a__isQid](X) = 2.X 20.51/20.85 [mark](X) = X 20.51/20.85 [U11](X1,X2) = X1 + 2.X2 + 1 20.51/20.85 [U12](X) = X 20.51/20.85 [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.51/20.85 [U22](X1,X2) = X1 + 2.X2 + 1 20.51/20.85 [U23](X) = X 20.51/20.85 [U31](X1,X2) = 2.X1 + 2.X2 + 1 20.51/20.85 [U32](X) = X 20.51/20.85 [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.51/20.85 [U42](X1,X2) = X1 + 2.X2 + 1 20.51/20.85 [U43](X) = X 20.51/20.85 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.51/20.85 [U52](X1,X2) = X1 + 2.X2 + 1 20.51/20.85 [U53](X) = X 20.51/20.85 [U61](X1,X2) = 2.X1 + 2.X2 + 2 20.51/20.85 [U62](X) = X + 2 20.51/20.85 [U71](X1,X2) = 2.X1 + 2.X2 + 2 20.51/20.85 [U72](X) = X 20.51/20.85 [__](X1,X2) = 2.X1 + X2 + 2 20.51/20.85 [a] = 2 20.51/20.85 [and](X1,X2) = X1 + 2.X2 20.51/20.85 [e] = 1 20.51/20.85 [fSNonEmpty] = 0 20.51/20.85 [i] = 0 20.51/20.85 [isList](X) = 2.X + 1 20.51/20.85 [isNeList](X) = 2.X + 1 20.51/20.85 [isNePal](X) = 2.X + 2 20.51/20.85 [isPal](X) = 2.X + 2 20.51/20.85 [isPalListKind](X) = 0 20.51/20.85 [isQid](X) = 2.X 20.51/20.85 [nil] = 2 20.51/20.85 [o] = 1 20.51/20.85 [tt] = 0 20.51/20.85 [u] = 1 20.51/20.85 [A__U11](X1,X2) = 0 20.51/20.85 [A__U12](X) = 0 20.51/20.85 [A__U21](X1,X2,X3) = 2.X2 + X3 + 2 20.51/20.85 [A__U22](X1,X2) = X1 + 2.X2 + 1 20.51/20.85 [A__U23](X) = 0 20.51/20.85 [A__U31](X1,X2) = 0 20.51/20.85 [A__U32](X) = 0 20.51/20.85 [A__U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.51/20.85 [A__U42](X1,X2) = X1 + 2.X2 + 1 20.51/20.85 [A__U43](X) = 0 20.51/20.85 [A__U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.51/20.85 [A__U52](X1,X2) = X1 + 2.X2 + 1 20.51/20.85 [A__U53](X) = 0 20.51/20.85 [A__U61](X1,X2) = 0 20.51/20.85 [A__U62](X) = 0 20.51/20.85 [A__U71](X1,X2) = 2.X1 + 2.X2 + 2 20.51/20.85 [A__U72](X) = 0 20.51/20.85 [A____](X1,X2) = 2.X1 + X2 + 1 20.51/20.85 [A__AND](X1,X2) = X1 + 2.X2 20.51/20.85 [A__ISLIST](X) = 2.X + 1 20.51/20.85 [A__ISNELIST](X) = 2.X + 1 20.51/20.85 [A__ISNEPAL](X) = 2.X 20.51/20.85 [A__ISPAL](X) = 2.X + 2 20.51/20.85 [A__ISPALLISTKIND](X) = 0 20.51/20.85 [A__ISQID](X) = 0 20.51/20.85 [MARK](X) = X 20.51/20.85 20.51/20.85 Problem 1: 20.51/20.85 20.51/20.85 SCC Processor: 20.51/20.85 -> Pairs: 20.51/20.85 A__U22(tt,V2:S) -> A__ISLIST(V2:S) 20.51/20.85 A__U41(tt,V1:S,V2:S) -> A__U42(a__isList(V1:S),V2:S) 20.51/20.85 A__U41(tt,V1:S,V2:S) -> A__ISLIST(V1:S) 20.51/20.85 A__U42(tt,V2:S) -> A__ISNELIST(V2:S) 20.51/20.85 A__U51(tt,V1:S,V2:S) -> A__U52(a__isNeList(V1:S),V2:S) 20.51/20.85 A__U51(tt,V1:S,V2:S) -> A__ISNELIST(V1:S) 20.51/20.85 A__U52(tt,V2:S) -> A__ISLIST(V2:S) 20.51/20.85 A__U71(tt,V:S) -> A__ISNEPAL(V:S) 20.51/20.85 A____(__(X:S,Y:S),Z:S) -> A____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.51/20.85 A____(__(X:S,Y:S),Z:S) -> A____(mark(Y:S),mark(Z:S)) 20.51/20.85 A____(__(X:S,Y:S),Z:S) -> MARK(X:S) 20.51/20.85 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S) 20.51/20.85 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 20.51/20.85 A____(nil,X:S) -> MARK(X:S) 20.51/20.85 A____(X:S,nil) -> MARK(X:S) 20.51/20.85 A__AND(tt,X:S) -> MARK(X:S) 20.51/20.85 A__ISLIST(__(V1:S,V2:S)) -> A__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.85 A__ISLIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.85 A__ISLIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.51/20.85 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.85 A__ISNELIST(__(V1:S,V2:S)) -> A__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.85 A__ISNELIST(__(V1:S,V2:S)) -> A__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.85 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.85 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.51/20.85 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.85 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.51/20.85 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.51/20.85 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.85 A__ISPAL(V:S) -> A__U71(a__isPalListKind(V:S),V:S) 20.51/20.85 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.85 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.85 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.51/20.85 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U12(X:S)) -> MARK(X:S) 20.51/20.85 MARK(U21(X1:S,X2:S,X3:S)) -> A__U21(mark(X1:S),X2:S,X3:S) 20.51/20.85 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.51/20.85 MARK(U22(X1:S,X2:S)) -> A__U22(mark(X1:S),X2:S) 20.51/20.85 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U23(X:S)) -> MARK(X:S) 20.51/20.85 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U32(X:S)) -> MARK(X:S) 20.51/20.85 MARK(U41(X1:S,X2:S,X3:S)) -> A__U41(mark(X1:S),X2:S,X3:S) 20.51/20.85 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.51/20.85 MARK(U42(X1:S,X2:S)) -> A__U42(mark(X1:S),X2:S) 20.51/20.85 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U43(X:S)) -> MARK(X:S) 20.51/20.85 MARK(U51(X1:S,X2:S,X3:S)) -> A__U51(mark(X1:S),X2:S,X3:S) 20.51/20.85 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.51/20.85 MARK(U52(X1:S,X2:S)) -> A__U52(mark(X1:S),X2:S) 20.51/20.85 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U53(X:S)) -> MARK(X:S) 20.51/20.85 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U62(X:S)) -> MARK(X:S) 20.51/20.85 MARK(U71(X1:S,X2:S)) -> A__U71(mark(X1:S),X2:S) 20.51/20.85 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U72(X:S)) -> MARK(X:S) 20.51/20.85 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 20.51/20.85 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.51/20.85 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.51/20.85 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.51/20.85 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.51/20.85 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.51/20.85 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.51/20.85 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.51/20.85 -> Rules: 20.51/20.85 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.51/20.85 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.51/20.85 a__U12(tt) -> tt 20.51/20.85 a__U12(X:S) -> U12(X:S) 20.51/20.85 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.51/20.85 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.51/20.85 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.51/20.85 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.51/20.85 a__U23(tt) -> tt 20.51/20.85 a__U23(X:S) -> U23(X:S) 20.51/20.85 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.51/20.85 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.51/20.85 a__U32(tt) -> tt 20.51/20.85 a__U32(X:S) -> U32(X:S) 20.51/20.85 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.51/20.85 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.51/20.85 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.51/20.85 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.51/20.85 a__U43(tt) -> tt 20.51/20.85 a__U43(X:S) -> U43(X:S) 20.51/20.85 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.51/20.85 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.51/20.85 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.51/20.85 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.51/20.85 a__U53(tt) -> tt 20.51/20.85 a__U53(X:S) -> U53(X:S) 20.51/20.85 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.51/20.85 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.51/20.85 a__U62(tt) -> tt 20.51/20.85 a__U62(X:S) -> U62(X:S) 20.51/20.85 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.51/20.85 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.51/20.85 a__U72(tt) -> tt 20.51/20.85 a__U72(X:S) -> U72(X:S) 20.51/20.85 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.51/20.85 a____(nil,X:S) -> mark(X:S) 20.51/20.85 a____(X:S,nil) -> mark(X:S) 20.51/20.85 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.51/20.85 a__and(tt,X:S) -> mark(X:S) 20.51/20.85 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.51/20.85 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.85 a__isList(nil) -> tt 20.51/20.85 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.51/20.85 a__isList(X:S) -> isList(X:S) 20.51/20.85 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.85 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.85 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.51/20.85 a__isNeList(X:S) -> isNeList(X:S) 20.51/20.85 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.51/20.85 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.51/20.85 a__isNePal(X:S) -> isNePal(X:S) 20.51/20.85 a__isPal(nil) -> tt 20.51/20.85 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.51/20.85 a__isPal(X:S) -> isPal(X:S) 20.51/20.85 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.85 a__isPalListKind(a) -> tt 20.51/20.85 a__isPalListKind(e) -> tt 20.51/20.85 a__isPalListKind(i) -> tt 20.51/20.85 a__isPalListKind(nil) -> tt 20.51/20.85 a__isPalListKind(o) -> tt 20.51/20.85 a__isPalListKind(u) -> tt 20.51/20.85 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.51/20.85 a__isQid(a) -> tt 20.51/20.85 a__isQid(e) -> tt 20.51/20.85 a__isQid(i) -> tt 20.51/20.85 a__isQid(o) -> tt 20.51/20.85 a__isQid(u) -> tt 20.51/20.85 a__isQid(X:S) -> isQid(X:S) 20.51/20.85 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.51/20.85 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.51/20.85 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.51/20.85 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.51/20.85 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.51/20.85 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.51/20.85 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.51/20.85 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.51/20.85 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.51/20.85 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.51/20.85 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.51/20.85 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.51/20.85 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.51/20.85 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.51/20.85 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.51/20.85 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.51/20.85 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.51/20.85 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.51/20.85 mark(a) -> a 20.51/20.85 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.51/20.85 mark(e) -> e 20.51/20.85 mark(i) -> i 20.51/20.85 mark(isList(X:S)) -> a__isList(X:S) 20.51/20.85 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.51/20.85 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.51/20.85 mark(isPal(X:S)) -> a__isPal(X:S) 20.51/20.85 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.51/20.85 mark(isQid(X:S)) -> a__isQid(X:S) 20.51/20.85 mark(nil) -> nil 20.51/20.85 mark(o) -> o 20.51/20.85 mark(tt) -> tt 20.51/20.85 mark(u) -> u 20.51/20.85 ->Strongly Connected Components: 20.51/20.85 ->->Cycle: 20.51/20.85 ->->-> Pairs: 20.51/20.85 A__U22(tt,V2:S) -> A__ISLIST(V2:S) 20.51/20.85 A__U41(tt,V1:S,V2:S) -> A__U42(a__isList(V1:S),V2:S) 20.51/20.85 A__U41(tt,V1:S,V2:S) -> A__ISLIST(V1:S) 20.51/20.85 A__U42(tt,V2:S) -> A__ISNELIST(V2:S) 20.51/20.85 A__U51(tt,V1:S,V2:S) -> A__U52(a__isNeList(V1:S),V2:S) 20.51/20.85 A__U51(tt,V1:S,V2:S) -> A__ISNELIST(V1:S) 20.51/20.85 A__U52(tt,V2:S) -> A__ISLIST(V2:S) 20.51/20.85 A__U71(tt,V:S) -> A__ISNEPAL(V:S) 20.51/20.85 A____(__(X:S,Y:S),Z:S) -> A____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.51/20.85 A____(__(X:S,Y:S),Z:S) -> A____(mark(Y:S),mark(Z:S)) 20.51/20.85 A____(__(X:S,Y:S),Z:S) -> MARK(X:S) 20.51/20.85 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S) 20.51/20.85 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 20.51/20.85 A____(nil,X:S) -> MARK(X:S) 20.51/20.85 A____(X:S,nil) -> MARK(X:S) 20.51/20.85 A__AND(tt,X:S) -> MARK(X:S) 20.51/20.85 A__ISLIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.85 A__ISLIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.51/20.85 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.85 A__ISNELIST(__(V1:S,V2:S)) -> A__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.85 A__ISNELIST(__(V1:S,V2:S)) -> A__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.85 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.85 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.51/20.85 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.85 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.51/20.85 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.51/20.85 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.85 A__ISPAL(V:S) -> A__U71(a__isPalListKind(V:S),V:S) 20.51/20.85 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.85 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.85 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.51/20.85 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U12(X:S)) -> MARK(X:S) 20.51/20.85 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.51/20.85 MARK(U22(X1:S,X2:S)) -> A__U22(mark(X1:S),X2:S) 20.51/20.85 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U23(X:S)) -> MARK(X:S) 20.51/20.85 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U32(X:S)) -> MARK(X:S) 20.51/20.85 MARK(U41(X1:S,X2:S,X3:S)) -> A__U41(mark(X1:S),X2:S,X3:S) 20.51/20.85 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.51/20.85 MARK(U42(X1:S,X2:S)) -> A__U42(mark(X1:S),X2:S) 20.51/20.85 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U43(X:S)) -> MARK(X:S) 20.51/20.85 MARK(U51(X1:S,X2:S,X3:S)) -> A__U51(mark(X1:S),X2:S,X3:S) 20.51/20.85 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.51/20.85 MARK(U52(X1:S,X2:S)) -> A__U52(mark(X1:S),X2:S) 20.51/20.85 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U53(X:S)) -> MARK(X:S) 20.51/20.85 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U62(X:S)) -> MARK(X:S) 20.51/20.85 MARK(U71(X1:S,X2:S)) -> A__U71(mark(X1:S),X2:S) 20.51/20.85 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U72(X:S)) -> MARK(X:S) 20.51/20.85 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 20.51/20.85 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.51/20.85 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.51/20.85 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.51/20.85 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.51/20.85 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.51/20.85 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.51/20.85 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.51/20.85 ->->-> Rules: 20.51/20.85 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.51/20.85 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.51/20.85 a__U12(tt) -> tt 20.51/20.85 a__U12(X:S) -> U12(X:S) 20.51/20.85 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.51/20.85 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.51/20.85 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.51/20.85 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.51/20.85 a__U23(tt) -> tt 20.51/20.85 a__U23(X:S) -> U23(X:S) 20.51/20.85 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.51/20.85 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.51/20.85 a__U32(tt) -> tt 20.51/20.85 a__U32(X:S) -> U32(X:S) 20.51/20.85 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.51/20.85 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.51/20.85 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.51/20.85 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.51/20.85 a__U43(tt) -> tt 20.51/20.85 a__U43(X:S) -> U43(X:S) 20.51/20.85 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.51/20.85 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.51/20.85 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.51/20.85 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.51/20.85 a__U53(tt) -> tt 20.51/20.85 a__U53(X:S) -> U53(X:S) 20.51/20.85 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.51/20.85 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.51/20.85 a__U62(tt) -> tt 20.51/20.85 a__U62(X:S) -> U62(X:S) 20.51/20.85 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.51/20.85 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.51/20.85 a__U72(tt) -> tt 20.51/20.85 a__U72(X:S) -> U72(X:S) 20.51/20.85 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.51/20.85 a____(nil,X:S) -> mark(X:S) 20.51/20.85 a____(X:S,nil) -> mark(X:S) 20.51/20.85 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.51/20.85 a__and(tt,X:S) -> mark(X:S) 20.51/20.85 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.51/20.85 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.85 a__isList(nil) -> tt 20.51/20.85 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.51/20.85 a__isList(X:S) -> isList(X:S) 20.51/20.85 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.85 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.85 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.51/20.85 a__isNeList(X:S) -> isNeList(X:S) 20.51/20.85 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.51/20.85 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.51/20.85 a__isNePal(X:S) -> isNePal(X:S) 20.51/20.85 a__isPal(nil) -> tt 20.51/20.85 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.51/20.85 a__isPal(X:S) -> isPal(X:S) 20.51/20.85 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.85 a__isPalListKind(a) -> tt 20.51/20.85 a__isPalListKind(e) -> tt 20.51/20.85 a__isPalListKind(i) -> tt 20.51/20.85 a__isPalListKind(nil) -> tt 20.51/20.85 a__isPalListKind(o) -> tt 20.51/20.85 a__isPalListKind(u) -> tt 20.51/20.85 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.51/20.85 a__isQid(a) -> tt 20.51/20.85 a__isQid(e) -> tt 20.51/20.85 a__isQid(i) -> tt 20.51/20.85 a__isQid(o) -> tt 20.51/20.85 a__isQid(u) -> tt 20.51/20.85 a__isQid(X:S) -> isQid(X:S) 20.51/20.85 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.51/20.85 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.51/20.85 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.51/20.85 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.51/20.85 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.51/20.85 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.51/20.85 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.51/20.85 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.51/20.85 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.51/20.85 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.51/20.85 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.51/20.85 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.51/20.85 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.51/20.85 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.51/20.85 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.51/20.85 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.51/20.85 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.51/20.85 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.51/20.85 mark(a) -> a 20.51/20.85 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.51/20.85 mark(e) -> e 20.51/20.85 mark(i) -> i 20.51/20.85 mark(isList(X:S)) -> a__isList(X:S) 20.51/20.85 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.51/20.85 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.51/20.85 mark(isPal(X:S)) -> a__isPal(X:S) 20.51/20.85 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.51/20.85 mark(isQid(X:S)) -> a__isQid(X:S) 20.51/20.85 mark(nil) -> nil 20.51/20.85 mark(o) -> o 20.51/20.85 mark(tt) -> tt 20.51/20.85 mark(u) -> u 20.51/20.85 20.51/20.85 Problem 1: 20.51/20.85 20.51/20.85 Reduction Pairs Processor: 20.51/20.85 -> Pairs: 20.51/20.85 A__U22(tt,V2:S) -> A__ISLIST(V2:S) 20.51/20.85 A__U41(tt,V1:S,V2:S) -> A__U42(a__isList(V1:S),V2:S) 20.51/20.85 A__U41(tt,V1:S,V2:S) -> A__ISLIST(V1:S) 20.51/20.85 A__U42(tt,V2:S) -> A__ISNELIST(V2:S) 20.51/20.85 A__U51(tt,V1:S,V2:S) -> A__U52(a__isNeList(V1:S),V2:S) 20.51/20.85 A__U51(tt,V1:S,V2:S) -> A__ISNELIST(V1:S) 20.51/20.85 A__U52(tt,V2:S) -> A__ISLIST(V2:S) 20.51/20.85 A__U71(tt,V:S) -> A__ISNEPAL(V:S) 20.51/20.85 A____(__(X:S,Y:S),Z:S) -> A____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.51/20.85 A____(__(X:S,Y:S),Z:S) -> A____(mark(Y:S),mark(Z:S)) 20.51/20.85 A____(__(X:S,Y:S),Z:S) -> MARK(X:S) 20.51/20.85 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S) 20.51/20.85 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 20.51/20.85 A____(nil,X:S) -> MARK(X:S) 20.51/20.85 A____(X:S,nil) -> MARK(X:S) 20.51/20.85 A__AND(tt,X:S) -> MARK(X:S) 20.51/20.85 A__ISLIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.85 A__ISLIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.51/20.85 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.85 A__ISNELIST(__(V1:S,V2:S)) -> A__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.85 A__ISNELIST(__(V1:S,V2:S)) -> A__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.85 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.85 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.51/20.85 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.85 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.51/20.85 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.51/20.85 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.85 A__ISPAL(V:S) -> A__U71(a__isPalListKind(V:S),V:S) 20.51/20.85 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.85 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.85 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.51/20.85 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U12(X:S)) -> MARK(X:S) 20.51/20.85 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.51/20.85 MARK(U22(X1:S,X2:S)) -> A__U22(mark(X1:S),X2:S) 20.51/20.85 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U23(X:S)) -> MARK(X:S) 20.51/20.85 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U32(X:S)) -> MARK(X:S) 20.51/20.85 MARK(U41(X1:S,X2:S,X3:S)) -> A__U41(mark(X1:S),X2:S,X3:S) 20.51/20.85 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.51/20.85 MARK(U42(X1:S,X2:S)) -> A__U42(mark(X1:S),X2:S) 20.51/20.85 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U43(X:S)) -> MARK(X:S) 20.51/20.85 MARK(U51(X1:S,X2:S,X3:S)) -> A__U51(mark(X1:S),X2:S,X3:S) 20.51/20.85 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.51/20.85 MARK(U52(X1:S,X2:S)) -> A__U52(mark(X1:S),X2:S) 20.51/20.85 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U53(X:S)) -> MARK(X:S) 20.51/20.85 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U62(X:S)) -> MARK(X:S) 20.51/20.85 MARK(U71(X1:S,X2:S)) -> A__U71(mark(X1:S),X2:S) 20.51/20.85 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U72(X:S)) -> MARK(X:S) 20.51/20.85 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 20.51/20.85 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.51/20.85 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.51/20.85 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.51/20.85 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.51/20.85 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.51/20.85 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.51/20.85 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.51/20.85 -> Rules: 20.51/20.85 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.51/20.85 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.51/20.85 a__U12(tt) -> tt 20.51/20.85 a__U12(X:S) -> U12(X:S) 20.51/20.85 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.51/20.85 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.51/20.85 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.51/20.85 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.51/20.85 a__U23(tt) -> tt 20.51/20.85 a__U23(X:S) -> U23(X:S) 20.51/20.85 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.51/20.85 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.51/20.85 a__U32(tt) -> tt 20.51/20.85 a__U32(X:S) -> U32(X:S) 20.51/20.85 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.51/20.85 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.51/20.85 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.51/20.85 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.51/20.85 a__U43(tt) -> tt 20.51/20.85 a__U43(X:S) -> U43(X:S) 20.51/20.85 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.51/20.85 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.51/20.85 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.51/20.85 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.51/20.85 a__U53(tt) -> tt 20.51/20.85 a__U53(X:S) -> U53(X:S) 20.51/20.85 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.51/20.85 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.51/20.85 a__U62(tt) -> tt 20.51/20.85 a__U62(X:S) -> U62(X:S) 20.51/20.85 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.51/20.85 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.51/20.85 a__U72(tt) -> tt 20.51/20.85 a__U72(X:S) -> U72(X:S) 20.51/20.85 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.51/20.85 a____(nil,X:S) -> mark(X:S) 20.51/20.85 a____(X:S,nil) -> mark(X:S) 20.51/20.85 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.51/20.85 a__and(tt,X:S) -> mark(X:S) 20.51/20.85 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.51/20.85 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.85 a__isList(nil) -> tt 20.51/20.85 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.51/20.85 a__isList(X:S) -> isList(X:S) 20.51/20.85 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.85 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.85 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.51/20.85 a__isNeList(X:S) -> isNeList(X:S) 20.51/20.85 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.51/20.85 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.51/20.85 a__isNePal(X:S) -> isNePal(X:S) 20.51/20.85 a__isPal(nil) -> tt 20.51/20.85 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.51/20.85 a__isPal(X:S) -> isPal(X:S) 20.51/20.85 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.85 a__isPalListKind(a) -> tt 20.51/20.85 a__isPalListKind(e) -> tt 20.51/20.85 a__isPalListKind(i) -> tt 20.51/20.85 a__isPalListKind(nil) -> tt 20.51/20.85 a__isPalListKind(o) -> tt 20.51/20.85 a__isPalListKind(u) -> tt 20.51/20.85 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.51/20.85 a__isQid(a) -> tt 20.51/20.85 a__isQid(e) -> tt 20.51/20.85 a__isQid(i) -> tt 20.51/20.85 a__isQid(o) -> tt 20.51/20.85 a__isQid(u) -> tt 20.51/20.85 a__isQid(X:S) -> isQid(X:S) 20.51/20.85 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.51/20.85 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.51/20.85 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.51/20.85 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.51/20.85 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.51/20.85 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.51/20.85 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.51/20.85 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.51/20.85 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.51/20.85 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.51/20.85 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.51/20.85 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.51/20.85 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.51/20.85 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.51/20.85 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.51/20.85 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.51/20.85 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.51/20.85 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.51/20.85 mark(a) -> a 20.51/20.85 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.51/20.85 mark(e) -> e 20.51/20.85 mark(i) -> i 20.51/20.85 mark(isList(X:S)) -> a__isList(X:S) 20.51/20.85 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.51/20.85 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.51/20.85 mark(isPal(X:S)) -> a__isPal(X:S) 20.51/20.85 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.51/20.85 mark(isQid(X:S)) -> a__isQid(X:S) 20.51/20.85 mark(nil) -> nil 20.51/20.85 mark(o) -> o 20.51/20.85 mark(tt) -> tt 20.51/20.85 mark(u) -> u 20.51/20.85 -> Usable rules: 20.51/20.85 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.51/20.85 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.51/20.85 a__U12(tt) -> tt 20.51/20.85 a__U12(X:S) -> U12(X:S) 20.51/20.85 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.51/20.85 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.51/20.85 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.51/20.85 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.51/20.85 a__U23(tt) -> tt 20.51/20.85 a__U23(X:S) -> U23(X:S) 20.51/20.85 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.51/20.85 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.51/20.85 a__U32(tt) -> tt 20.51/20.85 a__U32(X:S) -> U32(X:S) 20.51/20.85 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.51/20.85 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.51/20.85 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.51/20.85 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.51/20.85 a__U43(tt) -> tt 20.51/20.85 a__U43(X:S) -> U43(X:S) 20.51/20.85 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.51/20.85 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.51/20.85 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.51/20.85 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.51/20.85 a__U53(tt) -> tt 20.51/20.85 a__U53(X:S) -> U53(X:S) 20.51/20.85 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.51/20.85 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.51/20.85 a__U62(tt) -> tt 20.51/20.85 a__U62(X:S) -> U62(X:S) 20.51/20.85 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.51/20.85 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.51/20.85 a__U72(tt) -> tt 20.51/20.85 a__U72(X:S) -> U72(X:S) 20.51/20.85 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.51/20.85 a____(nil,X:S) -> mark(X:S) 20.51/20.85 a____(X:S,nil) -> mark(X:S) 20.51/20.85 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.51/20.85 a__and(tt,X:S) -> mark(X:S) 20.51/20.85 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.51/20.85 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.85 a__isList(nil) -> tt 20.51/20.85 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.51/20.85 a__isList(X:S) -> isList(X:S) 20.51/20.85 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.85 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.85 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.51/20.85 a__isNeList(X:S) -> isNeList(X:S) 20.51/20.85 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.51/20.85 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.51/20.85 a__isNePal(X:S) -> isNePal(X:S) 20.51/20.85 a__isPal(nil) -> tt 20.51/20.85 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.51/20.85 a__isPal(X:S) -> isPal(X:S) 20.51/20.85 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.85 a__isPalListKind(a) -> tt 20.51/20.85 a__isPalListKind(e) -> tt 20.51/20.85 a__isPalListKind(i) -> tt 20.51/20.85 a__isPalListKind(nil) -> tt 20.51/20.85 a__isPalListKind(o) -> tt 20.51/20.85 a__isPalListKind(u) -> tt 20.51/20.85 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.51/20.85 a__isQid(a) -> tt 20.51/20.85 a__isQid(e) -> tt 20.51/20.85 a__isQid(i) -> tt 20.51/20.85 a__isQid(o) -> tt 20.51/20.85 a__isQid(u) -> tt 20.51/20.85 a__isQid(X:S) -> isQid(X:S) 20.51/20.85 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.51/20.85 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.51/20.85 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.51/20.85 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.51/20.85 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.51/20.85 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.51/20.85 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.51/20.85 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.51/20.85 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.51/20.85 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.51/20.85 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.51/20.85 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.51/20.85 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.51/20.85 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.51/20.85 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.51/20.85 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.51/20.85 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.51/20.85 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.51/20.85 mark(a) -> a 20.51/20.85 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.51/20.85 mark(e) -> e 20.51/20.85 mark(i) -> i 20.51/20.85 mark(isList(X:S)) -> a__isList(X:S) 20.51/20.85 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.51/20.85 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.51/20.85 mark(isPal(X:S)) -> a__isPal(X:S) 20.51/20.85 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.51/20.85 mark(isQid(X:S)) -> a__isQid(X:S) 20.51/20.85 mark(nil) -> nil 20.51/20.85 mark(o) -> o 20.51/20.85 mark(tt) -> tt 20.51/20.85 mark(u) -> u 20.51/20.85 ->Interpretation type: 20.51/20.85 Linear 20.51/20.85 ->Coefficients: 20.51/20.85 Natural Numbers 20.51/20.85 ->Dimension: 20.51/20.85 1 20.51/20.85 ->Bound: 20.51/20.85 2 20.51/20.85 ->Interpretation: 20.51/20.85 20.51/20.85 [a__U11](X1,X2) = 2.X1 + 2.X2 + 1 20.51/20.85 [a__U12](X) = X 20.51/20.85 [a__U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.51/20.85 [a__U22](X1,X2) = X1 + 2.X2 + 1 20.51/20.85 [a__U23](X) = X 20.51/20.85 [a__U31](X1,X2) = 2.X1 + 2.X2 + 1 20.51/20.85 [a__U32](X) = 2.X + 1 20.51/20.85 [a__U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.51/20.85 [a__U42](X1,X2) = X1 + 2.X2 + 1 20.51/20.85 [a__U43](X) = X 20.51/20.85 [a__U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.51/20.85 [a__U52](X1,X2) = X1 + 2.X2 + 1 20.51/20.85 [a__U53](X) = X 20.51/20.85 [a__U61](X1,X2) = 2.X1 + X2 + 2 20.51/20.85 [a__U62](X) = X 20.51/20.85 [a__U71](X1,X2) = 2.X1 + X2 + 2 20.51/20.85 [a__U72](X) = X 20.51/20.85 [a____](X1,X2) = X1 + X2 + 2 20.51/20.85 [a__and](X1,X2) = X1 + X2 20.51/20.85 [a__isList](X) = 2.X + 1 20.51/20.85 [a__isNeList](X) = 2.X + 1 20.51/20.85 [a__isNePal](X) = X + 2 20.51/20.85 [a__isPal](X) = X + 2 20.51/20.85 [a__isPalListKind](X) = 0 20.51/20.85 [a__isQid](X) = X 20.51/20.85 [mark](X) = X 20.51/20.85 [U11](X1,X2) = 2.X1 + 2.X2 + 1 20.51/20.85 [U12](X) = X 20.51/20.85 [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.51/20.85 [U22](X1,X2) = X1 + 2.X2 + 1 20.51/20.85 [U23](X) = X 20.51/20.85 [U31](X1,X2) = 2.X1 + 2.X2 + 1 20.51/20.85 [U32](X) = 2.X + 1 20.51/20.85 [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.51/20.85 [U42](X1,X2) = X1 + 2.X2 + 1 20.51/20.85 [U43](X) = X 20.51/20.85 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.51/20.85 [U52](X1,X2) = X1 + 2.X2 + 1 20.51/20.85 [U53](X) = X 20.51/20.85 [U61](X1,X2) = 2.X1 + X2 + 2 20.51/20.85 [U62](X) = X 20.51/20.85 [U71](X1,X2) = 2.X1 + X2 + 2 20.51/20.85 [U72](X) = X 20.51/20.85 [__](X1,X2) = X1 + X2 + 2 20.51/20.85 [a] = 0 20.51/20.85 [and](X1,X2) = X1 + X2 20.51/20.85 [e] = 1 20.51/20.85 [fSNonEmpty] = 0 20.51/20.85 [i] = 2 20.51/20.85 [isList](X) = 2.X + 1 20.51/20.85 [isNeList](X) = 2.X + 1 20.51/20.85 [isNePal](X) = X + 2 20.51/20.85 [isPal](X) = X + 2 20.51/20.85 [isPalListKind](X) = 0 20.51/20.85 [isQid](X) = X 20.51/20.85 [nil] = 2 20.51/20.85 [o] = 0 20.51/20.85 [tt] = 0 20.51/20.85 [u] = 1 20.51/20.85 [A__U11](X1,X2) = 0 20.51/20.85 [A__U12](X) = 0 20.51/20.85 [A__U21](X1,X2,X3) = 0 20.51/20.85 [A__U22](X1,X2) = X1 + X2 + 1 20.51/20.85 [A__U23](X) = 0 20.51/20.85 [A__U31](X1,X2) = 0 20.51/20.85 [A__U32](X) = 0 20.51/20.85 [A__U41](X1,X2,X3) = 2.X3 + 2 20.51/20.85 [A__U42](X1,X2) = 2.X2 + 2 20.51/20.85 [A__U43](X) = 0 20.51/20.85 [A__U51](X1,X2,X3) = 2.X1 + 2.X2 + X3 + 1 20.51/20.85 [A__U52](X1,X2) = X1 + X2 20.51/20.85 [A__U53](X) = 0 20.51/20.85 [A__U61](X1,X2) = 0 20.51/20.85 [A__U62](X) = 0 20.51/20.85 [A__U71](X1,X2) = 2.X1 + 2.X2 + 2 20.51/20.85 [A__U72](X) = 0 20.51/20.85 [A____](X1,X2) = 2.X1 + 2.X2 + 2 20.51/20.85 [A__AND](X1,X2) = 2.X2 20.51/20.85 [A__ISLIST](X) = 0 20.51/20.85 [A__ISNELIST](X) = 2.X + 1 20.51/20.85 [A__ISNEPAL](X) = 2.X + 2 20.51/20.85 [A__ISPAL](X) = 2.X + 2 20.51/20.85 [A__ISPALLISTKIND](X) = 0 20.51/20.85 [A__ISQID](X) = 0 20.51/20.85 [MARK](X) = 2.X 20.51/20.85 20.51/20.85 Problem 1: 20.51/20.85 20.51/20.85 SCC Processor: 20.51/20.85 -> Pairs: 20.51/20.85 A__U41(tt,V1:S,V2:S) -> A__U42(a__isList(V1:S),V2:S) 20.51/20.85 A__U41(tt,V1:S,V2:S) -> A__ISLIST(V1:S) 20.51/20.85 A__U42(tt,V2:S) -> A__ISNELIST(V2:S) 20.51/20.85 A__U51(tt,V1:S,V2:S) -> A__U52(a__isNeList(V1:S),V2:S) 20.51/20.85 A__U51(tt,V1:S,V2:S) -> A__ISNELIST(V1:S) 20.51/20.85 A__U52(tt,V2:S) -> A__ISLIST(V2:S) 20.51/20.85 A__U71(tt,V:S) -> A__ISNEPAL(V:S) 20.51/20.85 A____(__(X:S,Y:S),Z:S) -> A____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.51/20.85 A____(__(X:S,Y:S),Z:S) -> A____(mark(Y:S),mark(Z:S)) 20.51/20.85 A____(__(X:S,Y:S),Z:S) -> MARK(X:S) 20.51/20.85 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S) 20.51/20.85 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 20.51/20.85 A____(nil,X:S) -> MARK(X:S) 20.51/20.85 A____(X:S,nil) -> MARK(X:S) 20.51/20.85 A__AND(tt,X:S) -> MARK(X:S) 20.51/20.85 A__ISLIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.85 A__ISLIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.51/20.85 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.85 A__ISNELIST(__(V1:S,V2:S)) -> A__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.85 A__ISNELIST(__(V1:S,V2:S)) -> A__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.85 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.85 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.51/20.85 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.85 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.51/20.85 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.51/20.85 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.85 A__ISPAL(V:S) -> A__U71(a__isPalListKind(V:S),V:S) 20.51/20.85 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.85 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.85 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.51/20.85 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U12(X:S)) -> MARK(X:S) 20.51/20.85 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.51/20.85 MARK(U22(X1:S,X2:S)) -> A__U22(mark(X1:S),X2:S) 20.51/20.85 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U23(X:S)) -> MARK(X:S) 20.51/20.85 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U32(X:S)) -> MARK(X:S) 20.51/20.85 MARK(U41(X1:S,X2:S,X3:S)) -> A__U41(mark(X1:S),X2:S,X3:S) 20.51/20.85 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.51/20.85 MARK(U42(X1:S,X2:S)) -> A__U42(mark(X1:S),X2:S) 20.51/20.85 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U43(X:S)) -> MARK(X:S) 20.51/20.85 MARK(U51(X1:S,X2:S,X3:S)) -> A__U51(mark(X1:S),X2:S,X3:S) 20.51/20.85 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.51/20.85 MARK(U52(X1:S,X2:S)) -> A__U52(mark(X1:S),X2:S) 20.51/20.85 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U53(X:S)) -> MARK(X:S) 20.51/20.85 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U62(X:S)) -> MARK(X:S) 20.51/20.85 MARK(U71(X1:S,X2:S)) -> A__U71(mark(X1:S),X2:S) 20.51/20.85 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U72(X:S)) -> MARK(X:S) 20.51/20.85 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 20.51/20.85 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.51/20.85 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.51/20.85 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.51/20.85 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.51/20.85 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.51/20.85 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.51/20.85 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.51/20.85 -> Rules: 20.51/20.85 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.51/20.85 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.51/20.85 a__U12(tt) -> tt 20.51/20.85 a__U12(X:S) -> U12(X:S) 20.51/20.85 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.51/20.85 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.51/20.85 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.51/20.85 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.51/20.85 a__U23(tt) -> tt 20.51/20.85 a__U23(X:S) -> U23(X:S) 20.51/20.85 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.51/20.85 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.51/20.85 a__U32(tt) -> tt 20.51/20.85 a__U32(X:S) -> U32(X:S) 20.51/20.85 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.51/20.85 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.51/20.85 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.51/20.85 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.51/20.85 a__U43(tt) -> tt 20.51/20.85 a__U43(X:S) -> U43(X:S) 20.51/20.85 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.51/20.85 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.51/20.85 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.51/20.85 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.51/20.85 a__U53(tt) -> tt 20.51/20.85 a__U53(X:S) -> U53(X:S) 20.51/20.85 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.51/20.85 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.51/20.85 a__U62(tt) -> tt 20.51/20.85 a__U62(X:S) -> U62(X:S) 20.51/20.85 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.51/20.85 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.51/20.85 a__U72(tt) -> tt 20.51/20.85 a__U72(X:S) -> U72(X:S) 20.51/20.85 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.51/20.85 a____(nil,X:S) -> mark(X:S) 20.51/20.85 a____(X:S,nil) -> mark(X:S) 20.51/20.85 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.51/20.85 a__and(tt,X:S) -> mark(X:S) 20.51/20.85 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.51/20.85 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.85 a__isList(nil) -> tt 20.51/20.85 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.51/20.85 a__isList(X:S) -> isList(X:S) 20.51/20.85 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.85 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.85 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.51/20.85 a__isNeList(X:S) -> isNeList(X:S) 20.51/20.85 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.51/20.85 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.51/20.85 a__isNePal(X:S) -> isNePal(X:S) 20.51/20.85 a__isPal(nil) -> tt 20.51/20.85 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.51/20.85 a__isPal(X:S) -> isPal(X:S) 20.51/20.85 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.85 a__isPalListKind(a) -> tt 20.51/20.85 a__isPalListKind(e) -> tt 20.51/20.85 a__isPalListKind(i) -> tt 20.51/20.85 a__isPalListKind(nil) -> tt 20.51/20.85 a__isPalListKind(o) -> tt 20.51/20.85 a__isPalListKind(u) -> tt 20.51/20.85 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.51/20.85 a__isQid(a) -> tt 20.51/20.85 a__isQid(e) -> tt 20.51/20.85 a__isQid(i) -> tt 20.51/20.85 a__isQid(o) -> tt 20.51/20.85 a__isQid(u) -> tt 20.51/20.85 a__isQid(X:S) -> isQid(X:S) 20.51/20.85 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.51/20.85 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.51/20.85 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.51/20.85 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.51/20.85 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.51/20.85 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.51/20.85 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.51/20.85 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.51/20.85 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.51/20.85 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.51/20.85 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.51/20.85 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.51/20.85 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.51/20.85 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.51/20.85 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.51/20.85 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.51/20.85 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.51/20.85 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.51/20.85 mark(a) -> a 20.51/20.85 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.51/20.85 mark(e) -> e 20.51/20.85 mark(i) -> i 20.51/20.85 mark(isList(X:S)) -> a__isList(X:S) 20.51/20.85 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.51/20.85 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.51/20.85 mark(isPal(X:S)) -> a__isPal(X:S) 20.51/20.85 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.51/20.85 mark(isQid(X:S)) -> a__isQid(X:S) 20.51/20.85 mark(nil) -> nil 20.51/20.85 mark(o) -> o 20.51/20.85 mark(tt) -> tt 20.51/20.85 mark(u) -> u 20.51/20.85 ->Strongly Connected Components: 20.51/20.85 ->->Cycle: 20.51/20.85 ->->-> Pairs: 20.51/20.85 A__U41(tt,V1:S,V2:S) -> A__U42(a__isList(V1:S),V2:S) 20.51/20.85 A__U41(tt,V1:S,V2:S) -> A__ISLIST(V1:S) 20.51/20.85 A__U42(tt,V2:S) -> A__ISNELIST(V2:S) 20.51/20.85 A__U51(tt,V1:S,V2:S) -> A__U52(a__isNeList(V1:S),V2:S) 20.51/20.85 A__U51(tt,V1:S,V2:S) -> A__ISNELIST(V1:S) 20.51/20.85 A__U52(tt,V2:S) -> A__ISLIST(V2:S) 20.51/20.85 A__U71(tt,V:S) -> A__ISNEPAL(V:S) 20.51/20.85 A____(__(X:S,Y:S),Z:S) -> A____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.51/20.85 A____(__(X:S,Y:S),Z:S) -> A____(mark(Y:S),mark(Z:S)) 20.51/20.85 A____(__(X:S,Y:S),Z:S) -> MARK(X:S) 20.51/20.85 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S) 20.51/20.85 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 20.51/20.85 A____(nil,X:S) -> MARK(X:S) 20.51/20.85 A____(X:S,nil) -> MARK(X:S) 20.51/20.85 A__AND(tt,X:S) -> MARK(X:S) 20.51/20.85 A__ISLIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.85 A__ISLIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.51/20.85 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.85 A__ISNELIST(__(V1:S,V2:S)) -> A__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.85 A__ISNELIST(__(V1:S,V2:S)) -> A__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.85 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.85 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.51/20.85 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.85 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.51/20.85 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.51/20.85 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.85 A__ISPAL(V:S) -> A__U71(a__isPalListKind(V:S),V:S) 20.51/20.85 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.85 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.85 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.51/20.85 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U12(X:S)) -> MARK(X:S) 20.51/20.85 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.51/20.85 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U23(X:S)) -> MARK(X:S) 20.51/20.85 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U32(X:S)) -> MARK(X:S) 20.51/20.85 MARK(U41(X1:S,X2:S,X3:S)) -> A__U41(mark(X1:S),X2:S,X3:S) 20.51/20.85 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.51/20.85 MARK(U42(X1:S,X2:S)) -> A__U42(mark(X1:S),X2:S) 20.51/20.85 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U43(X:S)) -> MARK(X:S) 20.51/20.85 MARK(U51(X1:S,X2:S,X3:S)) -> A__U51(mark(X1:S),X2:S,X3:S) 20.51/20.85 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.51/20.85 MARK(U52(X1:S,X2:S)) -> A__U52(mark(X1:S),X2:S) 20.51/20.85 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U53(X:S)) -> MARK(X:S) 20.51/20.85 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U62(X:S)) -> MARK(X:S) 20.51/20.85 MARK(U71(X1:S,X2:S)) -> A__U71(mark(X1:S),X2:S) 20.51/20.85 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U72(X:S)) -> MARK(X:S) 20.51/20.85 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 20.51/20.85 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.51/20.85 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.51/20.85 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.51/20.85 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.51/20.85 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.51/20.85 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.51/20.85 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.51/20.85 ->->-> Rules: 20.51/20.85 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.51/20.85 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.51/20.85 a__U12(tt) -> tt 20.51/20.85 a__U12(X:S) -> U12(X:S) 20.51/20.85 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.51/20.85 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.51/20.85 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.51/20.85 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.51/20.85 a__U23(tt) -> tt 20.51/20.85 a__U23(X:S) -> U23(X:S) 20.51/20.85 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.51/20.85 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.51/20.85 a__U32(tt) -> tt 20.51/20.85 a__U32(X:S) -> U32(X:S) 20.51/20.85 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.51/20.85 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.51/20.85 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.51/20.85 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.51/20.85 a__U43(tt) -> tt 20.51/20.85 a__U43(X:S) -> U43(X:S) 20.51/20.85 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.51/20.85 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.51/20.85 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.51/20.85 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.51/20.85 a__U53(tt) -> tt 20.51/20.85 a__U53(X:S) -> U53(X:S) 20.51/20.85 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.51/20.85 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.51/20.85 a__U62(tt) -> tt 20.51/20.85 a__U62(X:S) -> U62(X:S) 20.51/20.85 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.51/20.85 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.51/20.85 a__U72(tt) -> tt 20.51/20.85 a__U72(X:S) -> U72(X:S) 20.51/20.85 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.51/20.85 a____(nil,X:S) -> mark(X:S) 20.51/20.85 a____(X:S,nil) -> mark(X:S) 20.51/20.85 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.51/20.85 a__and(tt,X:S) -> mark(X:S) 20.51/20.85 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.51/20.85 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.85 a__isList(nil) -> tt 20.51/20.85 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.51/20.85 a__isList(X:S) -> isList(X:S) 20.51/20.85 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.85 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.85 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.51/20.85 a__isNeList(X:S) -> isNeList(X:S) 20.51/20.85 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.51/20.85 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.51/20.85 a__isNePal(X:S) -> isNePal(X:S) 20.51/20.85 a__isPal(nil) -> tt 20.51/20.85 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.51/20.85 a__isPal(X:S) -> isPal(X:S) 20.51/20.85 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.85 a__isPalListKind(a) -> tt 20.51/20.85 a__isPalListKind(e) -> tt 20.51/20.85 a__isPalListKind(i) -> tt 20.51/20.85 a__isPalListKind(nil) -> tt 20.51/20.85 a__isPalListKind(o) -> tt 20.51/20.85 a__isPalListKind(u) -> tt 20.51/20.85 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.51/20.85 a__isQid(a) -> tt 20.51/20.85 a__isQid(e) -> tt 20.51/20.85 a__isQid(i) -> tt 20.51/20.85 a__isQid(o) -> tt 20.51/20.85 a__isQid(u) -> tt 20.51/20.85 a__isQid(X:S) -> isQid(X:S) 20.51/20.85 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.51/20.85 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.51/20.85 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.51/20.85 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.51/20.85 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.51/20.85 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.51/20.85 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.51/20.85 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.51/20.85 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.51/20.85 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.51/20.85 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.51/20.85 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.51/20.85 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.51/20.85 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.51/20.85 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.51/20.85 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.51/20.85 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.51/20.85 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.51/20.85 mark(a) -> a 20.51/20.85 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.51/20.85 mark(e) -> e 20.51/20.85 mark(i) -> i 20.51/20.85 mark(isList(X:S)) -> a__isList(X:S) 20.51/20.85 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.51/20.85 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.51/20.85 mark(isPal(X:S)) -> a__isPal(X:S) 20.51/20.85 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.51/20.85 mark(isQid(X:S)) -> a__isQid(X:S) 20.51/20.85 mark(nil) -> nil 20.51/20.85 mark(o) -> o 20.51/20.85 mark(tt) -> tt 20.51/20.85 mark(u) -> u 20.51/20.85 20.51/20.85 Problem 1: 20.51/20.85 20.51/20.85 Reduction Pairs Processor: 20.51/20.85 -> Pairs: 20.51/20.85 A__U41(tt,V1:S,V2:S) -> A__U42(a__isList(V1:S),V2:S) 20.51/20.85 A__U41(tt,V1:S,V2:S) -> A__ISLIST(V1:S) 20.51/20.85 A__U42(tt,V2:S) -> A__ISNELIST(V2:S) 20.51/20.85 A__U51(tt,V1:S,V2:S) -> A__U52(a__isNeList(V1:S),V2:S) 20.51/20.85 A__U51(tt,V1:S,V2:S) -> A__ISNELIST(V1:S) 20.51/20.85 A__U52(tt,V2:S) -> A__ISLIST(V2:S) 20.51/20.85 A__U71(tt,V:S) -> A__ISNEPAL(V:S) 20.51/20.85 A____(__(X:S,Y:S),Z:S) -> A____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.51/20.85 A____(__(X:S,Y:S),Z:S) -> A____(mark(Y:S),mark(Z:S)) 20.51/20.85 A____(__(X:S,Y:S),Z:S) -> MARK(X:S) 20.51/20.85 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S) 20.51/20.85 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 20.51/20.85 A____(nil,X:S) -> MARK(X:S) 20.51/20.85 A____(X:S,nil) -> MARK(X:S) 20.51/20.85 A__AND(tt,X:S) -> MARK(X:S) 20.51/20.85 A__ISLIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.85 A__ISLIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.51/20.85 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.85 A__ISNELIST(__(V1:S,V2:S)) -> A__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.85 A__ISNELIST(__(V1:S,V2:S)) -> A__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.85 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.85 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.51/20.85 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.85 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.51/20.85 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.51/20.85 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.85 A__ISPAL(V:S) -> A__U71(a__isPalListKind(V:S),V:S) 20.51/20.85 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.85 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.85 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.51/20.85 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U12(X:S)) -> MARK(X:S) 20.51/20.85 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.51/20.85 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U23(X:S)) -> MARK(X:S) 20.51/20.85 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U32(X:S)) -> MARK(X:S) 20.51/20.85 MARK(U41(X1:S,X2:S,X3:S)) -> A__U41(mark(X1:S),X2:S,X3:S) 20.51/20.85 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.51/20.85 MARK(U42(X1:S,X2:S)) -> A__U42(mark(X1:S),X2:S) 20.51/20.85 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U43(X:S)) -> MARK(X:S) 20.51/20.85 MARK(U51(X1:S,X2:S,X3:S)) -> A__U51(mark(X1:S),X2:S,X3:S) 20.51/20.85 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.51/20.85 MARK(U52(X1:S,X2:S)) -> A__U52(mark(X1:S),X2:S) 20.51/20.85 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U53(X:S)) -> MARK(X:S) 20.51/20.85 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U62(X:S)) -> MARK(X:S) 20.51/20.85 MARK(U71(X1:S,X2:S)) -> A__U71(mark(X1:S),X2:S) 20.51/20.85 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(U72(X:S)) -> MARK(X:S) 20.51/20.85 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 20.51/20.85 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.51/20.85 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.51/20.85 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.85 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.51/20.85 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.51/20.85 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.51/20.85 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.51/20.85 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.51/20.85 -> Rules: 20.51/20.85 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.51/20.85 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.51/20.85 a__U12(tt) -> tt 20.51/20.85 a__U12(X:S) -> U12(X:S) 20.51/20.85 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.51/20.85 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.51/20.85 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.51/20.85 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.51/20.85 a__U23(tt) -> tt 20.51/20.85 a__U23(X:S) -> U23(X:S) 20.51/20.85 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.51/20.85 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.51/20.85 a__U32(tt) -> tt 20.51/20.85 a__U32(X:S) -> U32(X:S) 20.51/20.85 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.51/20.85 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.51/20.85 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.51/20.85 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.51/20.85 a__U43(tt) -> tt 20.51/20.85 a__U43(X:S) -> U43(X:S) 20.51/20.85 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.51/20.85 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.51/20.85 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.51/20.85 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.51/20.85 a__U53(tt) -> tt 20.51/20.85 a__U53(X:S) -> U53(X:S) 20.51/20.85 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.51/20.85 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.51/20.85 a__U62(tt) -> tt 20.51/20.85 a__U62(X:S) -> U62(X:S) 20.51/20.85 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.51/20.85 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.51/20.85 a__U72(tt) -> tt 20.51/20.85 a__U72(X:S) -> U72(X:S) 20.51/20.85 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.51/20.85 a____(nil,X:S) -> mark(X:S) 20.51/20.85 a____(X:S,nil) -> mark(X:S) 20.51/20.85 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.51/20.85 a__and(tt,X:S) -> mark(X:S) 20.51/20.85 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.51/20.85 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.85 a__isList(nil) -> tt 20.51/20.85 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.51/20.85 a__isList(X:S) -> isList(X:S) 20.51/20.85 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.85 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.85 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.51/20.85 a__isNeList(X:S) -> isNeList(X:S) 20.51/20.85 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.51/20.85 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.51/20.85 a__isNePal(X:S) -> isNePal(X:S) 20.51/20.85 a__isPal(nil) -> tt 20.51/20.85 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.51/20.85 a__isPal(X:S) -> isPal(X:S) 20.51/20.85 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.85 a__isPalListKind(a) -> tt 20.51/20.85 a__isPalListKind(e) -> tt 20.51/20.85 a__isPalListKind(i) -> tt 20.51/20.85 a__isPalListKind(nil) -> tt 20.51/20.85 a__isPalListKind(o) -> tt 20.51/20.85 a__isPalListKind(u) -> tt 20.51/20.85 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.51/20.85 a__isQid(a) -> tt 20.51/20.85 a__isQid(e) -> tt 20.51/20.85 a__isQid(i) -> tt 20.51/20.85 a__isQid(o) -> tt 20.51/20.85 a__isQid(u) -> tt 20.51/20.85 a__isQid(X:S) -> isQid(X:S) 20.51/20.85 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.51/20.85 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.51/20.85 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.51/20.85 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.51/20.85 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.51/20.85 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.51/20.85 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.51/20.85 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.51/20.85 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.51/20.85 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.51/20.85 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.51/20.85 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.51/20.85 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.51/20.85 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.51/20.85 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.51/20.85 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.51/20.85 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.51/20.85 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.51/20.85 mark(a) -> a 20.51/20.85 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.51/20.85 mark(e) -> e 20.51/20.85 mark(i) -> i 20.51/20.85 mark(isList(X:S)) -> a__isList(X:S) 20.51/20.85 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.51/20.85 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.51/20.85 mark(isPal(X:S)) -> a__isPal(X:S) 20.51/20.85 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.51/20.85 mark(isQid(X:S)) -> a__isQid(X:S) 20.51/20.85 mark(nil) -> nil 20.51/20.85 mark(o) -> o 20.51/20.85 mark(tt) -> tt 20.51/20.85 mark(u) -> u 20.51/20.85 -> Usable rules: 20.51/20.85 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.51/20.85 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.51/20.85 a__U12(tt) -> tt 20.51/20.85 a__U12(X:S) -> U12(X:S) 20.51/20.85 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.51/20.85 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.51/20.85 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.51/20.85 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.51/20.85 a__U23(tt) -> tt 20.51/20.85 a__U23(X:S) -> U23(X:S) 20.51/20.85 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.51/20.85 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.51/20.85 a__U32(tt) -> tt 20.51/20.85 a__U32(X:S) -> U32(X:S) 20.51/20.85 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.51/20.85 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.51/20.85 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.51/20.85 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.51/20.85 a__U43(tt) -> tt 20.51/20.85 a__U43(X:S) -> U43(X:S) 20.51/20.85 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.51/20.85 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.51/20.85 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.51/20.85 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.51/20.85 a__U53(tt) -> tt 20.51/20.85 a__U53(X:S) -> U53(X:S) 20.51/20.85 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.51/20.85 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.51/20.85 a__U62(tt) -> tt 20.51/20.85 a__U62(X:S) -> U62(X:S) 20.51/20.85 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.51/20.85 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.51/20.85 a__U72(tt) -> tt 20.51/20.85 a__U72(X:S) -> U72(X:S) 20.51/20.85 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.51/20.85 a____(nil,X:S) -> mark(X:S) 20.51/20.85 a____(X:S,nil) -> mark(X:S) 20.51/20.85 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.51/20.85 a__and(tt,X:S) -> mark(X:S) 20.51/20.85 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.51/20.85 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.85 a__isList(nil) -> tt 20.51/20.85 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.51/20.85 a__isList(X:S) -> isList(X:S) 20.51/20.85 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.85 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.85 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.51/20.85 a__isNeList(X:S) -> isNeList(X:S) 20.51/20.85 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.51/20.85 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.51/20.85 a__isNePal(X:S) -> isNePal(X:S) 20.51/20.85 a__isPal(nil) -> tt 20.51/20.85 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.51/20.85 a__isPal(X:S) -> isPal(X:S) 20.51/20.85 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.85 a__isPalListKind(a) -> tt 20.51/20.85 a__isPalListKind(e) -> tt 20.51/20.85 a__isPalListKind(i) -> tt 20.51/20.85 a__isPalListKind(nil) -> tt 20.51/20.85 a__isPalListKind(o) -> tt 20.51/20.85 a__isPalListKind(u) -> tt 20.51/20.85 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.51/20.85 a__isQid(a) -> tt 20.51/20.85 a__isQid(e) -> tt 20.51/20.85 a__isQid(i) -> tt 20.51/20.85 a__isQid(o) -> tt 20.51/20.85 a__isQid(u) -> tt 20.51/20.85 a__isQid(X:S) -> isQid(X:S) 20.51/20.85 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.51/20.85 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.51/20.85 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.51/20.85 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.51/20.85 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.51/20.85 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.51/20.85 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.51/20.85 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.51/20.85 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.51/20.85 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.51/20.85 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.51/20.85 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.51/20.85 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.51/20.85 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.51/20.85 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.51/20.85 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.51/20.85 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.51/20.85 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.51/20.85 mark(a) -> a 20.51/20.85 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.51/20.85 mark(e) -> e 20.51/20.85 mark(i) -> i 20.51/20.85 mark(isList(X:S)) -> a__isList(X:S) 20.51/20.85 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.51/20.85 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.51/20.85 mark(isPal(X:S)) -> a__isPal(X:S) 20.51/20.85 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.51/20.85 mark(isQid(X:S)) -> a__isQid(X:S) 20.51/20.85 mark(nil) -> nil 20.51/20.85 mark(o) -> o 20.51/20.85 mark(tt) -> tt 20.51/20.85 mark(u) -> u 20.51/20.85 ->Interpretation type: 20.51/20.85 Linear 20.51/20.85 ->Coefficients: 20.51/20.85 Natural Numbers 20.51/20.85 ->Dimension: 20.51/20.85 1 20.51/20.85 ->Bound: 20.51/20.85 2 20.51/20.85 ->Interpretation: 20.51/20.85 20.51/20.85 [a__U11](X1,X2) = 2.X1 + 2.X2 + 1 20.51/20.85 [a__U12](X) = X 20.51/20.85 [a__U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.51/20.85 [a__U22](X1,X2) = X1 + 2.X2 + 1 20.51/20.85 [a__U23](X) = X 20.51/20.85 [a__U31](X1,X2) = 2.X1 + 2.X2 + 1 20.51/20.85 [a__U32](X) = X 20.51/20.85 [a__U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.51/20.85 [a__U42](X1,X2) = X1 + 2.X2 + 1 20.51/20.85 [a__U43](X) = X 20.51/20.85 [a__U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.51/20.85 [a__U52](X1,X2) = X1 + 2.X2 + 1 20.51/20.85 [a__U53](X) = X 20.51/20.85 [a__U61](X1,X2) = X1 + 2.X2 + 2 20.51/20.85 [a__U62](X) = X + 1 20.51/20.85 [a__U71](X1,X2) = 2.X1 + 2.X2 + 2 20.51/20.85 [a__U72](X) = X 20.51/20.85 [a____](X1,X2) = 2.X1 + X2 + 2 20.51/20.85 [a__and](X1,X2) = X1 + X2 20.51/20.85 [a__isList](X) = 2.X + 1 20.51/20.85 [a__isNeList](X) = 2.X + 1 20.51/20.85 [a__isNePal](X) = 2.X + 2 20.51/20.85 [a__isPal](X) = 2.X + 2 20.51/20.85 [a__isPalListKind](X) = 0 20.51/20.85 [a__isQid](X) = 2.X + 1 20.51/20.85 [mark](X) = X 20.51/20.85 [U11](X1,X2) = 2.X1 + 2.X2 + 1 20.51/20.85 [U12](X) = X 20.51/20.85 [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.51/20.85 [U22](X1,X2) = X1 + 2.X2 + 1 20.51/20.85 [U23](X) = X 20.51/20.85 [U31](X1,X2) = 2.X1 + 2.X2 + 1 20.51/20.85 [U32](X) = X 20.51/20.85 [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.51/20.85 [U42](X1,X2) = X1 + 2.X2 + 1 20.51/20.85 [U43](X) = X 20.51/20.85 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.51/20.85 [U52](X1,X2) = X1 + 2.X2 + 1 20.51/20.85 [U53](X) = X 20.51/20.85 [U61](X1,X2) = X1 + 2.X2 + 2 20.51/20.85 [U62](X) = X + 1 20.51/20.85 [U71](X1,X2) = 2.X1 + 2.X2 + 2 20.51/20.85 [U72](X) = X 20.51/20.85 [__](X1,X2) = 2.X1 + X2 + 2 20.51/20.85 [a] = 2 20.51/20.85 [and](X1,X2) = X1 + X2 20.51/20.85 [e] = 0 20.51/20.85 [fSNonEmpty] = 0 20.51/20.85 [i] = 0 20.51/20.85 [isList](X) = 2.X + 1 20.51/20.85 [isNeList](X) = 2.X + 1 20.51/20.85 [isNePal](X) = 2.X + 2 20.51/20.85 [isPal](X) = 2.X + 2 20.51/20.85 [isPalListKind](X) = 0 20.51/20.85 [isQid](X) = 2.X + 1 20.51/20.85 [nil] = 0 20.51/20.85 [o] = 2 20.51/20.85 [tt] = 0 20.51/20.85 [u] = 2 20.51/20.85 [A__U11](X1,X2) = 0 20.51/20.85 [A__U12](X) = 0 20.51/20.85 [A__U21](X1,X2,X3) = 0 20.51/20.85 [A__U22](X1,X2) = 0 20.51/20.85 [A__U23](X) = 0 20.51/20.85 [A__U31](X1,X2) = 0 20.51/20.85 [A__U32](X) = 0 20.51/20.85 [A__U41](X1,X2,X3) = 2.X2 + 2.X3 + 2 20.51/20.85 [A__U42](X1,X2) = 2.X2 + 1 20.51/20.85 [A__U43](X) = 0 20.51/20.85 [A__U51](X1,X2,X3) = 2.X2 + 2.X3 + 2 20.51/20.86 [A__U52](X1,X2) = X1 + 2.X2 + 1 20.51/20.86 [A__U53](X) = 0 20.51/20.86 [A__U61](X1,X2) = 0 20.51/20.86 [A__U62](X) = 0 20.51/20.86 [A__U71](X1,X2) = 2.X1 + 2.X2 + 2 20.51/20.86 [A__U72](X) = 0 20.51/20.86 [A____](X1,X2) = 2.X1 + X2 20.51/20.86 [A__AND](X1,X2) = X1 + X2 20.51/20.86 [A__ISLIST](X) = 2.X + 1 20.51/20.86 [A__ISNELIST](X) = 2.X + 1 20.51/20.86 [A__ISNEPAL](X) = 2.X + 1 20.51/20.86 [A__ISPAL](X) = 2.X + 2 20.51/20.86 [A__ISPALLISTKIND](X) = 0 20.51/20.86 [A__ISQID](X) = 0 20.51/20.86 [MARK](X) = X 20.51/20.86 20.51/20.86 Problem 1: 20.51/20.86 20.51/20.86 SCC Processor: 20.51/20.86 -> Pairs: 20.51/20.86 A__U41(tt,V1:S,V2:S) -> A__ISLIST(V1:S) 20.51/20.86 A__U42(tt,V2:S) -> A__ISNELIST(V2:S) 20.51/20.86 A__U51(tt,V1:S,V2:S) -> A__U52(a__isNeList(V1:S),V2:S) 20.51/20.86 A__U51(tt,V1:S,V2:S) -> A__ISNELIST(V1:S) 20.51/20.86 A__U52(tt,V2:S) -> A__ISLIST(V2:S) 20.51/20.86 A__U71(tt,V:S) -> A__ISNEPAL(V:S) 20.51/20.86 A____(__(X:S,Y:S),Z:S) -> A____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.51/20.86 A____(__(X:S,Y:S),Z:S) -> A____(mark(Y:S),mark(Z:S)) 20.51/20.86 A____(__(X:S,Y:S),Z:S) -> MARK(X:S) 20.51/20.86 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S) 20.51/20.86 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 20.51/20.86 A____(nil,X:S) -> MARK(X:S) 20.51/20.86 A____(X:S,nil) -> MARK(X:S) 20.51/20.86 A__AND(tt,X:S) -> MARK(X:S) 20.51/20.86 A__ISLIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.86 A__ISLIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.51/20.86 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.86 A__ISNELIST(__(V1:S,V2:S)) -> A__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.86 A__ISNELIST(__(V1:S,V2:S)) -> A__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.86 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.86 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.51/20.86 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.86 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.51/20.86 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.51/20.86 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.86 A__ISPAL(V:S) -> A__U71(a__isPalListKind(V:S),V:S) 20.51/20.86 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.86 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.86 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.51/20.86 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.86 MARK(U12(X:S)) -> MARK(X:S) 20.51/20.86 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.51/20.86 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.86 MARK(U23(X:S)) -> MARK(X:S) 20.51/20.86 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.86 MARK(U32(X:S)) -> MARK(X:S) 20.51/20.86 MARK(U41(X1:S,X2:S,X3:S)) -> A__U41(mark(X1:S),X2:S,X3:S) 20.51/20.86 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.51/20.86 MARK(U42(X1:S,X2:S)) -> A__U42(mark(X1:S),X2:S) 20.51/20.86 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.86 MARK(U43(X:S)) -> MARK(X:S) 20.51/20.86 MARK(U51(X1:S,X2:S,X3:S)) -> A__U51(mark(X1:S),X2:S,X3:S) 20.51/20.86 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.51/20.86 MARK(U52(X1:S,X2:S)) -> A__U52(mark(X1:S),X2:S) 20.51/20.86 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.86 MARK(U53(X:S)) -> MARK(X:S) 20.51/20.86 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.86 MARK(U62(X:S)) -> MARK(X:S) 20.51/20.86 MARK(U71(X1:S,X2:S)) -> A__U71(mark(X1:S),X2:S) 20.51/20.86 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.86 MARK(U72(X:S)) -> MARK(X:S) 20.51/20.86 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 20.51/20.86 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.86 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.51/20.86 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.51/20.86 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.86 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.51/20.86 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.51/20.86 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.51/20.86 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.51/20.86 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.51/20.86 -> Rules: 20.51/20.86 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.51/20.86 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.51/20.86 a__U12(tt) -> tt 20.51/20.86 a__U12(X:S) -> U12(X:S) 20.51/20.86 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.51/20.86 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.51/20.86 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.51/20.86 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.51/20.86 a__U23(tt) -> tt 20.51/20.86 a__U23(X:S) -> U23(X:S) 20.51/20.86 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.51/20.86 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.51/20.86 a__U32(tt) -> tt 20.51/20.86 a__U32(X:S) -> U32(X:S) 20.51/20.86 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.51/20.86 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.51/20.86 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.51/20.86 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.51/20.86 a__U43(tt) -> tt 20.51/20.86 a__U43(X:S) -> U43(X:S) 20.51/20.86 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.51/20.86 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.51/20.86 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.51/20.86 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.51/20.86 a__U53(tt) -> tt 20.51/20.86 a__U53(X:S) -> U53(X:S) 20.51/20.86 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.51/20.86 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.51/20.86 a__U62(tt) -> tt 20.51/20.86 a__U62(X:S) -> U62(X:S) 20.51/20.86 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.51/20.86 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.51/20.86 a__U72(tt) -> tt 20.51/20.86 a__U72(X:S) -> U72(X:S) 20.51/20.86 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.51/20.86 a____(nil,X:S) -> mark(X:S) 20.51/20.86 a____(X:S,nil) -> mark(X:S) 20.51/20.86 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.51/20.86 a__and(tt,X:S) -> mark(X:S) 20.51/20.86 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.51/20.86 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.86 a__isList(nil) -> tt 20.51/20.86 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.51/20.86 a__isList(X:S) -> isList(X:S) 20.51/20.86 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.86 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.86 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.51/20.86 a__isNeList(X:S) -> isNeList(X:S) 20.51/20.86 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.51/20.86 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.51/20.86 a__isNePal(X:S) -> isNePal(X:S) 20.51/20.86 a__isPal(nil) -> tt 20.51/20.86 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.51/20.86 a__isPal(X:S) -> isPal(X:S) 20.51/20.86 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.86 a__isPalListKind(a) -> tt 20.51/20.86 a__isPalListKind(e) -> tt 20.51/20.86 a__isPalListKind(i) -> tt 20.51/20.86 a__isPalListKind(nil) -> tt 20.51/20.86 a__isPalListKind(o) -> tt 20.51/20.86 a__isPalListKind(u) -> tt 20.51/20.86 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.51/20.86 a__isQid(a) -> tt 20.51/20.86 a__isQid(e) -> tt 20.51/20.86 a__isQid(i) -> tt 20.51/20.86 a__isQid(o) -> tt 20.51/20.86 a__isQid(u) -> tt 20.51/20.86 a__isQid(X:S) -> isQid(X:S) 20.51/20.86 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.51/20.86 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.51/20.86 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.51/20.86 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.51/20.86 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.51/20.86 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.51/20.86 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.51/20.86 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.51/20.86 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.51/20.86 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.51/20.86 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.51/20.86 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.51/20.86 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.51/20.86 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.51/20.86 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.51/20.86 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.51/20.86 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.51/20.86 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.51/20.86 mark(a) -> a 20.51/20.86 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.51/20.86 mark(e) -> e 20.51/20.86 mark(i) -> i 20.51/20.86 mark(isList(X:S)) -> a__isList(X:S) 20.51/20.86 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.51/20.86 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.51/20.86 mark(isPal(X:S)) -> a__isPal(X:S) 20.51/20.86 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.51/20.86 mark(isQid(X:S)) -> a__isQid(X:S) 20.51/20.86 mark(nil) -> nil 20.51/20.86 mark(o) -> o 20.51/20.86 mark(tt) -> tt 20.51/20.86 mark(u) -> u 20.51/20.86 ->Strongly Connected Components: 20.51/20.86 ->->Cycle: 20.51/20.86 ->->-> Pairs: 20.51/20.86 A__U41(tt,V1:S,V2:S) -> A__ISLIST(V1:S) 20.51/20.86 A__U42(tt,V2:S) -> A__ISNELIST(V2:S) 20.51/20.86 A__U51(tt,V1:S,V2:S) -> A__U52(a__isNeList(V1:S),V2:S) 20.51/20.86 A__U51(tt,V1:S,V2:S) -> A__ISNELIST(V1:S) 20.51/20.86 A__U52(tt,V2:S) -> A__ISLIST(V2:S) 20.51/20.86 A__U71(tt,V:S) -> A__ISNEPAL(V:S) 20.51/20.86 A____(__(X:S,Y:S),Z:S) -> A____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.51/20.86 A____(__(X:S,Y:S),Z:S) -> A____(mark(Y:S),mark(Z:S)) 20.51/20.86 A____(__(X:S,Y:S),Z:S) -> MARK(X:S) 20.51/20.86 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S) 20.51/20.86 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 20.51/20.86 A____(nil,X:S) -> MARK(X:S) 20.51/20.86 A____(X:S,nil) -> MARK(X:S) 20.51/20.86 A__AND(tt,X:S) -> MARK(X:S) 20.51/20.86 A__ISLIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.86 A__ISLIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.51/20.86 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.86 A__ISNELIST(__(V1:S,V2:S)) -> A__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.86 A__ISNELIST(__(V1:S,V2:S)) -> A__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.86 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.86 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.51/20.86 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.86 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.51/20.86 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.51/20.86 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.86 A__ISPAL(V:S) -> A__U71(a__isPalListKind(V:S),V:S) 20.51/20.86 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.86 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.86 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.51/20.86 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.86 MARK(U12(X:S)) -> MARK(X:S) 20.51/20.86 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.51/20.86 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.86 MARK(U23(X:S)) -> MARK(X:S) 20.51/20.86 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.86 MARK(U32(X:S)) -> MARK(X:S) 20.51/20.86 MARK(U41(X1:S,X2:S,X3:S)) -> A__U41(mark(X1:S),X2:S,X3:S) 20.51/20.86 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.51/20.86 MARK(U42(X1:S,X2:S)) -> A__U42(mark(X1:S),X2:S) 20.51/20.86 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.86 MARK(U43(X:S)) -> MARK(X:S) 20.51/20.86 MARK(U51(X1:S,X2:S,X3:S)) -> A__U51(mark(X1:S),X2:S,X3:S) 20.51/20.86 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.51/20.86 MARK(U52(X1:S,X2:S)) -> A__U52(mark(X1:S),X2:S) 20.51/20.86 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.86 MARK(U53(X:S)) -> MARK(X:S) 20.51/20.86 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.86 MARK(U62(X:S)) -> MARK(X:S) 20.51/20.86 MARK(U71(X1:S,X2:S)) -> A__U71(mark(X1:S),X2:S) 20.51/20.86 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.86 MARK(U72(X:S)) -> MARK(X:S) 20.51/20.86 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 20.51/20.86 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.86 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.51/20.86 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.51/20.86 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.86 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.51/20.86 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.51/20.86 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.51/20.86 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.51/20.86 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.51/20.86 ->->-> Rules: 20.51/20.86 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.51/20.86 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.51/20.86 a__U12(tt) -> tt 20.51/20.86 a__U12(X:S) -> U12(X:S) 20.51/20.86 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.51/20.86 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.51/20.86 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.51/20.86 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.51/20.86 a__U23(tt) -> tt 20.51/20.86 a__U23(X:S) -> U23(X:S) 20.51/20.86 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.51/20.86 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.51/20.86 a__U32(tt) -> tt 20.51/20.86 a__U32(X:S) -> U32(X:S) 20.51/20.86 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.51/20.86 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.51/20.86 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.51/20.86 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.51/20.86 a__U43(tt) -> tt 20.51/20.86 a__U43(X:S) -> U43(X:S) 20.51/20.86 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.51/20.86 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.51/20.86 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.51/20.86 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.51/20.86 a__U53(tt) -> tt 20.51/20.86 a__U53(X:S) -> U53(X:S) 20.51/20.86 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.51/20.86 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.51/20.86 a__U62(tt) -> tt 20.51/20.86 a__U62(X:S) -> U62(X:S) 20.51/20.86 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.51/20.86 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.51/20.86 a__U72(tt) -> tt 20.51/20.86 a__U72(X:S) -> U72(X:S) 20.51/20.86 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.51/20.86 a____(nil,X:S) -> mark(X:S) 20.51/20.86 a____(X:S,nil) -> mark(X:S) 20.51/20.86 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.51/20.86 a__and(tt,X:S) -> mark(X:S) 20.51/20.86 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.51/20.86 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.86 a__isList(nil) -> tt 20.51/20.86 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.51/20.86 a__isList(X:S) -> isList(X:S) 20.51/20.86 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.86 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.86 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.51/20.86 a__isNeList(X:S) -> isNeList(X:S) 20.51/20.86 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.51/20.86 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.51/20.86 a__isNePal(X:S) -> isNePal(X:S) 20.51/20.86 a__isPal(nil) -> tt 20.51/20.86 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.51/20.86 a__isPal(X:S) -> isPal(X:S) 20.51/20.86 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.86 a__isPalListKind(a) -> tt 20.51/20.86 a__isPalListKind(e) -> tt 20.51/20.86 a__isPalListKind(i) -> tt 20.51/20.86 a__isPalListKind(nil) -> tt 20.51/20.86 a__isPalListKind(o) -> tt 20.51/20.86 a__isPalListKind(u) -> tt 20.51/20.86 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.51/20.86 a__isQid(a) -> tt 20.51/20.86 a__isQid(e) -> tt 20.51/20.86 a__isQid(i) -> tt 20.51/20.86 a__isQid(o) -> tt 20.51/20.86 a__isQid(u) -> tt 20.51/20.86 a__isQid(X:S) -> isQid(X:S) 20.51/20.86 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.51/20.86 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.51/20.86 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.51/20.86 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.51/20.86 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.51/20.86 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.51/20.86 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.51/20.86 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.51/20.86 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.51/20.86 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.51/20.86 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.51/20.86 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.51/20.86 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.51/20.86 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.51/20.86 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.51/20.86 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.51/20.86 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.51/20.86 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.51/20.86 mark(a) -> a 20.51/20.86 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.51/20.86 mark(e) -> e 20.51/20.86 mark(i) -> i 20.51/20.86 mark(isList(X:S)) -> a__isList(X:S) 20.51/20.86 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.51/20.86 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.51/20.86 mark(isPal(X:S)) -> a__isPal(X:S) 20.51/20.86 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.51/20.86 mark(isQid(X:S)) -> a__isQid(X:S) 20.51/20.86 mark(nil) -> nil 20.51/20.86 mark(o) -> o 20.51/20.86 mark(tt) -> tt 20.51/20.86 mark(u) -> u 20.51/20.86 20.51/20.86 Problem 1: 20.51/20.86 20.51/20.86 Reduction Pairs Processor: 20.51/20.86 -> Pairs: 20.51/20.86 A__U41(tt,V1:S,V2:S) -> A__ISLIST(V1:S) 20.51/20.86 A__U42(tt,V2:S) -> A__ISNELIST(V2:S) 20.51/20.86 A__U51(tt,V1:S,V2:S) -> A__U52(a__isNeList(V1:S),V2:S) 20.51/20.86 A__U51(tt,V1:S,V2:S) -> A__ISNELIST(V1:S) 20.51/20.86 A__U52(tt,V2:S) -> A__ISLIST(V2:S) 20.51/20.86 A__U71(tt,V:S) -> A__ISNEPAL(V:S) 20.51/20.86 A____(__(X:S,Y:S),Z:S) -> A____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.51/20.86 A____(__(X:S,Y:S),Z:S) -> A____(mark(Y:S),mark(Z:S)) 20.51/20.86 A____(__(X:S,Y:S),Z:S) -> MARK(X:S) 20.51/20.86 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S) 20.51/20.86 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 20.51/20.86 A____(nil,X:S) -> MARK(X:S) 20.51/20.86 A____(X:S,nil) -> MARK(X:S) 20.51/20.86 A__AND(tt,X:S) -> MARK(X:S) 20.51/20.86 A__ISLIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.86 A__ISLIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.51/20.86 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.86 A__ISNELIST(__(V1:S,V2:S)) -> A__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.86 A__ISNELIST(__(V1:S,V2:S)) -> A__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.86 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.86 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.51/20.86 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.86 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.51/20.86 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.51/20.86 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.86 A__ISPAL(V:S) -> A__U71(a__isPalListKind(V:S),V:S) 20.51/20.86 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.51/20.86 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.86 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.51/20.86 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.86 MARK(U12(X:S)) -> MARK(X:S) 20.51/20.86 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.51/20.86 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.86 MARK(U23(X:S)) -> MARK(X:S) 20.51/20.86 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.86 MARK(U32(X:S)) -> MARK(X:S) 20.51/20.86 MARK(U41(X1:S,X2:S,X3:S)) -> A__U41(mark(X1:S),X2:S,X3:S) 20.51/20.86 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.51/20.86 MARK(U42(X1:S,X2:S)) -> A__U42(mark(X1:S),X2:S) 20.51/20.86 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.86 MARK(U43(X:S)) -> MARK(X:S) 20.51/20.86 MARK(U51(X1:S,X2:S,X3:S)) -> A__U51(mark(X1:S),X2:S,X3:S) 20.51/20.86 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.51/20.86 MARK(U52(X1:S,X2:S)) -> A__U52(mark(X1:S),X2:S) 20.51/20.86 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.86 MARK(U53(X:S)) -> MARK(X:S) 20.51/20.86 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.86 MARK(U62(X:S)) -> MARK(X:S) 20.51/20.86 MARK(U71(X1:S,X2:S)) -> A__U71(mark(X1:S),X2:S) 20.51/20.86 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.86 MARK(U72(X:S)) -> MARK(X:S) 20.51/20.86 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 20.51/20.86 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.86 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.51/20.86 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.51/20.86 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.51/20.86 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.51/20.86 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.51/20.86 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.51/20.86 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.51/20.86 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.51/20.86 -> Rules: 20.51/20.86 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.51/20.86 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.51/20.86 a__U12(tt) -> tt 20.51/20.86 a__U12(X:S) -> U12(X:S) 20.51/20.86 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.51/20.86 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.51/20.86 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.51/20.86 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.51/20.86 a__U23(tt) -> tt 20.51/20.86 a__U23(X:S) -> U23(X:S) 20.51/20.86 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.51/20.86 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.51/20.86 a__U32(tt) -> tt 20.51/20.86 a__U32(X:S) -> U32(X:S) 20.51/20.86 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.51/20.86 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.51/20.86 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.51/20.86 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.51/20.86 a__U43(tt) -> tt 20.51/20.86 a__U43(X:S) -> U43(X:S) 20.51/20.86 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.51/20.86 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.51/20.86 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.51/20.86 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.51/20.86 a__U53(tt) -> tt 20.51/20.86 a__U53(X:S) -> U53(X:S) 20.51/20.86 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.51/20.86 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.51/20.86 a__U62(tt) -> tt 20.51/20.86 a__U62(X:S) -> U62(X:S) 20.51/20.86 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.51/20.86 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.51/20.86 a__U72(tt) -> tt 20.51/20.86 a__U72(X:S) -> U72(X:S) 20.51/20.86 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.51/20.86 a____(nil,X:S) -> mark(X:S) 20.51/20.86 a____(X:S,nil) -> mark(X:S) 20.51/20.86 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.51/20.86 a__and(tt,X:S) -> mark(X:S) 20.51/20.86 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.51/20.86 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.86 a__isList(nil) -> tt 20.51/20.86 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.51/20.86 a__isList(X:S) -> isList(X:S) 20.51/20.86 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.86 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.51/20.86 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.51/20.86 a__isNeList(X:S) -> isNeList(X:S) 20.51/20.86 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.51/20.86 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.51/20.86 a__isNePal(X:S) -> isNePal(X:S) 20.51/20.86 a__isPal(nil) -> tt 20.51/20.86 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.51/20.86 a__isPal(X:S) -> isPal(X:S) 20.51/20.86 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.51/20.86 a__isPalListKind(a) -> tt 20.51/20.86 a__isPalListKind(e) -> tt 20.51/20.86 a__isPalListKind(i) -> tt 20.51/20.86 a__isPalListKind(nil) -> tt 20.51/20.86 a__isPalListKind(o) -> tt 20.51/20.86 a__isPalListKind(u) -> tt 20.51/20.86 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.51/20.86 a__isQid(a) -> tt 20.51/20.86 a__isQid(e) -> tt 20.51/20.86 a__isQid(i) -> tt 20.51/20.86 a__isQid(o) -> tt 20.51/20.86 a__isQid(u) -> tt 20.51/20.86 a__isQid(X:S) -> isQid(X:S) 20.51/20.86 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.51/20.86 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.51/20.86 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.51/20.86 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.51/20.86 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.51/20.86 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.51/20.86 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.51/20.86 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.51/20.86 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.51/20.86 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.51/20.86 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.51/20.86 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.51/20.86 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.51/20.86 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.51/20.86 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.51/20.86 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.51/20.86 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.51/20.86 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.51/20.86 mark(a) -> a 20.51/20.86 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.51/20.86 mark(e) -> e 20.51/20.86 mark(i) -> i 20.51/20.86 mark(isList(X:S)) -> a__isList(X:S) 20.51/20.86 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.51/20.86 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.51/20.86 mark(isPal(X:S)) -> a__isPal(X:S) 20.51/20.86 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.51/20.86 mark(isQid(X:S)) -> a__isQid(X:S) 20.51/20.86 mark(nil) -> nil 20.51/20.86 mark(o) -> o 20.51/20.86 mark(tt) -> tt 20.51/20.86 mark(u) -> u 20.51/20.86 -> Usable rules: 20.51/20.86 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.51/20.86 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.51/20.86 a__U12(tt) -> tt 20.51/20.86 a__U12(X:S) -> U12(X:S) 20.51/20.86 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.51/20.86 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.51/20.86 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.51/20.86 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.51/20.86 a__U23(tt) -> tt 20.51/20.86 a__U23(X:S) -> U23(X:S) 20.51/20.86 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.51/20.86 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.51/20.86 a__U32(tt) -> tt 20.51/20.86 a__U32(X:S) -> U32(X:S) 20.51/20.86 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.51/20.86 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.51/20.86 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.51/20.86 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.51/20.86 a__U43(tt) -> tt 20.51/20.86 a__U43(X:S) -> U43(X:S) 20.51/20.86 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.51/20.86 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.51/20.86 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.51/20.86 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.59/20.86 a__U53(tt) -> tt 20.59/20.86 a__U53(X:S) -> U53(X:S) 20.59/20.86 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.59/20.86 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.59/20.86 a__U62(tt) -> tt 20.59/20.86 a__U62(X:S) -> U62(X:S) 20.59/20.86 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.59/20.86 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.59/20.86 a__U72(tt) -> tt 20.59/20.86 a__U72(X:S) -> U72(X:S) 20.59/20.86 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.86 a____(nil,X:S) -> mark(X:S) 20.59/20.86 a____(X:S,nil) -> mark(X:S) 20.59/20.86 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.59/20.86 a__and(tt,X:S) -> mark(X:S) 20.59/20.86 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.59/20.86 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.86 a__isList(nil) -> tt 20.59/20.86 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.59/20.86 a__isList(X:S) -> isList(X:S) 20.59/20.86 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.86 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.86 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.59/20.86 a__isNeList(X:S) -> isNeList(X:S) 20.59/20.86 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.86 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.59/20.86 a__isNePal(X:S) -> isNePal(X:S) 20.59/20.86 a__isPal(nil) -> tt 20.59/20.86 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.59/20.86 a__isPal(X:S) -> isPal(X:S) 20.59/20.86 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.86 a__isPalListKind(a) -> tt 20.59/20.86 a__isPalListKind(e) -> tt 20.59/20.86 a__isPalListKind(i) -> tt 20.59/20.86 a__isPalListKind(nil) -> tt 20.59/20.86 a__isPalListKind(o) -> tt 20.59/20.86 a__isPalListKind(u) -> tt 20.59/20.86 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.59/20.86 a__isQid(a) -> tt 20.59/20.86 a__isQid(e) -> tt 20.59/20.86 a__isQid(i) -> tt 20.59/20.86 a__isQid(o) -> tt 20.59/20.86 a__isQid(u) -> tt 20.59/20.86 a__isQid(X:S) -> isQid(X:S) 20.59/20.86 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.59/20.86 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.59/20.86 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.59/20.86 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.59/20.86 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.59/20.86 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.59/20.86 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.59/20.86 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.59/20.86 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.59/20.86 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.59/20.86 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.59/20.86 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.59/20.86 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.59/20.86 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.59/20.86 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.59/20.86 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.59/20.86 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.59/20.86 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.59/20.86 mark(a) -> a 20.59/20.86 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.59/20.86 mark(e) -> e 20.59/20.86 mark(i) -> i 20.59/20.86 mark(isList(X:S)) -> a__isList(X:S) 20.59/20.86 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.59/20.86 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.59/20.86 mark(isPal(X:S)) -> a__isPal(X:S) 20.59/20.86 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.59/20.86 mark(isQid(X:S)) -> a__isQid(X:S) 20.59/20.86 mark(nil) -> nil 20.59/20.86 mark(o) -> o 20.59/20.86 mark(tt) -> tt 20.59/20.86 mark(u) -> u 20.59/20.86 ->Interpretation type: 20.59/20.86 Linear 20.59/20.86 ->Coefficients: 20.59/20.86 Natural Numbers 20.59/20.86 ->Dimension: 20.59/20.86 1 20.59/20.86 ->Bound: 20.59/20.86 2 20.59/20.86 ->Interpretation: 20.59/20.86 20.59/20.86 [a__U11](X1,X2) = 2.X1 + 2.X2 + 1 20.59/20.86 [a__U12](X) = X 20.59/20.86 [a__U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.59/20.86 [a__U22](X1,X2) = X1 + 2.X2 + 1 20.59/20.86 [a__U23](X) = X 20.59/20.86 [a__U31](X1,X2) = 2.X1 + 2.X2 + 1 20.59/20.86 [a__U32](X) = 2.X 20.59/20.86 [a__U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.59/20.86 [a__U42](X1,X2) = X1 + 2.X2 + 1 20.59/20.86 [a__U43](X) = X 20.59/20.86 [a__U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.59/20.86 [a__U52](X1,X2) = X1 + 2.X2 + 1 20.59/20.86 [a__U53](X) = X 20.59/20.86 [a__U61](X1,X2) = 2.X1 + X2 20.59/20.86 [a__U62](X) = 2.X 20.59/20.86 [a__U71](X1,X2) = 2.X1 + 2.X2 + 2 20.59/20.86 [a__U72](X) = 2.X + 2 20.59/20.86 [a____](X1,X2) = 2.X1 + X2 + 2 20.59/20.86 [a__and](X1,X2) = X1 + X2 20.59/20.86 [a__isList](X) = 2.X + 1 20.59/20.86 [a__isNeList](X) = 2.X + 1 20.59/20.86 [a__isNePal](X) = X 20.59/20.86 [a__isPal](X) = 2.X + 2 20.59/20.86 [a__isPalListKind](X) = 0 20.59/20.86 [a__isQid](X) = 0 20.59/20.86 [mark](X) = X 20.59/20.86 [U11](X1,X2) = 2.X1 + 2.X2 + 1 20.59/20.86 [U12](X) = X 20.59/20.86 [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.59/20.86 [U22](X1,X2) = X1 + 2.X2 + 1 20.59/20.86 [U23](X) = X 20.59/20.86 [U31](X1,X2) = 2.X1 + 2.X2 + 1 20.59/20.86 [U32](X) = 2.X 20.59/20.86 [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.59/20.86 [U42](X1,X2) = X1 + 2.X2 + 1 20.59/20.86 [U43](X) = X 20.59/20.86 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.59/20.86 [U52](X1,X2) = X1 + 2.X2 + 1 20.59/20.86 [U53](X) = X 20.59/20.86 [U61](X1,X2) = 2.X1 + X2 20.59/20.86 [U62](X) = 2.X 20.59/20.86 [U71](X1,X2) = 2.X1 + 2.X2 + 2 20.59/20.86 [U72](X) = 2.X + 2 20.59/20.86 [__](X1,X2) = 2.X1 + X2 + 2 20.59/20.86 [a] = 1 20.59/20.86 [and](X1,X2) = X1 + X2 20.59/20.86 [e] = 2 20.59/20.86 [fSNonEmpty] = 0 20.59/20.86 [i] = 0 20.59/20.86 [isList](X) = 2.X + 1 20.59/20.86 [isNeList](X) = 2.X + 1 20.59/20.86 [isNePal](X) = X 20.59/20.86 [isPal](X) = 2.X + 2 20.59/20.86 [isPalListKind](X) = 0 20.59/20.86 [isQid](X) = 0 20.59/20.86 [nil] = 2 20.59/20.86 [o] = 1 20.59/20.86 [tt] = 0 20.59/20.86 [u] = 0 20.59/20.86 [A__U11](X1,X2) = 0 20.59/20.86 [A__U12](X) = 0 20.59/20.86 [A__U21](X1,X2,X3) = 0 20.59/20.86 [A__U22](X1,X2) = 0 20.59/20.86 [A__U23](X) = 0 20.59/20.86 [A__U31](X1,X2) = 0 20.59/20.86 [A__U32](X) = 0 20.59/20.86 [A__U41](X1,X2,X3) = 2.X1 + 2.X2 + X3 + 2 20.59/20.86 [A__U42](X1,X2) = X1 + 2.X2 + 2 20.59/20.86 [A__U43](X) = 0 20.59/20.86 [A__U51](X1,X2,X3) = 2.X1 + 2.X2 + X3 + 2 20.59/20.86 [A__U52](X1,X2) = X1 + 1 20.59/20.86 [A__U53](X) = 0 20.59/20.86 [A__U61](X1,X2) = 0 20.59/20.86 [A__U62](X) = 0 20.59/20.86 [A__U71](X1,X2) = 2.X1 + 2.X2 + 2 20.59/20.86 [A__U72](X) = 0 20.59/20.86 [A____](X1,X2) = 2.X1 + X2 20.59/20.86 [A__AND](X1,X2) = X1 + X2 + 1 20.59/20.86 [A__ISLIST](X) = 1 20.59/20.86 [A__ISNELIST](X) = X + 2 20.59/20.86 [A__ISNEPAL](X) = X + 1 20.59/20.86 [A__ISPAL](X) = 2.X + 2 20.59/20.86 [A__ISPALLISTKIND](X) = 1 20.59/20.86 [A__ISQID](X) = 0 20.59/20.86 [MARK](X) = X + 1 20.59/20.86 20.59/20.86 Problem 1: 20.59/20.86 20.59/20.86 SCC Processor: 20.59/20.86 -> Pairs: 20.59/20.86 A__U42(tt,V2:S) -> A__ISNELIST(V2:S) 20.59/20.86 A__U51(tt,V1:S,V2:S) -> A__U52(a__isNeList(V1:S),V2:S) 20.59/20.86 A__U51(tt,V1:S,V2:S) -> A__ISNELIST(V1:S) 20.59/20.86 A__U52(tt,V2:S) -> A__ISLIST(V2:S) 20.59/20.86 A__U71(tt,V:S) -> A__ISNEPAL(V:S) 20.59/20.86 A____(__(X:S,Y:S),Z:S) -> A____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.86 A____(__(X:S,Y:S),Z:S) -> A____(mark(Y:S),mark(Z:S)) 20.59/20.86 A____(__(X:S,Y:S),Z:S) -> MARK(X:S) 20.59/20.86 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S) 20.59/20.86 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 20.59/20.86 A____(nil,X:S) -> MARK(X:S) 20.59/20.86 A____(X:S,nil) -> MARK(X:S) 20.59/20.86 A__AND(tt,X:S) -> MARK(X:S) 20.59/20.86 A__ISLIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.86 A__ISLIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.86 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.86 A__ISNELIST(__(V1:S,V2:S)) -> A__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.86 A__ISNELIST(__(V1:S,V2:S)) -> A__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.86 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.86 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.86 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.86 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.86 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.59/20.86 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.86 A__ISPAL(V:S) -> A__U71(a__isPalListKind(V:S),V:S) 20.59/20.86 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.86 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.86 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.86 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.86 MARK(U12(X:S)) -> MARK(X:S) 20.59/20.86 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.86 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.86 MARK(U23(X:S)) -> MARK(X:S) 20.59/20.86 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.86 MARK(U32(X:S)) -> MARK(X:S) 20.59/20.86 MARK(U41(X1:S,X2:S,X3:S)) -> A__U41(mark(X1:S),X2:S,X3:S) 20.59/20.86 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.86 MARK(U42(X1:S,X2:S)) -> A__U42(mark(X1:S),X2:S) 20.59/20.86 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.86 MARK(U43(X:S)) -> MARK(X:S) 20.59/20.86 MARK(U51(X1:S,X2:S,X3:S)) -> A__U51(mark(X1:S),X2:S,X3:S) 20.59/20.86 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.86 MARK(U52(X1:S,X2:S)) -> A__U52(mark(X1:S),X2:S) 20.59/20.86 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.86 MARK(U53(X:S)) -> MARK(X:S) 20.59/20.86 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.86 MARK(U62(X:S)) -> MARK(X:S) 20.59/20.86 MARK(U71(X1:S,X2:S)) -> A__U71(mark(X1:S),X2:S) 20.59/20.86 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.86 MARK(U72(X:S)) -> MARK(X:S) 20.59/20.86 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 20.59/20.86 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.86 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.59/20.86 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.59/20.86 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.86 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.59/20.86 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.59/20.86 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.59/20.86 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.59/20.86 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.59/20.86 -> Rules: 20.59/20.86 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.59/20.86 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.59/20.86 a__U12(tt) -> tt 20.59/20.86 a__U12(X:S) -> U12(X:S) 20.59/20.86 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.59/20.86 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.59/20.86 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.59/20.86 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.59/20.86 a__U23(tt) -> tt 20.59/20.86 a__U23(X:S) -> U23(X:S) 20.59/20.86 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.59/20.86 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.59/20.86 a__U32(tt) -> tt 20.59/20.86 a__U32(X:S) -> U32(X:S) 20.59/20.86 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.59/20.86 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.59/20.86 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.59/20.86 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.59/20.86 a__U43(tt) -> tt 20.59/20.86 a__U43(X:S) -> U43(X:S) 20.59/20.86 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.59/20.86 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.59/20.86 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.59/20.86 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.59/20.86 a__U53(tt) -> tt 20.59/20.86 a__U53(X:S) -> U53(X:S) 20.59/20.86 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.59/20.86 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.59/20.86 a__U62(tt) -> tt 20.59/20.86 a__U62(X:S) -> U62(X:S) 20.59/20.86 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.59/20.86 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.59/20.86 a__U72(tt) -> tt 20.59/20.86 a__U72(X:S) -> U72(X:S) 20.59/20.86 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.86 a____(nil,X:S) -> mark(X:S) 20.59/20.86 a____(X:S,nil) -> mark(X:S) 20.59/20.86 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.59/20.86 a__and(tt,X:S) -> mark(X:S) 20.59/20.86 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.59/20.86 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.86 a__isList(nil) -> tt 20.59/20.86 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.59/20.86 a__isList(X:S) -> isList(X:S) 20.59/20.86 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.86 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.86 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.59/20.86 a__isNeList(X:S) -> isNeList(X:S) 20.59/20.86 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.86 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.59/20.86 a__isNePal(X:S) -> isNePal(X:S) 20.59/20.86 a__isPal(nil) -> tt 20.59/20.86 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.59/20.86 a__isPal(X:S) -> isPal(X:S) 20.59/20.86 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.86 a__isPalListKind(a) -> tt 20.59/20.86 a__isPalListKind(e) -> tt 20.59/20.86 a__isPalListKind(i) -> tt 20.59/20.86 a__isPalListKind(nil) -> tt 20.59/20.86 a__isPalListKind(o) -> tt 20.59/20.86 a__isPalListKind(u) -> tt 20.59/20.86 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.59/20.86 a__isQid(a) -> tt 20.59/20.86 a__isQid(e) -> tt 20.59/20.86 a__isQid(i) -> tt 20.59/20.86 a__isQid(o) -> tt 20.59/20.86 a__isQid(u) -> tt 20.59/20.86 a__isQid(X:S) -> isQid(X:S) 20.59/20.86 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.59/20.86 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.59/20.86 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.59/20.86 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.59/20.86 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.59/20.86 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.59/20.86 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.59/20.86 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.59/20.86 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.59/20.86 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.59/20.86 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.59/20.86 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.59/20.86 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.59/20.86 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.59/20.86 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.59/20.86 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.59/20.86 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.59/20.86 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.59/20.86 mark(a) -> a 20.59/20.86 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.59/20.86 mark(e) -> e 20.59/20.86 mark(i) -> i 20.59/20.86 mark(isList(X:S)) -> a__isList(X:S) 20.59/20.86 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.59/20.86 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.59/20.86 mark(isPal(X:S)) -> a__isPal(X:S) 20.59/20.86 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.59/20.86 mark(isQid(X:S)) -> a__isQid(X:S) 20.59/20.86 mark(nil) -> nil 20.59/20.86 mark(o) -> o 20.59/20.86 mark(tt) -> tt 20.59/20.86 mark(u) -> u 20.59/20.86 ->Strongly Connected Components: 20.59/20.86 ->->Cycle: 20.59/20.86 ->->-> Pairs: 20.59/20.86 A__U42(tt,V2:S) -> A__ISNELIST(V2:S) 20.59/20.86 A__U51(tt,V1:S,V2:S) -> A__U52(a__isNeList(V1:S),V2:S) 20.59/20.86 A__U51(tt,V1:S,V2:S) -> A__ISNELIST(V1:S) 20.59/20.86 A__U52(tt,V2:S) -> A__ISLIST(V2:S) 20.59/20.86 A__U71(tt,V:S) -> A__ISNEPAL(V:S) 20.59/20.86 A____(__(X:S,Y:S),Z:S) -> A____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.86 A____(__(X:S,Y:S),Z:S) -> A____(mark(Y:S),mark(Z:S)) 20.59/20.86 A____(__(X:S,Y:S),Z:S) -> MARK(X:S) 20.59/20.86 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S) 20.59/20.86 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 20.59/20.86 A____(nil,X:S) -> MARK(X:S) 20.59/20.86 A____(X:S,nil) -> MARK(X:S) 20.59/20.86 A__AND(tt,X:S) -> MARK(X:S) 20.59/20.86 A__ISLIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.86 A__ISLIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.86 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.86 A__ISNELIST(__(V1:S,V2:S)) -> A__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.86 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.86 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.86 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.86 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.86 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.59/20.86 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.86 A__ISPAL(V:S) -> A__U71(a__isPalListKind(V:S),V:S) 20.59/20.86 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.86 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.86 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.86 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.86 MARK(U12(X:S)) -> MARK(X:S) 20.59/20.86 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.86 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.86 MARK(U23(X:S)) -> MARK(X:S) 20.59/20.86 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.86 MARK(U32(X:S)) -> MARK(X:S) 20.59/20.86 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.86 MARK(U42(X1:S,X2:S)) -> A__U42(mark(X1:S),X2:S) 20.59/20.86 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.86 MARK(U43(X:S)) -> MARK(X:S) 20.59/20.86 MARK(U51(X1:S,X2:S,X3:S)) -> A__U51(mark(X1:S),X2:S,X3:S) 20.59/20.86 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.86 MARK(U52(X1:S,X2:S)) -> A__U52(mark(X1:S),X2:S) 20.59/20.86 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.86 MARK(U53(X:S)) -> MARK(X:S) 20.59/20.86 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.86 MARK(U62(X:S)) -> MARK(X:S) 20.59/20.86 MARK(U71(X1:S,X2:S)) -> A__U71(mark(X1:S),X2:S) 20.59/20.86 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.86 MARK(U72(X:S)) -> MARK(X:S) 20.59/20.86 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 20.59/20.86 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.86 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.59/20.86 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.59/20.86 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.86 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.59/20.86 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.59/20.86 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.59/20.86 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.59/20.86 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.59/20.86 ->->-> Rules: 20.59/20.86 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.59/20.86 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.59/20.86 a__U12(tt) -> tt 20.59/20.86 a__U12(X:S) -> U12(X:S) 20.59/20.86 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.59/20.86 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.59/20.86 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.59/20.86 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.59/20.86 a__U23(tt) -> tt 20.59/20.86 a__U23(X:S) -> U23(X:S) 20.59/20.86 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.59/20.86 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.59/20.86 a__U32(tt) -> tt 20.59/20.86 a__U32(X:S) -> U32(X:S) 20.59/20.86 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.59/20.86 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.59/20.86 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.59/20.86 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.59/20.86 a__U43(tt) -> tt 20.59/20.86 a__U43(X:S) -> U43(X:S) 20.59/20.86 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.59/20.86 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.59/20.86 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.59/20.86 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.59/20.86 a__U53(tt) -> tt 20.59/20.86 a__U53(X:S) -> U53(X:S) 20.59/20.86 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.59/20.86 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.59/20.86 a__U62(tt) -> tt 20.59/20.86 a__U62(X:S) -> U62(X:S) 20.59/20.86 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.59/20.86 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.59/20.86 a__U72(tt) -> tt 20.59/20.86 a__U72(X:S) -> U72(X:S) 20.59/20.86 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.86 a____(nil,X:S) -> mark(X:S) 20.59/20.86 a____(X:S,nil) -> mark(X:S) 20.59/20.86 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.59/20.86 a__and(tt,X:S) -> mark(X:S) 20.59/20.86 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.59/20.86 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.86 a__isList(nil) -> tt 20.59/20.86 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.59/20.86 a__isList(X:S) -> isList(X:S) 20.59/20.86 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.86 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.86 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.59/20.86 a__isNeList(X:S) -> isNeList(X:S) 20.59/20.86 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.86 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.59/20.86 a__isNePal(X:S) -> isNePal(X:S) 20.59/20.86 a__isPal(nil) -> tt 20.59/20.86 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.59/20.86 a__isPal(X:S) -> isPal(X:S) 20.59/20.86 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.86 a__isPalListKind(a) -> tt 20.59/20.86 a__isPalListKind(e) -> tt 20.59/20.86 a__isPalListKind(i) -> tt 20.59/20.86 a__isPalListKind(nil) -> tt 20.59/20.86 a__isPalListKind(o) -> tt 20.59/20.86 a__isPalListKind(u) -> tt 20.59/20.86 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.59/20.86 a__isQid(a) -> tt 20.59/20.86 a__isQid(e) -> tt 20.59/20.86 a__isQid(i) -> tt 20.59/20.86 a__isQid(o) -> tt 20.59/20.86 a__isQid(u) -> tt 20.59/20.86 a__isQid(X:S) -> isQid(X:S) 20.59/20.86 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.59/20.86 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.59/20.86 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.59/20.86 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.59/20.86 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.59/20.86 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.59/20.86 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.59/20.86 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.59/20.86 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.59/20.86 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.59/20.86 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.59/20.86 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.59/20.86 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.59/20.86 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.59/20.86 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.59/20.86 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.59/20.86 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.59/20.86 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.59/20.86 mark(a) -> a 20.59/20.86 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.59/20.86 mark(e) -> e 20.59/20.86 mark(i) -> i 20.59/20.86 mark(isList(X:S)) -> a__isList(X:S) 20.59/20.86 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.59/20.86 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.59/20.86 mark(isPal(X:S)) -> a__isPal(X:S) 20.59/20.86 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.59/20.86 mark(isQid(X:S)) -> a__isQid(X:S) 20.59/20.86 mark(nil) -> nil 20.59/20.86 mark(o) -> o 20.59/20.86 mark(tt) -> tt 20.59/20.86 mark(u) -> u 20.59/20.86 20.59/20.86 Problem 1: 20.59/20.86 20.59/20.86 Reduction Pairs Processor: 20.59/20.86 -> Pairs: 20.59/20.86 A__U42(tt,V2:S) -> A__ISNELIST(V2:S) 20.59/20.86 A__U51(tt,V1:S,V2:S) -> A__U52(a__isNeList(V1:S),V2:S) 20.59/20.86 A__U51(tt,V1:S,V2:S) -> A__ISNELIST(V1:S) 20.59/20.86 A__U52(tt,V2:S) -> A__ISLIST(V2:S) 20.59/20.86 A__U71(tt,V:S) -> A__ISNEPAL(V:S) 20.59/20.86 A____(__(X:S,Y:S),Z:S) -> A____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.86 A____(__(X:S,Y:S),Z:S) -> A____(mark(Y:S),mark(Z:S)) 20.59/20.86 A____(__(X:S,Y:S),Z:S) -> MARK(X:S) 20.59/20.86 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S) 20.59/20.86 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 20.59/20.86 A____(nil,X:S) -> MARK(X:S) 20.59/20.86 A____(X:S,nil) -> MARK(X:S) 20.59/20.86 A__AND(tt,X:S) -> MARK(X:S) 20.59/20.86 A__ISLIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.86 A__ISLIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.86 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.86 A__ISNELIST(__(V1:S,V2:S)) -> A__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.86 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.86 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.86 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.86 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.86 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.59/20.86 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.86 A__ISPAL(V:S) -> A__U71(a__isPalListKind(V:S),V:S) 20.59/20.86 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.86 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.86 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.86 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.86 MARK(U12(X:S)) -> MARK(X:S) 20.59/20.86 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.86 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.86 MARK(U23(X:S)) -> MARK(X:S) 20.59/20.86 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.86 MARK(U32(X:S)) -> MARK(X:S) 20.59/20.86 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.86 MARK(U42(X1:S,X2:S)) -> A__U42(mark(X1:S),X2:S) 20.59/20.86 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.86 MARK(U43(X:S)) -> MARK(X:S) 20.59/20.86 MARK(U51(X1:S,X2:S,X3:S)) -> A__U51(mark(X1:S),X2:S,X3:S) 20.59/20.86 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.86 MARK(U52(X1:S,X2:S)) -> A__U52(mark(X1:S),X2:S) 20.59/20.86 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.86 MARK(U53(X:S)) -> MARK(X:S) 20.59/20.86 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.86 MARK(U62(X:S)) -> MARK(X:S) 20.59/20.86 MARK(U71(X1:S,X2:S)) -> A__U71(mark(X1:S),X2:S) 20.59/20.86 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.86 MARK(U72(X:S)) -> MARK(X:S) 20.59/20.86 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 20.59/20.86 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.86 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.59/20.86 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.59/20.86 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.86 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.59/20.86 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.59/20.86 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.59/20.86 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.59/20.86 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.59/20.86 -> Rules: 20.59/20.86 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.59/20.86 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.59/20.86 a__U12(tt) -> tt 20.59/20.86 a__U12(X:S) -> U12(X:S) 20.59/20.86 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.59/20.86 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.59/20.86 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.59/20.86 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.59/20.86 a__U23(tt) -> tt 20.59/20.86 a__U23(X:S) -> U23(X:S) 20.59/20.86 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.59/20.86 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.59/20.86 a__U32(tt) -> tt 20.59/20.86 a__U32(X:S) -> U32(X:S) 20.59/20.86 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.59/20.86 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.59/20.86 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.59/20.86 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.59/20.86 a__U43(tt) -> tt 20.59/20.86 a__U43(X:S) -> U43(X:S) 20.59/20.86 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.59/20.86 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.59/20.86 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.59/20.86 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.59/20.86 a__U53(tt) -> tt 20.59/20.86 a__U53(X:S) -> U53(X:S) 20.59/20.86 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.59/20.86 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.59/20.86 a__U62(tt) -> tt 20.59/20.86 a__U62(X:S) -> U62(X:S) 20.59/20.86 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.59/20.86 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.59/20.86 a__U72(tt) -> tt 20.59/20.86 a__U72(X:S) -> U72(X:S) 20.59/20.86 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.86 a____(nil,X:S) -> mark(X:S) 20.59/20.86 a____(X:S,nil) -> mark(X:S) 20.59/20.86 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.59/20.86 a__and(tt,X:S) -> mark(X:S) 20.59/20.86 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.59/20.86 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.86 a__isList(nil) -> tt 20.59/20.86 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.59/20.86 a__isList(X:S) -> isList(X:S) 20.59/20.86 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.86 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.86 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.59/20.86 a__isNeList(X:S) -> isNeList(X:S) 20.59/20.86 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.86 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.59/20.86 a__isNePal(X:S) -> isNePal(X:S) 20.59/20.86 a__isPal(nil) -> tt 20.59/20.86 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.59/20.86 a__isPal(X:S) -> isPal(X:S) 20.59/20.86 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.86 a__isPalListKind(a) -> tt 20.59/20.86 a__isPalListKind(e) -> tt 20.59/20.86 a__isPalListKind(i) -> tt 20.59/20.86 a__isPalListKind(nil) -> tt 20.59/20.86 a__isPalListKind(o) -> tt 20.59/20.86 a__isPalListKind(u) -> tt 20.59/20.86 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.59/20.86 a__isQid(a) -> tt 20.59/20.86 a__isQid(e) -> tt 20.59/20.86 a__isQid(i) -> tt 20.59/20.86 a__isQid(o) -> tt 20.59/20.86 a__isQid(u) -> tt 20.59/20.86 a__isQid(X:S) -> isQid(X:S) 20.59/20.86 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.59/20.86 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.59/20.86 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.59/20.86 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.59/20.86 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.59/20.86 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.59/20.86 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.59/20.86 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.59/20.86 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.59/20.86 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.59/20.86 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.59/20.86 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.59/20.86 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.59/20.86 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.59/20.86 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.59/20.86 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.59/20.86 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.59/20.86 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.59/20.86 mark(a) -> a 20.59/20.86 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.59/20.86 mark(e) -> e 20.59/20.86 mark(i) -> i 20.59/20.86 mark(isList(X:S)) -> a__isList(X:S) 20.59/20.86 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.59/20.86 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.59/20.86 mark(isPal(X:S)) -> a__isPal(X:S) 20.59/20.86 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.59/20.86 mark(isQid(X:S)) -> a__isQid(X:S) 20.59/20.86 mark(nil) -> nil 20.59/20.86 mark(o) -> o 20.59/20.86 mark(tt) -> tt 20.59/20.86 mark(u) -> u 20.59/20.86 -> Usable rules: 20.59/20.86 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.59/20.86 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.59/20.86 a__U12(tt) -> tt 20.59/20.86 a__U12(X:S) -> U12(X:S) 20.59/20.86 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.59/20.86 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.59/20.86 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.59/20.86 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.59/20.86 a__U23(tt) -> tt 20.59/20.86 a__U23(X:S) -> U23(X:S) 20.59/20.86 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.59/20.86 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.59/20.86 a__U32(tt) -> tt 20.59/20.86 a__U32(X:S) -> U32(X:S) 20.59/20.86 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.59/20.86 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.59/20.86 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.59/20.86 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.59/20.86 a__U43(tt) -> tt 20.59/20.86 a__U43(X:S) -> U43(X:S) 20.59/20.86 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.59/20.86 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.59/20.86 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.59/20.86 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.59/20.86 a__U53(tt) -> tt 20.59/20.86 a__U53(X:S) -> U53(X:S) 20.59/20.86 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.59/20.86 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.59/20.86 a__U62(tt) -> tt 20.59/20.86 a__U62(X:S) -> U62(X:S) 20.59/20.86 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.59/20.86 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.59/20.86 a__U72(tt) -> tt 20.59/20.86 a__U72(X:S) -> U72(X:S) 20.59/20.86 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.86 a____(nil,X:S) -> mark(X:S) 20.59/20.86 a____(X:S,nil) -> mark(X:S) 20.59/20.86 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.59/20.86 a__and(tt,X:S) -> mark(X:S) 20.59/20.86 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.59/20.86 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.86 a__isList(nil) -> tt 20.59/20.86 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.59/20.86 a__isList(X:S) -> isList(X:S) 20.59/20.86 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.86 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.86 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.59/20.86 a__isNeList(X:S) -> isNeList(X:S) 20.59/20.86 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.86 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.59/20.86 a__isNePal(X:S) -> isNePal(X:S) 20.59/20.86 a__isPal(nil) -> tt 20.59/20.86 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.59/20.86 a__isPal(X:S) -> isPal(X:S) 20.59/20.86 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.86 a__isPalListKind(a) -> tt 20.59/20.86 a__isPalListKind(e) -> tt 20.59/20.86 a__isPalListKind(i) -> tt 20.59/20.86 a__isPalListKind(nil) -> tt 20.59/20.86 a__isPalListKind(o) -> tt 20.59/20.86 a__isPalListKind(u) -> tt 20.59/20.86 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.59/20.86 a__isQid(a) -> tt 20.59/20.86 a__isQid(e) -> tt 20.59/20.86 a__isQid(i) -> tt 20.59/20.86 a__isQid(o) -> tt 20.59/20.86 a__isQid(u) -> tt 20.59/20.86 a__isQid(X:S) -> isQid(X:S) 20.59/20.86 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.59/20.86 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.59/20.86 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.59/20.86 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.59/20.86 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.59/20.86 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.59/20.86 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.59/20.86 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.59/20.86 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.59/20.86 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.59/20.86 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.59/20.86 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.59/20.86 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.59/20.86 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.59/20.86 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.59/20.86 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.59/20.86 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.59/20.86 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.59/20.86 mark(a) -> a 20.59/20.86 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.59/20.86 mark(e) -> e 20.59/20.86 mark(i) -> i 20.59/20.86 mark(isList(X:S)) -> a__isList(X:S) 20.59/20.86 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.59/20.86 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.59/20.86 mark(isPal(X:S)) -> a__isPal(X:S) 20.59/20.86 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.59/20.86 mark(isQid(X:S)) -> a__isQid(X:S) 20.59/20.86 mark(nil) -> nil 20.59/20.86 mark(o) -> o 20.59/20.86 mark(tt) -> tt 20.59/20.86 mark(u) -> u 20.59/20.86 ->Interpretation type: 20.59/20.86 Linear 20.59/20.86 ->Coefficients: 20.59/20.86 Natural Numbers 20.59/20.86 ->Dimension: 20.59/20.86 1 20.59/20.86 ->Bound: 20.59/20.86 2 20.59/20.86 ->Interpretation: 20.59/20.86 20.59/20.86 [a__U11](X1,X2) = 2.X1 + 2.X2 + 1 20.59/20.86 [a__U12](X) = X 20.59/20.86 [a__U21](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 20.59/20.86 [a__U22](X1,X2) = X1 + 2.X2 + 1 20.59/20.86 [a__U23](X) = X 20.59/20.86 [a__U31](X1,X2) = 2.X1 + 2.X2 + 1 20.59/20.86 [a__U32](X) = 2.X 20.59/20.86 [a__U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.59/20.86 [a__U42](X1,X2) = X1 + 2.X2 + 1 20.59/20.86 [a__U43](X) = X 20.59/20.86 [a__U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.59/20.86 [a__U52](X1,X2) = X1 + 2.X2 + 1 20.59/20.86 [a__U53](X) = X 20.59/20.86 [a__U61](X1,X2) = X1 + X2 + 2 20.59/20.86 [a__U62](X) = 2.X + 2 20.59/20.86 [a__U71](X1,X2) = 2.X1 + X2 + 2 20.59/20.86 [a__U72](X) = X 20.59/20.86 [a____](X1,X2) = X1 + X2 + 2 20.59/20.86 [a__and](X1,X2) = X1 + X2 20.59/20.86 [a__isList](X) = 2.X + 1 20.59/20.86 [a__isNeList](X) = 2.X + 1 20.59/20.86 [a__isNePal](X) = X + 2 20.59/20.86 [a__isPal](X) = X + 2 20.59/20.86 [a__isPalListKind](X) = 0 20.59/20.86 [a__isQid](X) = 0 20.59/20.86 [mark](X) = X 20.59/20.86 [U11](X1,X2) = 2.X1 + 2.X2 + 1 20.59/20.86 [U12](X) = X 20.59/20.86 [U21](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 20.59/20.86 [U22](X1,X2) = X1 + 2.X2 + 1 20.59/20.86 [U23](X) = X 20.59/20.86 [U31](X1,X2) = 2.X1 + 2.X2 + 1 20.59/20.86 [U32](X) = 2.X 20.59/20.86 [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.59/20.86 [U42](X1,X2) = X1 + 2.X2 + 1 20.59/20.86 [U43](X) = X 20.59/20.86 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.59/20.86 [U52](X1,X2) = X1 + 2.X2 + 1 20.59/20.86 [U53](X) = X 20.59/20.86 [U61](X1,X2) = X1 + X2 + 2 20.59/20.86 [U62](X) = 2.X + 2 20.59/20.86 [U71](X1,X2) = 2.X1 + X2 + 2 20.59/20.86 [U72](X) = X 20.59/20.86 [__](X1,X2) = X1 + X2 + 2 20.59/20.86 [a] = 1 20.59/20.86 [and](X1,X2) = X1 + X2 20.59/20.86 [e] = 2 20.59/20.86 [fSNonEmpty] = 0 20.59/20.86 [i] = 1 20.59/20.86 [isList](X) = 2.X + 1 20.59/20.86 [isNeList](X) = 2.X + 1 20.59/20.86 [isNePal](X) = X + 2 20.59/20.86 [isPal](X) = X + 2 20.59/20.86 [isPalListKind](X) = 0 20.59/20.86 [isQid](X) = 0 20.59/20.86 [nil] = 2 20.59/20.86 [o] = 2 20.59/20.86 [tt] = 0 20.59/20.86 [u] = 1 20.59/20.86 [A__U11](X1,X2) = 0 20.59/20.86 [A__U12](X) = 0 20.59/20.86 [A__U21](X1,X2,X3) = 0 20.59/20.86 [A__U22](X1,X2) = 0 20.59/20.86 [A__U23](X) = 0 20.59/20.86 [A__U31](X1,X2) = 0 20.59/20.86 [A__U32](X) = 0 20.59/20.86 [A__U41](X1,X2,X3) = 0 20.59/20.86 [A__U42](X1,X2) = 2.X1 + X2 + 1 20.59/20.86 [A__U43](X) = 0 20.59/20.86 [A__U51](X1,X2,X3) = X2 + X3 20.59/20.86 [A__U52](X1,X2) = X2 20.59/20.86 [A__U53](X) = 0 20.59/20.86 [A__U61](X1,X2) = 0 20.59/20.86 [A__U62](X) = 0 20.59/20.86 [A__U71](X1,X2) = 2.X1 + 2.X2 + 1 20.59/20.86 [A__U72](X) = 0 20.59/20.86 [A____](X1,X2) = 2.X1 + 2.X2 + 1 20.59/20.86 [A__AND](X1,X2) = X1 + 2.X2 20.59/20.86 [A__ISLIST](X) = 0 20.59/20.86 [A__ISNELIST](X) = X 20.59/20.86 [A__ISNEPAL](X) = 2.X + 1 20.59/20.86 [A__ISPAL](X) = 2.X + 2 20.59/20.86 [A__ISPALLISTKIND](X) = 0 20.59/20.86 [A__ISQID](X) = 0 20.59/20.86 [MARK](X) = 2.X 20.59/20.86 20.59/20.86 Problem 1: 20.59/20.86 20.59/20.86 SCC Processor: 20.59/20.86 -> Pairs: 20.59/20.86 A__U51(tt,V1:S,V2:S) -> A__U52(a__isNeList(V1:S),V2:S) 20.59/20.86 A__U51(tt,V1:S,V2:S) -> A__ISNELIST(V1:S) 20.59/20.86 A__U52(tt,V2:S) -> A__ISLIST(V2:S) 20.59/20.86 A__U71(tt,V:S) -> A__ISNEPAL(V:S) 20.59/20.86 A____(__(X:S,Y:S),Z:S) -> A____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.86 A____(__(X:S,Y:S),Z:S) -> A____(mark(Y:S),mark(Z:S)) 20.59/20.86 A____(__(X:S,Y:S),Z:S) -> MARK(X:S) 20.59/20.86 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S) 20.59/20.86 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 20.59/20.86 A____(nil,X:S) -> MARK(X:S) 20.59/20.86 A____(X:S,nil) -> MARK(X:S) 20.59/20.86 A__AND(tt,X:S) -> MARK(X:S) 20.59/20.86 A__ISLIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.86 A__ISLIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.86 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.86 A__ISNELIST(__(V1:S,V2:S)) -> A__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.86 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.86 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.86 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.86 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.86 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.59/20.86 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.86 A__ISPAL(V:S) -> A__U71(a__isPalListKind(V:S),V:S) 20.59/20.86 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.86 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.86 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.86 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.86 MARK(U12(X:S)) -> MARK(X:S) 20.59/20.86 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.86 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.86 MARK(U23(X:S)) -> MARK(X:S) 20.59/20.86 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.86 MARK(U32(X:S)) -> MARK(X:S) 20.59/20.86 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.86 MARK(U42(X1:S,X2:S)) -> A__U42(mark(X1:S),X2:S) 20.59/20.86 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.86 MARK(U43(X:S)) -> MARK(X:S) 20.59/20.86 MARK(U51(X1:S,X2:S,X3:S)) -> A__U51(mark(X1:S),X2:S,X3:S) 20.59/20.86 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.86 MARK(U52(X1:S,X2:S)) -> A__U52(mark(X1:S),X2:S) 20.59/20.86 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.86 MARK(U53(X:S)) -> MARK(X:S) 20.59/20.86 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.86 MARK(U62(X:S)) -> MARK(X:S) 20.59/20.86 MARK(U71(X1:S,X2:S)) -> A__U71(mark(X1:S),X2:S) 20.59/20.86 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.86 MARK(U72(X:S)) -> MARK(X:S) 20.59/20.86 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 20.59/20.86 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.86 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.59/20.86 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.59/20.86 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.86 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.59/20.86 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.59/20.86 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.59/20.86 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.59/20.86 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.59/20.86 -> Rules: 20.59/20.86 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.59/20.86 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.59/20.86 a__U12(tt) -> tt 20.59/20.86 a__U12(X:S) -> U12(X:S) 20.59/20.86 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.59/20.86 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.59/20.86 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.59/20.86 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.59/20.86 a__U23(tt) -> tt 20.59/20.86 a__U23(X:S) -> U23(X:S) 20.59/20.86 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.59/20.86 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.59/20.86 a__U32(tt) -> tt 20.59/20.86 a__U32(X:S) -> U32(X:S) 20.59/20.86 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.59/20.86 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.59/20.86 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.59/20.86 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.59/20.86 a__U43(tt) -> tt 20.59/20.86 a__U43(X:S) -> U43(X:S) 20.59/20.86 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.59/20.86 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.59/20.86 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.59/20.86 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.59/20.86 a__U53(tt) -> tt 20.59/20.86 a__U53(X:S) -> U53(X:S) 20.59/20.86 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.59/20.86 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.59/20.86 a__U62(tt) -> tt 20.59/20.86 a__U62(X:S) -> U62(X:S) 20.59/20.86 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.59/20.86 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.59/20.86 a__U72(tt) -> tt 20.59/20.86 a__U72(X:S) -> U72(X:S) 20.59/20.86 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.86 a____(nil,X:S) -> mark(X:S) 20.59/20.86 a____(X:S,nil) -> mark(X:S) 20.59/20.86 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.59/20.86 a__and(tt,X:S) -> mark(X:S) 20.59/20.86 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.59/20.86 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.86 a__isList(nil) -> tt 20.59/20.86 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.59/20.86 a__isList(X:S) -> isList(X:S) 20.59/20.86 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.86 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.86 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.59/20.86 a__isNeList(X:S) -> isNeList(X:S) 20.59/20.86 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.86 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.59/20.86 a__isNePal(X:S) -> isNePal(X:S) 20.59/20.86 a__isPal(nil) -> tt 20.59/20.86 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.59/20.86 a__isPal(X:S) -> isPal(X:S) 20.59/20.86 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.86 a__isPalListKind(a) -> tt 20.59/20.86 a__isPalListKind(e) -> tt 20.59/20.86 a__isPalListKind(i) -> tt 20.59/20.86 a__isPalListKind(nil) -> tt 20.59/20.86 a__isPalListKind(o) -> tt 20.59/20.86 a__isPalListKind(u) -> tt 20.59/20.86 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.59/20.86 a__isQid(a) -> tt 20.59/20.86 a__isQid(e) -> tt 20.59/20.86 a__isQid(i) -> tt 20.59/20.86 a__isQid(o) -> tt 20.59/20.86 a__isQid(u) -> tt 20.59/20.86 a__isQid(X:S) -> isQid(X:S) 20.59/20.86 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.59/20.86 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.59/20.86 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.59/20.86 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.59/20.86 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.59/20.86 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.59/20.86 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.59/20.86 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.59/20.86 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.59/20.86 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.59/20.86 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.59/20.86 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.59/20.86 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.59/20.86 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.59/20.86 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.59/20.86 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.59/20.86 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.59/20.86 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.59/20.86 mark(a) -> a 20.59/20.86 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.59/20.86 mark(e) -> e 20.59/20.86 mark(i) -> i 20.59/20.86 mark(isList(X:S)) -> a__isList(X:S) 20.59/20.86 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.59/20.86 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.59/20.86 mark(isPal(X:S)) -> a__isPal(X:S) 20.59/20.86 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.59/20.86 mark(isQid(X:S)) -> a__isQid(X:S) 20.59/20.86 mark(nil) -> nil 20.59/20.86 mark(o) -> o 20.59/20.86 mark(tt) -> tt 20.59/20.86 mark(u) -> u 20.59/20.86 ->Strongly Connected Components: 20.59/20.86 ->->Cycle: 20.59/20.86 ->->-> Pairs: 20.59/20.86 A__U51(tt,V1:S,V2:S) -> A__U52(a__isNeList(V1:S),V2:S) 20.59/20.86 A__U51(tt,V1:S,V2:S) -> A__ISNELIST(V1:S) 20.59/20.86 A__U52(tt,V2:S) -> A__ISLIST(V2:S) 20.59/20.86 A__U71(tt,V:S) -> A__ISNEPAL(V:S) 20.59/20.86 A____(__(X:S,Y:S),Z:S) -> A____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.86 A____(__(X:S,Y:S),Z:S) -> A____(mark(Y:S),mark(Z:S)) 20.59/20.86 A____(__(X:S,Y:S),Z:S) -> MARK(X:S) 20.59/20.86 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S) 20.59/20.86 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 20.59/20.86 A____(nil,X:S) -> MARK(X:S) 20.59/20.86 A____(X:S,nil) -> MARK(X:S) 20.59/20.86 A__AND(tt,X:S) -> MARK(X:S) 20.59/20.86 A__ISLIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.86 A__ISLIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.86 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.86 A__ISNELIST(__(V1:S,V2:S)) -> A__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.86 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.86 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.86 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.86 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.86 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.59/20.86 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.86 A__ISPAL(V:S) -> A__U71(a__isPalListKind(V:S),V:S) 20.59/20.86 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.86 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.86 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.86 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.86 MARK(U12(X:S)) -> MARK(X:S) 20.59/20.86 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.86 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.86 MARK(U23(X:S)) -> MARK(X:S) 20.59/20.86 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.86 MARK(U32(X:S)) -> MARK(X:S) 20.59/20.86 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.86 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.86 MARK(U43(X:S)) -> MARK(X:S) 20.59/20.86 MARK(U51(X1:S,X2:S,X3:S)) -> A__U51(mark(X1:S),X2:S,X3:S) 20.59/20.86 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.86 MARK(U52(X1:S,X2:S)) -> A__U52(mark(X1:S),X2:S) 20.59/20.86 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.86 MARK(U53(X:S)) -> MARK(X:S) 20.59/20.86 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.86 MARK(U62(X:S)) -> MARK(X:S) 20.59/20.86 MARK(U71(X1:S,X2:S)) -> A__U71(mark(X1:S),X2:S) 20.59/20.86 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.86 MARK(U72(X:S)) -> MARK(X:S) 20.59/20.86 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 20.59/20.86 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.86 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.59/20.86 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.59/20.86 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.86 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.59/20.86 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.59/20.86 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.59/20.86 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.59/20.86 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.59/20.86 ->->-> Rules: 20.59/20.86 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.59/20.86 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.59/20.86 a__U12(tt) -> tt 20.59/20.86 a__U12(X:S) -> U12(X:S) 20.59/20.86 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.59/20.86 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.59/20.86 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.59/20.86 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.59/20.86 a__U23(tt) -> tt 20.59/20.86 a__U23(X:S) -> U23(X:S) 20.59/20.86 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.59/20.86 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.59/20.86 a__U32(tt) -> tt 20.59/20.86 a__U32(X:S) -> U32(X:S) 20.59/20.86 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.59/20.86 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.59/20.86 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.59/20.86 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.59/20.86 a__U43(tt) -> tt 20.59/20.86 a__U43(X:S) -> U43(X:S) 20.59/20.86 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.59/20.86 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.59/20.86 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.59/20.86 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.59/20.86 a__U53(tt) -> tt 20.59/20.86 a__U53(X:S) -> U53(X:S) 20.59/20.86 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.59/20.86 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.59/20.86 a__U62(tt) -> tt 20.59/20.86 a__U62(X:S) -> U62(X:S) 20.59/20.86 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.59/20.86 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.59/20.86 a__U72(tt) -> tt 20.59/20.86 a__U72(X:S) -> U72(X:S) 20.59/20.86 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.86 a____(nil,X:S) -> mark(X:S) 20.59/20.86 a____(X:S,nil) -> mark(X:S) 20.59/20.86 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.59/20.86 a__and(tt,X:S) -> mark(X:S) 20.59/20.86 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.59/20.86 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.86 a__isList(nil) -> tt 20.59/20.86 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.59/20.86 a__isList(X:S) -> isList(X:S) 20.59/20.86 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.86 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.86 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.59/20.86 a__isNeList(X:S) -> isNeList(X:S) 20.59/20.86 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.86 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.59/20.86 a__isNePal(X:S) -> isNePal(X:S) 20.59/20.86 a__isPal(nil) -> tt 20.59/20.86 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.59/20.86 a__isPal(X:S) -> isPal(X:S) 20.59/20.86 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.86 a__isPalListKind(a) -> tt 20.59/20.86 a__isPalListKind(e) -> tt 20.59/20.86 a__isPalListKind(i) -> tt 20.59/20.86 a__isPalListKind(nil) -> tt 20.59/20.86 a__isPalListKind(o) -> tt 20.59/20.86 a__isPalListKind(u) -> tt 20.59/20.86 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.59/20.86 a__isQid(a) -> tt 20.59/20.86 a__isQid(e) -> tt 20.59/20.86 a__isQid(i) -> tt 20.59/20.86 a__isQid(o) -> tt 20.59/20.86 a__isQid(u) -> tt 20.59/20.86 a__isQid(X:S) -> isQid(X:S) 20.59/20.86 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.59/20.86 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.59/20.86 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.59/20.86 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.59/20.86 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.59/20.86 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.59/20.86 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.59/20.86 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.59/20.86 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.59/20.86 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.59/20.86 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.59/20.86 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.59/20.86 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.59/20.86 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.59/20.86 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.59/20.86 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.59/20.86 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.59/20.86 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.59/20.86 mark(a) -> a 20.59/20.86 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.59/20.86 mark(e) -> e 20.59/20.86 mark(i) -> i 20.59/20.86 mark(isList(X:S)) -> a__isList(X:S) 20.59/20.86 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.59/20.86 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.59/20.86 mark(isPal(X:S)) -> a__isPal(X:S) 20.59/20.86 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.59/20.86 mark(isQid(X:S)) -> a__isQid(X:S) 20.59/20.86 mark(nil) -> nil 20.59/20.86 mark(o) -> o 20.59/20.86 mark(tt) -> tt 20.59/20.86 mark(u) -> u 20.59/20.86 20.59/20.86 Problem 1: 20.59/20.86 20.59/20.86 Reduction Pairs Processor: 20.59/20.86 -> Pairs: 20.59/20.86 A__U51(tt,V1:S,V2:S) -> A__U52(a__isNeList(V1:S),V2:S) 20.59/20.86 A__U51(tt,V1:S,V2:S) -> A__ISNELIST(V1:S) 20.59/20.86 A__U52(tt,V2:S) -> A__ISLIST(V2:S) 20.59/20.86 A__U71(tt,V:S) -> A__ISNEPAL(V:S) 20.59/20.86 A____(__(X:S,Y:S),Z:S) -> A____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.86 A____(__(X:S,Y:S),Z:S) -> A____(mark(Y:S),mark(Z:S)) 20.59/20.86 A____(__(X:S,Y:S),Z:S) -> MARK(X:S) 20.59/20.86 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S) 20.59/20.86 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 20.59/20.86 A____(nil,X:S) -> MARK(X:S) 20.59/20.86 A____(X:S,nil) -> MARK(X:S) 20.59/20.86 A__AND(tt,X:S) -> MARK(X:S) 20.59/20.86 A__ISLIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.86 A__ISLIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.86 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.86 A__ISNELIST(__(V1:S,V2:S)) -> A__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.86 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.86 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.86 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.86 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.86 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.59/20.86 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.86 A__ISPAL(V:S) -> A__U71(a__isPalListKind(V:S),V:S) 20.59/20.86 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.86 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.86 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.86 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.86 MARK(U12(X:S)) -> MARK(X:S) 20.59/20.86 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.86 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.86 MARK(U23(X:S)) -> MARK(X:S) 20.59/20.86 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.86 MARK(U32(X:S)) -> MARK(X:S) 20.59/20.86 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.86 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.86 MARK(U43(X:S)) -> MARK(X:S) 20.59/20.86 MARK(U51(X1:S,X2:S,X3:S)) -> A__U51(mark(X1:S),X2:S,X3:S) 20.59/20.86 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.86 MARK(U52(X1:S,X2:S)) -> A__U52(mark(X1:S),X2:S) 20.59/20.86 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.86 MARK(U53(X:S)) -> MARK(X:S) 20.59/20.86 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.86 MARK(U62(X:S)) -> MARK(X:S) 20.59/20.86 MARK(U71(X1:S,X2:S)) -> A__U71(mark(X1:S),X2:S) 20.59/20.86 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.86 MARK(U72(X:S)) -> MARK(X:S) 20.59/20.86 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 20.59/20.86 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.86 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.59/20.86 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.59/20.86 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.86 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.59/20.86 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.59/20.86 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.59/20.86 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.59/20.86 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.59/20.86 -> Rules: 20.59/20.86 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.59/20.86 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.59/20.86 a__U12(tt) -> tt 20.59/20.86 a__U12(X:S) -> U12(X:S) 20.59/20.86 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.59/20.86 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.59/20.86 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.59/20.86 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.59/20.86 a__U23(tt) -> tt 20.59/20.86 a__U23(X:S) -> U23(X:S) 20.59/20.86 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.59/20.86 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.59/20.86 a__U32(tt) -> tt 20.59/20.86 a__U32(X:S) -> U32(X:S) 20.59/20.86 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.59/20.86 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.59/20.86 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.59/20.86 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.59/20.86 a__U43(tt) -> tt 20.59/20.86 a__U43(X:S) -> U43(X:S) 20.59/20.86 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.59/20.86 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.59/20.86 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.59/20.86 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.59/20.86 a__U53(tt) -> tt 20.59/20.86 a__U53(X:S) -> U53(X:S) 20.59/20.86 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.59/20.86 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.59/20.86 a__U62(tt) -> tt 20.59/20.86 a__U62(X:S) -> U62(X:S) 20.59/20.86 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.59/20.86 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.59/20.86 a__U72(tt) -> tt 20.59/20.86 a__U72(X:S) -> U72(X:S) 20.59/20.86 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.86 a____(nil,X:S) -> mark(X:S) 20.59/20.86 a____(X:S,nil) -> mark(X:S) 20.59/20.86 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.59/20.86 a__and(tt,X:S) -> mark(X:S) 20.59/20.86 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.59/20.86 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.86 a__isList(nil) -> tt 20.59/20.86 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.59/20.86 a__isList(X:S) -> isList(X:S) 20.59/20.86 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.86 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.86 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.59/20.86 a__isNeList(X:S) -> isNeList(X:S) 20.59/20.86 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.86 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.59/20.86 a__isNePal(X:S) -> isNePal(X:S) 20.59/20.86 a__isPal(nil) -> tt 20.59/20.86 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.59/20.86 a__isPal(X:S) -> isPal(X:S) 20.59/20.86 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.86 a__isPalListKind(a) -> tt 20.59/20.86 a__isPalListKind(e) -> tt 20.59/20.86 a__isPalListKind(i) -> tt 20.59/20.86 a__isPalListKind(nil) -> tt 20.59/20.86 a__isPalListKind(o) -> tt 20.59/20.86 a__isPalListKind(u) -> tt 20.59/20.86 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.59/20.86 a__isQid(a) -> tt 20.59/20.86 a__isQid(e) -> tt 20.59/20.86 a__isQid(i) -> tt 20.59/20.86 a__isQid(o) -> tt 20.59/20.86 a__isQid(u) -> tt 20.59/20.86 a__isQid(X:S) -> isQid(X:S) 20.59/20.86 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.59/20.86 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.59/20.86 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.59/20.86 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.59/20.86 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.59/20.86 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.59/20.86 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.59/20.86 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.59/20.86 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.59/20.86 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.59/20.86 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.59/20.86 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.59/20.86 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.59/20.86 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.59/20.86 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.59/20.86 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.59/20.86 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.59/20.86 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.59/20.86 mark(a) -> a 20.59/20.86 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.59/20.86 mark(e) -> e 20.59/20.86 mark(i) -> i 20.59/20.86 mark(isList(X:S)) -> a__isList(X:S) 20.59/20.86 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.59/20.86 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.59/20.86 mark(isPal(X:S)) -> a__isPal(X:S) 20.59/20.86 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.59/20.86 mark(isQid(X:S)) -> a__isQid(X:S) 20.59/20.86 mark(nil) -> nil 20.59/20.86 mark(o) -> o 20.59/20.86 mark(tt) -> tt 20.59/20.86 mark(u) -> u 20.59/20.86 -> Usable rules: 20.59/20.86 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.59/20.86 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.59/20.86 a__U12(tt) -> tt 20.59/20.86 a__U12(X:S) -> U12(X:S) 20.59/20.86 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.59/20.86 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.59/20.86 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.59/20.86 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.59/20.86 a__U23(tt) -> tt 20.59/20.86 a__U23(X:S) -> U23(X:S) 20.59/20.86 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.59/20.86 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.59/20.86 a__U32(tt) -> tt 20.59/20.86 a__U32(X:S) -> U32(X:S) 20.59/20.86 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.59/20.86 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.59/20.86 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.59/20.86 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.59/20.86 a__U43(tt) -> tt 20.59/20.86 a__U43(X:S) -> U43(X:S) 20.59/20.86 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.59/20.86 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.59/20.86 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.59/20.86 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.59/20.86 a__U53(tt) -> tt 20.59/20.86 a__U53(X:S) -> U53(X:S) 20.59/20.86 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.59/20.86 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.59/20.86 a__U62(tt) -> tt 20.59/20.86 a__U62(X:S) -> U62(X:S) 20.59/20.86 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.59/20.86 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.59/20.86 a__U72(tt) -> tt 20.59/20.86 a__U72(X:S) -> U72(X:S) 20.59/20.86 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.86 a____(nil,X:S) -> mark(X:S) 20.59/20.86 a____(X:S,nil) -> mark(X:S) 20.59/20.86 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.59/20.86 a__and(tt,X:S) -> mark(X:S) 20.59/20.86 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.59/20.86 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.86 a__isList(nil) -> tt 20.59/20.86 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.59/20.86 a__isList(X:S) -> isList(X:S) 20.59/20.86 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.86 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.86 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.59/20.86 a__isNeList(X:S) -> isNeList(X:S) 20.59/20.86 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.86 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.59/20.86 a__isNePal(X:S) -> isNePal(X:S) 20.59/20.86 a__isPal(nil) -> tt 20.59/20.86 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.59/20.86 a__isPal(X:S) -> isPal(X:S) 20.59/20.86 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.86 a__isPalListKind(a) -> tt 20.59/20.86 a__isPalListKind(e) -> tt 20.59/20.86 a__isPalListKind(i) -> tt 20.59/20.86 a__isPalListKind(nil) -> tt 20.59/20.86 a__isPalListKind(o) -> tt 20.59/20.86 a__isPalListKind(u) -> tt 20.59/20.86 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.59/20.86 a__isQid(a) -> tt 20.59/20.86 a__isQid(e) -> tt 20.59/20.86 a__isQid(i) -> tt 20.59/20.86 a__isQid(o) -> tt 20.59/20.86 a__isQid(u) -> tt 20.59/20.86 a__isQid(X:S) -> isQid(X:S) 20.59/20.86 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.59/20.86 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.59/20.86 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.59/20.86 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.59/20.86 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.59/20.86 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.59/20.86 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.59/20.86 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.59/20.86 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.59/20.86 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.59/20.86 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.59/20.86 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.59/20.86 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.59/20.86 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.59/20.86 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.59/20.86 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.59/20.86 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.59/20.86 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.59/20.86 mark(a) -> a 20.59/20.86 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.59/20.86 mark(e) -> e 20.59/20.86 mark(i) -> i 20.59/20.86 mark(isList(X:S)) -> a__isList(X:S) 20.59/20.86 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.59/20.86 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.59/20.86 mark(isPal(X:S)) -> a__isPal(X:S) 20.59/20.86 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.59/20.86 mark(isQid(X:S)) -> a__isQid(X:S) 20.59/20.86 mark(nil) -> nil 20.59/20.86 mark(o) -> o 20.59/20.86 mark(tt) -> tt 20.59/20.86 mark(u) -> u 20.59/20.86 ->Interpretation type: 20.59/20.86 Linear 20.59/20.86 ->Coefficients: 20.59/20.86 Natural Numbers 20.59/20.86 ->Dimension: 20.59/20.86 1 20.59/20.86 ->Bound: 20.59/20.86 2 20.59/20.86 ->Interpretation: 20.59/20.86 20.59/20.86 [a__U11](X1,X2) = 2.X1 + 2.X2 + 1 20.59/20.86 [a__U12](X) = X 20.59/20.86 [a__U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.59/20.86 [a__U22](X1,X2) = X1 + 2.X2 + 1 20.59/20.86 [a__U23](X) = X 20.59/20.86 [a__U31](X1,X2) = X1 + 2.X2 + 1 20.59/20.86 [a__U32](X) = 2.X + 1 20.59/20.86 [a__U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.59/20.86 [a__U42](X1,X2) = X1 + 2.X2 + 1 20.59/20.86 [a__U43](X) = X 20.59/20.86 [a__U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.59/20.86 [a__U52](X1,X2) = X1 + 2.X2 + 1 20.59/20.86 [a__U53](X) = X 20.59/20.86 [a__U61](X1,X2) = 2.X1 + X2 + 1 20.59/20.86 [a__U62](X) = X + 1 20.59/20.86 [a__U71](X1,X2) = 2.X1 + X2 + 2 20.59/20.86 [a__U72](X) = X + 1 20.59/20.86 [a____](X1,X2) = X1 + X2 + 1 20.59/20.86 [a__and](X1,X2) = X1 + X2 20.59/20.86 [a__isList](X) = 2.X + 1 20.59/20.86 [a__isNeList](X) = 2.X + 1 20.59/20.86 [a__isNePal](X) = X + 1 20.59/20.86 [a__isPal](X) = X + 2 20.59/20.86 [a__isPalListKind](X) = 0 20.59/20.86 [a__isQid](X) = X 20.59/20.86 [mark](X) = X 20.59/20.86 [U11](X1,X2) = 2.X1 + 2.X2 + 1 20.59/20.86 [U12](X) = X 20.59/20.86 [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.59/20.86 [U22](X1,X2) = X1 + 2.X2 + 1 20.59/20.86 [U23](X) = X 20.59/20.86 [U31](X1,X2) = X1 + 2.X2 + 1 20.59/20.86 [U32](X) = 2.X + 1 20.59/20.86 [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.59/20.86 [U42](X1,X2) = X1 + 2.X2 + 1 20.59/20.86 [U43](X) = X 20.59/20.86 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.59/20.86 [U52](X1,X2) = X1 + 2.X2 + 1 20.59/20.86 [U53](X) = X 20.59/20.86 [U61](X1,X2) = 2.X1 + X2 + 1 20.59/20.86 [U62](X) = X + 1 20.59/20.86 [U71](X1,X2) = 2.X1 + X2 + 2 20.59/20.86 [U72](X) = X + 1 20.59/20.86 [__](X1,X2) = X1 + X2 + 1 20.59/20.86 [a] = 0 20.59/20.86 [and](X1,X2) = X1 + X2 20.59/20.86 [e] = 2 20.59/20.86 [fSNonEmpty] = 0 20.59/20.86 [i] = 1 20.59/20.86 [isList](X) = 2.X + 1 20.59/20.86 [isNeList](X) = 2.X + 1 20.59/20.86 [isNePal](X) = X + 1 20.59/20.86 [isPal](X) = X + 2 20.59/20.86 [isPalListKind](X) = 0 20.59/20.86 [isQid](X) = X 20.59/20.86 [nil] = 2 20.59/20.86 [o] = 1 20.59/20.86 [tt] = 0 20.59/20.86 [u] = 2 20.59/20.86 [A__U11](X1,X2) = 0 20.59/20.86 [A__U12](X) = 0 20.59/20.86 [A__U21](X1,X2,X3) = 0 20.59/20.86 [A__U22](X1,X2) = 0 20.59/20.86 [A__U23](X) = 0 20.59/20.86 [A__U31](X1,X2) = 0 20.59/20.86 [A__U32](X) = 0 20.59/20.86 [A__U41](X1,X2,X3) = 0 20.59/20.86 [A__U42](X1,X2) = 0 20.59/20.86 [A__U43](X) = 0 20.59/20.86 [A__U51](X1,X2,X3) = 2.X2 + 2.X3 + 2 20.59/20.86 [A__U52](X1,X2) = X1 + 2.X2 20.59/20.86 [A__U53](X) = 0 20.59/20.86 [A__U61](X1,X2) = 0 20.59/20.86 [A__U62](X) = 0 20.59/20.86 [A__U71](X1,X2) = 2.X1 + 2.X2 + 2 20.59/20.86 [A__U72](X) = 0 20.59/20.86 [A____](X1,X2) = 2.X1 + 2.X2 20.59/20.86 [A__AND](X1,X2) = 2.X1 + 2.X2 20.59/20.86 [A__ISLIST](X) = 2.X 20.59/20.86 [A__ISNELIST](X) = 2.X + 2 20.59/20.86 [A__ISNEPAL](X) = 2.X + 2 20.59/20.86 [A__ISPAL](X) = 2.X + 2 20.59/20.86 [A__ISPALLISTKIND](X) = 0 20.59/20.86 [A__ISQID](X) = 0 20.59/20.86 [MARK](X) = 2.X 20.59/20.86 20.59/20.86 Problem 1: 20.59/20.86 20.59/20.86 SCC Processor: 20.59/20.86 -> Pairs: 20.59/20.86 A__U51(tt,V1:S,V2:S) -> A__ISNELIST(V1:S) 20.59/20.86 A__U52(tt,V2:S) -> A__ISLIST(V2:S) 20.59/20.86 A__U71(tt,V:S) -> A__ISNEPAL(V:S) 20.59/20.87 A____(__(X:S,Y:S),Z:S) -> A____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.87 A____(__(X:S,Y:S),Z:S) -> A____(mark(Y:S),mark(Z:S)) 20.59/20.87 A____(__(X:S,Y:S),Z:S) -> MARK(X:S) 20.59/20.87 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S) 20.59/20.87 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 20.59/20.87 A____(nil,X:S) -> MARK(X:S) 20.59/20.87 A____(X:S,nil) -> MARK(X:S) 20.59/20.87 A__AND(tt,X:S) -> MARK(X:S) 20.59/20.87 A__ISLIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.87 A__ISLIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.87 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.87 A__ISNELIST(__(V1:S,V2:S)) -> A__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.87 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.87 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.87 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.87 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.87 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.59/20.87 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.87 A__ISPAL(V:S) -> A__U71(a__isPalListKind(V:S),V:S) 20.59/20.87 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.87 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.87 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.87 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U12(X:S)) -> MARK(X:S) 20.59/20.87 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.87 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U23(X:S)) -> MARK(X:S) 20.59/20.87 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U32(X:S)) -> MARK(X:S) 20.59/20.87 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.87 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U43(X:S)) -> MARK(X:S) 20.59/20.87 MARK(U51(X1:S,X2:S,X3:S)) -> A__U51(mark(X1:S),X2:S,X3:S) 20.59/20.87 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.87 MARK(U52(X1:S,X2:S)) -> A__U52(mark(X1:S),X2:S) 20.59/20.87 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U53(X:S)) -> MARK(X:S) 20.59/20.87 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U62(X:S)) -> MARK(X:S) 20.59/20.87 MARK(U71(X1:S,X2:S)) -> A__U71(mark(X1:S),X2:S) 20.59/20.87 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U72(X:S)) -> MARK(X:S) 20.59/20.87 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 20.59/20.87 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.59/20.87 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.59/20.87 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.59/20.87 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.59/20.87 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.59/20.87 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.59/20.87 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.59/20.87 -> Rules: 20.59/20.87 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.59/20.87 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.59/20.87 a__U12(tt) -> tt 20.59/20.87 a__U12(X:S) -> U12(X:S) 20.59/20.87 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.59/20.87 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.59/20.87 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.59/20.87 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.59/20.87 a__U23(tt) -> tt 20.59/20.87 a__U23(X:S) -> U23(X:S) 20.59/20.87 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.59/20.87 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.59/20.87 a__U32(tt) -> tt 20.59/20.87 a__U32(X:S) -> U32(X:S) 20.59/20.87 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.59/20.87 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.59/20.87 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.59/20.87 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.59/20.87 a__U43(tt) -> tt 20.59/20.87 a__U43(X:S) -> U43(X:S) 20.59/20.87 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.59/20.87 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.59/20.87 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.59/20.87 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.59/20.87 a__U53(tt) -> tt 20.59/20.87 a__U53(X:S) -> U53(X:S) 20.59/20.87 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.59/20.87 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.59/20.87 a__U62(tt) -> tt 20.59/20.87 a__U62(X:S) -> U62(X:S) 20.59/20.87 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.59/20.87 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.59/20.87 a__U72(tt) -> tt 20.59/20.87 a__U72(X:S) -> U72(X:S) 20.59/20.87 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.87 a____(nil,X:S) -> mark(X:S) 20.59/20.87 a____(X:S,nil) -> mark(X:S) 20.59/20.87 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.59/20.87 a__and(tt,X:S) -> mark(X:S) 20.59/20.87 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.59/20.87 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.87 a__isList(nil) -> tt 20.59/20.87 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.59/20.87 a__isList(X:S) -> isList(X:S) 20.59/20.87 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.87 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.87 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.59/20.87 a__isNeList(X:S) -> isNeList(X:S) 20.59/20.87 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.87 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.59/20.87 a__isNePal(X:S) -> isNePal(X:S) 20.59/20.87 a__isPal(nil) -> tt 20.59/20.87 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.59/20.87 a__isPal(X:S) -> isPal(X:S) 20.59/20.87 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.87 a__isPalListKind(a) -> tt 20.59/20.87 a__isPalListKind(e) -> tt 20.59/20.87 a__isPalListKind(i) -> tt 20.59/20.87 a__isPalListKind(nil) -> tt 20.59/20.87 a__isPalListKind(o) -> tt 20.59/20.87 a__isPalListKind(u) -> tt 20.59/20.87 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.59/20.87 a__isQid(a) -> tt 20.59/20.87 a__isQid(e) -> tt 20.59/20.87 a__isQid(i) -> tt 20.59/20.87 a__isQid(o) -> tt 20.59/20.87 a__isQid(u) -> tt 20.59/20.87 a__isQid(X:S) -> isQid(X:S) 20.59/20.87 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.59/20.87 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.59/20.87 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.59/20.87 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.59/20.87 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.59/20.87 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.59/20.87 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.59/20.87 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.59/20.87 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.59/20.87 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.59/20.87 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.59/20.87 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.59/20.87 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.59/20.87 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.59/20.87 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.59/20.87 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.59/20.87 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.59/20.87 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.59/20.87 mark(a) -> a 20.59/20.87 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.59/20.87 mark(e) -> e 20.59/20.87 mark(i) -> i 20.59/20.87 mark(isList(X:S)) -> a__isList(X:S) 20.59/20.87 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.59/20.87 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.59/20.87 mark(isPal(X:S)) -> a__isPal(X:S) 20.59/20.87 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.59/20.87 mark(isQid(X:S)) -> a__isQid(X:S) 20.59/20.87 mark(nil) -> nil 20.59/20.87 mark(o) -> o 20.59/20.87 mark(tt) -> tt 20.59/20.87 mark(u) -> u 20.59/20.87 ->Strongly Connected Components: 20.59/20.87 ->->Cycle: 20.59/20.87 ->->-> Pairs: 20.59/20.87 A__U51(tt,V1:S,V2:S) -> A__ISNELIST(V1:S) 20.59/20.87 A__U52(tt,V2:S) -> A__ISLIST(V2:S) 20.59/20.87 A__U71(tt,V:S) -> A__ISNEPAL(V:S) 20.59/20.87 A____(__(X:S,Y:S),Z:S) -> A____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.87 A____(__(X:S,Y:S),Z:S) -> A____(mark(Y:S),mark(Z:S)) 20.59/20.87 A____(__(X:S,Y:S),Z:S) -> MARK(X:S) 20.59/20.87 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S) 20.59/20.87 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 20.59/20.87 A____(nil,X:S) -> MARK(X:S) 20.59/20.87 A____(X:S,nil) -> MARK(X:S) 20.59/20.87 A__AND(tt,X:S) -> MARK(X:S) 20.59/20.87 A__ISLIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.87 A__ISLIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.87 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.87 A__ISNELIST(__(V1:S,V2:S)) -> A__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.87 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.87 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.87 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.87 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.87 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.59/20.87 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.87 A__ISPAL(V:S) -> A__U71(a__isPalListKind(V:S),V:S) 20.59/20.87 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.87 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.87 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.87 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U12(X:S)) -> MARK(X:S) 20.59/20.87 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.87 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U23(X:S)) -> MARK(X:S) 20.59/20.87 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U32(X:S)) -> MARK(X:S) 20.59/20.87 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.87 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U43(X:S)) -> MARK(X:S) 20.59/20.87 MARK(U51(X1:S,X2:S,X3:S)) -> A__U51(mark(X1:S),X2:S,X3:S) 20.59/20.87 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.87 MARK(U52(X1:S,X2:S)) -> A__U52(mark(X1:S),X2:S) 20.59/20.87 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U53(X:S)) -> MARK(X:S) 20.59/20.87 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U62(X:S)) -> MARK(X:S) 20.59/20.87 MARK(U71(X1:S,X2:S)) -> A__U71(mark(X1:S),X2:S) 20.59/20.87 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U72(X:S)) -> MARK(X:S) 20.59/20.87 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 20.59/20.87 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.59/20.87 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.59/20.87 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.59/20.87 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.59/20.87 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.59/20.87 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.59/20.87 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.59/20.87 ->->-> Rules: 20.59/20.87 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.59/20.87 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.59/20.87 a__U12(tt) -> tt 20.59/20.87 a__U12(X:S) -> U12(X:S) 20.59/20.87 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.59/20.87 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.59/20.87 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.59/20.87 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.59/20.87 a__U23(tt) -> tt 20.59/20.87 a__U23(X:S) -> U23(X:S) 20.59/20.87 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.59/20.87 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.59/20.87 a__U32(tt) -> tt 20.59/20.87 a__U32(X:S) -> U32(X:S) 20.59/20.87 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.59/20.87 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.59/20.87 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.59/20.87 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.59/20.87 a__U43(tt) -> tt 20.59/20.87 a__U43(X:S) -> U43(X:S) 20.59/20.87 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.59/20.87 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.59/20.87 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.59/20.87 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.59/20.87 a__U53(tt) -> tt 20.59/20.87 a__U53(X:S) -> U53(X:S) 20.59/20.87 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.59/20.87 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.59/20.87 a__U62(tt) -> tt 20.59/20.87 a__U62(X:S) -> U62(X:S) 20.59/20.87 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.59/20.87 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.59/20.87 a__U72(tt) -> tt 20.59/20.87 a__U72(X:S) -> U72(X:S) 20.59/20.87 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.87 a____(nil,X:S) -> mark(X:S) 20.59/20.87 a____(X:S,nil) -> mark(X:S) 20.59/20.87 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.59/20.87 a__and(tt,X:S) -> mark(X:S) 20.59/20.87 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.59/20.87 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.87 a__isList(nil) -> tt 20.59/20.87 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.59/20.87 a__isList(X:S) -> isList(X:S) 20.59/20.87 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.87 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.87 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.59/20.87 a__isNeList(X:S) -> isNeList(X:S) 20.59/20.87 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.87 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.59/20.87 a__isNePal(X:S) -> isNePal(X:S) 20.59/20.87 a__isPal(nil) -> tt 20.59/20.87 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.59/20.87 a__isPal(X:S) -> isPal(X:S) 20.59/20.87 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.87 a__isPalListKind(a) -> tt 20.59/20.87 a__isPalListKind(e) -> tt 20.59/20.87 a__isPalListKind(i) -> tt 20.59/20.87 a__isPalListKind(nil) -> tt 20.59/20.87 a__isPalListKind(o) -> tt 20.59/20.87 a__isPalListKind(u) -> tt 20.59/20.87 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.59/20.87 a__isQid(a) -> tt 20.59/20.87 a__isQid(e) -> tt 20.59/20.87 a__isQid(i) -> tt 20.59/20.87 a__isQid(o) -> tt 20.59/20.87 a__isQid(u) -> tt 20.59/20.87 a__isQid(X:S) -> isQid(X:S) 20.59/20.87 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.59/20.87 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.59/20.87 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.59/20.87 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.59/20.87 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.59/20.87 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.59/20.87 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.59/20.87 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.59/20.87 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.59/20.87 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.59/20.87 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.59/20.87 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.59/20.87 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.59/20.87 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.59/20.87 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.59/20.87 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.59/20.87 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.59/20.87 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.59/20.87 mark(a) -> a 20.59/20.87 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.59/20.87 mark(e) -> e 20.59/20.87 mark(i) -> i 20.59/20.87 mark(isList(X:S)) -> a__isList(X:S) 20.59/20.87 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.59/20.87 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.59/20.87 mark(isPal(X:S)) -> a__isPal(X:S) 20.59/20.87 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.59/20.87 mark(isQid(X:S)) -> a__isQid(X:S) 20.59/20.87 mark(nil) -> nil 20.59/20.87 mark(o) -> o 20.59/20.87 mark(tt) -> tt 20.59/20.87 mark(u) -> u 20.59/20.87 20.59/20.87 Problem 1: 20.59/20.87 20.59/20.87 Reduction Pairs Processor: 20.59/20.87 -> Pairs: 20.59/20.87 A__U51(tt,V1:S,V2:S) -> A__ISNELIST(V1:S) 20.59/20.87 A__U52(tt,V2:S) -> A__ISLIST(V2:S) 20.59/20.87 A__U71(tt,V:S) -> A__ISNEPAL(V:S) 20.59/20.87 A____(__(X:S,Y:S),Z:S) -> A____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.87 A____(__(X:S,Y:S),Z:S) -> A____(mark(Y:S),mark(Z:S)) 20.59/20.87 A____(__(X:S,Y:S),Z:S) -> MARK(X:S) 20.59/20.87 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S) 20.59/20.87 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 20.59/20.87 A____(nil,X:S) -> MARK(X:S) 20.59/20.87 A____(X:S,nil) -> MARK(X:S) 20.59/20.87 A__AND(tt,X:S) -> MARK(X:S) 20.59/20.87 A__ISLIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.87 A__ISLIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.87 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.87 A__ISNELIST(__(V1:S,V2:S)) -> A__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.87 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.87 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.87 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.87 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.87 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.59/20.87 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.87 A__ISPAL(V:S) -> A__U71(a__isPalListKind(V:S),V:S) 20.59/20.87 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.87 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.87 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.87 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U12(X:S)) -> MARK(X:S) 20.59/20.87 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.87 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U23(X:S)) -> MARK(X:S) 20.59/20.87 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U32(X:S)) -> MARK(X:S) 20.59/20.87 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.87 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U43(X:S)) -> MARK(X:S) 20.59/20.87 MARK(U51(X1:S,X2:S,X3:S)) -> A__U51(mark(X1:S),X2:S,X3:S) 20.59/20.87 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.87 MARK(U52(X1:S,X2:S)) -> A__U52(mark(X1:S),X2:S) 20.59/20.87 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U53(X:S)) -> MARK(X:S) 20.59/20.87 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U62(X:S)) -> MARK(X:S) 20.59/20.87 MARK(U71(X1:S,X2:S)) -> A__U71(mark(X1:S),X2:S) 20.59/20.87 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U72(X:S)) -> MARK(X:S) 20.59/20.87 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 20.59/20.87 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.59/20.87 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.59/20.87 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.59/20.87 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.59/20.87 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.59/20.87 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.59/20.87 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.59/20.87 -> Rules: 20.59/20.87 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.59/20.87 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.59/20.87 a__U12(tt) -> tt 20.59/20.87 a__U12(X:S) -> U12(X:S) 20.59/20.87 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.59/20.87 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.59/20.87 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.59/20.87 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.59/20.87 a__U23(tt) -> tt 20.59/20.87 a__U23(X:S) -> U23(X:S) 20.59/20.87 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.59/20.87 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.59/20.87 a__U32(tt) -> tt 20.59/20.87 a__U32(X:S) -> U32(X:S) 20.59/20.87 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.59/20.87 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.59/20.87 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.59/20.87 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.59/20.87 a__U43(tt) -> tt 20.59/20.87 a__U43(X:S) -> U43(X:S) 20.59/20.87 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.59/20.87 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.59/20.87 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.59/20.87 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.59/20.87 a__U53(tt) -> tt 20.59/20.87 a__U53(X:S) -> U53(X:S) 20.59/20.87 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.59/20.87 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.59/20.87 a__U62(tt) -> tt 20.59/20.87 a__U62(X:S) -> U62(X:S) 20.59/20.87 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.59/20.87 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.59/20.87 a__U72(tt) -> tt 20.59/20.87 a__U72(X:S) -> U72(X:S) 20.59/20.87 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.87 a____(nil,X:S) -> mark(X:S) 20.59/20.87 a____(X:S,nil) -> mark(X:S) 20.59/20.87 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.59/20.87 a__and(tt,X:S) -> mark(X:S) 20.59/20.87 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.59/20.87 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.87 a__isList(nil) -> tt 20.59/20.87 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.59/20.87 a__isList(X:S) -> isList(X:S) 20.59/20.87 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.87 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.87 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.59/20.87 a__isNeList(X:S) -> isNeList(X:S) 20.59/20.87 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.87 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.59/20.87 a__isNePal(X:S) -> isNePal(X:S) 20.59/20.87 a__isPal(nil) -> tt 20.59/20.87 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.59/20.87 a__isPal(X:S) -> isPal(X:S) 20.59/20.87 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.87 a__isPalListKind(a) -> tt 20.59/20.87 a__isPalListKind(e) -> tt 20.59/20.87 a__isPalListKind(i) -> tt 20.59/20.87 a__isPalListKind(nil) -> tt 20.59/20.87 a__isPalListKind(o) -> tt 20.59/20.87 a__isPalListKind(u) -> tt 20.59/20.87 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.59/20.87 a__isQid(a) -> tt 20.59/20.87 a__isQid(e) -> tt 20.59/20.87 a__isQid(i) -> tt 20.59/20.87 a__isQid(o) -> tt 20.59/20.87 a__isQid(u) -> tt 20.59/20.87 a__isQid(X:S) -> isQid(X:S) 20.59/20.87 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.59/20.87 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.59/20.87 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.59/20.87 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.59/20.87 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.59/20.87 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.59/20.87 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.59/20.87 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.59/20.87 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.59/20.87 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.59/20.87 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.59/20.87 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.59/20.87 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.59/20.87 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.59/20.87 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.59/20.87 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.59/20.87 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.59/20.87 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.59/20.87 mark(a) -> a 20.59/20.87 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.59/20.87 mark(e) -> e 20.59/20.87 mark(i) -> i 20.59/20.87 mark(isList(X:S)) -> a__isList(X:S) 20.59/20.87 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.59/20.87 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.59/20.87 mark(isPal(X:S)) -> a__isPal(X:S) 20.59/20.87 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.59/20.87 mark(isQid(X:S)) -> a__isQid(X:S) 20.59/20.87 mark(nil) -> nil 20.59/20.87 mark(o) -> o 20.59/20.87 mark(tt) -> tt 20.59/20.87 mark(u) -> u 20.59/20.87 -> Usable rules: 20.59/20.87 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.59/20.87 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.59/20.87 a__U12(tt) -> tt 20.59/20.87 a__U12(X:S) -> U12(X:S) 20.59/20.87 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.59/20.87 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.59/20.87 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.59/20.87 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.59/20.87 a__U23(tt) -> tt 20.59/20.87 a__U23(X:S) -> U23(X:S) 20.59/20.87 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.59/20.87 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.59/20.87 a__U32(tt) -> tt 20.59/20.87 a__U32(X:S) -> U32(X:S) 20.59/20.87 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.59/20.87 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.59/20.87 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.59/20.87 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.59/20.87 a__U43(tt) -> tt 20.59/20.87 a__U43(X:S) -> U43(X:S) 20.59/20.87 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.59/20.87 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.59/20.87 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.59/20.87 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.59/20.87 a__U53(tt) -> tt 20.59/20.87 a__U53(X:S) -> U53(X:S) 20.59/20.87 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.59/20.87 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.59/20.87 a__U62(tt) -> tt 20.59/20.87 a__U62(X:S) -> U62(X:S) 20.59/20.87 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.59/20.87 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.59/20.87 a__U72(tt) -> tt 20.59/20.87 a__U72(X:S) -> U72(X:S) 20.59/20.87 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.87 a____(nil,X:S) -> mark(X:S) 20.59/20.87 a____(X:S,nil) -> mark(X:S) 20.59/20.87 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.59/20.87 a__and(tt,X:S) -> mark(X:S) 20.59/20.87 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.59/20.87 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.87 a__isList(nil) -> tt 20.59/20.87 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.59/20.87 a__isList(X:S) -> isList(X:S) 20.59/20.87 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.87 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.87 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.59/20.87 a__isNeList(X:S) -> isNeList(X:S) 20.59/20.87 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.87 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.59/20.87 a__isNePal(X:S) -> isNePal(X:S) 20.59/20.87 a__isPal(nil) -> tt 20.59/20.87 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.59/20.87 a__isPal(X:S) -> isPal(X:S) 20.59/20.87 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.87 a__isPalListKind(a) -> tt 20.59/20.87 a__isPalListKind(e) -> tt 20.59/20.87 a__isPalListKind(i) -> tt 20.59/20.87 a__isPalListKind(nil) -> tt 20.59/20.87 a__isPalListKind(o) -> tt 20.59/20.87 a__isPalListKind(u) -> tt 20.59/20.87 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.59/20.87 a__isQid(a) -> tt 20.59/20.87 a__isQid(e) -> tt 20.59/20.87 a__isQid(i) -> tt 20.59/20.87 a__isQid(o) -> tt 20.59/20.87 a__isQid(u) -> tt 20.59/20.87 a__isQid(X:S) -> isQid(X:S) 20.59/20.87 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.59/20.87 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.59/20.87 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.59/20.87 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.59/20.87 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.59/20.87 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.59/20.87 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.59/20.87 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.59/20.87 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.59/20.87 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.59/20.87 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.59/20.87 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.59/20.87 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.59/20.87 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.59/20.87 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.59/20.87 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.59/20.87 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.59/20.87 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.59/20.87 mark(a) -> a 20.59/20.87 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.59/20.87 mark(e) -> e 20.59/20.87 mark(i) -> i 20.59/20.87 mark(isList(X:S)) -> a__isList(X:S) 20.59/20.87 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.59/20.87 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.59/20.87 mark(isPal(X:S)) -> a__isPal(X:S) 20.59/20.87 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.59/20.87 mark(isQid(X:S)) -> a__isQid(X:S) 20.59/20.87 mark(nil) -> nil 20.59/20.87 mark(o) -> o 20.59/20.87 mark(tt) -> tt 20.59/20.87 mark(u) -> u 20.59/20.87 ->Interpretation type: 20.59/20.87 Linear 20.59/20.87 ->Coefficients: 20.59/20.87 Natural Numbers 20.59/20.87 ->Dimension: 20.59/20.87 1 20.59/20.87 ->Bound: 20.59/20.87 2 20.59/20.87 ->Interpretation: 20.59/20.87 20.59/20.87 [a__U11](X1,X2) = X1 + 2.X2 20.59/20.87 [a__U12](X) = X 20.59/20.87 [a__U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.59/20.87 [a__U22](X1,X2) = X1 + 2.X2 + 1 20.59/20.87 [a__U23](X) = X 20.59/20.87 [a__U31](X1,X2) = 2.X1 + 2.X2 20.59/20.87 [a__U32](X) = X 20.59/20.87 [a__U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.59/20.87 [a__U42](X1,X2) = X1 + 2.X2 + 1 20.59/20.87 [a__U43](X) = X 20.59/20.87 [a__U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 1 20.59/20.87 [a__U52](X1,X2) = X1 + 2.X2 + 1 20.59/20.87 [a__U53](X) = X 20.59/20.87 [a__U61](X1,X2) = X1 + 2.X2 + 2 20.59/20.87 [a__U62](X) = X + 1 20.59/20.87 [a__U71](X1,X2) = 2.X1 + 2.X2 + 2 20.59/20.87 [a__U72](X) = X 20.59/20.87 [a____](X1,X2) = 2.X1 + X2 + 2 20.59/20.87 [a__and](X1,X2) = X1 + 2.X2 20.59/20.87 [a__isList](X) = 2.X + 1 20.59/20.87 [a__isNeList](X) = 2.X 20.59/20.87 [a__isNePal](X) = 2.X + 2 20.59/20.87 [a__isPal](X) = 2.X + 2 20.59/20.87 [a__isPalListKind](X) = 0 20.59/20.87 [a__isQid](X) = 2.X 20.59/20.87 [mark](X) = X 20.59/20.87 [U11](X1,X2) = X1 + 2.X2 20.59/20.87 [U12](X) = X 20.59/20.87 [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.59/20.87 [U22](X1,X2) = X1 + 2.X2 + 1 20.59/20.87 [U23](X) = X 20.59/20.87 [U31](X1,X2) = 2.X1 + 2.X2 20.59/20.87 [U32](X) = X 20.59/20.87 [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.59/20.87 [U42](X1,X2) = X1 + 2.X2 + 1 20.59/20.87 [U43](X) = X 20.59/20.87 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 1 20.59/20.87 [U52](X1,X2) = X1 + 2.X2 + 1 20.59/20.87 [U53](X) = X 20.59/20.87 [U61](X1,X2) = X1 + 2.X2 + 2 20.59/20.87 [U62](X) = X + 1 20.59/20.87 [U71](X1,X2) = 2.X1 + 2.X2 + 2 20.59/20.87 [U72](X) = X 20.59/20.87 [__](X1,X2) = 2.X1 + X2 + 2 20.59/20.87 [a] = 1 20.59/20.87 [and](X1,X2) = X1 + 2.X2 20.59/20.87 [e] = 1 20.59/20.87 [fSNonEmpty] = 0 20.59/20.87 [i] = 2 20.59/20.87 [isList](X) = 2.X + 1 20.59/20.87 [isNeList](X) = 2.X 20.59/20.87 [isNePal](X) = 2.X + 2 20.59/20.87 [isPal](X) = 2.X + 2 20.59/20.87 [isPalListKind](X) = 0 20.59/20.87 [isQid](X) = 2.X 20.59/20.87 [nil] = 2 20.59/20.87 [o] = 0 20.59/20.87 [tt] = 0 20.59/20.87 [u] = 2 20.59/20.87 [A__U11](X1,X2) = 0 20.59/20.87 [A__U12](X) = 0 20.59/20.87 [A__U21](X1,X2,X3) = 0 20.59/20.87 [A__U22](X1,X2) = 0 20.59/20.87 [A__U23](X) = 0 20.59/20.87 [A__U31](X1,X2) = 0 20.59/20.87 [A__U32](X) = 0 20.59/20.87 [A__U41](X1,X2,X3) = 0 20.59/20.87 [A__U42](X1,X2) = 0 20.59/20.87 [A__U43](X) = 0 20.59/20.87 [A__U51](X1,X2,X3) = 2.X2 + 2 20.59/20.87 [A__U52](X1,X2) = X2 + 2 20.59/20.87 [A__U53](X) = 0 20.59/20.87 [A__U61](X1,X2) = 0 20.59/20.87 [A__U62](X) = 0 20.59/20.87 [A__U71](X1,X2) = 2.X1 + 2.X2 + 2 20.59/20.87 [A__U72](X) = 0 20.59/20.87 [A____](X1,X2) = 2.X1 + X2 + 2 20.59/20.87 [A__AND](X1,X2) = X1 + 2.X2 + 1 20.59/20.87 [A__ISLIST](X) = X + 2 20.59/20.87 [A__ISNELIST](X) = X + 1 20.59/20.87 [A__ISNEPAL](X) = 2.X + 2 20.59/20.87 [A__ISPAL](X) = 2.X + 2 20.59/20.87 [A__ISPALLISTKIND](X) = 1 20.59/20.87 [A__ISQID](X) = 0 20.59/20.87 [MARK](X) = X + 1 20.59/20.87 20.59/20.87 Problem 1: 20.59/20.87 20.59/20.87 SCC Processor: 20.59/20.87 -> Pairs: 20.59/20.87 A__U52(tt,V2:S) -> A__ISLIST(V2:S) 20.59/20.87 A__U71(tt,V:S) -> A__ISNEPAL(V:S) 20.59/20.87 A____(__(X:S,Y:S),Z:S) -> A____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.87 A____(__(X:S,Y:S),Z:S) -> A____(mark(Y:S),mark(Z:S)) 20.59/20.87 A____(__(X:S,Y:S),Z:S) -> MARK(X:S) 20.59/20.87 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S) 20.59/20.87 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 20.59/20.87 A____(nil,X:S) -> MARK(X:S) 20.59/20.87 A____(X:S,nil) -> MARK(X:S) 20.59/20.87 A__AND(tt,X:S) -> MARK(X:S) 20.59/20.87 A__ISLIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.87 A__ISLIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.87 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.87 A__ISNELIST(__(V1:S,V2:S)) -> A__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.87 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.87 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.87 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.87 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.87 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.59/20.87 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.87 A__ISPAL(V:S) -> A__U71(a__isPalListKind(V:S),V:S) 20.59/20.87 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.87 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.87 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.87 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U12(X:S)) -> MARK(X:S) 20.59/20.87 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.87 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U23(X:S)) -> MARK(X:S) 20.59/20.87 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U32(X:S)) -> MARK(X:S) 20.59/20.87 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.87 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U43(X:S)) -> MARK(X:S) 20.59/20.87 MARK(U51(X1:S,X2:S,X3:S)) -> A__U51(mark(X1:S),X2:S,X3:S) 20.59/20.87 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.87 MARK(U52(X1:S,X2:S)) -> A__U52(mark(X1:S),X2:S) 20.59/20.87 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U53(X:S)) -> MARK(X:S) 20.59/20.87 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U62(X:S)) -> MARK(X:S) 20.59/20.87 MARK(U71(X1:S,X2:S)) -> A__U71(mark(X1:S),X2:S) 20.59/20.87 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U72(X:S)) -> MARK(X:S) 20.59/20.87 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 20.59/20.87 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.59/20.87 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.59/20.87 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.59/20.87 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.59/20.87 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.59/20.87 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.59/20.87 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.59/20.87 -> Rules: 20.59/20.87 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.59/20.87 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.59/20.87 a__U12(tt) -> tt 20.59/20.87 a__U12(X:S) -> U12(X:S) 20.59/20.87 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.59/20.87 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.59/20.87 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.59/20.87 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.59/20.87 a__U23(tt) -> tt 20.59/20.87 a__U23(X:S) -> U23(X:S) 20.59/20.87 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.59/20.87 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.59/20.87 a__U32(tt) -> tt 20.59/20.87 a__U32(X:S) -> U32(X:S) 20.59/20.87 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.59/20.87 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.59/20.87 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.59/20.87 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.59/20.87 a__U43(tt) -> tt 20.59/20.87 a__U43(X:S) -> U43(X:S) 20.59/20.87 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.59/20.87 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.59/20.87 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.59/20.87 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.59/20.87 a__U53(tt) -> tt 20.59/20.87 a__U53(X:S) -> U53(X:S) 20.59/20.87 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.59/20.87 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.59/20.87 a__U62(tt) -> tt 20.59/20.87 a__U62(X:S) -> U62(X:S) 20.59/20.87 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.59/20.87 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.59/20.87 a__U72(tt) -> tt 20.59/20.87 a__U72(X:S) -> U72(X:S) 20.59/20.87 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.87 a____(nil,X:S) -> mark(X:S) 20.59/20.87 a____(X:S,nil) -> mark(X:S) 20.59/20.87 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.59/20.87 a__and(tt,X:S) -> mark(X:S) 20.59/20.87 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.59/20.87 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.87 a__isList(nil) -> tt 20.59/20.87 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.59/20.87 a__isList(X:S) -> isList(X:S) 20.59/20.87 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.87 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.87 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.59/20.87 a__isNeList(X:S) -> isNeList(X:S) 20.59/20.87 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.87 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.59/20.87 a__isNePal(X:S) -> isNePal(X:S) 20.59/20.87 a__isPal(nil) -> tt 20.59/20.87 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.59/20.87 a__isPal(X:S) -> isPal(X:S) 20.59/20.87 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.87 a__isPalListKind(a) -> tt 20.59/20.87 a__isPalListKind(e) -> tt 20.59/20.87 a__isPalListKind(i) -> tt 20.59/20.87 a__isPalListKind(nil) -> tt 20.59/20.87 a__isPalListKind(o) -> tt 20.59/20.87 a__isPalListKind(u) -> tt 20.59/20.87 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.59/20.87 a__isQid(a) -> tt 20.59/20.87 a__isQid(e) -> tt 20.59/20.87 a__isQid(i) -> tt 20.59/20.87 a__isQid(o) -> tt 20.59/20.87 a__isQid(u) -> tt 20.59/20.87 a__isQid(X:S) -> isQid(X:S) 20.59/20.87 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.59/20.87 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.59/20.87 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.59/20.87 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.59/20.87 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.59/20.87 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.59/20.87 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.59/20.87 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.59/20.87 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.59/20.87 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.59/20.87 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.59/20.87 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.59/20.87 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.59/20.87 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.59/20.87 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.59/20.87 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.59/20.87 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.59/20.87 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.59/20.87 mark(a) -> a 20.59/20.87 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.59/20.87 mark(e) -> e 20.59/20.87 mark(i) -> i 20.59/20.87 mark(isList(X:S)) -> a__isList(X:S) 20.59/20.87 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.59/20.87 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.59/20.87 mark(isPal(X:S)) -> a__isPal(X:S) 20.59/20.87 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.59/20.87 mark(isQid(X:S)) -> a__isQid(X:S) 20.59/20.87 mark(nil) -> nil 20.59/20.87 mark(o) -> o 20.59/20.87 mark(tt) -> tt 20.59/20.87 mark(u) -> u 20.59/20.87 ->Strongly Connected Components: 20.59/20.87 ->->Cycle: 20.59/20.87 ->->-> Pairs: 20.59/20.87 A__U52(tt,V2:S) -> A__ISLIST(V2:S) 20.59/20.87 A__U71(tt,V:S) -> A__ISNEPAL(V:S) 20.59/20.87 A____(__(X:S,Y:S),Z:S) -> A____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.87 A____(__(X:S,Y:S),Z:S) -> A____(mark(Y:S),mark(Z:S)) 20.59/20.87 A____(__(X:S,Y:S),Z:S) -> MARK(X:S) 20.59/20.87 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S) 20.59/20.87 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 20.59/20.87 A____(nil,X:S) -> MARK(X:S) 20.59/20.87 A____(X:S,nil) -> MARK(X:S) 20.59/20.87 A__AND(tt,X:S) -> MARK(X:S) 20.59/20.87 A__ISLIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.87 A__ISLIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.87 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.87 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.87 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.87 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.87 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.87 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.59/20.87 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.87 A__ISPAL(V:S) -> A__U71(a__isPalListKind(V:S),V:S) 20.59/20.87 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.87 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.87 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.87 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U12(X:S)) -> MARK(X:S) 20.59/20.87 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.87 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U23(X:S)) -> MARK(X:S) 20.59/20.87 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U32(X:S)) -> MARK(X:S) 20.59/20.87 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.87 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U43(X:S)) -> MARK(X:S) 20.59/20.87 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.87 MARK(U52(X1:S,X2:S)) -> A__U52(mark(X1:S),X2:S) 20.59/20.87 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U53(X:S)) -> MARK(X:S) 20.59/20.87 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U62(X:S)) -> MARK(X:S) 20.59/20.87 MARK(U71(X1:S,X2:S)) -> A__U71(mark(X1:S),X2:S) 20.59/20.87 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U72(X:S)) -> MARK(X:S) 20.59/20.87 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 20.59/20.87 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.59/20.87 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.59/20.87 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.59/20.87 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.59/20.87 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.59/20.87 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.59/20.87 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.59/20.87 ->->-> Rules: 20.59/20.87 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.59/20.87 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.59/20.87 a__U12(tt) -> tt 20.59/20.87 a__U12(X:S) -> U12(X:S) 20.59/20.87 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.59/20.87 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.59/20.87 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.59/20.87 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.59/20.87 a__U23(tt) -> tt 20.59/20.87 a__U23(X:S) -> U23(X:S) 20.59/20.87 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.59/20.87 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.59/20.87 a__U32(tt) -> tt 20.59/20.87 a__U32(X:S) -> U32(X:S) 20.59/20.87 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.59/20.87 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.59/20.87 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.59/20.87 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.59/20.87 a__U43(tt) -> tt 20.59/20.87 a__U43(X:S) -> U43(X:S) 20.59/20.87 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.59/20.87 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.59/20.87 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.59/20.87 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.59/20.87 a__U53(tt) -> tt 20.59/20.87 a__U53(X:S) -> U53(X:S) 20.59/20.87 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.59/20.87 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.59/20.87 a__U62(tt) -> tt 20.59/20.87 a__U62(X:S) -> U62(X:S) 20.59/20.87 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.59/20.87 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.59/20.87 a__U72(tt) -> tt 20.59/20.87 a__U72(X:S) -> U72(X:S) 20.59/20.87 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.87 a____(nil,X:S) -> mark(X:S) 20.59/20.87 a____(X:S,nil) -> mark(X:S) 20.59/20.87 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.59/20.87 a__and(tt,X:S) -> mark(X:S) 20.59/20.87 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.59/20.87 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.87 a__isList(nil) -> tt 20.59/20.87 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.59/20.87 a__isList(X:S) -> isList(X:S) 20.59/20.87 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.87 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.87 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.59/20.87 a__isNeList(X:S) -> isNeList(X:S) 20.59/20.87 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.87 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.59/20.87 a__isNePal(X:S) -> isNePal(X:S) 20.59/20.87 a__isPal(nil) -> tt 20.59/20.87 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.59/20.87 a__isPal(X:S) -> isPal(X:S) 20.59/20.87 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.87 a__isPalListKind(a) -> tt 20.59/20.87 a__isPalListKind(e) -> tt 20.59/20.87 a__isPalListKind(i) -> tt 20.59/20.87 a__isPalListKind(nil) -> tt 20.59/20.87 a__isPalListKind(o) -> tt 20.59/20.87 a__isPalListKind(u) -> tt 20.59/20.87 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.59/20.87 a__isQid(a) -> tt 20.59/20.87 a__isQid(e) -> tt 20.59/20.87 a__isQid(i) -> tt 20.59/20.87 a__isQid(o) -> tt 20.59/20.87 a__isQid(u) -> tt 20.59/20.87 a__isQid(X:S) -> isQid(X:S) 20.59/20.87 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.59/20.87 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.59/20.87 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.59/20.87 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.59/20.87 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.59/20.87 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.59/20.87 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.59/20.87 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.59/20.87 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.59/20.87 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.59/20.87 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.59/20.87 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.59/20.87 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.59/20.87 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.59/20.87 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.59/20.87 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.59/20.87 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.59/20.87 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.59/20.87 mark(a) -> a 20.59/20.87 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.59/20.87 mark(e) -> e 20.59/20.87 mark(i) -> i 20.59/20.87 mark(isList(X:S)) -> a__isList(X:S) 20.59/20.87 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.59/20.87 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.59/20.87 mark(isPal(X:S)) -> a__isPal(X:S) 20.59/20.87 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.59/20.87 mark(isQid(X:S)) -> a__isQid(X:S) 20.59/20.87 mark(nil) -> nil 20.59/20.87 mark(o) -> o 20.59/20.87 mark(tt) -> tt 20.59/20.87 mark(u) -> u 20.59/20.87 20.59/20.87 Problem 1: 20.59/20.87 20.59/20.87 Reduction Pairs Processor: 20.59/20.87 -> Pairs: 20.59/20.87 A__U52(tt,V2:S) -> A__ISLIST(V2:S) 20.59/20.87 A__U71(tt,V:S) -> A__ISNEPAL(V:S) 20.59/20.87 A____(__(X:S,Y:S),Z:S) -> A____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.87 A____(__(X:S,Y:S),Z:S) -> A____(mark(Y:S),mark(Z:S)) 20.59/20.87 A____(__(X:S,Y:S),Z:S) -> MARK(X:S) 20.59/20.87 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S) 20.59/20.87 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 20.59/20.87 A____(nil,X:S) -> MARK(X:S) 20.59/20.87 A____(X:S,nil) -> MARK(X:S) 20.59/20.87 A__AND(tt,X:S) -> MARK(X:S) 20.59/20.87 A__ISLIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.87 A__ISLIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.87 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.87 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.87 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.87 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.87 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.87 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.59/20.87 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.87 A__ISPAL(V:S) -> A__U71(a__isPalListKind(V:S),V:S) 20.59/20.87 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.87 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.87 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.87 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U12(X:S)) -> MARK(X:S) 20.59/20.87 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.87 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U23(X:S)) -> MARK(X:S) 20.59/20.87 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U32(X:S)) -> MARK(X:S) 20.59/20.87 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.87 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U43(X:S)) -> MARK(X:S) 20.59/20.87 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.87 MARK(U52(X1:S,X2:S)) -> A__U52(mark(X1:S),X2:S) 20.59/20.87 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U53(X:S)) -> MARK(X:S) 20.59/20.87 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U62(X:S)) -> MARK(X:S) 20.59/20.87 MARK(U71(X1:S,X2:S)) -> A__U71(mark(X1:S),X2:S) 20.59/20.87 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U72(X:S)) -> MARK(X:S) 20.59/20.87 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 20.59/20.87 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.59/20.87 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.59/20.87 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.59/20.87 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.59/20.87 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.59/20.87 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.59/20.87 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.59/20.87 -> Rules: 20.59/20.87 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.59/20.87 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.59/20.87 a__U12(tt) -> tt 20.59/20.87 a__U12(X:S) -> U12(X:S) 20.59/20.87 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.59/20.87 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.59/20.87 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.59/20.87 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.59/20.87 a__U23(tt) -> tt 20.59/20.87 a__U23(X:S) -> U23(X:S) 20.59/20.87 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.59/20.87 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.59/20.87 a__U32(tt) -> tt 20.59/20.87 a__U32(X:S) -> U32(X:S) 20.59/20.87 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.59/20.87 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.59/20.87 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.59/20.87 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.59/20.87 a__U43(tt) -> tt 20.59/20.87 a__U43(X:S) -> U43(X:S) 20.59/20.87 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.59/20.87 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.59/20.87 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.59/20.87 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.59/20.87 a__U53(tt) -> tt 20.59/20.87 a__U53(X:S) -> U53(X:S) 20.59/20.87 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.59/20.87 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.59/20.87 a__U62(tt) -> tt 20.59/20.87 a__U62(X:S) -> U62(X:S) 20.59/20.87 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.59/20.87 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.59/20.87 a__U72(tt) -> tt 20.59/20.87 a__U72(X:S) -> U72(X:S) 20.59/20.87 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.87 a____(nil,X:S) -> mark(X:S) 20.59/20.87 a____(X:S,nil) -> mark(X:S) 20.59/20.87 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.59/20.87 a__and(tt,X:S) -> mark(X:S) 20.59/20.87 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.59/20.87 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.87 a__isList(nil) -> tt 20.59/20.87 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.59/20.87 a__isList(X:S) -> isList(X:S) 20.59/20.87 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.87 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.87 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.59/20.87 a__isNeList(X:S) -> isNeList(X:S) 20.59/20.87 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.87 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.59/20.87 a__isNePal(X:S) -> isNePal(X:S) 20.59/20.87 a__isPal(nil) -> tt 20.59/20.87 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.59/20.87 a__isPal(X:S) -> isPal(X:S) 20.59/20.87 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.87 a__isPalListKind(a) -> tt 20.59/20.87 a__isPalListKind(e) -> tt 20.59/20.87 a__isPalListKind(i) -> tt 20.59/20.87 a__isPalListKind(nil) -> tt 20.59/20.87 a__isPalListKind(o) -> tt 20.59/20.87 a__isPalListKind(u) -> tt 20.59/20.87 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.59/20.87 a__isQid(a) -> tt 20.59/20.87 a__isQid(e) -> tt 20.59/20.87 a__isQid(i) -> tt 20.59/20.87 a__isQid(o) -> tt 20.59/20.87 a__isQid(u) -> tt 20.59/20.87 a__isQid(X:S) -> isQid(X:S) 20.59/20.87 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.59/20.87 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.59/20.87 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.59/20.87 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.59/20.87 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.59/20.87 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.59/20.87 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.59/20.87 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.59/20.87 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.59/20.87 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.59/20.87 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.59/20.87 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.59/20.87 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.59/20.87 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.59/20.87 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.59/20.87 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.59/20.87 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.59/20.87 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.59/20.87 mark(a) -> a 20.59/20.87 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.59/20.87 mark(e) -> e 20.59/20.87 mark(i) -> i 20.59/20.87 mark(isList(X:S)) -> a__isList(X:S) 20.59/20.87 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.59/20.87 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.59/20.87 mark(isPal(X:S)) -> a__isPal(X:S) 20.59/20.87 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.59/20.87 mark(isQid(X:S)) -> a__isQid(X:S) 20.59/20.87 mark(nil) -> nil 20.59/20.87 mark(o) -> o 20.59/20.87 mark(tt) -> tt 20.59/20.87 mark(u) -> u 20.59/20.87 -> Usable rules: 20.59/20.87 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.59/20.87 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.59/20.87 a__U12(tt) -> tt 20.59/20.87 a__U12(X:S) -> U12(X:S) 20.59/20.87 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.59/20.87 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.59/20.87 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.59/20.87 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.59/20.87 a__U23(tt) -> tt 20.59/20.87 a__U23(X:S) -> U23(X:S) 20.59/20.87 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.59/20.87 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.59/20.87 a__U32(tt) -> tt 20.59/20.87 a__U32(X:S) -> U32(X:S) 20.59/20.87 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.59/20.87 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.59/20.87 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.59/20.87 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.59/20.87 a__U43(tt) -> tt 20.59/20.87 a__U43(X:S) -> U43(X:S) 20.59/20.87 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.59/20.87 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.59/20.87 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.59/20.87 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.59/20.87 a__U53(tt) -> tt 20.59/20.87 a__U53(X:S) -> U53(X:S) 20.59/20.87 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.59/20.87 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.59/20.87 a__U62(tt) -> tt 20.59/20.87 a__U62(X:S) -> U62(X:S) 20.59/20.87 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.59/20.87 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.59/20.87 a__U72(tt) -> tt 20.59/20.87 a__U72(X:S) -> U72(X:S) 20.59/20.87 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.87 a____(nil,X:S) -> mark(X:S) 20.59/20.87 a____(X:S,nil) -> mark(X:S) 20.59/20.87 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.59/20.87 a__and(tt,X:S) -> mark(X:S) 20.59/20.87 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.59/20.87 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.87 a__isList(nil) -> tt 20.59/20.87 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.59/20.87 a__isList(X:S) -> isList(X:S) 20.59/20.87 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.87 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.87 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.59/20.87 a__isNeList(X:S) -> isNeList(X:S) 20.59/20.87 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.87 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.59/20.87 a__isNePal(X:S) -> isNePal(X:S) 20.59/20.87 a__isPal(nil) -> tt 20.59/20.87 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.59/20.87 a__isPal(X:S) -> isPal(X:S) 20.59/20.87 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.87 a__isPalListKind(a) -> tt 20.59/20.87 a__isPalListKind(e) -> tt 20.59/20.87 a__isPalListKind(i) -> tt 20.59/20.87 a__isPalListKind(nil) -> tt 20.59/20.87 a__isPalListKind(o) -> tt 20.59/20.87 a__isPalListKind(u) -> tt 20.59/20.87 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.59/20.87 a__isQid(a) -> tt 20.59/20.87 a__isQid(e) -> tt 20.59/20.87 a__isQid(i) -> tt 20.59/20.87 a__isQid(o) -> tt 20.59/20.87 a__isQid(u) -> tt 20.59/20.87 a__isQid(X:S) -> isQid(X:S) 20.59/20.87 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.59/20.87 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.59/20.87 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.59/20.87 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.59/20.87 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.59/20.87 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.59/20.87 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.59/20.87 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.59/20.87 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.59/20.87 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.59/20.87 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.59/20.87 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.59/20.87 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.59/20.87 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.59/20.87 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.59/20.87 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.59/20.87 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.59/20.87 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.59/20.87 mark(a) -> a 20.59/20.87 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.59/20.87 mark(e) -> e 20.59/20.87 mark(i) -> i 20.59/20.87 mark(isList(X:S)) -> a__isList(X:S) 20.59/20.87 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.59/20.87 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.59/20.87 mark(isPal(X:S)) -> a__isPal(X:S) 20.59/20.87 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.59/20.87 mark(isQid(X:S)) -> a__isQid(X:S) 20.59/20.87 mark(nil) -> nil 20.59/20.87 mark(o) -> o 20.59/20.87 mark(tt) -> tt 20.59/20.87 mark(u) -> u 20.59/20.87 ->Interpretation type: 20.59/20.87 Linear 20.59/20.87 ->Coefficients: 20.59/20.87 Natural Numbers 20.59/20.87 ->Dimension: 20.59/20.87 1 20.59/20.87 ->Bound: 20.59/20.87 2 20.59/20.87 ->Interpretation: 20.59/20.87 20.59/20.87 [a__U11](X1,X2) = 2.X1 + 2.X2 + 1 20.59/20.87 [a__U12](X) = X + 1 20.59/20.87 [a__U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.59/20.87 [a__U22](X1,X2) = X1 + 2.X2 + 1 20.59/20.87 [a__U23](X) = X 20.59/20.87 [a__U31](X1,X2) = 2.X1 + 2.X2 20.59/20.87 [a__U32](X) = 2.X 20.59/20.87 [a__U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.59/20.87 [a__U42](X1,X2) = X1 + 2.X2 20.59/20.87 [a__U43](X) = X 20.59/20.87 [a__U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.59/20.87 [a__U52](X1,X2) = X1 + 2.X2 + 2 20.59/20.87 [a__U53](X) = X + 1 20.59/20.87 [a__U61](X1,X2) = 2.X1 + 2.X2 + 2 20.59/20.87 [a__U62](X) = 2.X 20.59/20.87 [a__U71](X1,X2) = 2.X1 + 2.X2 + 2 20.59/20.87 [a__U72](X) = X 20.59/20.87 [a____](X1,X2) = 2.X1 + X2 + 2 20.59/20.87 [a__and](X1,X2) = 2.X1 + X2 20.59/20.87 [a__isList](X) = 2.X + 1 20.59/20.87 [a__isNeList](X) = 2.X 20.59/20.87 [a__isNePal](X) = 2.X + 2 20.59/20.87 [a__isPal](X) = 2.X + 2 20.59/20.87 [a__isPalListKind](X) = 0 20.59/20.87 [a__isQid](X) = X 20.59/20.87 [mark](X) = X 20.59/20.87 [U11](X1,X2) = 2.X1 + 2.X2 + 1 20.59/20.87 [U12](X) = X + 1 20.59/20.87 [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.59/20.87 [U22](X1,X2) = X1 + 2.X2 + 1 20.59/20.87 [U23](X) = X 20.59/20.87 [U31](X1,X2) = 2.X1 + 2.X2 20.59/20.87 [U32](X) = 2.X 20.59/20.87 [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.59/20.87 [U42](X1,X2) = X1 + 2.X2 20.59/20.87 [U43](X) = X 20.59/20.87 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.59/20.87 [U52](X1,X2) = X1 + 2.X2 + 2 20.59/20.87 [U53](X) = X + 1 20.59/20.87 [U61](X1,X2) = 2.X1 + 2.X2 + 2 20.59/20.87 [U62](X) = 2.X 20.59/20.87 [U71](X1,X2) = 2.X1 + 2.X2 + 2 20.59/20.87 [U72](X) = X 20.59/20.87 [__](X1,X2) = 2.X1 + X2 + 2 20.59/20.87 [a] = 0 20.59/20.87 [and](X1,X2) = 2.X1 + X2 20.59/20.87 [e] = 2 20.59/20.87 [fSNonEmpty] = 0 20.59/20.87 [i] = 1 20.59/20.87 [isList](X) = 2.X + 1 20.59/20.87 [isNeList](X) = 2.X 20.59/20.87 [isNePal](X) = 2.X + 2 20.59/20.87 [isPal](X) = 2.X + 2 20.59/20.87 [isPalListKind](X) = 0 20.59/20.87 [isQid](X) = X 20.59/20.87 [nil] = 2 20.59/20.87 [o] = 2 20.59/20.87 [tt] = 0 20.59/20.87 [u] = 0 20.59/20.87 [A__U11](X1,X2) = 0 20.59/20.87 [A__U12](X) = 0 20.59/20.87 [A__U21](X1,X2,X3) = 0 20.59/20.87 [A__U22](X1,X2) = 0 20.59/20.87 [A__U23](X) = 0 20.59/20.87 [A__U31](X1,X2) = 0 20.59/20.87 [A__U32](X) = 0 20.59/20.87 [A__U41](X1,X2,X3) = 0 20.59/20.87 [A__U42](X1,X2) = 0 20.59/20.87 [A__U43](X) = 0 20.59/20.87 [A__U51](X1,X2,X3) = 0 20.59/20.87 [A__U52](X1,X2) = X1 + 2 20.59/20.87 [A__U53](X) = 0 20.59/20.87 [A__U61](X1,X2) = 0 20.59/20.87 [A__U62](X) = 0 20.59/20.87 [A__U71](X1,X2) = 2.X1 + 2.X2 + 2 20.59/20.87 [A__U72](X) = 0 20.59/20.87 [A____](X1,X2) = 2.X1 + X2 + 2 20.59/20.87 [A__AND](X1,X2) = X1 + X2 + 1 20.59/20.87 [A__ISLIST](X) = 1 20.59/20.87 [A__ISNELIST](X) = 2.X + 1 20.59/20.87 [A__ISNEPAL](X) = 2.X + 1 20.59/20.87 [A__ISPAL](X) = 2.X + 2 20.59/20.87 [A__ISPALLISTKIND](X) = 1 20.59/20.87 [A__ISQID](X) = 0 20.59/20.87 [MARK](X) = X + 1 20.59/20.87 20.59/20.87 Problem 1: 20.59/20.87 20.59/20.87 SCC Processor: 20.59/20.87 -> Pairs: 20.59/20.87 A__U71(tt,V:S) -> A__ISNEPAL(V:S) 20.59/20.87 A____(__(X:S,Y:S),Z:S) -> A____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.87 A____(__(X:S,Y:S),Z:S) -> A____(mark(Y:S),mark(Z:S)) 20.59/20.87 A____(__(X:S,Y:S),Z:S) -> MARK(X:S) 20.59/20.87 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S) 20.59/20.87 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 20.59/20.87 A____(nil,X:S) -> MARK(X:S) 20.59/20.87 A____(X:S,nil) -> MARK(X:S) 20.59/20.87 A__AND(tt,X:S) -> MARK(X:S) 20.59/20.87 A__ISLIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.87 A__ISLIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.87 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.87 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.87 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.87 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.87 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.87 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.59/20.87 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.87 A__ISPAL(V:S) -> A__U71(a__isPalListKind(V:S),V:S) 20.59/20.87 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.87 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.87 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.87 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U12(X:S)) -> MARK(X:S) 20.59/20.87 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.87 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U23(X:S)) -> MARK(X:S) 20.59/20.87 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U32(X:S)) -> MARK(X:S) 20.59/20.87 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.87 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U43(X:S)) -> MARK(X:S) 20.59/20.87 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.87 MARK(U52(X1:S,X2:S)) -> A__U52(mark(X1:S),X2:S) 20.59/20.87 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U53(X:S)) -> MARK(X:S) 20.59/20.87 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U62(X:S)) -> MARK(X:S) 20.59/20.87 MARK(U71(X1:S,X2:S)) -> A__U71(mark(X1:S),X2:S) 20.59/20.87 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U72(X:S)) -> MARK(X:S) 20.59/20.87 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 20.59/20.87 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.59/20.87 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.59/20.87 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.59/20.87 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.59/20.87 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.59/20.87 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.59/20.87 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.59/20.87 -> Rules: 20.59/20.87 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.59/20.87 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.59/20.87 a__U12(tt) -> tt 20.59/20.87 a__U12(X:S) -> U12(X:S) 20.59/20.87 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.59/20.87 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.59/20.87 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.59/20.87 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.59/20.87 a__U23(tt) -> tt 20.59/20.87 a__U23(X:S) -> U23(X:S) 20.59/20.87 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.59/20.87 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.59/20.87 a__U32(tt) -> tt 20.59/20.87 a__U32(X:S) -> U32(X:S) 20.59/20.87 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.59/20.87 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.59/20.87 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.59/20.87 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.59/20.87 a__U43(tt) -> tt 20.59/20.87 a__U43(X:S) -> U43(X:S) 20.59/20.87 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.59/20.87 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.59/20.87 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.59/20.87 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.59/20.87 a__U53(tt) -> tt 20.59/20.87 a__U53(X:S) -> U53(X:S) 20.59/20.87 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.59/20.87 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.59/20.87 a__U62(tt) -> tt 20.59/20.87 a__U62(X:S) -> U62(X:S) 20.59/20.87 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.59/20.87 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.59/20.87 a__U72(tt) -> tt 20.59/20.87 a__U72(X:S) -> U72(X:S) 20.59/20.87 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.87 a____(nil,X:S) -> mark(X:S) 20.59/20.87 a____(X:S,nil) -> mark(X:S) 20.59/20.87 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.59/20.87 a__and(tt,X:S) -> mark(X:S) 20.59/20.87 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.59/20.87 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.87 a__isList(nil) -> tt 20.59/20.87 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.59/20.87 a__isList(X:S) -> isList(X:S) 20.59/20.87 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.87 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.87 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.59/20.87 a__isNeList(X:S) -> isNeList(X:S) 20.59/20.87 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.87 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.59/20.87 a__isNePal(X:S) -> isNePal(X:S) 20.59/20.87 a__isPal(nil) -> tt 20.59/20.87 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.59/20.87 a__isPal(X:S) -> isPal(X:S) 20.59/20.87 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.87 a__isPalListKind(a) -> tt 20.59/20.87 a__isPalListKind(e) -> tt 20.59/20.87 a__isPalListKind(i) -> tt 20.59/20.87 a__isPalListKind(nil) -> tt 20.59/20.87 a__isPalListKind(o) -> tt 20.59/20.87 a__isPalListKind(u) -> tt 20.59/20.87 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.59/20.87 a__isQid(a) -> tt 20.59/20.87 a__isQid(e) -> tt 20.59/20.87 a__isQid(i) -> tt 20.59/20.87 a__isQid(o) -> tt 20.59/20.87 a__isQid(u) -> tt 20.59/20.87 a__isQid(X:S) -> isQid(X:S) 20.59/20.87 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.59/20.87 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.59/20.87 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.59/20.87 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.59/20.87 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.59/20.87 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.59/20.87 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.59/20.87 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.59/20.87 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.59/20.87 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.59/20.87 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.59/20.87 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.59/20.87 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.59/20.87 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.59/20.87 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.59/20.87 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.59/20.87 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.59/20.87 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.59/20.87 mark(a) -> a 20.59/20.87 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.59/20.87 mark(e) -> e 20.59/20.87 mark(i) -> i 20.59/20.87 mark(isList(X:S)) -> a__isList(X:S) 20.59/20.87 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.59/20.87 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.59/20.87 mark(isPal(X:S)) -> a__isPal(X:S) 20.59/20.87 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.59/20.87 mark(isQid(X:S)) -> a__isQid(X:S) 20.59/20.87 mark(nil) -> nil 20.59/20.87 mark(o) -> o 20.59/20.87 mark(tt) -> tt 20.59/20.87 mark(u) -> u 20.59/20.87 ->Strongly Connected Components: 20.59/20.87 ->->Cycle: 20.59/20.87 ->->-> Pairs: 20.59/20.87 A__U71(tt,V:S) -> A__ISNEPAL(V:S) 20.59/20.87 A____(__(X:S,Y:S),Z:S) -> A____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.87 A____(__(X:S,Y:S),Z:S) -> A____(mark(Y:S),mark(Z:S)) 20.59/20.87 A____(__(X:S,Y:S),Z:S) -> MARK(X:S) 20.59/20.87 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S) 20.59/20.87 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 20.59/20.87 A____(nil,X:S) -> MARK(X:S) 20.59/20.87 A____(X:S,nil) -> MARK(X:S) 20.59/20.87 A__AND(tt,X:S) -> MARK(X:S) 20.59/20.87 A__ISLIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.87 A__ISLIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.87 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.87 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.87 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.87 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.87 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.87 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.59/20.87 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.87 A__ISPAL(V:S) -> A__U71(a__isPalListKind(V:S),V:S) 20.59/20.87 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.87 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.87 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.87 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U12(X:S)) -> MARK(X:S) 20.59/20.87 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.87 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U23(X:S)) -> MARK(X:S) 20.59/20.87 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U32(X:S)) -> MARK(X:S) 20.59/20.87 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.87 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U43(X:S)) -> MARK(X:S) 20.59/20.87 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.87 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U53(X:S)) -> MARK(X:S) 20.59/20.87 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U62(X:S)) -> MARK(X:S) 20.59/20.87 MARK(U71(X1:S,X2:S)) -> A__U71(mark(X1:S),X2:S) 20.59/20.87 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U72(X:S)) -> MARK(X:S) 20.59/20.87 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 20.59/20.87 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.59/20.87 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.59/20.87 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.59/20.87 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.59/20.87 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.59/20.87 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.59/20.87 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.59/20.87 ->->-> Rules: 20.59/20.87 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.59/20.87 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.59/20.87 a__U12(tt) -> tt 20.59/20.87 a__U12(X:S) -> U12(X:S) 20.59/20.87 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.59/20.87 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.59/20.87 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.59/20.87 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.59/20.87 a__U23(tt) -> tt 20.59/20.87 a__U23(X:S) -> U23(X:S) 20.59/20.87 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.59/20.87 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.59/20.87 a__U32(tt) -> tt 20.59/20.87 a__U32(X:S) -> U32(X:S) 20.59/20.87 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.59/20.87 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.59/20.87 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.59/20.87 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.59/20.87 a__U43(tt) -> tt 20.59/20.87 a__U43(X:S) -> U43(X:S) 20.59/20.87 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.59/20.87 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.59/20.87 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.59/20.87 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.59/20.87 a__U53(tt) -> tt 20.59/20.87 a__U53(X:S) -> U53(X:S) 20.59/20.87 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.59/20.87 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.59/20.87 a__U62(tt) -> tt 20.59/20.87 a__U62(X:S) -> U62(X:S) 20.59/20.87 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.59/20.87 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.59/20.87 a__U72(tt) -> tt 20.59/20.87 a__U72(X:S) -> U72(X:S) 20.59/20.87 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.87 a____(nil,X:S) -> mark(X:S) 20.59/20.87 a____(X:S,nil) -> mark(X:S) 20.59/20.87 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.59/20.87 a__and(tt,X:S) -> mark(X:S) 20.59/20.87 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.59/20.87 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.87 a__isList(nil) -> tt 20.59/20.87 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.59/20.87 a__isList(X:S) -> isList(X:S) 20.59/20.87 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.87 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.87 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.59/20.87 a__isNeList(X:S) -> isNeList(X:S) 20.59/20.87 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.87 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.59/20.87 a__isNePal(X:S) -> isNePal(X:S) 20.59/20.87 a__isPal(nil) -> tt 20.59/20.87 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.59/20.87 a__isPal(X:S) -> isPal(X:S) 20.59/20.87 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.87 a__isPalListKind(a) -> tt 20.59/20.87 a__isPalListKind(e) -> tt 20.59/20.87 a__isPalListKind(i) -> tt 20.59/20.87 a__isPalListKind(nil) -> tt 20.59/20.87 a__isPalListKind(o) -> tt 20.59/20.87 a__isPalListKind(u) -> tt 20.59/20.87 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.59/20.87 a__isQid(a) -> tt 20.59/20.87 a__isQid(e) -> tt 20.59/20.87 a__isQid(i) -> tt 20.59/20.87 a__isQid(o) -> tt 20.59/20.87 a__isQid(u) -> tt 20.59/20.87 a__isQid(X:S) -> isQid(X:S) 20.59/20.87 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.59/20.87 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.59/20.87 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.59/20.87 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.59/20.87 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.59/20.87 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.59/20.87 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.59/20.87 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.59/20.87 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.59/20.87 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.59/20.87 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.59/20.87 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.59/20.87 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.59/20.87 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.59/20.87 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.59/20.87 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.59/20.87 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.59/20.87 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.59/20.87 mark(a) -> a 20.59/20.87 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.59/20.87 mark(e) -> e 20.59/20.87 mark(i) -> i 20.59/20.87 mark(isList(X:S)) -> a__isList(X:S) 20.59/20.87 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.59/20.87 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.59/20.87 mark(isPal(X:S)) -> a__isPal(X:S) 20.59/20.87 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.59/20.87 mark(isQid(X:S)) -> a__isQid(X:S) 20.59/20.87 mark(nil) -> nil 20.59/20.87 mark(o) -> o 20.59/20.87 mark(tt) -> tt 20.59/20.87 mark(u) -> u 20.59/20.87 20.59/20.87 Problem 1: 20.59/20.87 20.59/20.87 Reduction Pairs Processor: 20.59/20.87 -> Pairs: 20.59/20.87 A__U71(tt,V:S) -> A__ISNEPAL(V:S) 20.59/20.87 A____(__(X:S,Y:S),Z:S) -> A____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.87 A____(__(X:S,Y:S),Z:S) -> A____(mark(Y:S),mark(Z:S)) 20.59/20.87 A____(__(X:S,Y:S),Z:S) -> MARK(X:S) 20.59/20.87 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S) 20.59/20.87 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 20.59/20.87 A____(nil,X:S) -> MARK(X:S) 20.59/20.87 A____(X:S,nil) -> MARK(X:S) 20.59/20.87 A__AND(tt,X:S) -> MARK(X:S) 20.59/20.87 A__ISLIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.87 A__ISLIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.87 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.87 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.87 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.87 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.87 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.87 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.59/20.87 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.87 A__ISPAL(V:S) -> A__U71(a__isPalListKind(V:S),V:S) 20.59/20.87 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.87 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.87 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.87 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U12(X:S)) -> MARK(X:S) 20.59/20.87 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.87 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U23(X:S)) -> MARK(X:S) 20.59/20.87 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U32(X:S)) -> MARK(X:S) 20.59/20.87 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.87 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U43(X:S)) -> MARK(X:S) 20.59/20.87 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.87 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U53(X:S)) -> MARK(X:S) 20.59/20.87 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U62(X:S)) -> MARK(X:S) 20.59/20.87 MARK(U71(X1:S,X2:S)) -> A__U71(mark(X1:S),X2:S) 20.59/20.87 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U72(X:S)) -> MARK(X:S) 20.59/20.87 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 20.59/20.87 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.59/20.87 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.59/20.87 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.59/20.87 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.59/20.87 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.59/20.87 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.59/20.87 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.59/20.87 -> Rules: 20.59/20.87 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.59/20.87 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.59/20.87 a__U12(tt) -> tt 20.59/20.87 a__U12(X:S) -> U12(X:S) 20.59/20.87 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.59/20.87 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.59/20.87 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.59/20.87 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.59/20.87 a__U23(tt) -> tt 20.59/20.87 a__U23(X:S) -> U23(X:S) 20.59/20.87 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.59/20.87 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.59/20.87 a__U32(tt) -> tt 20.59/20.87 a__U32(X:S) -> U32(X:S) 20.59/20.87 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.59/20.87 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.59/20.87 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.59/20.87 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.59/20.87 a__U43(tt) -> tt 20.59/20.87 a__U43(X:S) -> U43(X:S) 20.59/20.87 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.59/20.87 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.59/20.87 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.59/20.87 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.59/20.87 a__U53(tt) -> tt 20.59/20.87 a__U53(X:S) -> U53(X:S) 20.59/20.87 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.59/20.87 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.59/20.87 a__U62(tt) -> tt 20.59/20.87 a__U62(X:S) -> U62(X:S) 20.59/20.87 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.59/20.87 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.59/20.87 a__U72(tt) -> tt 20.59/20.87 a__U72(X:S) -> U72(X:S) 20.59/20.87 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.87 a____(nil,X:S) -> mark(X:S) 20.59/20.87 a____(X:S,nil) -> mark(X:S) 20.59/20.87 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.59/20.87 a__and(tt,X:S) -> mark(X:S) 20.59/20.87 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.59/20.87 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.87 a__isList(nil) -> tt 20.59/20.87 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.59/20.87 a__isList(X:S) -> isList(X:S) 20.59/20.87 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.87 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.87 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.59/20.87 a__isNeList(X:S) -> isNeList(X:S) 20.59/20.87 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.87 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.59/20.87 a__isNePal(X:S) -> isNePal(X:S) 20.59/20.87 a__isPal(nil) -> tt 20.59/20.87 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.59/20.87 a__isPal(X:S) -> isPal(X:S) 20.59/20.87 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.87 a__isPalListKind(a) -> tt 20.59/20.87 a__isPalListKind(e) -> tt 20.59/20.87 a__isPalListKind(i) -> tt 20.59/20.87 a__isPalListKind(nil) -> tt 20.59/20.87 a__isPalListKind(o) -> tt 20.59/20.87 a__isPalListKind(u) -> tt 20.59/20.87 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.59/20.87 a__isQid(a) -> tt 20.59/20.87 a__isQid(e) -> tt 20.59/20.87 a__isQid(i) -> tt 20.59/20.87 a__isQid(o) -> tt 20.59/20.87 a__isQid(u) -> tt 20.59/20.87 a__isQid(X:S) -> isQid(X:S) 20.59/20.87 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.59/20.87 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.59/20.87 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.59/20.87 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.59/20.87 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.59/20.87 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.59/20.87 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.59/20.87 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.59/20.87 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.59/20.87 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.59/20.87 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.59/20.87 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.59/20.87 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.59/20.87 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.59/20.87 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.59/20.87 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.59/20.87 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.59/20.87 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.59/20.87 mark(a) -> a 20.59/20.87 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.59/20.87 mark(e) -> e 20.59/20.87 mark(i) -> i 20.59/20.87 mark(isList(X:S)) -> a__isList(X:S) 20.59/20.87 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.59/20.87 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.59/20.87 mark(isPal(X:S)) -> a__isPal(X:S) 20.59/20.87 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.59/20.87 mark(isQid(X:S)) -> a__isQid(X:S) 20.59/20.87 mark(nil) -> nil 20.59/20.87 mark(o) -> o 20.59/20.87 mark(tt) -> tt 20.59/20.87 mark(u) -> u 20.59/20.87 -> Usable rules: 20.59/20.87 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.59/20.87 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.59/20.87 a__U12(tt) -> tt 20.59/20.87 a__U12(X:S) -> U12(X:S) 20.59/20.87 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.59/20.87 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.59/20.87 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.59/20.87 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.59/20.87 a__U23(tt) -> tt 20.59/20.87 a__U23(X:S) -> U23(X:S) 20.59/20.87 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.59/20.87 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.59/20.87 a__U32(tt) -> tt 20.59/20.87 a__U32(X:S) -> U32(X:S) 20.59/20.87 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.59/20.87 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.59/20.87 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.59/20.87 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.59/20.87 a__U43(tt) -> tt 20.59/20.87 a__U43(X:S) -> U43(X:S) 20.59/20.87 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.59/20.87 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.59/20.87 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.59/20.87 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.59/20.87 a__U53(tt) -> tt 20.59/20.87 a__U53(X:S) -> U53(X:S) 20.59/20.87 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.59/20.87 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.59/20.87 a__U62(tt) -> tt 20.59/20.87 a__U62(X:S) -> U62(X:S) 20.59/20.87 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.59/20.87 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.59/20.87 a__U72(tt) -> tt 20.59/20.87 a__U72(X:S) -> U72(X:S) 20.59/20.87 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.87 a____(nil,X:S) -> mark(X:S) 20.59/20.87 a____(X:S,nil) -> mark(X:S) 20.59/20.87 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.59/20.87 a__and(tt,X:S) -> mark(X:S) 20.59/20.87 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.59/20.87 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.87 a__isList(nil) -> tt 20.59/20.87 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.59/20.87 a__isList(X:S) -> isList(X:S) 20.59/20.87 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.87 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.87 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.59/20.87 a__isNeList(X:S) -> isNeList(X:S) 20.59/20.87 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.87 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.59/20.87 a__isNePal(X:S) -> isNePal(X:S) 20.59/20.87 a__isPal(nil) -> tt 20.59/20.87 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.59/20.87 a__isPal(X:S) -> isPal(X:S) 20.59/20.87 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.87 a__isPalListKind(a) -> tt 20.59/20.87 a__isPalListKind(e) -> tt 20.59/20.87 a__isPalListKind(i) -> tt 20.59/20.87 a__isPalListKind(nil) -> tt 20.59/20.87 a__isPalListKind(o) -> tt 20.59/20.87 a__isPalListKind(u) -> tt 20.59/20.87 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.59/20.87 a__isQid(a) -> tt 20.59/20.87 a__isQid(e) -> tt 20.59/20.87 a__isQid(i) -> tt 20.59/20.87 a__isQid(o) -> tt 20.59/20.87 a__isQid(u) -> tt 20.59/20.87 a__isQid(X:S) -> isQid(X:S) 20.59/20.87 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.59/20.87 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.59/20.87 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.59/20.87 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.59/20.87 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.59/20.87 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.59/20.87 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.59/20.87 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.59/20.87 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.59/20.87 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.59/20.87 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.59/20.87 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.59/20.87 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.59/20.87 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.59/20.87 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.59/20.87 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.59/20.87 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.59/20.87 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.59/20.87 mark(a) -> a 20.59/20.87 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.59/20.87 mark(e) -> e 20.59/20.87 mark(i) -> i 20.59/20.87 mark(isList(X:S)) -> a__isList(X:S) 20.59/20.87 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.59/20.87 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.59/20.87 mark(isPal(X:S)) -> a__isPal(X:S) 20.59/20.87 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.59/20.87 mark(isQid(X:S)) -> a__isQid(X:S) 20.59/20.87 mark(nil) -> nil 20.59/20.87 mark(o) -> o 20.59/20.87 mark(tt) -> tt 20.59/20.87 mark(u) -> u 20.59/20.87 ->Interpretation type: 20.59/20.87 Linear 20.59/20.87 ->Coefficients: 20.59/20.87 Natural Numbers 20.59/20.87 ->Dimension: 20.59/20.87 1 20.59/20.87 ->Bound: 20.59/20.87 2 20.59/20.87 ->Interpretation: 20.59/20.87 20.59/20.87 [a__U11](X1,X2) = 2.X1 + 2.X2 + 1 20.59/20.87 [a__U12](X) = X 20.59/20.87 [a__U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.59/20.87 [a__U22](X1,X2) = X1 + 2.X2 + 1 20.59/20.87 [a__U23](X) = X 20.59/20.87 [a__U31](X1,X2) = 2.X1 + 1 20.59/20.87 [a__U32](X) = 2.X 20.59/20.87 [a__U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.59/20.87 [a__U42](X1,X2) = X1 + 2.X2 + 1 20.59/20.87 [a__U43](X) = X 20.59/20.87 [a__U51](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 20.59/20.87 [a__U52](X1,X2) = X1 + 2.X2 + 1 20.59/20.87 [a__U53](X) = X 20.59/20.87 [a__U61](X1,X2) = X1 + X2 + 2 20.59/20.87 [a__U62](X) = 2.X + 2 20.59/20.87 [a__U71](X1,X2) = 2.X1 + X2 + 2 20.59/20.87 [a__U72](X) = X 20.59/20.87 [a____](X1,X2) = X1 + X2 + 2 20.59/20.87 [a__and](X1,X2) = X1 + X2 20.59/20.87 [a__isList](X) = 2.X + 1 20.59/20.87 [a__isNeList](X) = 2.X + 1 20.59/20.87 [a__isNePal](X) = X + 2 20.59/20.87 [a__isPal](X) = X + 2 20.59/20.87 [a__isPalListKind](X) = 0 20.59/20.87 [a__isQid](X) = 0 20.59/20.87 [mark](X) = X 20.59/20.87 [U11](X1,X2) = 2.X1 + 2.X2 + 1 20.59/20.87 [U12](X) = X 20.59/20.87 [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.59/20.87 [U22](X1,X2) = X1 + 2.X2 + 1 20.59/20.87 [U23](X) = X 20.59/20.87 [U31](X1,X2) = 2.X1 + 1 20.59/20.87 [U32](X) = 2.X 20.59/20.87 [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.59/20.87 [U42](X1,X2) = X1 + 2.X2 + 1 20.59/20.87 [U43](X) = X 20.59/20.87 [U51](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 20.59/20.87 [U52](X1,X2) = X1 + 2.X2 + 1 20.59/20.87 [U53](X) = X 20.59/20.87 [U61](X1,X2) = X1 + X2 + 2 20.59/20.87 [U62](X) = 2.X + 2 20.59/20.87 [U71](X1,X2) = 2.X1 + X2 + 2 20.59/20.87 [U72](X) = X 20.59/20.87 [__](X1,X2) = X1 + X2 + 2 20.59/20.87 [a] = 2 20.59/20.87 [and](X1,X2) = X1 + X2 20.59/20.87 [e] = 1 20.59/20.87 [fSNonEmpty] = 0 20.59/20.87 [i] = 0 20.59/20.87 [isList](X) = 2.X + 1 20.59/20.87 [isNeList](X) = 2.X + 1 20.59/20.87 [isNePal](X) = X + 2 20.59/20.87 [isPal](X) = X + 2 20.59/20.87 [isPalListKind](X) = 0 20.59/20.87 [isQid](X) = 0 20.59/20.87 [nil] = 2 20.59/20.87 [o] = 2 20.59/20.87 [tt] = 0 20.59/20.87 [u] = 0 20.59/20.87 [A__U11](X1,X2) = 0 20.59/20.87 [A__U12](X) = 0 20.59/20.87 [A__U21](X1,X2,X3) = 0 20.59/20.87 [A__U22](X1,X2) = 0 20.59/20.87 [A__U23](X) = 0 20.59/20.87 [A__U31](X1,X2) = 0 20.59/20.87 [A__U32](X) = 0 20.59/20.87 [A__U41](X1,X2,X3) = 0 20.59/20.87 [A__U42](X1,X2) = 0 20.59/20.87 [A__U43](X) = 0 20.59/20.87 [A__U51](X1,X2,X3) = 0 20.59/20.87 [A__U52](X1,X2) = 0 20.59/20.87 [A__U53](X) = 0 20.59/20.87 [A__U61](X1,X2) = 0 20.59/20.87 [A__U62](X) = 0 20.59/20.87 [A__U71](X1,X2) = X1 + 2.X2 + 2 20.59/20.87 [A__U72](X) = 0 20.59/20.87 [A____](X1,X2) = 2.X1 + 2.X2 + 1 20.59/20.87 [A__AND](X1,X2) = 2.X1 + 2.X2 + 1 20.59/20.87 [A__ISLIST](X) = 2 20.59/20.87 [A__ISNELIST](X) = 2.X + 2 20.59/20.87 [A__ISNEPAL](X) = 2.X + 1 20.59/20.87 [A__ISPAL](X) = 2.X + 2 20.59/20.87 [A__ISPALLISTKIND](X) = 1 20.59/20.87 [A__ISQID](X) = 0 20.59/20.87 [MARK](X) = 2.X + 1 20.59/20.87 20.59/20.87 Problem 1: 20.59/20.87 20.59/20.87 SCC Processor: 20.59/20.87 -> Pairs: 20.59/20.87 A____(__(X:S,Y:S),Z:S) -> A____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.87 A____(__(X:S,Y:S),Z:S) -> A____(mark(Y:S),mark(Z:S)) 20.59/20.87 A____(__(X:S,Y:S),Z:S) -> MARK(X:S) 20.59/20.87 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S) 20.59/20.87 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 20.59/20.87 A____(nil,X:S) -> MARK(X:S) 20.59/20.87 A____(X:S,nil) -> MARK(X:S) 20.59/20.87 A__AND(tt,X:S) -> MARK(X:S) 20.59/20.87 A__ISLIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.87 A__ISLIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.87 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.87 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.87 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.87 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.87 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.87 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.59/20.87 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.87 A__ISPAL(V:S) -> A__U71(a__isPalListKind(V:S),V:S) 20.59/20.87 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.87 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.87 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.87 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U12(X:S)) -> MARK(X:S) 20.59/20.87 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.87 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U23(X:S)) -> MARK(X:S) 20.59/20.87 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U32(X:S)) -> MARK(X:S) 20.59/20.87 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.87 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U43(X:S)) -> MARK(X:S) 20.59/20.87 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.87 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U53(X:S)) -> MARK(X:S) 20.59/20.87 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U62(X:S)) -> MARK(X:S) 20.59/20.87 MARK(U71(X1:S,X2:S)) -> A__U71(mark(X1:S),X2:S) 20.59/20.87 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(U72(X:S)) -> MARK(X:S) 20.59/20.87 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 20.59/20.87 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.59/20.87 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.59/20.87 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.87 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.59/20.87 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.59/20.87 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.59/20.87 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.59/20.87 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.59/20.87 -> Rules: 20.59/20.87 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.59/20.87 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.59/20.87 a__U12(tt) -> tt 20.59/20.87 a__U12(X:S) -> U12(X:S) 20.59/20.87 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.59/20.87 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.59/20.87 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.59/20.87 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.59/20.87 a__U23(tt) -> tt 20.59/20.87 a__U23(X:S) -> U23(X:S) 20.59/20.87 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.59/20.87 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.59/20.87 a__U32(tt) -> tt 20.59/20.87 a__U32(X:S) -> U32(X:S) 20.59/20.87 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.59/20.88 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.59/20.88 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.59/20.88 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.59/20.88 a__U43(tt) -> tt 20.59/20.88 a__U43(X:S) -> U43(X:S) 20.59/20.88 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.59/20.88 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.59/20.88 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.59/20.88 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.59/20.88 a__U53(tt) -> tt 20.59/20.88 a__U53(X:S) -> U53(X:S) 20.59/20.88 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.59/20.88 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.59/20.88 a__U62(tt) -> tt 20.59/20.88 a__U62(X:S) -> U62(X:S) 20.59/20.88 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.59/20.88 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.59/20.88 a__U72(tt) -> tt 20.59/20.88 a__U72(X:S) -> U72(X:S) 20.59/20.88 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.88 a____(nil,X:S) -> mark(X:S) 20.59/20.88 a____(X:S,nil) -> mark(X:S) 20.59/20.88 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.59/20.88 a__and(tt,X:S) -> mark(X:S) 20.59/20.88 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.59/20.88 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.88 a__isList(nil) -> tt 20.59/20.88 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.59/20.88 a__isList(X:S) -> isList(X:S) 20.59/20.88 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.88 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.88 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.59/20.88 a__isNeList(X:S) -> isNeList(X:S) 20.59/20.88 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.88 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.59/20.88 a__isNePal(X:S) -> isNePal(X:S) 20.59/20.88 a__isPal(nil) -> tt 20.59/20.88 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.59/20.88 a__isPal(X:S) -> isPal(X:S) 20.59/20.88 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.88 a__isPalListKind(a) -> tt 20.59/20.88 a__isPalListKind(e) -> tt 20.59/20.88 a__isPalListKind(i) -> tt 20.59/20.88 a__isPalListKind(nil) -> tt 20.59/20.88 a__isPalListKind(o) -> tt 20.59/20.88 a__isPalListKind(u) -> tt 20.59/20.88 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.59/20.88 a__isQid(a) -> tt 20.59/20.88 a__isQid(e) -> tt 20.59/20.88 a__isQid(i) -> tt 20.59/20.88 a__isQid(o) -> tt 20.59/20.88 a__isQid(u) -> tt 20.59/20.88 a__isQid(X:S) -> isQid(X:S) 20.59/20.88 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.59/20.88 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.59/20.88 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.59/20.88 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.59/20.88 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.59/20.88 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.59/20.88 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.59/20.88 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.59/20.88 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.59/20.88 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.59/20.88 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.59/20.88 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.59/20.88 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.59/20.88 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.59/20.88 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.59/20.88 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.59/20.88 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.59/20.88 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.59/20.88 mark(a) -> a 20.59/20.88 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.59/20.88 mark(e) -> e 20.59/20.88 mark(i) -> i 20.59/20.88 mark(isList(X:S)) -> a__isList(X:S) 20.59/20.88 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.59/20.88 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.59/20.88 mark(isPal(X:S)) -> a__isPal(X:S) 20.59/20.88 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.59/20.88 mark(isQid(X:S)) -> a__isQid(X:S) 20.59/20.88 mark(nil) -> nil 20.59/20.88 mark(o) -> o 20.59/20.88 mark(tt) -> tt 20.59/20.88 mark(u) -> u 20.59/20.88 ->Strongly Connected Components: 20.59/20.88 ->->Cycle: 20.59/20.88 ->->-> Pairs: 20.59/20.88 A____(__(X:S,Y:S),Z:S) -> A____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.88 A____(__(X:S,Y:S),Z:S) -> A____(mark(Y:S),mark(Z:S)) 20.59/20.88 A____(__(X:S,Y:S),Z:S) -> MARK(X:S) 20.59/20.88 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S) 20.59/20.88 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 20.59/20.88 A____(nil,X:S) -> MARK(X:S) 20.59/20.88 A____(X:S,nil) -> MARK(X:S) 20.59/20.88 A__AND(tt,X:S) -> MARK(X:S) 20.59/20.88 A__ISLIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.88 A__ISLIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.88 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.88 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.88 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.88 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.88 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.88 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.59/20.88 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.88 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.88 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.88 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.88 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U12(X:S)) -> MARK(X:S) 20.59/20.88 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.88 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U23(X:S)) -> MARK(X:S) 20.59/20.88 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U32(X:S)) -> MARK(X:S) 20.59/20.88 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.88 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U43(X:S)) -> MARK(X:S) 20.59/20.88 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.88 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U53(X:S)) -> MARK(X:S) 20.59/20.88 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U62(X:S)) -> MARK(X:S) 20.59/20.88 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U72(X:S)) -> MARK(X:S) 20.59/20.88 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 20.59/20.88 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.59/20.88 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.59/20.88 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.59/20.88 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.59/20.88 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.59/20.88 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.59/20.88 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.59/20.88 ->->-> Rules: 20.59/20.88 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.59/20.88 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.59/20.88 a__U12(tt) -> tt 20.59/20.88 a__U12(X:S) -> U12(X:S) 20.59/20.88 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.59/20.88 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.59/20.88 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.59/20.88 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.59/20.88 a__U23(tt) -> tt 20.59/20.88 a__U23(X:S) -> U23(X:S) 20.59/20.88 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.59/20.88 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.59/20.88 a__U32(tt) -> tt 20.59/20.88 a__U32(X:S) -> U32(X:S) 20.59/20.88 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.59/20.88 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.59/20.88 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.59/20.88 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.59/20.88 a__U43(tt) -> tt 20.59/20.88 a__U43(X:S) -> U43(X:S) 20.59/20.88 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.59/20.88 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.59/20.88 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.59/20.88 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.59/20.88 a__U53(tt) -> tt 20.59/20.88 a__U53(X:S) -> U53(X:S) 20.59/20.88 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.59/20.88 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.59/20.88 a__U62(tt) -> tt 20.59/20.88 a__U62(X:S) -> U62(X:S) 20.59/20.88 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.59/20.88 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.59/20.88 a__U72(tt) -> tt 20.59/20.88 a__U72(X:S) -> U72(X:S) 20.59/20.88 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.88 a____(nil,X:S) -> mark(X:S) 20.59/20.88 a____(X:S,nil) -> mark(X:S) 20.59/20.88 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.59/20.88 a__and(tt,X:S) -> mark(X:S) 20.59/20.88 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.59/20.88 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.88 a__isList(nil) -> tt 20.59/20.88 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.59/20.88 a__isList(X:S) -> isList(X:S) 20.59/20.88 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.88 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.88 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.59/20.88 a__isNeList(X:S) -> isNeList(X:S) 20.59/20.88 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.88 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.59/20.88 a__isNePal(X:S) -> isNePal(X:S) 20.59/20.88 a__isPal(nil) -> tt 20.59/20.88 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.59/20.88 a__isPal(X:S) -> isPal(X:S) 20.59/20.88 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.88 a__isPalListKind(a) -> tt 20.59/20.88 a__isPalListKind(e) -> tt 20.59/20.88 a__isPalListKind(i) -> tt 20.59/20.88 a__isPalListKind(nil) -> tt 20.59/20.88 a__isPalListKind(o) -> tt 20.59/20.88 a__isPalListKind(u) -> tt 20.59/20.88 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.59/20.88 a__isQid(a) -> tt 20.59/20.88 a__isQid(e) -> tt 20.59/20.88 a__isQid(i) -> tt 20.59/20.88 a__isQid(o) -> tt 20.59/20.88 a__isQid(u) -> tt 20.59/20.88 a__isQid(X:S) -> isQid(X:S) 20.59/20.88 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.59/20.88 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.59/20.88 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.59/20.88 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.59/20.88 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.59/20.88 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.59/20.88 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.59/20.88 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.59/20.88 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.59/20.88 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.59/20.88 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.59/20.88 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.59/20.88 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.59/20.88 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.59/20.88 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.59/20.88 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.59/20.88 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.59/20.88 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.59/20.88 mark(a) -> a 20.59/20.88 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.59/20.88 mark(e) -> e 20.59/20.88 mark(i) -> i 20.59/20.88 mark(isList(X:S)) -> a__isList(X:S) 20.59/20.88 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.59/20.88 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.59/20.88 mark(isPal(X:S)) -> a__isPal(X:S) 20.59/20.88 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.59/20.88 mark(isQid(X:S)) -> a__isQid(X:S) 20.59/20.88 mark(nil) -> nil 20.59/20.88 mark(o) -> o 20.59/20.88 mark(tt) -> tt 20.59/20.88 mark(u) -> u 20.59/20.88 20.59/20.88 Problem 1: 20.59/20.88 20.59/20.88 Reduction Pairs Processor: 20.59/20.88 -> Pairs: 20.59/20.88 A____(__(X:S,Y:S),Z:S) -> A____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.88 A____(__(X:S,Y:S),Z:S) -> A____(mark(Y:S),mark(Z:S)) 20.59/20.88 A____(__(X:S,Y:S),Z:S) -> MARK(X:S) 20.59/20.88 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S) 20.59/20.88 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 20.59/20.88 A____(nil,X:S) -> MARK(X:S) 20.59/20.88 A____(X:S,nil) -> MARK(X:S) 20.59/20.88 A__AND(tt,X:S) -> MARK(X:S) 20.59/20.88 A__ISLIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.88 A__ISLIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.88 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.88 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.88 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.88 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.88 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.88 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.59/20.88 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.88 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.88 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.88 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.88 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U12(X:S)) -> MARK(X:S) 20.59/20.88 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.88 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U23(X:S)) -> MARK(X:S) 20.59/20.88 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U32(X:S)) -> MARK(X:S) 20.59/20.88 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.88 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U43(X:S)) -> MARK(X:S) 20.59/20.88 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.88 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U53(X:S)) -> MARK(X:S) 20.59/20.88 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U62(X:S)) -> MARK(X:S) 20.59/20.88 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U72(X:S)) -> MARK(X:S) 20.59/20.88 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 20.59/20.88 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.59/20.88 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.59/20.88 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.59/20.88 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.59/20.88 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.59/20.88 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.59/20.88 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.59/20.88 -> Rules: 20.59/20.88 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.59/20.88 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.59/20.88 a__U12(tt) -> tt 20.59/20.88 a__U12(X:S) -> U12(X:S) 20.59/20.88 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.59/20.88 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.59/20.88 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.59/20.88 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.59/20.88 a__U23(tt) -> tt 20.59/20.88 a__U23(X:S) -> U23(X:S) 20.59/20.88 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.59/20.88 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.59/20.88 a__U32(tt) -> tt 20.59/20.88 a__U32(X:S) -> U32(X:S) 20.59/20.88 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.59/20.88 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.59/20.88 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.59/20.88 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.59/20.88 a__U43(tt) -> tt 20.59/20.88 a__U43(X:S) -> U43(X:S) 20.59/20.88 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.59/20.88 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.59/20.88 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.59/20.88 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.59/20.88 a__U53(tt) -> tt 20.59/20.88 a__U53(X:S) -> U53(X:S) 20.59/20.88 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.59/20.88 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.59/20.88 a__U62(tt) -> tt 20.59/20.88 a__U62(X:S) -> U62(X:S) 20.59/20.88 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.59/20.88 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.59/20.88 a__U72(tt) -> tt 20.59/20.88 a__U72(X:S) -> U72(X:S) 20.59/20.88 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.88 a____(nil,X:S) -> mark(X:S) 20.59/20.88 a____(X:S,nil) -> mark(X:S) 20.59/20.88 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.59/20.88 a__and(tt,X:S) -> mark(X:S) 20.59/20.88 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.59/20.88 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.88 a__isList(nil) -> tt 20.59/20.88 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.59/20.88 a__isList(X:S) -> isList(X:S) 20.59/20.88 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.88 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.88 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.59/20.88 a__isNeList(X:S) -> isNeList(X:S) 20.59/20.88 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.88 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.59/20.88 a__isNePal(X:S) -> isNePal(X:S) 20.59/20.88 a__isPal(nil) -> tt 20.59/20.88 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.59/20.88 a__isPal(X:S) -> isPal(X:S) 20.59/20.88 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.88 a__isPalListKind(a) -> tt 20.59/20.88 a__isPalListKind(e) -> tt 20.59/20.88 a__isPalListKind(i) -> tt 20.59/20.88 a__isPalListKind(nil) -> tt 20.59/20.88 a__isPalListKind(o) -> tt 20.59/20.88 a__isPalListKind(u) -> tt 20.59/20.88 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.59/20.88 a__isQid(a) -> tt 20.59/20.88 a__isQid(e) -> tt 20.59/20.88 a__isQid(i) -> tt 20.59/20.88 a__isQid(o) -> tt 20.59/20.88 a__isQid(u) -> tt 20.59/20.88 a__isQid(X:S) -> isQid(X:S) 20.59/20.88 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.59/20.88 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.59/20.88 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.59/20.88 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.59/20.88 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.59/20.88 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.59/20.88 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.59/20.88 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.59/20.88 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.59/20.88 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.59/20.88 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.59/20.88 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.59/20.88 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.59/20.88 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.59/20.88 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.59/20.88 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.59/20.88 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.59/20.88 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.59/20.88 mark(a) -> a 20.59/20.88 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.59/20.88 mark(e) -> e 20.59/20.88 mark(i) -> i 20.59/20.88 mark(isList(X:S)) -> a__isList(X:S) 20.59/20.88 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.59/20.88 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.59/20.88 mark(isPal(X:S)) -> a__isPal(X:S) 20.59/20.88 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.59/20.88 mark(isQid(X:S)) -> a__isQid(X:S) 20.59/20.88 mark(nil) -> nil 20.59/20.88 mark(o) -> o 20.59/20.88 mark(tt) -> tt 20.59/20.88 mark(u) -> u 20.59/20.88 -> Usable rules: 20.59/20.88 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.59/20.88 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.59/20.88 a__U12(tt) -> tt 20.59/20.88 a__U12(X:S) -> U12(X:S) 20.59/20.88 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.59/20.88 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.59/20.88 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.59/20.88 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.59/20.88 a__U23(tt) -> tt 20.59/20.88 a__U23(X:S) -> U23(X:S) 20.59/20.88 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.59/20.88 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.59/20.88 a__U32(tt) -> tt 20.59/20.88 a__U32(X:S) -> U32(X:S) 20.59/20.88 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.59/20.88 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.59/20.88 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.59/20.88 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.59/20.88 a__U43(tt) -> tt 20.59/20.88 a__U43(X:S) -> U43(X:S) 20.59/20.88 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.59/20.88 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.59/20.88 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.59/20.88 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.59/20.88 a__U53(tt) -> tt 20.59/20.88 a__U53(X:S) -> U53(X:S) 20.59/20.88 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.59/20.88 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.59/20.88 a__U62(tt) -> tt 20.59/20.88 a__U62(X:S) -> U62(X:S) 20.59/20.88 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.59/20.88 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.59/20.88 a__U72(tt) -> tt 20.59/20.88 a__U72(X:S) -> U72(X:S) 20.59/20.88 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.88 a____(nil,X:S) -> mark(X:S) 20.59/20.88 a____(X:S,nil) -> mark(X:S) 20.59/20.88 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.59/20.88 a__and(tt,X:S) -> mark(X:S) 20.59/20.88 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.59/20.88 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.88 a__isList(nil) -> tt 20.59/20.88 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.59/20.88 a__isList(X:S) -> isList(X:S) 20.59/20.88 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.88 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.88 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.59/20.88 a__isNeList(X:S) -> isNeList(X:S) 20.59/20.88 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.88 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.59/20.88 a__isNePal(X:S) -> isNePal(X:S) 20.59/20.88 a__isPal(nil) -> tt 20.59/20.88 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.59/20.88 a__isPal(X:S) -> isPal(X:S) 20.59/20.88 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.88 a__isPalListKind(a) -> tt 20.59/20.88 a__isPalListKind(e) -> tt 20.59/20.88 a__isPalListKind(i) -> tt 20.59/20.88 a__isPalListKind(nil) -> tt 20.59/20.88 a__isPalListKind(o) -> tt 20.59/20.88 a__isPalListKind(u) -> tt 20.59/20.88 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.59/20.88 a__isQid(a) -> tt 20.59/20.88 a__isQid(e) -> tt 20.59/20.88 a__isQid(i) -> tt 20.59/20.88 a__isQid(o) -> tt 20.59/20.88 a__isQid(u) -> tt 20.59/20.88 a__isQid(X:S) -> isQid(X:S) 20.59/20.88 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.59/20.88 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.59/20.88 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.59/20.88 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.59/20.88 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.59/20.88 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.59/20.88 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.59/20.88 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.59/20.88 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.59/20.88 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.59/20.88 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.59/20.88 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.59/20.88 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.59/20.88 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.59/20.88 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.59/20.88 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.59/20.88 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.59/20.88 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.59/20.88 mark(a) -> a 20.59/20.88 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.59/20.88 mark(e) -> e 20.59/20.88 mark(i) -> i 20.59/20.88 mark(isList(X:S)) -> a__isList(X:S) 20.59/20.88 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.59/20.88 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.59/20.88 mark(isPal(X:S)) -> a__isPal(X:S) 20.59/20.88 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.59/20.88 mark(isQid(X:S)) -> a__isQid(X:S) 20.59/20.88 mark(nil) -> nil 20.59/20.88 mark(o) -> o 20.59/20.88 mark(tt) -> tt 20.59/20.88 mark(u) -> u 20.59/20.88 ->Interpretation type: 20.59/20.88 Linear 20.59/20.88 ->Coefficients: 20.59/20.88 Natural Numbers 20.59/20.88 ->Dimension: 20.59/20.88 1 20.59/20.88 ->Bound: 20.59/20.88 2 20.59/20.88 ->Interpretation: 20.59/20.88 20.59/20.88 [a__U11](X1,X2) = 2.X1 20.59/20.88 [a__U12](X) = 2.X 20.59/20.88 [a__U21](X1,X2,X3) = 2.X1 20.59/20.88 [a__U22](X1,X2) = 2.X1 20.59/20.88 [a__U23](X) = 2.X 20.59/20.88 [a__U31](X1,X2) = 2.X1 20.59/20.88 [a__U32](X) = 2.X 20.59/20.88 [a__U41](X1,X2,X3) = 2.X1 20.59/20.88 [a__U42](X1,X2) = 2.X1 20.59/20.88 [a__U43](X) = 2.X 20.59/20.88 [a__U51](X1,X2,X3) = 2.X1 20.59/20.88 [a__U52](X1,X2) = X1 20.59/20.88 [a__U53](X) = X 20.59/20.88 [a__U61](X1,X2) = X1 + 2.X2 + 1 20.59/20.88 [a__U62](X) = X + 1 20.59/20.88 [a__U71](X1,X2) = 2.X1 + 2.X2 + 2 20.59/20.88 [a__U72](X) = X 20.59/20.88 [a____](X1,X2) = 2.X1 + X2 + 2 20.59/20.88 [a__and](X1,X2) = 2.X1 + X2 20.59/20.88 [a__isList](X) = 0 20.59/20.88 [a__isNeList](X) = 0 20.59/20.88 [a__isNePal](X) = 2.X + 2 20.59/20.88 [a__isPal](X) = 2.X + 2 20.59/20.88 [a__isPalListKind](X) = 0 20.59/20.88 [a__isQid](X) = 0 20.59/20.88 [mark](X) = X 20.59/20.88 [U11](X1,X2) = 2.X1 20.59/20.88 [U12](X) = 2.X 20.59/20.88 [U21](X1,X2,X3) = 2.X1 20.59/20.88 [U22](X1,X2) = 2.X1 20.59/20.88 [U23](X) = 2.X 20.59/20.88 [U31](X1,X2) = 2.X1 20.59/20.88 [U32](X) = 2.X 20.59/20.88 [U41](X1,X2,X3) = 2.X1 20.59/20.88 [U42](X1,X2) = 2.X1 20.59/20.88 [U43](X) = 2.X 20.59/20.88 [U51](X1,X2,X3) = 2.X1 20.59/20.88 [U52](X1,X2) = X1 20.59/20.88 [U53](X) = X 20.59/20.88 [U61](X1,X2) = X1 + 2.X2 + 1 20.59/20.88 [U62](X) = X + 1 20.59/20.88 [U71](X1,X2) = 2.X1 + 2.X2 + 2 20.59/20.88 [U72](X) = X 20.59/20.88 [__](X1,X2) = 2.X1 + X2 + 2 20.59/20.88 [a] = 0 20.59/20.88 [and](X1,X2) = 2.X1 + X2 20.59/20.88 [e] = 1 20.59/20.88 [fSNonEmpty] = 0 20.59/20.88 [i] = 0 20.59/20.88 [isList](X) = 0 20.59/20.88 [isNeList](X) = 0 20.59/20.88 [isNePal](X) = 2.X + 2 20.59/20.88 [isPal](X) = 2.X + 2 20.59/20.88 [isPalListKind](X) = 0 20.59/20.88 [isQid](X) = 0 20.59/20.88 [nil] = 2 20.59/20.88 [o] = 2 20.59/20.88 [tt] = 0 20.59/20.88 [u] = 2 20.59/20.88 [A__U11](X1,X2) = 0 20.59/20.88 [A__U12](X) = 0 20.59/20.88 [A__U21](X1,X2,X3) = 0 20.59/20.88 [A__U22](X1,X2) = 0 20.59/20.88 [A__U23](X) = 0 20.59/20.88 [A__U31](X1,X2) = 0 20.59/20.88 [A__U32](X) = 0 20.59/20.88 [A__U41](X1,X2,X3) = 0 20.59/20.88 [A__U42](X1,X2) = 0 20.59/20.88 [A__U43](X) = 0 20.59/20.88 [A__U51](X1,X2,X3) = 0 20.59/20.88 [A__U52](X1,X2) = 0 20.59/20.88 [A__U53](X) = 0 20.59/20.88 [A__U61](X1,X2) = 0 20.59/20.88 [A__U62](X) = 0 20.59/20.88 [A__U71](X1,X2) = 0 20.59/20.88 [A__U72](X) = 0 20.59/20.88 [A____](X1,X2) = 2.X1 + X2 20.59/20.88 [A__AND](X1,X2) = 2.X1 + X2 + 2 20.59/20.88 [A__ISLIST](X) = 2 20.59/20.88 [A__ISNELIST](X) = 2 20.59/20.88 [A__ISNEPAL](X) = 2.X + 2 20.59/20.88 [A__ISPAL](X) = X + 2 20.59/20.88 [A__ISPALLISTKIND](X) = 2 20.59/20.88 [A__ISQID](X) = 0 20.59/20.88 [MARK](X) = X + 2 20.59/20.88 20.59/20.88 Problem 1: 20.59/20.88 20.59/20.88 SCC Processor: 20.59/20.88 -> Pairs: 20.59/20.88 A____(__(X:S,Y:S),Z:S) -> A____(mark(Y:S),mark(Z:S)) 20.59/20.88 A____(__(X:S,Y:S),Z:S) -> MARK(X:S) 20.59/20.88 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S) 20.59/20.88 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 20.59/20.88 A____(nil,X:S) -> MARK(X:S) 20.59/20.88 A____(X:S,nil) -> MARK(X:S) 20.59/20.88 A__AND(tt,X:S) -> MARK(X:S) 20.59/20.88 A__ISLIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.88 A__ISLIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.88 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.88 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.88 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.88 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.88 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.88 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.59/20.88 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.88 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.88 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.88 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.88 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U12(X:S)) -> MARK(X:S) 20.59/20.88 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.88 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U23(X:S)) -> MARK(X:S) 20.59/20.88 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U32(X:S)) -> MARK(X:S) 20.59/20.88 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.88 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U43(X:S)) -> MARK(X:S) 20.59/20.88 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.88 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U53(X:S)) -> MARK(X:S) 20.59/20.88 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U62(X:S)) -> MARK(X:S) 20.59/20.88 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U72(X:S)) -> MARK(X:S) 20.59/20.88 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 20.59/20.88 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.59/20.88 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.59/20.88 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.59/20.88 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.59/20.88 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.59/20.88 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.59/20.88 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.59/20.88 -> Rules: 20.59/20.88 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.59/20.88 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.59/20.88 a__U12(tt) -> tt 20.59/20.88 a__U12(X:S) -> U12(X:S) 20.59/20.88 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.59/20.88 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.59/20.88 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.59/20.88 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.59/20.88 a__U23(tt) -> tt 20.59/20.88 a__U23(X:S) -> U23(X:S) 20.59/20.88 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.59/20.88 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.59/20.88 a__U32(tt) -> tt 20.59/20.88 a__U32(X:S) -> U32(X:S) 20.59/20.88 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.59/20.88 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.59/20.88 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.59/20.88 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.59/20.88 a__U43(tt) -> tt 20.59/20.88 a__U43(X:S) -> U43(X:S) 20.59/20.88 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.59/20.88 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.59/20.88 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.59/20.88 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.59/20.88 a__U53(tt) -> tt 20.59/20.88 a__U53(X:S) -> U53(X:S) 20.59/20.88 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.59/20.88 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.59/20.88 a__U62(tt) -> tt 20.59/20.88 a__U62(X:S) -> U62(X:S) 20.59/20.88 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.59/20.88 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.59/20.88 a__U72(tt) -> tt 20.59/20.88 a__U72(X:S) -> U72(X:S) 20.59/20.88 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.88 a____(nil,X:S) -> mark(X:S) 20.59/20.88 a____(X:S,nil) -> mark(X:S) 20.59/20.88 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.59/20.88 a__and(tt,X:S) -> mark(X:S) 20.59/20.88 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.59/20.88 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.88 a__isList(nil) -> tt 20.59/20.88 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.59/20.88 a__isList(X:S) -> isList(X:S) 20.59/20.88 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.88 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.88 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.59/20.88 a__isNeList(X:S) -> isNeList(X:S) 20.59/20.88 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.88 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.59/20.88 a__isNePal(X:S) -> isNePal(X:S) 20.59/20.88 a__isPal(nil) -> tt 20.59/20.88 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.59/20.88 a__isPal(X:S) -> isPal(X:S) 20.59/20.88 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.88 a__isPalListKind(a) -> tt 20.59/20.88 a__isPalListKind(e) -> tt 20.59/20.88 a__isPalListKind(i) -> tt 20.59/20.88 a__isPalListKind(nil) -> tt 20.59/20.88 a__isPalListKind(o) -> tt 20.59/20.88 a__isPalListKind(u) -> tt 20.59/20.88 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.59/20.88 a__isQid(a) -> tt 20.59/20.88 a__isQid(e) -> tt 20.59/20.88 a__isQid(i) -> tt 20.59/20.88 a__isQid(o) -> tt 20.59/20.88 a__isQid(u) -> tt 20.59/20.88 a__isQid(X:S) -> isQid(X:S) 20.59/20.88 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.59/20.88 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.59/20.88 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.59/20.88 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.59/20.88 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.59/20.88 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.59/20.88 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.59/20.88 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.59/20.88 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.59/20.88 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.59/20.88 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.59/20.88 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.59/20.88 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.59/20.88 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.59/20.88 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.59/20.88 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.59/20.88 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.59/20.88 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.59/20.88 mark(a) -> a 20.59/20.88 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.59/20.88 mark(e) -> e 20.59/20.88 mark(i) -> i 20.59/20.88 mark(isList(X:S)) -> a__isList(X:S) 20.59/20.88 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.59/20.88 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.59/20.88 mark(isPal(X:S)) -> a__isPal(X:S) 20.59/20.88 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.59/20.88 mark(isQid(X:S)) -> a__isQid(X:S) 20.59/20.88 mark(nil) -> nil 20.59/20.88 mark(o) -> o 20.59/20.88 mark(tt) -> tt 20.59/20.88 mark(u) -> u 20.59/20.88 ->Strongly Connected Components: 20.59/20.88 ->->Cycle: 20.59/20.88 ->->-> Pairs: 20.59/20.88 A____(__(X:S,Y:S),Z:S) -> A____(mark(Y:S),mark(Z:S)) 20.59/20.88 A____(__(X:S,Y:S),Z:S) -> MARK(X:S) 20.59/20.88 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S) 20.59/20.88 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 20.59/20.88 A____(nil,X:S) -> MARK(X:S) 20.59/20.88 A____(X:S,nil) -> MARK(X:S) 20.59/20.88 A__AND(tt,X:S) -> MARK(X:S) 20.59/20.88 A__ISLIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.88 A__ISLIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.88 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.88 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.88 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.88 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.88 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.88 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.59/20.88 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.88 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.88 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.88 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.88 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U12(X:S)) -> MARK(X:S) 20.59/20.88 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.88 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U23(X:S)) -> MARK(X:S) 20.59/20.88 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U32(X:S)) -> MARK(X:S) 20.59/20.88 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.88 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U43(X:S)) -> MARK(X:S) 20.59/20.88 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.88 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U53(X:S)) -> MARK(X:S) 20.59/20.88 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U62(X:S)) -> MARK(X:S) 20.59/20.88 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U72(X:S)) -> MARK(X:S) 20.59/20.88 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 20.59/20.88 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.59/20.88 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.59/20.88 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.59/20.88 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.59/20.88 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.59/20.88 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.59/20.88 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.59/20.88 ->->-> Rules: 20.59/20.88 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.59/20.88 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.59/20.88 a__U12(tt) -> tt 20.59/20.88 a__U12(X:S) -> U12(X:S) 20.59/20.88 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.59/20.88 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.59/20.88 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.59/20.88 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.59/20.88 a__U23(tt) -> tt 20.59/20.88 a__U23(X:S) -> U23(X:S) 20.59/20.88 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.59/20.88 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.59/20.88 a__U32(tt) -> tt 20.59/20.88 a__U32(X:S) -> U32(X:S) 20.59/20.88 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.59/20.88 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.59/20.88 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.59/20.88 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.59/20.88 a__U43(tt) -> tt 20.59/20.88 a__U43(X:S) -> U43(X:S) 20.59/20.88 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.59/20.88 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.59/20.88 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.59/20.88 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.59/20.88 a__U53(tt) -> tt 20.59/20.88 a__U53(X:S) -> U53(X:S) 20.59/20.88 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.59/20.88 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.59/20.88 a__U62(tt) -> tt 20.59/20.88 a__U62(X:S) -> U62(X:S) 20.59/20.88 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.59/20.88 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.59/20.88 a__U72(tt) -> tt 20.59/20.88 a__U72(X:S) -> U72(X:S) 20.59/20.88 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.88 a____(nil,X:S) -> mark(X:S) 20.59/20.88 a____(X:S,nil) -> mark(X:S) 20.59/20.88 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.59/20.88 a__and(tt,X:S) -> mark(X:S) 20.59/20.88 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.59/20.88 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.88 a__isList(nil) -> tt 20.59/20.88 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.59/20.88 a__isList(X:S) -> isList(X:S) 20.59/20.88 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.88 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.88 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.59/20.88 a__isNeList(X:S) -> isNeList(X:S) 20.59/20.88 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.88 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.59/20.88 a__isNePal(X:S) -> isNePal(X:S) 20.59/20.88 a__isPal(nil) -> tt 20.59/20.88 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.59/20.88 a__isPal(X:S) -> isPal(X:S) 20.59/20.88 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.88 a__isPalListKind(a) -> tt 20.59/20.88 a__isPalListKind(e) -> tt 20.59/20.88 a__isPalListKind(i) -> tt 20.59/20.88 a__isPalListKind(nil) -> tt 20.59/20.88 a__isPalListKind(o) -> tt 20.59/20.88 a__isPalListKind(u) -> tt 20.59/20.88 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.59/20.88 a__isQid(a) -> tt 20.59/20.88 a__isQid(e) -> tt 20.59/20.88 a__isQid(i) -> tt 20.59/20.88 a__isQid(o) -> tt 20.59/20.88 a__isQid(u) -> tt 20.59/20.88 a__isQid(X:S) -> isQid(X:S) 20.59/20.88 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.59/20.88 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.59/20.88 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.59/20.88 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.59/20.88 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.59/20.88 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.59/20.88 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.59/20.88 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.59/20.88 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.59/20.88 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.59/20.88 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.59/20.88 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.59/20.88 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.59/20.88 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.59/20.88 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.59/20.88 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.59/20.88 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.59/20.88 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.59/20.88 mark(a) -> a 20.59/20.88 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.59/20.88 mark(e) -> e 20.59/20.88 mark(i) -> i 20.59/20.88 mark(isList(X:S)) -> a__isList(X:S) 20.59/20.88 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.59/20.88 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.59/20.88 mark(isPal(X:S)) -> a__isPal(X:S) 20.59/20.88 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.59/20.88 mark(isQid(X:S)) -> a__isQid(X:S) 20.59/20.88 mark(nil) -> nil 20.59/20.88 mark(o) -> o 20.59/20.88 mark(tt) -> tt 20.59/20.88 mark(u) -> u 20.59/20.88 20.59/20.88 Problem 1: 20.59/20.88 20.59/20.88 Reduction Pairs Processor: 20.59/20.88 -> Pairs: 20.59/20.88 A____(__(X:S,Y:S),Z:S) -> A____(mark(Y:S),mark(Z:S)) 20.59/20.88 A____(__(X:S,Y:S),Z:S) -> MARK(X:S) 20.59/20.88 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S) 20.59/20.88 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 20.59/20.88 A____(nil,X:S) -> MARK(X:S) 20.59/20.88 A____(X:S,nil) -> MARK(X:S) 20.59/20.88 A__AND(tt,X:S) -> MARK(X:S) 20.59/20.88 A__ISLIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.88 A__ISLIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.88 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.88 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.88 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.88 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.88 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.88 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.59/20.88 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.88 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.88 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.88 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.88 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U12(X:S)) -> MARK(X:S) 20.59/20.88 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.88 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U23(X:S)) -> MARK(X:S) 20.59/20.88 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U32(X:S)) -> MARK(X:S) 20.59/20.88 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.88 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U43(X:S)) -> MARK(X:S) 20.59/20.88 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.88 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U53(X:S)) -> MARK(X:S) 20.59/20.88 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U62(X:S)) -> MARK(X:S) 20.59/20.88 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U72(X:S)) -> MARK(X:S) 20.59/20.88 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 20.59/20.88 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.59/20.88 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.59/20.88 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.59/20.88 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.59/20.88 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.59/20.88 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.59/20.88 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.59/20.88 -> Rules: 20.59/20.88 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.59/20.88 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.59/20.88 a__U12(tt) -> tt 20.59/20.88 a__U12(X:S) -> U12(X:S) 20.59/20.88 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.59/20.88 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.59/20.88 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.59/20.88 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.59/20.88 a__U23(tt) -> tt 20.59/20.88 a__U23(X:S) -> U23(X:S) 20.59/20.88 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.59/20.88 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.59/20.88 a__U32(tt) -> tt 20.59/20.88 a__U32(X:S) -> U32(X:S) 20.59/20.88 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.59/20.88 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.59/20.88 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.59/20.88 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.59/20.88 a__U43(tt) -> tt 20.59/20.88 a__U43(X:S) -> U43(X:S) 20.59/20.88 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.59/20.88 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.59/20.88 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.59/20.88 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.59/20.88 a__U53(tt) -> tt 20.59/20.88 a__U53(X:S) -> U53(X:S) 20.59/20.88 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.59/20.88 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.59/20.88 a__U62(tt) -> tt 20.59/20.88 a__U62(X:S) -> U62(X:S) 20.59/20.88 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.59/20.88 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.59/20.88 a__U72(tt) -> tt 20.59/20.88 a__U72(X:S) -> U72(X:S) 20.59/20.88 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.88 a____(nil,X:S) -> mark(X:S) 20.59/20.88 a____(X:S,nil) -> mark(X:S) 20.59/20.88 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.59/20.88 a__and(tt,X:S) -> mark(X:S) 20.59/20.88 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.59/20.88 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.88 a__isList(nil) -> tt 20.59/20.88 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.59/20.88 a__isList(X:S) -> isList(X:S) 20.59/20.88 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.88 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.88 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.59/20.88 a__isNeList(X:S) -> isNeList(X:S) 20.59/20.88 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.88 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.59/20.88 a__isNePal(X:S) -> isNePal(X:S) 20.59/20.88 a__isPal(nil) -> tt 20.59/20.88 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.59/20.88 a__isPal(X:S) -> isPal(X:S) 20.59/20.88 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.88 a__isPalListKind(a) -> tt 20.59/20.88 a__isPalListKind(e) -> tt 20.59/20.88 a__isPalListKind(i) -> tt 20.59/20.88 a__isPalListKind(nil) -> tt 20.59/20.88 a__isPalListKind(o) -> tt 20.59/20.88 a__isPalListKind(u) -> tt 20.59/20.88 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.59/20.88 a__isQid(a) -> tt 20.59/20.88 a__isQid(e) -> tt 20.59/20.88 a__isQid(i) -> tt 20.59/20.88 a__isQid(o) -> tt 20.59/20.88 a__isQid(u) -> tt 20.59/20.88 a__isQid(X:S) -> isQid(X:S) 20.59/20.88 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.59/20.88 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.59/20.88 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.59/20.88 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.59/20.88 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.59/20.88 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.59/20.88 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.59/20.88 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.59/20.88 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.59/20.88 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.59/20.88 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.59/20.88 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.59/20.88 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.59/20.88 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.59/20.88 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.59/20.88 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.59/20.88 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.59/20.88 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.59/20.88 mark(a) -> a 20.59/20.88 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.59/20.88 mark(e) -> e 20.59/20.88 mark(i) -> i 20.59/20.88 mark(isList(X:S)) -> a__isList(X:S) 20.59/20.88 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.59/20.88 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.59/20.88 mark(isPal(X:S)) -> a__isPal(X:S) 20.59/20.88 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.59/20.88 mark(isQid(X:S)) -> a__isQid(X:S) 20.59/20.88 mark(nil) -> nil 20.59/20.88 mark(o) -> o 20.59/20.88 mark(tt) -> tt 20.59/20.88 mark(u) -> u 20.59/20.88 -> Usable rules: 20.59/20.88 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.59/20.88 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.59/20.88 a__U12(tt) -> tt 20.59/20.88 a__U12(X:S) -> U12(X:S) 20.59/20.88 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.59/20.88 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.59/20.88 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.59/20.88 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.59/20.88 a__U23(tt) -> tt 20.59/20.88 a__U23(X:S) -> U23(X:S) 20.59/20.88 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.59/20.88 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.59/20.88 a__U32(tt) -> tt 20.59/20.88 a__U32(X:S) -> U32(X:S) 20.59/20.88 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.59/20.88 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.59/20.88 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.59/20.88 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.59/20.88 a__U43(tt) -> tt 20.59/20.88 a__U43(X:S) -> U43(X:S) 20.59/20.88 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.59/20.88 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.59/20.88 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.59/20.88 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.59/20.88 a__U53(tt) -> tt 20.59/20.88 a__U53(X:S) -> U53(X:S) 20.59/20.88 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.59/20.88 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.59/20.88 a__U62(tt) -> tt 20.59/20.88 a__U62(X:S) -> U62(X:S) 20.59/20.88 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.59/20.88 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.59/20.88 a__U72(tt) -> tt 20.59/20.88 a__U72(X:S) -> U72(X:S) 20.59/20.88 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.88 a____(nil,X:S) -> mark(X:S) 20.59/20.88 a____(X:S,nil) -> mark(X:S) 20.59/20.88 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.59/20.88 a__and(tt,X:S) -> mark(X:S) 20.59/20.88 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.59/20.88 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.88 a__isList(nil) -> tt 20.59/20.88 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.59/20.88 a__isList(X:S) -> isList(X:S) 20.59/20.88 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.88 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.88 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.59/20.88 a__isNeList(X:S) -> isNeList(X:S) 20.59/20.88 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.88 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.59/20.88 a__isNePal(X:S) -> isNePal(X:S) 20.59/20.88 a__isPal(nil) -> tt 20.59/20.88 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.59/20.88 a__isPal(X:S) -> isPal(X:S) 20.59/20.88 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.88 a__isPalListKind(a) -> tt 20.59/20.88 a__isPalListKind(e) -> tt 20.59/20.88 a__isPalListKind(i) -> tt 20.59/20.88 a__isPalListKind(nil) -> tt 20.59/20.88 a__isPalListKind(o) -> tt 20.59/20.88 a__isPalListKind(u) -> tt 20.59/20.88 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.59/20.88 a__isQid(a) -> tt 20.59/20.88 a__isQid(e) -> tt 20.59/20.88 a__isQid(i) -> tt 20.59/20.88 a__isQid(o) -> tt 20.59/20.88 a__isQid(u) -> tt 20.59/20.88 a__isQid(X:S) -> isQid(X:S) 20.59/20.88 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.59/20.88 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.59/20.88 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.59/20.88 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.59/20.88 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.59/20.88 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.59/20.88 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.59/20.88 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.59/20.88 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.59/20.88 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.59/20.88 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.59/20.88 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.59/20.88 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.59/20.88 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.59/20.88 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.59/20.88 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.59/20.88 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.59/20.88 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.59/20.88 mark(a) -> a 20.59/20.88 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.59/20.88 mark(e) -> e 20.59/20.88 mark(i) -> i 20.59/20.88 mark(isList(X:S)) -> a__isList(X:S) 20.59/20.88 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.59/20.88 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.59/20.88 mark(isPal(X:S)) -> a__isPal(X:S) 20.59/20.88 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.59/20.88 mark(isQid(X:S)) -> a__isQid(X:S) 20.59/20.88 mark(nil) -> nil 20.59/20.88 mark(o) -> o 20.59/20.88 mark(tt) -> tt 20.59/20.88 mark(u) -> u 20.59/20.88 ->Interpretation type: 20.59/20.88 Linear 20.59/20.88 ->Coefficients: 20.59/20.88 Natural Numbers 20.59/20.88 ->Dimension: 20.59/20.88 1 20.59/20.88 ->Bound: 20.59/20.88 2 20.59/20.88 ->Interpretation: 20.59/20.88 20.59/20.88 [a__U11](X1,X2) = 2.X1 + 2.X2 + 1 20.59/20.88 [a__U12](X) = X 20.59/20.88 [a__U21](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 20.59/20.88 [a__U22](X1,X2) = X1 + 2.X2 + 1 20.59/20.88 [a__U23](X) = X 20.59/20.88 [a__U31](X1,X2) = 2.X1 + 2.X2 20.59/20.88 [a__U32](X) = 2.X 20.59/20.88 [a__U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.59/20.88 [a__U42](X1,X2) = X1 + 2.X2 + 1 20.59/20.88 [a__U43](X) = X 20.59/20.88 [a__U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.59/20.88 [a__U52](X1,X2) = X1 + 2.X2 + 1 20.59/20.88 [a__U53](X) = X 20.59/20.88 [a__U61](X1,X2) = 2.X1 + X2 + 1 20.59/20.88 [a__U62](X) = 2.X + 1 20.59/20.88 [a__U71](X1,X2) = 2.X1 + 2.X2 + 2 20.59/20.88 [a__U72](X) = 2.X 20.59/20.88 [a____](X1,X2) = 2.X1 + X2 + 2 20.59/20.88 [a__and](X1,X2) = X1 + X2 20.59/20.88 [a__isList](X) = 2.X + 1 20.59/20.88 [a__isNeList](X) = 2.X + 1 20.59/20.88 [a__isNePal](X) = X + 1 20.59/20.88 [a__isPal](X) = 2.X + 2 20.59/20.88 [a__isPalListKind](X) = 0 20.59/20.88 [a__isQid](X) = 0 20.59/20.88 [mark](X) = X 20.59/20.88 [U11](X1,X2) = 2.X1 + 2.X2 + 1 20.59/20.88 [U12](X) = X 20.59/20.88 [U21](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 20.59/20.88 [U22](X1,X2) = X1 + 2.X2 + 1 20.59/20.88 [U23](X) = X 20.59/20.88 [U31](X1,X2) = 2.X1 + 2.X2 20.59/20.88 [U32](X) = 2.X 20.59/20.88 [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.59/20.88 [U42](X1,X2) = X1 + 2.X2 + 1 20.59/20.88 [U43](X) = X 20.59/20.88 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.59/20.88 [U52](X1,X2) = X1 + 2.X2 + 1 20.59/20.88 [U53](X) = X 20.59/20.88 [U61](X1,X2) = 2.X1 + X2 + 1 20.59/20.88 [U62](X) = 2.X + 1 20.59/20.88 [U71](X1,X2) = 2.X1 + 2.X2 + 2 20.59/20.88 [U72](X) = 2.X 20.59/20.88 [__](X1,X2) = 2.X1 + X2 + 2 20.59/20.88 [a] = 2 20.59/20.88 [and](X1,X2) = X1 + X2 20.59/20.88 [e] = 2 20.59/20.88 [fSNonEmpty] = 0 20.59/20.88 [i] = 0 20.59/20.88 [isList](X) = 2.X + 1 20.59/20.88 [isNeList](X) = 2.X + 1 20.59/20.88 [isNePal](X) = X + 1 20.59/20.88 [isPal](X) = 2.X + 2 20.59/20.88 [isPalListKind](X) = 0 20.59/20.88 [isQid](X) = 0 20.59/20.88 [nil] = 2 20.59/20.88 [o] = 0 20.59/20.88 [tt] = 0 20.59/20.88 [u] = 0 20.59/20.88 [A__U11](X1,X2) = 0 20.59/20.88 [A__U12](X) = 0 20.59/20.88 [A__U21](X1,X2,X3) = 0 20.59/20.88 [A__U22](X1,X2) = 0 20.59/20.88 [A__U23](X) = 0 20.59/20.88 [A__U31](X1,X2) = 0 20.59/20.88 [A__U32](X) = 0 20.59/20.88 [A__U41](X1,X2,X3) = 0 20.59/20.88 [A__U42](X1,X2) = 0 20.59/20.88 [A__U43](X) = 0 20.59/20.88 [A__U51](X1,X2,X3) = 0 20.59/20.88 [A__U52](X1,X2) = 0 20.59/20.88 [A__U53](X) = 0 20.59/20.88 [A__U61](X1,X2) = 0 20.59/20.88 [A__U62](X) = 0 20.59/20.88 [A__U71](X1,X2) = 0 20.59/20.88 [A__U72](X) = 0 20.59/20.88 [A____](X1,X2) = 2.X1 + 2.X2 + 1 20.59/20.88 [A__AND](X1,X2) = 2.X1 + 2.X2 + 2 20.59/20.88 [A__ISLIST](X) = 2.X + 2 20.59/20.88 [A__ISNELIST](X) = 2 20.59/20.88 [A__ISNEPAL](X) = 2.X + 2 20.59/20.88 [A__ISPAL](X) = X + 2 20.59/20.88 [A__ISPALLISTKIND](X) = 2 20.59/20.88 [A__ISQID](X) = 0 20.59/20.88 [MARK](X) = 2.X + 2 20.59/20.88 20.59/20.88 Problem 1: 20.59/20.88 20.59/20.88 SCC Processor: 20.59/20.88 -> Pairs: 20.59/20.88 A____(__(X:S,Y:S),Z:S) -> MARK(X:S) 20.59/20.88 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S) 20.59/20.88 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 20.59/20.88 A____(nil,X:S) -> MARK(X:S) 20.59/20.88 A____(X:S,nil) -> MARK(X:S) 20.59/20.88 A__AND(tt,X:S) -> MARK(X:S) 20.59/20.88 A__ISLIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.88 A__ISLIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.88 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.88 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.88 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.88 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.88 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.88 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.59/20.88 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.88 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.88 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.88 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.88 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U12(X:S)) -> MARK(X:S) 20.59/20.88 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.88 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U23(X:S)) -> MARK(X:S) 20.59/20.88 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U32(X:S)) -> MARK(X:S) 20.59/20.88 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.88 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U43(X:S)) -> MARK(X:S) 20.59/20.88 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.88 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U53(X:S)) -> MARK(X:S) 20.59/20.88 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U62(X:S)) -> MARK(X:S) 20.59/20.88 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U72(X:S)) -> MARK(X:S) 20.59/20.88 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 20.59/20.88 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.59/20.88 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.59/20.88 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.59/20.88 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.59/20.88 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.59/20.88 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.59/20.88 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.59/20.88 -> Rules: 20.59/20.88 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.59/20.88 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.59/20.88 a__U12(tt) -> tt 20.59/20.88 a__U12(X:S) -> U12(X:S) 20.59/20.88 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.59/20.88 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.59/20.88 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.59/20.88 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.59/20.88 a__U23(tt) -> tt 20.59/20.88 a__U23(X:S) -> U23(X:S) 20.59/20.88 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.59/20.88 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.59/20.88 a__U32(tt) -> tt 20.59/20.88 a__U32(X:S) -> U32(X:S) 20.59/20.88 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.59/20.88 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.59/20.88 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.59/20.88 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.59/20.88 a__U43(tt) -> tt 20.59/20.88 a__U43(X:S) -> U43(X:S) 20.59/20.88 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.59/20.88 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.59/20.88 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.59/20.88 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.59/20.88 a__U53(tt) -> tt 20.59/20.88 a__U53(X:S) -> U53(X:S) 20.59/20.88 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.59/20.88 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.59/20.88 a__U62(tt) -> tt 20.59/20.88 a__U62(X:S) -> U62(X:S) 20.59/20.88 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.59/20.88 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.59/20.88 a__U72(tt) -> tt 20.59/20.88 a__U72(X:S) -> U72(X:S) 20.59/20.88 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.88 a____(nil,X:S) -> mark(X:S) 20.59/20.88 a____(X:S,nil) -> mark(X:S) 20.59/20.88 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.59/20.88 a__and(tt,X:S) -> mark(X:S) 20.59/20.88 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.59/20.88 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.88 a__isList(nil) -> tt 20.59/20.88 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.59/20.88 a__isList(X:S) -> isList(X:S) 20.59/20.88 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.88 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.88 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.59/20.88 a__isNeList(X:S) -> isNeList(X:S) 20.59/20.88 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.88 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.59/20.88 a__isNePal(X:S) -> isNePal(X:S) 20.59/20.88 a__isPal(nil) -> tt 20.59/20.88 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.59/20.88 a__isPal(X:S) -> isPal(X:S) 20.59/20.88 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.88 a__isPalListKind(a) -> tt 20.59/20.88 a__isPalListKind(e) -> tt 20.59/20.88 a__isPalListKind(i) -> tt 20.59/20.88 a__isPalListKind(nil) -> tt 20.59/20.88 a__isPalListKind(o) -> tt 20.59/20.88 a__isPalListKind(u) -> tt 20.59/20.88 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.59/20.88 a__isQid(a) -> tt 20.59/20.88 a__isQid(e) -> tt 20.59/20.88 a__isQid(i) -> tt 20.59/20.88 a__isQid(o) -> tt 20.59/20.88 a__isQid(u) -> tt 20.59/20.88 a__isQid(X:S) -> isQid(X:S) 20.59/20.88 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.59/20.88 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.59/20.88 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.59/20.88 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.59/20.88 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.59/20.88 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.59/20.88 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.59/20.88 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.59/20.88 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.59/20.88 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.59/20.88 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.59/20.88 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.59/20.88 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.59/20.88 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.59/20.88 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.59/20.88 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.59/20.88 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.59/20.88 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.59/20.88 mark(a) -> a 20.59/20.88 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.59/20.88 mark(e) -> e 20.59/20.88 mark(i) -> i 20.59/20.88 mark(isList(X:S)) -> a__isList(X:S) 20.59/20.88 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.59/20.88 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.59/20.88 mark(isPal(X:S)) -> a__isPal(X:S) 20.59/20.88 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.59/20.88 mark(isQid(X:S)) -> a__isQid(X:S) 20.59/20.88 mark(nil) -> nil 20.59/20.88 mark(o) -> o 20.59/20.88 mark(tt) -> tt 20.59/20.88 mark(u) -> u 20.59/20.88 ->Strongly Connected Components: 20.59/20.88 ->->Cycle: 20.59/20.88 ->->-> Pairs: 20.59/20.88 A____(__(X:S,Y:S),Z:S) -> MARK(X:S) 20.59/20.88 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S) 20.59/20.88 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 20.59/20.88 A____(nil,X:S) -> MARK(X:S) 20.59/20.88 A____(X:S,nil) -> MARK(X:S) 20.59/20.88 A__AND(tt,X:S) -> MARK(X:S) 20.59/20.88 A__ISLIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.88 A__ISLIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.88 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.88 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.88 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.88 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.88 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.88 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.59/20.88 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.88 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.88 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.88 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.88 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U12(X:S)) -> MARK(X:S) 20.59/20.88 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.88 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U23(X:S)) -> MARK(X:S) 20.59/20.88 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U32(X:S)) -> MARK(X:S) 20.59/20.88 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.88 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U43(X:S)) -> MARK(X:S) 20.59/20.88 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.88 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U53(X:S)) -> MARK(X:S) 20.59/20.88 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U62(X:S)) -> MARK(X:S) 20.59/20.88 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U72(X:S)) -> MARK(X:S) 20.59/20.88 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 20.59/20.88 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.59/20.88 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.59/20.88 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.59/20.88 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.59/20.88 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.59/20.88 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.59/20.88 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.59/20.88 ->->-> Rules: 20.59/20.88 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.59/20.88 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.59/20.88 a__U12(tt) -> tt 20.59/20.88 a__U12(X:S) -> U12(X:S) 20.59/20.88 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.59/20.88 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.59/20.88 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.59/20.88 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.59/20.88 a__U23(tt) -> tt 20.59/20.88 a__U23(X:S) -> U23(X:S) 20.59/20.88 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.59/20.88 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.59/20.88 a__U32(tt) -> tt 20.59/20.88 a__U32(X:S) -> U32(X:S) 20.59/20.88 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.59/20.88 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.59/20.88 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.59/20.88 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.59/20.88 a__U43(tt) -> tt 20.59/20.88 a__U43(X:S) -> U43(X:S) 20.59/20.88 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.59/20.88 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.59/20.88 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.59/20.88 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.59/20.88 a__U53(tt) -> tt 20.59/20.88 a__U53(X:S) -> U53(X:S) 20.59/20.88 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.59/20.88 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.59/20.88 a__U62(tt) -> tt 20.59/20.88 a__U62(X:S) -> U62(X:S) 20.59/20.88 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.59/20.88 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.59/20.88 a__U72(tt) -> tt 20.59/20.88 a__U72(X:S) -> U72(X:S) 20.59/20.88 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.88 a____(nil,X:S) -> mark(X:S) 20.59/20.88 a____(X:S,nil) -> mark(X:S) 20.59/20.88 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.59/20.88 a__and(tt,X:S) -> mark(X:S) 20.59/20.88 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.59/20.88 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.88 a__isList(nil) -> tt 20.59/20.88 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.59/20.88 a__isList(X:S) -> isList(X:S) 20.59/20.88 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.88 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.88 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.59/20.88 a__isNeList(X:S) -> isNeList(X:S) 20.59/20.88 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.88 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.59/20.88 a__isNePal(X:S) -> isNePal(X:S) 20.59/20.88 a__isPal(nil) -> tt 20.59/20.88 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.59/20.88 a__isPal(X:S) -> isPal(X:S) 20.59/20.88 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.88 a__isPalListKind(a) -> tt 20.59/20.88 a__isPalListKind(e) -> tt 20.59/20.88 a__isPalListKind(i) -> tt 20.59/20.88 a__isPalListKind(nil) -> tt 20.59/20.88 a__isPalListKind(o) -> tt 20.59/20.88 a__isPalListKind(u) -> tt 20.59/20.88 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.59/20.88 a__isQid(a) -> tt 20.59/20.88 a__isQid(e) -> tt 20.59/20.88 a__isQid(i) -> tt 20.59/20.88 a__isQid(o) -> tt 20.59/20.88 a__isQid(u) -> tt 20.59/20.88 a__isQid(X:S) -> isQid(X:S) 20.59/20.88 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.59/20.88 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.59/20.88 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.59/20.88 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.59/20.88 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.59/20.88 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.59/20.88 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.59/20.88 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.59/20.88 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.59/20.88 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.59/20.88 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.59/20.88 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.59/20.88 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.59/20.88 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.59/20.88 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.59/20.88 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.59/20.88 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.59/20.88 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.59/20.88 mark(a) -> a 20.59/20.88 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.59/20.88 mark(e) -> e 20.59/20.88 mark(i) -> i 20.59/20.88 mark(isList(X:S)) -> a__isList(X:S) 20.59/20.88 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.59/20.88 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.59/20.88 mark(isPal(X:S)) -> a__isPal(X:S) 20.59/20.88 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.59/20.88 mark(isQid(X:S)) -> a__isQid(X:S) 20.59/20.88 mark(nil) -> nil 20.59/20.88 mark(o) -> o 20.59/20.88 mark(tt) -> tt 20.59/20.88 mark(u) -> u 20.59/20.88 20.59/20.88 Problem 1: 20.59/20.88 20.59/20.88 Reduction Pairs Processor: 20.59/20.88 -> Pairs: 20.59/20.88 A____(__(X:S,Y:S),Z:S) -> MARK(X:S) 20.59/20.88 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S) 20.59/20.88 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 20.59/20.88 A____(nil,X:S) -> MARK(X:S) 20.59/20.88 A____(X:S,nil) -> MARK(X:S) 20.59/20.88 A__AND(tt,X:S) -> MARK(X:S) 20.59/20.88 A__ISLIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.88 A__ISLIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.88 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.88 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.88 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.88 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.88 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.88 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.59/20.88 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.88 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.88 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.88 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.88 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U12(X:S)) -> MARK(X:S) 20.59/20.88 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.88 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U23(X:S)) -> MARK(X:S) 20.59/20.88 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U32(X:S)) -> MARK(X:S) 20.59/20.88 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.88 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U43(X:S)) -> MARK(X:S) 20.59/20.88 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.88 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U53(X:S)) -> MARK(X:S) 20.59/20.88 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U62(X:S)) -> MARK(X:S) 20.59/20.88 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U72(X:S)) -> MARK(X:S) 20.59/20.88 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 20.59/20.88 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.59/20.88 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.59/20.88 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.59/20.88 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.59/20.88 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.59/20.88 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.59/20.88 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.59/20.88 -> Rules: 20.59/20.88 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.59/20.88 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.59/20.88 a__U12(tt) -> tt 20.59/20.88 a__U12(X:S) -> U12(X:S) 20.59/20.88 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.59/20.88 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.59/20.88 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.59/20.88 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.59/20.88 a__U23(tt) -> tt 20.59/20.88 a__U23(X:S) -> U23(X:S) 20.59/20.88 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.59/20.88 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.59/20.88 a__U32(tt) -> tt 20.59/20.88 a__U32(X:S) -> U32(X:S) 20.59/20.88 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.59/20.88 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.59/20.88 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.59/20.88 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.59/20.88 a__U43(tt) -> tt 20.59/20.88 a__U43(X:S) -> U43(X:S) 20.59/20.88 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.59/20.88 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.59/20.88 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.59/20.88 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.59/20.88 a__U53(tt) -> tt 20.59/20.88 a__U53(X:S) -> U53(X:S) 20.59/20.88 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.59/20.88 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.59/20.88 a__U62(tt) -> tt 20.59/20.88 a__U62(X:S) -> U62(X:S) 20.59/20.88 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.59/20.88 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.59/20.88 a__U72(tt) -> tt 20.59/20.88 a__U72(X:S) -> U72(X:S) 20.59/20.88 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.88 a____(nil,X:S) -> mark(X:S) 20.59/20.88 a____(X:S,nil) -> mark(X:S) 20.59/20.88 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.59/20.88 a__and(tt,X:S) -> mark(X:S) 20.59/20.88 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.59/20.88 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.88 a__isList(nil) -> tt 20.59/20.88 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.59/20.88 a__isList(X:S) -> isList(X:S) 20.59/20.88 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.88 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.88 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.59/20.88 a__isNeList(X:S) -> isNeList(X:S) 20.59/20.88 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.88 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.59/20.88 a__isNePal(X:S) -> isNePal(X:S) 20.59/20.88 a__isPal(nil) -> tt 20.59/20.88 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.59/20.88 a__isPal(X:S) -> isPal(X:S) 20.59/20.88 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.88 a__isPalListKind(a) -> tt 20.59/20.88 a__isPalListKind(e) -> tt 20.59/20.88 a__isPalListKind(i) -> tt 20.59/20.88 a__isPalListKind(nil) -> tt 20.59/20.88 a__isPalListKind(o) -> tt 20.59/20.88 a__isPalListKind(u) -> tt 20.59/20.88 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.59/20.88 a__isQid(a) -> tt 20.59/20.88 a__isQid(e) -> tt 20.59/20.88 a__isQid(i) -> tt 20.59/20.88 a__isQid(o) -> tt 20.59/20.88 a__isQid(u) -> tt 20.59/20.88 a__isQid(X:S) -> isQid(X:S) 20.59/20.88 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.59/20.88 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.59/20.88 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.59/20.88 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.59/20.88 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.59/20.88 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.59/20.88 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.59/20.88 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.59/20.88 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.59/20.88 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.59/20.88 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.59/20.88 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.59/20.88 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.59/20.88 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.59/20.88 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.59/20.88 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.59/20.88 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.59/20.88 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.59/20.88 mark(a) -> a 20.59/20.88 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.59/20.88 mark(e) -> e 20.59/20.88 mark(i) -> i 20.59/20.88 mark(isList(X:S)) -> a__isList(X:S) 20.59/20.88 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.59/20.88 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.59/20.88 mark(isPal(X:S)) -> a__isPal(X:S) 20.59/20.88 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.59/20.88 mark(isQid(X:S)) -> a__isQid(X:S) 20.59/20.88 mark(nil) -> nil 20.59/20.88 mark(o) -> o 20.59/20.88 mark(tt) -> tt 20.59/20.88 mark(u) -> u 20.59/20.88 -> Usable rules: 20.59/20.88 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.59/20.88 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.59/20.88 a__U12(tt) -> tt 20.59/20.88 a__U12(X:S) -> U12(X:S) 20.59/20.88 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.59/20.88 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.59/20.88 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.59/20.88 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.59/20.88 a__U23(tt) -> tt 20.59/20.88 a__U23(X:S) -> U23(X:S) 20.59/20.88 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.59/20.88 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.59/20.88 a__U32(tt) -> tt 20.59/20.88 a__U32(X:S) -> U32(X:S) 20.59/20.88 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.59/20.88 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.59/20.88 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.59/20.88 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.59/20.88 a__U43(tt) -> tt 20.59/20.88 a__U43(X:S) -> U43(X:S) 20.59/20.88 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.59/20.88 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.59/20.88 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.59/20.88 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.59/20.88 a__U53(tt) -> tt 20.59/20.88 a__U53(X:S) -> U53(X:S) 20.59/20.88 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.59/20.88 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.59/20.88 a__U62(tt) -> tt 20.59/20.88 a__U62(X:S) -> U62(X:S) 20.59/20.88 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.59/20.88 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.59/20.88 a__U72(tt) -> tt 20.59/20.88 a__U72(X:S) -> U72(X:S) 20.59/20.88 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.88 a____(nil,X:S) -> mark(X:S) 20.59/20.88 a____(X:S,nil) -> mark(X:S) 20.59/20.88 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.59/20.88 a__and(tt,X:S) -> mark(X:S) 20.59/20.88 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.59/20.88 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.88 a__isList(nil) -> tt 20.59/20.88 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.59/20.88 a__isList(X:S) -> isList(X:S) 20.59/20.88 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.88 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.88 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.59/20.88 a__isNeList(X:S) -> isNeList(X:S) 20.59/20.88 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.88 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.59/20.88 a__isNePal(X:S) -> isNePal(X:S) 20.59/20.88 a__isPal(nil) -> tt 20.59/20.88 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.59/20.88 a__isPal(X:S) -> isPal(X:S) 20.59/20.88 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.88 a__isPalListKind(a) -> tt 20.59/20.88 a__isPalListKind(e) -> tt 20.59/20.88 a__isPalListKind(i) -> tt 20.59/20.88 a__isPalListKind(nil) -> tt 20.59/20.88 a__isPalListKind(o) -> tt 20.59/20.88 a__isPalListKind(u) -> tt 20.59/20.88 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.59/20.88 a__isQid(a) -> tt 20.59/20.88 a__isQid(e) -> tt 20.59/20.88 a__isQid(i) -> tt 20.59/20.88 a__isQid(o) -> tt 20.59/20.88 a__isQid(u) -> tt 20.59/20.88 a__isQid(X:S) -> isQid(X:S) 20.59/20.88 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.59/20.88 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.59/20.88 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.59/20.88 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.59/20.88 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.59/20.88 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.59/20.88 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.59/20.88 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.59/20.88 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.59/20.88 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.59/20.88 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.59/20.88 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.59/20.88 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.59/20.88 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.59/20.88 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.59/20.88 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.59/20.88 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.59/20.88 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.59/20.88 mark(a) -> a 20.59/20.88 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.59/20.88 mark(e) -> e 20.59/20.88 mark(i) -> i 20.59/20.88 mark(isList(X:S)) -> a__isList(X:S) 20.59/20.88 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.59/20.88 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.59/20.88 mark(isPal(X:S)) -> a__isPal(X:S) 20.59/20.88 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.59/20.88 mark(isQid(X:S)) -> a__isQid(X:S) 20.59/20.88 mark(nil) -> nil 20.59/20.88 mark(o) -> o 20.59/20.88 mark(tt) -> tt 20.59/20.88 mark(u) -> u 20.59/20.88 ->Interpretation type: 20.59/20.88 Linear 20.59/20.88 ->Coefficients: 20.59/20.88 Natural Numbers 20.59/20.88 ->Dimension: 20.59/20.88 1 20.59/20.88 ->Bound: 20.59/20.88 2 20.59/20.88 ->Interpretation: 20.59/20.88 20.59/20.88 [a__U11](X1,X2) = 2.X1 + 2.X2 + 1 20.59/20.88 [a__U12](X) = X 20.59/20.88 [a__U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.59/20.88 [a__U22](X1,X2) = X1 + 2.X2 + 1 20.59/20.88 [a__U23](X) = X 20.59/20.88 [a__U31](X1,X2) = 2.X1 + 2.X2 + 1 20.59/20.88 [a__U32](X) = X + 1 20.59/20.88 [a__U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.59/20.88 [a__U42](X1,X2) = X1 + 2.X2 + 1 20.59/20.88 [a__U43](X) = X 20.59/20.88 [a__U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.59/20.88 [a__U52](X1,X2) = X1 + 2.X2 + 1 20.59/20.88 [a__U53](X) = X 20.59/20.88 [a__U61](X1,X2) = 2.X1 + 2.X2 + 2 20.59/20.88 [a__U62](X) = X 20.59/20.88 [a__U71](X1,X2) = 2.X1 + 2.X2 + 2 20.59/20.88 [a__U72](X) = X 20.59/20.88 [a____](X1,X2) = 2.X1 + X2 + 2 20.59/20.88 [a__and](X1,X2) = X1 + 2.X2 20.59/20.88 [a__isList](X) = 2.X + 1 20.59/20.88 [a__isNeList](X) = 2.X + 1 20.59/20.88 [a__isNePal](X) = 2.X + 2 20.59/20.88 [a__isPal](X) = 2.X + 2 20.59/20.88 [a__isPalListKind](X) = 0 20.59/20.88 [a__isQid](X) = 2.X 20.59/20.88 [mark](X) = X 20.59/20.88 [U11](X1,X2) = 2.X1 + 2.X2 + 1 20.59/20.88 [U12](X) = X 20.59/20.88 [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.59/20.88 [U22](X1,X2) = X1 + 2.X2 + 1 20.59/20.88 [U23](X) = X 20.59/20.88 [U31](X1,X2) = 2.X1 + 2.X2 + 1 20.59/20.88 [U32](X) = X + 1 20.59/20.88 [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.59/20.88 [U42](X1,X2) = X1 + 2.X2 + 1 20.59/20.88 [U43](X) = X 20.59/20.88 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.59/20.88 [U52](X1,X2) = X1 + 2.X2 + 1 20.59/20.88 [U53](X) = X 20.59/20.88 [U61](X1,X2) = 2.X1 + 2.X2 + 2 20.59/20.88 [U62](X) = X 20.59/20.88 [U71](X1,X2) = 2.X1 + 2.X2 + 2 20.59/20.88 [U72](X) = X 20.59/20.88 [__](X1,X2) = 2.X1 + X2 + 2 20.59/20.88 [a] = 1 20.59/20.88 [and](X1,X2) = X1 + 2.X2 20.59/20.88 [e] = 0 20.59/20.88 [fSNonEmpty] = 0 20.59/20.88 [i] = 1 20.59/20.88 [isList](X) = 2.X + 1 20.59/20.88 [isNeList](X) = 2.X + 1 20.59/20.88 [isNePal](X) = 2.X + 2 20.59/20.88 [isPal](X) = 2.X + 2 20.59/20.88 [isPalListKind](X) = 0 20.59/20.88 [isQid](X) = 2.X 20.59/20.88 [nil] = 2 20.59/20.88 [o] = 2 20.59/20.88 [tt] = 0 20.59/20.88 [u] = 2 20.59/20.88 [A__U11](X1,X2) = 0 20.59/20.88 [A__U12](X) = 0 20.59/20.88 [A__U21](X1,X2,X3) = 0 20.59/20.88 [A__U22](X1,X2) = 0 20.59/20.88 [A__U23](X) = 0 20.59/20.88 [A__U31](X1,X2) = 0 20.59/20.88 [A__U32](X) = 0 20.59/20.88 [A__U41](X1,X2,X3) = 0 20.59/20.88 [A__U42](X1,X2) = 0 20.59/20.88 [A__U43](X) = 0 20.59/20.88 [A__U51](X1,X2,X3) = 0 20.59/20.88 [A__U52](X1,X2) = 0 20.59/20.88 [A__U53](X) = 0 20.59/20.88 [A__U61](X1,X2) = 0 20.59/20.88 [A__U62](X) = 0 20.59/20.88 [A__U71](X1,X2) = 0 20.59/20.88 [A__U72](X) = 0 20.59/20.88 [A____](X1,X2) = 2.X1 + 2.X2 20.59/20.88 [A__AND](X1,X2) = 2.X2 20.59/20.88 [A__ISLIST](X) = 2.X + 2 20.59/20.88 [A__ISNELIST](X) = 2.X + 2 20.59/20.88 [A__ISNEPAL](X) = 2.X + 2 20.59/20.88 [A__ISPAL](X) = 2.X 20.59/20.88 [A__ISPALLISTKIND](X) = 0 20.59/20.88 [A__ISQID](X) = 0 20.59/20.88 [MARK](X) = 2.X 20.59/20.88 20.59/20.88 Problem 1: 20.59/20.88 20.59/20.88 SCC Processor: 20.59/20.88 -> Pairs: 20.59/20.88 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S) 20.59/20.88 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 20.59/20.88 A____(nil,X:S) -> MARK(X:S) 20.59/20.88 A____(X:S,nil) -> MARK(X:S) 20.59/20.88 A__AND(tt,X:S) -> MARK(X:S) 20.59/20.88 A__ISLIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.88 A__ISLIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.88 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.88 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.88 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.88 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.88 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.88 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.59/20.88 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.88 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.88 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.88 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.88 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U12(X:S)) -> MARK(X:S) 20.59/20.88 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.88 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U23(X:S)) -> MARK(X:S) 20.59/20.88 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U32(X:S)) -> MARK(X:S) 20.59/20.88 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.88 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U43(X:S)) -> MARK(X:S) 20.59/20.88 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.88 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U53(X:S)) -> MARK(X:S) 20.59/20.88 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U62(X:S)) -> MARK(X:S) 20.59/20.88 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U72(X:S)) -> MARK(X:S) 20.59/20.88 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 20.59/20.88 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.59/20.88 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.59/20.88 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.59/20.88 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.59/20.88 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.59/20.88 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.59/20.88 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.59/20.88 -> Rules: 20.59/20.88 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.59/20.88 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.59/20.88 a__U12(tt) -> tt 20.59/20.88 a__U12(X:S) -> U12(X:S) 20.59/20.88 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.59/20.88 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.59/20.88 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.59/20.88 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.59/20.88 a__U23(tt) -> tt 20.59/20.88 a__U23(X:S) -> U23(X:S) 20.59/20.88 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.59/20.88 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.59/20.88 a__U32(tt) -> tt 20.59/20.88 a__U32(X:S) -> U32(X:S) 20.59/20.88 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.59/20.88 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.59/20.88 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.59/20.88 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.59/20.88 a__U43(tt) -> tt 20.59/20.88 a__U43(X:S) -> U43(X:S) 20.59/20.88 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.59/20.88 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.59/20.88 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.59/20.88 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.59/20.88 a__U53(tt) -> tt 20.59/20.88 a__U53(X:S) -> U53(X:S) 20.59/20.88 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.59/20.88 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.59/20.88 a__U62(tt) -> tt 20.59/20.88 a__U62(X:S) -> U62(X:S) 20.59/20.88 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.59/20.88 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.59/20.88 a__U72(tt) -> tt 20.59/20.88 a__U72(X:S) -> U72(X:S) 20.59/20.88 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.88 a____(nil,X:S) -> mark(X:S) 20.59/20.88 a____(X:S,nil) -> mark(X:S) 20.59/20.88 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.59/20.88 a__and(tt,X:S) -> mark(X:S) 20.59/20.88 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.59/20.88 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.88 a__isList(nil) -> tt 20.59/20.88 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.59/20.88 a__isList(X:S) -> isList(X:S) 20.59/20.88 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.88 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.88 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.59/20.88 a__isNeList(X:S) -> isNeList(X:S) 20.59/20.88 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.88 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.59/20.88 a__isNePal(X:S) -> isNePal(X:S) 20.59/20.88 a__isPal(nil) -> tt 20.59/20.88 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.59/20.88 a__isPal(X:S) -> isPal(X:S) 20.59/20.88 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.88 a__isPalListKind(a) -> tt 20.59/20.88 a__isPalListKind(e) -> tt 20.59/20.88 a__isPalListKind(i) -> tt 20.59/20.88 a__isPalListKind(nil) -> tt 20.59/20.88 a__isPalListKind(o) -> tt 20.59/20.88 a__isPalListKind(u) -> tt 20.59/20.88 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.59/20.88 a__isQid(a) -> tt 20.59/20.88 a__isQid(e) -> tt 20.59/20.88 a__isQid(i) -> tt 20.59/20.88 a__isQid(o) -> tt 20.59/20.88 a__isQid(u) -> tt 20.59/20.88 a__isQid(X:S) -> isQid(X:S) 20.59/20.88 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.59/20.88 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.59/20.88 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.59/20.88 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.59/20.88 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.59/20.88 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.59/20.88 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.59/20.88 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.59/20.88 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.59/20.88 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.59/20.88 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.59/20.88 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.59/20.88 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.59/20.88 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.59/20.88 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.59/20.88 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.59/20.88 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.59/20.88 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.59/20.88 mark(a) -> a 20.59/20.88 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.59/20.88 mark(e) -> e 20.59/20.88 mark(i) -> i 20.59/20.88 mark(isList(X:S)) -> a__isList(X:S) 20.59/20.88 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.59/20.88 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.59/20.88 mark(isPal(X:S)) -> a__isPal(X:S) 20.59/20.88 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.59/20.88 mark(isQid(X:S)) -> a__isQid(X:S) 20.59/20.88 mark(nil) -> nil 20.59/20.88 mark(o) -> o 20.59/20.88 mark(tt) -> tt 20.59/20.88 mark(u) -> u 20.59/20.88 ->Strongly Connected Components: 20.59/20.88 ->->Cycle: 20.59/20.88 ->->-> Pairs: 20.59/20.88 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S) 20.59/20.88 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 20.59/20.88 A____(nil,X:S) -> MARK(X:S) 20.59/20.88 A____(X:S,nil) -> MARK(X:S) 20.59/20.88 A__AND(tt,X:S) -> MARK(X:S) 20.59/20.88 A__ISLIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.88 A__ISLIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.88 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.88 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.88 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.88 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.88 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.88 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.59/20.88 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.88 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.88 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.88 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.88 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U12(X:S)) -> MARK(X:S) 20.59/20.88 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.88 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U23(X:S)) -> MARK(X:S) 20.59/20.88 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U32(X:S)) -> MARK(X:S) 20.59/20.88 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.88 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U43(X:S)) -> MARK(X:S) 20.59/20.88 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.88 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U53(X:S)) -> MARK(X:S) 20.59/20.88 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U62(X:S)) -> MARK(X:S) 20.59/20.88 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(U72(X:S)) -> MARK(X:S) 20.59/20.88 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 20.59/20.88 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.59/20.88 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.59/20.88 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.88 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.59/20.89 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.59/20.89 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.59/20.89 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.59/20.89 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.59/20.89 ->->-> Rules: 20.59/20.89 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.59/20.89 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.59/20.89 a__U12(tt) -> tt 20.59/20.89 a__U12(X:S) -> U12(X:S) 20.59/20.89 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.59/20.89 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.59/20.89 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.59/20.89 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.59/20.89 a__U23(tt) -> tt 20.59/20.89 a__U23(X:S) -> U23(X:S) 20.59/20.89 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.59/20.89 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.59/20.89 a__U32(tt) -> tt 20.59/20.89 a__U32(X:S) -> U32(X:S) 20.59/20.89 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.59/20.89 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.59/20.89 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.59/20.89 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.59/20.89 a__U43(tt) -> tt 20.59/20.89 a__U43(X:S) -> U43(X:S) 20.59/20.89 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.59/20.89 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.59/20.89 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.59/20.89 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.59/20.89 a__U53(tt) -> tt 20.59/20.89 a__U53(X:S) -> U53(X:S) 20.59/20.89 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.59/20.89 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.59/20.89 a__U62(tt) -> tt 20.59/20.89 a__U62(X:S) -> U62(X:S) 20.59/20.89 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.59/20.89 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.59/20.89 a__U72(tt) -> tt 20.59/20.89 a__U72(X:S) -> U72(X:S) 20.59/20.89 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.89 a____(nil,X:S) -> mark(X:S) 20.59/20.89 a____(X:S,nil) -> mark(X:S) 20.59/20.89 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.59/20.89 a__and(tt,X:S) -> mark(X:S) 20.59/20.89 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.59/20.89 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.89 a__isList(nil) -> tt 20.59/20.89 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.59/20.89 a__isList(X:S) -> isList(X:S) 20.59/20.89 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.89 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.89 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.59/20.89 a__isNeList(X:S) -> isNeList(X:S) 20.59/20.89 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.89 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.59/20.89 a__isNePal(X:S) -> isNePal(X:S) 20.59/20.89 a__isPal(nil) -> tt 20.59/20.89 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.59/20.89 a__isPal(X:S) -> isPal(X:S) 20.59/20.89 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.89 a__isPalListKind(a) -> tt 20.59/20.89 a__isPalListKind(e) -> tt 20.59/20.89 a__isPalListKind(i) -> tt 20.59/20.89 a__isPalListKind(nil) -> tt 20.59/20.89 a__isPalListKind(o) -> tt 20.59/20.89 a__isPalListKind(u) -> tt 20.59/20.89 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.59/20.89 a__isQid(a) -> tt 20.59/20.89 a__isQid(e) -> tt 20.59/20.89 a__isQid(i) -> tt 20.59/20.89 a__isQid(o) -> tt 20.59/20.89 a__isQid(u) -> tt 20.59/20.89 a__isQid(X:S) -> isQid(X:S) 20.59/20.89 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.59/20.89 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.59/20.89 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.59/20.89 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.59/20.89 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.59/20.89 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.59/20.89 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.59/20.89 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.59/20.89 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.59/20.89 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.59/20.89 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.59/20.89 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.59/20.89 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.59/20.89 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.59/20.89 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.59/20.89 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.59/20.89 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.59/20.89 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.59/20.89 mark(a) -> a 20.59/20.89 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.59/20.89 mark(e) -> e 20.59/20.89 mark(i) -> i 20.59/20.89 mark(isList(X:S)) -> a__isList(X:S) 20.59/20.89 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.59/20.89 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.59/20.89 mark(isPal(X:S)) -> a__isPal(X:S) 20.59/20.89 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.59/20.89 mark(isQid(X:S)) -> a__isQid(X:S) 20.59/20.89 mark(nil) -> nil 20.59/20.89 mark(o) -> o 20.59/20.89 mark(tt) -> tt 20.59/20.89 mark(u) -> u 20.59/20.89 20.59/20.89 Problem 1: 20.59/20.89 20.59/20.89 Reduction Pairs Processor: 20.59/20.89 -> Pairs: 20.59/20.89 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S) 20.59/20.89 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 20.59/20.89 A____(nil,X:S) -> MARK(X:S) 20.59/20.89 A____(X:S,nil) -> MARK(X:S) 20.59/20.89 A__AND(tt,X:S) -> MARK(X:S) 20.59/20.89 A__ISLIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.89 A__ISLIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.89 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.89 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.89 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.89 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.89 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.89 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.59/20.89 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.89 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.89 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.89 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.89 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U12(X:S)) -> MARK(X:S) 20.59/20.89 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.89 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U23(X:S)) -> MARK(X:S) 20.59/20.89 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U32(X:S)) -> MARK(X:S) 20.59/20.89 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.89 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U43(X:S)) -> MARK(X:S) 20.59/20.89 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.89 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U53(X:S)) -> MARK(X:S) 20.59/20.89 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U62(X:S)) -> MARK(X:S) 20.59/20.89 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U72(X:S)) -> MARK(X:S) 20.59/20.89 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 20.59/20.89 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.59/20.89 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.59/20.89 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.59/20.89 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.59/20.89 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.59/20.89 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.59/20.89 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.59/20.89 -> Rules: 20.59/20.89 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.59/20.89 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.59/20.89 a__U12(tt) -> tt 20.59/20.89 a__U12(X:S) -> U12(X:S) 20.59/20.89 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.59/20.89 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.59/20.89 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.59/20.89 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.59/20.89 a__U23(tt) -> tt 20.59/20.89 a__U23(X:S) -> U23(X:S) 20.59/20.89 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.59/20.89 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.59/20.89 a__U32(tt) -> tt 20.59/20.89 a__U32(X:S) -> U32(X:S) 20.59/20.89 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.59/20.89 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.59/20.89 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.59/20.89 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.59/20.89 a__U43(tt) -> tt 20.59/20.89 a__U43(X:S) -> U43(X:S) 20.59/20.89 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.59/20.89 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.59/20.89 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.59/20.89 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.59/20.89 a__U53(tt) -> tt 20.59/20.89 a__U53(X:S) -> U53(X:S) 20.59/20.89 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.59/20.89 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.59/20.89 a__U62(tt) -> tt 20.59/20.89 a__U62(X:S) -> U62(X:S) 20.59/20.89 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.59/20.89 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.59/20.89 a__U72(tt) -> tt 20.59/20.89 a__U72(X:S) -> U72(X:S) 20.59/20.89 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.89 a____(nil,X:S) -> mark(X:S) 20.59/20.89 a____(X:S,nil) -> mark(X:S) 20.59/20.89 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.59/20.89 a__and(tt,X:S) -> mark(X:S) 20.59/20.89 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.59/20.89 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.89 a__isList(nil) -> tt 20.59/20.89 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.59/20.89 a__isList(X:S) -> isList(X:S) 20.59/20.89 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.89 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.89 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.59/20.89 a__isNeList(X:S) -> isNeList(X:S) 20.59/20.89 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.89 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.59/20.89 a__isNePal(X:S) -> isNePal(X:S) 20.59/20.89 a__isPal(nil) -> tt 20.59/20.89 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.59/20.89 a__isPal(X:S) -> isPal(X:S) 20.59/20.89 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.89 a__isPalListKind(a) -> tt 20.59/20.89 a__isPalListKind(e) -> tt 20.59/20.89 a__isPalListKind(i) -> tt 20.59/20.89 a__isPalListKind(nil) -> tt 20.59/20.89 a__isPalListKind(o) -> tt 20.59/20.89 a__isPalListKind(u) -> tt 20.59/20.89 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.59/20.89 a__isQid(a) -> tt 20.59/20.89 a__isQid(e) -> tt 20.59/20.89 a__isQid(i) -> tt 20.59/20.89 a__isQid(o) -> tt 20.59/20.89 a__isQid(u) -> tt 20.59/20.89 a__isQid(X:S) -> isQid(X:S) 20.59/20.89 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.59/20.89 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.59/20.89 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.59/20.89 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.59/20.89 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.59/20.89 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.59/20.89 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.59/20.89 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.59/20.89 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.59/20.89 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.59/20.89 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.59/20.89 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.59/20.89 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.59/20.89 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.59/20.89 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.59/20.89 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.59/20.89 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.59/20.89 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.59/20.89 mark(a) -> a 20.59/20.89 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.59/20.89 mark(e) -> e 20.59/20.89 mark(i) -> i 20.59/20.89 mark(isList(X:S)) -> a__isList(X:S) 20.59/20.89 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.59/20.89 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.59/20.89 mark(isPal(X:S)) -> a__isPal(X:S) 20.59/20.89 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.59/20.89 mark(isQid(X:S)) -> a__isQid(X:S) 20.59/20.89 mark(nil) -> nil 20.59/20.89 mark(o) -> o 20.59/20.89 mark(tt) -> tt 20.59/20.89 mark(u) -> u 20.59/20.89 -> Usable rules: 20.59/20.89 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.59/20.89 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.59/20.89 a__U12(tt) -> tt 20.59/20.89 a__U12(X:S) -> U12(X:S) 20.59/20.89 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.59/20.89 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.59/20.89 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.59/20.89 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.59/20.89 a__U23(tt) -> tt 20.59/20.89 a__U23(X:S) -> U23(X:S) 20.59/20.89 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.59/20.89 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.59/20.89 a__U32(tt) -> tt 20.59/20.89 a__U32(X:S) -> U32(X:S) 20.59/20.89 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.59/20.89 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.59/20.89 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.59/20.89 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.59/20.89 a__U43(tt) -> tt 20.59/20.89 a__U43(X:S) -> U43(X:S) 20.59/20.89 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.59/20.89 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.59/20.89 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.59/20.89 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.59/20.89 a__U53(tt) -> tt 20.59/20.89 a__U53(X:S) -> U53(X:S) 20.59/20.89 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.59/20.89 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.59/20.89 a__U62(tt) -> tt 20.59/20.89 a__U62(X:S) -> U62(X:S) 20.59/20.89 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.59/20.89 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.59/20.89 a__U72(tt) -> tt 20.59/20.89 a__U72(X:S) -> U72(X:S) 20.59/20.89 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.89 a____(nil,X:S) -> mark(X:S) 20.59/20.89 a____(X:S,nil) -> mark(X:S) 20.59/20.89 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.59/20.89 a__and(tt,X:S) -> mark(X:S) 20.59/20.89 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.59/20.89 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.89 a__isList(nil) -> tt 20.59/20.89 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.59/20.89 a__isList(X:S) -> isList(X:S) 20.59/20.89 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.89 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.89 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.59/20.89 a__isNeList(X:S) -> isNeList(X:S) 20.59/20.89 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.89 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.59/20.89 a__isNePal(X:S) -> isNePal(X:S) 20.59/20.89 a__isPal(nil) -> tt 20.59/20.89 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.59/20.89 a__isPal(X:S) -> isPal(X:S) 20.59/20.89 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.89 a__isPalListKind(a) -> tt 20.59/20.89 a__isPalListKind(e) -> tt 20.59/20.89 a__isPalListKind(i) -> tt 20.59/20.89 a__isPalListKind(nil) -> tt 20.59/20.89 a__isPalListKind(o) -> tt 20.59/20.89 a__isPalListKind(u) -> tt 20.59/20.89 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.59/20.89 a__isQid(a) -> tt 20.59/20.89 a__isQid(e) -> tt 20.59/20.89 a__isQid(i) -> tt 20.59/20.89 a__isQid(o) -> tt 20.59/20.89 a__isQid(u) -> tt 20.59/20.89 a__isQid(X:S) -> isQid(X:S) 20.59/20.89 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.59/20.89 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.59/20.89 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.59/20.89 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.59/20.89 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.59/20.89 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.59/20.89 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.59/20.89 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.59/20.89 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.59/20.89 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.59/20.89 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.59/20.89 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.59/20.89 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.59/20.89 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.59/20.89 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.59/20.89 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.59/20.89 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.59/20.89 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.59/20.89 mark(a) -> a 20.59/20.89 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.59/20.89 mark(e) -> e 20.59/20.89 mark(i) -> i 20.59/20.89 mark(isList(X:S)) -> a__isList(X:S) 20.59/20.89 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.59/20.89 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.59/20.89 mark(isPal(X:S)) -> a__isPal(X:S) 20.59/20.89 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.59/20.89 mark(isQid(X:S)) -> a__isQid(X:S) 20.59/20.89 mark(nil) -> nil 20.59/20.89 mark(o) -> o 20.59/20.89 mark(tt) -> tt 20.59/20.89 mark(u) -> u 20.59/20.89 ->Interpretation type: 20.59/20.89 Linear 20.59/20.89 ->Coefficients: 20.59/20.89 Natural Numbers 20.59/20.89 ->Dimension: 20.59/20.89 1 20.59/20.89 ->Bound: 20.59/20.89 2 20.59/20.89 ->Interpretation: 20.59/20.89 20.59/20.89 [a__U11](X1,X2) = X1 + 2.X2 20.59/20.89 [a__U12](X) = X 20.59/20.89 [a__U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.59/20.89 [a__U22](X1,X2) = X1 + 2.X2 + 2 20.59/20.89 [a__U23](X) = X + 2 20.59/20.89 [a__U31](X1,X2) = 2.X1 + X2 20.59/20.89 [a__U32](X) = 2.X 20.59/20.89 [a__U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 20.59/20.89 [a__U42](X1,X2) = X1 + 2.X2 20.59/20.89 [a__U43](X) = X 20.59/20.89 [a__U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.59/20.89 [a__U52](X1,X2) = X1 + 2.X2 + 2 20.59/20.89 [a__U53](X) = X + 2 20.59/20.89 [a__U61](X1,X2) = 2.X1 + 2.X2 + 2 20.59/20.89 [a__U62](X) = 2.X + 2 20.59/20.89 [a__U71](X1,X2) = 2.X1 + 2.X2 + 2 20.59/20.89 [a__U72](X) = X 20.59/20.89 [a____](X1,X2) = 2.X1 + X2 + 2 20.59/20.89 [a__and](X1,X2) = X1 + 2.X2 20.59/20.89 [a__isList](X) = 2.X 20.59/20.89 [a__isNeList](X) = 2.X 20.59/20.89 [a__isNePal](X) = 2.X + 2 20.59/20.89 [a__isPal](X) = 2.X + 2 20.59/20.89 [a__isPalListKind](X) = 0 20.59/20.89 [a__isQid](X) = 0 20.59/20.89 [mark](X) = X 20.59/20.89 [U11](X1,X2) = X1 + 2.X2 20.59/20.89 [U12](X) = X 20.59/20.89 [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.59/20.89 [U22](X1,X2) = X1 + 2.X2 + 2 20.59/20.89 [U23](X) = X + 2 20.59/20.89 [U31](X1,X2) = 2.X1 + X2 20.59/20.89 [U32](X) = 2.X 20.59/20.89 [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 20.59/20.89 [U42](X1,X2) = X1 + 2.X2 20.59/20.89 [U43](X) = X 20.59/20.89 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.59/20.89 [U52](X1,X2) = X1 + 2.X2 + 2 20.59/20.89 [U53](X) = X + 2 20.59/20.89 [U61](X1,X2) = 2.X1 + 2.X2 + 2 20.59/20.89 [U62](X) = 2.X + 2 20.59/20.89 [U71](X1,X2) = 2.X1 + 2.X2 + 2 20.59/20.89 [U72](X) = X 20.59/20.89 [__](X1,X2) = 2.X1 + X2 + 2 20.59/20.89 [a] = 1 20.59/20.89 [and](X1,X2) = X1 + 2.X2 20.59/20.89 [e] = 1 20.59/20.89 [fSNonEmpty] = 0 20.59/20.89 [i] = 1 20.59/20.89 [isList](X) = 2.X 20.59/20.89 [isNeList](X) = 2.X 20.59/20.89 [isNePal](X) = 2.X + 2 20.59/20.89 [isPal](X) = 2.X + 2 20.59/20.89 [isPalListKind](X) = 0 20.59/20.89 [isQid](X) = 0 20.59/20.89 [nil] = 1 20.59/20.89 [o] = 1 20.59/20.89 [tt] = 0 20.59/20.89 [u] = 1 20.59/20.89 [A__U11](X1,X2) = 0 20.59/20.89 [A__U12](X) = 0 20.59/20.89 [A__U21](X1,X2,X3) = 0 20.59/20.89 [A__U22](X1,X2) = 0 20.59/20.89 [A__U23](X) = 0 20.59/20.89 [A__U31](X1,X2) = 0 20.59/20.89 [A__U32](X) = 0 20.59/20.89 [A__U41](X1,X2,X3) = 0 20.59/20.89 [A__U42](X1,X2) = 0 20.59/20.89 [A__U43](X) = 0 20.59/20.89 [A__U51](X1,X2,X3) = 0 20.59/20.89 [A__U52](X1,X2) = 0 20.59/20.89 [A__U53](X) = 0 20.59/20.89 [A__U61](X1,X2) = 0 20.59/20.89 [A__U62](X) = 0 20.59/20.89 [A__U71](X1,X2) = 0 20.59/20.89 [A__U72](X) = 0 20.59/20.89 [A____](X1,X2) = 2.X1 + 2.X2 + 1 20.59/20.89 [A__AND](X1,X2) = 2.X2 + 2 20.59/20.89 [A__ISLIST](X) = 2.X + 2 20.59/20.89 [A__ISNELIST](X) = 2 20.59/20.89 [A__ISNEPAL](X) = 2.X + 2 20.59/20.89 [A__ISPAL](X) = 2.X + 2 20.59/20.89 [A__ISPALLISTKIND](X) = 2 20.59/20.89 [A__ISQID](X) = 0 20.59/20.89 [MARK](X) = 2.X + 2 20.59/20.89 20.59/20.89 Problem 1: 20.59/20.89 20.59/20.89 SCC Processor: 20.59/20.89 -> Pairs: 20.59/20.89 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 20.59/20.89 A____(nil,X:S) -> MARK(X:S) 20.59/20.89 A____(X:S,nil) -> MARK(X:S) 20.59/20.89 A__AND(tt,X:S) -> MARK(X:S) 20.59/20.89 A__ISLIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.89 A__ISLIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.89 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.89 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.89 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.89 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.89 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.89 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.59/20.89 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.89 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.89 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.89 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.89 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U12(X:S)) -> MARK(X:S) 20.59/20.89 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.89 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U23(X:S)) -> MARK(X:S) 20.59/20.89 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U32(X:S)) -> MARK(X:S) 20.59/20.89 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.89 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U43(X:S)) -> MARK(X:S) 20.59/20.89 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.89 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U53(X:S)) -> MARK(X:S) 20.59/20.89 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U62(X:S)) -> MARK(X:S) 20.59/20.89 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U72(X:S)) -> MARK(X:S) 20.59/20.89 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 20.59/20.89 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.59/20.89 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.59/20.89 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.59/20.89 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.59/20.89 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.59/20.89 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.59/20.89 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.59/20.89 -> Rules: 20.59/20.89 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.59/20.89 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.59/20.89 a__U12(tt) -> tt 20.59/20.89 a__U12(X:S) -> U12(X:S) 20.59/20.89 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.59/20.89 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.59/20.89 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.59/20.89 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.59/20.89 a__U23(tt) -> tt 20.59/20.89 a__U23(X:S) -> U23(X:S) 20.59/20.89 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.59/20.89 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.59/20.89 a__U32(tt) -> tt 20.59/20.89 a__U32(X:S) -> U32(X:S) 20.59/20.89 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.59/20.89 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.59/20.89 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.59/20.89 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.59/20.89 a__U43(tt) -> tt 20.59/20.89 a__U43(X:S) -> U43(X:S) 20.59/20.89 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.59/20.89 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.59/20.89 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.59/20.89 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.59/20.89 a__U53(tt) -> tt 20.59/20.89 a__U53(X:S) -> U53(X:S) 20.59/20.89 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.59/20.89 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.59/20.89 a__U62(tt) -> tt 20.59/20.89 a__U62(X:S) -> U62(X:S) 20.59/20.89 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.59/20.89 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.59/20.89 a__U72(tt) -> tt 20.59/20.89 a__U72(X:S) -> U72(X:S) 20.59/20.89 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.89 a____(nil,X:S) -> mark(X:S) 20.59/20.89 a____(X:S,nil) -> mark(X:S) 20.59/20.89 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.59/20.89 a__and(tt,X:S) -> mark(X:S) 20.59/20.89 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.59/20.89 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.89 a__isList(nil) -> tt 20.59/20.89 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.59/20.89 a__isList(X:S) -> isList(X:S) 20.59/20.89 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.89 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.89 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.59/20.89 a__isNeList(X:S) -> isNeList(X:S) 20.59/20.89 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.89 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.59/20.89 a__isNePal(X:S) -> isNePal(X:S) 20.59/20.89 a__isPal(nil) -> tt 20.59/20.89 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.59/20.89 a__isPal(X:S) -> isPal(X:S) 20.59/20.89 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.89 a__isPalListKind(a) -> tt 20.59/20.89 a__isPalListKind(e) -> tt 20.59/20.89 a__isPalListKind(i) -> tt 20.59/20.89 a__isPalListKind(nil) -> tt 20.59/20.89 a__isPalListKind(o) -> tt 20.59/20.89 a__isPalListKind(u) -> tt 20.59/20.89 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.59/20.89 a__isQid(a) -> tt 20.59/20.89 a__isQid(e) -> tt 20.59/20.89 a__isQid(i) -> tt 20.59/20.89 a__isQid(o) -> tt 20.59/20.89 a__isQid(u) -> tt 20.59/20.89 a__isQid(X:S) -> isQid(X:S) 20.59/20.89 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.59/20.89 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.59/20.89 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.59/20.89 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.59/20.89 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.59/20.89 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.59/20.89 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.59/20.89 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.59/20.89 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.59/20.89 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.59/20.89 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.59/20.89 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.59/20.89 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.59/20.89 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.59/20.89 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.59/20.89 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.59/20.89 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.59/20.89 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.59/20.89 mark(a) -> a 20.59/20.89 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.59/20.89 mark(e) -> e 20.59/20.89 mark(i) -> i 20.59/20.89 mark(isList(X:S)) -> a__isList(X:S) 20.59/20.89 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.59/20.89 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.59/20.89 mark(isPal(X:S)) -> a__isPal(X:S) 20.59/20.89 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.59/20.89 mark(isQid(X:S)) -> a__isQid(X:S) 20.59/20.89 mark(nil) -> nil 20.59/20.89 mark(o) -> o 20.59/20.89 mark(tt) -> tt 20.59/20.89 mark(u) -> u 20.59/20.89 ->Strongly Connected Components: 20.59/20.89 ->->Cycle: 20.59/20.89 ->->-> Pairs: 20.59/20.89 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 20.59/20.89 A____(nil,X:S) -> MARK(X:S) 20.59/20.89 A____(X:S,nil) -> MARK(X:S) 20.59/20.89 A__AND(tt,X:S) -> MARK(X:S) 20.59/20.89 A__ISLIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.89 A__ISLIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.89 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.89 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.89 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.89 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.89 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.89 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.59/20.89 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.89 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.89 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.89 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.89 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U12(X:S)) -> MARK(X:S) 20.59/20.89 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.89 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U23(X:S)) -> MARK(X:S) 20.59/20.89 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U32(X:S)) -> MARK(X:S) 20.59/20.89 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.89 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U43(X:S)) -> MARK(X:S) 20.59/20.89 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.89 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U53(X:S)) -> MARK(X:S) 20.59/20.89 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U62(X:S)) -> MARK(X:S) 20.59/20.89 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U72(X:S)) -> MARK(X:S) 20.59/20.89 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 20.59/20.89 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.59/20.89 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.59/20.89 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.59/20.89 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.59/20.89 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.59/20.89 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.59/20.89 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.59/20.89 ->->-> Rules: 20.59/20.89 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.59/20.89 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.59/20.89 a__U12(tt) -> tt 20.59/20.89 a__U12(X:S) -> U12(X:S) 20.59/20.89 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.59/20.89 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.59/20.89 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.59/20.89 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.59/20.89 a__U23(tt) -> tt 20.59/20.89 a__U23(X:S) -> U23(X:S) 20.59/20.89 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.59/20.89 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.59/20.89 a__U32(tt) -> tt 20.59/20.89 a__U32(X:S) -> U32(X:S) 20.59/20.89 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.59/20.89 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.59/20.89 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.59/20.89 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.59/20.89 a__U43(tt) -> tt 20.59/20.89 a__U43(X:S) -> U43(X:S) 20.59/20.89 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.59/20.89 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.59/20.89 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.59/20.89 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.59/20.89 a__U53(tt) -> tt 20.59/20.89 a__U53(X:S) -> U53(X:S) 20.59/20.89 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.59/20.89 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.59/20.89 a__U62(tt) -> tt 20.59/20.89 a__U62(X:S) -> U62(X:S) 20.59/20.89 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.59/20.89 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.59/20.89 a__U72(tt) -> tt 20.59/20.89 a__U72(X:S) -> U72(X:S) 20.59/20.89 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.89 a____(nil,X:S) -> mark(X:S) 20.59/20.89 a____(X:S,nil) -> mark(X:S) 20.59/20.89 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.59/20.89 a__and(tt,X:S) -> mark(X:S) 20.59/20.89 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.59/20.89 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.89 a__isList(nil) -> tt 20.59/20.89 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.59/20.89 a__isList(X:S) -> isList(X:S) 20.59/20.89 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.89 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.89 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.59/20.89 a__isNeList(X:S) -> isNeList(X:S) 20.59/20.89 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.89 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.59/20.89 a__isNePal(X:S) -> isNePal(X:S) 20.59/20.89 a__isPal(nil) -> tt 20.59/20.89 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.59/20.89 a__isPal(X:S) -> isPal(X:S) 20.59/20.89 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.89 a__isPalListKind(a) -> tt 20.59/20.89 a__isPalListKind(e) -> tt 20.59/20.89 a__isPalListKind(i) -> tt 20.59/20.89 a__isPalListKind(nil) -> tt 20.59/20.89 a__isPalListKind(o) -> tt 20.59/20.89 a__isPalListKind(u) -> tt 20.59/20.89 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.59/20.89 a__isQid(a) -> tt 20.59/20.89 a__isQid(e) -> tt 20.59/20.89 a__isQid(i) -> tt 20.59/20.89 a__isQid(o) -> tt 20.59/20.89 a__isQid(u) -> tt 20.59/20.89 a__isQid(X:S) -> isQid(X:S) 20.59/20.89 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.59/20.89 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.59/20.89 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.59/20.89 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.59/20.89 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.59/20.89 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.59/20.89 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.59/20.89 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.59/20.89 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.59/20.89 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.59/20.89 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.59/20.89 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.59/20.89 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.59/20.89 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.59/20.89 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.59/20.89 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.59/20.89 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.59/20.89 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.59/20.89 mark(a) -> a 20.59/20.89 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.59/20.89 mark(e) -> e 20.59/20.89 mark(i) -> i 20.59/20.89 mark(isList(X:S)) -> a__isList(X:S) 20.59/20.89 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.59/20.89 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.59/20.89 mark(isPal(X:S)) -> a__isPal(X:S) 20.59/20.89 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.59/20.89 mark(isQid(X:S)) -> a__isQid(X:S) 20.59/20.89 mark(nil) -> nil 20.59/20.89 mark(o) -> o 20.59/20.89 mark(tt) -> tt 20.59/20.89 mark(u) -> u 20.59/20.89 20.59/20.89 Problem 1: 20.59/20.89 20.59/20.89 Reduction Pairs Processor: 20.59/20.89 -> Pairs: 20.59/20.89 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 20.59/20.89 A____(nil,X:S) -> MARK(X:S) 20.59/20.89 A____(X:S,nil) -> MARK(X:S) 20.59/20.89 A__AND(tt,X:S) -> MARK(X:S) 20.59/20.89 A__ISLIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.89 A__ISLIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.89 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.89 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.89 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.89 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.89 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.89 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.59/20.89 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.89 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.89 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.89 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.89 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U12(X:S)) -> MARK(X:S) 20.59/20.89 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.89 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U23(X:S)) -> MARK(X:S) 20.59/20.89 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U32(X:S)) -> MARK(X:S) 20.59/20.89 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.89 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U43(X:S)) -> MARK(X:S) 20.59/20.89 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.89 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U53(X:S)) -> MARK(X:S) 20.59/20.89 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U62(X:S)) -> MARK(X:S) 20.59/20.89 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U72(X:S)) -> MARK(X:S) 20.59/20.89 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 20.59/20.89 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.59/20.89 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.59/20.89 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.59/20.89 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.59/20.89 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.59/20.89 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.59/20.89 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.59/20.89 -> Rules: 20.59/20.89 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.59/20.89 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.59/20.89 a__U12(tt) -> tt 20.59/20.89 a__U12(X:S) -> U12(X:S) 20.59/20.89 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.59/20.89 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.59/20.89 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.59/20.89 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.59/20.89 a__U23(tt) -> tt 20.59/20.89 a__U23(X:S) -> U23(X:S) 20.59/20.89 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.59/20.89 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.59/20.89 a__U32(tt) -> tt 20.59/20.89 a__U32(X:S) -> U32(X:S) 20.59/20.89 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.59/20.89 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.59/20.89 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.59/20.89 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.59/20.89 a__U43(tt) -> tt 20.59/20.89 a__U43(X:S) -> U43(X:S) 20.59/20.89 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.59/20.89 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.59/20.89 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.59/20.89 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.59/20.89 a__U53(tt) -> tt 20.59/20.89 a__U53(X:S) -> U53(X:S) 20.59/20.89 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.59/20.89 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.59/20.89 a__U62(tt) -> tt 20.59/20.89 a__U62(X:S) -> U62(X:S) 20.59/20.89 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.59/20.89 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.59/20.89 a__U72(tt) -> tt 20.59/20.89 a__U72(X:S) -> U72(X:S) 20.59/20.89 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.89 a____(nil,X:S) -> mark(X:S) 20.59/20.89 a____(X:S,nil) -> mark(X:S) 20.59/20.89 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.59/20.89 a__and(tt,X:S) -> mark(X:S) 20.59/20.89 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.59/20.89 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.89 a__isList(nil) -> tt 20.59/20.89 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.59/20.89 a__isList(X:S) -> isList(X:S) 20.59/20.89 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.89 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.89 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.59/20.89 a__isNeList(X:S) -> isNeList(X:S) 20.59/20.89 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.89 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.59/20.89 a__isNePal(X:S) -> isNePal(X:S) 20.59/20.89 a__isPal(nil) -> tt 20.59/20.89 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.59/20.89 a__isPal(X:S) -> isPal(X:S) 20.59/20.89 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.89 a__isPalListKind(a) -> tt 20.59/20.89 a__isPalListKind(e) -> tt 20.59/20.89 a__isPalListKind(i) -> tt 20.59/20.89 a__isPalListKind(nil) -> tt 20.59/20.89 a__isPalListKind(o) -> tt 20.59/20.89 a__isPalListKind(u) -> tt 20.59/20.89 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.59/20.89 a__isQid(a) -> tt 20.59/20.89 a__isQid(e) -> tt 20.59/20.89 a__isQid(i) -> tt 20.59/20.89 a__isQid(o) -> tt 20.59/20.89 a__isQid(u) -> tt 20.59/20.89 a__isQid(X:S) -> isQid(X:S) 20.59/20.89 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.59/20.89 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.59/20.89 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.59/20.89 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.59/20.89 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.59/20.89 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.59/20.89 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.59/20.89 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.59/20.89 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.59/20.89 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.59/20.89 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.59/20.89 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.59/20.89 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.59/20.89 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.59/20.89 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.59/20.89 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.59/20.89 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.59/20.89 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.59/20.89 mark(a) -> a 20.59/20.89 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.59/20.89 mark(e) -> e 20.59/20.89 mark(i) -> i 20.59/20.89 mark(isList(X:S)) -> a__isList(X:S) 20.59/20.89 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.59/20.89 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.59/20.89 mark(isPal(X:S)) -> a__isPal(X:S) 20.59/20.89 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.59/20.89 mark(isQid(X:S)) -> a__isQid(X:S) 20.59/20.89 mark(nil) -> nil 20.59/20.89 mark(o) -> o 20.59/20.89 mark(tt) -> tt 20.59/20.89 mark(u) -> u 20.59/20.89 -> Usable rules: 20.59/20.89 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.59/20.89 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.59/20.89 a__U12(tt) -> tt 20.59/20.89 a__U12(X:S) -> U12(X:S) 20.59/20.89 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.59/20.89 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.59/20.89 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.59/20.89 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.59/20.89 a__U23(tt) -> tt 20.59/20.89 a__U23(X:S) -> U23(X:S) 20.59/20.89 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.59/20.89 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.59/20.89 a__U32(tt) -> tt 20.59/20.89 a__U32(X:S) -> U32(X:S) 20.59/20.89 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.59/20.89 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.59/20.89 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.59/20.89 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.59/20.89 a__U43(tt) -> tt 20.59/20.89 a__U43(X:S) -> U43(X:S) 20.59/20.89 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.59/20.89 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.59/20.89 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.59/20.89 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.59/20.89 a__U53(tt) -> tt 20.59/20.89 a__U53(X:S) -> U53(X:S) 20.59/20.89 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.59/20.89 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.59/20.89 a__U62(tt) -> tt 20.59/20.89 a__U62(X:S) -> U62(X:S) 20.59/20.89 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.59/20.89 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.59/20.89 a__U72(tt) -> tt 20.59/20.89 a__U72(X:S) -> U72(X:S) 20.59/20.89 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.89 a____(nil,X:S) -> mark(X:S) 20.59/20.89 a____(X:S,nil) -> mark(X:S) 20.59/20.89 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.59/20.89 a__and(tt,X:S) -> mark(X:S) 20.59/20.89 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.59/20.89 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.89 a__isList(nil) -> tt 20.59/20.89 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.59/20.89 a__isList(X:S) -> isList(X:S) 20.59/20.89 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.89 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.89 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.59/20.89 a__isNeList(X:S) -> isNeList(X:S) 20.59/20.89 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.89 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.59/20.89 a__isNePal(X:S) -> isNePal(X:S) 20.59/20.89 a__isPal(nil) -> tt 20.59/20.89 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.59/20.89 a__isPal(X:S) -> isPal(X:S) 20.59/20.89 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.89 a__isPalListKind(a) -> tt 20.59/20.89 a__isPalListKind(e) -> tt 20.59/20.89 a__isPalListKind(i) -> tt 20.59/20.89 a__isPalListKind(nil) -> tt 20.59/20.89 a__isPalListKind(o) -> tt 20.59/20.89 a__isPalListKind(u) -> tt 20.59/20.89 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.59/20.89 a__isQid(a) -> tt 20.59/20.89 a__isQid(e) -> tt 20.59/20.89 a__isQid(i) -> tt 20.59/20.89 a__isQid(o) -> tt 20.59/20.89 a__isQid(u) -> tt 20.59/20.89 a__isQid(X:S) -> isQid(X:S) 20.59/20.89 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.59/20.89 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.59/20.89 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.59/20.89 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.59/20.89 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.59/20.89 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.59/20.89 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.59/20.89 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.59/20.89 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.59/20.89 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.59/20.89 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.59/20.89 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.59/20.89 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.59/20.89 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.59/20.89 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.59/20.89 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.59/20.89 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.59/20.89 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.59/20.89 mark(a) -> a 20.59/20.89 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.59/20.89 mark(e) -> e 20.59/20.89 mark(i) -> i 20.59/20.89 mark(isList(X:S)) -> a__isList(X:S) 20.59/20.89 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.59/20.89 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.59/20.89 mark(isPal(X:S)) -> a__isPal(X:S) 20.59/20.89 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.59/20.89 mark(isQid(X:S)) -> a__isQid(X:S) 20.59/20.89 mark(nil) -> nil 20.59/20.89 mark(o) -> o 20.59/20.89 mark(tt) -> tt 20.59/20.89 mark(u) -> u 20.59/20.89 ->Interpretation type: 20.59/20.89 Linear 20.59/20.89 ->Coefficients: 20.59/20.89 Natural Numbers 20.59/20.89 ->Dimension: 20.59/20.89 1 20.59/20.89 ->Bound: 20.59/20.89 2 20.59/20.89 ->Interpretation: 20.59/20.89 20.59/20.89 [a__U11](X1,X2) = 2.X1 + 2.X2 20.59/20.89 [a__U12](X) = X 20.59/20.89 [a__U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.59/20.89 [a__U22](X1,X2) = X1 + 2.X2 + 2 20.59/20.89 [a__U23](X) = X + 2 20.59/20.89 [a__U31](X1,X2) = 2.X1 + 2.X2 20.59/20.89 [a__U32](X) = 2.X 20.59/20.89 [a__U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.59/20.89 [a__U42](X1,X2) = X1 + 2.X2 + 2 20.59/20.89 [a__U43](X) = X + 2 20.59/20.89 [a__U51](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 20.59/20.89 [a__U52](X1,X2) = X1 + 2.X2 + 2 20.59/20.89 [a__U53](X) = X + 2 20.59/20.89 [a__U61](X1,X2) = 2.X1 + 2.X2 + 2 20.59/20.89 [a__U62](X) = 2.X + 2 20.59/20.89 [a__U71](X1,X2) = 2.X1 + 2.X2 + 2 20.59/20.89 [a__U72](X) = X 20.59/20.89 [a____](X1,X2) = 2.X1 + X2 + 2 20.59/20.89 [a__and](X1,X2) = X1 + 2.X2 20.59/20.89 [a__isList](X) = 2.X 20.59/20.89 [a__isNeList](X) = 2.X 20.59/20.89 [a__isNePal](X) = 2.X + 2 20.59/20.89 [a__isPal](X) = 2.X + 2 20.59/20.89 [a__isPalListKind](X) = 0 20.59/20.89 [a__isQid](X) = 0 20.59/20.89 [mark](X) = X 20.59/20.89 [U11](X1,X2) = 2.X1 + 2.X2 20.59/20.89 [U12](X) = X 20.59/20.89 [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.59/20.89 [U22](X1,X2) = X1 + 2.X2 + 2 20.59/20.89 [U23](X) = X + 2 20.59/20.89 [U31](X1,X2) = 2.X1 + 2.X2 20.59/20.89 [U32](X) = 2.X 20.59/20.89 [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.59/20.89 [U42](X1,X2) = X1 + 2.X2 + 2 20.59/20.89 [U43](X) = X + 2 20.59/20.89 [U51](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 20.59/20.89 [U52](X1,X2) = X1 + 2.X2 + 2 20.59/20.89 [U53](X) = X + 2 20.59/20.89 [U61](X1,X2) = 2.X1 + 2.X2 + 2 20.59/20.89 [U62](X) = 2.X + 2 20.59/20.89 [U71](X1,X2) = 2.X1 + 2.X2 + 2 20.59/20.89 [U72](X) = X 20.59/20.89 [__](X1,X2) = 2.X1 + X2 + 2 20.59/20.89 [a] = 1 20.59/20.89 [and](X1,X2) = X1 + 2.X2 20.59/20.89 [e] = 1 20.59/20.89 [fSNonEmpty] = 0 20.59/20.89 [i] = 0 20.59/20.89 [isList](X) = 2.X 20.59/20.89 [isNeList](X) = 2.X 20.59/20.89 [isNePal](X) = 2.X + 2 20.59/20.89 [isPal](X) = 2.X + 2 20.59/20.89 [isPalListKind](X) = 0 20.59/20.89 [isQid](X) = 0 20.59/20.89 [nil] = 2 20.59/20.89 [o] = 1 20.59/20.89 [tt] = 0 20.59/20.89 [u] = 1 20.59/20.89 [A__U11](X1,X2) = 0 20.59/20.89 [A__U12](X) = 0 20.59/20.89 [A__U21](X1,X2,X3) = 0 20.59/20.89 [A__U22](X1,X2) = 0 20.59/20.89 [A__U23](X) = 0 20.59/20.89 [A__U31](X1,X2) = 0 20.59/20.89 [A__U32](X) = 0 20.59/20.89 [A__U41](X1,X2,X3) = 0 20.59/20.89 [A__U42](X1,X2) = 0 20.59/20.89 [A__U43](X) = 0 20.59/20.89 [A__U51](X1,X2,X3) = 0 20.59/20.89 [A__U52](X1,X2) = 0 20.59/20.89 [A__U53](X) = 0 20.59/20.89 [A__U61](X1,X2) = 0 20.59/20.89 [A__U62](X) = 0 20.59/20.89 [A__U71](X1,X2) = 0 20.59/20.89 [A__U72](X) = 0 20.59/20.89 [A____](X1,X2) = 2.X1 + X2 + 2 20.59/20.89 [A__AND](X1,X2) = X1 + X2 + 2 20.59/20.89 [A__ISLIST](X) = X + 2 20.59/20.89 [A__ISNELIST](X) = X + 2 20.59/20.89 [A__ISNEPAL](X) = 2.X + 2 20.59/20.89 [A__ISPAL](X) = 2 20.59/20.89 [A__ISPALLISTKIND](X) = 2 20.59/20.89 [A__ISQID](X) = 0 20.59/20.89 [MARK](X) = X + 2 20.59/20.89 20.59/20.89 Problem 1: 20.59/20.89 20.59/20.89 SCC Processor: 20.59/20.89 -> Pairs: 20.59/20.89 A____(nil,X:S) -> MARK(X:S) 20.59/20.89 A____(X:S,nil) -> MARK(X:S) 20.59/20.89 A__AND(tt,X:S) -> MARK(X:S) 20.59/20.89 A__ISLIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.89 A__ISLIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.89 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.89 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.89 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.89 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.89 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.89 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.59/20.89 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.89 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.89 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.89 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.89 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U12(X:S)) -> MARK(X:S) 20.59/20.89 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.89 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U23(X:S)) -> MARK(X:S) 20.59/20.89 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U32(X:S)) -> MARK(X:S) 20.59/20.89 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.89 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U43(X:S)) -> MARK(X:S) 20.59/20.89 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.89 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U53(X:S)) -> MARK(X:S) 20.59/20.89 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U62(X:S)) -> MARK(X:S) 20.59/20.89 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U72(X:S)) -> MARK(X:S) 20.59/20.89 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 20.59/20.89 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.59/20.89 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.59/20.89 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.59/20.89 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.59/20.89 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.59/20.89 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.59/20.89 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.59/20.89 -> Rules: 20.59/20.89 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.59/20.89 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.59/20.89 a__U12(tt) -> tt 20.59/20.89 a__U12(X:S) -> U12(X:S) 20.59/20.89 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.59/20.89 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.59/20.89 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.59/20.89 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.59/20.89 a__U23(tt) -> tt 20.59/20.89 a__U23(X:S) -> U23(X:S) 20.59/20.89 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.59/20.89 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.59/20.89 a__U32(tt) -> tt 20.59/20.89 a__U32(X:S) -> U32(X:S) 20.59/20.89 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.59/20.89 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.59/20.89 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.59/20.89 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.59/20.89 a__U43(tt) -> tt 20.59/20.89 a__U43(X:S) -> U43(X:S) 20.59/20.89 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.59/20.89 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.59/20.89 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.59/20.89 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.59/20.89 a__U53(tt) -> tt 20.59/20.89 a__U53(X:S) -> U53(X:S) 20.59/20.89 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.59/20.89 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.59/20.89 a__U62(tt) -> tt 20.59/20.89 a__U62(X:S) -> U62(X:S) 20.59/20.89 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.59/20.89 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.59/20.89 a__U72(tt) -> tt 20.59/20.89 a__U72(X:S) -> U72(X:S) 20.59/20.89 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.89 a____(nil,X:S) -> mark(X:S) 20.59/20.89 a____(X:S,nil) -> mark(X:S) 20.59/20.89 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.59/20.89 a__and(tt,X:S) -> mark(X:S) 20.59/20.89 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.59/20.89 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.89 a__isList(nil) -> tt 20.59/20.89 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.59/20.89 a__isList(X:S) -> isList(X:S) 20.59/20.89 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.89 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.89 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.59/20.89 a__isNeList(X:S) -> isNeList(X:S) 20.59/20.89 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.89 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.59/20.89 a__isNePal(X:S) -> isNePal(X:S) 20.59/20.89 a__isPal(nil) -> tt 20.59/20.89 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.59/20.89 a__isPal(X:S) -> isPal(X:S) 20.59/20.89 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.89 a__isPalListKind(a) -> tt 20.59/20.89 a__isPalListKind(e) -> tt 20.59/20.89 a__isPalListKind(i) -> tt 20.59/20.89 a__isPalListKind(nil) -> tt 20.59/20.89 a__isPalListKind(o) -> tt 20.59/20.89 a__isPalListKind(u) -> tt 20.59/20.89 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.59/20.89 a__isQid(a) -> tt 20.59/20.89 a__isQid(e) -> tt 20.59/20.89 a__isQid(i) -> tt 20.59/20.89 a__isQid(o) -> tt 20.59/20.89 a__isQid(u) -> tt 20.59/20.89 a__isQid(X:S) -> isQid(X:S) 20.59/20.89 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.59/20.89 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.59/20.89 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.59/20.89 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.59/20.89 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.59/20.89 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.59/20.89 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.59/20.89 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.59/20.89 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.59/20.89 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.59/20.89 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.59/20.89 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.59/20.89 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.59/20.89 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.59/20.89 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.59/20.89 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.59/20.89 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.59/20.89 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.59/20.89 mark(a) -> a 20.59/20.89 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.59/20.89 mark(e) -> e 20.59/20.89 mark(i) -> i 20.59/20.89 mark(isList(X:S)) -> a__isList(X:S) 20.59/20.89 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.59/20.89 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.59/20.89 mark(isPal(X:S)) -> a__isPal(X:S) 20.59/20.89 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.59/20.89 mark(isQid(X:S)) -> a__isQid(X:S) 20.59/20.89 mark(nil) -> nil 20.59/20.89 mark(o) -> o 20.59/20.89 mark(tt) -> tt 20.59/20.89 mark(u) -> u 20.59/20.89 ->Strongly Connected Components: 20.59/20.89 ->->Cycle: 20.59/20.89 ->->-> Pairs: 20.59/20.89 A____(nil,X:S) -> MARK(X:S) 20.59/20.89 A____(X:S,nil) -> MARK(X:S) 20.59/20.89 A__AND(tt,X:S) -> MARK(X:S) 20.59/20.89 A__ISLIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.89 A__ISLIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.89 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.89 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.89 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.89 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.89 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.89 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.59/20.89 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.89 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.89 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.89 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.89 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U12(X:S)) -> MARK(X:S) 20.59/20.89 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.89 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U23(X:S)) -> MARK(X:S) 20.59/20.89 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U32(X:S)) -> MARK(X:S) 20.59/20.89 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.89 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U43(X:S)) -> MARK(X:S) 20.59/20.89 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.89 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U53(X:S)) -> MARK(X:S) 20.59/20.89 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U62(X:S)) -> MARK(X:S) 20.59/20.89 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U72(X:S)) -> MARK(X:S) 20.59/20.89 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 20.59/20.89 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.59/20.89 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.59/20.89 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.59/20.89 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.59/20.89 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.59/20.89 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.59/20.89 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.59/20.89 ->->-> Rules: 20.59/20.89 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.59/20.89 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.59/20.89 a__U12(tt) -> tt 20.59/20.89 a__U12(X:S) -> U12(X:S) 20.59/20.89 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.59/20.89 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.59/20.89 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.59/20.89 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.59/20.89 a__U23(tt) -> tt 20.59/20.89 a__U23(X:S) -> U23(X:S) 20.59/20.89 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.59/20.89 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.59/20.89 a__U32(tt) -> tt 20.59/20.89 a__U32(X:S) -> U32(X:S) 20.59/20.89 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.59/20.89 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.59/20.89 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.59/20.89 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.59/20.89 a__U43(tt) -> tt 20.59/20.89 a__U43(X:S) -> U43(X:S) 20.59/20.89 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.59/20.89 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.59/20.89 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.59/20.89 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.59/20.89 a__U53(tt) -> tt 20.59/20.89 a__U53(X:S) -> U53(X:S) 20.59/20.89 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.59/20.89 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.59/20.89 a__U62(tt) -> tt 20.59/20.89 a__U62(X:S) -> U62(X:S) 20.59/20.89 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.59/20.89 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.59/20.89 a__U72(tt) -> tt 20.59/20.89 a__U72(X:S) -> U72(X:S) 20.59/20.89 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.89 a____(nil,X:S) -> mark(X:S) 20.59/20.89 a____(X:S,nil) -> mark(X:S) 20.59/20.89 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.59/20.89 a__and(tt,X:S) -> mark(X:S) 20.59/20.89 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.59/20.89 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.89 a__isList(nil) -> tt 20.59/20.89 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.59/20.89 a__isList(X:S) -> isList(X:S) 20.59/20.89 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.89 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.89 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.59/20.89 a__isNeList(X:S) -> isNeList(X:S) 20.59/20.89 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.89 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.59/20.89 a__isNePal(X:S) -> isNePal(X:S) 20.59/20.89 a__isPal(nil) -> tt 20.59/20.89 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.59/20.89 a__isPal(X:S) -> isPal(X:S) 20.59/20.89 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.89 a__isPalListKind(a) -> tt 20.59/20.89 a__isPalListKind(e) -> tt 20.59/20.89 a__isPalListKind(i) -> tt 20.59/20.89 a__isPalListKind(nil) -> tt 20.59/20.89 a__isPalListKind(o) -> tt 20.59/20.89 a__isPalListKind(u) -> tt 20.59/20.89 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.59/20.89 a__isQid(a) -> tt 20.59/20.89 a__isQid(e) -> tt 20.59/20.89 a__isQid(i) -> tt 20.59/20.89 a__isQid(o) -> tt 20.59/20.89 a__isQid(u) -> tt 20.59/20.89 a__isQid(X:S) -> isQid(X:S) 20.59/20.89 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.59/20.89 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.59/20.89 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.59/20.89 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.59/20.89 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.59/20.89 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.59/20.89 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.59/20.89 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.59/20.89 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.59/20.89 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.59/20.89 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.59/20.89 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.59/20.89 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.59/20.89 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.59/20.89 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.59/20.89 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.59/20.89 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.59/20.89 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.59/20.89 mark(a) -> a 20.59/20.89 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.59/20.89 mark(e) -> e 20.59/20.89 mark(i) -> i 20.59/20.89 mark(isList(X:S)) -> a__isList(X:S) 20.59/20.89 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.59/20.89 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.59/20.89 mark(isPal(X:S)) -> a__isPal(X:S) 20.59/20.89 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.59/20.89 mark(isQid(X:S)) -> a__isQid(X:S) 20.59/20.89 mark(nil) -> nil 20.59/20.89 mark(o) -> o 20.59/20.89 mark(tt) -> tt 20.59/20.89 mark(u) -> u 20.59/20.89 20.59/20.89 Problem 1: 20.59/20.89 20.59/20.89 Reduction Pairs Processor: 20.59/20.89 -> Pairs: 20.59/20.89 A____(nil,X:S) -> MARK(X:S) 20.59/20.89 A____(X:S,nil) -> MARK(X:S) 20.59/20.89 A__AND(tt,X:S) -> MARK(X:S) 20.59/20.89 A__ISLIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.89 A__ISLIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.89 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.89 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.89 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.89 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.89 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.89 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.59/20.89 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.89 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.89 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.89 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.89 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U12(X:S)) -> MARK(X:S) 20.59/20.89 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.89 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U23(X:S)) -> MARK(X:S) 20.59/20.89 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U32(X:S)) -> MARK(X:S) 20.59/20.89 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.89 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U43(X:S)) -> MARK(X:S) 20.59/20.89 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.89 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U53(X:S)) -> MARK(X:S) 20.59/20.89 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U62(X:S)) -> MARK(X:S) 20.59/20.89 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U72(X:S)) -> MARK(X:S) 20.59/20.89 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 20.59/20.89 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.59/20.89 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.59/20.89 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.59/20.89 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.59/20.89 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.59/20.89 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.59/20.89 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.59/20.89 -> Rules: 20.59/20.89 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.59/20.89 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.59/20.89 a__U12(tt) -> tt 20.59/20.89 a__U12(X:S) -> U12(X:S) 20.59/20.89 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.59/20.89 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.59/20.89 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.59/20.89 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.59/20.89 a__U23(tt) -> tt 20.59/20.89 a__U23(X:S) -> U23(X:S) 20.59/20.89 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.59/20.89 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.59/20.89 a__U32(tt) -> tt 20.59/20.89 a__U32(X:S) -> U32(X:S) 20.59/20.89 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.59/20.89 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.59/20.89 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.59/20.89 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.59/20.89 a__U43(tt) -> tt 20.59/20.89 a__U43(X:S) -> U43(X:S) 20.59/20.89 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.59/20.89 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.59/20.89 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.59/20.89 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.59/20.89 a__U53(tt) -> tt 20.59/20.89 a__U53(X:S) -> U53(X:S) 20.59/20.89 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.59/20.89 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.59/20.89 a__U62(tt) -> tt 20.59/20.89 a__U62(X:S) -> U62(X:S) 20.59/20.89 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.59/20.89 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.59/20.89 a__U72(tt) -> tt 20.59/20.89 a__U72(X:S) -> U72(X:S) 20.59/20.89 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.89 a____(nil,X:S) -> mark(X:S) 20.59/20.89 a____(X:S,nil) -> mark(X:S) 20.59/20.89 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.59/20.89 a__and(tt,X:S) -> mark(X:S) 20.59/20.89 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.59/20.89 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.89 a__isList(nil) -> tt 20.59/20.89 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.59/20.89 a__isList(X:S) -> isList(X:S) 20.59/20.89 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.89 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.89 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.59/20.89 a__isNeList(X:S) -> isNeList(X:S) 20.59/20.89 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.89 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.59/20.89 a__isNePal(X:S) -> isNePal(X:S) 20.59/20.89 a__isPal(nil) -> tt 20.59/20.89 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.59/20.89 a__isPal(X:S) -> isPal(X:S) 20.59/20.89 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.89 a__isPalListKind(a) -> tt 20.59/20.89 a__isPalListKind(e) -> tt 20.59/20.89 a__isPalListKind(i) -> tt 20.59/20.89 a__isPalListKind(nil) -> tt 20.59/20.89 a__isPalListKind(o) -> tt 20.59/20.89 a__isPalListKind(u) -> tt 20.59/20.89 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.59/20.89 a__isQid(a) -> tt 20.59/20.89 a__isQid(e) -> tt 20.59/20.89 a__isQid(i) -> tt 20.59/20.89 a__isQid(o) -> tt 20.59/20.89 a__isQid(u) -> tt 20.59/20.89 a__isQid(X:S) -> isQid(X:S) 20.59/20.89 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.59/20.89 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.59/20.89 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.59/20.89 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.59/20.89 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.59/20.89 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.59/20.89 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.59/20.89 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.59/20.89 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.59/20.89 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.59/20.89 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.59/20.89 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.59/20.89 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.59/20.89 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.59/20.89 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.59/20.89 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.59/20.89 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.59/20.89 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.59/20.89 mark(a) -> a 20.59/20.89 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.59/20.89 mark(e) -> e 20.59/20.89 mark(i) -> i 20.59/20.89 mark(isList(X:S)) -> a__isList(X:S) 20.59/20.89 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.59/20.89 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.59/20.89 mark(isPal(X:S)) -> a__isPal(X:S) 20.59/20.89 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.59/20.89 mark(isQid(X:S)) -> a__isQid(X:S) 20.59/20.89 mark(nil) -> nil 20.59/20.89 mark(o) -> o 20.59/20.89 mark(tt) -> tt 20.59/20.89 mark(u) -> u 20.59/20.89 -> Usable rules: 20.59/20.89 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.59/20.89 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.59/20.89 a__U12(tt) -> tt 20.59/20.89 a__U12(X:S) -> U12(X:S) 20.59/20.89 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.59/20.89 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.59/20.89 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.59/20.89 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.59/20.89 a__U23(tt) -> tt 20.59/20.89 a__U23(X:S) -> U23(X:S) 20.59/20.89 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.59/20.89 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.59/20.89 a__U32(tt) -> tt 20.59/20.89 a__U32(X:S) -> U32(X:S) 20.59/20.89 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.59/20.89 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.59/20.89 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.59/20.89 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.59/20.89 a__U43(tt) -> tt 20.59/20.89 a__U43(X:S) -> U43(X:S) 20.59/20.89 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.59/20.89 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.59/20.89 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.59/20.89 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.59/20.89 a__U53(tt) -> tt 20.59/20.89 a__U53(X:S) -> U53(X:S) 20.59/20.89 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.59/20.89 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.59/20.89 a__U62(tt) -> tt 20.59/20.89 a__U62(X:S) -> U62(X:S) 20.59/20.89 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.59/20.89 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.59/20.89 a__U72(tt) -> tt 20.59/20.89 a__U72(X:S) -> U72(X:S) 20.59/20.89 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.89 a____(nil,X:S) -> mark(X:S) 20.59/20.89 a____(X:S,nil) -> mark(X:S) 20.59/20.89 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.59/20.89 a__and(tt,X:S) -> mark(X:S) 20.59/20.89 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.59/20.89 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.89 a__isList(nil) -> tt 20.59/20.89 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.59/20.89 a__isList(X:S) -> isList(X:S) 20.59/20.89 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.89 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.89 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.59/20.89 a__isNeList(X:S) -> isNeList(X:S) 20.59/20.89 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.89 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.59/20.89 a__isNePal(X:S) -> isNePal(X:S) 20.59/20.89 a__isPal(nil) -> tt 20.59/20.89 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.59/20.89 a__isPal(X:S) -> isPal(X:S) 20.59/20.89 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.89 a__isPalListKind(a) -> tt 20.59/20.89 a__isPalListKind(e) -> tt 20.59/20.89 a__isPalListKind(i) -> tt 20.59/20.89 a__isPalListKind(nil) -> tt 20.59/20.89 a__isPalListKind(o) -> tt 20.59/20.89 a__isPalListKind(u) -> tt 20.59/20.89 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.59/20.89 a__isQid(a) -> tt 20.59/20.89 a__isQid(e) -> tt 20.59/20.89 a__isQid(i) -> tt 20.59/20.89 a__isQid(o) -> tt 20.59/20.89 a__isQid(u) -> tt 20.59/20.89 a__isQid(X:S) -> isQid(X:S) 20.59/20.89 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.59/20.89 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.59/20.89 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.59/20.89 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.59/20.89 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.59/20.89 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.59/20.89 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.59/20.89 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.59/20.89 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.59/20.89 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.59/20.89 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.59/20.89 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.59/20.89 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.59/20.89 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.59/20.89 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.59/20.89 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.59/20.89 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.59/20.89 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.59/20.89 mark(a) -> a 20.59/20.89 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.59/20.89 mark(e) -> e 20.59/20.89 mark(i) -> i 20.59/20.89 mark(isList(X:S)) -> a__isList(X:S) 20.59/20.89 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.59/20.89 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.59/20.89 mark(isPal(X:S)) -> a__isPal(X:S) 20.59/20.89 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.59/20.89 mark(isQid(X:S)) -> a__isQid(X:S) 20.59/20.89 mark(nil) -> nil 20.59/20.89 mark(o) -> o 20.59/20.89 mark(tt) -> tt 20.59/20.89 mark(u) -> u 20.59/20.89 ->Interpretation type: 20.59/20.89 Linear 20.59/20.89 ->Coefficients: 20.59/20.89 Natural Numbers 20.59/20.89 ->Dimension: 20.59/20.89 1 20.59/20.89 ->Bound: 20.59/20.89 2 20.59/20.89 ->Interpretation: 20.59/20.89 20.59/20.89 [a__U11](X1,X2) = X1 + 2.X2 + 1 20.59/20.89 [a__U12](X) = X + 1 20.59/20.89 [a__U21](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 20.59/20.89 [a__U22](X1,X2) = X1 + 2.X2 + 1 20.59/20.89 [a__U23](X) = X 20.59/20.89 [a__U31](X1,X2) = 2.X1 + 2.X2 20.59/20.89 [a__U32](X) = X 20.59/20.89 [a__U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.59/20.89 [a__U42](X1,X2) = X1 + 2.X2 + 1 20.59/20.89 [a__U43](X) = X + 1 20.59/20.89 [a__U51](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 20.59/20.89 [a__U52](X1,X2) = X1 + 2.X2 + 1 20.59/20.89 [a__U53](X) = X 20.59/20.89 [a__U61](X1,X2) = 2.X1 + 2.X2 + 2 20.59/20.89 [a__U62](X) = X + 1 20.59/20.89 [a__U71](X1,X2) = 2.X1 + 2.X2 + 2 20.59/20.89 [a__U72](X) = X 20.59/20.89 [a____](X1,X2) = 2.X1 + X2 + 2 20.59/20.89 [a__and](X1,X2) = X1 + X2 20.59/20.89 [a__isList](X) = 2.X + 1 20.59/20.89 [a__isNeList](X) = 2.X 20.59/20.89 [a__isNePal](X) = 2.X + 2 20.59/20.89 [a__isPal](X) = 2.X + 2 20.59/20.89 [a__isPalListKind](X) = 0 20.59/20.89 [a__isQid](X) = 2.X 20.59/20.89 [mark](X) = X 20.59/20.89 [U11](X1,X2) = X1 + 2.X2 + 1 20.59/20.89 [U12](X) = X + 1 20.59/20.89 [U21](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 20.59/20.89 [U22](X1,X2) = X1 + 2.X2 + 1 20.59/20.89 [U23](X) = X 20.59/20.89 [U31](X1,X2) = 2.X1 + 2.X2 20.59/20.89 [U32](X) = X 20.59/20.89 [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.59/20.89 [U42](X1,X2) = X1 + 2.X2 + 1 20.59/20.89 [U43](X) = X + 1 20.59/20.89 [U51](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 20.59/20.89 [U52](X1,X2) = X1 + 2.X2 + 1 20.59/20.89 [U53](X) = X 20.59/20.89 [U61](X1,X2) = 2.X1 + 2.X2 + 2 20.59/20.89 [U62](X) = X + 1 20.59/20.89 [U71](X1,X2) = 2.X1 + 2.X2 + 2 20.59/20.89 [U72](X) = X 20.59/20.89 [__](X1,X2) = 2.X1 + X2 + 2 20.59/20.89 [a] = 1 20.59/20.89 [and](X1,X2) = X1 + X2 20.59/20.89 [e] = 1 20.59/20.89 [fSNonEmpty] = 0 20.59/20.89 [i] = 1 20.59/20.89 [isList](X) = 2.X + 1 20.59/20.89 [isNeList](X) = 2.X 20.59/20.89 [isNePal](X) = 2.X + 2 20.59/20.89 [isPal](X) = 2.X + 2 20.59/20.89 [isPalListKind](X) = 0 20.59/20.89 [isQid](X) = 2.X 20.59/20.89 [nil] = 2 20.59/20.89 [o] = 2 20.59/20.89 [tt] = 0 20.59/20.89 [u] = 0 20.59/20.89 [A__U11](X1,X2) = 0 20.59/20.89 [A__U12](X) = 0 20.59/20.89 [A__U21](X1,X2,X3) = 0 20.59/20.89 [A__U22](X1,X2) = 0 20.59/20.89 [A__U23](X) = 0 20.59/20.89 [A__U31](X1,X2) = 0 20.59/20.89 [A__U32](X) = 0 20.59/20.89 [A__U41](X1,X2,X3) = 0 20.59/20.89 [A__U42](X1,X2) = 0 20.59/20.89 [A__U43](X) = 0 20.59/20.89 [A__U51](X1,X2,X3) = 0 20.59/20.89 [A__U52](X1,X2) = 0 20.59/20.89 [A__U53](X) = 0 20.59/20.89 [A__U61](X1,X2) = 0 20.59/20.89 [A__U62](X) = 0 20.59/20.89 [A__U71](X1,X2) = 0 20.59/20.89 [A__U72](X) = 0 20.59/20.89 [A____](X1,X2) = 2.X1 + 2.X2 + 2 20.59/20.89 [A__AND](X1,X2) = 2.X1 + 2.X2 + 2 20.59/20.89 [A__ISLIST](X) = 2.X + 2 20.59/20.89 [A__ISNELIST](X) = 2 20.59/20.89 [A__ISNEPAL](X) = 2.X + 2 20.59/20.89 [A__ISPAL](X) = 2.X + 2 20.59/20.89 [A__ISPALLISTKIND](X) = 2 20.59/20.89 [A__ISQID](X) = 0 20.59/20.89 [MARK](X) = 2.X + 2 20.59/20.89 20.59/20.89 Problem 1: 20.59/20.89 20.59/20.89 SCC Processor: 20.59/20.89 -> Pairs: 20.59/20.89 A____(X:S,nil) -> MARK(X:S) 20.59/20.89 A__AND(tt,X:S) -> MARK(X:S) 20.59/20.89 A__ISLIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.89 A__ISLIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.89 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.89 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.89 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.89 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.89 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.89 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.59/20.89 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.89 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.89 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.89 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.89 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U12(X:S)) -> MARK(X:S) 20.59/20.89 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.89 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U23(X:S)) -> MARK(X:S) 20.59/20.89 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U32(X:S)) -> MARK(X:S) 20.59/20.89 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.89 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U43(X:S)) -> MARK(X:S) 20.59/20.89 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.89 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U53(X:S)) -> MARK(X:S) 20.59/20.89 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U62(X:S)) -> MARK(X:S) 20.59/20.89 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U72(X:S)) -> MARK(X:S) 20.59/20.89 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 20.59/20.89 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.59/20.89 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.59/20.89 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.59/20.89 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.59/20.89 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.59/20.89 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.59/20.89 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.59/20.89 -> Rules: 20.59/20.89 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.59/20.89 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.59/20.89 a__U12(tt) -> tt 20.59/20.89 a__U12(X:S) -> U12(X:S) 20.59/20.89 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.59/20.89 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.59/20.89 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.59/20.89 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.59/20.89 a__U23(tt) -> tt 20.59/20.89 a__U23(X:S) -> U23(X:S) 20.59/20.89 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.59/20.89 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.59/20.89 a__U32(tt) -> tt 20.59/20.89 a__U32(X:S) -> U32(X:S) 20.59/20.89 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.59/20.89 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.59/20.89 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.59/20.89 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.59/20.89 a__U43(tt) -> tt 20.59/20.89 a__U43(X:S) -> U43(X:S) 20.59/20.89 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.59/20.89 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.59/20.89 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.59/20.89 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.59/20.89 a__U53(tt) -> tt 20.59/20.89 a__U53(X:S) -> U53(X:S) 20.59/20.89 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.59/20.89 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.59/20.89 a__U62(tt) -> tt 20.59/20.89 a__U62(X:S) -> U62(X:S) 20.59/20.89 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.59/20.89 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.59/20.89 a__U72(tt) -> tt 20.59/20.89 a__U72(X:S) -> U72(X:S) 20.59/20.89 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.89 a____(nil,X:S) -> mark(X:S) 20.59/20.89 a____(X:S,nil) -> mark(X:S) 20.59/20.89 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.59/20.89 a__and(tt,X:S) -> mark(X:S) 20.59/20.89 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.59/20.89 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.89 a__isList(nil) -> tt 20.59/20.89 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.59/20.89 a__isList(X:S) -> isList(X:S) 20.59/20.89 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.89 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.89 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.59/20.89 a__isNeList(X:S) -> isNeList(X:S) 20.59/20.89 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.89 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.59/20.89 a__isNePal(X:S) -> isNePal(X:S) 20.59/20.89 a__isPal(nil) -> tt 20.59/20.89 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.59/20.89 a__isPal(X:S) -> isPal(X:S) 20.59/20.89 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.89 a__isPalListKind(a) -> tt 20.59/20.89 a__isPalListKind(e) -> tt 20.59/20.89 a__isPalListKind(i) -> tt 20.59/20.89 a__isPalListKind(nil) -> tt 20.59/20.89 a__isPalListKind(o) -> tt 20.59/20.89 a__isPalListKind(u) -> tt 20.59/20.89 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.59/20.89 a__isQid(a) -> tt 20.59/20.89 a__isQid(e) -> tt 20.59/20.89 a__isQid(i) -> tt 20.59/20.89 a__isQid(o) -> tt 20.59/20.89 a__isQid(u) -> tt 20.59/20.89 a__isQid(X:S) -> isQid(X:S) 20.59/20.89 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.59/20.89 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.59/20.89 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.59/20.89 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.59/20.89 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.59/20.89 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.59/20.89 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.59/20.89 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.59/20.89 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.59/20.89 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.59/20.89 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.59/20.89 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.59/20.89 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.59/20.89 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.59/20.89 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.59/20.89 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.59/20.89 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.59/20.89 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.59/20.89 mark(a) -> a 20.59/20.89 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.59/20.89 mark(e) -> e 20.59/20.89 mark(i) -> i 20.59/20.89 mark(isList(X:S)) -> a__isList(X:S) 20.59/20.89 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.59/20.89 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.59/20.89 mark(isPal(X:S)) -> a__isPal(X:S) 20.59/20.89 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.59/20.89 mark(isQid(X:S)) -> a__isQid(X:S) 20.59/20.89 mark(nil) -> nil 20.59/20.89 mark(o) -> o 20.59/20.89 mark(tt) -> tt 20.59/20.89 mark(u) -> u 20.59/20.89 ->Strongly Connected Components: 20.59/20.89 ->->Cycle: 20.59/20.89 ->->-> Pairs: 20.59/20.89 A____(X:S,nil) -> MARK(X:S) 20.59/20.89 A__AND(tt,X:S) -> MARK(X:S) 20.59/20.89 A__ISLIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.89 A__ISLIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.89 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.89 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.89 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.89 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.89 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.89 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.59/20.89 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.89 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.59/20.89 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.89 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.59/20.89 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U12(X:S)) -> MARK(X:S) 20.59/20.89 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.89 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U23(X:S)) -> MARK(X:S) 20.59/20.89 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U32(X:S)) -> MARK(X:S) 20.59/20.89 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.89 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U43(X:S)) -> MARK(X:S) 20.59/20.89 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.59/20.89 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U53(X:S)) -> MARK(X:S) 20.59/20.89 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U62(X:S)) -> MARK(X:S) 20.59/20.89 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(U72(X:S)) -> MARK(X:S) 20.59/20.89 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 20.59/20.89 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.59/20.89 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.59/20.89 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.59/20.89 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.59/20.89 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.59/20.89 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.59/20.89 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.59/20.89 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.59/20.89 ->->-> Rules: 20.59/20.89 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.59/20.89 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.59/20.89 a__U12(tt) -> tt 20.59/20.89 a__U12(X:S) -> U12(X:S) 20.59/20.89 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.59/20.89 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.59/20.89 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.59/20.89 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.59/20.89 a__U23(tt) -> tt 20.59/20.89 a__U23(X:S) -> U23(X:S) 20.59/20.89 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.59/20.89 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.59/20.89 a__U32(tt) -> tt 20.59/20.89 a__U32(X:S) -> U32(X:S) 20.59/20.89 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.59/20.89 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.59/20.89 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.59/20.89 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.59/20.89 a__U43(tt) -> tt 20.59/20.89 a__U43(X:S) -> U43(X:S) 20.59/20.89 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.59/20.89 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.59/20.89 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.59/20.89 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.59/20.89 a__U53(tt) -> tt 20.59/20.89 a__U53(X:S) -> U53(X:S) 20.59/20.89 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.59/20.89 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.59/20.89 a__U62(tt) -> tt 20.59/20.89 a__U62(X:S) -> U62(X:S) 20.59/20.89 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.59/20.89 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.59/20.89 a__U72(tt) -> tt 20.59/20.89 a__U72(X:S) -> U72(X:S) 20.59/20.89 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.59/20.89 a____(nil,X:S) -> mark(X:S) 20.59/20.89 a____(X:S,nil) -> mark(X:S) 20.59/20.89 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.59/20.89 a__and(tt,X:S) -> mark(X:S) 20.59/20.89 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.59/20.89 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.89 a__isList(nil) -> tt 20.59/20.89 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.59/20.89 a__isList(X:S) -> isList(X:S) 20.59/20.89 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.89 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.59/20.89 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.59/20.89 a__isNeList(X:S) -> isNeList(X:S) 20.59/20.89 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.59/20.89 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.59/20.89 a__isNePal(X:S) -> isNePal(X:S) 20.59/20.89 a__isPal(nil) -> tt 20.59/20.89 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.59/20.89 a__isPal(X:S) -> isPal(X:S) 20.59/20.89 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.59/20.89 a__isPalListKind(a) -> tt 20.59/20.89 a__isPalListKind(e) -> tt 20.59/20.89 a__isPalListKind(i) -> tt 20.59/20.89 a__isPalListKind(nil) -> tt 20.59/20.89 a__isPalListKind(o) -> tt 20.59/20.89 a__isPalListKind(u) -> tt 20.59/20.89 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.59/20.89 a__isQid(a) -> tt 20.59/20.89 a__isQid(e) -> tt 20.59/20.89 a__isQid(i) -> tt 20.59/20.89 a__isQid(o) -> tt 20.59/20.89 a__isQid(u) -> tt 20.59/20.89 a__isQid(X:S) -> isQid(X:S) 20.59/20.89 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.59/20.89 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.59/20.89 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.59/20.89 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.59/20.89 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.59/20.89 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.60/20.89 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.60/20.89 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.60/20.89 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.60/20.89 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.60/20.89 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.60/20.89 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.60/20.89 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.60/20.89 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.60/20.89 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.60/20.89 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.60/20.89 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.60/20.89 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.60/20.89 mark(a) -> a 20.60/20.89 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.60/20.89 mark(e) -> e 20.60/20.89 mark(i) -> i 20.60/20.89 mark(isList(X:S)) -> a__isList(X:S) 20.60/20.89 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.60/20.89 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.60/20.89 mark(isPal(X:S)) -> a__isPal(X:S) 20.60/20.89 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.60/20.89 mark(isQid(X:S)) -> a__isQid(X:S) 20.60/20.89 mark(nil) -> nil 20.60/20.89 mark(o) -> o 20.60/20.89 mark(tt) -> tt 20.60/20.89 mark(u) -> u 20.60/20.89 20.60/20.89 Problem 1: 20.60/20.89 20.60/20.89 Reduction Pairs Processor: 20.60/20.89 -> Pairs: 20.60/20.89 A____(X:S,nil) -> MARK(X:S) 20.60/20.89 A__AND(tt,X:S) -> MARK(X:S) 20.60/20.89 A__ISLIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.89 A__ISLIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.89 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.89 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.89 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.89 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.89 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.89 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.60/20.89 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.89 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.89 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.89 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.89 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.89 MARK(U12(X:S)) -> MARK(X:S) 20.60/20.89 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.89 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.89 MARK(U23(X:S)) -> MARK(X:S) 20.60/20.89 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.89 MARK(U32(X:S)) -> MARK(X:S) 20.60/20.89 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.89 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.89 MARK(U43(X:S)) -> MARK(X:S) 20.60/20.89 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.89 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.89 MARK(U53(X:S)) -> MARK(X:S) 20.60/20.89 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.89 MARK(U62(X:S)) -> MARK(X:S) 20.60/20.89 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.89 MARK(U72(X:S)) -> MARK(X:S) 20.60/20.89 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 20.60/20.89 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.89 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.60/20.89 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.60/20.89 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.89 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.60/20.89 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.60/20.89 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.60/20.89 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.60/20.89 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.60/20.89 -> Rules: 20.60/20.89 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.60/20.89 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.60/20.89 a__U12(tt) -> tt 20.60/20.89 a__U12(X:S) -> U12(X:S) 20.60/20.89 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.60/20.89 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.60/20.89 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.60/20.90 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.60/20.90 a__U23(tt) -> tt 20.60/20.90 a__U23(X:S) -> U23(X:S) 20.60/20.90 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.60/20.90 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.60/20.90 a__U32(tt) -> tt 20.60/20.90 a__U32(X:S) -> U32(X:S) 20.60/20.90 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.60/20.90 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.60/20.90 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.60/20.90 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.60/20.90 a__U43(tt) -> tt 20.60/20.90 a__U43(X:S) -> U43(X:S) 20.60/20.90 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.60/20.90 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.60/20.90 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.60/20.90 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.60/20.90 a__U53(tt) -> tt 20.60/20.90 a__U53(X:S) -> U53(X:S) 20.60/20.90 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.60/20.90 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.60/20.90 a__U62(tt) -> tt 20.60/20.90 a__U62(X:S) -> U62(X:S) 20.60/20.90 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.60/20.90 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.60/20.90 a__U72(tt) -> tt 20.60/20.90 a__U72(X:S) -> U72(X:S) 20.60/20.90 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.60/20.90 a____(nil,X:S) -> mark(X:S) 20.60/20.90 a____(X:S,nil) -> mark(X:S) 20.60/20.90 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.60/20.90 a__and(tt,X:S) -> mark(X:S) 20.60/20.90 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.60/20.90 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.90 a__isList(nil) -> tt 20.60/20.90 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.60/20.90 a__isList(X:S) -> isList(X:S) 20.60/20.90 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.90 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.90 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.60/20.90 a__isNeList(X:S) -> isNeList(X:S) 20.60/20.90 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.90 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.60/20.90 a__isNePal(X:S) -> isNePal(X:S) 20.60/20.90 a__isPal(nil) -> tt 20.60/20.90 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.60/20.90 a__isPal(X:S) -> isPal(X:S) 20.60/20.90 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.90 a__isPalListKind(a) -> tt 20.60/20.90 a__isPalListKind(e) -> tt 20.60/20.90 a__isPalListKind(i) -> tt 20.60/20.90 a__isPalListKind(nil) -> tt 20.60/20.90 a__isPalListKind(o) -> tt 20.60/20.90 a__isPalListKind(u) -> tt 20.60/20.90 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.60/20.90 a__isQid(a) -> tt 20.60/20.90 a__isQid(e) -> tt 20.60/20.90 a__isQid(i) -> tt 20.60/20.90 a__isQid(o) -> tt 20.60/20.90 a__isQid(u) -> tt 20.60/20.90 a__isQid(X:S) -> isQid(X:S) 20.60/20.90 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.60/20.90 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.60/20.90 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.60/20.90 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.60/20.90 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.60/20.90 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.60/20.90 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.60/20.90 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.60/20.90 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.60/20.90 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.60/20.90 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.60/20.90 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.60/20.90 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.60/20.90 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.60/20.90 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.60/20.90 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.60/20.90 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.60/20.90 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.60/20.90 mark(a) -> a 20.60/20.90 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.60/20.90 mark(e) -> e 20.60/20.90 mark(i) -> i 20.60/20.90 mark(isList(X:S)) -> a__isList(X:S) 20.60/20.90 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.60/20.90 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.60/20.90 mark(isPal(X:S)) -> a__isPal(X:S) 20.60/20.90 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.60/20.90 mark(isQid(X:S)) -> a__isQid(X:S) 20.60/20.90 mark(nil) -> nil 20.60/20.90 mark(o) -> o 20.60/20.90 mark(tt) -> tt 20.60/20.90 mark(u) -> u 20.60/20.90 -> Usable rules: 20.60/20.90 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.60/20.90 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.60/20.90 a__U12(tt) -> tt 20.60/20.90 a__U12(X:S) -> U12(X:S) 20.60/20.90 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.60/20.90 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.60/20.90 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.60/20.90 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.60/20.90 a__U23(tt) -> tt 20.60/20.90 a__U23(X:S) -> U23(X:S) 20.60/20.90 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.60/20.90 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.60/20.90 a__U32(tt) -> tt 20.60/20.90 a__U32(X:S) -> U32(X:S) 20.60/20.90 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.60/20.90 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.60/20.90 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.60/20.90 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.60/20.90 a__U43(tt) -> tt 20.60/20.90 a__U43(X:S) -> U43(X:S) 20.60/20.90 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.60/20.90 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.60/20.90 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.60/20.90 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.60/20.90 a__U53(tt) -> tt 20.60/20.90 a__U53(X:S) -> U53(X:S) 20.60/20.90 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.60/20.90 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.60/20.90 a__U62(tt) -> tt 20.60/20.90 a__U62(X:S) -> U62(X:S) 20.60/20.90 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.60/20.90 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.60/20.90 a__U72(tt) -> tt 20.60/20.90 a__U72(X:S) -> U72(X:S) 20.60/20.90 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.60/20.90 a____(nil,X:S) -> mark(X:S) 20.60/20.90 a____(X:S,nil) -> mark(X:S) 20.60/20.90 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.60/20.90 a__and(tt,X:S) -> mark(X:S) 20.60/20.90 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.60/20.90 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.90 a__isList(nil) -> tt 20.60/20.90 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.60/20.90 a__isList(X:S) -> isList(X:S) 20.60/20.90 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.90 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.90 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.60/20.90 a__isNeList(X:S) -> isNeList(X:S) 20.60/20.90 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.90 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.60/20.90 a__isNePal(X:S) -> isNePal(X:S) 20.60/20.90 a__isPal(nil) -> tt 20.60/20.90 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.60/20.90 a__isPal(X:S) -> isPal(X:S) 20.60/20.90 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.90 a__isPalListKind(a) -> tt 20.60/20.90 a__isPalListKind(e) -> tt 20.60/20.90 a__isPalListKind(i) -> tt 20.60/20.90 a__isPalListKind(nil) -> tt 20.60/20.90 a__isPalListKind(o) -> tt 20.60/20.90 a__isPalListKind(u) -> tt 20.60/20.90 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.60/20.90 a__isQid(a) -> tt 20.60/20.90 a__isQid(e) -> tt 20.60/20.90 a__isQid(i) -> tt 20.60/20.90 a__isQid(o) -> tt 20.60/20.90 a__isQid(u) -> tt 20.60/20.90 a__isQid(X:S) -> isQid(X:S) 20.60/20.90 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.60/20.90 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.60/20.90 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.60/20.90 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.60/20.90 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.60/20.90 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.60/20.90 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.60/20.90 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.60/20.90 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.60/20.90 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.60/20.90 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.60/20.90 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.60/20.90 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.60/20.90 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.60/20.90 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.60/20.90 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.60/20.90 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.60/20.90 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.60/20.90 mark(a) -> a 20.60/20.90 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.60/20.90 mark(e) -> e 20.60/20.90 mark(i) -> i 20.60/20.90 mark(isList(X:S)) -> a__isList(X:S) 20.60/20.90 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.60/20.90 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.60/20.90 mark(isPal(X:S)) -> a__isPal(X:S) 20.60/20.90 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.60/20.90 mark(isQid(X:S)) -> a__isQid(X:S) 20.60/20.90 mark(nil) -> nil 20.60/20.90 mark(o) -> o 20.60/20.90 mark(tt) -> tt 20.60/20.90 mark(u) -> u 20.60/20.90 ->Interpretation type: 20.60/20.90 Linear 20.60/20.90 ->Coefficients: 20.60/20.90 Natural Numbers 20.60/20.90 ->Dimension: 20.60/20.90 1 20.60/20.90 ->Bound: 20.60/20.90 2 20.60/20.90 ->Interpretation: 20.60/20.90 20.60/20.90 [a__U11](X1,X2) = 2.X1 + 2.X2 + 1 20.60/20.90 [a__U12](X) = X + 1 20.60/20.90 [a__U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.60/20.90 [a__U22](X1,X2) = X1 + 2.X2 + 1 20.60/20.90 [a__U23](X) = X 20.60/20.90 [a__U31](X1,X2) = 2.X1 + 2.X2 20.60/20.90 [a__U32](X) = 2.X 20.60/20.90 [a__U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.60/20.90 [a__U42](X1,X2) = X1 + 2.X2 + 1 20.60/20.90 [a__U43](X) = X + 1 20.60/20.90 [a__U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.60/20.90 [a__U52](X1,X2) = X1 + 2.X2 + 2 20.60/20.90 [a__U53](X) = X + 1 20.60/20.90 [a__U61](X1,X2) = 2.X1 + X2 20.60/20.90 [a__U62](X) = 2.X 20.60/20.90 [a__U71](X1,X2) = X1 + 2.X2 + 1 20.60/20.90 [a__U72](X) = 2.X 20.60/20.90 [a____](X1,X2) = 2.X1 + X2 + 2 20.60/20.90 [a__and](X1,X2) = X1 + X2 20.60/20.90 [a__isList](X) = 2.X + 1 20.60/20.90 [a__isNeList](X) = 2.X 20.60/20.90 [a__isNePal](X) = X 20.60/20.90 [a__isPal](X) = 2.X + 2 20.60/20.90 [a__isPalListKind](X) = 0 20.60/20.90 [a__isQid](X) = 0 20.60/20.90 [mark](X) = X 20.60/20.90 [U11](X1,X2) = 2.X1 + 2.X2 + 1 20.60/20.90 [U12](X) = X + 1 20.60/20.90 [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.60/20.90 [U22](X1,X2) = X1 + 2.X2 + 1 20.60/20.90 [U23](X) = X 20.60/20.90 [U31](X1,X2) = 2.X1 + 2.X2 20.60/20.90 [U32](X) = 2.X 20.60/20.90 [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.60/20.90 [U42](X1,X2) = X1 + 2.X2 + 1 20.60/20.90 [U43](X) = X + 1 20.60/20.90 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.60/20.90 [U52](X1,X2) = X1 + 2.X2 + 2 20.60/20.90 [U53](X) = X + 1 20.60/20.90 [U61](X1,X2) = 2.X1 + X2 20.60/20.90 [U62](X) = 2.X 20.60/20.90 [U71](X1,X2) = X1 + 2.X2 + 1 20.60/20.90 [U72](X) = 2.X 20.60/20.90 [__](X1,X2) = 2.X1 + X2 + 2 20.60/20.90 [a] = 1 20.60/20.90 [and](X1,X2) = X1 + X2 20.60/20.90 [e] = 1 20.60/20.90 [fSNonEmpty] = 0 20.60/20.90 [i] = 1 20.60/20.90 [isList](X) = 2.X + 1 20.60/20.90 [isNeList](X) = 2.X 20.60/20.90 [isNePal](X) = X 20.60/20.90 [isPal](X) = 2.X + 2 20.60/20.90 [isPalListKind](X) = 0 20.60/20.90 [isQid](X) = 0 20.60/20.90 [nil] = 2 20.60/20.90 [o] = 2 20.60/20.90 [tt] = 0 20.60/20.90 [u] = 1 20.60/20.90 [A__U11](X1,X2) = 0 20.60/20.90 [A__U12](X) = 0 20.60/20.90 [A__U21](X1,X2,X3) = 0 20.60/20.90 [A__U22](X1,X2) = 0 20.60/20.90 [A__U23](X) = 0 20.60/20.90 [A__U31](X1,X2) = 0 20.60/20.90 [A__U32](X) = 0 20.60/20.90 [A__U41](X1,X2,X3) = 0 20.60/20.90 [A__U42](X1,X2) = 0 20.60/20.90 [A__U43](X) = 0 20.60/20.90 [A__U51](X1,X2,X3) = 0 20.60/20.90 [A__U52](X1,X2) = 0 20.60/20.90 [A__U53](X) = 0 20.60/20.90 [A__U61](X1,X2) = 0 20.60/20.90 [A__U62](X) = 0 20.60/20.90 [A__U71](X1,X2) = 0 20.60/20.90 [A__U72](X) = 0 20.60/20.90 [A____](X1,X2) = 2.X1 + 2.X2 + 2 20.60/20.90 [A__AND](X1,X2) = 2.X2 + 2 20.60/20.90 [A__ISLIST](X) = 2.X + 2 20.60/20.90 [A__ISNELIST](X) = 2.X + 2 20.60/20.90 [A__ISNEPAL](X) = 2.X + 2 20.60/20.90 [A__ISPAL](X) = 2.X + 2 20.60/20.90 [A__ISPALLISTKIND](X) = 2 20.60/20.90 [A__ISQID](X) = 0 20.60/20.90 [MARK](X) = 2.X + 2 20.60/20.90 20.60/20.90 Problem 1: 20.60/20.90 20.60/20.90 SCC Processor: 20.60/20.90 -> Pairs: 20.60/20.90 A__AND(tt,X:S) -> MARK(X:S) 20.60/20.90 A__ISLIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.90 A__ISLIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.90 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.90 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.90 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.90 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.90 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.90 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.60/20.90 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.90 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.90 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.90 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.90 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U12(X:S)) -> MARK(X:S) 20.60/20.90 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.90 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U23(X:S)) -> MARK(X:S) 20.60/20.90 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U32(X:S)) -> MARK(X:S) 20.60/20.90 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.90 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U43(X:S)) -> MARK(X:S) 20.60/20.90 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.90 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U53(X:S)) -> MARK(X:S) 20.60/20.90 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U62(X:S)) -> MARK(X:S) 20.60/20.90 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U72(X:S)) -> MARK(X:S) 20.60/20.90 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 20.60/20.90 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.60/20.90 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.60/20.90 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.60/20.90 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.60/20.90 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.60/20.90 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.60/20.90 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.60/20.90 -> Rules: 20.60/20.90 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.60/20.90 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.60/20.90 a__U12(tt) -> tt 20.60/20.90 a__U12(X:S) -> U12(X:S) 20.60/20.90 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.60/20.90 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.60/20.90 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.60/20.90 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.60/20.90 a__U23(tt) -> tt 20.60/20.90 a__U23(X:S) -> U23(X:S) 20.60/20.90 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.60/20.90 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.60/20.90 a__U32(tt) -> tt 20.60/20.90 a__U32(X:S) -> U32(X:S) 20.60/20.90 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.60/20.90 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.60/20.90 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.60/20.90 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.60/20.90 a__U43(tt) -> tt 20.60/20.90 a__U43(X:S) -> U43(X:S) 20.60/20.90 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.60/20.90 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.60/20.90 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.60/20.90 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.60/20.90 a__U53(tt) -> tt 20.60/20.90 a__U53(X:S) -> U53(X:S) 20.60/20.90 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.60/20.90 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.60/20.90 a__U62(tt) -> tt 20.60/20.90 a__U62(X:S) -> U62(X:S) 20.60/20.90 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.60/20.90 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.60/20.90 a__U72(tt) -> tt 20.60/20.90 a__U72(X:S) -> U72(X:S) 20.60/20.90 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.60/20.90 a____(nil,X:S) -> mark(X:S) 20.60/20.90 a____(X:S,nil) -> mark(X:S) 20.60/20.90 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.60/20.90 a__and(tt,X:S) -> mark(X:S) 20.60/20.90 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.60/20.90 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.90 a__isList(nil) -> tt 20.60/20.90 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.60/20.90 a__isList(X:S) -> isList(X:S) 20.60/20.90 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.90 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.90 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.60/20.90 a__isNeList(X:S) -> isNeList(X:S) 20.60/20.90 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.90 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.60/20.90 a__isNePal(X:S) -> isNePal(X:S) 20.60/20.90 a__isPal(nil) -> tt 20.60/20.90 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.60/20.90 a__isPal(X:S) -> isPal(X:S) 20.60/20.90 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.90 a__isPalListKind(a) -> tt 20.60/20.90 a__isPalListKind(e) -> tt 20.60/20.90 a__isPalListKind(i) -> tt 20.60/20.90 a__isPalListKind(nil) -> tt 20.60/20.90 a__isPalListKind(o) -> tt 20.60/20.90 a__isPalListKind(u) -> tt 20.60/20.90 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.60/20.90 a__isQid(a) -> tt 20.60/20.90 a__isQid(e) -> tt 20.60/20.90 a__isQid(i) -> tt 20.60/20.90 a__isQid(o) -> tt 20.60/20.90 a__isQid(u) -> tt 20.60/20.90 a__isQid(X:S) -> isQid(X:S) 20.60/20.90 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.60/20.90 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.60/20.90 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.60/20.90 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.60/20.90 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.60/20.90 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.60/20.90 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.60/20.90 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.60/20.90 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.60/20.90 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.60/20.90 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.60/20.90 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.60/20.90 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.60/20.90 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.60/20.90 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.60/20.90 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.60/20.90 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.60/20.90 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.60/20.90 mark(a) -> a 20.60/20.90 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.60/20.90 mark(e) -> e 20.60/20.90 mark(i) -> i 20.60/20.90 mark(isList(X:S)) -> a__isList(X:S) 20.60/20.90 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.60/20.90 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.60/20.90 mark(isPal(X:S)) -> a__isPal(X:S) 20.60/20.90 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.60/20.90 mark(isQid(X:S)) -> a__isQid(X:S) 20.60/20.90 mark(nil) -> nil 20.60/20.90 mark(o) -> o 20.60/20.90 mark(tt) -> tt 20.60/20.90 mark(u) -> u 20.60/20.90 ->Strongly Connected Components: 20.60/20.90 ->->Cycle: 20.60/20.90 ->->-> Pairs: 20.60/20.90 A__AND(tt,X:S) -> MARK(X:S) 20.60/20.90 A__ISLIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.90 A__ISLIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.90 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.90 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.90 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.90 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.90 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.90 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.60/20.90 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.90 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.90 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.90 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.90 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U12(X:S)) -> MARK(X:S) 20.60/20.90 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.90 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U23(X:S)) -> MARK(X:S) 20.60/20.90 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U32(X:S)) -> MARK(X:S) 20.60/20.90 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.90 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U43(X:S)) -> MARK(X:S) 20.60/20.90 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.90 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U53(X:S)) -> MARK(X:S) 20.60/20.90 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U62(X:S)) -> MARK(X:S) 20.60/20.90 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U72(X:S)) -> MARK(X:S) 20.60/20.90 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.60/20.90 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.60/20.90 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.60/20.90 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.60/20.90 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.60/20.90 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.60/20.90 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.60/20.90 ->->-> Rules: 20.60/20.90 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.60/20.90 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.60/20.90 a__U12(tt) -> tt 20.60/20.90 a__U12(X:S) -> U12(X:S) 20.60/20.90 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.60/20.90 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.60/20.90 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.60/20.90 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.60/20.90 a__U23(tt) -> tt 20.60/20.90 a__U23(X:S) -> U23(X:S) 20.60/20.90 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.60/20.90 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.60/20.90 a__U32(tt) -> tt 20.60/20.90 a__U32(X:S) -> U32(X:S) 20.60/20.90 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.60/20.90 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.60/20.90 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.60/20.90 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.60/20.90 a__U43(tt) -> tt 20.60/20.90 a__U43(X:S) -> U43(X:S) 20.60/20.90 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.60/20.90 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.60/20.90 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.60/20.90 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.60/20.90 a__U53(tt) -> tt 20.60/20.90 a__U53(X:S) -> U53(X:S) 20.60/20.90 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.60/20.90 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.60/20.90 a__U62(tt) -> tt 20.60/20.90 a__U62(X:S) -> U62(X:S) 20.60/20.90 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.60/20.90 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.60/20.90 a__U72(tt) -> tt 20.60/20.90 a__U72(X:S) -> U72(X:S) 20.60/20.90 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.60/20.90 a____(nil,X:S) -> mark(X:S) 20.60/20.90 a____(X:S,nil) -> mark(X:S) 20.60/20.90 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.60/20.90 a__and(tt,X:S) -> mark(X:S) 20.60/20.90 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.60/20.90 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.90 a__isList(nil) -> tt 20.60/20.90 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.60/20.90 a__isList(X:S) -> isList(X:S) 20.60/20.90 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.90 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.90 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.60/20.90 a__isNeList(X:S) -> isNeList(X:S) 20.60/20.90 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.90 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.60/20.90 a__isNePal(X:S) -> isNePal(X:S) 20.60/20.90 a__isPal(nil) -> tt 20.60/20.90 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.60/20.90 a__isPal(X:S) -> isPal(X:S) 20.60/20.90 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.90 a__isPalListKind(a) -> tt 20.60/20.90 a__isPalListKind(e) -> tt 20.60/20.90 a__isPalListKind(i) -> tt 20.60/20.90 a__isPalListKind(nil) -> tt 20.60/20.90 a__isPalListKind(o) -> tt 20.60/20.90 a__isPalListKind(u) -> tt 20.60/20.90 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.60/20.90 a__isQid(a) -> tt 20.60/20.90 a__isQid(e) -> tt 20.60/20.90 a__isQid(i) -> tt 20.60/20.90 a__isQid(o) -> tt 20.60/20.90 a__isQid(u) -> tt 20.60/20.90 a__isQid(X:S) -> isQid(X:S) 20.60/20.90 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.60/20.90 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.60/20.90 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.60/20.90 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.60/20.90 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.60/20.90 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.60/20.90 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.60/20.90 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.60/20.90 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.60/20.90 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.60/20.90 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.60/20.90 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.60/20.90 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.60/20.90 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.60/20.90 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.60/20.90 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.60/20.90 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.60/20.90 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.60/20.90 mark(a) -> a 20.60/20.90 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.60/20.90 mark(e) -> e 20.60/20.90 mark(i) -> i 20.60/20.90 mark(isList(X:S)) -> a__isList(X:S) 20.60/20.90 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.60/20.90 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.60/20.90 mark(isPal(X:S)) -> a__isPal(X:S) 20.60/20.90 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.60/20.90 mark(isQid(X:S)) -> a__isQid(X:S) 20.60/20.90 mark(nil) -> nil 20.60/20.90 mark(o) -> o 20.60/20.90 mark(tt) -> tt 20.60/20.90 mark(u) -> u 20.60/20.90 20.60/20.90 Problem 1: 20.60/20.90 20.60/20.90 Reduction Pairs Processor: 20.60/20.90 -> Pairs: 20.60/20.90 A__AND(tt,X:S) -> MARK(X:S) 20.60/20.90 A__ISLIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.90 A__ISLIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.90 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.90 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.90 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.90 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.90 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.90 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.60/20.90 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.90 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.90 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.90 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.90 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U12(X:S)) -> MARK(X:S) 20.60/20.90 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.90 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U23(X:S)) -> MARK(X:S) 20.60/20.90 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U32(X:S)) -> MARK(X:S) 20.60/20.90 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.90 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U43(X:S)) -> MARK(X:S) 20.60/20.90 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.90 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U53(X:S)) -> MARK(X:S) 20.60/20.90 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U62(X:S)) -> MARK(X:S) 20.60/20.90 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U72(X:S)) -> MARK(X:S) 20.60/20.90 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.60/20.90 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.60/20.90 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.60/20.90 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.60/20.90 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.60/20.90 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.60/20.90 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.60/20.90 -> Rules: 20.60/20.90 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.60/20.90 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.60/20.90 a__U12(tt) -> tt 20.60/20.90 a__U12(X:S) -> U12(X:S) 20.60/20.90 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.60/20.90 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.60/20.90 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.60/20.90 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.60/20.90 a__U23(tt) -> tt 20.60/20.90 a__U23(X:S) -> U23(X:S) 20.60/20.90 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.60/20.90 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.60/20.90 a__U32(tt) -> tt 20.60/20.90 a__U32(X:S) -> U32(X:S) 20.60/20.90 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.60/20.90 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.60/20.90 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.60/20.90 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.60/20.90 a__U43(tt) -> tt 20.60/20.90 a__U43(X:S) -> U43(X:S) 20.60/20.90 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.60/20.90 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.60/20.90 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.60/20.90 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.60/20.90 a__U53(tt) -> tt 20.60/20.90 a__U53(X:S) -> U53(X:S) 20.60/20.90 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.60/20.90 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.60/20.90 a__U62(tt) -> tt 20.60/20.90 a__U62(X:S) -> U62(X:S) 20.60/20.90 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.60/20.90 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.60/20.90 a__U72(tt) -> tt 20.60/20.90 a__U72(X:S) -> U72(X:S) 20.60/20.90 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.60/20.90 a____(nil,X:S) -> mark(X:S) 20.60/20.90 a____(X:S,nil) -> mark(X:S) 20.60/20.90 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.60/20.90 a__and(tt,X:S) -> mark(X:S) 20.60/20.90 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.60/20.90 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.90 a__isList(nil) -> tt 20.60/20.90 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.60/20.90 a__isList(X:S) -> isList(X:S) 20.60/20.90 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.90 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.90 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.60/20.90 a__isNeList(X:S) -> isNeList(X:S) 20.60/20.90 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.90 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.60/20.90 a__isNePal(X:S) -> isNePal(X:S) 20.60/20.90 a__isPal(nil) -> tt 20.60/20.90 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.60/20.90 a__isPal(X:S) -> isPal(X:S) 20.60/20.90 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.90 a__isPalListKind(a) -> tt 20.60/20.90 a__isPalListKind(e) -> tt 20.60/20.90 a__isPalListKind(i) -> tt 20.60/20.90 a__isPalListKind(nil) -> tt 20.60/20.90 a__isPalListKind(o) -> tt 20.60/20.90 a__isPalListKind(u) -> tt 20.60/20.90 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.60/20.90 a__isQid(a) -> tt 20.60/20.90 a__isQid(e) -> tt 20.60/20.90 a__isQid(i) -> tt 20.60/20.90 a__isQid(o) -> tt 20.60/20.90 a__isQid(u) -> tt 20.60/20.90 a__isQid(X:S) -> isQid(X:S) 20.60/20.90 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.60/20.90 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.60/20.90 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.60/20.90 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.60/20.90 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.60/20.90 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.60/20.90 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.60/20.90 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.60/20.90 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.60/20.90 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.60/20.90 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.60/20.90 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.60/20.90 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.60/20.90 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.60/20.90 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.60/20.90 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.60/20.90 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.60/20.90 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.60/20.90 mark(a) -> a 20.60/20.90 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.60/20.90 mark(e) -> e 20.60/20.90 mark(i) -> i 20.60/20.90 mark(isList(X:S)) -> a__isList(X:S) 20.60/20.90 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.60/20.90 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.60/20.90 mark(isPal(X:S)) -> a__isPal(X:S) 20.60/20.90 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.60/20.90 mark(isQid(X:S)) -> a__isQid(X:S) 20.60/20.90 mark(nil) -> nil 20.60/20.90 mark(o) -> o 20.60/20.90 mark(tt) -> tt 20.60/20.90 mark(u) -> u 20.60/20.90 -> Usable rules: 20.60/20.90 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.60/20.90 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.60/20.90 a__U12(tt) -> tt 20.60/20.90 a__U12(X:S) -> U12(X:S) 20.60/20.90 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.60/20.90 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.60/20.90 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.60/20.90 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.60/20.90 a__U23(tt) -> tt 20.60/20.90 a__U23(X:S) -> U23(X:S) 20.60/20.90 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.60/20.90 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.60/20.90 a__U32(tt) -> tt 20.60/20.90 a__U32(X:S) -> U32(X:S) 20.60/20.90 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.60/20.90 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.60/20.90 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.60/20.90 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.60/20.90 a__U43(tt) -> tt 20.60/20.90 a__U43(X:S) -> U43(X:S) 20.60/20.90 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.60/20.90 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.60/20.90 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.60/20.90 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.60/20.90 a__U53(tt) -> tt 20.60/20.90 a__U53(X:S) -> U53(X:S) 20.60/20.90 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.60/20.90 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.60/20.90 a__U62(tt) -> tt 20.60/20.90 a__U62(X:S) -> U62(X:S) 20.60/20.90 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.60/20.90 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.60/20.90 a__U72(tt) -> tt 20.60/20.90 a__U72(X:S) -> U72(X:S) 20.60/20.90 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.60/20.90 a____(nil,X:S) -> mark(X:S) 20.60/20.90 a____(X:S,nil) -> mark(X:S) 20.60/20.90 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.60/20.90 a__and(tt,X:S) -> mark(X:S) 20.60/20.90 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.60/20.90 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.90 a__isList(nil) -> tt 20.60/20.90 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.60/20.90 a__isList(X:S) -> isList(X:S) 20.60/20.90 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.90 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.90 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.60/20.90 a__isNeList(X:S) -> isNeList(X:S) 20.60/20.90 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.90 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.60/20.90 a__isNePal(X:S) -> isNePal(X:S) 20.60/20.90 a__isPal(nil) -> tt 20.60/20.90 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.60/20.90 a__isPal(X:S) -> isPal(X:S) 20.60/20.90 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.90 a__isPalListKind(a) -> tt 20.60/20.90 a__isPalListKind(e) -> tt 20.60/20.90 a__isPalListKind(i) -> tt 20.60/20.90 a__isPalListKind(nil) -> tt 20.60/20.90 a__isPalListKind(o) -> tt 20.60/20.90 a__isPalListKind(u) -> tt 20.60/20.90 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.60/20.90 a__isQid(a) -> tt 20.60/20.90 a__isQid(e) -> tt 20.60/20.90 a__isQid(i) -> tt 20.60/20.90 a__isQid(o) -> tt 20.60/20.90 a__isQid(u) -> tt 20.60/20.90 a__isQid(X:S) -> isQid(X:S) 20.60/20.90 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.60/20.90 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.60/20.90 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.60/20.90 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.60/20.90 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.60/20.90 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.60/20.90 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.60/20.90 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.60/20.90 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.60/20.90 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.60/20.90 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.60/20.90 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.60/20.90 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.60/20.90 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.60/20.90 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.60/20.90 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.60/20.90 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.60/20.90 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.60/20.90 mark(a) -> a 20.60/20.90 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.60/20.90 mark(e) -> e 20.60/20.90 mark(i) -> i 20.60/20.90 mark(isList(X:S)) -> a__isList(X:S) 20.60/20.90 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.60/20.90 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.60/20.90 mark(isPal(X:S)) -> a__isPal(X:S) 20.60/20.90 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.60/20.90 mark(isQid(X:S)) -> a__isQid(X:S) 20.60/20.90 mark(nil) -> nil 20.60/20.90 mark(o) -> o 20.60/20.90 mark(tt) -> tt 20.60/20.90 mark(u) -> u 20.60/20.90 ->Interpretation type: 20.60/20.90 Linear 20.60/20.90 ->Coefficients: 20.60/20.90 Natural Numbers 20.60/20.90 ->Dimension: 20.60/20.90 1 20.60/20.90 ->Bound: 20.60/20.90 2 20.60/20.90 ->Interpretation: 20.60/20.90 20.60/20.90 [a__U11](X1,X2) = 2.X1 + 2.X2 + 1 20.60/20.90 [a__U12](X) = X + 1 20.60/20.90 [a__U21](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 20.60/20.90 [a__U22](X1,X2) = X1 + 2.X2 + 1 20.60/20.90 [a__U23](X) = X 20.60/20.90 [a__U31](X1,X2) = 2.X1 20.60/20.90 [a__U32](X) = 2.X 20.60/20.90 [a__U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.60/20.90 [a__U42](X1,X2) = X1 + 2.X2 + 1 20.60/20.90 [a__U43](X) = X + 1 20.60/20.90 [a__U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.60/20.90 [a__U52](X1,X2) = X1 + 2.X2 + 2 20.60/20.90 [a__U53](X) = X + 1 20.60/20.90 [a__U61](X1,X2) = 2.X1 + X2 20.60/20.90 [a__U62](X) = 2.X 20.60/20.90 [a__U71](X1,X2) = 2.X1 + X2 20.60/20.90 [a__U72](X) = X 20.60/20.90 [a____](X1,X2) = X1 + X2 + 2 20.60/20.90 [a__and](X1,X2) = X1 + X2 20.60/20.90 [a__isList](X) = 2.X + 1 20.60/20.90 [a__isNeList](X) = 2.X 20.60/20.90 [a__isNePal](X) = X 20.60/20.90 [a__isPal](X) = X + 2 20.60/20.90 [a__isPalListKind](X) = 0 20.60/20.90 [a__isQid](X) = 0 20.60/20.90 [mark](X) = X 20.60/20.90 [U11](X1,X2) = 2.X1 + 2.X2 + 1 20.60/20.90 [U12](X) = X + 1 20.60/20.90 [U21](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 20.60/20.90 [U22](X1,X2) = X1 + 2.X2 + 1 20.60/20.90 [U23](X) = X 20.60/20.90 [U31](X1,X2) = 2.X1 20.60/20.90 [U32](X) = 2.X 20.60/20.90 [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.60/20.90 [U42](X1,X2) = X1 + 2.X2 + 1 20.60/20.90 [U43](X) = X + 1 20.60/20.90 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.60/20.90 [U52](X1,X2) = X1 + 2.X2 + 2 20.60/20.90 [U53](X) = X + 1 20.60/20.90 [U61](X1,X2) = 2.X1 + X2 20.60/20.90 [U62](X) = 2.X 20.60/20.90 [U71](X1,X2) = 2.X1 + X2 20.60/20.90 [U72](X) = X 20.60/20.90 [__](X1,X2) = X1 + X2 + 2 20.60/20.90 [a] = 2 20.60/20.90 [and](X1,X2) = X1 + X2 20.60/20.90 [e] = 2 20.60/20.90 [fSNonEmpty] = 0 20.60/20.90 [i] = 0 20.60/20.90 [isList](X) = 2.X + 1 20.60/20.90 [isNeList](X) = 2.X 20.60/20.90 [isNePal](X) = X 20.60/20.90 [isPal](X) = X + 2 20.60/20.90 [isPalListKind](X) = 0 20.60/20.90 [isQid](X) = 0 20.60/20.90 [nil] = 2 20.60/20.90 [o] = 0 20.60/20.90 [tt] = 0 20.60/20.90 [u] = 2 20.60/20.90 [A__U11](X1,X2) = 0 20.60/20.90 [A__U12](X) = 0 20.60/20.90 [A__U21](X1,X2,X3) = 0 20.60/20.90 [A__U22](X1,X2) = 0 20.60/20.90 [A__U23](X) = 0 20.60/20.90 [A__U31](X1,X2) = 0 20.60/20.90 [A__U32](X) = 0 20.60/20.90 [A__U41](X1,X2,X3) = 0 20.60/20.90 [A__U42](X1,X2) = 0 20.60/20.90 [A__U43](X) = 0 20.60/20.90 [A__U51](X1,X2,X3) = 0 20.60/20.90 [A__U52](X1,X2) = 0 20.60/20.90 [A__U53](X) = 0 20.60/20.90 [A__U61](X1,X2) = 0 20.60/20.90 [A__U62](X) = 0 20.60/20.90 [A__U71](X1,X2) = 0 20.60/20.90 [A__U72](X) = 0 20.60/20.90 [A____](X1,X2) = 0 20.60/20.90 [A__AND](X1,X2) = X2 + 2 20.60/20.90 [A__ISLIST](X) = X + 2 20.60/20.90 [A__ISNELIST](X) = 2.X + 2 20.60/20.90 [A__ISNEPAL](X) = X + 2 20.60/20.90 [A__ISPAL](X) = X + 2 20.60/20.90 [A__ISPALLISTKIND](X) = 2 20.60/20.90 [A__ISQID](X) = 0 20.60/20.90 [MARK](X) = X + 2 20.60/20.90 20.60/20.90 Problem 1: 20.60/20.90 20.60/20.90 SCC Processor: 20.60/20.90 -> Pairs: 20.60/20.90 A__AND(tt,X:S) -> MARK(X:S) 20.60/20.90 A__ISLIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.90 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.90 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.90 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.90 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.90 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.90 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.60/20.90 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.90 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.90 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.90 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.90 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U12(X:S)) -> MARK(X:S) 20.60/20.90 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.90 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U23(X:S)) -> MARK(X:S) 20.60/20.90 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U32(X:S)) -> MARK(X:S) 20.60/20.90 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.90 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U43(X:S)) -> MARK(X:S) 20.60/20.90 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.90 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U53(X:S)) -> MARK(X:S) 20.60/20.90 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U62(X:S)) -> MARK(X:S) 20.60/20.90 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U72(X:S)) -> MARK(X:S) 20.60/20.90 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.60/20.90 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.60/20.90 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.60/20.90 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.60/20.90 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.60/20.90 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.60/20.90 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.60/20.90 -> Rules: 20.60/20.90 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.60/20.90 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.60/20.90 a__U12(tt) -> tt 20.60/20.90 a__U12(X:S) -> U12(X:S) 20.60/20.90 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.60/20.90 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.60/20.90 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.60/20.90 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.60/20.90 a__U23(tt) -> tt 20.60/20.90 a__U23(X:S) -> U23(X:S) 20.60/20.90 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.60/20.90 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.60/20.90 a__U32(tt) -> tt 20.60/20.90 a__U32(X:S) -> U32(X:S) 20.60/20.90 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.60/20.90 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.60/20.90 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.60/20.90 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.60/20.90 a__U43(tt) -> tt 20.60/20.90 a__U43(X:S) -> U43(X:S) 20.60/20.90 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.60/20.90 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.60/20.90 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.60/20.90 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.60/20.90 a__U53(tt) -> tt 20.60/20.90 a__U53(X:S) -> U53(X:S) 20.60/20.90 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.60/20.90 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.60/20.90 a__U62(tt) -> tt 20.60/20.90 a__U62(X:S) -> U62(X:S) 20.60/20.90 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.60/20.90 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.60/20.90 a__U72(tt) -> tt 20.60/20.90 a__U72(X:S) -> U72(X:S) 20.60/20.90 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.60/20.90 a____(nil,X:S) -> mark(X:S) 20.60/20.90 a____(X:S,nil) -> mark(X:S) 20.60/20.90 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.60/20.90 a__and(tt,X:S) -> mark(X:S) 20.60/20.90 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.60/20.90 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.90 a__isList(nil) -> tt 20.60/20.90 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.60/20.90 a__isList(X:S) -> isList(X:S) 20.60/20.90 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.90 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.90 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.60/20.90 a__isNeList(X:S) -> isNeList(X:S) 20.60/20.90 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.90 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.60/20.90 a__isNePal(X:S) -> isNePal(X:S) 20.60/20.90 a__isPal(nil) -> tt 20.60/20.90 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.60/20.90 a__isPal(X:S) -> isPal(X:S) 20.60/20.90 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.90 a__isPalListKind(a) -> tt 20.60/20.90 a__isPalListKind(e) -> tt 20.60/20.90 a__isPalListKind(i) -> tt 20.60/20.90 a__isPalListKind(nil) -> tt 20.60/20.90 a__isPalListKind(o) -> tt 20.60/20.90 a__isPalListKind(u) -> tt 20.60/20.90 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.60/20.90 a__isQid(a) -> tt 20.60/20.90 a__isQid(e) -> tt 20.60/20.90 a__isQid(i) -> tt 20.60/20.90 a__isQid(o) -> tt 20.60/20.90 a__isQid(u) -> tt 20.60/20.90 a__isQid(X:S) -> isQid(X:S) 20.60/20.90 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.60/20.90 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.60/20.90 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.60/20.90 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.60/20.90 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.60/20.90 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.60/20.90 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.60/20.90 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.60/20.90 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.60/20.90 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.60/20.90 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.60/20.90 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.60/20.90 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.60/20.90 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.60/20.90 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.60/20.90 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.60/20.90 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.60/20.90 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.60/20.90 mark(a) -> a 20.60/20.90 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.60/20.90 mark(e) -> e 20.60/20.90 mark(i) -> i 20.60/20.90 mark(isList(X:S)) -> a__isList(X:S) 20.60/20.90 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.60/20.90 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.60/20.90 mark(isPal(X:S)) -> a__isPal(X:S) 20.60/20.90 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.60/20.90 mark(isQid(X:S)) -> a__isQid(X:S) 20.60/20.90 mark(nil) -> nil 20.60/20.90 mark(o) -> o 20.60/20.90 mark(tt) -> tt 20.60/20.90 mark(u) -> u 20.60/20.90 ->Strongly Connected Components: 20.60/20.90 ->->Cycle: 20.60/20.90 ->->-> Pairs: 20.60/20.90 A__AND(tt,X:S) -> MARK(X:S) 20.60/20.90 A__ISLIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.90 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.90 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.90 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.90 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.90 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.90 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.60/20.90 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.90 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.90 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.90 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.90 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U12(X:S)) -> MARK(X:S) 20.60/20.90 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.90 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U23(X:S)) -> MARK(X:S) 20.60/20.90 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U32(X:S)) -> MARK(X:S) 20.60/20.90 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.90 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U43(X:S)) -> MARK(X:S) 20.60/20.90 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.90 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U53(X:S)) -> MARK(X:S) 20.60/20.90 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U62(X:S)) -> MARK(X:S) 20.60/20.90 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U72(X:S)) -> MARK(X:S) 20.60/20.90 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.60/20.90 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.60/20.90 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.60/20.90 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.60/20.90 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.60/20.90 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.60/20.90 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.60/20.90 ->->-> Rules: 20.60/20.90 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.60/20.90 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.60/20.90 a__U12(tt) -> tt 20.60/20.90 a__U12(X:S) -> U12(X:S) 20.60/20.90 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.60/20.90 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.60/20.90 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.60/20.90 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.60/20.90 a__U23(tt) -> tt 20.60/20.90 a__U23(X:S) -> U23(X:S) 20.60/20.90 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.60/20.90 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.60/20.90 a__U32(tt) -> tt 20.60/20.90 a__U32(X:S) -> U32(X:S) 20.60/20.90 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.60/20.90 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.60/20.90 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.60/20.90 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.60/20.90 a__U43(tt) -> tt 20.60/20.90 a__U43(X:S) -> U43(X:S) 20.60/20.90 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.60/20.90 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.60/20.90 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.60/20.90 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.60/20.90 a__U53(tt) -> tt 20.60/20.90 a__U53(X:S) -> U53(X:S) 20.60/20.90 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.60/20.90 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.60/20.90 a__U62(tt) -> tt 20.60/20.90 a__U62(X:S) -> U62(X:S) 20.60/20.90 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.60/20.90 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.60/20.90 a__U72(tt) -> tt 20.60/20.90 a__U72(X:S) -> U72(X:S) 20.60/20.90 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.60/20.90 a____(nil,X:S) -> mark(X:S) 20.60/20.90 a____(X:S,nil) -> mark(X:S) 20.60/20.90 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.60/20.90 a__and(tt,X:S) -> mark(X:S) 20.60/20.90 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.60/20.90 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.90 a__isList(nil) -> tt 20.60/20.90 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.60/20.90 a__isList(X:S) -> isList(X:S) 20.60/20.90 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.90 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.90 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.60/20.90 a__isNeList(X:S) -> isNeList(X:S) 20.60/20.90 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.90 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.60/20.90 a__isNePal(X:S) -> isNePal(X:S) 20.60/20.90 a__isPal(nil) -> tt 20.60/20.90 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.60/20.90 a__isPal(X:S) -> isPal(X:S) 20.60/20.90 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.90 a__isPalListKind(a) -> tt 20.60/20.90 a__isPalListKind(e) -> tt 20.60/20.90 a__isPalListKind(i) -> tt 20.60/20.90 a__isPalListKind(nil) -> tt 20.60/20.90 a__isPalListKind(o) -> tt 20.60/20.90 a__isPalListKind(u) -> tt 20.60/20.90 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.60/20.90 a__isQid(a) -> tt 20.60/20.90 a__isQid(e) -> tt 20.60/20.90 a__isQid(i) -> tt 20.60/20.90 a__isQid(o) -> tt 20.60/20.90 a__isQid(u) -> tt 20.60/20.90 a__isQid(X:S) -> isQid(X:S) 20.60/20.90 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.60/20.90 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.60/20.90 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.60/20.90 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.60/20.90 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.60/20.90 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.60/20.90 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.60/20.90 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.60/20.90 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.60/20.90 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.60/20.90 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.60/20.90 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.60/20.90 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.60/20.90 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.60/20.90 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.60/20.90 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.60/20.90 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.60/20.90 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.60/20.90 mark(a) -> a 20.60/20.90 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.60/20.90 mark(e) -> e 20.60/20.90 mark(i) -> i 20.60/20.90 mark(isList(X:S)) -> a__isList(X:S) 20.60/20.90 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.60/20.90 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.60/20.90 mark(isPal(X:S)) -> a__isPal(X:S) 20.60/20.90 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.60/20.90 mark(isQid(X:S)) -> a__isQid(X:S) 20.60/20.90 mark(nil) -> nil 20.60/20.90 mark(o) -> o 20.60/20.90 mark(tt) -> tt 20.60/20.90 mark(u) -> u 20.60/20.90 20.60/20.90 Problem 1: 20.60/20.90 20.60/20.90 Reduction Pairs Processor: 20.60/20.90 -> Pairs: 20.60/20.90 A__AND(tt,X:S) -> MARK(X:S) 20.60/20.90 A__ISLIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.90 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.90 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.90 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.90 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.90 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.90 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.60/20.90 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.90 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.90 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.90 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.90 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U12(X:S)) -> MARK(X:S) 20.60/20.90 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.90 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U23(X:S)) -> MARK(X:S) 20.60/20.90 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U32(X:S)) -> MARK(X:S) 20.60/20.90 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.90 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U43(X:S)) -> MARK(X:S) 20.60/20.90 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.90 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U53(X:S)) -> MARK(X:S) 20.60/20.90 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U62(X:S)) -> MARK(X:S) 20.60/20.90 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U72(X:S)) -> MARK(X:S) 20.60/20.90 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.60/20.90 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.60/20.90 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.60/20.90 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.60/20.90 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.60/20.90 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.60/20.90 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.60/20.90 -> Rules: 20.60/20.90 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.60/20.90 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.60/20.90 a__U12(tt) -> tt 20.60/20.90 a__U12(X:S) -> U12(X:S) 20.60/20.90 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.60/20.90 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.60/20.90 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.60/20.90 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.60/20.90 a__U23(tt) -> tt 20.60/20.90 a__U23(X:S) -> U23(X:S) 20.60/20.90 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.60/20.90 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.60/20.90 a__U32(tt) -> tt 20.60/20.90 a__U32(X:S) -> U32(X:S) 20.60/20.90 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.60/20.90 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.60/20.90 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.60/20.90 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.60/20.90 a__U43(tt) -> tt 20.60/20.90 a__U43(X:S) -> U43(X:S) 20.60/20.90 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.60/20.90 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.60/20.90 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.60/20.90 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.60/20.90 a__U53(tt) -> tt 20.60/20.90 a__U53(X:S) -> U53(X:S) 20.60/20.90 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.60/20.90 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.60/20.90 a__U62(tt) -> tt 20.60/20.90 a__U62(X:S) -> U62(X:S) 20.60/20.90 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.60/20.90 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.60/20.90 a__U72(tt) -> tt 20.60/20.90 a__U72(X:S) -> U72(X:S) 20.60/20.90 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.60/20.90 a____(nil,X:S) -> mark(X:S) 20.60/20.90 a____(X:S,nil) -> mark(X:S) 20.60/20.90 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.60/20.90 a__and(tt,X:S) -> mark(X:S) 20.60/20.90 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.60/20.90 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.90 a__isList(nil) -> tt 20.60/20.90 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.60/20.90 a__isList(X:S) -> isList(X:S) 20.60/20.90 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.90 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.90 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.60/20.90 a__isNeList(X:S) -> isNeList(X:S) 20.60/20.90 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.90 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.60/20.90 a__isNePal(X:S) -> isNePal(X:S) 20.60/20.90 a__isPal(nil) -> tt 20.60/20.90 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.60/20.90 a__isPal(X:S) -> isPal(X:S) 20.60/20.90 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.90 a__isPalListKind(a) -> tt 20.60/20.90 a__isPalListKind(e) -> tt 20.60/20.90 a__isPalListKind(i) -> tt 20.60/20.90 a__isPalListKind(nil) -> tt 20.60/20.90 a__isPalListKind(o) -> tt 20.60/20.90 a__isPalListKind(u) -> tt 20.60/20.90 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.60/20.90 a__isQid(a) -> tt 20.60/20.90 a__isQid(e) -> tt 20.60/20.90 a__isQid(i) -> tt 20.60/20.90 a__isQid(o) -> tt 20.60/20.90 a__isQid(u) -> tt 20.60/20.90 a__isQid(X:S) -> isQid(X:S) 20.60/20.90 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.60/20.90 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.60/20.90 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.60/20.90 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.60/20.90 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.60/20.90 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.60/20.90 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.60/20.90 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.60/20.90 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.60/20.90 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.60/20.90 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.60/20.90 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.60/20.90 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.60/20.90 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.60/20.90 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.60/20.90 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.60/20.90 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.60/20.90 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.60/20.90 mark(a) -> a 20.60/20.90 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.60/20.90 mark(e) -> e 20.60/20.90 mark(i) -> i 20.60/20.90 mark(isList(X:S)) -> a__isList(X:S) 20.60/20.90 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.60/20.90 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.60/20.90 mark(isPal(X:S)) -> a__isPal(X:S) 20.60/20.90 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.60/20.90 mark(isQid(X:S)) -> a__isQid(X:S) 20.60/20.90 mark(nil) -> nil 20.60/20.90 mark(o) -> o 20.60/20.90 mark(tt) -> tt 20.60/20.90 mark(u) -> u 20.60/20.90 -> Usable rules: 20.60/20.90 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.60/20.90 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.60/20.90 a__U12(tt) -> tt 20.60/20.90 a__U12(X:S) -> U12(X:S) 20.60/20.90 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.60/20.90 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.60/20.90 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.60/20.90 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.60/20.90 a__U23(tt) -> tt 20.60/20.90 a__U23(X:S) -> U23(X:S) 20.60/20.90 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.60/20.90 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.60/20.90 a__U32(tt) -> tt 20.60/20.90 a__U32(X:S) -> U32(X:S) 20.60/20.90 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.60/20.90 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.60/20.90 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.60/20.90 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.60/20.90 a__U43(tt) -> tt 20.60/20.90 a__U43(X:S) -> U43(X:S) 20.60/20.90 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.60/20.90 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.60/20.90 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.60/20.90 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.60/20.90 a__U53(tt) -> tt 20.60/20.90 a__U53(X:S) -> U53(X:S) 20.60/20.90 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.60/20.90 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.60/20.90 a__U62(tt) -> tt 20.60/20.90 a__U62(X:S) -> U62(X:S) 20.60/20.90 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.60/20.90 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.60/20.90 a__U72(tt) -> tt 20.60/20.90 a__U72(X:S) -> U72(X:S) 20.60/20.90 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.60/20.90 a____(nil,X:S) -> mark(X:S) 20.60/20.90 a____(X:S,nil) -> mark(X:S) 20.60/20.90 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.60/20.90 a__and(tt,X:S) -> mark(X:S) 20.60/20.90 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.60/20.90 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.90 a__isList(nil) -> tt 20.60/20.90 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.60/20.90 a__isList(X:S) -> isList(X:S) 20.60/20.90 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.90 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.90 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.60/20.90 a__isNeList(X:S) -> isNeList(X:S) 20.60/20.90 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.90 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.60/20.90 a__isNePal(X:S) -> isNePal(X:S) 20.60/20.90 a__isPal(nil) -> tt 20.60/20.90 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.60/20.90 a__isPal(X:S) -> isPal(X:S) 20.60/20.90 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.90 a__isPalListKind(a) -> tt 20.60/20.90 a__isPalListKind(e) -> tt 20.60/20.90 a__isPalListKind(i) -> tt 20.60/20.90 a__isPalListKind(nil) -> tt 20.60/20.90 a__isPalListKind(o) -> tt 20.60/20.90 a__isPalListKind(u) -> tt 20.60/20.90 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.60/20.90 a__isQid(a) -> tt 20.60/20.90 a__isQid(e) -> tt 20.60/20.90 a__isQid(i) -> tt 20.60/20.90 a__isQid(o) -> tt 20.60/20.90 a__isQid(u) -> tt 20.60/20.90 a__isQid(X:S) -> isQid(X:S) 20.60/20.90 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.60/20.90 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.60/20.90 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.60/20.90 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.60/20.90 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.60/20.90 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.60/20.90 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.60/20.90 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.60/20.90 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.60/20.90 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.60/20.90 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.60/20.90 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.60/20.90 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.60/20.90 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.60/20.90 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.60/20.90 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.60/20.90 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.60/20.90 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.60/20.90 mark(a) -> a 20.60/20.90 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.60/20.90 mark(e) -> e 20.60/20.90 mark(i) -> i 20.60/20.90 mark(isList(X:S)) -> a__isList(X:S) 20.60/20.90 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.60/20.90 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.60/20.90 mark(isPal(X:S)) -> a__isPal(X:S) 20.60/20.90 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.60/20.90 mark(isQid(X:S)) -> a__isQid(X:S) 20.60/20.90 mark(nil) -> nil 20.60/20.90 mark(o) -> o 20.60/20.90 mark(tt) -> tt 20.60/20.90 mark(u) -> u 20.60/20.90 ->Interpretation type: 20.60/20.90 Linear 20.60/20.90 ->Coefficients: 20.60/20.90 Natural Numbers 20.60/20.90 ->Dimension: 20.60/20.90 1 20.60/20.90 ->Bound: 20.60/20.90 2 20.60/20.90 ->Interpretation: 20.60/20.90 20.60/20.90 [a__U11](X1,X2) = 2.X1 + 2.X2 20.60/20.90 [a__U12](X) = X 20.60/20.90 [a__U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.60/20.90 [a__U22](X1,X2) = X1 + 2.X2 + 1 20.60/20.90 [a__U23](X) = X 20.60/20.90 [a__U31](X1,X2) = 2.X1 + 2.X2 20.60/20.90 [a__U32](X) = 2.X 20.60/20.90 [a__U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.60/20.90 [a__U42](X1,X2) = X1 + 2.X2 + 1 20.60/20.90 [a__U43](X) = X 20.60/20.90 [a__U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.60/20.90 [a__U52](X1,X2) = X1 + 2.X2 + 2 20.60/20.90 [a__U53](X) = X 20.60/20.90 [a__U61](X1,X2) = 2.X1 + X2 20.60/20.90 [a__U62](X) = 2.X 20.60/20.90 [a__U71](X1,X2) = 2.X1 + 2.X2 + 2 20.60/20.90 [a__U72](X) = 2.X 20.60/20.90 [a____](X1,X2) = 2.X1 + X2 + 2 20.60/20.90 [a__and](X1,X2) = X1 + X2 20.60/20.90 [a__isList](X) = 2.X + 1 20.60/20.90 [a__isNeList](X) = 2.X 20.60/20.90 [a__isNePal](X) = X + 1 20.60/20.90 [a__isPal](X) = 2.X + 2 20.60/20.90 [a__isPalListKind](X) = 0 20.60/20.90 [a__isQid](X) = 0 20.60/20.90 [mark](X) = X 20.60/20.90 [U11](X1,X2) = 2.X1 + 2.X2 20.60/20.90 [U12](X) = X 20.60/20.90 [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.60/20.90 [U22](X1,X2) = X1 + 2.X2 + 1 20.60/20.90 [U23](X) = X 20.60/20.90 [U31](X1,X2) = 2.X1 + 2.X2 20.60/20.90 [U32](X) = 2.X 20.60/20.90 [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.60/20.90 [U42](X1,X2) = X1 + 2.X2 + 1 20.60/20.90 [U43](X) = X 20.60/20.90 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.60/20.90 [U52](X1,X2) = X1 + 2.X2 + 2 20.60/20.90 [U53](X) = X 20.60/20.90 [U61](X1,X2) = 2.X1 + X2 20.60/20.90 [U62](X) = 2.X 20.60/20.90 [U71](X1,X2) = 2.X1 + 2.X2 + 2 20.60/20.90 [U72](X) = 2.X 20.60/20.90 [__](X1,X2) = 2.X1 + X2 + 2 20.60/20.90 [a] = 1 20.60/20.90 [and](X1,X2) = X1 + X2 20.60/20.90 [e] = 1 20.60/20.90 [fSNonEmpty] = 0 20.60/20.90 [i] = 1 20.60/20.90 [isList](X) = 2.X + 1 20.60/20.90 [isNeList](X) = 2.X 20.60/20.90 [isNePal](X) = X + 1 20.60/20.90 [isPal](X) = 2.X + 2 20.60/20.90 [isPalListKind](X) = 0 20.60/20.90 [isQid](X) = 0 20.60/20.90 [nil] = 2 20.60/20.90 [o] = 1 20.60/20.90 [tt] = 0 20.60/20.90 [u] = 1 20.60/20.90 [A__U11](X1,X2) = 0 20.60/20.90 [A__U12](X) = 0 20.60/20.90 [A__U21](X1,X2,X3) = 0 20.60/20.90 [A__U22](X1,X2) = 0 20.60/20.90 [A__U23](X) = 0 20.60/20.90 [A__U31](X1,X2) = 0 20.60/20.90 [A__U32](X) = 0 20.60/20.90 [A__U41](X1,X2,X3) = 0 20.60/20.90 [A__U42](X1,X2) = 0 20.60/20.90 [A__U43](X) = 0 20.60/20.90 [A__U51](X1,X2,X3) = 0 20.60/20.90 [A__U52](X1,X2) = 0 20.60/20.90 [A__U53](X) = 0 20.60/20.90 [A__U61](X1,X2) = 0 20.60/20.90 [A__U62](X) = 0 20.60/20.90 [A__U71](X1,X2) = 0 20.60/20.90 [A__U72](X) = 0 20.60/20.90 [A____](X1,X2) = 0 20.60/20.90 [A__AND](X1,X2) = 2.X1 + 2.X2 + 2 20.60/20.90 [A__ISLIST](X) = 2.X + 2 20.60/20.90 [A__ISNELIST](X) = 2 20.60/20.90 [A__ISNEPAL](X) = 2.X + 2 20.60/20.90 [A__ISPAL](X) = 2 20.60/20.90 [A__ISPALLISTKIND](X) = 2 20.60/20.90 [A__ISQID](X) = 0 20.60/20.90 [MARK](X) = 2.X + 2 20.60/20.90 20.60/20.90 Problem 1: 20.60/20.90 20.60/20.90 SCC Processor: 20.60/20.90 -> Pairs: 20.60/20.90 A__AND(tt,X:S) -> MARK(X:S) 20.60/20.90 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.90 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.90 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.90 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.90 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.90 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.60/20.90 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.90 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.90 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.90 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.90 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U12(X:S)) -> MARK(X:S) 20.60/20.90 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.90 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U23(X:S)) -> MARK(X:S) 20.60/20.90 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U32(X:S)) -> MARK(X:S) 20.60/20.90 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.90 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U43(X:S)) -> MARK(X:S) 20.60/20.90 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.90 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U53(X:S)) -> MARK(X:S) 20.60/20.90 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U62(X:S)) -> MARK(X:S) 20.60/20.90 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U72(X:S)) -> MARK(X:S) 20.60/20.90 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.60/20.90 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.60/20.90 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.60/20.90 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.60/20.90 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.60/20.90 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.60/20.90 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.60/20.90 -> Rules: 20.60/20.90 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.60/20.90 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.60/20.90 a__U12(tt) -> tt 20.60/20.90 a__U12(X:S) -> U12(X:S) 20.60/20.90 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.60/20.90 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.60/20.90 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.60/20.90 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.60/20.90 a__U23(tt) -> tt 20.60/20.90 a__U23(X:S) -> U23(X:S) 20.60/20.90 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.60/20.90 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.60/20.90 a__U32(tt) -> tt 20.60/20.90 a__U32(X:S) -> U32(X:S) 20.60/20.90 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.60/20.90 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.60/20.90 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.60/20.90 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.60/20.90 a__U43(tt) -> tt 20.60/20.90 a__U43(X:S) -> U43(X:S) 20.60/20.90 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.60/20.90 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.60/20.90 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.60/20.90 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.60/20.90 a__U53(tt) -> tt 20.60/20.90 a__U53(X:S) -> U53(X:S) 20.60/20.90 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.60/20.90 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.60/20.90 a__U62(tt) -> tt 20.60/20.90 a__U62(X:S) -> U62(X:S) 20.60/20.90 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.60/20.90 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.60/20.90 a__U72(tt) -> tt 20.60/20.90 a__U72(X:S) -> U72(X:S) 20.60/20.90 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.60/20.90 a____(nil,X:S) -> mark(X:S) 20.60/20.90 a____(X:S,nil) -> mark(X:S) 20.60/20.90 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.60/20.90 a__and(tt,X:S) -> mark(X:S) 20.60/20.90 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.60/20.90 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.90 a__isList(nil) -> tt 20.60/20.90 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.60/20.90 a__isList(X:S) -> isList(X:S) 20.60/20.90 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.90 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.90 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.60/20.90 a__isNeList(X:S) -> isNeList(X:S) 20.60/20.90 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.90 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.60/20.90 a__isNePal(X:S) -> isNePal(X:S) 20.60/20.90 a__isPal(nil) -> tt 20.60/20.90 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.60/20.90 a__isPal(X:S) -> isPal(X:S) 20.60/20.90 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.90 a__isPalListKind(a) -> tt 20.60/20.90 a__isPalListKind(e) -> tt 20.60/20.90 a__isPalListKind(i) -> tt 20.60/20.90 a__isPalListKind(nil) -> tt 20.60/20.90 a__isPalListKind(o) -> tt 20.60/20.90 a__isPalListKind(u) -> tt 20.60/20.90 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.60/20.90 a__isQid(a) -> tt 20.60/20.90 a__isQid(e) -> tt 20.60/20.90 a__isQid(i) -> tt 20.60/20.90 a__isQid(o) -> tt 20.60/20.90 a__isQid(u) -> tt 20.60/20.90 a__isQid(X:S) -> isQid(X:S) 20.60/20.90 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.60/20.90 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.60/20.90 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.60/20.90 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.60/20.90 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.60/20.90 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.60/20.90 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.60/20.90 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.60/20.90 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.60/20.90 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.60/20.90 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.60/20.90 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.60/20.90 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.60/20.90 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.60/20.90 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.60/20.90 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.60/20.90 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.60/20.90 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.60/20.90 mark(a) -> a 20.60/20.90 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.60/20.90 mark(e) -> e 20.60/20.90 mark(i) -> i 20.60/20.90 mark(isList(X:S)) -> a__isList(X:S) 20.60/20.90 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.60/20.90 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.60/20.90 mark(isPal(X:S)) -> a__isPal(X:S) 20.60/20.90 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.60/20.90 mark(isQid(X:S)) -> a__isQid(X:S) 20.60/20.90 mark(nil) -> nil 20.60/20.90 mark(o) -> o 20.60/20.90 mark(tt) -> tt 20.60/20.90 mark(u) -> u 20.60/20.90 ->Strongly Connected Components: 20.60/20.90 ->->Cycle: 20.60/20.90 ->->-> Pairs: 20.60/20.90 A__AND(tt,X:S) -> MARK(X:S) 20.60/20.90 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.90 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.90 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.90 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.90 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.90 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.60/20.90 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.90 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.90 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.90 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.90 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U12(X:S)) -> MARK(X:S) 20.60/20.90 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.90 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U23(X:S)) -> MARK(X:S) 20.60/20.90 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U32(X:S)) -> MARK(X:S) 20.60/20.90 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.90 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U43(X:S)) -> MARK(X:S) 20.60/20.90 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.90 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U53(X:S)) -> MARK(X:S) 20.60/20.90 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U62(X:S)) -> MARK(X:S) 20.60/20.90 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U72(X:S)) -> MARK(X:S) 20.60/20.90 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.60/20.90 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.60/20.90 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.60/20.90 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.60/20.90 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.60/20.90 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.60/20.90 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.60/20.90 ->->-> Rules: 20.60/20.90 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.60/20.90 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.60/20.90 a__U12(tt) -> tt 20.60/20.90 a__U12(X:S) -> U12(X:S) 20.60/20.90 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.60/20.90 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.60/20.90 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.60/20.90 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.60/20.90 a__U23(tt) -> tt 20.60/20.90 a__U23(X:S) -> U23(X:S) 20.60/20.90 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.60/20.90 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.60/20.90 a__U32(tt) -> tt 20.60/20.90 a__U32(X:S) -> U32(X:S) 20.60/20.90 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.60/20.90 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.60/20.90 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.60/20.90 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.60/20.90 a__U43(tt) -> tt 20.60/20.90 a__U43(X:S) -> U43(X:S) 20.60/20.90 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.60/20.90 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.60/20.90 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.60/20.90 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.60/20.90 a__U53(tt) -> tt 20.60/20.90 a__U53(X:S) -> U53(X:S) 20.60/20.90 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.60/20.90 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.60/20.90 a__U62(tt) -> tt 20.60/20.90 a__U62(X:S) -> U62(X:S) 20.60/20.90 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.60/20.90 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.60/20.90 a__U72(tt) -> tt 20.60/20.90 a__U72(X:S) -> U72(X:S) 20.60/20.90 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.60/20.90 a____(nil,X:S) -> mark(X:S) 20.60/20.90 a____(X:S,nil) -> mark(X:S) 20.60/20.90 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.60/20.90 a__and(tt,X:S) -> mark(X:S) 20.60/20.90 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.60/20.90 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.90 a__isList(nil) -> tt 20.60/20.90 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.60/20.90 a__isList(X:S) -> isList(X:S) 20.60/20.90 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.90 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.90 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.60/20.90 a__isNeList(X:S) -> isNeList(X:S) 20.60/20.90 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.90 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.60/20.90 a__isNePal(X:S) -> isNePal(X:S) 20.60/20.90 a__isPal(nil) -> tt 20.60/20.90 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.60/20.90 a__isPal(X:S) -> isPal(X:S) 20.60/20.90 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.90 a__isPalListKind(a) -> tt 20.60/20.90 a__isPalListKind(e) -> tt 20.60/20.90 a__isPalListKind(i) -> tt 20.60/20.90 a__isPalListKind(nil) -> tt 20.60/20.90 a__isPalListKind(o) -> tt 20.60/20.90 a__isPalListKind(u) -> tt 20.60/20.90 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.60/20.90 a__isQid(a) -> tt 20.60/20.90 a__isQid(e) -> tt 20.60/20.90 a__isQid(i) -> tt 20.60/20.90 a__isQid(o) -> tt 20.60/20.90 a__isQid(u) -> tt 20.60/20.90 a__isQid(X:S) -> isQid(X:S) 20.60/20.90 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.60/20.90 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.60/20.90 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.60/20.90 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.60/20.90 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.60/20.90 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.60/20.90 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.60/20.90 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.60/20.90 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.60/20.90 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.60/20.90 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.60/20.90 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.60/20.90 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.60/20.90 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.60/20.90 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.60/20.90 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.60/20.90 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.60/20.90 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.60/20.90 mark(a) -> a 20.60/20.90 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.60/20.90 mark(e) -> e 20.60/20.90 mark(i) -> i 20.60/20.90 mark(isList(X:S)) -> a__isList(X:S) 20.60/20.90 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.60/20.90 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.60/20.90 mark(isPal(X:S)) -> a__isPal(X:S) 20.60/20.90 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.60/20.90 mark(isQid(X:S)) -> a__isQid(X:S) 20.60/20.90 mark(nil) -> nil 20.60/20.90 mark(o) -> o 20.60/20.90 mark(tt) -> tt 20.60/20.90 mark(u) -> u 20.60/20.90 20.60/20.90 Problem 1: 20.60/20.90 20.60/20.90 Reduction Pairs Processor: 20.60/20.90 -> Pairs: 20.60/20.90 A__AND(tt,X:S) -> MARK(X:S) 20.60/20.90 A__ISLIST(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.90 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.90 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.90 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.90 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.90 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.60/20.90 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.90 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.90 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.90 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.90 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U12(X:S)) -> MARK(X:S) 20.60/20.90 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.90 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U23(X:S)) -> MARK(X:S) 20.60/20.90 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U32(X:S)) -> MARK(X:S) 20.60/20.90 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.90 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U43(X:S)) -> MARK(X:S) 20.60/20.90 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.90 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U53(X:S)) -> MARK(X:S) 20.60/20.90 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U62(X:S)) -> MARK(X:S) 20.60/20.90 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(U72(X:S)) -> MARK(X:S) 20.60/20.90 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.60/20.90 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.60/20.90 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.90 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.60/20.90 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.60/20.90 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.60/20.90 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.60/20.90 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.60/20.90 -> Rules: 20.60/20.90 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.60/20.90 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.60/20.90 a__U12(tt) -> tt 20.60/20.90 a__U12(X:S) -> U12(X:S) 20.60/20.90 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.60/20.90 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.60/20.90 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.60/20.90 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.60/20.90 a__U23(tt) -> tt 20.60/20.90 a__U23(X:S) -> U23(X:S) 20.60/20.90 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.60/20.90 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.60/20.90 a__U32(tt) -> tt 20.60/20.90 a__U32(X:S) -> U32(X:S) 20.60/20.90 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.60/20.90 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.60/20.90 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.60/20.90 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.60/20.90 a__U43(tt) -> tt 20.60/20.90 a__U43(X:S) -> U43(X:S) 20.60/20.90 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.60/20.90 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.60/20.90 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.60/20.90 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.60/20.90 a__U53(tt) -> tt 20.60/20.90 a__U53(X:S) -> U53(X:S) 20.60/20.90 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.60/20.90 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.60/20.90 a__U62(tt) -> tt 20.60/20.90 a__U62(X:S) -> U62(X:S) 20.60/20.90 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.60/20.90 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.60/20.90 a__U72(tt) -> tt 20.60/20.90 a__U72(X:S) -> U72(X:S) 20.60/20.90 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.60/20.90 a____(nil,X:S) -> mark(X:S) 20.60/20.90 a____(X:S,nil) -> mark(X:S) 20.60/20.90 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.60/20.90 a__and(tt,X:S) -> mark(X:S) 20.60/20.90 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.60/20.90 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.90 a__isList(nil) -> tt 20.60/20.90 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.60/20.90 a__isList(X:S) -> isList(X:S) 20.60/20.90 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.90 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.90 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.60/20.90 a__isNeList(X:S) -> isNeList(X:S) 20.60/20.90 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.90 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.60/20.90 a__isNePal(X:S) -> isNePal(X:S) 20.60/20.90 a__isPal(nil) -> tt 20.60/20.90 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.60/20.90 a__isPal(X:S) -> isPal(X:S) 20.60/20.90 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.90 a__isPalListKind(a) -> tt 20.60/20.90 a__isPalListKind(e) -> tt 20.60/20.90 a__isPalListKind(i) -> tt 20.60/20.90 a__isPalListKind(nil) -> tt 20.60/20.90 a__isPalListKind(o) -> tt 20.60/20.90 a__isPalListKind(u) -> tt 20.60/20.90 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.60/20.90 a__isQid(a) -> tt 20.60/20.90 a__isQid(e) -> tt 20.60/20.90 a__isQid(i) -> tt 20.60/20.90 a__isQid(o) -> tt 20.60/20.90 a__isQid(u) -> tt 20.60/20.90 a__isQid(X:S) -> isQid(X:S) 20.60/20.90 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.60/20.90 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.60/20.90 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.60/20.90 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.60/20.90 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.60/20.90 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.60/20.90 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.60/20.90 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.60/20.90 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.60/20.90 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.60/20.90 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.60/20.90 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.60/20.90 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.60/20.90 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.60/20.90 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.60/20.90 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.60/20.90 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.60/20.90 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.60/20.90 mark(a) -> a 20.60/20.90 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.60/20.90 mark(e) -> e 20.60/20.90 mark(i) -> i 20.60/20.90 mark(isList(X:S)) -> a__isList(X:S) 20.60/20.90 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.60/20.90 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.60/20.90 mark(isPal(X:S)) -> a__isPal(X:S) 20.60/20.90 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.60/20.90 mark(isQid(X:S)) -> a__isQid(X:S) 20.60/20.90 mark(nil) -> nil 20.60/20.90 mark(o) -> o 20.60/20.90 mark(tt) -> tt 20.60/20.90 mark(u) -> u 20.60/20.90 -> Usable rules: 20.60/20.90 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.60/20.90 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.60/20.90 a__U12(tt) -> tt 20.60/20.90 a__U12(X:S) -> U12(X:S) 20.60/20.90 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.60/20.90 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.60/20.90 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.60/20.90 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.60/20.90 a__U23(tt) -> tt 20.60/20.90 a__U23(X:S) -> U23(X:S) 20.60/20.90 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.60/20.90 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.60/20.90 a__U32(tt) -> tt 20.60/20.90 a__U32(X:S) -> U32(X:S) 20.60/20.90 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.60/20.90 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.60/20.90 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.60/20.90 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.60/20.90 a__U43(tt) -> tt 20.60/20.90 a__U43(X:S) -> U43(X:S) 20.60/20.90 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.60/20.90 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.60/20.90 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.60/20.90 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.60/20.90 a__U53(tt) -> tt 20.60/20.90 a__U53(X:S) -> U53(X:S) 20.60/20.90 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.60/20.90 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.60/20.90 a__U62(tt) -> tt 20.60/20.90 a__U62(X:S) -> U62(X:S) 20.60/20.90 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.60/20.90 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.60/20.90 a__U72(tt) -> tt 20.60/20.90 a__U72(X:S) -> U72(X:S) 20.60/20.90 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.60/20.90 a____(nil,X:S) -> mark(X:S) 20.60/20.90 a____(X:S,nil) -> mark(X:S) 20.60/20.90 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.60/20.90 a__and(tt,X:S) -> mark(X:S) 20.60/20.90 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.60/20.90 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.90 a__isList(nil) -> tt 20.60/20.90 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.60/20.90 a__isList(X:S) -> isList(X:S) 20.60/20.90 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.90 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.90 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.60/20.90 a__isNeList(X:S) -> isNeList(X:S) 20.60/20.90 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.90 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.60/20.90 a__isNePal(X:S) -> isNePal(X:S) 20.60/20.90 a__isPal(nil) -> tt 20.60/20.90 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.60/20.90 a__isPal(X:S) -> isPal(X:S) 20.60/20.90 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.90 a__isPalListKind(a) -> tt 20.60/20.90 a__isPalListKind(e) -> tt 20.60/20.90 a__isPalListKind(i) -> tt 20.60/20.90 a__isPalListKind(nil) -> tt 20.60/20.90 a__isPalListKind(o) -> tt 20.60/20.90 a__isPalListKind(u) -> tt 20.60/20.90 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.60/20.90 a__isQid(a) -> tt 20.60/20.90 a__isQid(e) -> tt 20.60/20.90 a__isQid(i) -> tt 20.60/20.90 a__isQid(o) -> tt 20.60/20.90 a__isQid(u) -> tt 20.60/20.90 a__isQid(X:S) -> isQid(X:S) 20.60/20.90 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.60/20.90 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.60/20.90 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.60/20.90 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.60/20.90 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.60/20.90 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.60/20.90 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.60/20.90 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.60/20.90 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.60/20.90 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.60/20.90 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.60/20.90 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.60/20.90 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.60/20.90 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.60/20.90 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.60/20.90 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.60/20.90 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.60/20.90 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.60/20.90 mark(a) -> a 20.60/20.90 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.60/20.90 mark(e) -> e 20.60/20.90 mark(i) -> i 20.60/20.90 mark(isList(X:S)) -> a__isList(X:S) 20.60/20.90 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.60/20.90 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.60/20.90 mark(isPal(X:S)) -> a__isPal(X:S) 20.60/20.90 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.60/20.90 mark(isQid(X:S)) -> a__isQid(X:S) 20.60/20.90 mark(nil) -> nil 20.60/20.90 mark(o) -> o 20.60/20.90 mark(tt) -> tt 20.60/20.90 mark(u) -> u 20.60/20.90 ->Interpretation type: 20.60/20.90 Linear 20.60/20.90 ->Coefficients: 20.60/20.90 Natural Numbers 20.60/20.90 ->Dimension: 20.60/20.90 1 20.60/20.90 ->Bound: 20.60/20.90 2 20.60/20.90 ->Interpretation: 20.60/20.90 20.60/20.90 [a__U11](X1,X2) = 2.X1 + 2.X2 + 1 20.60/20.90 [a__U12](X) = X 20.60/20.90 [a__U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.60/20.90 [a__U22](X1,X2) = X1 + 2.X2 + 1 20.60/20.90 [a__U23](X) = X 20.60/20.90 [a__U31](X1,X2) = 2.X1 + 2.X2 + 1 20.60/20.90 [a__U32](X) = X + 1 20.60/20.90 [a__U41](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 20.60/20.90 [a__U42](X1,X2) = X1 + 2.X2 + 1 20.60/20.90 [a__U43](X) = X 20.60/20.90 [a__U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.60/20.90 [a__U52](X1,X2) = X1 + 2.X2 + 1 20.60/20.90 [a__U53](X) = X 20.60/20.90 [a__U61](X1,X2) = 2.X1 + 2.X2 + 2 20.60/20.91 [a__U62](X) = X + 2 20.60/20.91 [a__U71](X1,X2) = 2.X1 + 2.X2 + 2 20.60/20.91 [a__U72](X) = X 20.60/20.91 [a____](X1,X2) = 2.X1 + X2 + 1 20.60/20.91 [a__and](X1,X2) = X1 + 2.X2 20.60/20.91 [a__isList](X) = 2.X + 1 20.60/20.91 [a__isNeList](X) = 2.X + 1 20.60/20.91 [a__isNePal](X) = 2.X + 2 20.60/20.91 [a__isPal](X) = 2.X + 2 20.60/20.91 [a__isPalListKind](X) = 0 20.60/20.91 [a__isQid](X) = 2.X 20.60/20.91 [mark](X) = X 20.60/20.91 [U11](X1,X2) = 2.X1 + 2.X2 + 1 20.60/20.91 [U12](X) = X 20.60/20.91 [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.60/20.91 [U22](X1,X2) = X1 + 2.X2 + 1 20.60/20.91 [U23](X) = X 20.60/20.91 [U31](X1,X2) = 2.X1 + 2.X2 + 1 20.60/20.91 [U32](X) = X + 1 20.60/20.91 [U41](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 20.60/20.91 [U42](X1,X2) = X1 + 2.X2 + 1 20.60/20.91 [U43](X) = X 20.60/20.91 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.60/20.91 [U52](X1,X2) = X1 + 2.X2 + 1 20.60/20.91 [U53](X) = X 20.60/20.91 [U61](X1,X2) = 2.X1 + 2.X2 + 2 20.60/20.91 [U62](X) = X + 2 20.60/20.91 [U71](X1,X2) = 2.X1 + 2.X2 + 2 20.60/20.91 [U72](X) = X 20.60/20.91 [__](X1,X2) = 2.X1 + X2 + 1 20.60/20.91 [a] = 0 20.60/20.91 [and](X1,X2) = X1 + 2.X2 20.60/20.91 [e] = 1 20.60/20.91 [fSNonEmpty] = 0 20.60/20.91 [i] = 0 20.60/20.91 [isList](X) = 2.X + 1 20.60/20.91 [isNeList](X) = 2.X + 1 20.60/20.91 [isNePal](X) = 2.X + 2 20.60/20.91 [isPal](X) = 2.X + 2 20.60/20.91 [isPalListKind](X) = 0 20.60/20.91 [isQid](X) = 2.X 20.60/20.91 [nil] = 1 20.60/20.91 [o] = 0 20.60/20.91 [tt] = 0 20.60/20.91 [u] = 1 20.60/20.91 [A__U11](X1,X2) = 0 20.60/20.91 [A__U12](X) = 0 20.60/20.91 [A__U21](X1,X2,X3) = 0 20.60/20.91 [A__U22](X1,X2) = 0 20.60/20.91 [A__U23](X) = 0 20.60/20.91 [A__U31](X1,X2) = 0 20.60/20.91 [A__U32](X) = 0 20.60/20.91 [A__U41](X1,X2,X3) = 0 20.60/20.91 [A__U42](X1,X2) = 0 20.60/20.91 [A__U43](X) = 0 20.60/20.91 [A__U51](X1,X2,X3) = 0 20.60/20.91 [A__U52](X1,X2) = 0 20.60/20.91 [A__U53](X) = 0 20.60/20.91 [A__U61](X1,X2) = 0 20.60/20.91 [A__U62](X) = 0 20.60/20.91 [A__U71](X1,X2) = 0 20.60/20.91 [A__U72](X) = 0 20.60/20.91 [A____](X1,X2) = 0 20.60/20.91 [A__AND](X1,X2) = 2.X2 20.60/20.91 [A__ISLIST](X) = 2.X + 2 20.60/20.91 [A__ISNELIST](X) = 2.X + 1 20.60/20.91 [A__ISNEPAL](X) = 2.X 20.60/20.91 [A__ISPAL](X) = 2.X 20.60/20.91 [A__ISPALLISTKIND](X) = 0 20.60/20.91 [A__ISQID](X) = 0 20.60/20.91 [MARK](X) = 2.X 20.60/20.91 20.60/20.91 Problem 1: 20.60/20.91 20.60/20.91 SCC Processor: 20.60/20.91 -> Pairs: 20.60/20.91 A__AND(tt,X:S) -> MARK(X:S) 20.60/20.91 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.91 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.91 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.91 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.91 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.60/20.91 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.91 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.91 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.91 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.91 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U12(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.91 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U23(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U32(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.91 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U43(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.91 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U53(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U62(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U72(X:S)) -> MARK(X:S) 20.60/20.91 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.60/20.91 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.60/20.91 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(isList(X:S)) -> A__ISLIST(X:S) 20.60/20.91 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.60/20.91 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.60/20.91 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.60/20.91 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.60/20.91 -> Rules: 20.60/20.91 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.60/20.91 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.60/20.91 a__U12(tt) -> tt 20.60/20.91 a__U12(X:S) -> U12(X:S) 20.60/20.91 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.60/20.91 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.60/20.91 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.60/20.91 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.60/20.91 a__U23(tt) -> tt 20.60/20.91 a__U23(X:S) -> U23(X:S) 20.60/20.91 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.60/20.91 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.60/20.91 a__U32(tt) -> tt 20.60/20.91 a__U32(X:S) -> U32(X:S) 20.60/20.91 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.60/20.91 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.60/20.91 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.60/20.91 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.60/20.91 a__U43(tt) -> tt 20.60/20.91 a__U43(X:S) -> U43(X:S) 20.60/20.91 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.60/20.91 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.60/20.91 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.60/20.91 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.60/20.91 a__U53(tt) -> tt 20.60/20.91 a__U53(X:S) -> U53(X:S) 20.60/20.91 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.60/20.91 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.60/20.91 a__U62(tt) -> tt 20.60/20.91 a__U62(X:S) -> U62(X:S) 20.60/20.91 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.60/20.91 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.60/20.91 a__U72(tt) -> tt 20.60/20.91 a__U72(X:S) -> U72(X:S) 20.60/20.91 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.60/20.91 a____(nil,X:S) -> mark(X:S) 20.60/20.91 a____(X:S,nil) -> mark(X:S) 20.60/20.91 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.60/20.91 a__and(tt,X:S) -> mark(X:S) 20.60/20.91 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.60/20.91 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.91 a__isList(nil) -> tt 20.60/20.91 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.60/20.91 a__isList(X:S) -> isList(X:S) 20.60/20.91 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.91 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.91 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.60/20.91 a__isNeList(X:S) -> isNeList(X:S) 20.60/20.91 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.91 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.60/20.91 a__isNePal(X:S) -> isNePal(X:S) 20.60/20.91 a__isPal(nil) -> tt 20.60/20.91 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.60/20.91 a__isPal(X:S) -> isPal(X:S) 20.60/20.91 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.91 a__isPalListKind(a) -> tt 20.60/20.91 a__isPalListKind(e) -> tt 20.60/20.91 a__isPalListKind(i) -> tt 20.60/20.91 a__isPalListKind(nil) -> tt 20.60/20.91 a__isPalListKind(o) -> tt 20.60/20.91 a__isPalListKind(u) -> tt 20.60/20.91 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.60/20.91 a__isQid(a) -> tt 20.60/20.91 a__isQid(e) -> tt 20.60/20.91 a__isQid(i) -> tt 20.60/20.91 a__isQid(o) -> tt 20.60/20.91 a__isQid(u) -> tt 20.60/20.91 a__isQid(X:S) -> isQid(X:S) 20.60/20.91 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.60/20.91 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.60/20.91 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.60/20.91 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.60/20.91 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.60/20.91 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.60/20.91 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.60/20.91 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.60/20.91 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.60/20.91 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.60/20.91 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.60/20.91 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.60/20.91 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.60/20.91 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.60/20.91 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.60/20.91 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.60/20.91 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.60/20.91 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.60/20.91 mark(a) -> a 20.60/20.91 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.60/20.91 mark(e) -> e 20.60/20.91 mark(i) -> i 20.60/20.91 mark(isList(X:S)) -> a__isList(X:S) 20.60/20.91 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.60/20.91 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.60/20.91 mark(isPal(X:S)) -> a__isPal(X:S) 20.60/20.91 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.60/20.91 mark(isQid(X:S)) -> a__isQid(X:S) 20.60/20.91 mark(nil) -> nil 20.60/20.91 mark(o) -> o 20.60/20.91 mark(tt) -> tt 20.60/20.91 mark(u) -> u 20.60/20.91 ->Strongly Connected Components: 20.60/20.91 ->->Cycle: 20.60/20.91 ->->-> Pairs: 20.60/20.91 A__AND(tt,X:S) -> MARK(X:S) 20.60/20.91 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.91 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.91 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.91 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.91 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.60/20.91 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.91 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.91 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.91 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.91 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U12(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.91 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U23(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U32(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.91 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U43(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.91 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U53(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U62(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U72(X:S)) -> MARK(X:S) 20.60/20.91 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.60/20.91 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.60/20.91 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.60/20.91 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.60/20.91 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.60/20.91 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.60/20.91 ->->-> Rules: 20.60/20.91 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.60/20.91 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.60/20.91 a__U12(tt) -> tt 20.60/20.91 a__U12(X:S) -> U12(X:S) 20.60/20.91 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.60/20.91 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.60/20.91 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.60/20.91 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.60/20.91 a__U23(tt) -> tt 20.60/20.91 a__U23(X:S) -> U23(X:S) 20.60/20.91 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.60/20.91 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.60/20.91 a__U32(tt) -> tt 20.60/20.91 a__U32(X:S) -> U32(X:S) 20.60/20.91 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.60/20.91 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.60/20.91 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.60/20.91 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.60/20.91 a__U43(tt) -> tt 20.60/20.91 a__U43(X:S) -> U43(X:S) 20.60/20.91 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.60/20.91 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.60/20.91 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.60/20.91 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.60/20.91 a__U53(tt) -> tt 20.60/20.91 a__U53(X:S) -> U53(X:S) 20.60/20.91 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.60/20.91 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.60/20.91 a__U62(tt) -> tt 20.60/20.91 a__U62(X:S) -> U62(X:S) 20.60/20.91 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.60/20.91 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.60/20.91 a__U72(tt) -> tt 20.60/20.91 a__U72(X:S) -> U72(X:S) 20.60/20.91 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.60/20.91 a____(nil,X:S) -> mark(X:S) 20.60/20.91 a____(X:S,nil) -> mark(X:S) 20.60/20.91 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.60/20.91 a__and(tt,X:S) -> mark(X:S) 20.60/20.91 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.60/20.91 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.91 a__isList(nil) -> tt 20.60/20.91 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.60/20.91 a__isList(X:S) -> isList(X:S) 20.60/20.91 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.91 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.91 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.60/20.91 a__isNeList(X:S) -> isNeList(X:S) 20.60/20.91 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.91 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.60/20.91 a__isNePal(X:S) -> isNePal(X:S) 20.60/20.91 a__isPal(nil) -> tt 20.60/20.91 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.60/20.91 a__isPal(X:S) -> isPal(X:S) 20.60/20.91 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.91 a__isPalListKind(a) -> tt 20.60/20.91 a__isPalListKind(e) -> tt 20.60/20.91 a__isPalListKind(i) -> tt 20.60/20.91 a__isPalListKind(nil) -> tt 20.60/20.91 a__isPalListKind(o) -> tt 20.60/20.91 a__isPalListKind(u) -> tt 20.60/20.91 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.60/20.91 a__isQid(a) -> tt 20.60/20.91 a__isQid(e) -> tt 20.60/20.91 a__isQid(i) -> tt 20.60/20.91 a__isQid(o) -> tt 20.60/20.91 a__isQid(u) -> tt 20.60/20.91 a__isQid(X:S) -> isQid(X:S) 20.60/20.91 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.60/20.91 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.60/20.91 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.60/20.91 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.60/20.91 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.60/20.91 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.60/20.91 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.60/20.91 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.60/20.91 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.60/20.91 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.60/20.91 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.60/20.91 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.60/20.91 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.60/20.91 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.60/20.91 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.60/20.91 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.60/20.91 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.60/20.91 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.60/20.91 mark(a) -> a 20.60/20.91 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.60/20.91 mark(e) -> e 20.60/20.91 mark(i) -> i 20.60/20.91 mark(isList(X:S)) -> a__isList(X:S) 20.60/20.91 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.60/20.91 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.60/20.91 mark(isPal(X:S)) -> a__isPal(X:S) 20.60/20.91 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.60/20.91 mark(isQid(X:S)) -> a__isQid(X:S) 20.60/20.91 mark(nil) -> nil 20.60/20.91 mark(o) -> o 20.60/20.91 mark(tt) -> tt 20.60/20.91 mark(u) -> u 20.60/20.91 20.60/20.91 Problem 1: 20.60/20.91 20.60/20.91 Reduction Pairs Processor: 20.60/20.91 -> Pairs: 20.60/20.91 A__AND(tt,X:S) -> MARK(X:S) 20.60/20.91 A__ISNELIST(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.91 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.91 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.91 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.91 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.60/20.91 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.91 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.91 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.91 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.91 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U12(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.91 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U23(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U32(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.91 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U43(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.91 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U53(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U62(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U72(X:S)) -> MARK(X:S) 20.60/20.91 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.60/20.91 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.60/20.91 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.60/20.91 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.60/20.91 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.60/20.91 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.60/20.91 -> Rules: 20.60/20.91 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.60/20.91 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.60/20.91 a__U12(tt) -> tt 20.60/20.91 a__U12(X:S) -> U12(X:S) 20.60/20.91 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.60/20.91 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.60/20.91 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.60/20.91 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.60/20.91 a__U23(tt) -> tt 20.60/20.91 a__U23(X:S) -> U23(X:S) 20.60/20.91 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.60/20.91 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.60/20.91 a__U32(tt) -> tt 20.60/20.91 a__U32(X:S) -> U32(X:S) 20.60/20.91 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.60/20.91 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.60/20.91 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.60/20.91 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.60/20.91 a__U43(tt) -> tt 20.60/20.91 a__U43(X:S) -> U43(X:S) 20.60/20.91 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.60/20.91 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.60/20.91 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.60/20.91 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.60/20.91 a__U53(tt) -> tt 20.60/20.91 a__U53(X:S) -> U53(X:S) 20.60/20.91 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.60/20.91 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.60/20.91 a__U62(tt) -> tt 20.60/20.91 a__U62(X:S) -> U62(X:S) 20.60/20.91 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.60/20.91 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.60/20.91 a__U72(tt) -> tt 20.60/20.91 a__U72(X:S) -> U72(X:S) 20.60/20.91 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.60/20.91 a____(nil,X:S) -> mark(X:S) 20.60/20.91 a____(X:S,nil) -> mark(X:S) 20.60/20.91 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.60/20.91 a__and(tt,X:S) -> mark(X:S) 20.60/20.91 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.60/20.91 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.91 a__isList(nil) -> tt 20.60/20.91 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.60/20.91 a__isList(X:S) -> isList(X:S) 20.60/20.91 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.91 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.91 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.60/20.91 a__isNeList(X:S) -> isNeList(X:S) 20.60/20.91 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.91 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.60/20.91 a__isNePal(X:S) -> isNePal(X:S) 20.60/20.91 a__isPal(nil) -> tt 20.60/20.91 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.60/20.91 a__isPal(X:S) -> isPal(X:S) 20.60/20.91 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.91 a__isPalListKind(a) -> tt 20.60/20.91 a__isPalListKind(e) -> tt 20.60/20.91 a__isPalListKind(i) -> tt 20.60/20.91 a__isPalListKind(nil) -> tt 20.60/20.91 a__isPalListKind(o) -> tt 20.60/20.91 a__isPalListKind(u) -> tt 20.60/20.91 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.60/20.91 a__isQid(a) -> tt 20.60/20.91 a__isQid(e) -> tt 20.60/20.91 a__isQid(i) -> tt 20.60/20.91 a__isQid(o) -> tt 20.60/20.91 a__isQid(u) -> tt 20.60/20.91 a__isQid(X:S) -> isQid(X:S) 20.60/20.91 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.60/20.91 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.60/20.91 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.60/20.91 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.60/20.91 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.60/20.91 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.60/20.91 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.60/20.91 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.60/20.91 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.60/20.91 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.60/20.91 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.60/20.91 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.60/20.91 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.60/20.91 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.60/20.91 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.60/20.91 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.60/20.91 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.60/20.91 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.60/20.91 mark(a) -> a 20.60/20.91 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.60/20.91 mark(e) -> e 20.60/20.91 mark(i) -> i 20.60/20.91 mark(isList(X:S)) -> a__isList(X:S) 20.60/20.91 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.60/20.91 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.60/20.91 mark(isPal(X:S)) -> a__isPal(X:S) 20.60/20.91 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.60/20.91 mark(isQid(X:S)) -> a__isQid(X:S) 20.60/20.91 mark(nil) -> nil 20.60/20.91 mark(o) -> o 20.60/20.91 mark(tt) -> tt 20.60/20.91 mark(u) -> u 20.60/20.91 -> Usable rules: 20.60/20.91 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.60/20.91 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.60/20.91 a__U12(tt) -> tt 20.60/20.91 a__U12(X:S) -> U12(X:S) 20.60/20.91 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.60/20.91 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.60/20.91 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.60/20.91 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.60/20.91 a__U23(tt) -> tt 20.60/20.91 a__U23(X:S) -> U23(X:S) 20.60/20.91 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.60/20.91 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.60/20.91 a__U32(tt) -> tt 20.60/20.91 a__U32(X:S) -> U32(X:S) 20.60/20.91 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.60/20.91 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.60/20.91 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.60/20.91 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.60/20.91 a__U43(tt) -> tt 20.60/20.91 a__U43(X:S) -> U43(X:S) 20.60/20.91 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.60/20.91 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.60/20.91 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.60/20.91 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.60/20.91 a__U53(tt) -> tt 20.60/20.91 a__U53(X:S) -> U53(X:S) 20.60/20.91 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.60/20.91 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.60/20.91 a__U62(tt) -> tt 20.60/20.91 a__U62(X:S) -> U62(X:S) 20.60/20.91 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.60/20.91 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.60/20.91 a__U72(tt) -> tt 20.60/20.91 a__U72(X:S) -> U72(X:S) 20.60/20.91 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.60/20.91 a____(nil,X:S) -> mark(X:S) 20.60/20.91 a____(X:S,nil) -> mark(X:S) 20.60/20.91 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.60/20.91 a__and(tt,X:S) -> mark(X:S) 20.60/20.91 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.60/20.91 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.91 a__isList(nil) -> tt 20.60/20.91 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.60/20.91 a__isList(X:S) -> isList(X:S) 20.60/20.91 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.91 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.91 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.60/20.91 a__isNeList(X:S) -> isNeList(X:S) 20.60/20.91 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.91 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.60/20.91 a__isNePal(X:S) -> isNePal(X:S) 20.60/20.91 a__isPal(nil) -> tt 20.60/20.91 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.60/20.91 a__isPal(X:S) -> isPal(X:S) 20.60/20.91 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.91 a__isPalListKind(a) -> tt 20.60/20.91 a__isPalListKind(e) -> tt 20.60/20.91 a__isPalListKind(i) -> tt 20.60/20.91 a__isPalListKind(nil) -> tt 20.60/20.91 a__isPalListKind(o) -> tt 20.60/20.91 a__isPalListKind(u) -> tt 20.60/20.91 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.60/20.91 a__isQid(a) -> tt 20.60/20.91 a__isQid(e) -> tt 20.60/20.91 a__isQid(i) -> tt 20.60/20.91 a__isQid(o) -> tt 20.60/20.91 a__isQid(u) -> tt 20.60/20.91 a__isQid(X:S) -> isQid(X:S) 20.60/20.91 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.60/20.91 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.60/20.91 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.60/20.91 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.60/20.91 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.60/20.91 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.60/20.91 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.60/20.91 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.60/20.91 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.60/20.91 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.60/20.91 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.60/20.91 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.60/20.91 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.60/20.91 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.60/20.91 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.60/20.91 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.60/20.91 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.60/20.91 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.60/20.91 mark(a) -> a 20.60/20.91 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.60/20.91 mark(e) -> e 20.60/20.91 mark(i) -> i 20.60/20.91 mark(isList(X:S)) -> a__isList(X:S) 20.60/20.91 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.60/20.91 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.60/20.91 mark(isPal(X:S)) -> a__isPal(X:S) 20.60/20.91 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.60/20.91 mark(isQid(X:S)) -> a__isQid(X:S) 20.60/20.91 mark(nil) -> nil 20.60/20.91 mark(o) -> o 20.60/20.91 mark(tt) -> tt 20.60/20.91 mark(u) -> u 20.60/20.91 ->Interpretation type: 20.60/20.91 Linear 20.60/20.91 ->Coefficients: 20.60/20.91 Natural Numbers 20.60/20.91 ->Dimension: 20.60/20.91 1 20.60/20.91 ->Bound: 20.60/20.91 2 20.60/20.91 ->Interpretation: 20.60/20.91 20.60/20.91 [a__U11](X1,X2) = 2.X1 + 2.X2 20.60/20.91 [a__U12](X) = X 20.60/20.91 [a__U21](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 20.60/20.91 [a__U22](X1,X2) = X1 + 2.X2 + 2 20.60/20.91 [a__U23](X) = X + 2 20.60/20.91 [a__U31](X1,X2) = 2.X1 + 2.X2 20.60/20.91 [a__U32](X) = X 20.60/20.91 [a__U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.60/20.91 [a__U42](X1,X2) = X1 + 2.X2 + 1 20.60/20.91 [a__U43](X) = X 20.60/20.91 [a__U51](X1,X2,X3) = X1 + 2.X2 + 2.X3 20.60/20.91 [a__U52](X1,X2) = X1 + 2.X2 20.60/20.91 [a__U53](X) = X 20.60/20.91 [a__U61](X1,X2) = 2.X1 + 2.X2 20.60/20.91 [a__U62](X) = X 20.60/20.91 [a__U71](X1,X2) = 2.X1 + 2.X2 + 2 20.60/20.91 [a__U72](X) = X 20.60/20.91 [a____](X1,X2) = 2.X1 + X2 + 1 20.60/20.91 [a__and](X1,X2) = X1 + 2.X2 20.60/20.91 [a__isList](X) = 2.X 20.60/20.91 [a__isNeList](X) = 2.X 20.60/20.91 [a__isNePal](X) = 2.X + 2 20.60/20.91 [a__isPal](X) = 2.X + 2 20.60/20.91 [a__isPalListKind](X) = 0 20.60/20.91 [a__isQid](X) = 2.X 20.60/20.91 [mark](X) = X 20.60/20.91 [U11](X1,X2) = 2.X1 + 2.X2 20.60/20.91 [U12](X) = X 20.60/20.91 [U21](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 20.60/20.91 [U22](X1,X2) = X1 + 2.X2 + 2 20.60/20.91 [U23](X) = X + 2 20.60/20.91 [U31](X1,X2) = 2.X1 + 2.X2 20.60/20.91 [U32](X) = X 20.60/20.91 [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.60/20.91 [U42](X1,X2) = X1 + 2.X2 + 1 20.60/20.91 [U43](X) = X 20.60/20.91 [U51](X1,X2,X3) = X1 + 2.X2 + 2.X3 20.60/20.91 [U52](X1,X2) = X1 + 2.X2 20.60/20.91 [U53](X) = X 20.60/20.91 [U61](X1,X2) = 2.X1 + 2.X2 20.60/20.91 [U62](X) = X 20.60/20.91 [U71](X1,X2) = 2.X1 + 2.X2 + 2 20.60/20.91 [U72](X) = X 20.60/20.91 [__](X1,X2) = 2.X1 + X2 + 1 20.60/20.91 [a] = 0 20.60/20.91 [and](X1,X2) = X1 + 2.X2 20.60/20.91 [e] = 1 20.60/20.91 [fSNonEmpty] = 0 20.60/20.91 [i] = 0 20.60/20.91 [isList](X) = 2.X 20.60/20.91 [isNeList](X) = 2.X 20.60/20.91 [isNePal](X) = 2.X + 2 20.60/20.91 [isPal](X) = 2.X + 2 20.60/20.91 [isPalListKind](X) = 0 20.60/20.91 [isQid](X) = 2.X 20.60/20.91 [nil] = 1 20.60/20.91 [o] = 1 20.60/20.91 [tt] = 0 20.60/20.91 [u] = 1 20.60/20.91 [A__U11](X1,X2) = 0 20.60/20.91 [A__U12](X) = 0 20.60/20.91 [A__U21](X1,X2,X3) = 0 20.60/20.91 [A__U22](X1,X2) = 0 20.60/20.91 [A__U23](X) = 0 20.60/20.91 [A__U31](X1,X2) = 0 20.60/20.91 [A__U32](X) = 0 20.60/20.91 [A__U41](X1,X2,X3) = 0 20.60/20.91 [A__U42](X1,X2) = 0 20.60/20.91 [A__U43](X) = 0 20.60/20.91 [A__U51](X1,X2,X3) = 0 20.60/20.91 [A__U52](X1,X2) = 0 20.60/20.91 [A__U53](X) = 0 20.60/20.91 [A__U61](X1,X2) = 0 20.60/20.91 [A__U62](X) = 0 20.60/20.91 [A__U71](X1,X2) = 0 20.60/20.91 [A__U72](X) = 0 20.60/20.91 [A____](X1,X2) = 0 20.60/20.91 [A__AND](X1,X2) = 2.X2 + 2 20.60/20.91 [A__ISLIST](X) = 0 20.60/20.91 [A__ISNELIST](X) = X + 2 20.60/20.91 [A__ISNEPAL](X) = 2.X + 2 20.60/20.91 [A__ISPAL](X) = X + 2 20.60/20.91 [A__ISPALLISTKIND](X) = 2 20.60/20.91 [A__ISQID](X) = 0 20.60/20.91 [MARK](X) = 2.X + 2 20.60/20.91 20.60/20.91 Problem 1: 20.60/20.91 20.60/20.91 SCC Processor: 20.60/20.91 -> Pairs: 20.60/20.91 A__AND(tt,X:S) -> MARK(X:S) 20.60/20.91 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.91 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.91 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.91 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.60/20.91 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.91 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.91 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.91 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.91 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U12(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.91 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U23(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U32(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.91 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U43(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.91 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U53(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U62(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U72(X:S)) -> MARK(X:S) 20.60/20.91 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.60/20.91 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.60/20.91 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.60/20.91 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.60/20.91 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.60/20.91 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.60/20.91 -> Rules: 20.60/20.91 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.60/20.91 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.60/20.91 a__U12(tt) -> tt 20.60/20.91 a__U12(X:S) -> U12(X:S) 20.60/20.91 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.60/20.91 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.60/20.91 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.60/20.91 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.60/20.91 a__U23(tt) -> tt 20.60/20.91 a__U23(X:S) -> U23(X:S) 20.60/20.91 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.60/20.91 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.60/20.91 a__U32(tt) -> tt 20.60/20.91 a__U32(X:S) -> U32(X:S) 20.60/20.91 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.60/20.91 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.60/20.91 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.60/20.91 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.60/20.91 a__U43(tt) -> tt 20.60/20.91 a__U43(X:S) -> U43(X:S) 20.60/20.91 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.60/20.91 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.60/20.91 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.60/20.91 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.60/20.91 a__U53(tt) -> tt 20.60/20.91 a__U53(X:S) -> U53(X:S) 20.60/20.91 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.60/20.91 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.60/20.91 a__U62(tt) -> tt 20.60/20.91 a__U62(X:S) -> U62(X:S) 20.60/20.91 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.60/20.91 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.60/20.91 a__U72(tt) -> tt 20.60/20.91 a__U72(X:S) -> U72(X:S) 20.60/20.91 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.60/20.91 a____(nil,X:S) -> mark(X:S) 20.60/20.91 a____(X:S,nil) -> mark(X:S) 20.60/20.91 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.60/20.91 a__and(tt,X:S) -> mark(X:S) 20.60/20.91 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.60/20.91 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.91 a__isList(nil) -> tt 20.60/20.91 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.60/20.91 a__isList(X:S) -> isList(X:S) 20.60/20.91 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.91 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.91 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.60/20.91 a__isNeList(X:S) -> isNeList(X:S) 20.60/20.91 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.91 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.60/20.91 a__isNePal(X:S) -> isNePal(X:S) 20.60/20.91 a__isPal(nil) -> tt 20.60/20.91 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.60/20.91 a__isPal(X:S) -> isPal(X:S) 20.60/20.91 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.91 a__isPalListKind(a) -> tt 20.60/20.91 a__isPalListKind(e) -> tt 20.60/20.91 a__isPalListKind(i) -> tt 20.60/20.91 a__isPalListKind(nil) -> tt 20.60/20.91 a__isPalListKind(o) -> tt 20.60/20.91 a__isPalListKind(u) -> tt 20.60/20.91 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.60/20.91 a__isQid(a) -> tt 20.60/20.91 a__isQid(e) -> tt 20.60/20.91 a__isQid(i) -> tt 20.60/20.91 a__isQid(o) -> tt 20.60/20.91 a__isQid(u) -> tt 20.60/20.91 a__isQid(X:S) -> isQid(X:S) 20.60/20.91 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.60/20.91 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.60/20.91 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.60/20.91 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.60/20.91 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.60/20.91 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.60/20.91 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.60/20.91 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.60/20.91 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.60/20.91 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.60/20.91 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.60/20.91 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.60/20.91 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.60/20.91 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.60/20.91 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.60/20.91 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.60/20.91 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.60/20.91 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.60/20.91 mark(a) -> a 20.60/20.91 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.60/20.91 mark(e) -> e 20.60/20.91 mark(i) -> i 20.60/20.91 mark(isList(X:S)) -> a__isList(X:S) 20.60/20.91 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.60/20.91 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.60/20.91 mark(isPal(X:S)) -> a__isPal(X:S) 20.60/20.91 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.60/20.91 mark(isQid(X:S)) -> a__isQid(X:S) 20.60/20.91 mark(nil) -> nil 20.60/20.91 mark(o) -> o 20.60/20.91 mark(tt) -> tt 20.60/20.91 mark(u) -> u 20.60/20.91 ->Strongly Connected Components: 20.60/20.91 ->->Cycle: 20.60/20.91 ->->-> Pairs: 20.60/20.91 A__AND(tt,X:S) -> MARK(X:S) 20.60/20.91 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.91 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.91 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.91 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.60/20.91 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.91 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.91 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.91 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.91 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U12(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.91 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U23(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U32(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.91 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U43(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.91 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U53(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U62(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U72(X:S)) -> MARK(X:S) 20.60/20.91 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.60/20.91 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.60/20.91 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.60/20.91 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.60/20.91 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.60/20.91 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.60/20.91 ->->-> Rules: 20.60/20.91 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.60/20.91 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.60/20.91 a__U12(tt) -> tt 20.60/20.91 a__U12(X:S) -> U12(X:S) 20.60/20.91 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.60/20.91 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.60/20.91 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.60/20.91 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.60/20.91 a__U23(tt) -> tt 20.60/20.91 a__U23(X:S) -> U23(X:S) 20.60/20.91 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.60/20.91 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.60/20.91 a__U32(tt) -> tt 20.60/20.91 a__U32(X:S) -> U32(X:S) 20.60/20.91 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.60/20.91 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.60/20.91 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.60/20.91 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.60/20.91 a__U43(tt) -> tt 20.60/20.91 a__U43(X:S) -> U43(X:S) 20.60/20.91 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.60/20.91 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.60/20.91 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.60/20.91 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.60/20.91 a__U53(tt) -> tt 20.60/20.91 a__U53(X:S) -> U53(X:S) 20.60/20.91 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.60/20.91 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.60/20.91 a__U62(tt) -> tt 20.60/20.91 a__U62(X:S) -> U62(X:S) 20.60/20.91 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.60/20.91 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.60/20.91 a__U72(tt) -> tt 20.60/20.91 a__U72(X:S) -> U72(X:S) 20.60/20.91 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.60/20.91 a____(nil,X:S) -> mark(X:S) 20.60/20.91 a____(X:S,nil) -> mark(X:S) 20.60/20.91 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.60/20.91 a__and(tt,X:S) -> mark(X:S) 20.60/20.91 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.60/20.91 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.91 a__isList(nil) -> tt 20.60/20.91 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.60/20.91 a__isList(X:S) -> isList(X:S) 20.60/20.91 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.91 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.91 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.60/20.91 a__isNeList(X:S) -> isNeList(X:S) 20.60/20.91 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.91 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.60/20.91 a__isNePal(X:S) -> isNePal(X:S) 20.60/20.91 a__isPal(nil) -> tt 20.60/20.91 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.60/20.91 a__isPal(X:S) -> isPal(X:S) 20.60/20.91 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.91 a__isPalListKind(a) -> tt 20.60/20.91 a__isPalListKind(e) -> tt 20.60/20.91 a__isPalListKind(i) -> tt 20.60/20.91 a__isPalListKind(nil) -> tt 20.60/20.91 a__isPalListKind(o) -> tt 20.60/20.91 a__isPalListKind(u) -> tt 20.60/20.91 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.60/20.91 a__isQid(a) -> tt 20.60/20.91 a__isQid(e) -> tt 20.60/20.91 a__isQid(i) -> tt 20.60/20.91 a__isQid(o) -> tt 20.60/20.91 a__isQid(u) -> tt 20.60/20.91 a__isQid(X:S) -> isQid(X:S) 20.60/20.91 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.60/20.91 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.60/20.91 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.60/20.91 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.60/20.91 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.60/20.91 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.60/20.91 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.60/20.91 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.60/20.91 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.60/20.91 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.60/20.91 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.60/20.91 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.60/20.91 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.60/20.91 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.60/20.91 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.60/20.91 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.60/20.91 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.60/20.91 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.60/20.91 mark(a) -> a 20.60/20.91 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.60/20.91 mark(e) -> e 20.60/20.91 mark(i) -> i 20.60/20.91 mark(isList(X:S)) -> a__isList(X:S) 20.60/20.91 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.60/20.91 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.60/20.91 mark(isPal(X:S)) -> a__isPal(X:S) 20.60/20.91 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.60/20.91 mark(isQid(X:S)) -> a__isQid(X:S) 20.60/20.91 mark(nil) -> nil 20.60/20.91 mark(o) -> o 20.60/20.91 mark(tt) -> tt 20.60/20.91 mark(u) -> u 20.60/20.91 20.60/20.91 Problem 1: 20.60/20.91 20.60/20.91 Reduction Pairs Processor: 20.60/20.91 -> Pairs: 20.60/20.91 A__AND(tt,X:S) -> MARK(X:S) 20.60/20.91 A__ISNELIST(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.91 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.91 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.91 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.60/20.91 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.91 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.91 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.91 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.91 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U12(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.91 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U23(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U32(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.91 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U43(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.91 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U53(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U62(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U72(X:S)) -> MARK(X:S) 20.60/20.91 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.60/20.91 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.60/20.91 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.60/20.91 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.60/20.91 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.60/20.91 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.60/20.91 -> Rules: 20.60/20.91 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.60/20.91 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.60/20.91 a__U12(tt) -> tt 20.60/20.91 a__U12(X:S) -> U12(X:S) 20.60/20.91 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.60/20.91 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.60/20.91 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.60/20.91 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.60/20.91 a__U23(tt) -> tt 20.60/20.91 a__U23(X:S) -> U23(X:S) 20.60/20.91 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.60/20.91 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.60/20.91 a__U32(tt) -> tt 20.60/20.91 a__U32(X:S) -> U32(X:S) 20.60/20.91 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.60/20.91 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.60/20.91 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.60/20.91 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.60/20.91 a__U43(tt) -> tt 20.60/20.91 a__U43(X:S) -> U43(X:S) 20.60/20.91 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.60/20.91 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.60/20.91 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.60/20.91 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.60/20.91 a__U53(tt) -> tt 20.60/20.91 a__U53(X:S) -> U53(X:S) 20.60/20.91 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.60/20.91 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.60/20.91 a__U62(tt) -> tt 20.60/20.91 a__U62(X:S) -> U62(X:S) 20.60/20.91 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.60/20.91 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.60/20.91 a__U72(tt) -> tt 20.60/20.91 a__U72(X:S) -> U72(X:S) 20.60/20.91 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.60/20.91 a____(nil,X:S) -> mark(X:S) 20.60/20.91 a____(X:S,nil) -> mark(X:S) 20.60/20.91 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.60/20.91 a__and(tt,X:S) -> mark(X:S) 20.60/20.91 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.60/20.91 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.91 a__isList(nil) -> tt 20.60/20.91 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.60/20.91 a__isList(X:S) -> isList(X:S) 20.60/20.91 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.91 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.91 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.60/20.91 a__isNeList(X:S) -> isNeList(X:S) 20.60/20.91 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.91 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.60/20.91 a__isNePal(X:S) -> isNePal(X:S) 20.60/20.91 a__isPal(nil) -> tt 20.60/20.91 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.60/20.91 a__isPal(X:S) -> isPal(X:S) 20.60/20.91 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.91 a__isPalListKind(a) -> tt 20.60/20.91 a__isPalListKind(e) -> tt 20.60/20.91 a__isPalListKind(i) -> tt 20.60/20.91 a__isPalListKind(nil) -> tt 20.60/20.91 a__isPalListKind(o) -> tt 20.60/20.91 a__isPalListKind(u) -> tt 20.60/20.91 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.60/20.91 a__isQid(a) -> tt 20.60/20.91 a__isQid(e) -> tt 20.60/20.91 a__isQid(i) -> tt 20.60/20.91 a__isQid(o) -> tt 20.60/20.91 a__isQid(u) -> tt 20.60/20.91 a__isQid(X:S) -> isQid(X:S) 20.60/20.91 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.60/20.91 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.60/20.91 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.60/20.91 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.60/20.91 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.60/20.91 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.60/20.91 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.60/20.91 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.60/20.91 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.60/20.91 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.60/20.91 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.60/20.91 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.60/20.91 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.60/20.91 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.60/20.91 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.60/20.91 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.60/20.91 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.60/20.91 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.60/20.91 mark(a) -> a 20.60/20.91 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.60/20.91 mark(e) -> e 20.60/20.91 mark(i) -> i 20.60/20.91 mark(isList(X:S)) -> a__isList(X:S) 20.60/20.91 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.60/20.91 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.60/20.91 mark(isPal(X:S)) -> a__isPal(X:S) 20.60/20.91 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.60/20.91 mark(isQid(X:S)) -> a__isQid(X:S) 20.60/20.91 mark(nil) -> nil 20.60/20.91 mark(o) -> o 20.60/20.91 mark(tt) -> tt 20.60/20.91 mark(u) -> u 20.60/20.91 -> Usable rules: 20.60/20.91 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.60/20.91 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.60/20.91 a__U12(tt) -> tt 20.60/20.91 a__U12(X:S) -> U12(X:S) 20.60/20.91 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.60/20.91 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.60/20.91 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.60/20.91 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.60/20.91 a__U23(tt) -> tt 20.60/20.91 a__U23(X:S) -> U23(X:S) 20.60/20.91 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.60/20.91 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.60/20.91 a__U32(tt) -> tt 20.60/20.91 a__U32(X:S) -> U32(X:S) 20.60/20.91 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.60/20.91 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.60/20.91 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.60/20.91 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.60/20.91 a__U43(tt) -> tt 20.60/20.91 a__U43(X:S) -> U43(X:S) 20.60/20.91 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.60/20.91 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.60/20.91 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.60/20.91 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.60/20.91 a__U53(tt) -> tt 20.60/20.91 a__U53(X:S) -> U53(X:S) 20.60/20.91 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.60/20.91 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.60/20.91 a__U62(tt) -> tt 20.60/20.91 a__U62(X:S) -> U62(X:S) 20.60/20.91 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.60/20.91 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.60/20.91 a__U72(tt) -> tt 20.60/20.91 a__U72(X:S) -> U72(X:S) 20.60/20.91 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.60/20.91 a____(nil,X:S) -> mark(X:S) 20.60/20.91 a____(X:S,nil) -> mark(X:S) 20.60/20.91 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.60/20.91 a__and(tt,X:S) -> mark(X:S) 20.60/20.91 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.60/20.91 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.91 a__isList(nil) -> tt 20.60/20.91 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.60/20.91 a__isList(X:S) -> isList(X:S) 20.60/20.91 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.91 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.91 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.60/20.91 a__isNeList(X:S) -> isNeList(X:S) 20.60/20.91 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.91 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.60/20.91 a__isNePal(X:S) -> isNePal(X:S) 20.60/20.91 a__isPal(nil) -> tt 20.60/20.91 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.60/20.91 a__isPal(X:S) -> isPal(X:S) 20.60/20.91 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.91 a__isPalListKind(a) -> tt 20.60/20.91 a__isPalListKind(e) -> tt 20.60/20.91 a__isPalListKind(i) -> tt 20.60/20.91 a__isPalListKind(nil) -> tt 20.60/20.91 a__isPalListKind(o) -> tt 20.60/20.91 a__isPalListKind(u) -> tt 20.60/20.91 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.60/20.91 a__isQid(a) -> tt 20.60/20.91 a__isQid(e) -> tt 20.60/20.91 a__isQid(i) -> tt 20.60/20.91 a__isQid(o) -> tt 20.60/20.91 a__isQid(u) -> tt 20.60/20.91 a__isQid(X:S) -> isQid(X:S) 20.60/20.91 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.60/20.91 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.60/20.91 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.60/20.91 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.60/20.91 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.60/20.91 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.60/20.91 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.60/20.91 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.60/20.91 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.60/20.91 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.60/20.91 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.60/20.91 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.60/20.91 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.60/20.91 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.60/20.91 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.60/20.91 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.60/20.91 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.60/20.91 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.60/20.91 mark(a) -> a 20.60/20.91 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.60/20.91 mark(e) -> e 20.60/20.91 mark(i) -> i 20.60/20.91 mark(isList(X:S)) -> a__isList(X:S) 20.60/20.91 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.60/20.91 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.60/20.91 mark(isPal(X:S)) -> a__isPal(X:S) 20.60/20.91 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.60/20.91 mark(isQid(X:S)) -> a__isQid(X:S) 20.60/20.91 mark(nil) -> nil 20.60/20.91 mark(o) -> o 20.60/20.91 mark(tt) -> tt 20.60/20.91 mark(u) -> u 20.60/20.91 ->Interpretation type: 20.60/20.91 Linear 20.60/20.91 ->Coefficients: 20.60/20.91 Natural Numbers 20.60/20.91 ->Dimension: 20.60/20.91 1 20.60/20.91 ->Bound: 20.60/20.91 2 20.60/20.91 ->Interpretation: 20.60/20.91 20.60/20.91 [a__U11](X1,X2) = 2.X1 + 2.X2 20.60/20.91 [a__U12](X) = X 20.60/20.91 [a__U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.60/20.91 [a__U22](X1,X2) = X1 + 2.X2 + 2 20.60/20.91 [a__U23](X) = X + 2 20.60/20.91 [a__U31](X1,X2) = 2.X1 + 2.X2 20.60/20.91 [a__U32](X) = X 20.60/20.91 [a__U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.60/20.91 [a__U42](X1,X2) = X1 + 2.X2 + 2 20.60/20.91 [a__U43](X) = X + 2 20.60/20.91 [a__U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.60/20.91 [a__U52](X1,X2) = X1 + 2.X2 + 2 20.60/20.91 [a__U53](X) = X + 1 20.60/20.91 [a__U61](X1,X2) = X1 + 2.X2 + 2 20.60/20.91 [a__U62](X) = X + 2 20.60/20.91 [a__U71](X1,X2) = 2.X1 + 2.X2 + 2 20.60/20.91 [a__U72](X) = X 20.60/20.91 [a____](X1,X2) = 2.X1 + X2 + 2 20.60/20.91 [a__and](X1,X2) = X1 + 2.X2 20.60/20.91 [a__isList](X) = 2.X 20.60/20.91 [a__isNeList](X) = 2.X 20.60/20.91 [a__isNePal](X) = 2.X + 2 20.60/20.91 [a__isPal](X) = 2.X + 2 20.60/20.91 [a__isPalListKind](X) = 0 20.60/20.91 [a__isQid](X) = 2.X 20.60/20.91 [mark](X) = X 20.60/20.91 [U11](X1,X2) = 2.X1 + 2.X2 20.60/20.91 [U12](X) = X 20.60/20.91 [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.60/20.91 [U22](X1,X2) = X1 + 2.X2 + 2 20.60/20.91 [U23](X) = X + 2 20.60/20.91 [U31](X1,X2) = 2.X1 + 2.X2 20.60/20.91 [U32](X) = X 20.60/20.91 [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.60/20.91 [U42](X1,X2) = X1 + 2.X2 + 2 20.60/20.91 [U43](X) = X + 2 20.60/20.91 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.60/20.91 [U52](X1,X2) = X1 + 2.X2 + 2 20.60/20.91 [U53](X) = X + 1 20.60/20.91 [U61](X1,X2) = X1 + 2.X2 + 2 20.60/20.91 [U62](X) = X + 2 20.60/20.91 [U71](X1,X2) = 2.X1 + 2.X2 + 2 20.60/20.91 [U72](X) = X 20.60/20.91 [__](X1,X2) = 2.X1 + X2 + 2 20.60/20.91 [a] = 1 20.60/20.91 [and](X1,X2) = X1 + 2.X2 20.60/20.91 [e] = 1 20.60/20.91 [fSNonEmpty] = 0 20.60/20.91 [i] = 1 20.60/20.91 [isList](X) = 2.X 20.60/20.91 [isNeList](X) = 2.X 20.60/20.91 [isNePal](X) = 2.X + 2 20.60/20.91 [isPal](X) = 2.X + 2 20.60/20.91 [isPalListKind](X) = 0 20.60/20.91 [isQid](X) = 2.X 20.60/20.91 [nil] = 1 20.60/20.91 [o] = 2 20.60/20.91 [tt] = 0 20.60/20.91 [u] = 2 20.60/20.91 [A__U11](X1,X2) = 0 20.60/20.91 [A__U12](X) = 0 20.60/20.91 [A__U21](X1,X2,X3) = 0 20.60/20.91 [A__U22](X1,X2) = 0 20.60/20.91 [A__U23](X) = 0 20.60/20.91 [A__U31](X1,X2) = 0 20.60/20.91 [A__U32](X) = 0 20.60/20.91 [A__U41](X1,X2,X3) = 0 20.60/20.91 [A__U42](X1,X2) = 0 20.60/20.91 [A__U43](X) = 0 20.60/20.91 [A__U51](X1,X2,X3) = 0 20.60/20.91 [A__U52](X1,X2) = 0 20.60/20.91 [A__U53](X) = 0 20.60/20.91 [A__U61](X1,X2) = 0 20.60/20.91 [A__U62](X) = 0 20.60/20.91 [A__U71](X1,X2) = 0 20.60/20.91 [A__U72](X) = 0 20.60/20.91 [A____](X1,X2) = 0 20.60/20.91 [A__AND](X1,X2) = 2.X1 + 2.X2 + 2 20.60/20.91 [A__ISLIST](X) = 0 20.60/20.91 [A__ISNELIST](X) = X + 2 20.60/20.91 [A__ISNEPAL](X) = 2.X + 2 20.60/20.91 [A__ISPAL](X) = 2.X + 2 20.60/20.91 [A__ISPALLISTKIND](X) = 2 20.60/20.91 [A__ISQID](X) = 0 20.60/20.91 [MARK](X) = 2.X + 2 20.60/20.91 20.60/20.91 Problem 1: 20.60/20.91 20.60/20.91 SCC Processor: 20.60/20.91 -> Pairs: 20.60/20.91 A__AND(tt,X:S) -> MARK(X:S) 20.60/20.91 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.91 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.91 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.60/20.91 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.91 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.91 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.91 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.91 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U12(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.91 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U23(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U32(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.91 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U43(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.91 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U53(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U62(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U72(X:S)) -> MARK(X:S) 20.60/20.91 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.60/20.91 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.60/20.91 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.60/20.91 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.60/20.91 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.60/20.91 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.60/20.91 -> Rules: 20.60/20.91 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.60/20.91 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.60/20.91 a__U12(tt) -> tt 20.60/20.91 a__U12(X:S) -> U12(X:S) 20.60/20.91 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.60/20.91 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.60/20.91 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.60/20.91 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.60/20.91 a__U23(tt) -> tt 20.60/20.91 a__U23(X:S) -> U23(X:S) 20.60/20.91 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.60/20.91 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.60/20.91 a__U32(tt) -> tt 20.60/20.91 a__U32(X:S) -> U32(X:S) 20.60/20.91 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.60/20.91 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.60/20.91 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.60/20.91 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.60/20.91 a__U43(tt) -> tt 20.60/20.91 a__U43(X:S) -> U43(X:S) 20.60/20.91 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.60/20.91 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.60/20.91 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.60/20.91 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.60/20.91 a__U53(tt) -> tt 20.60/20.91 a__U53(X:S) -> U53(X:S) 20.60/20.91 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.60/20.91 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.60/20.91 a__U62(tt) -> tt 20.60/20.91 a__U62(X:S) -> U62(X:S) 20.60/20.91 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.60/20.91 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.60/20.91 a__U72(tt) -> tt 20.60/20.91 a__U72(X:S) -> U72(X:S) 20.60/20.91 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.60/20.91 a____(nil,X:S) -> mark(X:S) 20.60/20.91 a____(X:S,nil) -> mark(X:S) 20.60/20.91 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.60/20.91 a__and(tt,X:S) -> mark(X:S) 20.60/20.91 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.60/20.91 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.91 a__isList(nil) -> tt 20.60/20.91 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.60/20.91 a__isList(X:S) -> isList(X:S) 20.60/20.91 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.91 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.91 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.60/20.91 a__isNeList(X:S) -> isNeList(X:S) 20.60/20.91 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.91 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.60/20.91 a__isNePal(X:S) -> isNePal(X:S) 20.60/20.91 a__isPal(nil) -> tt 20.60/20.91 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.60/20.91 a__isPal(X:S) -> isPal(X:S) 20.60/20.91 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.91 a__isPalListKind(a) -> tt 20.60/20.91 a__isPalListKind(e) -> tt 20.60/20.91 a__isPalListKind(i) -> tt 20.60/20.91 a__isPalListKind(nil) -> tt 20.60/20.91 a__isPalListKind(o) -> tt 20.60/20.91 a__isPalListKind(u) -> tt 20.60/20.91 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.60/20.91 a__isQid(a) -> tt 20.60/20.91 a__isQid(e) -> tt 20.60/20.91 a__isQid(i) -> tt 20.60/20.91 a__isQid(o) -> tt 20.60/20.91 a__isQid(u) -> tt 20.60/20.91 a__isQid(X:S) -> isQid(X:S) 20.60/20.91 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.60/20.91 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.60/20.91 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.60/20.91 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.60/20.91 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.60/20.91 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.60/20.91 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.60/20.91 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.60/20.91 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.60/20.91 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.60/20.91 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.60/20.91 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.60/20.91 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.60/20.91 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.60/20.91 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.60/20.91 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.60/20.91 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.60/20.91 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.60/20.91 mark(a) -> a 20.60/20.91 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.60/20.91 mark(e) -> e 20.60/20.91 mark(i) -> i 20.60/20.91 mark(isList(X:S)) -> a__isList(X:S) 20.60/20.91 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.60/20.91 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.60/20.91 mark(isPal(X:S)) -> a__isPal(X:S) 20.60/20.91 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.60/20.91 mark(isQid(X:S)) -> a__isQid(X:S) 20.60/20.91 mark(nil) -> nil 20.60/20.91 mark(o) -> o 20.60/20.91 mark(tt) -> tt 20.60/20.91 mark(u) -> u 20.60/20.91 ->Strongly Connected Components: 20.60/20.91 ->->Cycle: 20.60/20.91 ->->-> Pairs: 20.60/20.91 A__AND(tt,X:S) -> MARK(X:S) 20.60/20.91 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.91 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.91 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.60/20.91 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.91 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.91 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.91 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.91 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U12(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.91 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U23(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U32(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.91 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U43(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.91 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U53(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U62(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U72(X:S)) -> MARK(X:S) 20.60/20.91 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.60/20.91 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.60/20.91 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.60/20.91 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.60/20.91 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.60/20.91 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.60/20.91 ->->-> Rules: 20.60/20.91 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.60/20.91 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.60/20.91 a__U12(tt) -> tt 20.60/20.91 a__U12(X:S) -> U12(X:S) 20.60/20.91 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.60/20.91 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.60/20.91 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.60/20.91 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.60/20.91 a__U23(tt) -> tt 20.60/20.91 a__U23(X:S) -> U23(X:S) 20.60/20.91 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.60/20.91 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.60/20.91 a__U32(tt) -> tt 20.60/20.91 a__U32(X:S) -> U32(X:S) 20.60/20.91 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.60/20.91 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.60/20.91 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.60/20.91 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.60/20.91 a__U43(tt) -> tt 20.60/20.91 a__U43(X:S) -> U43(X:S) 20.60/20.91 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.60/20.91 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.60/20.91 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.60/20.91 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.60/20.91 a__U53(tt) -> tt 20.60/20.91 a__U53(X:S) -> U53(X:S) 20.60/20.91 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.60/20.91 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.60/20.91 a__U62(tt) -> tt 20.60/20.91 a__U62(X:S) -> U62(X:S) 20.60/20.91 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.60/20.91 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.60/20.91 a__U72(tt) -> tt 20.60/20.91 a__U72(X:S) -> U72(X:S) 20.60/20.91 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.60/20.91 a____(nil,X:S) -> mark(X:S) 20.60/20.91 a____(X:S,nil) -> mark(X:S) 20.60/20.91 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.60/20.91 a__and(tt,X:S) -> mark(X:S) 20.60/20.91 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.60/20.91 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.91 a__isList(nil) -> tt 20.60/20.91 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.60/20.91 a__isList(X:S) -> isList(X:S) 20.60/20.91 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.91 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.91 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.60/20.91 a__isNeList(X:S) -> isNeList(X:S) 20.60/20.91 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.91 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.60/20.91 a__isNePal(X:S) -> isNePal(X:S) 20.60/20.91 a__isPal(nil) -> tt 20.60/20.91 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.60/20.91 a__isPal(X:S) -> isPal(X:S) 20.60/20.91 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.91 a__isPalListKind(a) -> tt 20.60/20.91 a__isPalListKind(e) -> tt 20.60/20.91 a__isPalListKind(i) -> tt 20.60/20.91 a__isPalListKind(nil) -> tt 20.60/20.91 a__isPalListKind(o) -> tt 20.60/20.91 a__isPalListKind(u) -> tt 20.60/20.91 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.60/20.91 a__isQid(a) -> tt 20.60/20.91 a__isQid(e) -> tt 20.60/20.91 a__isQid(i) -> tt 20.60/20.91 a__isQid(o) -> tt 20.60/20.91 a__isQid(u) -> tt 20.60/20.91 a__isQid(X:S) -> isQid(X:S) 20.60/20.91 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.60/20.91 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.60/20.91 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.60/20.91 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.60/20.91 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.60/20.91 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.60/20.91 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.60/20.91 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.60/20.91 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.60/20.91 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.60/20.91 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.60/20.91 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.60/20.91 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.60/20.91 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.60/20.91 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.60/20.91 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.60/20.91 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.60/20.91 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.60/20.91 mark(a) -> a 20.60/20.91 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.60/20.91 mark(e) -> e 20.60/20.91 mark(i) -> i 20.60/20.91 mark(isList(X:S)) -> a__isList(X:S) 20.60/20.91 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.60/20.91 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.60/20.91 mark(isPal(X:S)) -> a__isPal(X:S) 20.60/20.91 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.60/20.91 mark(isQid(X:S)) -> a__isQid(X:S) 20.60/20.91 mark(nil) -> nil 20.60/20.91 mark(o) -> o 20.60/20.91 mark(tt) -> tt 20.60/20.91 mark(u) -> u 20.60/20.91 20.60/20.91 Problem 1: 20.60/20.91 20.60/20.91 Reduction Pairs Processor: 20.60/20.91 -> Pairs: 20.60/20.91 A__AND(tt,X:S) -> MARK(X:S) 20.60/20.91 A__ISNELIST(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.91 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.91 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.60/20.91 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.91 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.91 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.91 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.91 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U12(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.91 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U23(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U32(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.91 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U43(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.91 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U53(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U62(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U72(X:S)) -> MARK(X:S) 20.60/20.91 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.60/20.91 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.60/20.91 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.60/20.91 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.60/20.91 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.60/20.91 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.60/20.91 -> Rules: 20.60/20.91 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.60/20.91 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.60/20.91 a__U12(tt) -> tt 20.60/20.91 a__U12(X:S) -> U12(X:S) 20.60/20.91 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.60/20.91 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.60/20.91 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.60/20.91 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.60/20.91 a__U23(tt) -> tt 20.60/20.91 a__U23(X:S) -> U23(X:S) 20.60/20.91 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.60/20.91 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.60/20.91 a__U32(tt) -> tt 20.60/20.91 a__U32(X:S) -> U32(X:S) 20.60/20.91 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.60/20.91 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.60/20.91 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.60/20.91 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.60/20.91 a__U43(tt) -> tt 20.60/20.91 a__U43(X:S) -> U43(X:S) 20.60/20.91 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.60/20.91 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.60/20.91 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.60/20.91 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.60/20.91 a__U53(tt) -> tt 20.60/20.91 a__U53(X:S) -> U53(X:S) 20.60/20.91 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.60/20.91 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.60/20.91 a__U62(tt) -> tt 20.60/20.91 a__U62(X:S) -> U62(X:S) 20.60/20.91 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.60/20.91 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.60/20.91 a__U72(tt) -> tt 20.60/20.91 a__U72(X:S) -> U72(X:S) 20.60/20.91 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.60/20.91 a____(nil,X:S) -> mark(X:S) 20.60/20.91 a____(X:S,nil) -> mark(X:S) 20.60/20.91 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.60/20.91 a__and(tt,X:S) -> mark(X:S) 20.60/20.91 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.60/20.91 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.91 a__isList(nil) -> tt 20.60/20.91 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.60/20.91 a__isList(X:S) -> isList(X:S) 20.60/20.91 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.91 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.91 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.60/20.91 a__isNeList(X:S) -> isNeList(X:S) 20.60/20.91 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.91 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.60/20.91 a__isNePal(X:S) -> isNePal(X:S) 20.60/20.91 a__isPal(nil) -> tt 20.60/20.91 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.60/20.91 a__isPal(X:S) -> isPal(X:S) 20.60/20.91 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.91 a__isPalListKind(a) -> tt 20.60/20.91 a__isPalListKind(e) -> tt 20.60/20.91 a__isPalListKind(i) -> tt 20.60/20.91 a__isPalListKind(nil) -> tt 20.60/20.91 a__isPalListKind(o) -> tt 20.60/20.91 a__isPalListKind(u) -> tt 20.60/20.91 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.60/20.91 a__isQid(a) -> tt 20.60/20.91 a__isQid(e) -> tt 20.60/20.91 a__isQid(i) -> tt 20.60/20.91 a__isQid(o) -> tt 20.60/20.91 a__isQid(u) -> tt 20.60/20.91 a__isQid(X:S) -> isQid(X:S) 20.60/20.91 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.60/20.91 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.60/20.91 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.60/20.91 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.60/20.91 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.60/20.91 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.60/20.91 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.60/20.91 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.60/20.91 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.60/20.91 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.60/20.91 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.60/20.91 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.60/20.91 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.60/20.91 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.60/20.91 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.60/20.91 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.60/20.91 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.60/20.91 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.60/20.91 mark(a) -> a 20.60/20.91 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.60/20.91 mark(e) -> e 20.60/20.91 mark(i) -> i 20.60/20.91 mark(isList(X:S)) -> a__isList(X:S) 20.60/20.91 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.60/20.91 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.60/20.91 mark(isPal(X:S)) -> a__isPal(X:S) 20.60/20.91 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.60/20.91 mark(isQid(X:S)) -> a__isQid(X:S) 20.60/20.91 mark(nil) -> nil 20.60/20.91 mark(o) -> o 20.60/20.91 mark(tt) -> tt 20.60/20.91 mark(u) -> u 20.60/20.91 -> Usable rules: 20.60/20.91 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.60/20.91 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.60/20.91 a__U12(tt) -> tt 20.60/20.91 a__U12(X:S) -> U12(X:S) 20.60/20.91 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.60/20.91 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.60/20.91 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.60/20.91 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.60/20.91 a__U23(tt) -> tt 20.60/20.91 a__U23(X:S) -> U23(X:S) 20.60/20.91 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.60/20.91 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.60/20.91 a__U32(tt) -> tt 20.60/20.91 a__U32(X:S) -> U32(X:S) 20.60/20.91 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.60/20.91 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.60/20.91 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.60/20.91 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.60/20.91 a__U43(tt) -> tt 20.60/20.91 a__U43(X:S) -> U43(X:S) 20.60/20.91 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.60/20.91 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.60/20.91 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.60/20.91 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.60/20.91 a__U53(tt) -> tt 20.60/20.91 a__U53(X:S) -> U53(X:S) 20.60/20.91 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.60/20.91 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.60/20.91 a__U62(tt) -> tt 20.60/20.91 a__U62(X:S) -> U62(X:S) 20.60/20.91 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.60/20.91 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.60/20.91 a__U72(tt) -> tt 20.60/20.91 a__U72(X:S) -> U72(X:S) 20.60/20.91 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.60/20.91 a____(nil,X:S) -> mark(X:S) 20.60/20.91 a____(X:S,nil) -> mark(X:S) 20.60/20.91 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.60/20.91 a__and(tt,X:S) -> mark(X:S) 20.60/20.91 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.60/20.91 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.91 a__isList(nil) -> tt 20.60/20.91 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.60/20.91 a__isList(X:S) -> isList(X:S) 20.60/20.91 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.91 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.91 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.60/20.91 a__isNeList(X:S) -> isNeList(X:S) 20.60/20.91 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.91 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.60/20.91 a__isNePal(X:S) -> isNePal(X:S) 20.60/20.91 a__isPal(nil) -> tt 20.60/20.91 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.60/20.91 a__isPal(X:S) -> isPal(X:S) 20.60/20.91 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.91 a__isPalListKind(a) -> tt 20.60/20.91 a__isPalListKind(e) -> tt 20.60/20.91 a__isPalListKind(i) -> tt 20.60/20.91 a__isPalListKind(nil) -> tt 20.60/20.91 a__isPalListKind(o) -> tt 20.60/20.91 a__isPalListKind(u) -> tt 20.60/20.91 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.60/20.91 a__isQid(a) -> tt 20.60/20.91 a__isQid(e) -> tt 20.60/20.91 a__isQid(i) -> tt 20.60/20.91 a__isQid(o) -> tt 20.60/20.91 a__isQid(u) -> tt 20.60/20.91 a__isQid(X:S) -> isQid(X:S) 20.60/20.91 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.60/20.91 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.60/20.91 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.60/20.91 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.60/20.91 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.60/20.91 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.60/20.91 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.60/20.91 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.60/20.91 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.60/20.91 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.60/20.91 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.60/20.91 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.60/20.91 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.60/20.91 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.60/20.91 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.60/20.91 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.60/20.91 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.60/20.91 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.60/20.91 mark(a) -> a 20.60/20.91 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.60/20.91 mark(e) -> e 20.60/20.91 mark(i) -> i 20.60/20.91 mark(isList(X:S)) -> a__isList(X:S) 20.60/20.91 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.60/20.91 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.60/20.91 mark(isPal(X:S)) -> a__isPal(X:S) 20.60/20.91 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.60/20.91 mark(isQid(X:S)) -> a__isQid(X:S) 20.60/20.91 mark(nil) -> nil 20.60/20.91 mark(o) -> o 20.60/20.91 mark(tt) -> tt 20.60/20.91 mark(u) -> u 20.60/20.91 ->Interpretation type: 20.60/20.91 Linear 20.60/20.91 ->Coefficients: 20.60/20.91 Natural Numbers 20.60/20.91 ->Dimension: 20.60/20.91 1 20.60/20.91 ->Bound: 20.60/20.91 2 20.60/20.91 ->Interpretation: 20.60/20.91 20.60/20.91 [a__U11](X1,X2) = 2.X1 + 2.X2 + 1 20.60/20.91 [a__U12](X) = X 20.60/20.91 [a__U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.60/20.91 [a__U22](X1,X2) = X1 + 2.X2 + 1 20.60/20.91 [a__U23](X) = X 20.60/20.91 [a__U31](X1,X2) = 2.X1 + X2 + 1 20.60/20.91 [a__U32](X) = 2.X + 1 20.60/20.91 [a__U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.60/20.91 [a__U42](X1,X2) = X1 + 2.X2 + 1 20.60/20.91 [a__U43](X) = X 20.60/20.91 [a__U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.60/20.91 [a__U52](X1,X2) = X1 + 2.X2 + 1 20.60/20.91 [a__U53](X) = X 20.60/20.91 [a__U61](X1,X2) = 2.X1 + X2 + 1 20.60/20.91 [a__U62](X) = 2.X 20.60/20.91 [a__U71](X1,X2) = X1 + X2 + 2 20.60/20.91 [a__U72](X) = X 20.60/20.91 [a____](X1,X2) = 2.X1 + X2 + 2 20.60/20.91 [a__and](X1,X2) = 2.X1 + X2 20.60/20.91 [a__isList](X) = 2.X + 1 20.60/20.91 [a__isNeList](X) = 2.X + 1 20.60/20.91 [a__isNePal](X) = X + 1 20.60/20.91 [a__isPal](X) = X + 2 20.60/20.91 [a__isPalListKind](X) = 0 20.60/20.91 [a__isQid](X) = 0 20.60/20.91 [mark](X) = X 20.60/20.91 [U11](X1,X2) = 2.X1 + 2.X2 + 1 20.60/20.91 [U12](X) = X 20.60/20.91 [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.60/20.91 [U22](X1,X2) = X1 + 2.X2 + 1 20.60/20.91 [U23](X) = X 20.60/20.91 [U31](X1,X2) = 2.X1 + X2 + 1 20.60/20.91 [U32](X) = 2.X + 1 20.60/20.91 [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.60/20.91 [U42](X1,X2) = X1 + 2.X2 + 1 20.60/20.91 [U43](X) = X 20.60/20.91 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.60/20.91 [U52](X1,X2) = X1 + 2.X2 + 1 20.60/20.91 [U53](X) = X 20.60/20.91 [U61](X1,X2) = 2.X1 + X2 + 1 20.60/20.91 [U62](X) = 2.X 20.60/20.91 [U71](X1,X2) = X1 + X2 + 2 20.60/20.91 [U72](X) = X 20.60/20.91 [__](X1,X2) = 2.X1 + X2 + 2 20.60/20.91 [a] = 1 20.60/20.91 [and](X1,X2) = 2.X1 + X2 20.60/20.91 [e] = 0 20.60/20.91 [fSNonEmpty] = 0 20.60/20.91 [i] = 1 20.60/20.91 [isList](X) = 2.X + 1 20.60/20.91 [isNeList](X) = 2.X + 1 20.60/20.91 [isNePal](X) = X + 1 20.60/20.91 [isPal](X) = X + 2 20.60/20.91 [isPalListKind](X) = 0 20.60/20.91 [isQid](X) = 0 20.60/20.91 [nil] = 0 20.60/20.91 [o] = 1 20.60/20.91 [tt] = 0 20.60/20.91 [u] = 1 20.60/20.91 [A__U11](X1,X2) = 0 20.60/20.91 [A__U12](X) = 0 20.60/20.91 [A__U21](X1,X2,X3) = 0 20.60/20.91 [A__U22](X1,X2) = 0 20.60/20.91 [A__U23](X) = 0 20.60/20.91 [A__U31](X1,X2) = 0 20.60/20.91 [A__U32](X) = 0 20.60/20.91 [A__U41](X1,X2,X3) = 0 20.60/20.91 [A__U42](X1,X2) = 0 20.60/20.91 [A__U43](X) = 0 20.60/20.91 [A__U51](X1,X2,X3) = 0 20.60/20.91 [A__U52](X1,X2) = 0 20.60/20.91 [A__U53](X) = 0 20.60/20.91 [A__U61](X1,X2) = 0 20.60/20.91 [A__U62](X) = 0 20.60/20.91 [A__U71](X1,X2) = 0 20.60/20.91 [A__U72](X) = 0 20.60/20.91 [A____](X1,X2) = 0 20.60/20.91 [A__AND](X1,X2) = 2.X2 + 1 20.60/20.91 [A__ISLIST](X) = 0 20.60/20.91 [A__ISNELIST](X) = 2 20.60/20.91 [A__ISNEPAL](X) = 2.X + 2 20.60/20.91 [A__ISPAL](X) = X + 2 20.60/20.91 [A__ISPALLISTKIND](X) = 1 20.60/20.91 [A__ISQID](X) = 0 20.60/20.91 [MARK](X) = 2.X + 1 20.60/20.91 20.60/20.91 Problem 1: 20.60/20.91 20.60/20.91 SCC Processor: 20.60/20.91 -> Pairs: 20.60/20.91 A__AND(tt,X:S) -> MARK(X:S) 20.60/20.91 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.91 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.60/20.91 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.91 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.91 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.91 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.91 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U12(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.91 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U23(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U32(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.91 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U43(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.91 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U53(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U62(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U72(X:S)) -> MARK(X:S) 20.60/20.91 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.60/20.91 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.60/20.91 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(isNeList(X:S)) -> A__ISNELIST(X:S) 20.60/20.91 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.60/20.91 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.60/20.91 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.60/20.91 -> Rules: 20.60/20.91 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.60/20.91 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.60/20.91 a__U12(tt) -> tt 20.60/20.91 a__U12(X:S) -> U12(X:S) 20.60/20.91 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.60/20.91 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.60/20.91 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.60/20.91 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.60/20.91 a__U23(tt) -> tt 20.60/20.91 a__U23(X:S) -> U23(X:S) 20.60/20.91 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.60/20.91 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.60/20.91 a__U32(tt) -> tt 20.60/20.91 a__U32(X:S) -> U32(X:S) 20.60/20.91 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.60/20.91 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.60/20.91 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.60/20.91 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.60/20.91 a__U43(tt) -> tt 20.60/20.91 a__U43(X:S) -> U43(X:S) 20.60/20.91 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.60/20.91 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.60/20.91 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.60/20.91 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.60/20.91 a__U53(tt) -> tt 20.60/20.91 a__U53(X:S) -> U53(X:S) 20.60/20.91 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.60/20.91 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.60/20.91 a__U62(tt) -> tt 20.60/20.91 a__U62(X:S) -> U62(X:S) 20.60/20.91 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.60/20.91 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.60/20.91 a__U72(tt) -> tt 20.60/20.91 a__U72(X:S) -> U72(X:S) 20.60/20.91 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.60/20.91 a____(nil,X:S) -> mark(X:S) 20.60/20.91 a____(X:S,nil) -> mark(X:S) 20.60/20.91 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.60/20.91 a__and(tt,X:S) -> mark(X:S) 20.60/20.91 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.60/20.91 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.91 a__isList(nil) -> tt 20.60/20.91 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.60/20.91 a__isList(X:S) -> isList(X:S) 20.60/20.91 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.91 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.91 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.60/20.91 a__isNeList(X:S) -> isNeList(X:S) 20.60/20.91 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.91 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.60/20.91 a__isNePal(X:S) -> isNePal(X:S) 20.60/20.91 a__isPal(nil) -> tt 20.60/20.91 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.60/20.91 a__isPal(X:S) -> isPal(X:S) 20.60/20.91 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.91 a__isPalListKind(a) -> tt 20.60/20.91 a__isPalListKind(e) -> tt 20.60/20.91 a__isPalListKind(i) -> tt 20.60/20.91 a__isPalListKind(nil) -> tt 20.60/20.91 a__isPalListKind(o) -> tt 20.60/20.91 a__isPalListKind(u) -> tt 20.60/20.91 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.60/20.91 a__isQid(a) -> tt 20.60/20.91 a__isQid(e) -> tt 20.60/20.91 a__isQid(i) -> tt 20.60/20.91 a__isQid(o) -> tt 20.60/20.91 a__isQid(u) -> tt 20.60/20.91 a__isQid(X:S) -> isQid(X:S) 20.60/20.91 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.60/20.91 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.60/20.91 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.60/20.91 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.60/20.91 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.60/20.91 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.60/20.91 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.60/20.91 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.60/20.91 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.60/20.91 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.60/20.91 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.60/20.91 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.60/20.91 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.60/20.91 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.60/20.91 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.60/20.91 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.60/20.91 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.60/20.91 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.60/20.91 mark(a) -> a 20.60/20.91 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.60/20.91 mark(e) -> e 20.60/20.91 mark(i) -> i 20.60/20.91 mark(isList(X:S)) -> a__isList(X:S) 20.60/20.91 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.60/20.91 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.60/20.91 mark(isPal(X:S)) -> a__isPal(X:S) 20.60/20.91 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.60/20.91 mark(isQid(X:S)) -> a__isQid(X:S) 20.60/20.91 mark(nil) -> nil 20.60/20.91 mark(o) -> o 20.60/20.91 mark(tt) -> tt 20.60/20.91 mark(u) -> u 20.60/20.91 ->Strongly Connected Components: 20.60/20.91 ->->Cycle: 20.60/20.91 ->->-> Pairs: 20.60/20.91 A__AND(tt,X:S) -> MARK(X:S) 20.60/20.91 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.91 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.60/20.91 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.91 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.91 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.91 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.91 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U12(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.91 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U23(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U32(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.91 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U43(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.91 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U53(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U62(X:S)) -> MARK(X:S) 20.60/20.91 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.91 MARK(U72(X:S)) -> MARK(X:S) 20.60/20.91 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.60/20.92 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.60/20.92 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.60/20.92 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.60/20.92 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.60/20.92 ->->-> Rules: 20.60/20.92 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.60/20.92 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.60/20.92 a__U12(tt) -> tt 20.60/20.92 a__U12(X:S) -> U12(X:S) 20.60/20.92 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.60/20.92 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.60/20.92 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.60/20.92 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.60/20.92 a__U23(tt) -> tt 20.60/20.92 a__U23(X:S) -> U23(X:S) 20.60/20.92 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.60/20.92 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.60/20.92 a__U32(tt) -> tt 20.60/20.92 a__U32(X:S) -> U32(X:S) 20.60/20.92 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.60/20.92 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.60/20.92 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.60/20.92 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.60/20.92 a__U43(tt) -> tt 20.60/20.92 a__U43(X:S) -> U43(X:S) 20.60/20.92 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.60/20.92 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.60/20.92 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.60/20.92 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.60/20.92 a__U53(tt) -> tt 20.60/20.92 a__U53(X:S) -> U53(X:S) 20.60/20.92 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.60/20.92 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.60/20.92 a__U62(tt) -> tt 20.60/20.92 a__U62(X:S) -> U62(X:S) 20.60/20.92 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.60/20.92 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.60/20.92 a__U72(tt) -> tt 20.60/20.92 a__U72(X:S) -> U72(X:S) 20.60/20.92 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.60/20.92 a____(nil,X:S) -> mark(X:S) 20.60/20.92 a____(X:S,nil) -> mark(X:S) 20.60/20.92 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.60/20.92 a__and(tt,X:S) -> mark(X:S) 20.60/20.92 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.60/20.92 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.92 a__isList(nil) -> tt 20.60/20.92 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.60/20.92 a__isList(X:S) -> isList(X:S) 20.60/20.92 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.92 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.92 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.60/20.92 a__isNeList(X:S) -> isNeList(X:S) 20.60/20.92 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.92 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.60/20.92 a__isNePal(X:S) -> isNePal(X:S) 20.60/20.92 a__isPal(nil) -> tt 20.60/20.92 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.60/20.92 a__isPal(X:S) -> isPal(X:S) 20.60/20.92 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.92 a__isPalListKind(a) -> tt 20.60/20.92 a__isPalListKind(e) -> tt 20.60/20.92 a__isPalListKind(i) -> tt 20.60/20.92 a__isPalListKind(nil) -> tt 20.60/20.92 a__isPalListKind(o) -> tt 20.60/20.92 a__isPalListKind(u) -> tt 20.60/20.92 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.60/20.92 a__isQid(a) -> tt 20.60/20.92 a__isQid(e) -> tt 20.60/20.92 a__isQid(i) -> tt 20.60/20.92 a__isQid(o) -> tt 20.60/20.92 a__isQid(u) -> tt 20.60/20.92 a__isQid(X:S) -> isQid(X:S) 20.60/20.92 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.60/20.92 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.60/20.92 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.60/20.92 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.60/20.92 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.60/20.92 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.60/20.92 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.60/20.92 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.60/20.92 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.60/20.92 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.60/20.92 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.60/20.92 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.60/20.92 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.60/20.92 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.60/20.92 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.60/20.92 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.60/20.92 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.60/20.92 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.60/20.92 mark(a) -> a 20.60/20.92 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.60/20.92 mark(e) -> e 20.60/20.92 mark(i) -> i 20.60/20.92 mark(isList(X:S)) -> a__isList(X:S) 20.60/20.92 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.60/20.92 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.60/20.92 mark(isPal(X:S)) -> a__isPal(X:S) 20.60/20.92 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.60/20.92 mark(isQid(X:S)) -> a__isQid(X:S) 20.60/20.92 mark(nil) -> nil 20.60/20.92 mark(o) -> o 20.60/20.92 mark(tt) -> tt 20.60/20.92 mark(u) -> u 20.60/20.92 20.60/20.92 Problem 1: 20.60/20.92 20.60/20.92 Reduction Pairs Processor: 20.60/20.92 -> Pairs: 20.60/20.92 A__AND(tt,X:S) -> MARK(X:S) 20.60/20.92 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.92 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.60/20.92 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.92 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.92 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.92 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.92 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U12(X:S)) -> MARK(X:S) 20.60/20.92 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.92 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U23(X:S)) -> MARK(X:S) 20.60/20.92 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U32(X:S)) -> MARK(X:S) 20.60/20.92 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.92 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U43(X:S)) -> MARK(X:S) 20.60/20.92 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.92 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U53(X:S)) -> MARK(X:S) 20.60/20.92 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U62(X:S)) -> MARK(X:S) 20.60/20.92 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U72(X:S)) -> MARK(X:S) 20.60/20.92 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.60/20.92 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.60/20.92 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.60/20.92 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.60/20.92 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.60/20.92 -> Rules: 20.60/20.92 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.60/20.92 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.60/20.92 a__U12(tt) -> tt 20.60/20.92 a__U12(X:S) -> U12(X:S) 20.60/20.92 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.60/20.92 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.60/20.92 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.60/20.92 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.60/20.92 a__U23(tt) -> tt 20.60/20.92 a__U23(X:S) -> U23(X:S) 20.60/20.92 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.60/20.92 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.60/20.92 a__U32(tt) -> tt 20.60/20.92 a__U32(X:S) -> U32(X:S) 20.60/20.92 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.60/20.92 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.60/20.92 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.60/20.92 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.60/20.92 a__U43(tt) -> tt 20.60/20.92 a__U43(X:S) -> U43(X:S) 20.60/20.92 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.60/20.92 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.60/20.92 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.60/20.92 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.60/20.92 a__U53(tt) -> tt 20.60/20.92 a__U53(X:S) -> U53(X:S) 20.60/20.92 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.60/20.92 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.60/20.92 a__U62(tt) -> tt 20.60/20.92 a__U62(X:S) -> U62(X:S) 20.60/20.92 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.60/20.92 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.60/20.92 a__U72(tt) -> tt 20.60/20.92 a__U72(X:S) -> U72(X:S) 20.60/20.92 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.60/20.92 a____(nil,X:S) -> mark(X:S) 20.60/20.92 a____(X:S,nil) -> mark(X:S) 20.60/20.92 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.60/20.92 a__and(tt,X:S) -> mark(X:S) 20.60/20.92 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.60/20.92 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.92 a__isList(nil) -> tt 20.60/20.92 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.60/20.92 a__isList(X:S) -> isList(X:S) 20.60/20.92 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.92 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.92 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.60/20.92 a__isNeList(X:S) -> isNeList(X:S) 20.60/20.92 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.92 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.60/20.92 a__isNePal(X:S) -> isNePal(X:S) 20.60/20.92 a__isPal(nil) -> tt 20.60/20.92 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.60/20.92 a__isPal(X:S) -> isPal(X:S) 20.60/20.92 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.92 a__isPalListKind(a) -> tt 20.60/20.92 a__isPalListKind(e) -> tt 20.60/20.92 a__isPalListKind(i) -> tt 20.60/20.92 a__isPalListKind(nil) -> tt 20.60/20.92 a__isPalListKind(o) -> tt 20.60/20.92 a__isPalListKind(u) -> tt 20.60/20.92 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.60/20.92 a__isQid(a) -> tt 20.60/20.92 a__isQid(e) -> tt 20.60/20.92 a__isQid(i) -> tt 20.60/20.92 a__isQid(o) -> tt 20.60/20.92 a__isQid(u) -> tt 20.60/20.92 a__isQid(X:S) -> isQid(X:S) 20.60/20.92 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.60/20.92 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.60/20.92 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.60/20.92 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.60/20.92 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.60/20.92 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.60/20.92 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.60/20.92 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.60/20.92 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.60/20.92 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.60/20.92 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.60/20.92 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.60/20.92 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.60/20.92 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.60/20.92 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.60/20.92 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.60/20.92 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.60/20.92 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.60/20.92 mark(a) -> a 20.60/20.92 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.60/20.92 mark(e) -> e 20.60/20.92 mark(i) -> i 20.60/20.92 mark(isList(X:S)) -> a__isList(X:S) 20.60/20.92 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.60/20.92 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.60/20.92 mark(isPal(X:S)) -> a__isPal(X:S) 20.60/20.92 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.60/20.92 mark(isQid(X:S)) -> a__isQid(X:S) 20.60/20.92 mark(nil) -> nil 20.60/20.92 mark(o) -> o 20.60/20.92 mark(tt) -> tt 20.60/20.92 mark(u) -> u 20.60/20.92 -> Usable rules: 20.60/20.92 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.60/20.92 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.60/20.92 a__U12(tt) -> tt 20.60/20.92 a__U12(X:S) -> U12(X:S) 20.60/20.92 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.60/20.92 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.60/20.92 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.60/20.92 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.60/20.92 a__U23(tt) -> tt 20.60/20.92 a__U23(X:S) -> U23(X:S) 20.60/20.92 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.60/20.92 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.60/20.92 a__U32(tt) -> tt 20.60/20.92 a__U32(X:S) -> U32(X:S) 20.60/20.92 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.60/20.92 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.60/20.92 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.60/20.92 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.60/20.92 a__U43(tt) -> tt 20.60/20.92 a__U43(X:S) -> U43(X:S) 20.60/20.92 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.60/20.92 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.60/20.92 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.60/20.92 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.60/20.92 a__U53(tt) -> tt 20.60/20.92 a__U53(X:S) -> U53(X:S) 20.60/20.92 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.60/20.92 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.60/20.92 a__U62(tt) -> tt 20.60/20.92 a__U62(X:S) -> U62(X:S) 20.60/20.92 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.60/20.92 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.60/20.92 a__U72(tt) -> tt 20.60/20.92 a__U72(X:S) -> U72(X:S) 20.60/20.92 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.60/20.92 a____(nil,X:S) -> mark(X:S) 20.60/20.92 a____(X:S,nil) -> mark(X:S) 20.60/20.92 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.60/20.92 a__and(tt,X:S) -> mark(X:S) 20.60/20.92 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.60/20.92 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.92 a__isList(nil) -> tt 20.60/20.92 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.60/20.92 a__isList(X:S) -> isList(X:S) 20.60/20.92 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.92 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.92 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.60/20.92 a__isNeList(X:S) -> isNeList(X:S) 20.60/20.92 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.92 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.60/20.92 a__isNePal(X:S) -> isNePal(X:S) 20.60/20.92 a__isPal(nil) -> tt 20.60/20.92 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.60/20.92 a__isPal(X:S) -> isPal(X:S) 20.60/20.92 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.92 a__isPalListKind(a) -> tt 20.60/20.92 a__isPalListKind(e) -> tt 20.60/20.92 a__isPalListKind(i) -> tt 20.60/20.92 a__isPalListKind(nil) -> tt 20.60/20.92 a__isPalListKind(o) -> tt 20.60/20.92 a__isPalListKind(u) -> tt 20.60/20.92 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.60/20.92 a__isQid(a) -> tt 20.60/20.92 a__isQid(e) -> tt 20.60/20.92 a__isQid(i) -> tt 20.60/20.92 a__isQid(o) -> tt 20.60/20.92 a__isQid(u) -> tt 20.60/20.92 a__isQid(X:S) -> isQid(X:S) 20.60/20.92 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.60/20.92 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.60/20.92 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.60/20.92 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.60/20.92 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.60/20.92 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.60/20.92 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.60/20.92 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.60/20.92 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.60/20.92 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.60/20.92 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.60/20.92 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.60/20.92 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.60/20.92 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.60/20.92 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.60/20.92 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.60/20.92 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.60/20.92 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.60/20.92 mark(a) -> a 20.60/20.92 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.60/20.92 mark(e) -> e 20.60/20.92 mark(i) -> i 20.60/20.92 mark(isList(X:S)) -> a__isList(X:S) 20.60/20.92 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.60/20.92 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.60/20.92 mark(isPal(X:S)) -> a__isPal(X:S) 20.60/20.92 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.60/20.92 mark(isQid(X:S)) -> a__isQid(X:S) 20.60/20.92 mark(nil) -> nil 20.60/20.92 mark(o) -> o 20.60/20.92 mark(tt) -> tt 20.60/20.92 mark(u) -> u 20.60/20.92 ->Interpretation type: 20.60/20.92 Linear 20.60/20.92 ->Coefficients: 20.60/20.92 Natural Numbers 20.60/20.92 ->Dimension: 20.60/20.92 1 20.60/20.92 ->Bound: 20.60/20.92 2 20.60/20.92 ->Interpretation: 20.60/20.92 20.60/20.92 [a__U11](X1,X2) = 2.X1 + 2.X2 20.60/20.92 [a__U12](X) = X 20.60/20.92 [a__U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.60/20.92 [a__U22](X1,X2) = X1 + 2.X2 + 1 20.60/20.92 [a__U23](X) = X + 1 20.60/20.92 [a__U31](X1,X2) = 2.X1 + 2.X2 20.60/20.92 [a__U32](X) = X 20.60/20.92 [a__U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.60/20.92 [a__U42](X1,X2) = X1 + 2.X2 + 2 20.60/20.92 [a__U43](X) = X + 2 20.60/20.92 [a__U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 20.60/20.92 [a__U52](X1,X2) = X1 + 2.X2 20.60/20.92 [a__U53](X) = X 20.60/20.92 [a__U61](X1,X2) = 2.X1 + 2.X2 + 2 20.60/20.92 [a__U62](X) = X + 2 20.60/20.92 [a__U71](X1,X2) = 2.X1 + 2.X2 + 2 20.60/20.92 [a__U72](X) = X 20.60/20.92 [a____](X1,X2) = 2.X1 + X2 + 2 20.60/20.92 [a__and](X1,X2) = X1 + 2.X2 20.60/20.92 [a__isList](X) = 2.X 20.60/20.92 [a__isNeList](X) = 2.X 20.60/20.92 [a__isNePal](X) = 2.X + 2 20.60/20.92 [a__isPal](X) = 2.X + 2 20.60/20.92 [a__isPalListKind](X) = 0 20.60/20.92 [a__isQid](X) = 2.X 20.60/20.92 [mark](X) = X 20.60/20.92 [U11](X1,X2) = 2.X1 + 2.X2 20.60/20.92 [U12](X) = X 20.60/20.92 [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.60/20.92 [U22](X1,X2) = X1 + 2.X2 + 1 20.60/20.92 [U23](X) = X + 1 20.60/20.92 [U31](X1,X2) = 2.X1 + 2.X2 20.60/20.92 [U32](X) = X 20.60/20.92 [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.60/20.92 [U42](X1,X2) = X1 + 2.X2 + 2 20.60/20.92 [U43](X) = X + 2 20.60/20.92 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 20.60/20.92 [U52](X1,X2) = X1 + 2.X2 20.60/20.92 [U53](X) = X 20.60/20.92 [U61](X1,X2) = 2.X1 + 2.X2 + 2 20.60/20.92 [U62](X) = X + 2 20.60/20.92 [U71](X1,X2) = 2.X1 + 2.X2 + 2 20.60/20.92 [U72](X) = X 20.60/20.92 [__](X1,X2) = 2.X1 + X2 + 2 20.60/20.92 [a] = 2 20.60/20.92 [and](X1,X2) = X1 + 2.X2 20.60/20.92 [e] = 1 20.60/20.92 [fSNonEmpty] = 0 20.60/20.92 [i] = 1 20.60/20.92 [isList](X) = 2.X 20.60/20.92 [isNeList](X) = 2.X 20.60/20.92 [isNePal](X) = 2.X + 2 20.60/20.92 [isPal](X) = 2.X + 2 20.60/20.92 [isPalListKind](X) = 0 20.60/20.92 [isQid](X) = 2.X 20.60/20.92 [nil] = 1 20.60/20.92 [o] = 1 20.60/20.92 [tt] = 0 20.60/20.92 [u] = 2 20.60/20.92 [A__U11](X1,X2) = 0 20.60/20.92 [A__U12](X) = 0 20.60/20.92 [A__U21](X1,X2,X3) = 0 20.60/20.92 [A__U22](X1,X2) = 0 20.60/20.92 [A__U23](X) = 0 20.60/20.92 [A__U31](X1,X2) = 0 20.60/20.92 [A__U32](X) = 0 20.60/20.92 [A__U41](X1,X2,X3) = 0 20.60/20.92 [A__U42](X1,X2) = 0 20.60/20.92 [A__U43](X) = 0 20.60/20.92 [A__U51](X1,X2,X3) = 0 20.60/20.92 [A__U52](X1,X2) = 0 20.60/20.92 [A__U53](X) = 0 20.60/20.92 [A__U61](X1,X2) = 0 20.60/20.92 [A__U62](X) = 0 20.60/20.92 [A__U71](X1,X2) = 0 20.60/20.92 [A__U72](X) = 0 20.60/20.92 [A____](X1,X2) = 0 20.60/20.92 [A__AND](X1,X2) = X1 + 2.X2 + 2 20.60/20.92 [A__ISLIST](X) = 0 20.60/20.92 [A__ISNELIST](X) = 0 20.60/20.92 [A__ISNEPAL](X) = 2.X + 2 20.60/20.92 [A__ISPAL](X) = 2.X + 2 20.60/20.92 [A__ISPALLISTKIND](X) = 2 20.60/20.92 [A__ISQID](X) = 0 20.60/20.92 [MARK](X) = 2.X + 2 20.60/20.92 20.60/20.92 Problem 1: 20.60/20.92 20.60/20.92 SCC Processor: 20.60/20.92 -> Pairs: 20.60/20.92 A__AND(tt,X:S) -> MARK(X:S) 20.60/20.92 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.60/20.92 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.92 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.92 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.92 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.92 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U12(X:S)) -> MARK(X:S) 20.60/20.92 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.92 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U23(X:S)) -> MARK(X:S) 20.60/20.92 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U32(X:S)) -> MARK(X:S) 20.60/20.92 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.92 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U43(X:S)) -> MARK(X:S) 20.60/20.92 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.92 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U53(X:S)) -> MARK(X:S) 20.60/20.92 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U62(X:S)) -> MARK(X:S) 20.60/20.92 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U72(X:S)) -> MARK(X:S) 20.60/20.92 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.60/20.92 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.60/20.92 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.60/20.92 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.60/20.92 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.60/20.92 -> Rules: 20.60/20.92 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.60/20.92 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.60/20.92 a__U12(tt) -> tt 20.60/20.92 a__U12(X:S) -> U12(X:S) 20.60/20.92 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.60/20.92 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.60/20.92 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.60/20.92 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.60/20.92 a__U23(tt) -> tt 20.60/20.92 a__U23(X:S) -> U23(X:S) 20.60/20.92 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.60/20.92 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.60/20.92 a__U32(tt) -> tt 20.60/20.92 a__U32(X:S) -> U32(X:S) 20.60/20.92 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.60/20.92 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.60/20.92 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.60/20.92 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.60/20.92 a__U43(tt) -> tt 20.60/20.92 a__U43(X:S) -> U43(X:S) 20.60/20.92 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.60/20.92 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.60/20.92 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.60/20.92 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.60/20.92 a__U53(tt) -> tt 20.60/20.92 a__U53(X:S) -> U53(X:S) 20.60/20.92 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.60/20.92 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.60/20.92 a__U62(tt) -> tt 20.60/20.92 a__U62(X:S) -> U62(X:S) 20.60/20.92 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.60/20.92 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.60/20.92 a__U72(tt) -> tt 20.60/20.92 a__U72(X:S) -> U72(X:S) 20.60/20.92 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.60/20.92 a____(nil,X:S) -> mark(X:S) 20.60/20.92 a____(X:S,nil) -> mark(X:S) 20.60/20.92 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.60/20.92 a__and(tt,X:S) -> mark(X:S) 20.60/20.92 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.60/20.92 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.92 a__isList(nil) -> tt 20.60/20.92 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.60/20.92 a__isList(X:S) -> isList(X:S) 20.60/20.92 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.92 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.92 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.60/20.92 a__isNeList(X:S) -> isNeList(X:S) 20.60/20.92 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.92 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.60/20.92 a__isNePal(X:S) -> isNePal(X:S) 20.60/20.92 a__isPal(nil) -> tt 20.60/20.92 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.60/20.92 a__isPal(X:S) -> isPal(X:S) 20.60/20.92 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.92 a__isPalListKind(a) -> tt 20.60/20.92 a__isPalListKind(e) -> tt 20.60/20.92 a__isPalListKind(i) -> tt 20.60/20.92 a__isPalListKind(nil) -> tt 20.60/20.92 a__isPalListKind(o) -> tt 20.60/20.92 a__isPalListKind(u) -> tt 20.60/20.92 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.60/20.92 a__isQid(a) -> tt 20.60/20.92 a__isQid(e) -> tt 20.60/20.92 a__isQid(i) -> tt 20.60/20.92 a__isQid(o) -> tt 20.60/20.92 a__isQid(u) -> tt 20.60/20.92 a__isQid(X:S) -> isQid(X:S) 20.60/20.92 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.60/20.92 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.60/20.92 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.60/20.92 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.60/20.92 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.60/20.92 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.60/20.92 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.60/20.92 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.60/20.92 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.60/20.92 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.60/20.92 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.60/20.92 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.60/20.92 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.60/20.92 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.60/20.92 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.60/20.92 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.60/20.92 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.60/20.92 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.60/20.92 mark(a) -> a 20.60/20.92 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.60/20.92 mark(e) -> e 20.60/20.92 mark(i) -> i 20.60/20.92 mark(isList(X:S)) -> a__isList(X:S) 20.60/20.92 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.60/20.92 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.60/20.92 mark(isPal(X:S)) -> a__isPal(X:S) 20.60/20.92 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.60/20.92 mark(isQid(X:S)) -> a__isQid(X:S) 20.60/20.92 mark(nil) -> nil 20.60/20.92 mark(o) -> o 20.60/20.92 mark(tt) -> tt 20.60/20.92 mark(u) -> u 20.60/20.92 ->Strongly Connected Components: 20.60/20.92 ->->Cycle: 20.60/20.92 ->->-> Pairs: 20.60/20.92 A__AND(tt,X:S) -> MARK(X:S) 20.60/20.92 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.60/20.92 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.92 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.92 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.92 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.92 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U12(X:S)) -> MARK(X:S) 20.60/20.92 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.92 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U23(X:S)) -> MARK(X:S) 20.60/20.92 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U32(X:S)) -> MARK(X:S) 20.60/20.92 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.92 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U43(X:S)) -> MARK(X:S) 20.60/20.92 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.92 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U53(X:S)) -> MARK(X:S) 20.60/20.92 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U62(X:S)) -> MARK(X:S) 20.60/20.92 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U72(X:S)) -> MARK(X:S) 20.60/20.92 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.60/20.92 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.60/20.92 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.60/20.92 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.60/20.92 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.60/20.92 ->->-> Rules: 20.60/20.92 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.60/20.92 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.60/20.92 a__U12(tt) -> tt 20.60/20.92 a__U12(X:S) -> U12(X:S) 20.60/20.92 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.60/20.92 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.60/20.92 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.60/20.92 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.60/20.92 a__U23(tt) -> tt 20.60/20.92 a__U23(X:S) -> U23(X:S) 20.60/20.92 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.60/20.92 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.60/20.92 a__U32(tt) -> tt 20.60/20.92 a__U32(X:S) -> U32(X:S) 20.60/20.92 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.60/20.92 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.60/20.92 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.60/20.92 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.60/20.92 a__U43(tt) -> tt 20.60/20.92 a__U43(X:S) -> U43(X:S) 20.60/20.92 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.60/20.92 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.60/20.92 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.60/20.92 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.60/20.92 a__U53(tt) -> tt 20.60/20.92 a__U53(X:S) -> U53(X:S) 20.60/20.92 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.60/20.92 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.60/20.92 a__U62(tt) -> tt 20.60/20.92 a__U62(X:S) -> U62(X:S) 20.60/20.92 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.60/20.92 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.60/20.92 a__U72(tt) -> tt 20.60/20.92 a__U72(X:S) -> U72(X:S) 20.60/20.92 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.60/20.92 a____(nil,X:S) -> mark(X:S) 20.60/20.92 a____(X:S,nil) -> mark(X:S) 20.60/20.92 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.60/20.92 a__and(tt,X:S) -> mark(X:S) 20.60/20.92 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.60/20.92 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.92 a__isList(nil) -> tt 20.60/20.92 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.60/20.92 a__isList(X:S) -> isList(X:S) 20.60/20.92 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.92 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.92 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.60/20.92 a__isNeList(X:S) -> isNeList(X:S) 20.60/20.92 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.92 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.60/20.92 a__isNePal(X:S) -> isNePal(X:S) 20.60/20.92 a__isPal(nil) -> tt 20.60/20.92 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.60/20.92 a__isPal(X:S) -> isPal(X:S) 20.60/20.92 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.92 a__isPalListKind(a) -> tt 20.60/20.92 a__isPalListKind(e) -> tt 20.60/20.92 a__isPalListKind(i) -> tt 20.60/20.92 a__isPalListKind(nil) -> tt 20.60/20.92 a__isPalListKind(o) -> tt 20.60/20.92 a__isPalListKind(u) -> tt 20.60/20.92 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.60/20.92 a__isQid(a) -> tt 20.60/20.92 a__isQid(e) -> tt 20.60/20.92 a__isQid(i) -> tt 20.60/20.92 a__isQid(o) -> tt 20.60/20.92 a__isQid(u) -> tt 20.60/20.92 a__isQid(X:S) -> isQid(X:S) 20.60/20.92 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.60/20.92 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.60/20.92 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.60/20.92 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.60/20.92 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.60/20.92 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.60/20.92 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.60/20.92 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.60/20.92 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.60/20.92 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.60/20.92 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.60/20.92 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.60/20.92 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.60/20.92 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.60/20.92 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.60/20.92 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.60/20.92 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.60/20.92 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.60/20.92 mark(a) -> a 20.60/20.92 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.60/20.92 mark(e) -> e 20.60/20.92 mark(i) -> i 20.60/20.92 mark(isList(X:S)) -> a__isList(X:S) 20.60/20.92 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.60/20.92 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.60/20.92 mark(isPal(X:S)) -> a__isPal(X:S) 20.60/20.92 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.60/20.92 mark(isQid(X:S)) -> a__isQid(X:S) 20.60/20.92 mark(nil) -> nil 20.60/20.92 mark(o) -> o 20.60/20.92 mark(tt) -> tt 20.60/20.92 mark(u) -> u 20.60/20.92 20.60/20.92 Problem 1: 20.60/20.92 20.60/20.92 Reduction Pairs Processor: 20.60/20.92 -> Pairs: 20.60/20.92 A__AND(tt,X:S) -> MARK(X:S) 20.60/20.92 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__AND(a__isQid(I:S),isPalListKind(I:S)) 20.60/20.92 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.92 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.92 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.92 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.92 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U12(X:S)) -> MARK(X:S) 20.60/20.92 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.92 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U23(X:S)) -> MARK(X:S) 20.60/20.92 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U32(X:S)) -> MARK(X:S) 20.60/20.92 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.92 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U43(X:S)) -> MARK(X:S) 20.60/20.92 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.92 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U53(X:S)) -> MARK(X:S) 20.60/20.92 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U62(X:S)) -> MARK(X:S) 20.60/20.92 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U72(X:S)) -> MARK(X:S) 20.60/20.92 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.60/20.92 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.60/20.92 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.60/20.92 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.60/20.92 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.60/20.92 -> Rules: 20.60/20.92 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.60/20.92 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.60/20.92 a__U12(tt) -> tt 20.60/20.92 a__U12(X:S) -> U12(X:S) 20.60/20.92 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.60/20.92 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.60/20.92 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.60/20.92 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.60/20.92 a__U23(tt) -> tt 20.60/20.92 a__U23(X:S) -> U23(X:S) 20.60/20.92 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.60/20.92 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.60/20.92 a__U32(tt) -> tt 20.60/20.92 a__U32(X:S) -> U32(X:S) 20.60/20.92 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.60/20.92 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.60/20.92 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.60/20.92 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.60/20.92 a__U43(tt) -> tt 20.60/20.92 a__U43(X:S) -> U43(X:S) 20.60/20.92 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.60/20.92 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.60/20.92 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.60/20.92 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.60/20.92 a__U53(tt) -> tt 20.60/20.92 a__U53(X:S) -> U53(X:S) 20.60/20.92 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.60/20.92 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.60/20.92 a__U62(tt) -> tt 20.60/20.92 a__U62(X:S) -> U62(X:S) 20.60/20.92 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.60/20.92 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.60/20.92 a__U72(tt) -> tt 20.60/20.92 a__U72(X:S) -> U72(X:S) 20.60/20.92 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.60/20.92 a____(nil,X:S) -> mark(X:S) 20.60/20.92 a____(X:S,nil) -> mark(X:S) 20.60/20.92 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.60/20.92 a__and(tt,X:S) -> mark(X:S) 20.60/20.92 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.60/20.92 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.92 a__isList(nil) -> tt 20.60/20.92 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.60/20.92 a__isList(X:S) -> isList(X:S) 20.60/20.92 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.92 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.92 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.60/20.92 a__isNeList(X:S) -> isNeList(X:S) 20.60/20.92 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.92 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.60/20.92 a__isNePal(X:S) -> isNePal(X:S) 20.60/20.92 a__isPal(nil) -> tt 20.60/20.92 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.60/20.92 a__isPal(X:S) -> isPal(X:S) 20.60/20.92 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.92 a__isPalListKind(a) -> tt 20.60/20.92 a__isPalListKind(e) -> tt 20.60/20.92 a__isPalListKind(i) -> tt 20.60/20.92 a__isPalListKind(nil) -> tt 20.60/20.92 a__isPalListKind(o) -> tt 20.60/20.92 a__isPalListKind(u) -> tt 20.60/20.92 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.60/20.92 a__isQid(a) -> tt 20.60/20.92 a__isQid(e) -> tt 20.60/20.92 a__isQid(i) -> tt 20.60/20.92 a__isQid(o) -> tt 20.60/20.92 a__isQid(u) -> tt 20.60/20.92 a__isQid(X:S) -> isQid(X:S) 20.60/20.92 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.60/20.92 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.60/20.92 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.60/20.92 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.60/20.92 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.60/20.92 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.60/20.92 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.60/20.92 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.60/20.92 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.60/20.92 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.60/20.92 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.60/20.92 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.60/20.92 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.60/20.92 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.60/20.92 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.60/20.92 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.60/20.92 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.60/20.92 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.60/20.92 mark(a) -> a 20.60/20.92 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.60/20.92 mark(e) -> e 20.60/20.92 mark(i) -> i 20.60/20.92 mark(isList(X:S)) -> a__isList(X:S) 20.60/20.92 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.60/20.92 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.60/20.92 mark(isPal(X:S)) -> a__isPal(X:S) 20.60/20.92 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.60/20.92 mark(isQid(X:S)) -> a__isQid(X:S) 20.60/20.92 mark(nil) -> nil 20.60/20.92 mark(o) -> o 20.60/20.92 mark(tt) -> tt 20.60/20.92 mark(u) -> u 20.60/20.92 -> Usable rules: 20.60/20.92 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.60/20.92 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.60/20.92 a__U12(tt) -> tt 20.60/20.92 a__U12(X:S) -> U12(X:S) 20.60/20.92 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.60/20.92 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.60/20.92 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.60/20.92 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.60/20.92 a__U23(tt) -> tt 20.60/20.92 a__U23(X:S) -> U23(X:S) 20.60/20.92 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.60/20.92 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.60/20.92 a__U32(tt) -> tt 20.60/20.92 a__U32(X:S) -> U32(X:S) 20.60/20.92 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.60/20.92 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.60/20.92 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.60/20.92 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.60/20.92 a__U43(tt) -> tt 20.60/20.92 a__U43(X:S) -> U43(X:S) 20.60/20.92 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.60/20.92 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.60/20.92 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.60/20.92 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.60/20.92 a__U53(tt) -> tt 20.60/20.92 a__U53(X:S) -> U53(X:S) 20.60/20.92 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.60/20.92 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.60/20.92 a__U62(tt) -> tt 20.60/20.92 a__U62(X:S) -> U62(X:S) 20.60/20.92 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.60/20.92 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.60/20.92 a__U72(tt) -> tt 20.60/20.92 a__U72(X:S) -> U72(X:S) 20.60/20.92 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.60/20.92 a____(nil,X:S) -> mark(X:S) 20.60/20.92 a____(X:S,nil) -> mark(X:S) 20.60/20.92 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.60/20.92 a__and(tt,X:S) -> mark(X:S) 20.60/20.92 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.60/20.92 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.92 a__isList(nil) -> tt 20.60/20.92 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.60/20.92 a__isList(X:S) -> isList(X:S) 20.60/20.92 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.92 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.92 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.60/20.92 a__isNeList(X:S) -> isNeList(X:S) 20.60/20.92 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.92 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.60/20.92 a__isNePal(X:S) -> isNePal(X:S) 20.60/20.92 a__isPal(nil) -> tt 20.60/20.92 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.60/20.92 a__isPal(X:S) -> isPal(X:S) 20.60/20.92 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.92 a__isPalListKind(a) -> tt 20.60/20.92 a__isPalListKind(e) -> tt 20.60/20.92 a__isPalListKind(i) -> tt 20.60/20.92 a__isPalListKind(nil) -> tt 20.60/20.92 a__isPalListKind(o) -> tt 20.60/20.92 a__isPalListKind(u) -> tt 20.60/20.92 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.60/20.92 a__isQid(a) -> tt 20.60/20.92 a__isQid(e) -> tt 20.60/20.92 a__isQid(i) -> tt 20.60/20.92 a__isQid(o) -> tt 20.60/20.92 a__isQid(u) -> tt 20.60/20.92 a__isQid(X:S) -> isQid(X:S) 20.60/20.92 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.60/20.92 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.60/20.92 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.60/20.92 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.60/20.92 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.60/20.92 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.60/20.92 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.60/20.92 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.60/20.92 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.60/20.92 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.60/20.92 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.60/20.92 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.60/20.92 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.60/20.92 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.60/20.92 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.60/20.92 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.60/20.92 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.60/20.92 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.60/20.92 mark(a) -> a 20.60/20.92 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.60/20.92 mark(e) -> e 20.60/20.92 mark(i) -> i 20.60/20.92 mark(isList(X:S)) -> a__isList(X:S) 20.60/20.92 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.60/20.92 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.60/20.92 mark(isPal(X:S)) -> a__isPal(X:S) 20.60/20.92 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.60/20.92 mark(isQid(X:S)) -> a__isQid(X:S) 20.60/20.92 mark(nil) -> nil 20.60/20.92 mark(o) -> o 20.60/20.92 mark(tt) -> tt 20.60/20.92 mark(u) -> u 20.60/20.92 ->Interpretation type: 20.60/20.92 Linear 20.60/20.92 ->Coefficients: 20.60/20.92 Natural Numbers 20.60/20.92 ->Dimension: 20.60/20.92 1 20.60/20.92 ->Bound: 20.60/20.92 2 20.60/20.92 ->Interpretation: 20.60/20.92 20.60/20.92 [a__U11](X1,X2) = 2.X1 + 2.X2 + 1 20.60/20.92 [a__U12](X) = X + 1 20.60/20.92 [a__U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.60/20.92 [a__U22](X1,X2) = X1 + 2.X2 + 1 20.60/20.92 [a__U23](X) = X 20.60/20.92 [a__U31](X1,X2) = 2.X1 + 2.X2 20.60/20.92 [a__U32](X) = 2.X 20.60/20.92 [a__U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.60/20.92 [a__U42](X1,X2) = X1 + 2.X2 + 1 20.60/20.92 [a__U43](X) = X + 1 20.60/20.92 [a__U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.60/20.92 [a__U52](X1,X2) = X1 + 2.X2 + 2 20.60/20.92 [a__U53](X) = X + 1 20.60/20.92 [a__U61](X1,X2) = 2.X1 + 2.X2 + 2 20.60/20.92 [a__U62](X) = X + 1 20.60/20.92 [a__U71](X1,X2) = 2.X1 + 2.X2 + 2 20.60/20.92 [a__U72](X) = X 20.60/20.92 [a____](X1,X2) = 2.X1 + X2 + 2 20.60/20.92 [a__and](X1,X2) = X1 + 2.X2 20.60/20.92 [a__isList](X) = 2.X + 1 20.60/20.92 [a__isNeList](X) = 2.X 20.60/20.92 [a__isNePal](X) = 2.X + 2 20.60/20.92 [a__isPal](X) = 2.X + 2 20.60/20.92 [a__isPalListKind](X) = 0 20.60/20.92 [a__isQid](X) = X 20.60/20.92 [mark](X) = X 20.60/20.92 [U11](X1,X2) = 2.X1 + 2.X2 + 1 20.60/20.92 [U12](X) = X + 1 20.60/20.92 [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.60/20.92 [U22](X1,X2) = X1 + 2.X2 + 1 20.60/20.92 [U23](X) = X 20.60/20.92 [U31](X1,X2) = 2.X1 + 2.X2 20.60/20.92 [U32](X) = 2.X 20.60/20.92 [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.60/20.92 [U42](X1,X2) = X1 + 2.X2 + 1 20.60/20.92 [U43](X) = X + 1 20.60/20.92 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.60/20.92 [U52](X1,X2) = X1 + 2.X2 + 2 20.60/20.92 [U53](X) = X + 1 20.60/20.92 [U61](X1,X2) = 2.X1 + 2.X2 + 2 20.60/20.92 [U62](X) = X + 1 20.60/20.92 [U71](X1,X2) = 2.X1 + 2.X2 + 2 20.60/20.92 [U72](X) = X 20.60/20.92 [__](X1,X2) = 2.X1 + X2 + 2 20.60/20.92 [a] = 1 20.60/20.92 [and](X1,X2) = X1 + 2.X2 20.60/20.92 [e] = 1 20.60/20.92 [fSNonEmpty] = 0 20.60/20.92 [i] = 1 20.60/20.92 [isList](X) = 2.X + 1 20.60/20.92 [isNeList](X) = 2.X 20.60/20.92 [isNePal](X) = 2.X + 2 20.60/20.92 [isPal](X) = 2.X + 2 20.60/20.92 [isPalListKind](X) = 0 20.60/20.92 [isQid](X) = X 20.60/20.92 [nil] = 1 20.60/20.92 [o] = 1 20.60/20.92 [tt] = 0 20.60/20.92 [u] = 1 20.60/20.92 [A__U11](X1,X2) = 0 20.60/20.92 [A__U12](X) = 0 20.60/20.92 [A__U21](X1,X2,X3) = 0 20.60/20.92 [A__U22](X1,X2) = 0 20.60/20.92 [A__U23](X) = 0 20.60/20.92 [A__U31](X1,X2) = 0 20.60/20.92 [A__U32](X) = 0 20.60/20.92 [A__U41](X1,X2,X3) = 0 20.60/20.92 [A__U42](X1,X2) = 0 20.60/20.92 [A__U43](X) = 0 20.60/20.92 [A__U51](X1,X2,X3) = 0 20.60/20.92 [A__U52](X1,X2) = 0 20.60/20.92 [A__U53](X) = 0 20.60/20.92 [A__U61](X1,X2) = 0 20.60/20.92 [A__U62](X) = 0 20.60/20.92 [A__U71](X1,X2) = 0 20.60/20.92 [A__U72](X) = 0 20.60/20.92 [A____](X1,X2) = 0 20.60/20.92 [A__AND](X1,X2) = X1 + 2.X2 + 1 20.60/20.92 [A__ISLIST](X) = 0 20.60/20.92 [A__ISNELIST](X) = 0 20.60/20.92 [A__ISNEPAL](X) = 2.X + 1 20.60/20.92 [A__ISPAL](X) = 2.X + 2 20.60/20.92 [A__ISPALLISTKIND](X) = 1 20.60/20.92 [A__ISQID](X) = 0 20.60/20.92 [MARK](X) = 2.X + 1 20.60/20.92 20.60/20.92 Problem 1: 20.60/20.92 20.60/20.92 SCC Processor: 20.60/20.92 -> Pairs: 20.60/20.92 A__AND(tt,X:S) -> MARK(X:S) 20.60/20.92 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.92 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.92 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.92 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.92 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U12(X:S)) -> MARK(X:S) 20.60/20.92 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.92 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U23(X:S)) -> MARK(X:S) 20.60/20.92 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U32(X:S)) -> MARK(X:S) 20.60/20.92 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.92 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U43(X:S)) -> MARK(X:S) 20.60/20.92 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.92 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U53(X:S)) -> MARK(X:S) 20.60/20.92 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U62(X:S)) -> MARK(X:S) 20.60/20.92 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U72(X:S)) -> MARK(X:S) 20.60/20.92 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.60/20.92 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.60/20.92 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.60/20.92 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.60/20.92 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.60/20.92 -> Rules: 20.60/20.92 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.60/20.92 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.60/20.92 a__U12(tt) -> tt 20.60/20.92 a__U12(X:S) -> U12(X:S) 20.60/20.92 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.60/20.92 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.60/20.92 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.60/20.92 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.60/20.92 a__U23(tt) -> tt 20.60/20.92 a__U23(X:S) -> U23(X:S) 20.60/20.92 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.60/20.92 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.60/20.92 a__U32(tt) -> tt 20.60/20.92 a__U32(X:S) -> U32(X:S) 20.60/20.92 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.60/20.92 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.60/20.92 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.60/20.92 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.60/20.92 a__U43(tt) -> tt 20.60/20.92 a__U43(X:S) -> U43(X:S) 20.60/20.92 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.60/20.92 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.60/20.92 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.60/20.92 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.60/20.92 a__U53(tt) -> tt 20.60/20.92 a__U53(X:S) -> U53(X:S) 20.60/20.92 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.60/20.92 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.60/20.92 a__U62(tt) -> tt 20.60/20.92 a__U62(X:S) -> U62(X:S) 20.60/20.92 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.60/20.92 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.60/20.92 a__U72(tt) -> tt 20.60/20.92 a__U72(X:S) -> U72(X:S) 20.60/20.92 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.60/20.92 a____(nil,X:S) -> mark(X:S) 20.60/20.92 a____(X:S,nil) -> mark(X:S) 20.60/20.92 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.60/20.92 a__and(tt,X:S) -> mark(X:S) 20.60/20.92 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.60/20.92 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.92 a__isList(nil) -> tt 20.60/20.92 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.60/20.92 a__isList(X:S) -> isList(X:S) 20.60/20.92 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.92 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.92 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.60/20.92 a__isNeList(X:S) -> isNeList(X:S) 20.60/20.92 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.92 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.60/20.92 a__isNePal(X:S) -> isNePal(X:S) 20.60/20.92 a__isPal(nil) -> tt 20.60/20.92 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.60/20.92 a__isPal(X:S) -> isPal(X:S) 20.60/20.92 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.92 a__isPalListKind(a) -> tt 20.60/20.92 a__isPalListKind(e) -> tt 20.60/20.92 a__isPalListKind(i) -> tt 20.60/20.92 a__isPalListKind(nil) -> tt 20.60/20.92 a__isPalListKind(o) -> tt 20.60/20.92 a__isPalListKind(u) -> tt 20.60/20.92 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.60/20.92 a__isQid(a) -> tt 20.60/20.92 a__isQid(e) -> tt 20.60/20.92 a__isQid(i) -> tt 20.60/20.92 a__isQid(o) -> tt 20.60/20.92 a__isQid(u) -> tt 20.60/20.92 a__isQid(X:S) -> isQid(X:S) 20.60/20.92 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.60/20.92 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.60/20.92 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.60/20.92 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.60/20.92 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.60/20.92 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.60/20.92 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.60/20.92 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.60/20.92 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.60/20.92 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.60/20.92 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.60/20.92 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.60/20.92 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.60/20.92 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.60/20.92 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.60/20.92 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.60/20.92 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.60/20.92 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.60/20.92 mark(a) -> a 20.60/20.92 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.60/20.92 mark(e) -> e 20.60/20.92 mark(i) -> i 20.60/20.92 mark(isList(X:S)) -> a__isList(X:S) 20.60/20.92 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.60/20.92 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.60/20.92 mark(isPal(X:S)) -> a__isPal(X:S) 20.60/20.92 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.60/20.92 mark(isQid(X:S)) -> a__isQid(X:S) 20.60/20.92 mark(nil) -> nil 20.60/20.92 mark(o) -> o 20.60/20.92 mark(tt) -> tt 20.60/20.92 mark(u) -> u 20.60/20.92 ->Strongly Connected Components: 20.60/20.92 ->->Cycle: 20.60/20.92 ->->-> Pairs: 20.60/20.92 A__AND(tt,X:S) -> MARK(X:S) 20.60/20.92 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.92 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.92 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.92 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.92 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U12(X:S)) -> MARK(X:S) 20.60/20.92 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.92 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U23(X:S)) -> MARK(X:S) 20.60/20.92 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U32(X:S)) -> MARK(X:S) 20.60/20.92 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.92 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U43(X:S)) -> MARK(X:S) 20.60/20.92 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.92 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U53(X:S)) -> MARK(X:S) 20.60/20.92 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U62(X:S)) -> MARK(X:S) 20.60/20.92 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U72(X:S)) -> MARK(X:S) 20.60/20.92 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.60/20.92 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.60/20.92 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.60/20.92 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.60/20.92 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.60/20.92 ->->-> Rules: 20.60/20.92 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.60/20.92 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.60/20.92 a__U12(tt) -> tt 20.60/20.92 a__U12(X:S) -> U12(X:S) 20.60/20.92 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.60/20.92 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.60/20.92 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.60/20.92 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.60/20.92 a__U23(tt) -> tt 20.60/20.92 a__U23(X:S) -> U23(X:S) 20.60/20.92 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.60/20.92 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.60/20.92 a__U32(tt) -> tt 20.60/20.92 a__U32(X:S) -> U32(X:S) 20.60/20.92 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.60/20.92 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.60/20.92 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.60/20.92 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.60/20.92 a__U43(tt) -> tt 20.60/20.92 a__U43(X:S) -> U43(X:S) 20.60/20.92 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.60/20.92 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.60/20.92 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.60/20.92 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.60/20.92 a__U53(tt) -> tt 20.60/20.92 a__U53(X:S) -> U53(X:S) 20.60/20.92 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.60/20.92 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.60/20.92 a__U62(tt) -> tt 20.60/20.92 a__U62(X:S) -> U62(X:S) 20.60/20.92 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.60/20.92 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.60/20.92 a__U72(tt) -> tt 20.60/20.92 a__U72(X:S) -> U72(X:S) 20.60/20.92 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.60/20.92 a____(nil,X:S) -> mark(X:S) 20.60/20.92 a____(X:S,nil) -> mark(X:S) 20.60/20.92 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.60/20.92 a__and(tt,X:S) -> mark(X:S) 20.60/20.92 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.60/20.92 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.92 a__isList(nil) -> tt 20.60/20.92 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.60/20.92 a__isList(X:S) -> isList(X:S) 20.60/20.92 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.92 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.92 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.60/20.92 a__isNeList(X:S) -> isNeList(X:S) 20.60/20.92 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.92 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.60/20.92 a__isNePal(X:S) -> isNePal(X:S) 20.60/20.92 a__isPal(nil) -> tt 20.60/20.92 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.60/20.92 a__isPal(X:S) -> isPal(X:S) 20.60/20.92 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.92 a__isPalListKind(a) -> tt 20.60/20.92 a__isPalListKind(e) -> tt 20.60/20.92 a__isPalListKind(i) -> tt 20.60/20.92 a__isPalListKind(nil) -> tt 20.60/20.92 a__isPalListKind(o) -> tt 20.60/20.92 a__isPalListKind(u) -> tt 20.60/20.92 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.60/20.92 a__isQid(a) -> tt 20.60/20.92 a__isQid(e) -> tt 20.60/20.92 a__isQid(i) -> tt 20.60/20.92 a__isQid(o) -> tt 20.60/20.92 a__isQid(u) -> tt 20.60/20.92 a__isQid(X:S) -> isQid(X:S) 20.60/20.92 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.60/20.92 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.60/20.92 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.60/20.92 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.60/20.92 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.60/20.92 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.60/20.92 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.60/20.92 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.60/20.92 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.60/20.92 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.60/20.92 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.60/20.92 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.60/20.92 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.60/20.92 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.60/20.92 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.60/20.92 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.60/20.92 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.60/20.92 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.60/20.92 mark(a) -> a 20.60/20.92 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.60/20.92 mark(e) -> e 20.60/20.92 mark(i) -> i 20.60/20.92 mark(isList(X:S)) -> a__isList(X:S) 20.60/20.92 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.60/20.92 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.60/20.92 mark(isPal(X:S)) -> a__isPal(X:S) 20.60/20.92 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.60/20.92 mark(isQid(X:S)) -> a__isQid(X:S) 20.60/20.92 mark(nil) -> nil 20.60/20.92 mark(o) -> o 20.60/20.92 mark(tt) -> tt 20.60/20.92 mark(u) -> u 20.60/20.92 20.60/20.92 Problem 1: 20.60/20.92 20.60/20.92 Reduction Pairs Processor: 20.60/20.92 -> Pairs: 20.60/20.92 A__AND(tt,X:S) -> MARK(X:S) 20.60/20.92 A__ISNEPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.92 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.92 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.92 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.92 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U12(X:S)) -> MARK(X:S) 20.60/20.92 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.92 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U23(X:S)) -> MARK(X:S) 20.60/20.92 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U32(X:S)) -> MARK(X:S) 20.60/20.92 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.92 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U43(X:S)) -> MARK(X:S) 20.60/20.92 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.92 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U53(X:S)) -> MARK(X:S) 20.60/20.92 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U62(X:S)) -> MARK(X:S) 20.60/20.92 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U72(X:S)) -> MARK(X:S) 20.60/20.92 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.60/20.92 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.60/20.92 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.60/20.92 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.60/20.92 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.60/20.92 -> Rules: 20.60/20.92 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.60/20.92 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.60/20.92 a__U12(tt) -> tt 20.60/20.92 a__U12(X:S) -> U12(X:S) 20.60/20.92 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.60/20.92 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.60/20.92 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.60/20.92 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.60/20.92 a__U23(tt) -> tt 20.60/20.92 a__U23(X:S) -> U23(X:S) 20.60/20.92 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.60/20.92 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.60/20.92 a__U32(tt) -> tt 20.60/20.92 a__U32(X:S) -> U32(X:S) 20.60/20.92 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.60/20.92 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.60/20.92 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.60/20.92 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.60/20.92 a__U43(tt) -> tt 20.60/20.92 a__U43(X:S) -> U43(X:S) 20.60/20.92 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.60/20.92 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.60/20.92 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.60/20.92 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.60/20.92 a__U53(tt) -> tt 20.60/20.92 a__U53(X:S) -> U53(X:S) 20.60/20.92 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.60/20.92 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.60/20.92 a__U62(tt) -> tt 20.60/20.92 a__U62(X:S) -> U62(X:S) 20.60/20.92 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.60/20.92 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.60/20.92 a__U72(tt) -> tt 20.60/20.92 a__U72(X:S) -> U72(X:S) 20.60/20.92 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.60/20.92 a____(nil,X:S) -> mark(X:S) 20.60/20.92 a____(X:S,nil) -> mark(X:S) 20.60/20.92 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.60/20.92 a__and(tt,X:S) -> mark(X:S) 20.60/20.92 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.60/20.92 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.92 a__isList(nil) -> tt 20.60/20.92 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.60/20.92 a__isList(X:S) -> isList(X:S) 20.60/20.92 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.92 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.92 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.60/20.92 a__isNeList(X:S) -> isNeList(X:S) 20.60/20.92 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.92 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.60/20.92 a__isNePal(X:S) -> isNePal(X:S) 20.60/20.92 a__isPal(nil) -> tt 20.60/20.92 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.60/20.92 a__isPal(X:S) -> isPal(X:S) 20.60/20.92 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.92 a__isPalListKind(a) -> tt 20.60/20.92 a__isPalListKind(e) -> tt 20.60/20.92 a__isPalListKind(i) -> tt 20.60/20.92 a__isPalListKind(nil) -> tt 20.60/20.92 a__isPalListKind(o) -> tt 20.60/20.92 a__isPalListKind(u) -> tt 20.60/20.92 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.60/20.92 a__isQid(a) -> tt 20.60/20.92 a__isQid(e) -> tt 20.60/20.92 a__isQid(i) -> tt 20.60/20.92 a__isQid(o) -> tt 20.60/20.92 a__isQid(u) -> tt 20.60/20.92 a__isQid(X:S) -> isQid(X:S) 20.60/20.92 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.60/20.92 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.60/20.92 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.60/20.92 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.60/20.92 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.60/20.92 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.60/20.92 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.60/20.92 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.60/20.92 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.60/20.92 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.60/20.92 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.60/20.92 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.60/20.92 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.60/20.92 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.60/20.92 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.60/20.92 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.60/20.92 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.60/20.92 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.60/20.92 mark(a) -> a 20.60/20.92 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.60/20.92 mark(e) -> e 20.60/20.92 mark(i) -> i 20.60/20.92 mark(isList(X:S)) -> a__isList(X:S) 20.60/20.92 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.60/20.92 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.60/20.92 mark(isPal(X:S)) -> a__isPal(X:S) 20.60/20.92 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.60/20.92 mark(isQid(X:S)) -> a__isQid(X:S) 20.60/20.92 mark(nil) -> nil 20.60/20.92 mark(o) -> o 20.60/20.92 mark(tt) -> tt 20.60/20.92 mark(u) -> u 20.60/20.92 -> Usable rules: 20.60/20.92 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.60/20.92 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.60/20.92 a__U12(tt) -> tt 20.60/20.92 a__U12(X:S) -> U12(X:S) 20.60/20.92 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.60/20.92 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.60/20.92 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.60/20.92 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.60/20.92 a__U23(tt) -> tt 20.60/20.92 a__U23(X:S) -> U23(X:S) 20.60/20.92 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.60/20.92 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.60/20.92 a__U32(tt) -> tt 20.60/20.92 a__U32(X:S) -> U32(X:S) 20.60/20.92 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.60/20.92 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.60/20.92 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.60/20.92 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.60/20.92 a__U43(tt) -> tt 20.60/20.92 a__U43(X:S) -> U43(X:S) 20.60/20.92 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.60/20.92 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.60/20.92 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.60/20.92 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.60/20.92 a__U53(tt) -> tt 20.60/20.92 a__U53(X:S) -> U53(X:S) 20.60/20.92 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.60/20.92 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.60/20.92 a__U62(tt) -> tt 20.60/20.92 a__U62(X:S) -> U62(X:S) 20.60/20.92 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.60/20.92 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.60/20.92 a__U72(tt) -> tt 20.60/20.92 a__U72(X:S) -> U72(X:S) 20.60/20.92 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.60/20.92 a____(nil,X:S) -> mark(X:S) 20.60/20.92 a____(X:S,nil) -> mark(X:S) 20.60/20.92 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.60/20.92 a__and(tt,X:S) -> mark(X:S) 20.60/20.92 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.60/20.92 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.92 a__isList(nil) -> tt 20.60/20.92 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.60/20.92 a__isList(X:S) -> isList(X:S) 20.60/20.92 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.92 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.92 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.60/20.92 a__isNeList(X:S) -> isNeList(X:S) 20.60/20.92 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.92 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.60/20.92 a__isNePal(X:S) -> isNePal(X:S) 20.60/20.92 a__isPal(nil) -> tt 20.60/20.92 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.60/20.92 a__isPal(X:S) -> isPal(X:S) 20.60/20.92 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.92 a__isPalListKind(a) -> tt 20.60/20.92 a__isPalListKind(e) -> tt 20.60/20.92 a__isPalListKind(i) -> tt 20.60/20.92 a__isPalListKind(nil) -> tt 20.60/20.92 a__isPalListKind(o) -> tt 20.60/20.92 a__isPalListKind(u) -> tt 20.60/20.92 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.60/20.92 a__isQid(a) -> tt 20.60/20.92 a__isQid(e) -> tt 20.60/20.92 a__isQid(i) -> tt 20.60/20.92 a__isQid(o) -> tt 20.60/20.92 a__isQid(u) -> tt 20.60/20.92 a__isQid(X:S) -> isQid(X:S) 20.60/20.92 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.60/20.92 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.60/20.92 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.60/20.92 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.60/20.92 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.60/20.92 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.60/20.92 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.60/20.92 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.60/20.92 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.60/20.92 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.60/20.92 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.60/20.92 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.60/20.92 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.60/20.92 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.60/20.92 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.60/20.92 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.60/20.92 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.60/20.92 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.60/20.92 mark(a) -> a 20.60/20.92 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.60/20.92 mark(e) -> e 20.60/20.92 mark(i) -> i 20.60/20.92 mark(isList(X:S)) -> a__isList(X:S) 20.60/20.92 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.60/20.92 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.60/20.92 mark(isPal(X:S)) -> a__isPal(X:S) 20.60/20.92 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.60/20.92 mark(isQid(X:S)) -> a__isQid(X:S) 20.60/20.92 mark(nil) -> nil 20.60/20.92 mark(o) -> o 20.60/20.92 mark(tt) -> tt 20.60/20.92 mark(u) -> u 20.60/20.92 ->Interpretation type: 20.60/20.92 Linear 20.60/20.92 ->Coefficients: 20.60/20.92 Natural Numbers 20.60/20.92 ->Dimension: 20.60/20.92 1 20.60/20.92 ->Bound: 20.60/20.92 2 20.60/20.92 ->Interpretation: 20.60/20.92 20.60/20.92 [a__U11](X1,X2) = 2.X1 20.60/20.92 [a__U12](X) = 2.X 20.60/20.92 [a__U21](X1,X2,X3) = 2.X1 20.60/20.92 [a__U22](X1,X2) = 2.X1 20.60/20.92 [a__U23](X) = 2.X 20.60/20.92 [a__U31](X1,X2) = 2.X1 20.60/20.92 [a__U32](X) = 2.X 20.60/20.92 [a__U41](X1,X2,X3) = X1 20.60/20.92 [a__U42](X1,X2) = 2.X1 20.60/20.92 [a__U43](X) = 2.X 20.60/20.92 [a__U51](X1,X2,X3) = 2.X1 20.60/20.92 [a__U52](X1,X2) = X1 20.60/20.92 [a__U53](X) = X 20.60/20.92 [a__U61](X1,X2) = X1 + 2.X2 + 2 20.60/20.92 [a__U62](X) = X 20.60/20.92 [a__U71](X1,X2) = 2.X1 + 2.X2 + 2 20.60/20.92 [a__U72](X) = X 20.60/20.92 [a____](X1,X2) = 2.X1 + X2 + 2 20.60/20.92 [a__and](X1,X2) = X1 + 2.X2 20.60/20.92 [a__isList](X) = 0 20.60/20.92 [a__isNeList](X) = 0 20.60/20.92 [a__isNePal](X) = 2.X + 2 20.60/20.92 [a__isPal](X) = 2.X + 2 20.60/20.92 [a__isPalListKind](X) = 0 20.60/20.92 [a__isQid](X) = 0 20.60/20.92 [mark](X) = X 20.60/20.92 [U11](X1,X2) = 2.X1 20.60/20.92 [U12](X) = 2.X 20.60/20.92 [U21](X1,X2,X3) = 2.X1 20.60/20.92 [U22](X1,X2) = 2.X1 20.60/20.92 [U23](X) = 2.X 20.60/20.92 [U31](X1,X2) = 2.X1 20.60/20.92 [U32](X) = 2.X 20.60/20.92 [U41](X1,X2,X3) = X1 20.60/20.92 [U42](X1,X2) = 2.X1 20.60/20.92 [U43](X) = 2.X 20.60/20.92 [U51](X1,X2,X3) = 2.X1 20.60/20.92 [U52](X1,X2) = X1 20.60/20.92 [U53](X) = X 20.60/20.92 [U61](X1,X2) = X1 + 2.X2 + 2 20.60/20.92 [U62](X) = X 20.60/20.92 [U71](X1,X2) = 2.X1 + 2.X2 + 2 20.60/20.92 [U72](X) = X 20.60/20.92 [__](X1,X2) = 2.X1 + X2 + 2 20.60/20.92 [a] = 1 20.60/20.92 [and](X1,X2) = X1 + 2.X2 20.60/20.92 [e] = 1 20.60/20.92 [fSNonEmpty] = 0 20.60/20.92 [i] = 1 20.60/20.92 [isList](X) = 0 20.60/20.92 [isNeList](X) = 0 20.60/20.92 [isNePal](X) = 2.X + 2 20.60/20.92 [isPal](X) = 2.X + 2 20.60/20.92 [isPalListKind](X) = 0 20.60/20.92 [isQid](X) = 0 20.60/20.92 [nil] = 2 20.60/20.92 [o] = 2 20.60/20.92 [tt] = 0 20.60/20.92 [u] = 2 20.60/20.92 [A__U11](X1,X2) = 0 20.60/20.92 [A__U12](X) = 0 20.60/20.92 [A__U21](X1,X2,X3) = 0 20.60/20.92 [A__U22](X1,X2) = 0 20.60/20.92 [A__U23](X) = 0 20.60/20.92 [A__U31](X1,X2) = 0 20.60/20.92 [A__U32](X) = 0 20.60/20.92 [A__U41](X1,X2,X3) = 0 20.60/20.92 [A__U42](X1,X2) = 0 20.60/20.92 [A__U43](X) = 0 20.60/20.92 [A__U51](X1,X2,X3) = 0 20.60/20.92 [A__U52](X1,X2) = 0 20.60/20.92 [A__U53](X) = 0 20.60/20.92 [A__U61](X1,X2) = 0 20.60/20.92 [A__U62](X) = 0 20.60/20.92 [A__U71](X1,X2) = 0 20.60/20.92 [A__U72](X) = 0 20.60/20.92 [A____](X1,X2) = 0 20.60/20.92 [A__AND](X1,X2) = 2.X1 + 2.X2 + 1 20.60/20.92 [A__ISLIST](X) = 0 20.60/20.92 [A__ISNELIST](X) = 0 20.60/20.92 [A__ISNEPAL](X) = 2.X + 2 20.60/20.92 [A__ISPAL](X) = 2 20.60/20.92 [A__ISPALLISTKIND](X) = 1 20.60/20.92 [A__ISQID](X) = 0 20.60/20.92 [MARK](X) = 2.X + 1 20.60/20.92 20.60/20.92 Problem 1: 20.60/20.92 20.60/20.92 SCC Processor: 20.60/20.92 -> Pairs: 20.60/20.92 A__AND(tt,X:S) -> MARK(X:S) 20.60/20.92 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.92 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.92 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.92 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U12(X:S)) -> MARK(X:S) 20.60/20.92 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.92 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U23(X:S)) -> MARK(X:S) 20.60/20.92 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U32(X:S)) -> MARK(X:S) 20.60/20.92 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.92 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U43(X:S)) -> MARK(X:S) 20.60/20.92 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.92 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U53(X:S)) -> MARK(X:S) 20.60/20.92 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U62(X:S)) -> MARK(X:S) 20.60/20.92 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U72(X:S)) -> MARK(X:S) 20.60/20.92 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.60/20.92 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.60/20.92 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S) 20.60/20.92 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.60/20.92 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.60/20.92 -> Rules: 20.60/20.92 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.60/20.92 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.60/20.92 a__U12(tt) -> tt 20.60/20.92 a__U12(X:S) -> U12(X:S) 20.60/20.92 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.60/20.92 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.60/20.92 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.60/20.92 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.60/20.92 a__U23(tt) -> tt 20.60/20.92 a__U23(X:S) -> U23(X:S) 20.60/20.92 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.60/20.92 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.60/20.92 a__U32(tt) -> tt 20.60/20.92 a__U32(X:S) -> U32(X:S) 20.60/20.92 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.60/20.92 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.60/20.92 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.60/20.92 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.60/20.92 a__U43(tt) -> tt 20.60/20.92 a__U43(X:S) -> U43(X:S) 20.60/20.92 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.60/20.92 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.60/20.92 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.60/20.92 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.60/20.92 a__U53(tt) -> tt 20.60/20.92 a__U53(X:S) -> U53(X:S) 20.60/20.92 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.60/20.92 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.60/20.92 a__U62(tt) -> tt 20.60/20.92 a__U62(X:S) -> U62(X:S) 20.60/20.92 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.60/20.92 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.60/20.92 a__U72(tt) -> tt 20.60/20.92 a__U72(X:S) -> U72(X:S) 20.60/20.92 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.60/20.92 a____(nil,X:S) -> mark(X:S) 20.60/20.92 a____(X:S,nil) -> mark(X:S) 20.60/20.92 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.60/20.92 a__and(tt,X:S) -> mark(X:S) 20.60/20.92 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.60/20.92 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.92 a__isList(nil) -> tt 20.60/20.92 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.60/20.92 a__isList(X:S) -> isList(X:S) 20.60/20.92 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.92 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.92 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.60/20.92 a__isNeList(X:S) -> isNeList(X:S) 20.60/20.92 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.92 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.60/20.92 a__isNePal(X:S) -> isNePal(X:S) 20.60/20.92 a__isPal(nil) -> tt 20.60/20.92 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.60/20.92 a__isPal(X:S) -> isPal(X:S) 20.60/20.92 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.92 a__isPalListKind(a) -> tt 20.60/20.92 a__isPalListKind(e) -> tt 20.60/20.92 a__isPalListKind(i) -> tt 20.60/20.92 a__isPalListKind(nil) -> tt 20.60/20.92 a__isPalListKind(o) -> tt 20.60/20.92 a__isPalListKind(u) -> tt 20.60/20.92 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.60/20.92 a__isQid(a) -> tt 20.60/20.92 a__isQid(e) -> tt 20.60/20.92 a__isQid(i) -> tt 20.60/20.92 a__isQid(o) -> tt 20.60/20.92 a__isQid(u) -> tt 20.60/20.92 a__isQid(X:S) -> isQid(X:S) 20.60/20.92 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.60/20.92 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.60/20.92 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.60/20.92 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.60/20.92 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.60/20.92 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.60/20.92 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.60/20.92 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.60/20.92 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.60/20.92 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.60/20.92 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.60/20.92 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.60/20.92 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.60/20.92 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.60/20.92 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.60/20.92 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.60/20.92 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.60/20.92 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.60/20.92 mark(a) -> a 20.60/20.92 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.60/20.92 mark(e) -> e 20.60/20.92 mark(i) -> i 20.60/20.92 mark(isList(X:S)) -> a__isList(X:S) 20.60/20.92 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.60/20.92 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.60/20.92 mark(isPal(X:S)) -> a__isPal(X:S) 20.60/20.92 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.60/20.92 mark(isQid(X:S)) -> a__isQid(X:S) 20.60/20.92 mark(nil) -> nil 20.60/20.92 mark(o) -> o 20.60/20.92 mark(tt) -> tt 20.60/20.92 mark(u) -> u 20.60/20.92 ->Strongly Connected Components: 20.60/20.92 ->->Cycle: 20.60/20.92 ->->-> Pairs: 20.60/20.92 A__AND(tt,X:S) -> MARK(X:S) 20.60/20.92 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.92 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.92 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.92 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U12(X:S)) -> MARK(X:S) 20.60/20.92 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.92 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U23(X:S)) -> MARK(X:S) 20.60/20.92 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U32(X:S)) -> MARK(X:S) 20.60/20.92 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.92 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U43(X:S)) -> MARK(X:S) 20.60/20.92 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.92 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U53(X:S)) -> MARK(X:S) 20.60/20.92 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U62(X:S)) -> MARK(X:S) 20.60/20.92 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U72(X:S)) -> MARK(X:S) 20.60/20.92 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.60/20.92 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.60/20.92 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.60/20.92 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.60/20.92 ->->-> Rules: 20.60/20.92 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.60/20.92 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.60/20.92 a__U12(tt) -> tt 20.60/20.92 a__U12(X:S) -> U12(X:S) 20.60/20.92 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.60/20.92 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.60/20.92 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.60/20.92 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.60/20.92 a__U23(tt) -> tt 20.60/20.92 a__U23(X:S) -> U23(X:S) 20.60/20.92 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.60/20.92 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.60/20.92 a__U32(tt) -> tt 20.60/20.92 a__U32(X:S) -> U32(X:S) 20.60/20.92 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.60/20.92 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.60/20.92 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.60/20.92 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.60/20.92 a__U43(tt) -> tt 20.60/20.92 a__U43(X:S) -> U43(X:S) 20.60/20.92 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.60/20.92 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.60/20.92 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.60/20.92 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.60/20.92 a__U53(tt) -> tt 20.60/20.92 a__U53(X:S) -> U53(X:S) 20.60/20.92 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.60/20.92 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.60/20.92 a__U62(tt) -> tt 20.60/20.92 a__U62(X:S) -> U62(X:S) 20.60/20.92 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.60/20.92 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.60/20.92 a__U72(tt) -> tt 20.60/20.92 a__U72(X:S) -> U72(X:S) 20.60/20.92 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.60/20.92 a____(nil,X:S) -> mark(X:S) 20.60/20.92 a____(X:S,nil) -> mark(X:S) 20.60/20.92 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.60/20.92 a__and(tt,X:S) -> mark(X:S) 20.60/20.92 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.60/20.92 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.92 a__isList(nil) -> tt 20.60/20.92 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.60/20.92 a__isList(X:S) -> isList(X:S) 20.60/20.92 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.92 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.92 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.60/20.92 a__isNeList(X:S) -> isNeList(X:S) 20.60/20.92 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.92 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.60/20.92 a__isNePal(X:S) -> isNePal(X:S) 20.60/20.92 a__isPal(nil) -> tt 20.60/20.92 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.60/20.92 a__isPal(X:S) -> isPal(X:S) 20.60/20.92 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.92 a__isPalListKind(a) -> tt 20.60/20.92 a__isPalListKind(e) -> tt 20.60/20.92 a__isPalListKind(i) -> tt 20.60/20.92 a__isPalListKind(nil) -> tt 20.60/20.92 a__isPalListKind(o) -> tt 20.60/20.92 a__isPalListKind(u) -> tt 20.60/20.92 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.60/20.92 a__isQid(a) -> tt 20.60/20.92 a__isQid(e) -> tt 20.60/20.92 a__isQid(i) -> tt 20.60/20.92 a__isQid(o) -> tt 20.60/20.92 a__isQid(u) -> tt 20.60/20.92 a__isQid(X:S) -> isQid(X:S) 20.60/20.92 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.60/20.92 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.60/20.92 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.60/20.92 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.60/20.92 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.60/20.92 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.60/20.92 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.60/20.92 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.60/20.92 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.60/20.92 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.60/20.92 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.60/20.92 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.60/20.92 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.60/20.92 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.60/20.92 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.60/20.92 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.60/20.92 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.60/20.92 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.60/20.92 mark(a) -> a 20.60/20.92 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.60/20.92 mark(e) -> e 20.60/20.92 mark(i) -> i 20.60/20.92 mark(isList(X:S)) -> a__isList(X:S) 20.60/20.92 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.60/20.92 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.60/20.92 mark(isPal(X:S)) -> a__isPal(X:S) 20.60/20.92 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.60/20.92 mark(isQid(X:S)) -> a__isQid(X:S) 20.60/20.92 mark(nil) -> nil 20.60/20.92 mark(o) -> o 20.60/20.92 mark(tt) -> tt 20.60/20.92 mark(u) -> u 20.60/20.92 20.60/20.92 Problem 1: 20.60/20.92 20.60/20.92 Reduction Pairs Processor: 20.60/20.92 -> Pairs: 20.60/20.92 A__AND(tt,X:S) -> MARK(X:S) 20.60/20.92 A__ISPAL(V:S) -> A__ISPALLISTKIND(V:S) 20.60/20.92 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.92 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.92 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U12(X:S)) -> MARK(X:S) 20.60/20.92 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.92 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U23(X:S)) -> MARK(X:S) 20.60/20.92 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U32(X:S)) -> MARK(X:S) 20.60/20.92 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.92 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U43(X:S)) -> MARK(X:S) 20.60/20.92 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.92 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U53(X:S)) -> MARK(X:S) 20.60/20.92 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U62(X:S)) -> MARK(X:S) 20.60/20.92 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(U72(X:S)) -> MARK(X:S) 20.60/20.92 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.60/20.92 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.60/20.92 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.92 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.60/20.92 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.60/20.92 -> Rules: 20.60/20.92 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.60/20.92 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.60/20.92 a__U12(tt) -> tt 20.60/20.92 a__U12(X:S) -> U12(X:S) 20.60/20.92 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.60/20.92 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.60/20.92 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.60/20.92 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.60/20.92 a__U23(tt) -> tt 20.60/20.92 a__U23(X:S) -> U23(X:S) 20.60/20.92 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.60/20.92 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.60/20.92 a__U32(tt) -> tt 20.60/20.92 a__U32(X:S) -> U32(X:S) 20.60/20.92 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.60/20.92 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.60/20.92 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.60/20.92 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.60/20.92 a__U43(tt) -> tt 20.60/20.92 a__U43(X:S) -> U43(X:S) 20.60/20.92 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.60/20.92 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.60/20.92 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.60/20.92 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.60/20.92 a__U53(tt) -> tt 20.60/20.92 a__U53(X:S) -> U53(X:S) 20.60/20.92 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.60/20.92 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.60/20.92 a__U62(tt) -> tt 20.60/20.92 a__U62(X:S) -> U62(X:S) 20.60/20.92 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.60/20.92 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.60/20.92 a__U72(tt) -> tt 20.60/20.92 a__U72(X:S) -> U72(X:S) 20.60/20.92 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.60/20.92 a____(nil,X:S) -> mark(X:S) 20.60/20.92 a____(X:S,nil) -> mark(X:S) 20.60/20.92 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.60/20.92 a__and(tt,X:S) -> mark(X:S) 20.60/20.92 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.60/20.92 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.92 a__isList(nil) -> tt 20.60/20.92 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.60/20.92 a__isList(X:S) -> isList(X:S) 20.60/20.92 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.92 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.92 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.60/20.92 a__isNeList(X:S) -> isNeList(X:S) 20.60/20.92 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.92 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.60/20.92 a__isNePal(X:S) -> isNePal(X:S) 20.60/20.92 a__isPal(nil) -> tt 20.60/20.92 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.60/20.92 a__isPal(X:S) -> isPal(X:S) 20.60/20.92 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.92 a__isPalListKind(a) -> tt 20.60/20.92 a__isPalListKind(e) -> tt 20.60/20.92 a__isPalListKind(i) -> tt 20.60/20.92 a__isPalListKind(nil) -> tt 20.60/20.92 a__isPalListKind(o) -> tt 20.60/20.92 a__isPalListKind(u) -> tt 20.60/20.92 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.60/20.92 a__isQid(a) -> tt 20.60/20.92 a__isQid(e) -> tt 20.60/20.92 a__isQid(i) -> tt 20.60/20.92 a__isQid(o) -> tt 20.60/20.92 a__isQid(u) -> tt 20.60/20.92 a__isQid(X:S) -> isQid(X:S) 20.60/20.92 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.60/20.92 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.60/20.92 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.60/20.92 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.60/20.92 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.60/20.92 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.60/20.92 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.60/20.92 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.60/20.92 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.60/20.92 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.60/20.92 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.60/20.92 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.60/20.92 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.60/20.92 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.60/20.92 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.60/20.92 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.60/20.92 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.60/20.92 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.60/20.92 mark(a) -> a 20.60/20.92 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.60/20.92 mark(e) -> e 20.60/20.92 mark(i) -> i 20.60/20.92 mark(isList(X:S)) -> a__isList(X:S) 20.60/20.92 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.60/20.92 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.60/20.92 mark(isPal(X:S)) -> a__isPal(X:S) 20.60/20.92 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.60/20.92 mark(isQid(X:S)) -> a__isQid(X:S) 20.60/20.92 mark(nil) -> nil 20.60/20.92 mark(o) -> o 20.60/20.92 mark(tt) -> tt 20.60/20.92 mark(u) -> u 20.60/20.92 -> Usable rules: 20.60/20.92 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.60/20.92 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.60/20.92 a__U12(tt) -> tt 20.60/20.92 a__U12(X:S) -> U12(X:S) 20.60/20.92 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.60/20.92 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.60/20.92 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.60/20.92 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.60/20.92 a__U23(tt) -> tt 20.60/20.92 a__U23(X:S) -> U23(X:S) 20.60/20.92 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.60/20.92 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.60/20.92 a__U32(tt) -> tt 20.60/20.92 a__U32(X:S) -> U32(X:S) 20.60/20.92 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.60/20.92 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.60/20.92 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.60/20.92 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.60/20.92 a__U43(tt) -> tt 20.60/20.92 a__U43(X:S) -> U43(X:S) 20.60/20.92 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.60/20.92 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.60/20.92 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.60/20.92 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.60/20.92 a__U53(tt) -> tt 20.60/20.92 a__U53(X:S) -> U53(X:S) 20.60/20.92 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.60/20.92 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.60/20.92 a__U62(tt) -> tt 20.60/20.92 a__U62(X:S) -> U62(X:S) 20.60/20.92 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.60/20.92 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.60/20.92 a__U72(tt) -> tt 20.60/20.92 a__U72(X:S) -> U72(X:S) 20.60/20.92 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.60/20.92 a____(nil,X:S) -> mark(X:S) 20.60/20.92 a____(X:S,nil) -> mark(X:S) 20.60/20.92 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.60/20.92 a__and(tt,X:S) -> mark(X:S) 20.60/20.92 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.60/20.92 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.92 a__isList(nil) -> tt 20.60/20.92 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.60/20.92 a__isList(X:S) -> isList(X:S) 20.60/20.92 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.92 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.92 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.60/20.92 a__isNeList(X:S) -> isNeList(X:S) 20.60/20.92 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.92 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.60/20.92 a__isNePal(X:S) -> isNePal(X:S) 20.60/20.92 a__isPal(nil) -> tt 20.60/20.92 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.60/20.92 a__isPal(X:S) -> isPal(X:S) 20.60/20.92 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.92 a__isPalListKind(a) -> tt 20.60/20.92 a__isPalListKind(e) -> tt 20.60/20.92 a__isPalListKind(i) -> tt 20.60/20.92 a__isPalListKind(nil) -> tt 20.60/20.92 a__isPalListKind(o) -> tt 20.60/20.92 a__isPalListKind(u) -> tt 20.60/20.92 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.60/20.92 a__isQid(a) -> tt 20.60/20.92 a__isQid(e) -> tt 20.60/20.92 a__isQid(i) -> tt 20.60/20.92 a__isQid(o) -> tt 20.60/20.92 a__isQid(u) -> tt 20.60/20.92 a__isQid(X:S) -> isQid(X:S) 20.60/20.92 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.60/20.92 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.60/20.92 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.60/20.92 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.60/20.93 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.60/20.93 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.60/20.93 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.60/20.93 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.60/20.93 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.60/20.93 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.60/20.93 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.60/20.93 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.60/20.93 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.60/20.93 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.60/20.93 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.60/20.93 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.60/20.93 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.60/20.93 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.60/20.93 mark(a) -> a 20.60/20.93 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.60/20.93 mark(e) -> e 20.60/20.93 mark(i) -> i 20.60/20.93 mark(isList(X:S)) -> a__isList(X:S) 20.60/20.93 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.60/20.93 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.60/20.93 mark(isPal(X:S)) -> a__isPal(X:S) 20.60/20.93 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.60/20.93 mark(isQid(X:S)) -> a__isQid(X:S) 20.60/20.93 mark(nil) -> nil 20.60/20.93 mark(o) -> o 20.60/20.93 mark(tt) -> tt 20.60/20.93 mark(u) -> u 20.60/20.93 ->Interpretation type: 20.60/20.93 Linear 20.60/20.93 ->Coefficients: 20.60/20.93 Natural Numbers 20.60/20.93 ->Dimension: 20.60/20.93 1 20.60/20.93 ->Bound: 20.60/20.93 2 20.60/20.93 ->Interpretation: 20.60/20.93 20.60/20.93 [a__U11](X1,X2) = 2.X1 + 2.X2 + 1 20.60/20.93 [a__U12](X) = X 20.60/20.93 [a__U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.60/20.93 [a__U22](X1,X2) = X1 + 2.X2 + 1 20.60/20.93 [a__U23](X) = X 20.60/20.93 [a__U31](X1,X2) = 2.X1 + 2.X2 + 1 20.60/20.93 [a__U32](X) = X 20.60/20.93 [a__U41](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 20.60/20.93 [a__U42](X1,X2) = X1 + 2.X2 + 1 20.60/20.93 [a__U43](X) = X 20.60/20.93 [a__U51](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 20.60/20.93 [a__U52](X1,X2) = X1 + 2.X2 + 1 20.60/20.93 [a__U53](X) = X 20.60/20.93 [a__U61](X1,X2) = X1 + 2.X2 + 2 20.60/20.93 [a__U62](X) = X 20.60/20.93 [a__U71](X1,X2) = 2.X1 + 2.X2 + 2 20.60/20.93 [a__U72](X) = X 20.60/20.93 [a____](X1,X2) = 2.X1 + X2 + 2 20.60/20.93 [a__and](X1,X2) = X1 + 2.X2 20.60/20.93 [a__isList](X) = 2.X + 1 20.60/20.93 [a__isNeList](X) = 2.X + 1 20.60/20.93 [a__isNePal](X) = 2.X + 2 20.60/20.93 [a__isPal](X) = 2.X + 2 20.60/20.93 [a__isPalListKind](X) = 0 20.60/20.93 [a__isQid](X) = 2.X + 1 20.60/20.93 [mark](X) = X 20.60/20.93 [U11](X1,X2) = 2.X1 + 2.X2 + 1 20.60/20.93 [U12](X) = X 20.60/20.93 [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.60/20.93 [U22](X1,X2) = X1 + 2.X2 + 1 20.60/20.93 [U23](X) = X 20.60/20.93 [U31](X1,X2) = 2.X1 + 2.X2 + 1 20.60/20.93 [U32](X) = X 20.60/20.93 [U41](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 20.60/20.93 [U42](X1,X2) = X1 + 2.X2 + 1 20.60/20.93 [U43](X) = X 20.60/20.93 [U51](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 20.60/20.93 [U52](X1,X2) = X1 + 2.X2 + 1 20.60/20.93 [U53](X) = X 20.60/20.93 [U61](X1,X2) = X1 + 2.X2 + 2 20.60/20.93 [U62](X) = X 20.60/20.93 [U71](X1,X2) = 2.X1 + 2.X2 + 2 20.60/20.93 [U72](X) = X 20.60/20.93 [__](X1,X2) = 2.X1 + X2 + 2 20.60/20.93 [a] = 1 20.60/20.93 [and](X1,X2) = X1 + 2.X2 20.60/20.93 [e] = 1 20.60/20.93 [fSNonEmpty] = 0 20.60/20.93 [i] = 2 20.60/20.93 [isList](X) = 2.X + 1 20.60/20.93 [isNeList](X) = 2.X + 1 20.60/20.93 [isNePal](X) = 2.X + 2 20.60/20.93 [isPal](X) = 2.X + 2 20.60/20.93 [isPalListKind](X) = 0 20.60/20.93 [isQid](X) = 2.X + 1 20.60/20.93 [nil] = 2 20.60/20.93 [o] = 2 20.60/20.93 [tt] = 0 20.60/20.93 [u] = 2 20.60/20.93 [A__U11](X1,X2) = 0 20.60/20.93 [A__U12](X) = 0 20.60/20.93 [A__U21](X1,X2,X3) = 0 20.60/20.93 [A__U22](X1,X2) = 0 20.60/20.93 [A__U23](X) = 0 20.60/20.93 [A__U31](X1,X2) = 0 20.60/20.93 [A__U32](X) = 0 20.60/20.93 [A__U41](X1,X2,X3) = 0 20.60/20.93 [A__U42](X1,X2) = 0 20.60/20.93 [A__U43](X) = 0 20.60/20.93 [A__U51](X1,X2,X3) = 0 20.60/20.93 [A__U52](X1,X2) = 0 20.60/20.93 [A__U53](X) = 0 20.60/20.93 [A__U61](X1,X2) = 0 20.60/20.93 [A__U62](X) = 0 20.60/20.93 [A__U71](X1,X2) = 0 20.60/20.93 [A__U72](X) = 0 20.60/20.93 [A____](X1,X2) = 0 20.60/20.93 [A__AND](X1,X2) = X1 + 2.X2 20.60/20.93 [A__ISLIST](X) = 0 20.60/20.93 [A__ISNELIST](X) = 0 20.60/20.93 [A__ISNEPAL](X) = 0 20.60/20.93 [A__ISPAL](X) = X + 2 20.60/20.93 [A__ISPALLISTKIND](X) = 0 20.60/20.93 [A__ISQID](X) = 0 20.60/20.93 [MARK](X) = X 20.60/20.93 20.60/20.93 Problem 1: 20.60/20.93 20.60/20.93 SCC Processor: 20.60/20.93 -> Pairs: 20.60/20.93 A__AND(tt,X:S) -> MARK(X:S) 20.60/20.93 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.93 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.93 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(U12(X:S)) -> MARK(X:S) 20.60/20.93 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.93 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(U23(X:S)) -> MARK(X:S) 20.60/20.93 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(U32(X:S)) -> MARK(X:S) 20.60/20.93 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.93 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(U43(X:S)) -> MARK(X:S) 20.60/20.93 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.93 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(U53(X:S)) -> MARK(X:S) 20.60/20.93 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(U62(X:S)) -> MARK(X:S) 20.60/20.93 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(U72(X:S)) -> MARK(X:S) 20.60/20.93 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.60/20.93 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.60/20.93 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(isPal(X:S)) -> A__ISPAL(X:S) 20.60/20.93 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.60/20.93 -> Rules: 20.60/20.93 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.60/20.93 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.60/20.93 a__U12(tt) -> tt 20.60/20.93 a__U12(X:S) -> U12(X:S) 20.60/20.93 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.60/20.93 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.60/20.93 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.60/20.93 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.60/20.93 a__U23(tt) -> tt 20.60/20.93 a__U23(X:S) -> U23(X:S) 20.60/20.93 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.60/20.93 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.60/20.93 a__U32(tt) -> tt 20.60/20.93 a__U32(X:S) -> U32(X:S) 20.60/20.93 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.60/20.93 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.60/20.93 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.60/20.93 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.60/20.93 a__U43(tt) -> tt 20.60/20.93 a__U43(X:S) -> U43(X:S) 20.60/20.93 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.60/20.93 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.60/20.93 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.60/20.93 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.60/20.93 a__U53(tt) -> tt 20.60/20.93 a__U53(X:S) -> U53(X:S) 20.60/20.93 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.60/20.93 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.60/20.93 a__U62(tt) -> tt 20.60/20.93 a__U62(X:S) -> U62(X:S) 20.60/20.93 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.60/20.93 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.60/20.93 a__U72(tt) -> tt 20.60/20.93 a__U72(X:S) -> U72(X:S) 20.60/20.93 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.60/20.93 a____(nil,X:S) -> mark(X:S) 20.60/20.93 a____(X:S,nil) -> mark(X:S) 20.60/20.93 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.60/20.93 a__and(tt,X:S) -> mark(X:S) 20.60/20.93 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.60/20.93 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.93 a__isList(nil) -> tt 20.60/20.93 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.60/20.93 a__isList(X:S) -> isList(X:S) 20.60/20.93 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.93 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.93 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.60/20.93 a__isNeList(X:S) -> isNeList(X:S) 20.60/20.93 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.93 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.60/20.93 a__isNePal(X:S) -> isNePal(X:S) 20.60/20.93 a__isPal(nil) -> tt 20.60/20.93 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.60/20.93 a__isPal(X:S) -> isPal(X:S) 20.60/20.93 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.93 a__isPalListKind(a) -> tt 20.60/20.93 a__isPalListKind(e) -> tt 20.60/20.93 a__isPalListKind(i) -> tt 20.60/20.93 a__isPalListKind(nil) -> tt 20.60/20.93 a__isPalListKind(o) -> tt 20.60/20.93 a__isPalListKind(u) -> tt 20.60/20.93 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.60/20.93 a__isQid(a) -> tt 20.60/20.93 a__isQid(e) -> tt 20.60/20.93 a__isQid(i) -> tt 20.60/20.93 a__isQid(o) -> tt 20.60/20.93 a__isQid(u) -> tt 20.60/20.93 a__isQid(X:S) -> isQid(X:S) 20.60/20.93 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.60/20.93 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.60/20.93 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.60/20.93 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.60/20.93 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.60/20.93 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.60/20.93 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.60/20.93 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.60/20.93 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.60/20.93 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.60/20.93 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.60/20.93 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.60/20.93 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.60/20.93 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.60/20.93 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.60/20.93 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.60/20.93 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.60/20.93 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.60/20.93 mark(a) -> a 20.60/20.93 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.60/20.93 mark(e) -> e 20.60/20.93 mark(i) -> i 20.60/20.93 mark(isList(X:S)) -> a__isList(X:S) 20.60/20.93 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.60/20.93 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.60/20.93 mark(isPal(X:S)) -> a__isPal(X:S) 20.60/20.93 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.60/20.93 mark(isQid(X:S)) -> a__isQid(X:S) 20.60/20.93 mark(nil) -> nil 20.60/20.93 mark(o) -> o 20.60/20.93 mark(tt) -> tt 20.60/20.93 mark(u) -> u 20.60/20.93 ->Strongly Connected Components: 20.60/20.93 ->->Cycle: 20.60/20.93 ->->-> Pairs: 20.60/20.93 A__AND(tt,X:S) -> MARK(X:S) 20.60/20.93 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.93 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.93 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(U12(X:S)) -> MARK(X:S) 20.60/20.93 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.93 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(U23(X:S)) -> MARK(X:S) 20.60/20.93 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(U32(X:S)) -> MARK(X:S) 20.60/20.93 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.93 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(U43(X:S)) -> MARK(X:S) 20.60/20.93 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.93 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(U53(X:S)) -> MARK(X:S) 20.60/20.93 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(U62(X:S)) -> MARK(X:S) 20.60/20.93 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(U72(X:S)) -> MARK(X:S) 20.60/20.93 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.60/20.93 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.60/20.93 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.60/20.93 ->->-> Rules: 20.60/20.93 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.60/20.93 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.60/20.93 a__U12(tt) -> tt 20.60/20.93 a__U12(X:S) -> U12(X:S) 20.60/20.93 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.60/20.93 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.60/20.93 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.60/20.93 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.60/20.93 a__U23(tt) -> tt 20.60/20.93 a__U23(X:S) -> U23(X:S) 20.60/20.93 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.60/20.93 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.60/20.93 a__U32(tt) -> tt 20.60/20.93 a__U32(X:S) -> U32(X:S) 20.60/20.93 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.60/20.93 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.60/20.93 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.60/20.93 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.60/20.93 a__U43(tt) -> tt 20.60/20.93 a__U43(X:S) -> U43(X:S) 20.60/20.93 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.60/20.93 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.60/20.93 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.60/20.93 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.60/20.93 a__U53(tt) -> tt 20.60/20.93 a__U53(X:S) -> U53(X:S) 20.60/20.93 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.60/20.93 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.60/20.93 a__U62(tt) -> tt 20.60/20.93 a__U62(X:S) -> U62(X:S) 20.60/20.93 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.60/20.93 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.60/20.93 a__U72(tt) -> tt 20.60/20.93 a__U72(X:S) -> U72(X:S) 20.60/20.93 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.60/20.93 a____(nil,X:S) -> mark(X:S) 20.60/20.93 a____(X:S,nil) -> mark(X:S) 20.60/20.93 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.60/20.93 a__and(tt,X:S) -> mark(X:S) 20.60/20.93 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.60/20.93 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.93 a__isList(nil) -> tt 20.60/20.93 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.60/20.93 a__isList(X:S) -> isList(X:S) 20.60/20.93 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.93 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.93 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.60/20.93 a__isNeList(X:S) -> isNeList(X:S) 20.60/20.93 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.93 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.60/20.93 a__isNePal(X:S) -> isNePal(X:S) 20.60/20.93 a__isPal(nil) -> tt 20.60/20.93 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.60/20.93 a__isPal(X:S) -> isPal(X:S) 20.60/20.93 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.93 a__isPalListKind(a) -> tt 20.60/20.93 a__isPalListKind(e) -> tt 20.60/20.93 a__isPalListKind(i) -> tt 20.60/20.93 a__isPalListKind(nil) -> tt 20.60/20.93 a__isPalListKind(o) -> tt 20.60/20.93 a__isPalListKind(u) -> tt 20.60/20.93 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.60/20.93 a__isQid(a) -> tt 20.60/20.93 a__isQid(e) -> tt 20.60/20.93 a__isQid(i) -> tt 20.60/20.93 a__isQid(o) -> tt 20.60/20.93 a__isQid(u) -> tt 20.60/20.93 a__isQid(X:S) -> isQid(X:S) 20.60/20.93 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.60/20.93 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.60/20.93 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.60/20.93 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.60/20.93 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.60/20.93 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.60/20.93 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.60/20.93 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.60/20.93 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.60/20.93 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.60/20.93 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.60/20.93 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.60/20.93 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.60/20.93 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.60/20.93 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.60/20.93 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.60/20.93 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.60/20.93 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.60/20.93 mark(a) -> a 20.60/20.93 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.60/20.93 mark(e) -> e 20.60/20.93 mark(i) -> i 20.60/20.93 mark(isList(X:S)) -> a__isList(X:S) 20.60/20.93 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.60/20.93 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.60/20.93 mark(isPal(X:S)) -> a__isPal(X:S) 20.60/20.93 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.60/20.93 mark(isQid(X:S)) -> a__isQid(X:S) 20.60/20.93 mark(nil) -> nil 20.60/20.93 mark(o) -> o 20.60/20.93 mark(tt) -> tt 20.60/20.93 mark(u) -> u 20.60/20.93 20.60/20.93 Problem 1: 20.60/20.93 20.60/20.93 Reduction Pairs Processor: 20.60/20.93 -> Pairs: 20.60/20.93 A__AND(tt,X:S) -> MARK(X:S) 20.60/20.93 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.93 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.93 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(U12(X:S)) -> MARK(X:S) 20.60/20.93 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.93 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(U23(X:S)) -> MARK(X:S) 20.60/20.93 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(U32(X:S)) -> MARK(X:S) 20.60/20.93 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.93 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(U43(X:S)) -> MARK(X:S) 20.60/20.93 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.93 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(U53(X:S)) -> MARK(X:S) 20.60/20.93 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(U62(X:S)) -> MARK(X:S) 20.60/20.93 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(U72(X:S)) -> MARK(X:S) 20.60/20.93 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.60/20.93 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.60/20.93 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.60/20.93 -> Rules: 20.60/20.93 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.60/20.93 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.60/20.93 a__U12(tt) -> tt 20.60/20.93 a__U12(X:S) -> U12(X:S) 20.60/20.93 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.60/20.93 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.60/20.93 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.60/20.93 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.60/20.93 a__U23(tt) -> tt 20.60/20.93 a__U23(X:S) -> U23(X:S) 20.60/20.93 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.60/20.93 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.60/20.93 a__U32(tt) -> tt 20.60/20.93 a__U32(X:S) -> U32(X:S) 20.60/20.93 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.60/20.93 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.60/20.93 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.60/20.93 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.60/20.93 a__U43(tt) -> tt 20.60/20.93 a__U43(X:S) -> U43(X:S) 20.60/20.93 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.60/20.93 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.60/20.93 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.60/20.93 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.60/20.93 a__U53(tt) -> tt 20.60/20.93 a__U53(X:S) -> U53(X:S) 20.60/20.93 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.60/20.93 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.60/20.93 a__U62(tt) -> tt 20.60/20.93 a__U62(X:S) -> U62(X:S) 20.60/20.93 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.60/20.93 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.60/20.93 a__U72(tt) -> tt 20.60/20.93 a__U72(X:S) -> U72(X:S) 20.60/20.93 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.60/20.93 a____(nil,X:S) -> mark(X:S) 20.60/20.93 a____(X:S,nil) -> mark(X:S) 20.60/20.93 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.60/20.93 a__and(tt,X:S) -> mark(X:S) 20.60/20.93 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.60/20.93 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.93 a__isList(nil) -> tt 20.60/20.93 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.60/20.93 a__isList(X:S) -> isList(X:S) 20.60/20.93 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.93 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.93 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.60/20.93 a__isNeList(X:S) -> isNeList(X:S) 20.60/20.93 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.93 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.60/20.93 a__isNePal(X:S) -> isNePal(X:S) 20.60/20.93 a__isPal(nil) -> tt 20.60/20.93 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.60/20.93 a__isPal(X:S) -> isPal(X:S) 20.60/20.93 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.93 a__isPalListKind(a) -> tt 20.60/20.93 a__isPalListKind(e) -> tt 20.60/20.93 a__isPalListKind(i) -> tt 20.60/20.93 a__isPalListKind(nil) -> tt 20.60/20.93 a__isPalListKind(o) -> tt 20.60/20.93 a__isPalListKind(u) -> tt 20.60/20.93 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.60/20.93 a__isQid(a) -> tt 20.60/20.93 a__isQid(e) -> tt 20.60/20.93 a__isQid(i) -> tt 20.60/20.93 a__isQid(o) -> tt 20.60/20.93 a__isQid(u) -> tt 20.60/20.93 a__isQid(X:S) -> isQid(X:S) 20.60/20.93 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.60/20.93 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.60/20.93 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.60/20.93 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.60/20.93 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.60/20.93 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.60/20.93 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.60/20.93 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.60/20.93 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.60/20.93 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.60/20.93 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.60/20.93 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.60/20.93 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.60/20.93 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.60/20.93 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.60/20.93 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.60/20.93 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.60/20.93 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.60/20.93 mark(a) -> a 20.60/20.93 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.60/20.93 mark(e) -> e 20.60/20.93 mark(i) -> i 20.60/20.93 mark(isList(X:S)) -> a__isList(X:S) 20.60/20.93 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.60/20.93 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.60/20.93 mark(isPal(X:S)) -> a__isPal(X:S) 20.60/20.93 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.60/20.93 mark(isQid(X:S)) -> a__isQid(X:S) 20.60/20.93 mark(nil) -> nil 20.60/20.93 mark(o) -> o 20.60/20.93 mark(tt) -> tt 20.60/20.93 mark(u) -> u 20.60/20.93 -> Usable rules: 20.60/20.93 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.60/20.93 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.60/20.93 a__U12(tt) -> tt 20.60/20.93 a__U12(X:S) -> U12(X:S) 20.60/20.93 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.60/20.93 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.60/20.93 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.60/20.93 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.60/20.93 a__U23(tt) -> tt 20.60/20.93 a__U23(X:S) -> U23(X:S) 20.60/20.93 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.60/20.93 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.60/20.93 a__U32(tt) -> tt 20.60/20.93 a__U32(X:S) -> U32(X:S) 20.60/20.93 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.60/20.93 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.60/20.93 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.60/20.93 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.60/20.93 a__U43(tt) -> tt 20.60/20.93 a__U43(X:S) -> U43(X:S) 20.60/20.93 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.60/20.93 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.60/20.93 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.60/20.93 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.60/20.93 a__U53(tt) -> tt 20.60/20.93 a__U53(X:S) -> U53(X:S) 20.60/20.93 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.60/20.93 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.60/20.93 a__U62(tt) -> tt 20.60/20.93 a__U62(X:S) -> U62(X:S) 20.60/20.93 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.60/20.93 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.60/20.93 a__U72(tt) -> tt 20.60/20.93 a__U72(X:S) -> U72(X:S) 20.60/20.93 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.60/20.93 a____(nil,X:S) -> mark(X:S) 20.60/20.93 a____(X:S,nil) -> mark(X:S) 20.60/20.93 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.60/20.93 a__and(tt,X:S) -> mark(X:S) 20.60/20.93 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.60/20.93 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.93 a__isList(nil) -> tt 20.60/20.93 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.60/20.93 a__isList(X:S) -> isList(X:S) 20.60/20.93 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.93 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.93 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.60/20.93 a__isNeList(X:S) -> isNeList(X:S) 20.60/20.93 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.93 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.60/20.93 a__isNePal(X:S) -> isNePal(X:S) 20.60/20.93 a__isPal(nil) -> tt 20.60/20.93 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.60/20.93 a__isPal(X:S) -> isPal(X:S) 20.60/20.93 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.93 a__isPalListKind(a) -> tt 20.60/20.93 a__isPalListKind(e) -> tt 20.60/20.93 a__isPalListKind(i) -> tt 20.60/20.93 a__isPalListKind(nil) -> tt 20.60/20.93 a__isPalListKind(o) -> tt 20.60/20.93 a__isPalListKind(u) -> tt 20.60/20.93 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.60/20.93 a__isQid(a) -> tt 20.60/20.93 a__isQid(e) -> tt 20.60/20.93 a__isQid(i) -> tt 20.60/20.93 a__isQid(o) -> tt 20.60/20.93 a__isQid(u) -> tt 20.60/20.93 a__isQid(X:S) -> isQid(X:S) 20.60/20.93 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.60/20.93 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.60/20.93 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.60/20.93 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.60/20.93 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.60/20.93 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.60/20.93 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.60/20.93 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.60/20.93 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.60/20.93 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.60/20.93 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.60/20.93 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.60/20.93 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.60/20.93 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.60/20.93 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.60/20.93 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.60/20.93 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.60/20.93 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.60/20.93 mark(a) -> a 20.60/20.93 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.60/20.93 mark(e) -> e 20.60/20.93 mark(i) -> i 20.60/20.93 mark(isList(X:S)) -> a__isList(X:S) 20.60/20.93 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.60/20.93 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.60/20.93 mark(isPal(X:S)) -> a__isPal(X:S) 20.60/20.93 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.60/20.93 mark(isQid(X:S)) -> a__isQid(X:S) 20.60/20.93 mark(nil) -> nil 20.60/20.93 mark(o) -> o 20.60/20.93 mark(tt) -> tt 20.60/20.93 mark(u) -> u 20.60/20.93 ->Interpretation type: 20.60/20.93 Linear 20.60/20.93 ->Coefficients: 20.60/20.93 Natural Numbers 20.60/20.93 ->Dimension: 20.60/20.93 1 20.60/20.93 ->Bound: 20.60/20.93 2 20.60/20.93 ->Interpretation: 20.60/20.93 20.60/20.93 [a__U11](X1,X2) = 2.X1 + 2.X2 + 1 20.60/20.93 [a__U12](X) = X 20.60/20.93 [a__U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.60/20.93 [a__U22](X1,X2) = X1 + 2.X2 + 1 20.60/20.93 [a__U23](X) = X 20.60/20.93 [a__U31](X1,X2) = 2.X1 + 2.X2 20.60/20.93 [a__U32](X) = 2.X 20.60/20.93 [a__U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.60/20.93 [a__U42](X1,X2) = X1 + 2.X2 + 1 20.60/20.93 [a__U43](X) = X + 1 20.60/20.93 [a__U51](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 20.60/20.93 [a__U52](X1,X2) = X1 + 2.X2 + 2 20.60/20.93 [a__U53](X) = X + 1 20.60/20.93 [a__U61](X1,X2) = X1 + 2.X2 + 2 20.60/20.93 [a__U62](X) = 2.X 20.60/20.93 [a__U71](X1,X2) = X1 + 2.X2 + 2 20.60/20.93 [a__U72](X) = X 20.60/20.93 [a____](X1,X2) = 2.X1 + X2 + 2 20.60/20.93 [a__and](X1,X2) = 2.X1 + X2 20.60/20.93 [a__isList](X) = 2.X + 1 20.60/20.93 [a__isNeList](X) = 2.X 20.60/20.93 [a__isNePal](X) = 2.X + 2 20.60/20.93 [a__isPal](X) = 2.X + 2 20.60/20.93 [a__isPalListKind](X) = 0 20.60/20.93 [a__isQid](X) = X 20.60/20.93 [mark](X) = X 20.60/20.93 [U11](X1,X2) = 2.X1 + 2.X2 + 1 20.60/20.93 [U12](X) = X 20.60/20.93 [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.60/20.93 [U22](X1,X2) = X1 + 2.X2 + 1 20.60/20.93 [U23](X) = X 20.60/20.93 [U31](X1,X2) = 2.X1 + 2.X2 20.60/20.93 [U32](X) = 2.X 20.60/20.93 [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.60/20.93 [U42](X1,X2) = X1 + 2.X2 + 1 20.60/20.93 [U43](X) = X + 1 20.60/20.93 [U51](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 20.60/20.93 [U52](X1,X2) = X1 + 2.X2 + 2 20.60/20.93 [U53](X) = X + 1 20.60/20.93 [U61](X1,X2) = X1 + 2.X2 + 2 20.60/20.93 [U62](X) = 2.X 20.60/20.93 [U71](X1,X2) = X1 + 2.X2 + 2 20.60/20.93 [U72](X) = X 20.60/20.93 [__](X1,X2) = 2.X1 + X2 + 2 20.60/20.93 [a] = 1 20.60/20.93 [and](X1,X2) = 2.X1 + X2 20.60/20.93 [e] = 0 20.60/20.93 [fSNonEmpty] = 0 20.60/20.93 [i] = 0 20.60/20.93 [isList](X) = 2.X + 1 20.60/20.93 [isNeList](X) = 2.X 20.60/20.93 [isNePal](X) = 2.X + 2 20.60/20.93 [isPal](X) = 2.X + 2 20.60/20.93 [isPalListKind](X) = 0 20.60/20.93 [isQid](X) = X 20.60/20.93 [nil] = 1 20.60/20.93 [o] = 0 20.60/20.93 [tt] = 0 20.60/20.93 [u] = 1 20.60/20.93 [A__U11](X1,X2) = 0 20.60/20.93 [A__U12](X) = 0 20.60/20.93 [A__U21](X1,X2,X3) = 0 20.60/20.93 [A__U22](X1,X2) = 0 20.60/20.93 [A__U23](X) = 0 20.60/20.93 [A__U31](X1,X2) = 0 20.60/20.93 [A__U32](X) = 0 20.60/20.93 [A__U41](X1,X2,X3) = 0 20.60/20.93 [A__U42](X1,X2) = 0 20.60/20.93 [A__U43](X) = 0 20.60/20.93 [A__U51](X1,X2,X3) = 0 20.60/20.93 [A__U52](X1,X2) = 0 20.60/20.93 [A__U53](X) = 0 20.60/20.93 [A__U61](X1,X2) = 0 20.60/20.93 [A__U62](X) = 0 20.60/20.93 [A__U71](X1,X2) = 0 20.60/20.93 [A__U72](X) = 0 20.60/20.93 [A____](X1,X2) = 0 20.60/20.93 [A__AND](X1,X2) = 2.X2 + 2 20.60/20.93 [A__ISLIST](X) = 0 20.60/20.93 [A__ISNELIST](X) = 0 20.60/20.93 [A__ISNEPAL](X) = 0 20.60/20.93 [A__ISPAL](X) = 0 20.60/20.93 [A__ISPALLISTKIND](X) = 2 20.60/20.93 [A__ISQID](X) = 0 20.60/20.93 [MARK](X) = 2.X + 2 20.60/20.93 20.60/20.93 Problem 1: 20.60/20.93 20.60/20.93 SCC Processor: 20.60/20.93 -> Pairs: 20.60/20.93 A__AND(tt,X:S) -> MARK(X:S) 20.60/20.93 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.93 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.93 MARK(U12(X:S)) -> MARK(X:S) 20.60/20.93 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.93 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(U23(X:S)) -> MARK(X:S) 20.60/20.93 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(U32(X:S)) -> MARK(X:S) 20.60/20.93 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.93 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(U43(X:S)) -> MARK(X:S) 20.60/20.93 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.93 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(U53(X:S)) -> MARK(X:S) 20.60/20.93 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(U62(X:S)) -> MARK(X:S) 20.60/20.93 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(U72(X:S)) -> MARK(X:S) 20.60/20.93 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.60/20.93 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.60/20.93 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.60/20.93 -> Rules: 20.60/20.93 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.60/20.93 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.60/20.93 a__U12(tt) -> tt 20.60/20.93 a__U12(X:S) -> U12(X:S) 20.60/20.93 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.60/20.93 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.60/20.93 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.60/20.93 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.60/20.93 a__U23(tt) -> tt 20.60/20.93 a__U23(X:S) -> U23(X:S) 20.60/20.93 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.60/20.93 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.60/20.93 a__U32(tt) -> tt 20.60/20.93 a__U32(X:S) -> U32(X:S) 20.60/20.93 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.60/20.93 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.60/20.93 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.60/20.93 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.60/20.93 a__U43(tt) -> tt 20.60/20.93 a__U43(X:S) -> U43(X:S) 20.60/20.93 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.60/20.93 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.60/20.93 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.60/20.93 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.60/20.93 a__U53(tt) -> tt 20.60/20.93 a__U53(X:S) -> U53(X:S) 20.60/20.93 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.60/20.93 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.60/20.93 a__U62(tt) -> tt 20.60/20.93 a__U62(X:S) -> U62(X:S) 20.60/20.93 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.60/20.93 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.60/20.93 a__U72(tt) -> tt 20.60/20.93 a__U72(X:S) -> U72(X:S) 20.60/20.93 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.60/20.93 a____(nil,X:S) -> mark(X:S) 20.60/20.93 a____(X:S,nil) -> mark(X:S) 20.60/20.93 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.60/20.93 a__and(tt,X:S) -> mark(X:S) 20.60/20.93 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.60/20.93 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.93 a__isList(nil) -> tt 20.60/20.93 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.60/20.93 a__isList(X:S) -> isList(X:S) 20.60/20.93 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.93 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.93 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.60/20.93 a__isNeList(X:S) -> isNeList(X:S) 20.60/20.93 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.93 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.60/20.93 a__isNePal(X:S) -> isNePal(X:S) 20.60/20.93 a__isPal(nil) -> tt 20.60/20.93 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.60/20.93 a__isPal(X:S) -> isPal(X:S) 20.60/20.93 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.93 a__isPalListKind(a) -> tt 20.60/20.93 a__isPalListKind(e) -> tt 20.60/20.93 a__isPalListKind(i) -> tt 20.60/20.93 a__isPalListKind(nil) -> tt 20.60/20.93 a__isPalListKind(o) -> tt 20.60/20.93 a__isPalListKind(u) -> tt 20.60/20.93 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.60/20.93 a__isQid(a) -> tt 20.60/20.93 a__isQid(e) -> tt 20.60/20.93 a__isQid(i) -> tt 20.60/20.93 a__isQid(o) -> tt 20.60/20.93 a__isQid(u) -> tt 20.60/20.93 a__isQid(X:S) -> isQid(X:S) 20.60/20.93 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.60/20.93 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.60/20.93 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.60/20.93 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.60/20.93 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.60/20.93 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.60/20.93 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.60/20.93 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.60/20.93 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.60/20.93 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.60/20.93 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.60/20.93 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.60/20.93 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.60/20.93 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.60/20.93 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.60/20.93 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.60/20.93 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.60/20.93 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.60/20.93 mark(a) -> a 20.60/20.93 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.60/20.93 mark(e) -> e 20.60/20.93 mark(i) -> i 20.60/20.93 mark(isList(X:S)) -> a__isList(X:S) 20.60/20.93 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.60/20.93 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.60/20.93 mark(isPal(X:S)) -> a__isPal(X:S) 20.60/20.93 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.60/20.93 mark(isQid(X:S)) -> a__isQid(X:S) 20.60/20.93 mark(nil) -> nil 20.60/20.93 mark(o) -> o 20.60/20.93 mark(tt) -> tt 20.60/20.93 mark(u) -> u 20.60/20.93 ->Strongly Connected Components: 20.60/20.93 ->->Cycle: 20.60/20.93 ->->-> Pairs: 20.60/20.93 A__AND(tt,X:S) -> MARK(X:S) 20.60/20.93 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.93 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.93 MARK(U12(X:S)) -> MARK(X:S) 20.60/20.93 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.93 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(U23(X:S)) -> MARK(X:S) 20.60/20.93 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(U32(X:S)) -> MARK(X:S) 20.60/20.93 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.93 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(U43(X:S)) -> MARK(X:S) 20.60/20.93 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.93 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(U53(X:S)) -> MARK(X:S) 20.60/20.93 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(U62(X:S)) -> MARK(X:S) 20.60/20.93 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(U72(X:S)) -> MARK(X:S) 20.60/20.93 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.60/20.93 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.60/20.93 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.60/20.93 ->->-> Rules: 20.60/20.93 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.60/20.93 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.60/20.93 a__U12(tt) -> tt 20.60/20.93 a__U12(X:S) -> U12(X:S) 20.60/20.93 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.60/20.93 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.60/20.93 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.60/20.93 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.60/20.93 a__U23(tt) -> tt 20.60/20.93 a__U23(X:S) -> U23(X:S) 20.60/20.93 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.60/20.93 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.60/20.93 a__U32(tt) -> tt 20.60/20.93 a__U32(X:S) -> U32(X:S) 20.60/20.93 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.60/20.93 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.60/20.93 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.60/20.93 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.60/20.93 a__U43(tt) -> tt 20.60/20.93 a__U43(X:S) -> U43(X:S) 20.60/20.93 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.60/20.93 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.60/20.93 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.60/20.93 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.60/20.93 a__U53(tt) -> tt 20.60/20.93 a__U53(X:S) -> U53(X:S) 20.60/20.93 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.60/20.93 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.60/20.93 a__U62(tt) -> tt 20.60/20.93 a__U62(X:S) -> U62(X:S) 20.60/20.93 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.60/20.93 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.60/20.93 a__U72(tt) -> tt 20.60/20.93 a__U72(X:S) -> U72(X:S) 20.60/20.93 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.60/20.93 a____(nil,X:S) -> mark(X:S) 20.60/20.93 a____(X:S,nil) -> mark(X:S) 20.60/20.93 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.60/20.93 a__and(tt,X:S) -> mark(X:S) 20.60/20.93 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.60/20.93 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.93 a__isList(nil) -> tt 20.60/20.93 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.60/20.93 a__isList(X:S) -> isList(X:S) 20.60/20.93 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.93 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.93 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.60/20.93 a__isNeList(X:S) -> isNeList(X:S) 20.60/20.93 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.93 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.60/20.93 a__isNePal(X:S) -> isNePal(X:S) 20.60/20.93 a__isPal(nil) -> tt 20.60/20.93 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.60/20.93 a__isPal(X:S) -> isPal(X:S) 20.60/20.93 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.93 a__isPalListKind(a) -> tt 20.60/20.93 a__isPalListKind(e) -> tt 20.60/20.93 a__isPalListKind(i) -> tt 20.60/20.93 a__isPalListKind(nil) -> tt 20.60/20.93 a__isPalListKind(o) -> tt 20.60/20.93 a__isPalListKind(u) -> tt 20.60/20.93 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.60/20.93 a__isQid(a) -> tt 20.60/20.93 a__isQid(e) -> tt 20.60/20.93 a__isQid(i) -> tt 20.60/20.93 a__isQid(o) -> tt 20.60/20.93 a__isQid(u) -> tt 20.60/20.93 a__isQid(X:S) -> isQid(X:S) 20.60/20.93 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.60/20.93 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.60/20.93 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.60/20.93 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.60/20.93 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.60/20.93 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.60/20.93 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.60/20.93 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.60/20.93 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.60/20.93 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.60/20.93 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.60/20.93 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.60/20.93 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.60/20.93 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.60/20.93 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.60/20.93 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.60/20.93 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.60/20.93 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.60/20.93 mark(a) -> a 20.60/20.93 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.60/20.93 mark(e) -> e 20.60/20.93 mark(i) -> i 20.60/20.93 mark(isList(X:S)) -> a__isList(X:S) 20.60/20.93 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.60/20.93 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.60/20.93 mark(isPal(X:S)) -> a__isPal(X:S) 20.60/20.93 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.60/20.93 mark(isQid(X:S)) -> a__isQid(X:S) 20.60/20.93 mark(nil) -> nil 20.60/20.93 mark(o) -> o 20.60/20.93 mark(tt) -> tt 20.60/20.93 mark(u) -> u 20.60/20.93 20.60/20.93 Problem 1: 20.60/20.93 20.60/20.93 Reduction Pairs Processor: 20.60/20.93 -> Pairs: 20.60/20.93 A__AND(tt,X:S) -> MARK(X:S) 20.60/20.93 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.93 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.93 MARK(U12(X:S)) -> MARK(X:S) 20.60/20.93 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.93 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(U23(X:S)) -> MARK(X:S) 20.60/20.93 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(U32(X:S)) -> MARK(X:S) 20.60/20.93 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.93 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(U43(X:S)) -> MARK(X:S) 20.60/20.93 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.93 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(U53(X:S)) -> MARK(X:S) 20.60/20.93 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(U62(X:S)) -> MARK(X:S) 20.60/20.93 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(U72(X:S)) -> MARK(X:S) 20.60/20.93 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.60/20.93 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.60/20.93 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.60/20.93 -> Rules: 20.60/20.93 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.60/20.93 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.60/20.93 a__U12(tt) -> tt 20.60/20.93 a__U12(X:S) -> U12(X:S) 20.60/20.93 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.60/20.93 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.60/20.93 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.60/20.93 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.60/20.93 a__U23(tt) -> tt 20.60/20.93 a__U23(X:S) -> U23(X:S) 20.60/20.93 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.60/20.93 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.60/20.93 a__U32(tt) -> tt 20.60/20.93 a__U32(X:S) -> U32(X:S) 20.60/20.93 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.60/20.93 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.60/20.93 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.60/20.93 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.60/20.93 a__U43(tt) -> tt 20.60/20.93 a__U43(X:S) -> U43(X:S) 20.60/20.93 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.60/20.93 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.60/20.93 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.60/20.93 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.60/20.93 a__U53(tt) -> tt 20.60/20.93 a__U53(X:S) -> U53(X:S) 20.60/20.93 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.60/20.93 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.60/20.93 a__U62(tt) -> tt 20.60/20.93 a__U62(X:S) -> U62(X:S) 20.60/20.93 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.60/20.93 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.60/20.93 a__U72(tt) -> tt 20.60/20.93 a__U72(X:S) -> U72(X:S) 20.60/20.93 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.60/20.93 a____(nil,X:S) -> mark(X:S) 20.60/20.93 a____(X:S,nil) -> mark(X:S) 20.60/20.93 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.60/20.93 a__and(tt,X:S) -> mark(X:S) 20.60/20.93 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.60/20.93 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.93 a__isList(nil) -> tt 20.60/20.93 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.60/20.93 a__isList(X:S) -> isList(X:S) 20.60/20.93 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.93 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.93 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.60/20.93 a__isNeList(X:S) -> isNeList(X:S) 20.60/20.93 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.93 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.60/20.93 a__isNePal(X:S) -> isNePal(X:S) 20.60/20.93 a__isPal(nil) -> tt 20.60/20.93 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.60/20.93 a__isPal(X:S) -> isPal(X:S) 20.60/20.93 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.93 a__isPalListKind(a) -> tt 20.60/20.93 a__isPalListKind(e) -> tt 20.60/20.93 a__isPalListKind(i) -> tt 20.60/20.93 a__isPalListKind(nil) -> tt 20.60/20.93 a__isPalListKind(o) -> tt 20.60/20.93 a__isPalListKind(u) -> tt 20.60/20.93 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.60/20.93 a__isQid(a) -> tt 20.60/20.93 a__isQid(e) -> tt 20.60/20.93 a__isQid(i) -> tt 20.60/20.93 a__isQid(o) -> tt 20.60/20.93 a__isQid(u) -> tt 20.60/20.93 a__isQid(X:S) -> isQid(X:S) 20.60/20.93 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.60/20.93 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.60/20.93 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.60/20.93 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.60/20.93 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.60/20.93 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.60/20.93 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.60/20.93 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.60/20.93 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.60/20.93 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.60/20.93 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.60/20.93 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.60/20.93 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.60/20.93 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.60/20.93 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.60/20.93 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.60/20.93 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.60/20.93 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.60/20.93 mark(a) -> a 20.60/20.93 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.60/20.93 mark(e) -> e 20.60/20.93 mark(i) -> i 20.60/20.93 mark(isList(X:S)) -> a__isList(X:S) 20.60/20.93 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.60/20.93 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.60/20.93 mark(isPal(X:S)) -> a__isPal(X:S) 20.60/20.93 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.60/20.93 mark(isQid(X:S)) -> a__isQid(X:S) 20.60/20.93 mark(nil) -> nil 20.60/20.93 mark(o) -> o 20.60/20.93 mark(tt) -> tt 20.60/20.93 mark(u) -> u 20.60/20.93 -> Usable rules: 20.60/20.93 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.60/20.93 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.60/20.93 a__U12(tt) -> tt 20.60/20.93 a__U12(X:S) -> U12(X:S) 20.60/20.93 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.60/20.93 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.60/20.93 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.60/20.93 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.60/20.93 a__U23(tt) -> tt 20.60/20.93 a__U23(X:S) -> U23(X:S) 20.60/20.93 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.60/20.93 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.60/20.93 a__U32(tt) -> tt 20.60/20.93 a__U32(X:S) -> U32(X:S) 20.60/20.93 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.60/20.93 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.60/20.93 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.60/20.93 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.60/20.93 a__U43(tt) -> tt 20.60/20.93 a__U43(X:S) -> U43(X:S) 20.60/20.93 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.60/20.93 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.60/20.93 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.60/20.93 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.60/20.93 a__U53(tt) -> tt 20.60/20.93 a__U53(X:S) -> U53(X:S) 20.60/20.93 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.60/20.93 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.60/20.93 a__U62(tt) -> tt 20.60/20.93 a__U62(X:S) -> U62(X:S) 20.60/20.93 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.60/20.93 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.60/20.93 a__U72(tt) -> tt 20.60/20.93 a__U72(X:S) -> U72(X:S) 20.60/20.93 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.60/20.93 a____(nil,X:S) -> mark(X:S) 20.60/20.93 a____(X:S,nil) -> mark(X:S) 20.60/20.93 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.60/20.93 a__and(tt,X:S) -> mark(X:S) 20.60/20.93 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.60/20.93 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.93 a__isList(nil) -> tt 20.60/20.93 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.60/20.93 a__isList(X:S) -> isList(X:S) 20.60/20.93 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.93 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.93 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.60/20.93 a__isNeList(X:S) -> isNeList(X:S) 20.60/20.93 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.93 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.60/20.93 a__isNePal(X:S) -> isNePal(X:S) 20.60/20.93 a__isPal(nil) -> tt 20.60/20.93 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.60/20.93 a__isPal(X:S) -> isPal(X:S) 20.60/20.93 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.93 a__isPalListKind(a) -> tt 20.60/20.93 a__isPalListKind(e) -> tt 20.60/20.93 a__isPalListKind(i) -> tt 20.60/20.93 a__isPalListKind(nil) -> tt 20.60/20.93 a__isPalListKind(o) -> tt 20.60/20.93 a__isPalListKind(u) -> tt 20.60/20.93 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.60/20.93 a__isQid(a) -> tt 20.60/20.93 a__isQid(e) -> tt 20.60/20.93 a__isQid(i) -> tt 20.60/20.93 a__isQid(o) -> tt 20.60/20.93 a__isQid(u) -> tt 20.60/20.93 a__isQid(X:S) -> isQid(X:S) 20.60/20.93 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.60/20.93 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.60/20.93 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.60/20.93 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.60/20.93 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.60/20.93 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.60/20.93 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.60/20.93 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.60/20.93 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.60/20.93 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.60/20.93 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.60/20.93 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.60/20.93 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.60/20.93 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.60/20.93 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.60/20.93 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.60/20.93 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.60/20.93 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.60/20.93 mark(a) -> a 20.60/20.93 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.60/20.93 mark(e) -> e 20.60/20.93 mark(i) -> i 20.60/20.93 mark(isList(X:S)) -> a__isList(X:S) 20.60/20.93 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.60/20.93 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.60/20.93 mark(isPal(X:S)) -> a__isPal(X:S) 20.60/20.93 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.60/20.93 mark(isQid(X:S)) -> a__isQid(X:S) 20.60/20.93 mark(nil) -> nil 20.60/20.93 mark(o) -> o 20.60/20.93 mark(tt) -> tt 20.60/20.93 mark(u) -> u 20.60/20.93 ->Interpretation type: 20.60/20.93 Linear 20.60/20.93 ->Coefficients: 20.60/20.93 Natural Numbers 20.60/20.93 ->Dimension: 20.60/20.93 1 20.60/20.93 ->Bound: 20.60/20.93 2 20.60/20.93 ->Interpretation: 20.60/20.93 20.60/20.93 [a__U11](X1,X2) = 2.X1 + 2.X2 + 1 20.60/20.93 [a__U12](X) = X + 1 20.60/20.93 [a__U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.60/20.93 [a__U22](X1,X2) = X1 + 2.X2 + 1 20.60/20.93 [a__U23](X) = X 20.60/20.93 [a__U31](X1,X2) = 2.X1 + 2.X2 20.60/20.93 [a__U32](X) = X 20.60/20.93 [a__U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.60/20.93 [a__U42](X1,X2) = X1 + 2.X2 + 1 20.60/20.93 [a__U43](X) = X + 1 20.60/20.93 [a__U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.60/20.93 [a__U52](X1,X2) = X1 + 2.X2 + 2 20.60/20.93 [a__U53](X) = X + 1 20.60/20.93 [a__U61](X1,X2) = X1 + 2.X2 + 2 20.60/20.93 [a__U62](X) = X 20.60/20.93 [a__U71](X1,X2) = 2.X1 + 2.X2 + 2 20.60/20.93 [a__U72](X) = X 20.60/20.93 [a____](X1,X2) = 2.X1 + X2 + 2 20.60/20.93 [a__and](X1,X2) = X1 + 2.X2 20.60/20.93 [a__isList](X) = 2.X + 1 20.60/20.93 [a__isNeList](X) = 2.X 20.60/20.93 [a__isNePal](X) = 2.X + 2 20.60/20.93 [a__isPal](X) = 2.X + 2 20.60/20.93 [a__isPalListKind](X) = 0 20.60/20.93 [a__isQid](X) = 2.X 20.60/20.93 [mark](X) = X 20.60/20.93 [U11](X1,X2) = 2.X1 + 2.X2 + 1 20.60/20.93 [U12](X) = X + 1 20.60/20.93 [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.60/20.93 [U22](X1,X2) = X1 + 2.X2 + 1 20.60/20.93 [U23](X) = X 20.60/20.93 [U31](X1,X2) = 2.X1 + 2.X2 20.60/20.93 [U32](X) = X 20.60/20.93 [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.60/20.93 [U42](X1,X2) = X1 + 2.X2 + 1 20.60/20.93 [U43](X) = X + 1 20.60/20.93 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.60/20.93 [U52](X1,X2) = X1 + 2.X2 + 2 20.60/20.93 [U53](X) = X + 1 20.60/20.93 [U61](X1,X2) = X1 + 2.X2 + 2 20.60/20.93 [U62](X) = X 20.60/20.93 [U71](X1,X2) = 2.X1 + 2.X2 + 2 20.60/20.93 [U72](X) = X 20.60/20.93 [__](X1,X2) = 2.X1 + X2 + 2 20.60/20.93 [a] = 2 20.60/20.93 [and](X1,X2) = X1 + 2.X2 20.60/20.93 [e] = 2 20.60/20.93 [fSNonEmpty] = 0 20.60/20.93 [i] = 2 20.60/20.93 [isList](X) = 2.X + 1 20.60/20.93 [isNeList](X) = 2.X 20.60/20.93 [isNePal](X) = 2.X + 2 20.60/20.93 [isPal](X) = 2.X + 2 20.60/20.93 [isPalListKind](X) = 0 20.60/20.93 [isQid](X) = 2.X 20.60/20.93 [nil] = 2 20.60/20.93 [o] = 2 20.60/20.93 [tt] = 0 20.60/20.93 [u] = 0 20.60/20.93 [A__U11](X1,X2) = 0 20.60/20.93 [A__U12](X) = 0 20.60/20.93 [A__U21](X1,X2,X3) = 0 20.60/20.93 [A__U22](X1,X2) = 0 20.60/20.93 [A__U23](X) = 0 20.60/20.93 [A__U31](X1,X2) = 0 20.60/20.93 [A__U32](X) = 0 20.60/20.93 [A__U41](X1,X2,X3) = 0 20.60/20.93 [A__U42](X1,X2) = 0 20.60/20.93 [A__U43](X) = 0 20.60/20.93 [A__U51](X1,X2,X3) = 0 20.60/20.93 [A__U52](X1,X2) = 0 20.60/20.93 [A__U53](X) = 0 20.60/20.93 [A__U61](X1,X2) = 0 20.60/20.93 [A__U62](X) = 0 20.60/20.93 [A__U71](X1,X2) = 0 20.60/20.93 [A__U72](X) = 0 20.60/20.93 [A____](X1,X2) = 0 20.60/20.93 [A__AND](X1,X2) = X1 + 2.X2 + 2 20.60/20.93 [A__ISLIST](X) = 0 20.60/20.93 [A__ISNELIST](X) = 0 20.60/20.93 [A__ISNEPAL](X) = 0 20.60/20.93 [A__ISPAL](X) = 0 20.60/20.93 [A__ISPALLISTKIND](X) = 2 20.60/20.93 [A__ISQID](X) = 0 20.60/20.93 [MARK](X) = 2.X + 2 20.60/20.93 20.60/20.93 Problem 1: 20.60/20.93 20.60/20.93 SCC Processor: 20.60/20.93 -> Pairs: 20.60/20.93 A__AND(tt,X:S) -> MARK(X:S) 20.60/20.93 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.93 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.93 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.93 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(U23(X:S)) -> MARK(X:S) 20.60/20.93 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(U32(X:S)) -> MARK(X:S) 20.60/20.93 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.93 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(U43(X:S)) -> MARK(X:S) 20.60/20.93 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.93 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(U53(X:S)) -> MARK(X:S) 20.60/20.93 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(U62(X:S)) -> MARK(X:S) 20.60/20.93 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(U72(X:S)) -> MARK(X:S) 20.60/20.93 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.60/20.93 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.60/20.93 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.60/20.93 -> Rules: 20.60/20.93 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.60/20.93 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.60/20.93 a__U12(tt) -> tt 20.60/20.93 a__U12(X:S) -> U12(X:S) 20.60/20.93 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.60/20.93 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.60/20.93 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.60/20.93 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.60/20.93 a__U23(tt) -> tt 20.60/20.93 a__U23(X:S) -> U23(X:S) 20.60/20.93 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.60/20.93 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.60/20.93 a__U32(tt) -> tt 20.60/20.93 a__U32(X:S) -> U32(X:S) 20.60/20.93 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.60/20.93 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.60/20.93 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.60/20.93 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.60/20.93 a__U43(tt) -> tt 20.60/20.93 a__U43(X:S) -> U43(X:S) 20.60/20.93 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.60/20.93 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.60/20.93 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.60/20.93 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.60/20.93 a__U53(tt) -> tt 20.60/20.93 a__U53(X:S) -> U53(X:S) 20.60/20.93 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.60/20.93 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.60/20.93 a__U62(tt) -> tt 20.60/20.93 a__U62(X:S) -> U62(X:S) 20.60/20.93 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.60/20.93 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.60/20.93 a__U72(tt) -> tt 20.60/20.93 a__U72(X:S) -> U72(X:S) 20.60/20.93 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.60/20.93 a____(nil,X:S) -> mark(X:S) 20.60/20.93 a____(X:S,nil) -> mark(X:S) 20.60/20.93 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.60/20.93 a__and(tt,X:S) -> mark(X:S) 20.60/20.93 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.60/20.93 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.93 a__isList(nil) -> tt 20.60/20.93 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.60/20.93 a__isList(X:S) -> isList(X:S) 20.60/20.93 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.93 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.93 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.60/20.93 a__isNeList(X:S) -> isNeList(X:S) 20.60/20.93 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.93 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.60/20.93 a__isNePal(X:S) -> isNePal(X:S) 20.60/20.93 a__isPal(nil) -> tt 20.60/20.93 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.60/20.93 a__isPal(X:S) -> isPal(X:S) 20.60/20.93 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.93 a__isPalListKind(a) -> tt 20.60/20.93 a__isPalListKind(e) -> tt 20.60/20.93 a__isPalListKind(i) -> tt 20.60/20.93 a__isPalListKind(nil) -> tt 20.60/20.93 a__isPalListKind(o) -> tt 20.60/20.93 a__isPalListKind(u) -> tt 20.60/20.93 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.60/20.93 a__isQid(a) -> tt 20.60/20.93 a__isQid(e) -> tt 20.60/20.93 a__isQid(i) -> tt 20.60/20.93 a__isQid(o) -> tt 20.60/20.93 a__isQid(u) -> tt 20.60/20.93 a__isQid(X:S) -> isQid(X:S) 20.60/20.93 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.60/20.93 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.60/20.93 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.60/20.93 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.60/20.93 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.60/20.93 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.60/20.93 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.60/20.93 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.60/20.93 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.60/20.93 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.60/20.93 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.60/20.93 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.60/20.93 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.60/20.93 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.60/20.93 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.60/20.93 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.60/20.93 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.60/20.93 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.60/20.93 mark(a) -> a 20.60/20.93 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.60/20.93 mark(e) -> e 20.60/20.93 mark(i) -> i 20.60/20.93 mark(isList(X:S)) -> a__isList(X:S) 20.60/20.93 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.60/20.93 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.60/20.93 mark(isPal(X:S)) -> a__isPal(X:S) 20.60/20.93 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.60/20.93 mark(isQid(X:S)) -> a__isQid(X:S) 20.60/20.93 mark(nil) -> nil 20.60/20.93 mark(o) -> o 20.60/20.93 mark(tt) -> tt 20.60/20.93 mark(u) -> u 20.60/20.93 ->Strongly Connected Components: 20.60/20.93 ->->Cycle: 20.60/20.93 ->->-> Pairs: 20.60/20.93 A__AND(tt,X:S) -> MARK(X:S) 20.60/20.93 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.93 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.93 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.93 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(U23(X:S)) -> MARK(X:S) 20.60/20.93 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(U32(X:S)) -> MARK(X:S) 20.60/20.93 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.93 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(U43(X:S)) -> MARK(X:S) 20.60/20.93 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.93 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(U53(X:S)) -> MARK(X:S) 20.60/20.93 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(U62(X:S)) -> MARK(X:S) 20.60/20.93 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(U72(X:S)) -> MARK(X:S) 20.60/20.93 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.60/20.93 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.60/20.93 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.60/20.93 ->->-> Rules: 20.60/20.93 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.60/20.93 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.60/20.93 a__U12(tt) -> tt 20.60/20.93 a__U12(X:S) -> U12(X:S) 20.60/20.93 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.60/20.93 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.60/20.93 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.60/20.93 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.60/20.93 a__U23(tt) -> tt 20.60/20.93 a__U23(X:S) -> U23(X:S) 20.60/20.93 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.60/20.93 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.60/20.93 a__U32(tt) -> tt 20.60/20.93 a__U32(X:S) -> U32(X:S) 20.60/20.93 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.60/20.93 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.60/20.93 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.60/20.93 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.60/20.93 a__U43(tt) -> tt 20.60/20.93 a__U43(X:S) -> U43(X:S) 20.60/20.93 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.60/20.93 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.60/20.93 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.60/20.93 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.60/20.93 a__U53(tt) -> tt 20.60/20.93 a__U53(X:S) -> U53(X:S) 20.60/20.93 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.60/20.93 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.60/20.93 a__U62(tt) -> tt 20.60/20.93 a__U62(X:S) -> U62(X:S) 20.60/20.93 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.60/20.93 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.60/20.93 a__U72(tt) -> tt 20.60/20.93 a__U72(X:S) -> U72(X:S) 20.60/20.93 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.60/20.93 a____(nil,X:S) -> mark(X:S) 20.60/20.93 a____(X:S,nil) -> mark(X:S) 20.60/20.93 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.60/20.93 a__and(tt,X:S) -> mark(X:S) 20.60/20.93 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.60/20.93 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.93 a__isList(nil) -> tt 20.60/20.93 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.60/20.93 a__isList(X:S) -> isList(X:S) 20.60/20.93 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.93 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.60/20.93 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.60/20.93 a__isNeList(X:S) -> isNeList(X:S) 20.60/20.93 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.60/20.93 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.60/20.93 a__isNePal(X:S) -> isNePal(X:S) 20.60/20.93 a__isPal(nil) -> tt 20.60/20.93 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.60/20.93 a__isPal(X:S) -> isPal(X:S) 20.60/20.93 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.93 a__isPalListKind(a) -> tt 20.60/20.93 a__isPalListKind(e) -> tt 20.60/20.93 a__isPalListKind(i) -> tt 20.60/20.93 a__isPalListKind(nil) -> tt 20.60/20.93 a__isPalListKind(o) -> tt 20.60/20.93 a__isPalListKind(u) -> tt 20.60/20.93 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.60/20.93 a__isQid(a) -> tt 20.60/20.93 a__isQid(e) -> tt 20.60/20.93 a__isQid(i) -> tt 20.60/20.93 a__isQid(o) -> tt 20.60/20.93 a__isQid(u) -> tt 20.60/20.93 a__isQid(X:S) -> isQid(X:S) 20.60/20.93 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.60/20.93 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.60/20.93 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.60/20.93 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.60/20.93 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.60/20.93 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.60/20.93 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.60/20.93 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.60/20.93 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.60/20.93 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.60/20.93 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.60/20.93 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.60/20.93 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.60/20.93 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.60/20.93 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.60/20.93 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.60/20.93 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.60/20.93 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.60/20.93 mark(a) -> a 20.60/20.93 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.60/20.93 mark(e) -> e 20.60/20.93 mark(i) -> i 20.60/20.93 mark(isList(X:S)) -> a__isList(X:S) 20.60/20.93 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.60/20.93 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.60/20.93 mark(isPal(X:S)) -> a__isPal(X:S) 20.60/20.93 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.60/20.93 mark(isQid(X:S)) -> a__isQid(X:S) 20.60/20.93 mark(nil) -> nil 20.60/20.93 mark(o) -> o 20.60/20.93 mark(tt) -> tt 20.60/20.93 mark(u) -> u 20.60/20.93 20.60/20.93 Problem 1: 20.60/20.93 20.60/20.93 Reduction Pairs Processor: 20.60/20.93 -> Pairs: 20.60/20.93 A__AND(tt,X:S) -> MARK(X:S) 20.60/20.93 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.60/20.93 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.60/20.93 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.93 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(U23(X:S)) -> MARK(X:S) 20.60/20.93 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(U32(X:S)) -> MARK(X:S) 20.60/20.93 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.93 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(U43(X:S)) -> MARK(X:S) 20.60/20.93 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.60/20.93 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(U53(X:S)) -> MARK(X:S) 20.60/20.93 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(U62(X:S)) -> MARK(X:S) 20.60/20.93 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(U72(X:S)) -> MARK(X:S) 20.60/20.93 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.60/20.93 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.60/20.93 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.60/20.93 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.60/20.93 -> Rules: 20.60/20.93 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.60/20.93 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.60/20.93 a__U12(tt) -> tt 20.60/20.93 a__U12(X:S) -> U12(X:S) 20.60/20.93 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.60/20.93 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.60/20.93 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.60/20.93 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.60/20.93 a__U23(tt) -> tt 20.60/20.93 a__U23(X:S) -> U23(X:S) 20.60/20.93 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.60/20.93 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.60/20.93 a__U32(tt) -> tt 20.60/20.93 a__U32(X:S) -> U32(X:S) 20.60/20.93 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.60/20.93 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.60/20.93 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.60/20.93 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.60/20.93 a__U43(tt) -> tt 20.60/20.93 a__U43(X:S) -> U43(X:S) 20.60/20.93 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.60/20.93 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.60/20.93 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.60/20.93 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.93 a__U53(tt) -> tt 20.62/20.93 a__U53(X:S) -> U53(X:S) 20.62/20.93 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.93 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.93 a__U62(tt) -> tt 20.62/20.93 a__U62(X:S) -> U62(X:S) 20.62/20.93 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.93 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.93 a__U72(tt) -> tt 20.62/20.93 a__U72(X:S) -> U72(X:S) 20.62/20.93 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.93 a____(nil,X:S) -> mark(X:S) 20.62/20.93 a____(X:S,nil) -> mark(X:S) 20.62/20.93 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.93 a__and(tt,X:S) -> mark(X:S) 20.62/20.93 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.93 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.93 a__isList(nil) -> tt 20.62/20.93 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.93 a__isList(X:S) -> isList(X:S) 20.62/20.93 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.93 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.93 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.93 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.93 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.93 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.93 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.93 a__isPal(nil) -> tt 20.62/20.93 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.93 a__isPal(X:S) -> isPal(X:S) 20.62/20.93 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.93 a__isPalListKind(a) -> tt 20.62/20.93 a__isPalListKind(e) -> tt 20.62/20.93 a__isPalListKind(i) -> tt 20.62/20.93 a__isPalListKind(nil) -> tt 20.62/20.93 a__isPalListKind(o) -> tt 20.62/20.93 a__isPalListKind(u) -> tt 20.62/20.93 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.93 a__isQid(a) -> tt 20.62/20.93 a__isQid(e) -> tt 20.62/20.93 a__isQid(i) -> tt 20.62/20.93 a__isQid(o) -> tt 20.62/20.93 a__isQid(u) -> tt 20.62/20.93 a__isQid(X:S) -> isQid(X:S) 20.62/20.93 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.93 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.93 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.93 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.93 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.93 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.93 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.93 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.93 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.93 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.93 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.93 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.93 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.93 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.93 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.93 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.93 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.93 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.93 mark(a) -> a 20.62/20.93 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.93 mark(e) -> e 20.62/20.93 mark(i) -> i 20.62/20.93 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.93 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.93 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.93 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.93 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.93 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.93 mark(nil) -> nil 20.62/20.93 mark(o) -> o 20.62/20.93 mark(tt) -> tt 20.62/20.93 mark(u) -> u 20.62/20.93 -> Usable rules: 20.62/20.93 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.93 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.93 a__U12(tt) -> tt 20.62/20.93 a__U12(X:S) -> U12(X:S) 20.62/20.93 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.93 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.93 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.93 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.93 a__U23(tt) -> tt 20.62/20.93 a__U23(X:S) -> U23(X:S) 20.62/20.93 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.93 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.93 a__U32(tt) -> tt 20.62/20.93 a__U32(X:S) -> U32(X:S) 20.62/20.93 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.93 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.93 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.93 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.93 a__U43(tt) -> tt 20.62/20.93 a__U43(X:S) -> U43(X:S) 20.62/20.93 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.93 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.93 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.93 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.93 a__U53(tt) -> tt 20.62/20.93 a__U53(X:S) -> U53(X:S) 20.62/20.93 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.93 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.93 a__U62(tt) -> tt 20.62/20.93 a__U62(X:S) -> U62(X:S) 20.62/20.93 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.93 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.93 a__U72(tt) -> tt 20.62/20.93 a__U72(X:S) -> U72(X:S) 20.62/20.93 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.93 a____(nil,X:S) -> mark(X:S) 20.62/20.93 a____(X:S,nil) -> mark(X:S) 20.62/20.93 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.93 a__and(tt,X:S) -> mark(X:S) 20.62/20.93 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.93 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.93 a__isList(nil) -> tt 20.62/20.93 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.93 a__isList(X:S) -> isList(X:S) 20.62/20.93 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.93 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.93 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.93 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.93 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.93 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.93 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.93 a__isPal(nil) -> tt 20.62/20.93 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.93 a__isPal(X:S) -> isPal(X:S) 20.62/20.93 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.93 a__isPalListKind(a) -> tt 20.62/20.93 a__isPalListKind(e) -> tt 20.62/20.93 a__isPalListKind(i) -> tt 20.62/20.93 a__isPalListKind(nil) -> tt 20.62/20.93 a__isPalListKind(o) -> tt 20.62/20.93 a__isPalListKind(u) -> tt 20.62/20.93 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.93 a__isQid(a) -> tt 20.62/20.93 a__isQid(e) -> tt 20.62/20.93 a__isQid(i) -> tt 20.62/20.93 a__isQid(o) -> tt 20.62/20.93 a__isQid(u) -> tt 20.62/20.93 a__isQid(X:S) -> isQid(X:S) 20.62/20.93 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.93 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.93 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.93 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.93 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.93 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.93 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.93 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.93 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.93 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.93 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.93 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.93 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.93 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.93 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.93 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.93 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.93 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.93 mark(a) -> a 20.62/20.93 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.93 mark(e) -> e 20.62/20.93 mark(i) -> i 20.62/20.93 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.93 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.93 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.93 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.93 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.93 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.93 mark(nil) -> nil 20.62/20.93 mark(o) -> o 20.62/20.93 mark(tt) -> tt 20.62/20.93 mark(u) -> u 20.62/20.93 ->Interpretation type: 20.62/20.93 Linear 20.62/20.93 ->Coefficients: 20.62/20.93 Natural Numbers 20.62/20.93 ->Dimension: 20.62/20.93 1 20.62/20.93 ->Bound: 20.62/20.93 2 20.62/20.93 ->Interpretation: 20.62/20.93 20.62/20.93 [a__U11](X1,X2) = 2.X1 + 2.X2 20.62/20.93 [a__U12](X) = 0 20.62/20.93 [a__U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.62/20.93 [a__U22](X1,X2) = X1 + 2.X2 + 2 20.62/20.93 [a__U23](X) = X + 2 20.62/20.93 [a__U31](X1,X2) = 2.X1 + 2.X2 + 2 20.62/20.93 [a__U32](X) = X 20.62/20.93 [a__U41](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 20.62/20.93 [a__U42](X1,X2) = X1 + 2.X2 + 2 20.62/20.93 [a__U43](X) = X 20.62/20.93 [a__U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.62/20.93 [a__U52](X1,X2) = X1 + 2.X2 20.62/20.93 [a__U53](X) = X 20.62/20.93 [a__U61](X1,X2) = X1 + 2.X2 + 2 20.62/20.93 [a__U62](X) = X 20.62/20.93 [a__U71](X1,X2) = 2.X1 + 2.X2 + 2 20.62/20.93 [a__U72](X) = X 20.62/20.93 [a____](X1,X2) = X1 + X2 + 2 20.62/20.93 [a__and](X1,X2) = X1 + X2 20.62/20.93 [a__isList](X) = 2.X 20.62/20.93 [a__isNeList](X) = 2.X + 2 20.62/20.93 [a__isNePal](X) = 2.X + 2 20.62/20.93 [a__isPal](X) = 2.X + 2 20.62/20.93 [a__isPalListKind](X) = 0 20.62/20.93 [a__isQid](X) = X + 2 20.62/20.93 [mark](X) = X 20.62/20.93 [U11](X1,X2) = 2.X1 + 2.X2 20.62/20.93 [U12](X) = 0 20.62/20.93 [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.62/20.93 [U22](X1,X2) = X1 + 2.X2 + 2 20.62/20.93 [U23](X) = X + 2 20.62/20.93 [U31](X1,X2) = 2.X1 + 2.X2 + 2 20.62/20.93 [U32](X) = X 20.62/20.93 [U41](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 20.62/20.93 [U42](X1,X2) = X1 + 2.X2 + 2 20.62/20.93 [U43](X) = X 20.62/20.93 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.62/20.93 [U52](X1,X2) = X1 + 2.X2 20.62/20.93 [U53](X) = X 20.62/20.93 [U61](X1,X2) = X1 + 2.X2 + 2 20.62/20.93 [U62](X) = X 20.62/20.93 [U71](X1,X2) = 2.X1 + 2.X2 + 2 20.62/20.93 [U72](X) = X 20.62/20.93 [__](X1,X2) = X1 + X2 + 2 20.62/20.93 [a] = 1 20.62/20.93 [and](X1,X2) = X1 + X2 20.62/20.93 [e] = 2 20.62/20.93 [fSNonEmpty] = 0 20.62/20.93 [i] = 2 20.62/20.93 [isList](X) = 2.X 20.62/20.93 [isNeList](X) = 2.X + 2 20.62/20.93 [isNePal](X) = 2.X + 2 20.62/20.93 [isPal](X) = 2.X + 2 20.62/20.93 [isPalListKind](X) = 0 20.62/20.93 [isQid](X) = X + 2 20.62/20.93 [nil] = 2 20.62/20.93 [o] = 2 20.62/20.93 [tt] = 0 20.62/20.93 [u] = 2 20.62/20.93 [A__U11](X1,X2) = 0 20.62/20.93 [A__U12](X) = 0 20.62/20.93 [A__U21](X1,X2,X3) = 0 20.62/20.93 [A__U22](X1,X2) = 0 20.62/20.93 [A__U23](X) = 0 20.62/20.93 [A__U31](X1,X2) = 0 20.62/20.93 [A__U32](X) = 0 20.62/20.93 [A__U41](X1,X2,X3) = 0 20.62/20.93 [A__U42](X1,X2) = 0 20.62/20.93 [A__U43](X) = 0 20.62/20.93 [A__U51](X1,X2,X3) = 0 20.62/20.93 [A__U52](X1,X2) = 0 20.62/20.93 [A__U53](X) = 0 20.62/20.93 [A__U61](X1,X2) = 0 20.62/20.93 [A__U62](X) = 0 20.62/20.93 [A__U71](X1,X2) = 0 20.62/20.93 [A__U72](X) = 0 20.62/20.93 [A____](X1,X2) = 0 20.62/20.93 [A__AND](X1,X2) = 2.X1 + 2.X2 + 2 20.62/20.93 [A__ISLIST](X) = 0 20.62/20.93 [A__ISNELIST](X) = 0 20.62/20.93 [A__ISNEPAL](X) = 0 20.62/20.93 [A__ISPAL](X) = 0 20.62/20.93 [A__ISPALLISTKIND](X) = 2 20.62/20.93 [A__ISQID](X) = 0 20.62/20.93 [MARK](X) = 2.X + 2 20.62/20.93 20.62/20.93 Problem 1: 20.62/20.93 20.62/20.93 SCC Processor: 20.62/20.93 -> Pairs: 20.62/20.93 A__AND(tt,X:S) -> MARK(X:S) 20.62/20.93 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.93 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.62/20.93 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.93 MARK(U23(X:S)) -> MARK(X:S) 20.62/20.93 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.93 MARK(U32(X:S)) -> MARK(X:S) 20.62/20.93 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.62/20.93 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.93 MARK(U43(X:S)) -> MARK(X:S) 20.62/20.93 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.62/20.93 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.93 MARK(U53(X:S)) -> MARK(X:S) 20.62/20.93 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.93 MARK(U62(X:S)) -> MARK(X:S) 20.62/20.93 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.93 MARK(U72(X:S)) -> MARK(X:S) 20.62/20.93 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.93 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.62/20.93 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.62/20.93 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.93 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.62/20.93 -> Rules: 20.62/20.93 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.93 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.93 a__U12(tt) -> tt 20.62/20.93 a__U12(X:S) -> U12(X:S) 20.62/20.93 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.93 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.93 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.93 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.93 a__U23(tt) -> tt 20.62/20.93 a__U23(X:S) -> U23(X:S) 20.62/20.93 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.93 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.93 a__U32(tt) -> tt 20.62/20.93 a__U32(X:S) -> U32(X:S) 20.62/20.93 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.93 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.93 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.93 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.93 a__U43(tt) -> tt 20.62/20.93 a__U43(X:S) -> U43(X:S) 20.62/20.93 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.93 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.93 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.93 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.93 a__U53(tt) -> tt 20.62/20.93 a__U53(X:S) -> U53(X:S) 20.62/20.93 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.93 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.93 a__U62(tt) -> tt 20.62/20.93 a__U62(X:S) -> U62(X:S) 20.62/20.93 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.93 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.93 a__U72(tt) -> tt 20.62/20.93 a__U72(X:S) -> U72(X:S) 20.62/20.93 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.93 a____(nil,X:S) -> mark(X:S) 20.62/20.93 a____(X:S,nil) -> mark(X:S) 20.62/20.93 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.93 a__and(tt,X:S) -> mark(X:S) 20.62/20.93 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.93 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.93 a__isList(nil) -> tt 20.62/20.93 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.93 a__isList(X:S) -> isList(X:S) 20.62/20.93 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.93 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.93 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.93 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.93 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.93 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.93 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.93 a__isPal(nil) -> tt 20.62/20.93 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.93 a__isPal(X:S) -> isPal(X:S) 20.62/20.93 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.93 a__isPalListKind(a) -> tt 20.62/20.93 a__isPalListKind(e) -> tt 20.62/20.93 a__isPalListKind(i) -> tt 20.62/20.93 a__isPalListKind(nil) -> tt 20.62/20.93 a__isPalListKind(o) -> tt 20.62/20.93 a__isPalListKind(u) -> tt 20.62/20.93 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.93 a__isQid(a) -> tt 20.62/20.93 a__isQid(e) -> tt 20.62/20.93 a__isQid(i) -> tt 20.62/20.93 a__isQid(o) -> tt 20.62/20.93 a__isQid(u) -> tt 20.62/20.93 a__isQid(X:S) -> isQid(X:S) 20.62/20.93 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.93 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.93 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.93 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.93 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.93 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.93 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.93 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.93 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.93 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.93 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.93 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.93 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.93 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.93 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.93 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.93 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.93 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.93 mark(a) -> a 20.62/20.93 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.93 mark(e) -> e 20.62/20.93 mark(i) -> i 20.62/20.93 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.93 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.93 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.93 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.93 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.93 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.93 mark(nil) -> nil 20.62/20.93 mark(o) -> o 20.62/20.93 mark(tt) -> tt 20.62/20.93 mark(u) -> u 20.62/20.93 ->Strongly Connected Components: 20.62/20.93 ->->Cycle: 20.62/20.93 ->->-> Pairs: 20.62/20.93 A__AND(tt,X:S) -> MARK(X:S) 20.62/20.93 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.93 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.62/20.93 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.93 MARK(U23(X:S)) -> MARK(X:S) 20.62/20.93 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.93 MARK(U32(X:S)) -> MARK(X:S) 20.62/20.93 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.62/20.93 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.93 MARK(U43(X:S)) -> MARK(X:S) 20.62/20.93 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.62/20.93 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.93 MARK(U53(X:S)) -> MARK(X:S) 20.62/20.93 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.93 MARK(U62(X:S)) -> MARK(X:S) 20.62/20.93 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.93 MARK(U72(X:S)) -> MARK(X:S) 20.62/20.93 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.93 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.62/20.93 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.62/20.93 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.93 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.62/20.93 ->->-> Rules: 20.62/20.93 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.93 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.93 a__U12(tt) -> tt 20.62/20.93 a__U12(X:S) -> U12(X:S) 20.62/20.93 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.93 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.93 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.93 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.93 a__U23(tt) -> tt 20.62/20.93 a__U23(X:S) -> U23(X:S) 20.62/20.93 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.93 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.93 a__U32(tt) -> tt 20.62/20.93 a__U32(X:S) -> U32(X:S) 20.62/20.93 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.93 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.93 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.93 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.93 a__U43(tt) -> tt 20.62/20.93 a__U43(X:S) -> U43(X:S) 20.62/20.93 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.93 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.93 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.93 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.93 a__U53(tt) -> tt 20.62/20.93 a__U53(X:S) -> U53(X:S) 20.62/20.93 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.93 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.93 a__U62(tt) -> tt 20.62/20.93 a__U62(X:S) -> U62(X:S) 20.62/20.93 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.93 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.93 a__U72(tt) -> tt 20.62/20.93 a__U72(X:S) -> U72(X:S) 20.62/20.93 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.93 a____(nil,X:S) -> mark(X:S) 20.62/20.93 a____(X:S,nil) -> mark(X:S) 20.62/20.93 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.93 a__and(tt,X:S) -> mark(X:S) 20.62/20.93 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.93 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.93 a__isList(nil) -> tt 20.62/20.93 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.93 a__isList(X:S) -> isList(X:S) 20.62/20.93 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.93 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.93 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.93 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.94 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.94 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.94 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.94 a__isPal(nil) -> tt 20.62/20.94 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.94 a__isPal(X:S) -> isPal(X:S) 20.62/20.94 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.94 a__isPalListKind(a) -> tt 20.62/20.94 a__isPalListKind(e) -> tt 20.62/20.94 a__isPalListKind(i) -> tt 20.62/20.94 a__isPalListKind(nil) -> tt 20.62/20.94 a__isPalListKind(o) -> tt 20.62/20.94 a__isPalListKind(u) -> tt 20.62/20.94 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.94 a__isQid(a) -> tt 20.62/20.94 a__isQid(e) -> tt 20.62/20.94 a__isQid(i) -> tt 20.62/20.94 a__isQid(o) -> tt 20.62/20.94 a__isQid(u) -> tt 20.62/20.94 a__isQid(X:S) -> isQid(X:S) 20.62/20.94 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.94 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.94 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.94 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.94 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.94 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.94 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.94 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.94 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.94 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.94 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.94 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.94 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.94 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.94 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.94 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.94 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.94 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.94 mark(a) -> a 20.62/20.94 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.94 mark(e) -> e 20.62/20.94 mark(i) -> i 20.62/20.94 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.94 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.94 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.94 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.94 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.94 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.94 mark(nil) -> nil 20.62/20.94 mark(o) -> o 20.62/20.94 mark(tt) -> tt 20.62/20.94 mark(u) -> u 20.62/20.94 20.62/20.94 Problem 1: 20.62/20.94 20.62/20.94 Reduction Pairs Processor: 20.62/20.94 -> Pairs: 20.62/20.94 A__AND(tt,X:S) -> MARK(X:S) 20.62/20.94 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.94 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.62/20.94 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(U23(X:S)) -> MARK(X:S) 20.62/20.94 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(U32(X:S)) -> MARK(X:S) 20.62/20.94 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.62/20.94 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(U43(X:S)) -> MARK(X:S) 20.62/20.94 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.62/20.94 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(U53(X:S)) -> MARK(X:S) 20.62/20.94 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(U62(X:S)) -> MARK(X:S) 20.62/20.94 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(U72(X:S)) -> MARK(X:S) 20.62/20.94 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.62/20.94 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.62/20.94 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.62/20.94 -> Rules: 20.62/20.94 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.94 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.94 a__U12(tt) -> tt 20.62/20.94 a__U12(X:S) -> U12(X:S) 20.62/20.94 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.94 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.94 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.94 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.94 a__U23(tt) -> tt 20.62/20.94 a__U23(X:S) -> U23(X:S) 20.62/20.94 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.94 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.94 a__U32(tt) -> tt 20.62/20.94 a__U32(X:S) -> U32(X:S) 20.62/20.94 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.94 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.94 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.94 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.94 a__U43(tt) -> tt 20.62/20.94 a__U43(X:S) -> U43(X:S) 20.62/20.94 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.94 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.94 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.94 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.94 a__U53(tt) -> tt 20.62/20.94 a__U53(X:S) -> U53(X:S) 20.62/20.94 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.94 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.94 a__U62(tt) -> tt 20.62/20.94 a__U62(X:S) -> U62(X:S) 20.62/20.94 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.94 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.94 a__U72(tt) -> tt 20.62/20.94 a__U72(X:S) -> U72(X:S) 20.62/20.94 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.94 a____(nil,X:S) -> mark(X:S) 20.62/20.94 a____(X:S,nil) -> mark(X:S) 20.62/20.94 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.94 a__and(tt,X:S) -> mark(X:S) 20.62/20.94 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.94 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.94 a__isList(nil) -> tt 20.62/20.94 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.94 a__isList(X:S) -> isList(X:S) 20.62/20.94 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.94 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.94 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.94 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.94 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.94 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.94 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.94 a__isPal(nil) -> tt 20.62/20.94 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.94 a__isPal(X:S) -> isPal(X:S) 20.62/20.94 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.94 a__isPalListKind(a) -> tt 20.62/20.94 a__isPalListKind(e) -> tt 20.62/20.94 a__isPalListKind(i) -> tt 20.62/20.94 a__isPalListKind(nil) -> tt 20.62/20.94 a__isPalListKind(o) -> tt 20.62/20.94 a__isPalListKind(u) -> tt 20.62/20.94 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.94 a__isQid(a) -> tt 20.62/20.94 a__isQid(e) -> tt 20.62/20.94 a__isQid(i) -> tt 20.62/20.94 a__isQid(o) -> tt 20.62/20.94 a__isQid(u) -> tt 20.62/20.94 a__isQid(X:S) -> isQid(X:S) 20.62/20.94 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.94 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.94 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.94 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.94 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.94 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.94 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.94 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.94 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.94 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.94 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.94 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.94 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.94 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.94 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.94 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.94 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.94 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.94 mark(a) -> a 20.62/20.94 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.94 mark(e) -> e 20.62/20.94 mark(i) -> i 20.62/20.94 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.94 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.94 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.94 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.94 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.94 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.94 mark(nil) -> nil 20.62/20.94 mark(o) -> o 20.62/20.94 mark(tt) -> tt 20.62/20.94 mark(u) -> u 20.62/20.94 -> Usable rules: 20.62/20.94 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.94 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.94 a__U12(tt) -> tt 20.62/20.94 a__U12(X:S) -> U12(X:S) 20.62/20.94 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.94 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.94 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.94 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.94 a__U23(tt) -> tt 20.62/20.94 a__U23(X:S) -> U23(X:S) 20.62/20.94 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.94 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.94 a__U32(tt) -> tt 20.62/20.94 a__U32(X:S) -> U32(X:S) 20.62/20.94 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.94 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.94 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.94 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.94 a__U43(tt) -> tt 20.62/20.94 a__U43(X:S) -> U43(X:S) 20.62/20.94 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.94 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.94 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.94 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.94 a__U53(tt) -> tt 20.62/20.94 a__U53(X:S) -> U53(X:S) 20.62/20.94 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.94 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.94 a__U62(tt) -> tt 20.62/20.94 a__U62(X:S) -> U62(X:S) 20.62/20.94 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.94 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.94 a__U72(tt) -> tt 20.62/20.94 a__U72(X:S) -> U72(X:S) 20.62/20.94 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.94 a____(nil,X:S) -> mark(X:S) 20.62/20.94 a____(X:S,nil) -> mark(X:S) 20.62/20.94 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.94 a__and(tt,X:S) -> mark(X:S) 20.62/20.94 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.94 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.94 a__isList(nil) -> tt 20.62/20.94 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.94 a__isList(X:S) -> isList(X:S) 20.62/20.94 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.94 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.94 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.94 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.94 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.94 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.94 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.94 a__isPal(nil) -> tt 20.62/20.94 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.94 a__isPal(X:S) -> isPal(X:S) 20.62/20.94 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.94 a__isPalListKind(a) -> tt 20.62/20.94 a__isPalListKind(e) -> tt 20.62/20.94 a__isPalListKind(i) -> tt 20.62/20.94 a__isPalListKind(nil) -> tt 20.62/20.94 a__isPalListKind(o) -> tt 20.62/20.94 a__isPalListKind(u) -> tt 20.62/20.94 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.94 a__isQid(a) -> tt 20.62/20.94 a__isQid(e) -> tt 20.62/20.94 a__isQid(i) -> tt 20.62/20.94 a__isQid(o) -> tt 20.62/20.94 a__isQid(u) -> tt 20.62/20.94 a__isQid(X:S) -> isQid(X:S) 20.62/20.94 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.94 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.94 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.94 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.94 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.94 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.94 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.94 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.94 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.94 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.94 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.94 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.94 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.94 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.94 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.94 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.94 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.94 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.94 mark(a) -> a 20.62/20.94 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.94 mark(e) -> e 20.62/20.94 mark(i) -> i 20.62/20.94 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.94 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.94 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.94 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.94 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.94 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.94 mark(nil) -> nil 20.62/20.94 mark(o) -> o 20.62/20.94 mark(tt) -> tt 20.62/20.94 mark(u) -> u 20.62/20.94 ->Interpretation type: 20.62/20.94 Linear 20.62/20.94 ->Coefficients: 20.62/20.94 Natural Numbers 20.62/20.94 ->Dimension: 20.62/20.94 1 20.62/20.94 ->Bound: 20.62/20.94 2 20.62/20.94 ->Interpretation: 20.62/20.94 20.62/20.94 [a__U11](X1,X2) = 2.X1 + X2 + 1 20.62/20.94 [a__U12](X) = 0 20.62/20.94 [a__U21](X1,X2,X3) = 2.X1 + 2.X2 + X3 + 2 20.62/20.94 [a__U22](X1,X2) = X1 + X2 + 1 20.62/20.94 [a__U23](X) = X 20.62/20.94 [a__U31](X1,X2) = 2.X1 + 2.X2 + 1 20.62/20.94 [a__U32](X) = X + 1 20.62/20.94 [a__U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.62/20.94 [a__U42](X1,X2) = X1 + 2.X2 + 1 20.62/20.94 [a__U43](X) = X 20.62/20.94 [a__U51](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 20.62/20.94 [a__U52](X1,X2) = X1 + X2 + 1 20.62/20.94 [a__U53](X) = X 20.62/20.94 [a__U61](X1,X2) = 2.X1 + 2.X2 + 1 20.62/20.94 [a__U62](X) = X + 1 20.62/20.94 [a__U71](X1,X2) = 2.X1 + 2.X2 + 2 20.62/20.94 [a__U72](X) = X 20.62/20.94 [a____](X1,X2) = 2.X1 + X2 + 2 20.62/20.94 [a__and](X1,X2) = X1 + 2.X2 20.62/20.94 [a__isList](X) = X + 1 20.62/20.94 [a__isNeList](X) = 2.X + 1 20.62/20.94 [a__isNePal](X) = 2.X + 2 20.62/20.94 [a__isPal](X) = 2.X + 2 20.62/20.94 [a__isPalListKind](X) = 0 20.62/20.94 [a__isQid](X) = 2.X 20.62/20.94 [mark](X) = X 20.62/20.94 [U11](X1,X2) = 2.X1 + X2 + 1 20.62/20.94 [U12](X) = 0 20.62/20.94 [U21](X1,X2,X3) = 2.X1 + 2.X2 + X3 + 2 20.62/20.94 [U22](X1,X2) = X1 + X2 + 1 20.62/20.94 [U23](X) = X 20.62/20.94 [U31](X1,X2) = 2.X1 + 2.X2 + 1 20.62/20.94 [U32](X) = X + 1 20.62/20.94 [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.62/20.94 [U42](X1,X2) = X1 + 2.X2 + 1 20.62/20.94 [U43](X) = X 20.62/20.94 [U51](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 20.62/20.94 [U52](X1,X2) = X1 + X2 + 1 20.62/20.94 [U53](X) = X 20.62/20.94 [U61](X1,X2) = 2.X1 + 2.X2 + 1 20.62/20.94 [U62](X) = X + 1 20.62/20.94 [U71](X1,X2) = 2.X1 + 2.X2 + 2 20.62/20.94 [U72](X) = X 20.62/20.94 [__](X1,X2) = 2.X1 + X2 + 2 20.62/20.94 [a] = 2 20.62/20.94 [and](X1,X2) = X1 + 2.X2 20.62/20.94 [e] = 2 20.62/20.94 [fSNonEmpty] = 0 20.62/20.94 [i] = 2 20.62/20.94 [isList](X) = X + 1 20.62/20.94 [isNeList](X) = 2.X + 1 20.62/20.94 [isNePal](X) = 2.X + 2 20.62/20.94 [isPal](X) = 2.X + 2 20.62/20.94 [isPalListKind](X) = 0 20.62/20.94 [isQid](X) = 2.X 20.62/20.94 [nil] = 1 20.62/20.94 [o] = 1 20.62/20.94 [tt] = 0 20.62/20.94 [u] = 0 20.62/20.94 [A__U11](X1,X2) = 0 20.62/20.94 [A__U12](X) = 0 20.62/20.94 [A__U21](X1,X2,X3) = 0 20.62/20.94 [A__U22](X1,X2) = 0 20.62/20.94 [A__U23](X) = 0 20.62/20.94 [A__U31](X1,X2) = 0 20.62/20.94 [A__U32](X) = 0 20.62/20.94 [A__U41](X1,X2,X3) = 0 20.62/20.94 [A__U42](X1,X2) = 0 20.62/20.94 [A__U43](X) = 0 20.62/20.94 [A__U51](X1,X2,X3) = 0 20.62/20.94 [A__U52](X1,X2) = 0 20.62/20.94 [A__U53](X) = 0 20.62/20.94 [A__U61](X1,X2) = 0 20.62/20.94 [A__U62](X) = 0 20.62/20.94 [A__U71](X1,X2) = 0 20.62/20.94 [A__U72](X) = 0 20.62/20.94 [A____](X1,X2) = 0 20.62/20.94 [A__AND](X1,X2) = X1 + 2.X2 + 2 20.62/20.94 [A__ISLIST](X) = 0 20.62/20.94 [A__ISNELIST](X) = 0 20.62/20.94 [A__ISNEPAL](X) = 0 20.62/20.94 [A__ISPAL](X) = 0 20.62/20.94 [A__ISPALLISTKIND](X) = 2 20.62/20.94 [A__ISQID](X) = 0 20.62/20.94 [MARK](X) = 2.X + 2 20.62/20.94 20.62/20.94 Problem 1: 20.62/20.94 20.62/20.94 SCC Processor: 20.62/20.94 -> Pairs: 20.62/20.94 A__AND(tt,X:S) -> MARK(X:S) 20.62/20.94 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.94 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.62/20.94 MARK(U23(X:S)) -> MARK(X:S) 20.62/20.94 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(U32(X:S)) -> MARK(X:S) 20.62/20.94 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.62/20.94 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(U43(X:S)) -> MARK(X:S) 20.62/20.94 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.62/20.94 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(U53(X:S)) -> MARK(X:S) 20.62/20.94 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(U62(X:S)) -> MARK(X:S) 20.62/20.94 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(U72(X:S)) -> MARK(X:S) 20.62/20.94 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.62/20.94 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.62/20.94 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.62/20.94 -> Rules: 20.62/20.94 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.94 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.94 a__U12(tt) -> tt 20.62/20.94 a__U12(X:S) -> U12(X:S) 20.62/20.94 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.94 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.94 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.94 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.94 a__U23(tt) -> tt 20.62/20.94 a__U23(X:S) -> U23(X:S) 20.62/20.94 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.94 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.94 a__U32(tt) -> tt 20.62/20.94 a__U32(X:S) -> U32(X:S) 20.62/20.94 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.94 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.94 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.94 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.94 a__U43(tt) -> tt 20.62/20.94 a__U43(X:S) -> U43(X:S) 20.62/20.94 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.94 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.94 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.94 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.94 a__U53(tt) -> tt 20.62/20.94 a__U53(X:S) -> U53(X:S) 20.62/20.94 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.94 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.94 a__U62(tt) -> tt 20.62/20.94 a__U62(X:S) -> U62(X:S) 20.62/20.94 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.94 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.94 a__U72(tt) -> tt 20.62/20.94 a__U72(X:S) -> U72(X:S) 20.62/20.94 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.94 a____(nil,X:S) -> mark(X:S) 20.62/20.94 a____(X:S,nil) -> mark(X:S) 20.62/20.94 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.94 a__and(tt,X:S) -> mark(X:S) 20.62/20.94 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.94 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.94 a__isList(nil) -> tt 20.62/20.94 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.94 a__isList(X:S) -> isList(X:S) 20.62/20.94 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.94 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.94 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.94 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.94 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.94 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.94 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.94 a__isPal(nil) -> tt 20.62/20.94 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.94 a__isPal(X:S) -> isPal(X:S) 20.62/20.94 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.94 a__isPalListKind(a) -> tt 20.62/20.94 a__isPalListKind(e) -> tt 20.62/20.94 a__isPalListKind(i) -> tt 20.62/20.94 a__isPalListKind(nil) -> tt 20.62/20.94 a__isPalListKind(o) -> tt 20.62/20.94 a__isPalListKind(u) -> tt 20.62/20.94 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.94 a__isQid(a) -> tt 20.62/20.94 a__isQid(e) -> tt 20.62/20.94 a__isQid(i) -> tt 20.62/20.94 a__isQid(o) -> tt 20.62/20.94 a__isQid(u) -> tt 20.62/20.94 a__isQid(X:S) -> isQid(X:S) 20.62/20.94 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.94 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.94 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.94 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.94 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.94 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.94 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.94 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.94 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.94 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.94 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.94 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.94 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.94 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.94 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.94 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.94 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.94 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.94 mark(a) -> a 20.62/20.94 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.94 mark(e) -> e 20.62/20.94 mark(i) -> i 20.62/20.94 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.94 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.94 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.94 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.94 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.94 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.94 mark(nil) -> nil 20.62/20.94 mark(o) -> o 20.62/20.94 mark(tt) -> tt 20.62/20.94 mark(u) -> u 20.62/20.94 ->Strongly Connected Components: 20.62/20.94 ->->Cycle: 20.62/20.94 ->->-> Pairs: 20.62/20.94 A__AND(tt,X:S) -> MARK(X:S) 20.62/20.94 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.94 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.62/20.94 MARK(U23(X:S)) -> MARK(X:S) 20.62/20.94 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(U32(X:S)) -> MARK(X:S) 20.62/20.94 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.62/20.94 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(U43(X:S)) -> MARK(X:S) 20.62/20.94 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.62/20.94 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(U53(X:S)) -> MARK(X:S) 20.62/20.94 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(U62(X:S)) -> MARK(X:S) 20.62/20.94 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(U72(X:S)) -> MARK(X:S) 20.62/20.94 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.62/20.94 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.62/20.94 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.62/20.94 ->->-> Rules: 20.62/20.94 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.94 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.94 a__U12(tt) -> tt 20.62/20.94 a__U12(X:S) -> U12(X:S) 20.62/20.94 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.94 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.94 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.94 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.94 a__U23(tt) -> tt 20.62/20.94 a__U23(X:S) -> U23(X:S) 20.62/20.94 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.94 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.94 a__U32(tt) -> tt 20.62/20.94 a__U32(X:S) -> U32(X:S) 20.62/20.94 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.94 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.94 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.94 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.94 a__U43(tt) -> tt 20.62/20.94 a__U43(X:S) -> U43(X:S) 20.62/20.94 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.94 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.94 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.94 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.94 a__U53(tt) -> tt 20.62/20.94 a__U53(X:S) -> U53(X:S) 20.62/20.94 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.94 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.94 a__U62(tt) -> tt 20.62/20.94 a__U62(X:S) -> U62(X:S) 20.62/20.94 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.94 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.94 a__U72(tt) -> tt 20.62/20.94 a__U72(X:S) -> U72(X:S) 20.62/20.94 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.94 a____(nil,X:S) -> mark(X:S) 20.62/20.94 a____(X:S,nil) -> mark(X:S) 20.62/20.94 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.94 a__and(tt,X:S) -> mark(X:S) 20.62/20.94 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.94 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.94 a__isList(nil) -> tt 20.62/20.94 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.94 a__isList(X:S) -> isList(X:S) 20.62/20.94 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.94 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.94 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.94 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.94 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.94 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.94 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.94 a__isPal(nil) -> tt 20.62/20.94 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.94 a__isPal(X:S) -> isPal(X:S) 20.62/20.94 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.94 a__isPalListKind(a) -> tt 20.62/20.94 a__isPalListKind(e) -> tt 20.62/20.94 a__isPalListKind(i) -> tt 20.62/20.94 a__isPalListKind(nil) -> tt 20.62/20.94 a__isPalListKind(o) -> tt 20.62/20.94 a__isPalListKind(u) -> tt 20.62/20.94 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.94 a__isQid(a) -> tt 20.62/20.94 a__isQid(e) -> tt 20.62/20.94 a__isQid(i) -> tt 20.62/20.94 a__isQid(o) -> tt 20.62/20.94 a__isQid(u) -> tt 20.62/20.94 a__isQid(X:S) -> isQid(X:S) 20.62/20.94 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.94 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.94 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.94 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.94 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.94 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.94 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.94 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.94 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.94 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.94 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.94 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.94 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.94 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.94 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.94 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.94 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.94 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.94 mark(a) -> a 20.62/20.94 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.94 mark(e) -> e 20.62/20.94 mark(i) -> i 20.62/20.94 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.94 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.94 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.94 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.94 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.94 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.94 mark(nil) -> nil 20.62/20.94 mark(o) -> o 20.62/20.94 mark(tt) -> tt 20.62/20.94 mark(u) -> u 20.62/20.94 20.62/20.94 Problem 1: 20.62/20.94 20.62/20.94 Reduction Pairs Processor: 20.62/20.94 -> Pairs: 20.62/20.94 A__AND(tt,X:S) -> MARK(X:S) 20.62/20.94 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.94 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.62/20.94 MARK(U23(X:S)) -> MARK(X:S) 20.62/20.94 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(U32(X:S)) -> MARK(X:S) 20.62/20.94 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.62/20.94 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(U43(X:S)) -> MARK(X:S) 20.62/20.94 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.62/20.94 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(U53(X:S)) -> MARK(X:S) 20.62/20.94 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(U62(X:S)) -> MARK(X:S) 20.62/20.94 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(U72(X:S)) -> MARK(X:S) 20.62/20.94 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.62/20.94 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.62/20.94 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.62/20.94 -> Rules: 20.62/20.94 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.94 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.94 a__U12(tt) -> tt 20.62/20.94 a__U12(X:S) -> U12(X:S) 20.62/20.94 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.94 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.94 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.94 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.94 a__U23(tt) -> tt 20.62/20.94 a__U23(X:S) -> U23(X:S) 20.62/20.94 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.94 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.94 a__U32(tt) -> tt 20.62/20.94 a__U32(X:S) -> U32(X:S) 20.62/20.94 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.94 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.94 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.94 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.94 a__U43(tt) -> tt 20.62/20.94 a__U43(X:S) -> U43(X:S) 20.62/20.94 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.94 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.94 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.94 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.94 a__U53(tt) -> tt 20.62/20.94 a__U53(X:S) -> U53(X:S) 20.62/20.94 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.94 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.94 a__U62(tt) -> tt 20.62/20.94 a__U62(X:S) -> U62(X:S) 20.62/20.94 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.94 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.94 a__U72(tt) -> tt 20.62/20.94 a__U72(X:S) -> U72(X:S) 20.62/20.94 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.94 a____(nil,X:S) -> mark(X:S) 20.62/20.94 a____(X:S,nil) -> mark(X:S) 20.62/20.94 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.94 a__and(tt,X:S) -> mark(X:S) 20.62/20.94 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.94 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.94 a__isList(nil) -> tt 20.62/20.94 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.94 a__isList(X:S) -> isList(X:S) 20.62/20.94 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.94 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.94 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.94 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.94 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.94 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.94 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.94 a__isPal(nil) -> tt 20.62/20.94 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.94 a__isPal(X:S) -> isPal(X:S) 20.62/20.94 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.94 a__isPalListKind(a) -> tt 20.62/20.94 a__isPalListKind(e) -> tt 20.62/20.94 a__isPalListKind(i) -> tt 20.62/20.94 a__isPalListKind(nil) -> tt 20.62/20.94 a__isPalListKind(o) -> tt 20.62/20.94 a__isPalListKind(u) -> tt 20.62/20.94 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.94 a__isQid(a) -> tt 20.62/20.94 a__isQid(e) -> tt 20.62/20.94 a__isQid(i) -> tt 20.62/20.94 a__isQid(o) -> tt 20.62/20.94 a__isQid(u) -> tt 20.62/20.94 a__isQid(X:S) -> isQid(X:S) 20.62/20.94 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.94 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.94 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.94 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.94 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.94 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.94 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.94 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.94 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.94 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.94 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.94 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.94 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.94 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.94 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.94 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.94 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.94 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.94 mark(a) -> a 20.62/20.94 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.94 mark(e) -> e 20.62/20.94 mark(i) -> i 20.62/20.94 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.94 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.94 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.94 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.94 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.94 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.94 mark(nil) -> nil 20.62/20.94 mark(o) -> o 20.62/20.94 mark(tt) -> tt 20.62/20.94 mark(u) -> u 20.62/20.94 -> Usable rules: 20.62/20.94 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.94 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.94 a__U12(tt) -> tt 20.62/20.94 a__U12(X:S) -> U12(X:S) 20.62/20.94 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.94 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.94 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.94 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.94 a__U23(tt) -> tt 20.62/20.94 a__U23(X:S) -> U23(X:S) 20.62/20.94 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.94 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.94 a__U32(tt) -> tt 20.62/20.94 a__U32(X:S) -> U32(X:S) 20.62/20.94 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.94 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.94 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.94 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.94 a__U43(tt) -> tt 20.62/20.94 a__U43(X:S) -> U43(X:S) 20.62/20.94 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.94 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.94 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.94 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.94 a__U53(tt) -> tt 20.62/20.94 a__U53(X:S) -> U53(X:S) 20.62/20.94 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.94 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.94 a__U62(tt) -> tt 20.62/20.94 a__U62(X:S) -> U62(X:S) 20.62/20.94 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.94 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.94 a__U72(tt) -> tt 20.62/20.94 a__U72(X:S) -> U72(X:S) 20.62/20.94 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.94 a____(nil,X:S) -> mark(X:S) 20.62/20.94 a____(X:S,nil) -> mark(X:S) 20.62/20.94 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.94 a__and(tt,X:S) -> mark(X:S) 20.62/20.94 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.94 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.94 a__isList(nil) -> tt 20.62/20.94 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.94 a__isList(X:S) -> isList(X:S) 20.62/20.94 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.94 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.94 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.94 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.94 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.94 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.94 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.94 a__isPal(nil) -> tt 20.62/20.94 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.94 a__isPal(X:S) -> isPal(X:S) 20.62/20.94 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.94 a__isPalListKind(a) -> tt 20.62/20.94 a__isPalListKind(e) -> tt 20.62/20.94 a__isPalListKind(i) -> tt 20.62/20.94 a__isPalListKind(nil) -> tt 20.62/20.94 a__isPalListKind(o) -> tt 20.62/20.94 a__isPalListKind(u) -> tt 20.62/20.94 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.94 a__isQid(a) -> tt 20.62/20.94 a__isQid(e) -> tt 20.62/20.94 a__isQid(i) -> tt 20.62/20.94 a__isQid(o) -> tt 20.62/20.94 a__isQid(u) -> tt 20.62/20.94 a__isQid(X:S) -> isQid(X:S) 20.62/20.94 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.94 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.94 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.94 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.94 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.94 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.94 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.94 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.94 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.94 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.94 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.94 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.94 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.94 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.94 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.94 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.94 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.94 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.94 mark(a) -> a 20.62/20.94 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.94 mark(e) -> e 20.62/20.94 mark(i) -> i 20.62/20.94 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.94 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.94 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.94 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.94 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.94 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.94 mark(nil) -> nil 20.62/20.94 mark(o) -> o 20.62/20.94 mark(tt) -> tt 20.62/20.94 mark(u) -> u 20.62/20.94 ->Interpretation type: 20.62/20.94 Linear 20.62/20.94 ->Coefficients: 20.62/20.94 Natural Numbers 20.62/20.94 ->Dimension: 20.62/20.94 1 20.62/20.94 ->Bound: 20.62/20.94 2 20.62/20.94 ->Interpretation: 20.62/20.94 20.62/20.94 [a__U11](X1,X2) = 2.X1 + X2 20.62/20.94 [a__U12](X) = 0 20.62/20.94 [a__U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.62/20.94 [a__U22](X1,X2) = 2.X2 + 2 20.62/20.94 [a__U23](X) = X + 2 20.62/20.94 [a__U31](X1,X2) = 2.X1 + 2.X2 + 2 20.62/20.94 [a__U32](X) = X 20.62/20.94 [a__U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.62/20.94 [a__U42](X1,X2) = X1 + 2.X2 + 2 20.62/20.94 [a__U43](X) = X 20.62/20.94 [a__U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.62/20.94 [a__U52](X1,X2) = X1 + 2.X2 20.62/20.94 [a__U53](X) = X 20.62/20.94 [a__U61](X1,X2) = 2.X1 + 2.X2 + 2 20.62/20.94 [a__U62](X) = X 20.62/20.94 [a__U71](X1,X2) = 2.X1 + 2.X2 + 2 20.62/20.94 [a__U72](X) = X 20.62/20.94 [a____](X1,X2) = 2.X1 + X2 + 2 20.62/20.94 [a__and](X1,X2) = X1 + 2.X2 20.62/20.94 [a__isList](X) = 2.X 20.62/20.94 [a__isNeList](X) = 2.X + 2 20.62/20.94 [a__isNePal](X) = 2.X + 2 20.62/20.94 [a__isPal](X) = 2.X + 2 20.62/20.94 [a__isPalListKind](X) = 0 20.62/20.94 [a__isQid](X) = 2.X + 2 20.62/20.94 [mark](X) = X 20.62/20.94 [U11](X1,X2) = 2.X1 + X2 20.62/20.94 [U12](X) = 0 20.62/20.94 [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.62/20.94 [U22](X1,X2) = 2.X2 + 2 20.62/20.94 [U23](X) = X + 2 20.62/20.94 [U31](X1,X2) = 2.X1 + 2.X2 + 2 20.62/20.94 [U32](X) = X 20.62/20.94 [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.62/20.94 [U42](X1,X2) = X1 + 2.X2 + 2 20.62/20.94 [U43](X) = X 20.62/20.94 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.62/20.94 [U52](X1,X2) = X1 + 2.X2 20.62/20.94 [U53](X) = X 20.62/20.94 [U61](X1,X2) = 2.X1 + 2.X2 + 2 20.62/20.94 [U62](X) = X 20.62/20.94 [U71](X1,X2) = 2.X1 + 2.X2 + 2 20.62/20.94 [U72](X) = X 20.62/20.94 [__](X1,X2) = 2.X1 + X2 + 2 20.62/20.94 [a] = 1 20.62/20.94 [and](X1,X2) = X1 + 2.X2 20.62/20.94 [e] = 2 20.62/20.94 [fSNonEmpty] = 0 20.62/20.94 [i] = 2 20.62/20.94 [isList](X) = 2.X 20.62/20.94 [isNeList](X) = 2.X + 2 20.62/20.94 [isNePal](X) = 2.X + 2 20.62/20.94 [isPal](X) = 2.X + 2 20.62/20.94 [isPalListKind](X) = 0 20.62/20.94 [isQid](X) = 2.X + 2 20.62/20.94 [nil] = 2 20.62/20.94 [o] = 2 20.62/20.94 [tt] = 0 20.62/20.94 [u] = 2 20.62/20.94 [A__U11](X1,X2) = 0 20.62/20.94 [A__U12](X) = 0 20.62/20.94 [A__U21](X1,X2,X3) = 0 20.62/20.94 [A__U22](X1,X2) = 0 20.62/20.94 [A__U23](X) = 0 20.62/20.94 [A__U31](X1,X2) = 0 20.62/20.94 [A__U32](X) = 0 20.62/20.94 [A__U41](X1,X2,X3) = 0 20.62/20.94 [A__U42](X1,X2) = 0 20.62/20.94 [A__U43](X) = 0 20.62/20.94 [A__U51](X1,X2,X3) = 0 20.62/20.94 [A__U52](X1,X2) = 0 20.62/20.94 [A__U53](X) = 0 20.62/20.94 [A__U61](X1,X2) = 0 20.62/20.94 [A__U62](X) = 0 20.62/20.94 [A__U71](X1,X2) = 0 20.62/20.94 [A__U72](X) = 0 20.62/20.94 [A____](X1,X2) = 0 20.62/20.94 [A__AND](X1,X2) = 2.X1 + 2.X2 + 2 20.62/20.94 [A__ISLIST](X) = 0 20.62/20.94 [A__ISNELIST](X) = 0 20.62/20.94 [A__ISNEPAL](X) = 0 20.62/20.94 [A__ISPAL](X) = 0 20.62/20.94 [A__ISPALLISTKIND](X) = 2 20.62/20.94 [A__ISQID](X) = 0 20.62/20.94 [MARK](X) = 2.X + 2 20.62/20.94 20.62/20.94 Problem 1: 20.62/20.94 20.62/20.94 SCC Processor: 20.62/20.94 -> Pairs: 20.62/20.94 A__AND(tt,X:S) -> MARK(X:S) 20.62/20.94 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.94 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.62/20.94 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(U32(X:S)) -> MARK(X:S) 20.62/20.94 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.62/20.94 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(U43(X:S)) -> MARK(X:S) 20.62/20.94 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.62/20.94 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(U53(X:S)) -> MARK(X:S) 20.62/20.94 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(U62(X:S)) -> MARK(X:S) 20.62/20.94 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(U72(X:S)) -> MARK(X:S) 20.62/20.94 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.62/20.94 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.62/20.94 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.62/20.94 -> Rules: 20.62/20.94 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.94 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.94 a__U12(tt) -> tt 20.62/20.94 a__U12(X:S) -> U12(X:S) 20.62/20.94 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.94 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.94 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.94 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.94 a__U23(tt) -> tt 20.62/20.94 a__U23(X:S) -> U23(X:S) 20.62/20.94 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.94 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.94 a__U32(tt) -> tt 20.62/20.94 a__U32(X:S) -> U32(X:S) 20.62/20.94 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.94 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.94 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.94 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.94 a__U43(tt) -> tt 20.62/20.94 a__U43(X:S) -> U43(X:S) 20.62/20.94 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.94 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.94 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.94 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.94 a__U53(tt) -> tt 20.62/20.94 a__U53(X:S) -> U53(X:S) 20.62/20.94 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.94 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.94 a__U62(tt) -> tt 20.62/20.94 a__U62(X:S) -> U62(X:S) 20.62/20.94 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.94 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.94 a__U72(tt) -> tt 20.62/20.94 a__U72(X:S) -> U72(X:S) 20.62/20.94 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.94 a____(nil,X:S) -> mark(X:S) 20.62/20.94 a____(X:S,nil) -> mark(X:S) 20.62/20.94 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.94 a__and(tt,X:S) -> mark(X:S) 20.62/20.94 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.94 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.94 a__isList(nil) -> tt 20.62/20.94 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.94 a__isList(X:S) -> isList(X:S) 20.62/20.94 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.94 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.94 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.94 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.94 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.94 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.94 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.94 a__isPal(nil) -> tt 20.62/20.94 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.94 a__isPal(X:S) -> isPal(X:S) 20.62/20.94 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.94 a__isPalListKind(a) -> tt 20.62/20.94 a__isPalListKind(e) -> tt 20.62/20.94 a__isPalListKind(i) -> tt 20.62/20.94 a__isPalListKind(nil) -> tt 20.62/20.94 a__isPalListKind(o) -> tt 20.62/20.94 a__isPalListKind(u) -> tt 20.62/20.94 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.94 a__isQid(a) -> tt 20.62/20.94 a__isQid(e) -> tt 20.62/20.94 a__isQid(i) -> tt 20.62/20.94 a__isQid(o) -> tt 20.62/20.94 a__isQid(u) -> tt 20.62/20.94 a__isQid(X:S) -> isQid(X:S) 20.62/20.94 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.94 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.94 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.94 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.94 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.94 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.94 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.94 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.94 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.94 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.94 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.94 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.94 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.94 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.94 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.94 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.94 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.94 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.94 mark(a) -> a 20.62/20.94 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.94 mark(e) -> e 20.62/20.94 mark(i) -> i 20.62/20.94 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.94 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.94 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.94 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.94 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.94 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.94 mark(nil) -> nil 20.62/20.94 mark(o) -> o 20.62/20.94 mark(tt) -> tt 20.62/20.94 mark(u) -> u 20.62/20.94 ->Strongly Connected Components: 20.62/20.94 ->->Cycle: 20.62/20.94 ->->-> Pairs: 20.62/20.94 A__AND(tt,X:S) -> MARK(X:S) 20.62/20.94 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.94 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.62/20.94 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(U32(X:S)) -> MARK(X:S) 20.62/20.94 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.62/20.94 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(U43(X:S)) -> MARK(X:S) 20.62/20.94 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.62/20.94 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(U53(X:S)) -> MARK(X:S) 20.62/20.94 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(U62(X:S)) -> MARK(X:S) 20.62/20.94 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(U72(X:S)) -> MARK(X:S) 20.62/20.94 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.62/20.94 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.62/20.94 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.62/20.94 ->->-> Rules: 20.62/20.94 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.94 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.94 a__U12(tt) -> tt 20.62/20.94 a__U12(X:S) -> U12(X:S) 20.62/20.94 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.94 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.94 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.94 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.94 a__U23(tt) -> tt 20.62/20.94 a__U23(X:S) -> U23(X:S) 20.62/20.94 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.94 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.94 a__U32(tt) -> tt 20.62/20.94 a__U32(X:S) -> U32(X:S) 20.62/20.94 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.94 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.94 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.94 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.94 a__U43(tt) -> tt 20.62/20.94 a__U43(X:S) -> U43(X:S) 20.62/20.94 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.94 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.94 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.94 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.94 a__U53(tt) -> tt 20.62/20.94 a__U53(X:S) -> U53(X:S) 20.62/20.94 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.94 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.94 a__U62(tt) -> tt 20.62/20.94 a__U62(X:S) -> U62(X:S) 20.62/20.94 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.94 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.94 a__U72(tt) -> tt 20.62/20.94 a__U72(X:S) -> U72(X:S) 20.62/20.94 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.94 a____(nil,X:S) -> mark(X:S) 20.62/20.94 a____(X:S,nil) -> mark(X:S) 20.62/20.94 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.94 a__and(tt,X:S) -> mark(X:S) 20.62/20.94 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.94 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.94 a__isList(nil) -> tt 20.62/20.94 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.94 a__isList(X:S) -> isList(X:S) 20.62/20.94 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.94 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.94 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.94 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.94 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.94 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.94 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.94 a__isPal(nil) -> tt 20.62/20.94 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.94 a__isPal(X:S) -> isPal(X:S) 20.62/20.94 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.94 a__isPalListKind(a) -> tt 20.62/20.94 a__isPalListKind(e) -> tt 20.62/20.94 a__isPalListKind(i) -> tt 20.62/20.94 a__isPalListKind(nil) -> tt 20.62/20.94 a__isPalListKind(o) -> tt 20.62/20.94 a__isPalListKind(u) -> tt 20.62/20.94 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.94 a__isQid(a) -> tt 20.62/20.94 a__isQid(e) -> tt 20.62/20.94 a__isQid(i) -> tt 20.62/20.94 a__isQid(o) -> tt 20.62/20.94 a__isQid(u) -> tt 20.62/20.94 a__isQid(X:S) -> isQid(X:S) 20.62/20.94 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.94 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.94 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.94 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.94 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.94 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.94 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.94 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.94 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.94 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.94 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.94 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.94 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.94 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.94 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.94 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.94 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.94 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.94 mark(a) -> a 20.62/20.94 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.94 mark(e) -> e 20.62/20.94 mark(i) -> i 20.62/20.94 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.94 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.94 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.94 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.94 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.94 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.94 mark(nil) -> nil 20.62/20.94 mark(o) -> o 20.62/20.94 mark(tt) -> tt 20.62/20.94 mark(u) -> u 20.62/20.94 20.62/20.94 Problem 1: 20.62/20.94 20.62/20.94 Reduction Pairs Processor: 20.62/20.94 -> Pairs: 20.62/20.94 A__AND(tt,X:S) -> MARK(X:S) 20.62/20.94 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.94 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.62/20.94 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(U32(X:S)) -> MARK(X:S) 20.62/20.94 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.62/20.94 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(U43(X:S)) -> MARK(X:S) 20.62/20.94 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.62/20.94 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(U53(X:S)) -> MARK(X:S) 20.62/20.94 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(U62(X:S)) -> MARK(X:S) 20.62/20.94 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(U72(X:S)) -> MARK(X:S) 20.62/20.94 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.62/20.94 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.62/20.94 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.62/20.94 -> Rules: 20.62/20.94 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.94 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.94 a__U12(tt) -> tt 20.62/20.94 a__U12(X:S) -> U12(X:S) 20.62/20.94 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.94 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.94 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.94 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.94 a__U23(tt) -> tt 20.62/20.94 a__U23(X:S) -> U23(X:S) 20.62/20.94 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.94 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.94 a__U32(tt) -> tt 20.62/20.94 a__U32(X:S) -> U32(X:S) 20.62/20.94 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.94 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.94 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.94 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.94 a__U43(tt) -> tt 20.62/20.94 a__U43(X:S) -> U43(X:S) 20.62/20.94 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.94 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.94 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.94 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.94 a__U53(tt) -> tt 20.62/20.94 a__U53(X:S) -> U53(X:S) 20.62/20.94 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.94 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.94 a__U62(tt) -> tt 20.62/20.94 a__U62(X:S) -> U62(X:S) 20.62/20.94 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.94 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.94 a__U72(tt) -> tt 20.62/20.94 a__U72(X:S) -> U72(X:S) 20.62/20.94 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.94 a____(nil,X:S) -> mark(X:S) 20.62/20.94 a____(X:S,nil) -> mark(X:S) 20.62/20.94 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.94 a__and(tt,X:S) -> mark(X:S) 20.62/20.94 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.94 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.94 a__isList(nil) -> tt 20.62/20.94 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.94 a__isList(X:S) -> isList(X:S) 20.62/20.94 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.94 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.94 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.94 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.94 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.94 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.94 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.94 a__isPal(nil) -> tt 20.62/20.94 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.94 a__isPal(X:S) -> isPal(X:S) 20.62/20.94 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.94 a__isPalListKind(a) -> tt 20.62/20.94 a__isPalListKind(e) -> tt 20.62/20.94 a__isPalListKind(i) -> tt 20.62/20.94 a__isPalListKind(nil) -> tt 20.62/20.94 a__isPalListKind(o) -> tt 20.62/20.94 a__isPalListKind(u) -> tt 20.62/20.94 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.94 a__isQid(a) -> tt 20.62/20.94 a__isQid(e) -> tt 20.62/20.94 a__isQid(i) -> tt 20.62/20.94 a__isQid(o) -> tt 20.62/20.94 a__isQid(u) -> tt 20.62/20.94 a__isQid(X:S) -> isQid(X:S) 20.62/20.94 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.94 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.94 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.94 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.94 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.94 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.94 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.94 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.94 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.94 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.94 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.94 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.94 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.94 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.94 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.94 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.94 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.94 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.94 mark(a) -> a 20.62/20.94 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.94 mark(e) -> e 20.62/20.94 mark(i) -> i 20.62/20.94 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.94 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.94 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.94 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.94 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.94 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.94 mark(nil) -> nil 20.62/20.94 mark(o) -> o 20.62/20.94 mark(tt) -> tt 20.62/20.94 mark(u) -> u 20.62/20.94 -> Usable rules: 20.62/20.94 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.94 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.94 a__U12(tt) -> tt 20.62/20.94 a__U12(X:S) -> U12(X:S) 20.62/20.94 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.94 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.94 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.94 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.94 a__U23(tt) -> tt 20.62/20.94 a__U23(X:S) -> U23(X:S) 20.62/20.94 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.94 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.94 a__U32(tt) -> tt 20.62/20.94 a__U32(X:S) -> U32(X:S) 20.62/20.94 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.94 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.94 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.94 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.94 a__U43(tt) -> tt 20.62/20.94 a__U43(X:S) -> U43(X:S) 20.62/20.94 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.94 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.94 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.94 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.94 a__U53(tt) -> tt 20.62/20.94 a__U53(X:S) -> U53(X:S) 20.62/20.94 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.94 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.94 a__U62(tt) -> tt 20.62/20.94 a__U62(X:S) -> U62(X:S) 20.62/20.94 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.94 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.94 a__U72(tt) -> tt 20.62/20.94 a__U72(X:S) -> U72(X:S) 20.62/20.94 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.94 a____(nil,X:S) -> mark(X:S) 20.62/20.94 a____(X:S,nil) -> mark(X:S) 20.62/20.94 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.94 a__and(tt,X:S) -> mark(X:S) 20.62/20.94 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.94 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.94 a__isList(nil) -> tt 20.62/20.94 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.94 a__isList(X:S) -> isList(X:S) 20.62/20.94 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.94 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.94 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.94 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.94 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.94 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.94 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.94 a__isPal(nil) -> tt 20.62/20.94 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.94 a__isPal(X:S) -> isPal(X:S) 20.62/20.94 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.94 a__isPalListKind(a) -> tt 20.62/20.94 a__isPalListKind(e) -> tt 20.62/20.94 a__isPalListKind(i) -> tt 20.62/20.94 a__isPalListKind(nil) -> tt 20.62/20.94 a__isPalListKind(o) -> tt 20.62/20.94 a__isPalListKind(u) -> tt 20.62/20.94 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.94 a__isQid(a) -> tt 20.62/20.94 a__isQid(e) -> tt 20.62/20.94 a__isQid(i) -> tt 20.62/20.94 a__isQid(o) -> tt 20.62/20.94 a__isQid(u) -> tt 20.62/20.94 a__isQid(X:S) -> isQid(X:S) 20.62/20.94 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.94 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.94 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.94 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.94 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.94 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.94 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.94 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.94 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.94 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.94 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.94 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.94 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.94 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.94 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.94 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.94 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.94 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.94 mark(a) -> a 20.62/20.94 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.94 mark(e) -> e 20.62/20.94 mark(i) -> i 20.62/20.94 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.94 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.94 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.94 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.94 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.94 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.94 mark(nil) -> nil 20.62/20.94 mark(o) -> o 20.62/20.94 mark(tt) -> tt 20.62/20.94 mark(u) -> u 20.62/20.94 ->Interpretation type: 20.62/20.94 Linear 20.62/20.94 ->Coefficients: 20.62/20.94 Natural Numbers 20.62/20.94 ->Dimension: 20.62/20.94 1 20.62/20.94 ->Bound: 20.62/20.94 2 20.62/20.94 ->Interpretation: 20.62/20.94 20.62/20.94 [a__U11](X1,X2) = 2.X1 + 2.X2 20.62/20.94 [a__U12](X) = 0 20.62/20.94 [a__U21](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 20.62/20.94 [a__U22](X1,X2) = X1 + 2.X2 + 2 20.62/20.94 [a__U23](X) = X + 2 20.62/20.94 [a__U31](X1,X2) = 2.X1 + X2 + 1 20.62/20.94 [a__U32](X) = 2.X + 1 20.62/20.94 [a__U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.62/20.94 [a__U42](X1,X2) = X1 + 2.X2 + 2 20.62/20.94 [a__U43](X) = X + 1 20.62/20.94 [a__U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.62/20.94 [a__U52](X1,X2) = X1 + 2.X2 + 1 20.62/20.94 [a__U53](X) = X 20.62/20.94 [a__U61](X1,X2) = X1 + 2.X2 20.62/20.94 [a__U62](X) = 2.X 20.62/20.94 [a__U71](X1,X2) = 2.X1 + 2.X2 + 1 20.62/20.94 [a__U72](X) = X 20.62/20.94 [a____](X1,X2) = 2.X1 + X2 + 2 20.62/20.94 [a__and](X1,X2) = 2.X1 + X2 20.62/20.94 [a__isList](X) = 2.X 20.62/20.94 [a__isNeList](X) = 2.X + 1 20.62/20.94 [a__isNePal](X) = 2.X + 1 20.62/20.94 [a__isPal](X) = 2.X + 1 20.62/20.94 [a__isPalListKind](X) = 0 20.62/20.94 [a__isQid](X) = 0 20.62/20.94 [mark](X) = X 20.62/20.94 [U11](X1,X2) = 2.X1 + 2.X2 20.62/20.94 [U12](X) = 0 20.62/20.94 [U21](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 20.62/20.94 [U22](X1,X2) = X1 + 2.X2 + 2 20.62/20.94 [U23](X) = X + 2 20.62/20.94 [U31](X1,X2) = 2.X1 + X2 + 1 20.62/20.94 [U32](X) = 2.X + 1 20.62/20.94 [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.62/20.94 [U42](X1,X2) = X1 + 2.X2 + 2 20.62/20.94 [U43](X) = X + 1 20.62/20.94 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.62/20.94 [U52](X1,X2) = X1 + 2.X2 + 1 20.62/20.94 [U53](X) = X 20.62/20.94 [U61](X1,X2) = X1 + 2.X2 20.62/20.94 [U62](X) = 2.X 20.62/20.94 [U71](X1,X2) = 2.X1 + 2.X2 + 1 20.62/20.94 [U72](X) = X 20.62/20.94 [__](X1,X2) = 2.X1 + X2 + 2 20.62/20.94 [a] = 0 20.62/20.94 [and](X1,X2) = 2.X1 + X2 20.62/20.94 [e] = 1 20.62/20.94 [fSNonEmpty] = 0 20.62/20.94 [i] = 1 20.62/20.94 [isList](X) = 2.X 20.62/20.94 [isNeList](X) = 2.X + 1 20.62/20.94 [isNePal](X) = 2.X + 1 20.62/20.94 [isPal](X) = 2.X + 1 20.62/20.94 [isPalListKind](X) = 0 20.62/20.94 [isQid](X) = 0 20.62/20.94 [nil] = 2 20.62/20.94 [o] = 1 20.62/20.94 [tt] = 0 20.62/20.94 [u] = 0 20.62/20.94 [A__U11](X1,X2) = 0 20.62/20.94 [A__U12](X) = 0 20.62/20.94 [A__U21](X1,X2,X3) = 0 20.62/20.94 [A__U22](X1,X2) = 0 20.62/20.94 [A__U23](X) = 0 20.62/20.94 [A__U31](X1,X2) = 0 20.62/20.94 [A__U32](X) = 0 20.62/20.94 [A__U41](X1,X2,X3) = 0 20.62/20.94 [A__U42](X1,X2) = 0 20.62/20.94 [A__U43](X) = 0 20.62/20.94 [A__U51](X1,X2,X3) = 0 20.62/20.94 [A__U52](X1,X2) = 0 20.62/20.94 [A__U53](X) = 0 20.62/20.94 [A__U61](X1,X2) = 0 20.62/20.94 [A__U62](X) = 0 20.62/20.94 [A__U71](X1,X2) = 0 20.62/20.94 [A__U72](X) = 0 20.62/20.94 [A____](X1,X2) = 0 20.62/20.94 [A__AND](X1,X2) = X1 + 2.X2 + 2 20.62/20.94 [A__ISLIST](X) = 0 20.62/20.94 [A__ISNELIST](X) = 0 20.62/20.94 [A__ISNEPAL](X) = 0 20.62/20.94 [A__ISPAL](X) = 0 20.62/20.94 [A__ISPALLISTKIND](X) = 2 20.62/20.94 [A__ISQID](X) = 0 20.62/20.94 [MARK](X) = 2.X + 2 20.62/20.94 20.62/20.94 Problem 1: 20.62/20.94 20.62/20.94 SCC Processor: 20.62/20.94 -> Pairs: 20.62/20.94 A__AND(tt,X:S) -> MARK(X:S) 20.62/20.94 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.94 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.62/20.94 MARK(U32(X:S)) -> MARK(X:S) 20.62/20.94 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.62/20.94 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(U43(X:S)) -> MARK(X:S) 20.62/20.94 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.62/20.94 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(U53(X:S)) -> MARK(X:S) 20.62/20.94 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(U62(X:S)) -> MARK(X:S) 20.62/20.94 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(U72(X:S)) -> MARK(X:S) 20.62/20.94 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.62/20.94 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.62/20.94 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.62/20.94 -> Rules: 20.62/20.94 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.94 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.94 a__U12(tt) -> tt 20.62/20.94 a__U12(X:S) -> U12(X:S) 20.62/20.94 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.94 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.94 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.94 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.94 a__U23(tt) -> tt 20.62/20.94 a__U23(X:S) -> U23(X:S) 20.62/20.94 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.94 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.94 a__U32(tt) -> tt 20.62/20.94 a__U32(X:S) -> U32(X:S) 20.62/20.94 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.94 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.94 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.94 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.94 a__U43(tt) -> tt 20.62/20.94 a__U43(X:S) -> U43(X:S) 20.62/20.94 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.94 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.94 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.94 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.94 a__U53(tt) -> tt 20.62/20.94 a__U53(X:S) -> U53(X:S) 20.62/20.94 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.94 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.94 a__U62(tt) -> tt 20.62/20.94 a__U62(X:S) -> U62(X:S) 20.62/20.94 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.94 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.94 a__U72(tt) -> tt 20.62/20.94 a__U72(X:S) -> U72(X:S) 20.62/20.94 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.94 a____(nil,X:S) -> mark(X:S) 20.62/20.94 a____(X:S,nil) -> mark(X:S) 20.62/20.94 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.94 a__and(tt,X:S) -> mark(X:S) 20.62/20.94 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.94 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.94 a__isList(nil) -> tt 20.62/20.94 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.94 a__isList(X:S) -> isList(X:S) 20.62/20.94 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.94 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.94 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.94 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.94 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.94 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.94 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.94 a__isPal(nil) -> tt 20.62/20.94 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.94 a__isPal(X:S) -> isPal(X:S) 20.62/20.94 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.94 a__isPalListKind(a) -> tt 20.62/20.94 a__isPalListKind(e) -> tt 20.62/20.94 a__isPalListKind(i) -> tt 20.62/20.94 a__isPalListKind(nil) -> tt 20.62/20.94 a__isPalListKind(o) -> tt 20.62/20.94 a__isPalListKind(u) -> tt 20.62/20.94 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.94 a__isQid(a) -> tt 20.62/20.94 a__isQid(e) -> tt 20.62/20.94 a__isQid(i) -> tt 20.62/20.94 a__isQid(o) -> tt 20.62/20.94 a__isQid(u) -> tt 20.62/20.94 a__isQid(X:S) -> isQid(X:S) 20.62/20.94 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.94 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.94 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.94 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.94 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.94 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.94 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.94 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.94 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.94 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.94 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.94 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.94 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.94 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.94 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.94 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.94 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.94 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.94 mark(a) -> a 20.62/20.94 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.94 mark(e) -> e 20.62/20.94 mark(i) -> i 20.62/20.94 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.94 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.94 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.94 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.94 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.94 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.94 mark(nil) -> nil 20.62/20.94 mark(o) -> o 20.62/20.94 mark(tt) -> tt 20.62/20.94 mark(u) -> u 20.62/20.94 ->Strongly Connected Components: 20.62/20.94 ->->Cycle: 20.62/20.94 ->->-> Pairs: 20.62/20.94 A__AND(tt,X:S) -> MARK(X:S) 20.62/20.94 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.94 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.62/20.94 MARK(U32(X:S)) -> MARK(X:S) 20.62/20.94 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.62/20.94 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(U43(X:S)) -> MARK(X:S) 20.62/20.94 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.62/20.94 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(U53(X:S)) -> MARK(X:S) 20.62/20.94 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(U62(X:S)) -> MARK(X:S) 20.62/20.94 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(U72(X:S)) -> MARK(X:S) 20.62/20.94 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.62/20.94 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.62/20.94 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.62/20.94 ->->-> Rules: 20.62/20.94 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.94 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.94 a__U12(tt) -> tt 20.62/20.94 a__U12(X:S) -> U12(X:S) 20.62/20.94 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.94 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.94 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.94 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.94 a__U23(tt) -> tt 20.62/20.94 a__U23(X:S) -> U23(X:S) 20.62/20.94 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.94 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.94 a__U32(tt) -> tt 20.62/20.94 a__U32(X:S) -> U32(X:S) 20.62/20.94 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.94 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.94 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.94 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.94 a__U43(tt) -> tt 20.62/20.94 a__U43(X:S) -> U43(X:S) 20.62/20.94 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.94 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.94 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.94 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.94 a__U53(tt) -> tt 20.62/20.94 a__U53(X:S) -> U53(X:S) 20.62/20.94 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.94 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.94 a__U62(tt) -> tt 20.62/20.94 a__U62(X:S) -> U62(X:S) 20.62/20.94 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.94 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.94 a__U72(tt) -> tt 20.62/20.94 a__U72(X:S) -> U72(X:S) 20.62/20.94 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.94 a____(nil,X:S) -> mark(X:S) 20.62/20.94 a____(X:S,nil) -> mark(X:S) 20.62/20.94 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.94 a__and(tt,X:S) -> mark(X:S) 20.62/20.94 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.94 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.94 a__isList(nil) -> tt 20.62/20.94 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.94 a__isList(X:S) -> isList(X:S) 20.62/20.94 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.94 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.94 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.94 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.94 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.94 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.94 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.94 a__isPal(nil) -> tt 20.62/20.94 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.94 a__isPal(X:S) -> isPal(X:S) 20.62/20.94 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.94 a__isPalListKind(a) -> tt 20.62/20.94 a__isPalListKind(e) -> tt 20.62/20.94 a__isPalListKind(i) -> tt 20.62/20.94 a__isPalListKind(nil) -> tt 20.62/20.94 a__isPalListKind(o) -> tt 20.62/20.94 a__isPalListKind(u) -> tt 20.62/20.94 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.94 a__isQid(a) -> tt 20.62/20.94 a__isQid(e) -> tt 20.62/20.94 a__isQid(i) -> tt 20.62/20.94 a__isQid(o) -> tt 20.62/20.94 a__isQid(u) -> tt 20.62/20.94 a__isQid(X:S) -> isQid(X:S) 20.62/20.94 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.94 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.94 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.94 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.94 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.94 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.94 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.94 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.94 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.94 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.94 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.94 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.94 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.94 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.94 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.94 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.94 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.94 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.94 mark(a) -> a 20.62/20.94 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.94 mark(e) -> e 20.62/20.94 mark(i) -> i 20.62/20.94 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.94 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.94 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.94 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.94 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.94 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.94 mark(nil) -> nil 20.62/20.94 mark(o) -> o 20.62/20.94 mark(tt) -> tt 20.62/20.94 mark(u) -> u 20.62/20.94 20.62/20.94 Problem 1: 20.62/20.94 20.62/20.94 Reduction Pairs Processor: 20.62/20.94 -> Pairs: 20.62/20.94 A__AND(tt,X:S) -> MARK(X:S) 20.62/20.94 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.94 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.62/20.94 MARK(U32(X:S)) -> MARK(X:S) 20.62/20.94 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.62/20.94 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(U43(X:S)) -> MARK(X:S) 20.62/20.94 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.62/20.94 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(U53(X:S)) -> MARK(X:S) 20.62/20.94 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(U62(X:S)) -> MARK(X:S) 20.62/20.94 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(U72(X:S)) -> MARK(X:S) 20.62/20.94 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.62/20.94 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.62/20.94 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.62/20.94 -> Rules: 20.62/20.94 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.94 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.94 a__U12(tt) -> tt 20.62/20.94 a__U12(X:S) -> U12(X:S) 20.62/20.94 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.94 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.94 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.94 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.94 a__U23(tt) -> tt 20.62/20.94 a__U23(X:S) -> U23(X:S) 20.62/20.94 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.94 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.94 a__U32(tt) -> tt 20.62/20.94 a__U32(X:S) -> U32(X:S) 20.62/20.94 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.94 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.94 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.94 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.94 a__U43(tt) -> tt 20.62/20.94 a__U43(X:S) -> U43(X:S) 20.62/20.94 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.94 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.94 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.94 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.94 a__U53(tt) -> tt 20.62/20.94 a__U53(X:S) -> U53(X:S) 20.62/20.94 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.94 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.94 a__U62(tt) -> tt 20.62/20.94 a__U62(X:S) -> U62(X:S) 20.62/20.94 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.94 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.94 a__U72(tt) -> tt 20.62/20.94 a__U72(X:S) -> U72(X:S) 20.62/20.94 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.94 a____(nil,X:S) -> mark(X:S) 20.62/20.94 a____(X:S,nil) -> mark(X:S) 20.62/20.94 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.94 a__and(tt,X:S) -> mark(X:S) 20.62/20.94 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.94 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.94 a__isList(nil) -> tt 20.62/20.94 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.94 a__isList(X:S) -> isList(X:S) 20.62/20.94 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.94 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.94 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.94 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.94 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.94 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.94 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.94 a__isPal(nil) -> tt 20.62/20.94 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.94 a__isPal(X:S) -> isPal(X:S) 20.62/20.94 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.94 a__isPalListKind(a) -> tt 20.62/20.94 a__isPalListKind(e) -> tt 20.62/20.94 a__isPalListKind(i) -> tt 20.62/20.94 a__isPalListKind(nil) -> tt 20.62/20.94 a__isPalListKind(o) -> tt 20.62/20.94 a__isPalListKind(u) -> tt 20.62/20.94 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.94 a__isQid(a) -> tt 20.62/20.94 a__isQid(e) -> tt 20.62/20.94 a__isQid(i) -> tt 20.62/20.94 a__isQid(o) -> tt 20.62/20.94 a__isQid(u) -> tt 20.62/20.94 a__isQid(X:S) -> isQid(X:S) 20.62/20.94 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.94 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.94 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.94 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.94 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.94 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.94 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.94 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.94 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.94 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.94 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.94 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.94 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.94 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.94 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.94 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.94 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.94 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.94 mark(a) -> a 20.62/20.94 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.94 mark(e) -> e 20.62/20.94 mark(i) -> i 20.62/20.94 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.94 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.94 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.94 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.94 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.94 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.94 mark(nil) -> nil 20.62/20.94 mark(o) -> o 20.62/20.94 mark(tt) -> tt 20.62/20.94 mark(u) -> u 20.62/20.94 -> Usable rules: 20.62/20.94 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.94 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.94 a__U12(tt) -> tt 20.62/20.94 a__U12(X:S) -> U12(X:S) 20.62/20.94 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.94 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.94 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.94 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.94 a__U23(tt) -> tt 20.62/20.94 a__U23(X:S) -> U23(X:S) 20.62/20.94 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.94 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.94 a__U32(tt) -> tt 20.62/20.94 a__U32(X:S) -> U32(X:S) 20.62/20.94 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.94 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.94 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.94 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.94 a__U43(tt) -> tt 20.62/20.94 a__U43(X:S) -> U43(X:S) 20.62/20.94 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.94 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.94 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.94 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.94 a__U53(tt) -> tt 20.62/20.94 a__U53(X:S) -> U53(X:S) 20.62/20.94 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.94 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.94 a__U62(tt) -> tt 20.62/20.94 a__U62(X:S) -> U62(X:S) 20.62/20.94 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.94 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.94 a__U72(tt) -> tt 20.62/20.94 a__U72(X:S) -> U72(X:S) 20.62/20.94 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.94 a____(nil,X:S) -> mark(X:S) 20.62/20.94 a____(X:S,nil) -> mark(X:S) 20.62/20.94 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.94 a__and(tt,X:S) -> mark(X:S) 20.62/20.94 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.94 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.94 a__isList(nil) -> tt 20.62/20.94 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.94 a__isList(X:S) -> isList(X:S) 20.62/20.94 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.94 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.94 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.94 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.94 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.94 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.94 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.94 a__isPal(nil) -> tt 20.62/20.94 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.94 a__isPal(X:S) -> isPal(X:S) 20.62/20.94 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.94 a__isPalListKind(a) -> tt 20.62/20.94 a__isPalListKind(e) -> tt 20.62/20.94 a__isPalListKind(i) -> tt 20.62/20.94 a__isPalListKind(nil) -> tt 20.62/20.94 a__isPalListKind(o) -> tt 20.62/20.94 a__isPalListKind(u) -> tt 20.62/20.94 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.94 a__isQid(a) -> tt 20.62/20.94 a__isQid(e) -> tt 20.62/20.94 a__isQid(i) -> tt 20.62/20.94 a__isQid(o) -> tt 20.62/20.94 a__isQid(u) -> tt 20.62/20.94 a__isQid(X:S) -> isQid(X:S) 20.62/20.94 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.94 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.94 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.94 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.94 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.94 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.94 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.94 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.94 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.94 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.94 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.94 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.94 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.94 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.94 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.94 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.94 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.94 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.94 mark(a) -> a 20.62/20.94 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.94 mark(e) -> e 20.62/20.94 mark(i) -> i 20.62/20.94 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.94 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.94 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.94 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.94 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.94 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.94 mark(nil) -> nil 20.62/20.94 mark(o) -> o 20.62/20.94 mark(tt) -> tt 20.62/20.94 mark(u) -> u 20.62/20.94 ->Interpretation type: 20.62/20.94 Linear 20.62/20.94 ->Coefficients: 20.62/20.94 Natural Numbers 20.62/20.94 ->Dimension: 20.62/20.94 1 20.62/20.94 ->Bound: 20.62/20.94 2 20.62/20.94 ->Interpretation: 20.62/20.94 20.62/20.94 [a__U11](X1,X2) = 2.X1 + X2 20.62/20.94 [a__U12](X) = 0 20.62/20.94 [a__U21](X1,X2,X3) = X1 + 2.X2 + X3 + 2 20.62/20.94 [a__U22](X1,X2) = 2.X1 + X2 + 2 20.62/20.94 [a__U23](X) = X + 2 20.62/20.94 [a__U31](X1,X2) = 2.X1 + 2.X2 + 2 20.62/20.94 [a__U32](X) = 2.X + 2 20.62/20.94 [a__U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.62/20.94 [a__U42](X1,X2) = 2.X1 + 2.X2 + 2 20.62/20.94 [a__U43](X) = X 20.62/20.94 [a__U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.62/20.94 [a__U52](X1,X2) = X1 + X2 20.62/20.94 [a__U53](X) = X 20.62/20.94 [a__U61](X1,X2) = X1 + 2.X2 20.62/20.94 [a__U62](X) = 2.X 20.62/20.94 [a__U71](X1,X2) = X1 + 2.X2 + 2 20.62/20.94 [a__U72](X) = X + 2 20.62/20.94 [a____](X1,X2) = 2.X1 + X2 + 2 20.62/20.94 [a__and](X1,X2) = 2.X1 + X2 20.62/20.94 [a__isList](X) = X 20.62/20.94 [a__isNeList](X) = 2.X + 2 20.62/20.94 [a__isNePal](X) = 2.X 20.62/20.94 [a__isPal](X) = 2.X + 2 20.62/20.94 [a__isPalListKind](X) = 0 20.62/20.94 [a__isQid](X) = X 20.62/20.94 [mark](X) = X 20.62/20.94 [U11](X1,X2) = 2.X1 + X2 20.62/20.94 [U12](X) = 0 20.62/20.94 [U21](X1,X2,X3) = X1 + 2.X2 + X3 + 2 20.62/20.94 [U22](X1,X2) = 2.X1 + X2 + 2 20.62/20.94 [U23](X) = X + 2 20.62/20.94 [U31](X1,X2) = 2.X1 + 2.X2 + 2 20.62/20.94 [U32](X) = 2.X + 2 20.62/20.94 [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.62/20.94 [U42](X1,X2) = 2.X1 + 2.X2 + 2 20.62/20.94 [U43](X) = X 20.62/20.94 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.62/20.94 [U52](X1,X2) = X1 + X2 20.62/20.94 [U53](X) = X 20.62/20.94 [U61](X1,X2) = X1 + 2.X2 20.62/20.94 [U62](X) = 2.X 20.62/20.94 [U71](X1,X2) = X1 + 2.X2 + 2 20.62/20.94 [U72](X) = X + 2 20.62/20.94 [__](X1,X2) = 2.X1 + X2 + 2 20.62/20.94 [a] = 2 20.62/20.94 [and](X1,X2) = 2.X1 + X2 20.62/20.94 [e] = 2 20.62/20.94 [fSNonEmpty] = 0 20.62/20.94 [i] = 1 20.62/20.94 [isList](X) = X 20.62/20.94 [isNeList](X) = 2.X + 2 20.62/20.94 [isNePal](X) = 2.X 20.62/20.94 [isPal](X) = 2.X + 2 20.62/20.94 [isPalListKind](X) = 0 20.62/20.94 [isQid](X) = X 20.62/20.94 [nil] = 2 20.62/20.94 [o] = 2 20.62/20.94 [tt] = 0 20.62/20.94 [u] = 2 20.62/20.94 [A__U11](X1,X2) = 0 20.62/20.94 [A__U12](X) = 0 20.62/20.94 [A__U21](X1,X2,X3) = 0 20.62/20.94 [A__U22](X1,X2) = 0 20.62/20.94 [A__U23](X) = 0 20.62/20.94 [A__U31](X1,X2) = 0 20.62/20.94 [A__U32](X) = 0 20.62/20.94 [A__U41](X1,X2,X3) = 0 20.62/20.94 [A__U42](X1,X2) = 0 20.62/20.94 [A__U43](X) = 0 20.62/20.94 [A__U51](X1,X2,X3) = 0 20.62/20.94 [A__U52](X1,X2) = 0 20.62/20.94 [A__U53](X) = 0 20.62/20.94 [A__U61](X1,X2) = 0 20.62/20.94 [A__U62](X) = 0 20.62/20.94 [A__U71](X1,X2) = 0 20.62/20.94 [A__U72](X) = 0 20.62/20.94 [A____](X1,X2) = 0 20.62/20.94 [A__AND](X1,X2) = 2.X1 + 2.X2 + 2 20.62/20.94 [A__ISLIST](X) = 0 20.62/20.94 [A__ISNELIST](X) = 0 20.62/20.94 [A__ISNEPAL](X) = 0 20.62/20.94 [A__ISPAL](X) = 0 20.62/20.94 [A__ISPALLISTKIND](X) = 2 20.62/20.94 [A__ISQID](X) = 0 20.62/20.94 [MARK](X) = 2.X + 2 20.62/20.94 20.62/20.94 Problem 1: 20.62/20.94 20.62/20.94 SCC Processor: 20.62/20.94 -> Pairs: 20.62/20.94 A__AND(tt,X:S) -> MARK(X:S) 20.62/20.94 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.94 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.62/20.94 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.62/20.94 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.94 MARK(U43(X:S)) -> MARK(X:S) 20.62/20.94 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.62/20.94 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(U53(X:S)) -> MARK(X:S) 20.62/20.95 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(U62(X:S)) -> MARK(X:S) 20.62/20.95 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(U72(X:S)) -> MARK(X:S) 20.62/20.95 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.62/20.95 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.62/20.95 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.62/20.95 -> Rules: 20.62/20.95 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.95 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.95 a__U12(tt) -> tt 20.62/20.95 a__U12(X:S) -> U12(X:S) 20.62/20.95 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.95 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.95 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.95 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.95 a__U23(tt) -> tt 20.62/20.95 a__U23(X:S) -> U23(X:S) 20.62/20.95 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.95 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.95 a__U32(tt) -> tt 20.62/20.95 a__U32(X:S) -> U32(X:S) 20.62/20.95 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.95 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.95 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.95 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.95 a__U43(tt) -> tt 20.62/20.95 a__U43(X:S) -> U43(X:S) 20.62/20.95 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.95 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.95 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.95 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.95 a__U53(tt) -> tt 20.62/20.95 a__U53(X:S) -> U53(X:S) 20.62/20.95 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.95 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.95 a__U62(tt) -> tt 20.62/20.95 a__U62(X:S) -> U62(X:S) 20.62/20.95 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.95 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.95 a__U72(tt) -> tt 20.62/20.95 a__U72(X:S) -> U72(X:S) 20.62/20.95 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.95 a____(nil,X:S) -> mark(X:S) 20.62/20.95 a____(X:S,nil) -> mark(X:S) 20.62/20.95 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.95 a__and(tt,X:S) -> mark(X:S) 20.62/20.95 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.95 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.95 a__isList(nil) -> tt 20.62/20.95 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.95 a__isList(X:S) -> isList(X:S) 20.62/20.95 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.95 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.95 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.95 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.95 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.95 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.95 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.95 a__isPal(nil) -> tt 20.62/20.95 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.95 a__isPal(X:S) -> isPal(X:S) 20.62/20.95 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.95 a__isPalListKind(a) -> tt 20.62/20.95 a__isPalListKind(e) -> tt 20.62/20.95 a__isPalListKind(i) -> tt 20.62/20.95 a__isPalListKind(nil) -> tt 20.62/20.95 a__isPalListKind(o) -> tt 20.62/20.95 a__isPalListKind(u) -> tt 20.62/20.95 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.95 a__isQid(a) -> tt 20.62/20.95 a__isQid(e) -> tt 20.62/20.95 a__isQid(i) -> tt 20.62/20.95 a__isQid(o) -> tt 20.62/20.95 a__isQid(u) -> tt 20.62/20.95 a__isQid(X:S) -> isQid(X:S) 20.62/20.95 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.95 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.95 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.95 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.95 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.95 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.95 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.95 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.95 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.95 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.95 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.95 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.95 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.95 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.95 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.95 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.95 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.95 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.95 mark(a) -> a 20.62/20.95 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.95 mark(e) -> e 20.62/20.95 mark(i) -> i 20.62/20.95 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.95 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.95 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.95 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.95 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.95 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.95 mark(nil) -> nil 20.62/20.95 mark(o) -> o 20.62/20.95 mark(tt) -> tt 20.62/20.95 mark(u) -> u 20.62/20.95 ->Strongly Connected Components: 20.62/20.95 ->->Cycle: 20.62/20.95 ->->-> Pairs: 20.62/20.95 A__AND(tt,X:S) -> MARK(X:S) 20.62/20.95 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.95 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.62/20.95 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.62/20.95 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(U43(X:S)) -> MARK(X:S) 20.62/20.95 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.62/20.95 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(U53(X:S)) -> MARK(X:S) 20.62/20.95 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(U62(X:S)) -> MARK(X:S) 20.62/20.95 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(U72(X:S)) -> MARK(X:S) 20.62/20.95 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.62/20.95 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.62/20.95 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.62/20.95 ->->-> Rules: 20.62/20.95 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.95 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.95 a__U12(tt) -> tt 20.62/20.95 a__U12(X:S) -> U12(X:S) 20.62/20.95 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.95 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.95 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.95 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.95 a__U23(tt) -> tt 20.62/20.95 a__U23(X:S) -> U23(X:S) 20.62/20.95 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.95 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.95 a__U32(tt) -> tt 20.62/20.95 a__U32(X:S) -> U32(X:S) 20.62/20.95 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.95 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.95 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.95 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.95 a__U43(tt) -> tt 20.62/20.95 a__U43(X:S) -> U43(X:S) 20.62/20.95 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.95 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.95 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.95 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.95 a__U53(tt) -> tt 20.62/20.95 a__U53(X:S) -> U53(X:S) 20.62/20.95 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.95 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.95 a__U62(tt) -> tt 20.62/20.95 a__U62(X:S) -> U62(X:S) 20.62/20.95 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.95 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.95 a__U72(tt) -> tt 20.62/20.95 a__U72(X:S) -> U72(X:S) 20.62/20.95 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.95 a____(nil,X:S) -> mark(X:S) 20.62/20.95 a____(X:S,nil) -> mark(X:S) 20.62/20.95 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.95 a__and(tt,X:S) -> mark(X:S) 20.62/20.95 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.95 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.95 a__isList(nil) -> tt 20.62/20.95 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.95 a__isList(X:S) -> isList(X:S) 20.62/20.95 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.95 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.95 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.95 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.95 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.95 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.95 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.95 a__isPal(nil) -> tt 20.62/20.95 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.95 a__isPal(X:S) -> isPal(X:S) 20.62/20.95 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.95 a__isPalListKind(a) -> tt 20.62/20.95 a__isPalListKind(e) -> tt 20.62/20.95 a__isPalListKind(i) -> tt 20.62/20.95 a__isPalListKind(nil) -> tt 20.62/20.95 a__isPalListKind(o) -> tt 20.62/20.95 a__isPalListKind(u) -> tt 20.62/20.95 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.95 a__isQid(a) -> tt 20.62/20.95 a__isQid(e) -> tt 20.62/20.95 a__isQid(i) -> tt 20.62/20.95 a__isQid(o) -> tt 20.62/20.95 a__isQid(u) -> tt 20.62/20.95 a__isQid(X:S) -> isQid(X:S) 20.62/20.95 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.95 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.95 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.95 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.95 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.95 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.95 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.95 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.95 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.95 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.95 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.95 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.95 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.95 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.95 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.95 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.95 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.95 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.95 mark(a) -> a 20.62/20.95 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.95 mark(e) -> e 20.62/20.95 mark(i) -> i 20.62/20.95 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.95 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.95 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.95 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.95 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.95 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.95 mark(nil) -> nil 20.62/20.95 mark(o) -> o 20.62/20.95 mark(tt) -> tt 20.62/20.95 mark(u) -> u 20.62/20.95 20.62/20.95 Problem 1: 20.62/20.95 20.62/20.95 Reduction Pairs Processor: 20.62/20.95 -> Pairs: 20.62/20.95 A__AND(tt,X:S) -> MARK(X:S) 20.62/20.95 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.95 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.62/20.95 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.62/20.95 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(U43(X:S)) -> MARK(X:S) 20.62/20.95 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.62/20.95 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(U53(X:S)) -> MARK(X:S) 20.62/20.95 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(U62(X:S)) -> MARK(X:S) 20.62/20.95 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(U72(X:S)) -> MARK(X:S) 20.62/20.95 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.62/20.95 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.62/20.95 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.62/20.95 -> Rules: 20.62/20.95 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.95 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.95 a__U12(tt) -> tt 20.62/20.95 a__U12(X:S) -> U12(X:S) 20.62/20.95 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.95 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.95 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.95 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.95 a__U23(tt) -> tt 20.62/20.95 a__U23(X:S) -> U23(X:S) 20.62/20.95 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.95 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.95 a__U32(tt) -> tt 20.62/20.95 a__U32(X:S) -> U32(X:S) 20.62/20.95 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.95 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.95 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.95 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.95 a__U43(tt) -> tt 20.62/20.95 a__U43(X:S) -> U43(X:S) 20.62/20.95 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.95 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.95 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.95 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.95 a__U53(tt) -> tt 20.62/20.95 a__U53(X:S) -> U53(X:S) 20.62/20.95 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.95 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.95 a__U62(tt) -> tt 20.62/20.95 a__U62(X:S) -> U62(X:S) 20.62/20.95 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.95 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.95 a__U72(tt) -> tt 20.62/20.95 a__U72(X:S) -> U72(X:S) 20.62/20.95 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.95 a____(nil,X:S) -> mark(X:S) 20.62/20.95 a____(X:S,nil) -> mark(X:S) 20.62/20.95 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.95 a__and(tt,X:S) -> mark(X:S) 20.62/20.95 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.95 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.95 a__isList(nil) -> tt 20.62/20.95 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.95 a__isList(X:S) -> isList(X:S) 20.62/20.95 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.95 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.95 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.95 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.95 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.95 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.95 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.95 a__isPal(nil) -> tt 20.62/20.95 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.95 a__isPal(X:S) -> isPal(X:S) 20.62/20.95 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.95 a__isPalListKind(a) -> tt 20.62/20.95 a__isPalListKind(e) -> tt 20.62/20.95 a__isPalListKind(i) -> tt 20.62/20.95 a__isPalListKind(nil) -> tt 20.62/20.95 a__isPalListKind(o) -> tt 20.62/20.95 a__isPalListKind(u) -> tt 20.62/20.95 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.95 a__isQid(a) -> tt 20.62/20.95 a__isQid(e) -> tt 20.62/20.95 a__isQid(i) -> tt 20.62/20.95 a__isQid(o) -> tt 20.62/20.95 a__isQid(u) -> tt 20.62/20.95 a__isQid(X:S) -> isQid(X:S) 20.62/20.95 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.95 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.95 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.95 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.95 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.95 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.95 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.95 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.95 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.95 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.95 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.95 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.95 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.95 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.95 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.95 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.95 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.95 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.95 mark(a) -> a 20.62/20.95 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.95 mark(e) -> e 20.62/20.95 mark(i) -> i 20.62/20.95 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.95 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.95 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.95 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.95 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.95 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.95 mark(nil) -> nil 20.62/20.95 mark(o) -> o 20.62/20.95 mark(tt) -> tt 20.62/20.95 mark(u) -> u 20.62/20.95 -> Usable rules: 20.62/20.95 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.95 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.95 a__U12(tt) -> tt 20.62/20.95 a__U12(X:S) -> U12(X:S) 20.62/20.95 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.95 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.95 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.95 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.95 a__U23(tt) -> tt 20.62/20.95 a__U23(X:S) -> U23(X:S) 20.62/20.95 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.95 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.95 a__U32(tt) -> tt 20.62/20.95 a__U32(X:S) -> U32(X:S) 20.62/20.95 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.95 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.95 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.95 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.95 a__U43(tt) -> tt 20.62/20.95 a__U43(X:S) -> U43(X:S) 20.62/20.95 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.95 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.95 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.95 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.95 a__U53(tt) -> tt 20.62/20.95 a__U53(X:S) -> U53(X:S) 20.62/20.95 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.95 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.95 a__U62(tt) -> tt 20.62/20.95 a__U62(X:S) -> U62(X:S) 20.62/20.95 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.95 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.95 a__U72(tt) -> tt 20.62/20.95 a__U72(X:S) -> U72(X:S) 20.62/20.95 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.95 a____(nil,X:S) -> mark(X:S) 20.62/20.95 a____(X:S,nil) -> mark(X:S) 20.62/20.95 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.95 a__and(tt,X:S) -> mark(X:S) 20.62/20.95 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.95 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.95 a__isList(nil) -> tt 20.62/20.95 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.95 a__isList(X:S) -> isList(X:S) 20.62/20.95 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.95 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.95 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.95 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.95 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.95 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.95 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.95 a__isPal(nil) -> tt 20.62/20.95 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.95 a__isPal(X:S) -> isPal(X:S) 20.62/20.95 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.95 a__isPalListKind(a) -> tt 20.62/20.95 a__isPalListKind(e) -> tt 20.62/20.95 a__isPalListKind(i) -> tt 20.62/20.95 a__isPalListKind(nil) -> tt 20.62/20.95 a__isPalListKind(o) -> tt 20.62/20.95 a__isPalListKind(u) -> tt 20.62/20.95 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.95 a__isQid(a) -> tt 20.62/20.95 a__isQid(e) -> tt 20.62/20.95 a__isQid(i) -> tt 20.62/20.95 a__isQid(o) -> tt 20.62/20.95 a__isQid(u) -> tt 20.62/20.95 a__isQid(X:S) -> isQid(X:S) 20.62/20.95 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.95 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.95 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.95 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.95 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.95 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.95 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.95 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.95 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.95 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.95 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.95 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.95 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.95 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.95 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.95 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.95 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.95 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.95 mark(a) -> a 20.62/20.95 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.95 mark(e) -> e 20.62/20.95 mark(i) -> i 20.62/20.95 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.95 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.95 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.95 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.95 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.95 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.95 mark(nil) -> nil 20.62/20.95 mark(o) -> o 20.62/20.95 mark(tt) -> tt 20.62/20.95 mark(u) -> u 20.62/20.95 ->Interpretation type: 20.62/20.95 Linear 20.62/20.95 ->Coefficients: 20.62/20.95 Natural Numbers 20.62/20.95 ->Dimension: 20.62/20.95 1 20.62/20.95 ->Bound: 20.62/20.95 2 20.62/20.95 ->Interpretation: 20.62/20.95 20.62/20.95 [a__U11](X1,X2) = 2.X1 + 2.X2 20.62/20.95 [a__U12](X) = X 20.62/20.95 [a__U21](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 20.62/20.95 [a__U22](X1,X2) = X1 + 2.X2 + 2 20.62/20.95 [a__U23](X) = X + 2 20.62/20.95 [a__U31](X1,X2) = X1 + 2.X2 20.62/20.95 [a__U32](X) = 0 20.62/20.95 [a__U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.62/20.95 [a__U42](X1,X2) = X1 + 2.X2 + 2 20.62/20.95 [a__U43](X) = X + 2 20.62/20.95 [a__U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.62/20.95 [a__U52](X1,X2) = X1 + 2.X2 + 2 20.62/20.95 [a__U53](X) = X + 2 20.62/20.95 [a__U61](X1,X2) = 2.X1 + 2.X2 + 2 20.62/20.95 [a__U62](X) = X 20.62/20.95 [a__U71](X1,X2) = X1 + 2.X2 + 2 20.62/20.95 [a__U72](X) = X 20.62/20.95 [a____](X1,X2) = 2.X1 + X2 + 2 20.62/20.95 [a__and](X1,X2) = X1 + 2.X2 20.62/20.95 [a__isList](X) = 2.X 20.62/20.95 [a__isNeList](X) = 2.X 20.62/20.95 [a__isNePal](X) = 2.X + 2 20.62/20.95 [a__isPal](X) = 2.X + 2 20.62/20.95 [a__isPalListKind](X) = 0 20.62/20.95 [a__isQid](X) = 2 20.62/20.95 [mark](X) = X 20.62/20.95 [U11](X1,X2) = 2.X1 + 2.X2 20.62/20.95 [U12](X) = X 20.62/20.95 [U21](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 20.62/20.95 [U22](X1,X2) = X1 + 2.X2 + 2 20.62/20.95 [U23](X) = X + 2 20.62/20.95 [U31](X1,X2) = X1 + 2.X2 20.62/20.95 [U32](X) = 0 20.62/20.95 [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.62/20.95 [U42](X1,X2) = X1 + 2.X2 + 2 20.62/20.95 [U43](X) = X + 2 20.62/20.95 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.62/20.95 [U52](X1,X2) = X1 + 2.X2 + 2 20.62/20.95 [U53](X) = X + 2 20.62/20.95 [U61](X1,X2) = 2.X1 + 2.X2 + 2 20.62/20.95 [U62](X) = X 20.62/20.95 [U71](X1,X2) = X1 + 2.X2 + 2 20.62/20.95 [U72](X) = X 20.62/20.95 [__](X1,X2) = 2.X1 + X2 + 2 20.62/20.95 [a] = 2 20.62/20.95 [and](X1,X2) = X1 + 2.X2 20.62/20.95 [e] = 0 20.62/20.95 [fSNonEmpty] = 0 20.62/20.95 [i] = 2 20.62/20.95 [isList](X) = 2.X 20.62/20.95 [isNeList](X) = 2.X 20.62/20.95 [isNePal](X) = 2.X + 2 20.62/20.95 [isPal](X) = 2.X + 2 20.62/20.95 [isPalListKind](X) = 0 20.62/20.95 [isQid](X) = 2 20.62/20.95 [nil] = 2 20.62/20.95 [o] = 2 20.62/20.95 [tt] = 0 20.62/20.95 [u] = 0 20.62/20.95 [A__U11](X1,X2) = 0 20.62/20.95 [A__U12](X) = 0 20.62/20.95 [A__U21](X1,X2,X3) = 0 20.62/20.95 [A__U22](X1,X2) = 0 20.62/20.95 [A__U23](X) = 0 20.62/20.95 [A__U31](X1,X2) = 0 20.62/20.95 [A__U32](X) = 0 20.62/20.95 [A__U41](X1,X2,X3) = 0 20.62/20.95 [A__U42](X1,X2) = 0 20.62/20.95 [A__U43](X) = 0 20.62/20.95 [A__U51](X1,X2,X3) = 0 20.62/20.95 [A__U52](X1,X2) = 0 20.62/20.95 [A__U53](X) = 0 20.62/20.95 [A__U61](X1,X2) = 0 20.62/20.95 [A__U62](X) = 0 20.62/20.95 [A__U71](X1,X2) = 0 20.62/20.95 [A__U72](X) = 0 20.62/20.95 [A____](X1,X2) = 0 20.62/20.95 [A__AND](X1,X2) = X1 + 2.X2 + 2 20.62/20.95 [A__ISLIST](X) = 0 20.62/20.95 [A__ISNELIST](X) = 0 20.62/20.95 [A__ISNEPAL](X) = 0 20.62/20.95 [A__ISPAL](X) = 0 20.62/20.95 [A__ISPALLISTKIND](X) = 2 20.62/20.95 [A__ISQID](X) = 0 20.62/20.95 [MARK](X) = 2.X + 2 20.62/20.95 20.62/20.95 Problem 1: 20.62/20.95 20.62/20.95 SCC Processor: 20.62/20.95 -> Pairs: 20.62/20.95 A__AND(tt,X:S) -> MARK(X:S) 20.62/20.95 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.95 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.62/20.95 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(U43(X:S)) -> MARK(X:S) 20.62/20.95 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.62/20.95 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(U53(X:S)) -> MARK(X:S) 20.62/20.95 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(U62(X:S)) -> MARK(X:S) 20.62/20.95 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(U72(X:S)) -> MARK(X:S) 20.62/20.95 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.62/20.95 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.62/20.95 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.62/20.95 -> Rules: 20.62/20.95 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.95 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.95 a__U12(tt) -> tt 20.62/20.95 a__U12(X:S) -> U12(X:S) 20.62/20.95 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.95 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.95 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.95 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.95 a__U23(tt) -> tt 20.62/20.95 a__U23(X:S) -> U23(X:S) 20.62/20.95 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.95 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.95 a__U32(tt) -> tt 20.62/20.95 a__U32(X:S) -> U32(X:S) 20.62/20.95 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.95 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.95 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.95 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.95 a__U43(tt) -> tt 20.62/20.95 a__U43(X:S) -> U43(X:S) 20.62/20.95 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.95 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.95 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.95 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.95 a__U53(tt) -> tt 20.62/20.95 a__U53(X:S) -> U53(X:S) 20.62/20.95 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.95 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.95 a__U62(tt) -> tt 20.62/20.95 a__U62(X:S) -> U62(X:S) 20.62/20.95 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.95 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.95 a__U72(tt) -> tt 20.62/20.95 a__U72(X:S) -> U72(X:S) 20.62/20.95 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.95 a____(nil,X:S) -> mark(X:S) 20.62/20.95 a____(X:S,nil) -> mark(X:S) 20.62/20.95 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.95 a__and(tt,X:S) -> mark(X:S) 20.62/20.95 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.95 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.95 a__isList(nil) -> tt 20.62/20.95 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.95 a__isList(X:S) -> isList(X:S) 20.62/20.95 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.95 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.95 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.95 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.95 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.95 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.95 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.95 a__isPal(nil) -> tt 20.62/20.95 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.95 a__isPal(X:S) -> isPal(X:S) 20.62/20.95 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.95 a__isPalListKind(a) -> tt 20.62/20.95 a__isPalListKind(e) -> tt 20.62/20.95 a__isPalListKind(i) -> tt 20.62/20.95 a__isPalListKind(nil) -> tt 20.62/20.95 a__isPalListKind(o) -> tt 20.62/20.95 a__isPalListKind(u) -> tt 20.62/20.95 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.95 a__isQid(a) -> tt 20.62/20.95 a__isQid(e) -> tt 20.62/20.95 a__isQid(i) -> tt 20.62/20.95 a__isQid(o) -> tt 20.62/20.95 a__isQid(u) -> tt 20.62/20.95 a__isQid(X:S) -> isQid(X:S) 20.62/20.95 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.95 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.95 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.95 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.95 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.95 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.95 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.95 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.95 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.95 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.95 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.95 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.95 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.95 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.95 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.95 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.95 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.95 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.95 mark(a) -> a 20.62/20.95 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.95 mark(e) -> e 20.62/20.95 mark(i) -> i 20.62/20.95 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.95 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.95 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.95 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.95 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.95 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.95 mark(nil) -> nil 20.62/20.95 mark(o) -> o 20.62/20.95 mark(tt) -> tt 20.62/20.95 mark(u) -> u 20.62/20.95 ->Strongly Connected Components: 20.62/20.95 ->->Cycle: 20.62/20.95 ->->-> Pairs: 20.62/20.95 A__AND(tt,X:S) -> MARK(X:S) 20.62/20.95 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.95 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.62/20.95 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(U43(X:S)) -> MARK(X:S) 20.62/20.95 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.62/20.95 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(U53(X:S)) -> MARK(X:S) 20.62/20.95 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(U62(X:S)) -> MARK(X:S) 20.62/20.95 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(U72(X:S)) -> MARK(X:S) 20.62/20.95 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.62/20.95 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.62/20.95 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.62/20.95 ->->-> Rules: 20.62/20.95 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.95 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.95 a__U12(tt) -> tt 20.62/20.95 a__U12(X:S) -> U12(X:S) 20.62/20.95 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.95 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.95 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.95 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.95 a__U23(tt) -> tt 20.62/20.95 a__U23(X:S) -> U23(X:S) 20.62/20.95 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.95 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.95 a__U32(tt) -> tt 20.62/20.95 a__U32(X:S) -> U32(X:S) 20.62/20.95 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.95 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.95 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.95 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.95 a__U43(tt) -> tt 20.62/20.95 a__U43(X:S) -> U43(X:S) 20.62/20.95 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.95 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.95 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.95 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.95 a__U53(tt) -> tt 20.62/20.95 a__U53(X:S) -> U53(X:S) 20.62/20.95 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.95 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.95 a__U62(tt) -> tt 20.62/20.95 a__U62(X:S) -> U62(X:S) 20.62/20.95 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.95 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.95 a__U72(tt) -> tt 20.62/20.95 a__U72(X:S) -> U72(X:S) 20.62/20.95 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.95 a____(nil,X:S) -> mark(X:S) 20.62/20.95 a____(X:S,nil) -> mark(X:S) 20.62/20.95 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.95 a__and(tt,X:S) -> mark(X:S) 20.62/20.95 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.95 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.95 a__isList(nil) -> tt 20.62/20.95 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.95 a__isList(X:S) -> isList(X:S) 20.62/20.95 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.95 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.95 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.95 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.95 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.95 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.95 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.95 a__isPal(nil) -> tt 20.62/20.95 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.95 a__isPal(X:S) -> isPal(X:S) 20.62/20.95 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.95 a__isPalListKind(a) -> tt 20.62/20.95 a__isPalListKind(e) -> tt 20.62/20.95 a__isPalListKind(i) -> tt 20.62/20.95 a__isPalListKind(nil) -> tt 20.62/20.95 a__isPalListKind(o) -> tt 20.62/20.95 a__isPalListKind(u) -> tt 20.62/20.95 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.95 a__isQid(a) -> tt 20.62/20.95 a__isQid(e) -> tt 20.62/20.95 a__isQid(i) -> tt 20.62/20.95 a__isQid(o) -> tt 20.62/20.95 a__isQid(u) -> tt 20.62/20.95 a__isQid(X:S) -> isQid(X:S) 20.62/20.95 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.95 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.95 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.95 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.95 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.95 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.95 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.95 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.95 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.95 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.95 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.95 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.95 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.95 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.95 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.95 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.95 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.95 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.95 mark(a) -> a 20.62/20.95 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.95 mark(e) -> e 20.62/20.95 mark(i) -> i 20.62/20.95 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.95 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.95 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.95 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.95 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.95 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.95 mark(nil) -> nil 20.62/20.95 mark(o) -> o 20.62/20.95 mark(tt) -> tt 20.62/20.95 mark(u) -> u 20.62/20.95 20.62/20.95 Problem 1: 20.62/20.95 20.62/20.95 Reduction Pairs Processor: 20.62/20.95 -> Pairs: 20.62/20.95 A__AND(tt,X:S) -> MARK(X:S) 20.62/20.95 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.95 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.62/20.95 MARK(U42(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(U43(X:S)) -> MARK(X:S) 20.62/20.95 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.62/20.95 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(U53(X:S)) -> MARK(X:S) 20.62/20.95 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(U62(X:S)) -> MARK(X:S) 20.62/20.95 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(U72(X:S)) -> MARK(X:S) 20.62/20.95 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.62/20.95 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.62/20.95 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.62/20.95 -> Rules: 20.62/20.95 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.95 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.95 a__U12(tt) -> tt 20.62/20.95 a__U12(X:S) -> U12(X:S) 20.62/20.95 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.95 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.95 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.95 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.95 a__U23(tt) -> tt 20.62/20.95 a__U23(X:S) -> U23(X:S) 20.62/20.95 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.95 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.95 a__U32(tt) -> tt 20.62/20.95 a__U32(X:S) -> U32(X:S) 20.62/20.95 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.95 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.95 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.95 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.95 a__U43(tt) -> tt 20.62/20.95 a__U43(X:S) -> U43(X:S) 20.62/20.95 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.95 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.95 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.95 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.95 a__U53(tt) -> tt 20.62/20.95 a__U53(X:S) -> U53(X:S) 20.62/20.95 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.95 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.95 a__U62(tt) -> tt 20.62/20.95 a__U62(X:S) -> U62(X:S) 20.62/20.95 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.95 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.95 a__U72(tt) -> tt 20.62/20.95 a__U72(X:S) -> U72(X:S) 20.62/20.95 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.95 a____(nil,X:S) -> mark(X:S) 20.62/20.95 a____(X:S,nil) -> mark(X:S) 20.62/20.95 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.95 a__and(tt,X:S) -> mark(X:S) 20.62/20.95 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.95 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.95 a__isList(nil) -> tt 20.62/20.95 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.95 a__isList(X:S) -> isList(X:S) 20.62/20.95 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.95 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.95 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.95 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.95 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.95 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.95 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.95 a__isPal(nil) -> tt 20.62/20.95 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.95 a__isPal(X:S) -> isPal(X:S) 20.62/20.95 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.95 a__isPalListKind(a) -> tt 20.62/20.95 a__isPalListKind(e) -> tt 20.62/20.95 a__isPalListKind(i) -> tt 20.62/20.95 a__isPalListKind(nil) -> tt 20.62/20.95 a__isPalListKind(o) -> tt 20.62/20.95 a__isPalListKind(u) -> tt 20.62/20.95 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.95 a__isQid(a) -> tt 20.62/20.95 a__isQid(e) -> tt 20.62/20.95 a__isQid(i) -> tt 20.62/20.95 a__isQid(o) -> tt 20.62/20.95 a__isQid(u) -> tt 20.62/20.95 a__isQid(X:S) -> isQid(X:S) 20.62/20.95 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.95 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.95 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.95 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.95 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.95 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.95 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.95 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.95 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.95 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.95 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.95 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.95 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.95 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.95 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.95 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.95 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.95 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.95 mark(a) -> a 20.62/20.95 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.95 mark(e) -> e 20.62/20.95 mark(i) -> i 20.62/20.95 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.95 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.95 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.95 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.95 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.95 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.95 mark(nil) -> nil 20.62/20.95 mark(o) -> o 20.62/20.95 mark(tt) -> tt 20.62/20.95 mark(u) -> u 20.62/20.95 -> Usable rules: 20.62/20.95 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.95 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.95 a__U12(tt) -> tt 20.62/20.95 a__U12(X:S) -> U12(X:S) 20.62/20.95 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.95 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.95 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.95 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.95 a__U23(tt) -> tt 20.62/20.95 a__U23(X:S) -> U23(X:S) 20.62/20.95 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.95 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.95 a__U32(tt) -> tt 20.62/20.95 a__U32(X:S) -> U32(X:S) 20.62/20.95 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.95 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.95 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.95 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.95 a__U43(tt) -> tt 20.62/20.95 a__U43(X:S) -> U43(X:S) 20.62/20.95 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.95 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.95 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.95 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.95 a__U53(tt) -> tt 20.62/20.95 a__U53(X:S) -> U53(X:S) 20.62/20.95 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.95 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.95 a__U62(tt) -> tt 20.62/20.95 a__U62(X:S) -> U62(X:S) 20.62/20.95 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.95 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.95 a__U72(tt) -> tt 20.62/20.95 a__U72(X:S) -> U72(X:S) 20.62/20.95 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.95 a____(nil,X:S) -> mark(X:S) 20.62/20.95 a____(X:S,nil) -> mark(X:S) 20.62/20.95 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.95 a__and(tt,X:S) -> mark(X:S) 20.62/20.95 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.95 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.95 a__isList(nil) -> tt 20.62/20.95 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.95 a__isList(X:S) -> isList(X:S) 20.62/20.95 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.95 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.95 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.95 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.95 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.95 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.95 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.95 a__isPal(nil) -> tt 20.62/20.95 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.95 a__isPal(X:S) -> isPal(X:S) 20.62/20.95 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.95 a__isPalListKind(a) -> tt 20.62/20.95 a__isPalListKind(e) -> tt 20.62/20.95 a__isPalListKind(i) -> tt 20.62/20.95 a__isPalListKind(nil) -> tt 20.62/20.95 a__isPalListKind(o) -> tt 20.62/20.95 a__isPalListKind(u) -> tt 20.62/20.95 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.95 a__isQid(a) -> tt 20.62/20.95 a__isQid(e) -> tt 20.62/20.95 a__isQid(i) -> tt 20.62/20.95 a__isQid(o) -> tt 20.62/20.95 a__isQid(u) -> tt 20.62/20.95 a__isQid(X:S) -> isQid(X:S) 20.62/20.95 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.95 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.95 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.95 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.95 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.95 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.95 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.95 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.95 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.95 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.95 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.95 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.95 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.95 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.95 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.95 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.95 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.95 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.95 mark(a) -> a 20.62/20.95 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.95 mark(e) -> e 20.62/20.95 mark(i) -> i 20.62/20.95 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.95 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.95 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.95 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.95 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.95 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.95 mark(nil) -> nil 20.62/20.95 mark(o) -> o 20.62/20.95 mark(tt) -> tt 20.62/20.95 mark(u) -> u 20.62/20.95 ->Interpretation type: 20.62/20.95 Linear 20.62/20.95 ->Coefficients: 20.62/20.95 Natural Numbers 20.62/20.95 ->Dimension: 20.62/20.95 1 20.62/20.95 ->Bound: 20.62/20.95 2 20.62/20.95 ->Interpretation: 20.62/20.95 20.62/20.95 [a__U11](X1,X2) = 2.X2 20.62/20.95 [a__U12](X) = 0 20.62/20.95 [a__U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.62/20.95 [a__U22](X1,X2) = X1 + 2.X2 + 2 20.62/20.95 [a__U23](X) = 2 20.62/20.95 [a__U31](X1,X2) = 2.X1 + 2.X2 + 2 20.62/20.95 [a__U32](X) = X + 2 20.62/20.95 [a__U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.62/20.95 [a__U42](X1,X2) = X1 + 2.X2 + 2 20.62/20.95 [a__U43](X) = X 20.62/20.95 [a__U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.62/20.95 [a__U52](X1,X2) = X1 + 2.X2 20.62/20.95 [a__U53](X) = X 20.62/20.95 [a__U61](X1,X2) = 2.X1 + 2.X2 + 2 20.62/20.95 [a__U62](X) = X + 2 20.62/20.95 [a__U71](X1,X2) = 2.X1 + 2.X2 + 2 20.62/20.95 [a__U72](X) = X 20.62/20.95 [a____](X1,X2) = 2.X1 + X2 + 2 20.62/20.95 [a__and](X1,X2) = X1 + 2.X2 20.62/20.95 [a__isList](X) = 2.X 20.62/20.95 [a__isNeList](X) = 2.X + 2 20.62/20.95 [a__isNePal](X) = 2.X + 2 20.62/20.95 [a__isPal](X) = 2.X + 2 20.62/20.95 [a__isPalListKind](X) = 0 20.62/20.95 [a__isQid](X) = 2.X 20.62/20.95 [mark](X) = X 20.62/20.95 [U11](X1,X2) = 2.X2 20.62/20.95 [U12](X) = 0 20.62/20.95 [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.62/20.95 [U22](X1,X2) = X1 + 2.X2 + 2 20.62/20.95 [U23](X) = 2 20.62/20.95 [U31](X1,X2) = 2.X1 + 2.X2 + 2 20.62/20.95 [U32](X) = X + 2 20.62/20.95 [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.62/20.95 [U42](X1,X2) = X1 + 2.X2 + 2 20.62/20.95 [U43](X) = X 20.62/20.95 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.62/20.95 [U52](X1,X2) = X1 + 2.X2 20.62/20.95 [U53](X) = X 20.62/20.95 [U61](X1,X2) = 2.X1 + 2.X2 + 2 20.62/20.95 [U62](X) = X + 2 20.62/20.95 [U71](X1,X2) = 2.X1 + 2.X2 + 2 20.62/20.95 [U72](X) = X 20.62/20.95 [__](X1,X2) = 2.X1 + X2 + 2 20.62/20.95 [a] = 0 20.62/20.95 [and](X1,X2) = X1 + 2.X2 20.62/20.95 [e] = 0 20.62/20.95 [fSNonEmpty] = 0 20.62/20.95 [i] = 2 20.62/20.95 [isList](X) = 2.X 20.62/20.95 [isNeList](X) = 2.X + 2 20.62/20.95 [isNePal](X) = 2.X + 2 20.62/20.95 [isPal](X) = 2.X + 2 20.62/20.95 [isPalListKind](X) = 0 20.62/20.95 [isQid](X) = 2.X 20.62/20.95 [nil] = 2 20.62/20.95 [o] = 2 20.62/20.95 [tt] = 0 20.62/20.95 [u] = 2 20.62/20.95 [A__U11](X1,X2) = 0 20.62/20.95 [A__U12](X) = 0 20.62/20.95 [A__U21](X1,X2,X3) = 0 20.62/20.95 [A__U22](X1,X2) = 0 20.62/20.95 [A__U23](X) = 0 20.62/20.95 [A__U31](X1,X2) = 0 20.62/20.95 [A__U32](X) = 0 20.62/20.95 [A__U41](X1,X2,X3) = 0 20.62/20.95 [A__U42](X1,X2) = 0 20.62/20.95 [A__U43](X) = 0 20.62/20.95 [A__U51](X1,X2,X3) = 0 20.62/20.95 [A__U52](X1,X2) = 0 20.62/20.95 [A__U53](X) = 0 20.62/20.95 [A__U61](X1,X2) = 0 20.62/20.95 [A__U62](X) = 0 20.62/20.95 [A__U71](X1,X2) = 0 20.62/20.95 [A__U72](X) = 0 20.62/20.95 [A____](X1,X2) = 0 20.62/20.95 [A__AND](X1,X2) = 2.X1 + 2.X2 + 2 20.62/20.95 [A__ISLIST](X) = 0 20.62/20.95 [A__ISNELIST](X) = 0 20.62/20.95 [A__ISNEPAL](X) = 0 20.62/20.95 [A__ISPAL](X) = 0 20.62/20.95 [A__ISPALLISTKIND](X) = 2 20.62/20.95 [A__ISQID](X) = 0 20.62/20.95 [MARK](X) = 2.X + 2 20.62/20.95 20.62/20.95 Problem 1: 20.62/20.95 20.62/20.95 SCC Processor: 20.62/20.95 -> Pairs: 20.62/20.95 A__AND(tt,X:S) -> MARK(X:S) 20.62/20.95 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.95 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.62/20.95 MARK(U43(X:S)) -> MARK(X:S) 20.62/20.95 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.62/20.95 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(U53(X:S)) -> MARK(X:S) 20.62/20.95 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(U62(X:S)) -> MARK(X:S) 20.62/20.95 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(U72(X:S)) -> MARK(X:S) 20.62/20.95 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.62/20.95 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.62/20.95 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.62/20.95 -> Rules: 20.62/20.95 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.95 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.95 a__U12(tt) -> tt 20.62/20.95 a__U12(X:S) -> U12(X:S) 20.62/20.95 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.95 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.95 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.95 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.95 a__U23(tt) -> tt 20.62/20.95 a__U23(X:S) -> U23(X:S) 20.62/20.95 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.95 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.95 a__U32(tt) -> tt 20.62/20.95 a__U32(X:S) -> U32(X:S) 20.62/20.95 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.95 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.95 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.95 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.95 a__U43(tt) -> tt 20.62/20.95 a__U43(X:S) -> U43(X:S) 20.62/20.95 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.95 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.95 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.95 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.95 a__U53(tt) -> tt 20.62/20.95 a__U53(X:S) -> U53(X:S) 20.62/20.95 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.95 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.95 a__U62(tt) -> tt 20.62/20.95 a__U62(X:S) -> U62(X:S) 20.62/20.95 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.95 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.95 a__U72(tt) -> tt 20.62/20.95 a__U72(X:S) -> U72(X:S) 20.62/20.95 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.95 a____(nil,X:S) -> mark(X:S) 20.62/20.95 a____(X:S,nil) -> mark(X:S) 20.62/20.95 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.95 a__and(tt,X:S) -> mark(X:S) 20.62/20.95 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.95 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.95 a__isList(nil) -> tt 20.62/20.95 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.95 a__isList(X:S) -> isList(X:S) 20.62/20.95 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.95 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.95 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.95 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.95 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.95 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.95 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.95 a__isPal(nil) -> tt 20.62/20.95 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.95 a__isPal(X:S) -> isPal(X:S) 20.62/20.95 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.95 a__isPalListKind(a) -> tt 20.62/20.95 a__isPalListKind(e) -> tt 20.62/20.95 a__isPalListKind(i) -> tt 20.62/20.95 a__isPalListKind(nil) -> tt 20.62/20.95 a__isPalListKind(o) -> tt 20.62/20.95 a__isPalListKind(u) -> tt 20.62/20.95 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.95 a__isQid(a) -> tt 20.62/20.95 a__isQid(e) -> tt 20.62/20.95 a__isQid(i) -> tt 20.62/20.95 a__isQid(o) -> tt 20.62/20.95 a__isQid(u) -> tt 20.62/20.95 a__isQid(X:S) -> isQid(X:S) 20.62/20.95 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.95 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.95 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.95 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.95 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.95 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.95 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.95 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.95 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.95 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.95 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.95 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.95 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.95 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.95 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.95 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.95 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.95 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.95 mark(a) -> a 20.62/20.95 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.95 mark(e) -> e 20.62/20.95 mark(i) -> i 20.62/20.95 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.95 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.95 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.95 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.95 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.95 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.95 mark(nil) -> nil 20.62/20.95 mark(o) -> o 20.62/20.95 mark(tt) -> tt 20.62/20.95 mark(u) -> u 20.62/20.95 ->Strongly Connected Components: 20.62/20.95 ->->Cycle: 20.62/20.95 ->->-> Pairs: 20.62/20.95 A__AND(tt,X:S) -> MARK(X:S) 20.62/20.95 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.95 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.62/20.95 MARK(U43(X:S)) -> MARK(X:S) 20.62/20.95 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.62/20.95 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(U53(X:S)) -> MARK(X:S) 20.62/20.95 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(U62(X:S)) -> MARK(X:S) 20.62/20.95 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(U72(X:S)) -> MARK(X:S) 20.62/20.95 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.62/20.95 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.62/20.95 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.62/20.95 ->->-> Rules: 20.62/20.95 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.95 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.95 a__U12(tt) -> tt 20.62/20.95 a__U12(X:S) -> U12(X:S) 20.62/20.95 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.95 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.95 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.95 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.95 a__U23(tt) -> tt 20.62/20.95 a__U23(X:S) -> U23(X:S) 20.62/20.95 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.95 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.95 a__U32(tt) -> tt 20.62/20.95 a__U32(X:S) -> U32(X:S) 20.62/20.95 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.95 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.95 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.95 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.95 a__U43(tt) -> tt 20.62/20.95 a__U43(X:S) -> U43(X:S) 20.62/20.95 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.95 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.95 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.95 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.95 a__U53(tt) -> tt 20.62/20.95 a__U53(X:S) -> U53(X:S) 20.62/20.95 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.95 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.95 a__U62(tt) -> tt 20.62/20.95 a__U62(X:S) -> U62(X:S) 20.62/20.95 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.95 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.95 a__U72(tt) -> tt 20.62/20.95 a__U72(X:S) -> U72(X:S) 20.62/20.95 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.95 a____(nil,X:S) -> mark(X:S) 20.62/20.95 a____(X:S,nil) -> mark(X:S) 20.62/20.95 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.95 a__and(tt,X:S) -> mark(X:S) 20.62/20.95 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.95 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.95 a__isList(nil) -> tt 20.62/20.95 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.95 a__isList(X:S) -> isList(X:S) 20.62/20.95 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.95 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.95 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.95 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.95 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.95 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.95 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.95 a__isPal(nil) -> tt 20.62/20.95 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.95 a__isPal(X:S) -> isPal(X:S) 20.62/20.95 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.95 a__isPalListKind(a) -> tt 20.62/20.95 a__isPalListKind(e) -> tt 20.62/20.95 a__isPalListKind(i) -> tt 20.62/20.95 a__isPalListKind(nil) -> tt 20.62/20.95 a__isPalListKind(o) -> tt 20.62/20.95 a__isPalListKind(u) -> tt 20.62/20.95 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.95 a__isQid(a) -> tt 20.62/20.95 a__isQid(e) -> tt 20.62/20.95 a__isQid(i) -> tt 20.62/20.95 a__isQid(o) -> tt 20.62/20.95 a__isQid(u) -> tt 20.62/20.95 a__isQid(X:S) -> isQid(X:S) 20.62/20.95 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.95 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.95 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.95 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.95 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.95 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.95 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.95 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.95 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.95 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.95 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.95 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.95 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.95 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.95 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.95 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.95 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.95 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.95 mark(a) -> a 20.62/20.95 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.95 mark(e) -> e 20.62/20.95 mark(i) -> i 20.62/20.95 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.95 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.95 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.95 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.95 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.95 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.95 mark(nil) -> nil 20.62/20.95 mark(o) -> o 20.62/20.95 mark(tt) -> tt 20.62/20.95 mark(u) -> u 20.62/20.95 20.62/20.95 Problem 1: 20.62/20.95 20.62/20.95 Reduction Pairs Processor: 20.62/20.95 -> Pairs: 20.62/20.95 A__AND(tt,X:S) -> MARK(X:S) 20.62/20.95 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.95 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.62/20.95 MARK(U43(X:S)) -> MARK(X:S) 20.62/20.95 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.62/20.95 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(U53(X:S)) -> MARK(X:S) 20.62/20.95 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(U62(X:S)) -> MARK(X:S) 20.62/20.95 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(U72(X:S)) -> MARK(X:S) 20.62/20.95 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.62/20.95 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.62/20.95 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.62/20.95 -> Rules: 20.62/20.95 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.95 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.95 a__U12(tt) -> tt 20.62/20.95 a__U12(X:S) -> U12(X:S) 20.62/20.95 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.95 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.95 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.95 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.95 a__U23(tt) -> tt 20.62/20.95 a__U23(X:S) -> U23(X:S) 20.62/20.95 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.95 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.95 a__U32(tt) -> tt 20.62/20.95 a__U32(X:S) -> U32(X:S) 20.62/20.95 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.95 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.95 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.95 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.95 a__U43(tt) -> tt 20.62/20.95 a__U43(X:S) -> U43(X:S) 20.62/20.95 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.95 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.95 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.95 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.95 a__U53(tt) -> tt 20.62/20.95 a__U53(X:S) -> U53(X:S) 20.62/20.95 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.95 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.95 a__U62(tt) -> tt 20.62/20.95 a__U62(X:S) -> U62(X:S) 20.62/20.95 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.95 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.95 a__U72(tt) -> tt 20.62/20.95 a__U72(X:S) -> U72(X:S) 20.62/20.95 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.95 a____(nil,X:S) -> mark(X:S) 20.62/20.95 a____(X:S,nil) -> mark(X:S) 20.62/20.95 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.95 a__and(tt,X:S) -> mark(X:S) 20.62/20.95 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.95 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.95 a__isList(nil) -> tt 20.62/20.95 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.95 a__isList(X:S) -> isList(X:S) 20.62/20.95 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.95 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.95 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.95 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.95 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.95 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.95 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.95 a__isPal(nil) -> tt 20.62/20.95 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.95 a__isPal(X:S) -> isPal(X:S) 20.62/20.95 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.95 a__isPalListKind(a) -> tt 20.62/20.95 a__isPalListKind(e) -> tt 20.62/20.95 a__isPalListKind(i) -> tt 20.62/20.95 a__isPalListKind(nil) -> tt 20.62/20.95 a__isPalListKind(o) -> tt 20.62/20.95 a__isPalListKind(u) -> tt 20.62/20.95 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.95 a__isQid(a) -> tt 20.62/20.95 a__isQid(e) -> tt 20.62/20.95 a__isQid(i) -> tt 20.62/20.95 a__isQid(o) -> tt 20.62/20.95 a__isQid(u) -> tt 20.62/20.95 a__isQid(X:S) -> isQid(X:S) 20.62/20.95 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.95 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.95 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.95 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.95 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.95 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.95 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.95 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.95 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.95 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.95 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.95 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.95 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.95 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.95 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.95 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.95 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.95 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.95 mark(a) -> a 20.62/20.95 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.95 mark(e) -> e 20.62/20.95 mark(i) -> i 20.62/20.95 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.95 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.95 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.95 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.95 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.95 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.95 mark(nil) -> nil 20.62/20.95 mark(o) -> o 20.62/20.95 mark(tt) -> tt 20.62/20.95 mark(u) -> u 20.62/20.95 -> Usable rules: 20.62/20.95 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.95 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.95 a__U12(tt) -> tt 20.62/20.95 a__U12(X:S) -> U12(X:S) 20.62/20.95 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.95 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.95 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.95 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.95 a__U23(tt) -> tt 20.62/20.95 a__U23(X:S) -> U23(X:S) 20.62/20.95 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.95 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.95 a__U32(tt) -> tt 20.62/20.95 a__U32(X:S) -> U32(X:S) 20.62/20.95 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.95 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.95 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.95 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.95 a__U43(tt) -> tt 20.62/20.95 a__U43(X:S) -> U43(X:S) 20.62/20.95 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.95 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.95 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.95 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.95 a__U53(tt) -> tt 20.62/20.95 a__U53(X:S) -> U53(X:S) 20.62/20.95 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.95 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.95 a__U62(tt) -> tt 20.62/20.95 a__U62(X:S) -> U62(X:S) 20.62/20.95 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.95 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.95 a__U72(tt) -> tt 20.62/20.95 a__U72(X:S) -> U72(X:S) 20.62/20.95 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.95 a____(nil,X:S) -> mark(X:S) 20.62/20.95 a____(X:S,nil) -> mark(X:S) 20.62/20.95 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.95 a__and(tt,X:S) -> mark(X:S) 20.62/20.95 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.95 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.95 a__isList(nil) -> tt 20.62/20.95 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.95 a__isList(X:S) -> isList(X:S) 20.62/20.95 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.95 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.95 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.95 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.95 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.95 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.95 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.95 a__isPal(nil) -> tt 20.62/20.95 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.95 a__isPal(X:S) -> isPal(X:S) 20.62/20.95 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.95 a__isPalListKind(a) -> tt 20.62/20.95 a__isPalListKind(e) -> tt 20.62/20.95 a__isPalListKind(i) -> tt 20.62/20.95 a__isPalListKind(nil) -> tt 20.62/20.95 a__isPalListKind(o) -> tt 20.62/20.95 a__isPalListKind(u) -> tt 20.62/20.95 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.95 a__isQid(a) -> tt 20.62/20.95 a__isQid(e) -> tt 20.62/20.95 a__isQid(i) -> tt 20.62/20.95 a__isQid(o) -> tt 20.62/20.95 a__isQid(u) -> tt 20.62/20.95 a__isQid(X:S) -> isQid(X:S) 20.62/20.95 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.95 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.95 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.95 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.95 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.95 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.95 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.95 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.95 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.95 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.95 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.95 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.95 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.95 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.95 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.95 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.95 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.95 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.95 mark(a) -> a 20.62/20.95 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.95 mark(e) -> e 20.62/20.95 mark(i) -> i 20.62/20.95 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.95 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.95 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.95 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.95 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.95 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.95 mark(nil) -> nil 20.62/20.95 mark(o) -> o 20.62/20.95 mark(tt) -> tt 20.62/20.95 mark(u) -> u 20.62/20.95 ->Interpretation type: 20.62/20.95 Linear 20.62/20.95 ->Coefficients: 20.62/20.95 Natural Numbers 20.62/20.95 ->Dimension: 20.62/20.95 1 20.62/20.95 ->Bound: 20.62/20.95 2 20.62/20.95 ->Interpretation: 20.62/20.95 20.62/20.95 [a__U11](X1,X2) = 2.X1 + X2 20.62/20.95 [a__U12](X) = 0 20.62/20.95 [a__U21](X1,X2,X3) = X2 + X3 + 2 20.62/20.95 [a__U22](X1,X2) = X2 + 2 20.62/20.95 [a__U23](X) = X + 1 20.62/20.95 [a__U31](X1,X2) = 2.X1 + 2.X2 + 1 20.62/20.95 [a__U32](X) = 0 20.62/20.95 [a__U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.62/20.95 [a__U42](X1,X2) = 2.X2 + 2 20.62/20.95 [a__U43](X) = X + 1 20.62/20.95 [a__U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.62/20.95 [a__U52](X1,X2) = X1 + 2.X2 + 1 20.62/20.95 [a__U53](X) = X 20.62/20.95 [a__U61](X1,X2) = 2.X1 + 2.X2 20.62/20.95 [a__U62](X) = X 20.62/20.95 [a__U71](X1,X2) = X1 + 2.X2 + 2 20.62/20.95 [a__U72](X) = X + 2 20.62/20.95 [a____](X1,X2) = 2.X1 + X2 + 2 20.62/20.95 [a__and](X1,X2) = X1 + 2.X2 20.62/20.95 [a__isList](X) = X + 1 20.62/20.95 [a__isNeList](X) = 2.X + 1 20.62/20.95 [a__isNePal](X) = 2.X 20.62/20.95 [a__isPal](X) = 2.X + 2 20.62/20.95 [a__isPalListKind](X) = 0 20.62/20.95 [a__isQid](X) = 2.X 20.62/20.95 [mark](X) = X 20.62/20.95 [U11](X1,X2) = 2.X1 + X2 20.62/20.95 [U12](X) = 0 20.62/20.95 [U21](X1,X2,X3) = X2 + X3 + 2 20.62/20.95 [U22](X1,X2) = X2 + 2 20.62/20.95 [U23](X) = X + 1 20.62/20.95 [U31](X1,X2) = 2.X1 + 2.X2 + 1 20.62/20.95 [U32](X) = 0 20.62/20.95 [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.62/20.95 [U42](X1,X2) = 2.X2 + 2 20.62/20.95 [U43](X) = X + 1 20.62/20.95 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.62/20.95 [U52](X1,X2) = X1 + 2.X2 + 1 20.62/20.95 [U53](X) = X 20.62/20.95 [U61](X1,X2) = 2.X1 + 2.X2 20.62/20.95 [U62](X) = X 20.62/20.95 [U71](X1,X2) = X1 + 2.X2 + 2 20.62/20.95 [U72](X) = X + 2 20.62/20.95 [__](X1,X2) = 2.X1 + X2 + 2 20.62/20.95 [a] = 1 20.62/20.95 [and](X1,X2) = X1 + 2.X2 20.62/20.95 [e] = 2 20.62/20.95 [fSNonEmpty] = 0 20.62/20.95 [i] = 0 20.62/20.95 [isList](X) = X + 1 20.62/20.95 [isNeList](X) = 2.X + 1 20.62/20.95 [isNePal](X) = 2.X 20.62/20.95 [isPal](X) = 2.X + 2 20.62/20.95 [isPalListKind](X) = 0 20.62/20.95 [isQid](X) = 2.X 20.62/20.95 [nil] = 2 20.62/20.95 [o] = 2 20.62/20.95 [tt] = 0 20.62/20.95 [u] = 0 20.62/20.95 [A__U11](X1,X2) = 0 20.62/20.95 [A__U12](X) = 0 20.62/20.95 [A__U21](X1,X2,X3) = 0 20.62/20.95 [A__U22](X1,X2) = 0 20.62/20.95 [A__U23](X) = 0 20.62/20.95 [A__U31](X1,X2) = 0 20.62/20.95 [A__U32](X) = 0 20.62/20.95 [A__U41](X1,X2,X3) = 0 20.62/20.95 [A__U42](X1,X2) = 0 20.62/20.95 [A__U43](X) = 0 20.62/20.95 [A__U51](X1,X2,X3) = 0 20.62/20.95 [A__U52](X1,X2) = 0 20.62/20.95 [A__U53](X) = 0 20.62/20.95 [A__U61](X1,X2) = 0 20.62/20.95 [A__U62](X) = 0 20.62/20.95 [A__U71](X1,X2) = 0 20.62/20.95 [A__U72](X) = 0 20.62/20.95 [A____](X1,X2) = 0 20.62/20.95 [A__AND](X1,X2) = 2.X1 + 2.X2 + 2 20.62/20.95 [A__ISLIST](X) = 0 20.62/20.95 [A__ISNELIST](X) = 0 20.62/20.95 [A__ISNEPAL](X) = 0 20.62/20.95 [A__ISPAL](X) = 0 20.62/20.95 [A__ISPALLISTKIND](X) = 2 20.62/20.95 [A__ISQID](X) = 0 20.62/20.95 [MARK](X) = 2.X + 2 20.62/20.95 20.62/20.95 Problem 1: 20.62/20.95 20.62/20.95 SCC Processor: 20.62/20.95 -> Pairs: 20.62/20.95 A__AND(tt,X:S) -> MARK(X:S) 20.62/20.95 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.95 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.62/20.95 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.62/20.95 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(U53(X:S)) -> MARK(X:S) 20.62/20.95 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(U62(X:S)) -> MARK(X:S) 20.62/20.95 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(U72(X:S)) -> MARK(X:S) 20.62/20.95 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.62/20.95 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.62/20.95 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.62/20.95 -> Rules: 20.62/20.95 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.95 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.95 a__U12(tt) -> tt 20.62/20.95 a__U12(X:S) -> U12(X:S) 20.62/20.95 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.95 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.95 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.95 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.95 a__U23(tt) -> tt 20.62/20.95 a__U23(X:S) -> U23(X:S) 20.62/20.95 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.95 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.95 a__U32(tt) -> tt 20.62/20.95 a__U32(X:S) -> U32(X:S) 20.62/20.95 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.95 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.95 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.95 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.95 a__U43(tt) -> tt 20.62/20.95 a__U43(X:S) -> U43(X:S) 20.62/20.95 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.95 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.95 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.95 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.95 a__U53(tt) -> tt 20.62/20.95 a__U53(X:S) -> U53(X:S) 20.62/20.95 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.95 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.95 a__U62(tt) -> tt 20.62/20.95 a__U62(X:S) -> U62(X:S) 20.62/20.95 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.95 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.95 a__U72(tt) -> tt 20.62/20.95 a__U72(X:S) -> U72(X:S) 20.62/20.95 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.95 a____(nil,X:S) -> mark(X:S) 20.62/20.95 a____(X:S,nil) -> mark(X:S) 20.62/20.95 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.95 a__and(tt,X:S) -> mark(X:S) 20.62/20.95 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.95 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.95 a__isList(nil) -> tt 20.62/20.95 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.95 a__isList(X:S) -> isList(X:S) 20.62/20.95 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.95 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.95 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.95 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.95 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.95 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.95 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.95 a__isPal(nil) -> tt 20.62/20.95 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.95 a__isPal(X:S) -> isPal(X:S) 20.62/20.95 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.95 a__isPalListKind(a) -> tt 20.62/20.95 a__isPalListKind(e) -> tt 20.62/20.95 a__isPalListKind(i) -> tt 20.62/20.95 a__isPalListKind(nil) -> tt 20.62/20.95 a__isPalListKind(o) -> tt 20.62/20.95 a__isPalListKind(u) -> tt 20.62/20.95 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.95 a__isQid(a) -> tt 20.62/20.95 a__isQid(e) -> tt 20.62/20.95 a__isQid(i) -> tt 20.62/20.95 a__isQid(o) -> tt 20.62/20.95 a__isQid(u) -> tt 20.62/20.95 a__isQid(X:S) -> isQid(X:S) 20.62/20.95 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.95 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.95 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.95 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.95 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.95 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.95 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.95 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.95 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.95 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.95 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.95 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.95 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.95 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.95 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.95 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.95 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.95 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.95 mark(a) -> a 20.62/20.95 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.95 mark(e) -> e 20.62/20.95 mark(i) -> i 20.62/20.95 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.95 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.95 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.95 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.95 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.95 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.95 mark(nil) -> nil 20.62/20.95 mark(o) -> o 20.62/20.95 mark(tt) -> tt 20.62/20.95 mark(u) -> u 20.62/20.95 ->Strongly Connected Components: 20.62/20.95 ->->Cycle: 20.62/20.95 ->->-> Pairs: 20.62/20.95 A__AND(tt,X:S) -> MARK(X:S) 20.62/20.95 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.95 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.62/20.95 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.62/20.95 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(U53(X:S)) -> MARK(X:S) 20.62/20.95 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(U62(X:S)) -> MARK(X:S) 20.62/20.95 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(U72(X:S)) -> MARK(X:S) 20.62/20.95 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.62/20.95 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.62/20.95 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.62/20.95 ->->-> Rules: 20.62/20.95 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.95 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.95 a__U12(tt) -> tt 20.62/20.95 a__U12(X:S) -> U12(X:S) 20.62/20.95 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.95 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.95 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.95 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.95 a__U23(tt) -> tt 20.62/20.95 a__U23(X:S) -> U23(X:S) 20.62/20.95 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.95 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.95 a__U32(tt) -> tt 20.62/20.95 a__U32(X:S) -> U32(X:S) 20.62/20.95 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.95 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.95 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.95 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.95 a__U43(tt) -> tt 20.62/20.95 a__U43(X:S) -> U43(X:S) 20.62/20.95 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.95 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.95 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.95 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.95 a__U53(tt) -> tt 20.62/20.95 a__U53(X:S) -> U53(X:S) 20.62/20.95 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.95 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.95 a__U62(tt) -> tt 20.62/20.95 a__U62(X:S) -> U62(X:S) 20.62/20.95 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.95 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.95 a__U72(tt) -> tt 20.62/20.95 a__U72(X:S) -> U72(X:S) 20.62/20.95 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.95 a____(nil,X:S) -> mark(X:S) 20.62/20.95 a____(X:S,nil) -> mark(X:S) 20.62/20.95 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.95 a__and(tt,X:S) -> mark(X:S) 20.62/20.95 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.95 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.95 a__isList(nil) -> tt 20.62/20.95 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.95 a__isList(X:S) -> isList(X:S) 20.62/20.95 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.95 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.95 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.95 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.95 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.95 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.95 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.95 a__isPal(nil) -> tt 20.62/20.95 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.95 a__isPal(X:S) -> isPal(X:S) 20.62/20.95 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.95 a__isPalListKind(a) -> tt 20.62/20.95 a__isPalListKind(e) -> tt 20.62/20.95 a__isPalListKind(i) -> tt 20.62/20.95 a__isPalListKind(nil) -> tt 20.62/20.95 a__isPalListKind(o) -> tt 20.62/20.95 a__isPalListKind(u) -> tt 20.62/20.95 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.95 a__isQid(a) -> tt 20.62/20.95 a__isQid(e) -> tt 20.62/20.95 a__isQid(i) -> tt 20.62/20.95 a__isQid(o) -> tt 20.62/20.95 a__isQid(u) -> tt 20.62/20.95 a__isQid(X:S) -> isQid(X:S) 20.62/20.95 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.95 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.95 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.95 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.95 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.95 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.95 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.95 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.95 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.95 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.95 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.95 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.95 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.95 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.95 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.95 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.95 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.95 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.95 mark(a) -> a 20.62/20.95 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.95 mark(e) -> e 20.62/20.95 mark(i) -> i 20.62/20.95 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.95 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.95 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.95 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.95 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.95 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.95 mark(nil) -> nil 20.62/20.95 mark(o) -> o 20.62/20.95 mark(tt) -> tt 20.62/20.95 mark(u) -> u 20.62/20.95 20.62/20.95 Problem 1: 20.62/20.95 20.62/20.95 Reduction Pairs Processor: 20.62/20.95 -> Pairs: 20.62/20.95 A__AND(tt,X:S) -> MARK(X:S) 20.62/20.95 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.95 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.62/20.95 MARK(U51(X1:S,X2:S,X3:S)) -> MARK(X1:S) 20.62/20.95 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(U53(X:S)) -> MARK(X:S) 20.62/20.95 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(U62(X:S)) -> MARK(X:S) 20.62/20.95 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(U72(X:S)) -> MARK(X:S) 20.62/20.95 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.62/20.95 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.62/20.95 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.95 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.62/20.95 -> Rules: 20.62/20.95 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.95 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.95 a__U12(tt) -> tt 20.62/20.95 a__U12(X:S) -> U12(X:S) 20.62/20.95 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.95 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.95 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.95 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.95 a__U23(tt) -> tt 20.62/20.95 a__U23(X:S) -> U23(X:S) 20.62/20.95 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.95 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.95 a__U32(tt) -> tt 20.62/20.95 a__U32(X:S) -> U32(X:S) 20.62/20.95 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.95 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.95 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.95 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.95 a__U43(tt) -> tt 20.62/20.95 a__U43(X:S) -> U43(X:S) 20.62/20.95 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.95 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.95 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.95 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.95 a__U53(tt) -> tt 20.62/20.95 a__U53(X:S) -> U53(X:S) 20.62/20.95 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.95 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.95 a__U62(tt) -> tt 20.62/20.95 a__U62(X:S) -> U62(X:S) 20.62/20.95 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.95 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.95 a__U72(tt) -> tt 20.62/20.95 a__U72(X:S) -> U72(X:S) 20.62/20.95 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.95 a____(nil,X:S) -> mark(X:S) 20.62/20.95 a____(X:S,nil) -> mark(X:S) 20.62/20.95 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.95 a__and(tt,X:S) -> mark(X:S) 20.62/20.95 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.95 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.95 a__isList(nil) -> tt 20.62/20.95 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.95 a__isList(X:S) -> isList(X:S) 20.62/20.95 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.95 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.95 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.95 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.95 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.95 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.95 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.95 a__isPal(nil) -> tt 20.62/20.95 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.95 a__isPal(X:S) -> isPal(X:S) 20.62/20.95 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.95 a__isPalListKind(a) -> tt 20.62/20.95 a__isPalListKind(e) -> tt 20.62/20.95 a__isPalListKind(i) -> tt 20.62/20.95 a__isPalListKind(nil) -> tt 20.62/20.95 a__isPalListKind(o) -> tt 20.62/20.95 a__isPalListKind(u) -> tt 20.62/20.95 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.95 a__isQid(a) -> tt 20.62/20.95 a__isQid(e) -> tt 20.62/20.95 a__isQid(i) -> tt 20.62/20.95 a__isQid(o) -> tt 20.62/20.95 a__isQid(u) -> tt 20.62/20.95 a__isQid(X:S) -> isQid(X:S) 20.62/20.95 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.95 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.95 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.95 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.95 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.95 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.95 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.95 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.95 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.95 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.95 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.95 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.95 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.95 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.95 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.95 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.95 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.95 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.95 mark(a) -> a 20.62/20.95 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.95 mark(e) -> e 20.62/20.95 mark(i) -> i 20.62/20.95 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.95 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.95 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.95 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.95 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.95 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.95 mark(nil) -> nil 20.62/20.95 mark(o) -> o 20.62/20.95 mark(tt) -> tt 20.62/20.95 mark(u) -> u 20.62/20.95 -> Usable rules: 20.62/20.95 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.95 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.95 a__U12(tt) -> tt 20.62/20.95 a__U12(X:S) -> U12(X:S) 20.62/20.95 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.95 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.95 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.95 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.95 a__U23(tt) -> tt 20.62/20.95 a__U23(X:S) -> U23(X:S) 20.62/20.95 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.95 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.95 a__U32(tt) -> tt 20.62/20.95 a__U32(X:S) -> U32(X:S) 20.62/20.95 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.95 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.95 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.95 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.95 a__U43(tt) -> tt 20.62/20.95 a__U43(X:S) -> U43(X:S) 20.62/20.95 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.96 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.96 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.96 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.96 a__U53(tt) -> tt 20.62/20.96 a__U53(X:S) -> U53(X:S) 20.62/20.96 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.96 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.96 a__U62(tt) -> tt 20.62/20.96 a__U62(X:S) -> U62(X:S) 20.62/20.96 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.96 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.96 a__U72(tt) -> tt 20.62/20.96 a__U72(X:S) -> U72(X:S) 20.62/20.96 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.96 a____(nil,X:S) -> mark(X:S) 20.62/20.96 a____(X:S,nil) -> mark(X:S) 20.62/20.96 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.96 a__and(tt,X:S) -> mark(X:S) 20.62/20.96 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.96 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.96 a__isList(nil) -> tt 20.62/20.96 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.96 a__isList(X:S) -> isList(X:S) 20.62/20.96 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.96 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.96 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.96 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.96 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.96 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.96 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.96 a__isPal(nil) -> tt 20.62/20.96 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.96 a__isPal(X:S) -> isPal(X:S) 20.62/20.96 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.96 a__isPalListKind(a) -> tt 20.62/20.96 a__isPalListKind(e) -> tt 20.62/20.96 a__isPalListKind(i) -> tt 20.62/20.96 a__isPalListKind(nil) -> tt 20.62/20.96 a__isPalListKind(o) -> tt 20.62/20.96 a__isPalListKind(u) -> tt 20.62/20.96 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.96 a__isQid(a) -> tt 20.62/20.96 a__isQid(e) -> tt 20.62/20.96 a__isQid(i) -> tt 20.62/20.96 a__isQid(o) -> tt 20.62/20.96 a__isQid(u) -> tt 20.62/20.96 a__isQid(X:S) -> isQid(X:S) 20.62/20.96 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.96 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.96 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.96 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.96 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.96 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.96 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.96 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.96 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.96 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.96 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.96 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.96 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.96 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.96 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.96 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.96 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.96 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.96 mark(a) -> a 20.62/20.96 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.96 mark(e) -> e 20.62/20.96 mark(i) -> i 20.62/20.96 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.96 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.96 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.96 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.96 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.96 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.96 mark(nil) -> nil 20.62/20.96 mark(o) -> o 20.62/20.96 mark(tt) -> tt 20.62/20.96 mark(u) -> u 20.62/20.96 ->Interpretation type: 20.62/20.96 Linear 20.62/20.96 ->Coefficients: 20.62/20.96 Natural Numbers 20.62/20.96 ->Dimension: 20.62/20.96 1 20.62/20.96 ->Bound: 20.62/20.96 2 20.62/20.96 ->Interpretation: 20.62/20.96 20.62/20.96 [a__U11](X1,X2) = 2.X1 + 2.X2 20.62/20.96 [a__U12](X) = 0 20.62/20.96 [a__U21](X1,X2,X3) = 2.X1 + X3 + 2 20.62/20.96 [a__U22](X1,X2) = 1 20.62/20.96 [a__U23](X) = 1 20.62/20.96 [a__U31](X1,X2) = 2.X1 + 2.X2 20.62/20.96 [a__U32](X) = X 20.62/20.96 [a__U41](X1,X2,X3) = 2.X1 + X2 + 2.X3 + 2 20.62/20.96 [a__U42](X1,X2) = 2.X2 + 2 20.62/20.96 [a__U43](X) = X + 2 20.62/20.96 [a__U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.62/20.96 [a__U52](X1,X2) = X1 + 2.X2 + 2 20.62/20.96 [a__U53](X) = X + 1 20.62/20.96 [a__U61](X1,X2) = 2.X1 + 2.X2 + 1 20.62/20.96 [a__U62](X) = X + 1 20.62/20.96 [a__U71](X1,X2) = 2.X1 + 2.X2 + 1 20.62/20.96 [a__U72](X) = X 20.62/20.96 [a____](X1,X2) = 2.X1 + X2 + 2 20.62/20.96 [a__and](X1,X2) = X1 + 2.X2 20.62/20.96 [a__isList](X) = 2.X + 1 20.62/20.96 [a__isNeList](X) = 2.X 20.62/20.96 [a__isNePal](X) = 2.X + 1 20.62/20.96 [a__isPal](X) = 2.X + 1 20.62/20.96 [a__isPalListKind](X) = 0 20.62/20.96 [a__isQid](X) = 2.X 20.62/20.96 [mark](X) = X 20.62/20.96 [U11](X1,X2) = 2.X1 + 2.X2 20.62/20.96 [U12](X) = 0 20.62/20.96 [U21](X1,X2,X3) = 2.X1 + X3 + 2 20.62/20.96 [U22](X1,X2) = 1 20.62/20.96 [U23](X) = 1 20.62/20.96 [U31](X1,X2) = 2.X1 + 2.X2 20.62/20.96 [U32](X) = X 20.62/20.96 [U41](X1,X2,X3) = 2.X1 + X2 + 2.X3 + 2 20.62/20.96 [U42](X1,X2) = 2.X2 + 2 20.62/20.96 [U43](X) = X + 2 20.62/20.96 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.62/20.96 [U52](X1,X2) = X1 + 2.X2 + 2 20.62/20.96 [U53](X) = X + 1 20.62/20.96 [U61](X1,X2) = 2.X1 + 2.X2 + 1 20.62/20.96 [U62](X) = X + 1 20.62/20.96 [U71](X1,X2) = 2.X1 + 2.X2 + 1 20.62/20.96 [U72](X) = X 20.62/20.96 [__](X1,X2) = 2.X1 + X2 + 2 20.62/20.96 [a] = 1 20.62/20.96 [and](X1,X2) = X1 + 2.X2 20.62/20.96 [e] = 2 20.62/20.96 [fSNonEmpty] = 0 20.62/20.96 [i] = 2 20.62/20.96 [isList](X) = 2.X + 1 20.62/20.96 [isNeList](X) = 2.X 20.62/20.96 [isNePal](X) = 2.X + 1 20.62/20.96 [isPal](X) = 2.X + 1 20.62/20.96 [isPalListKind](X) = 0 20.62/20.96 [isQid](X) = 2.X 20.62/20.96 [nil] = 2 20.62/20.96 [o] = 2 20.62/20.96 [tt] = 0 20.62/20.96 [u] = 2 20.62/20.96 [A__U11](X1,X2) = 0 20.62/20.96 [A__U12](X) = 0 20.62/20.96 [A__U21](X1,X2,X3) = 0 20.62/20.96 [A__U22](X1,X2) = 0 20.62/20.96 [A__U23](X) = 0 20.62/20.96 [A__U31](X1,X2) = 0 20.62/20.96 [A__U32](X) = 0 20.62/20.96 [A__U41](X1,X2,X3) = 0 20.62/20.96 [A__U42](X1,X2) = 0 20.62/20.96 [A__U43](X) = 0 20.62/20.96 [A__U51](X1,X2,X3) = 0 20.62/20.96 [A__U52](X1,X2) = 0 20.62/20.96 [A__U53](X) = 0 20.62/20.96 [A__U61](X1,X2) = 0 20.62/20.96 [A__U62](X) = 0 20.62/20.96 [A__U71](X1,X2) = 0 20.62/20.96 [A__U72](X) = 0 20.62/20.96 [A____](X1,X2) = 0 20.62/20.96 [A__AND](X1,X2) = 2.X1 + 2.X2 + 2 20.62/20.96 [A__ISLIST](X) = 0 20.62/20.96 [A__ISNELIST](X) = 0 20.62/20.96 [A__ISNEPAL](X) = 0 20.62/20.96 [A__ISPAL](X) = 0 20.62/20.96 [A__ISPALLISTKIND](X) = 2 20.62/20.96 [A__ISQID](X) = 0 20.62/20.96 [MARK](X) = 2.X + 2 20.62/20.96 20.62/20.96 Problem 1: 20.62/20.96 20.62/20.96 SCC Processor: 20.62/20.96 -> Pairs: 20.62/20.96 A__AND(tt,X:S) -> MARK(X:S) 20.62/20.96 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.96 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.62/20.96 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.96 MARK(U53(X:S)) -> MARK(X:S) 20.62/20.96 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.96 MARK(U62(X:S)) -> MARK(X:S) 20.62/20.96 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.96 MARK(U72(X:S)) -> MARK(X:S) 20.62/20.96 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.96 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.62/20.96 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.62/20.96 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.96 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.62/20.96 -> Rules: 20.62/20.96 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.96 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.96 a__U12(tt) -> tt 20.62/20.96 a__U12(X:S) -> U12(X:S) 20.62/20.96 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.96 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.96 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.96 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.96 a__U23(tt) -> tt 20.62/20.96 a__U23(X:S) -> U23(X:S) 20.62/20.96 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.96 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.96 a__U32(tt) -> tt 20.62/20.96 a__U32(X:S) -> U32(X:S) 20.62/20.96 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.96 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.96 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.96 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.96 a__U43(tt) -> tt 20.62/20.96 a__U43(X:S) -> U43(X:S) 20.62/20.96 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.96 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.96 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.96 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.96 a__U53(tt) -> tt 20.62/20.96 a__U53(X:S) -> U53(X:S) 20.62/20.96 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.96 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.96 a__U62(tt) -> tt 20.62/20.96 a__U62(X:S) -> U62(X:S) 20.62/20.96 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.96 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.96 a__U72(tt) -> tt 20.62/20.96 a__U72(X:S) -> U72(X:S) 20.62/20.96 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.96 a____(nil,X:S) -> mark(X:S) 20.62/20.96 a____(X:S,nil) -> mark(X:S) 20.62/20.96 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.96 a__and(tt,X:S) -> mark(X:S) 20.62/20.96 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.96 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.96 a__isList(nil) -> tt 20.62/20.96 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.96 a__isList(X:S) -> isList(X:S) 20.62/20.96 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.96 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.96 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.96 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.96 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.96 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.96 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.96 a__isPal(nil) -> tt 20.62/20.96 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.96 a__isPal(X:S) -> isPal(X:S) 20.62/20.96 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.96 a__isPalListKind(a) -> tt 20.62/20.96 a__isPalListKind(e) -> tt 20.62/20.96 a__isPalListKind(i) -> tt 20.62/20.96 a__isPalListKind(nil) -> tt 20.62/20.96 a__isPalListKind(o) -> tt 20.62/20.96 a__isPalListKind(u) -> tt 20.62/20.96 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.96 a__isQid(a) -> tt 20.62/20.96 a__isQid(e) -> tt 20.62/20.96 a__isQid(i) -> tt 20.62/20.96 a__isQid(o) -> tt 20.62/20.96 a__isQid(u) -> tt 20.62/20.96 a__isQid(X:S) -> isQid(X:S) 20.62/20.96 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.96 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.96 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.96 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.96 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.96 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.96 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.96 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.96 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.96 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.96 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.96 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.96 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.96 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.96 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.96 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.96 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.96 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.96 mark(a) -> a 20.62/20.96 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.96 mark(e) -> e 20.62/20.96 mark(i) -> i 20.62/20.96 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.96 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.96 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.96 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.96 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.96 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.96 mark(nil) -> nil 20.62/20.96 mark(o) -> o 20.62/20.96 mark(tt) -> tt 20.62/20.96 mark(u) -> u 20.62/20.96 ->Strongly Connected Components: 20.62/20.96 ->->Cycle: 20.62/20.96 ->->-> Pairs: 20.62/20.96 A__AND(tt,X:S) -> MARK(X:S) 20.62/20.96 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.96 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.62/20.96 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.96 MARK(U53(X:S)) -> MARK(X:S) 20.62/20.96 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.96 MARK(U62(X:S)) -> MARK(X:S) 20.62/20.96 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.96 MARK(U72(X:S)) -> MARK(X:S) 20.62/20.96 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.96 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.62/20.96 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.62/20.96 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.96 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.62/20.96 ->->-> Rules: 20.62/20.96 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.96 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.96 a__U12(tt) -> tt 20.62/20.96 a__U12(X:S) -> U12(X:S) 20.62/20.96 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.96 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.96 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.96 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.96 a__U23(tt) -> tt 20.62/20.96 a__U23(X:S) -> U23(X:S) 20.62/20.96 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.96 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.96 a__U32(tt) -> tt 20.62/20.96 a__U32(X:S) -> U32(X:S) 20.62/20.96 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.96 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.96 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.96 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.96 a__U43(tt) -> tt 20.62/20.96 a__U43(X:S) -> U43(X:S) 20.62/20.96 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.96 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.96 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.96 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.96 a__U53(tt) -> tt 20.62/20.96 a__U53(X:S) -> U53(X:S) 20.62/20.96 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.96 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.96 a__U62(tt) -> tt 20.62/20.96 a__U62(X:S) -> U62(X:S) 20.62/20.96 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.96 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.96 a__U72(tt) -> tt 20.62/20.96 a__U72(X:S) -> U72(X:S) 20.62/20.96 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.96 a____(nil,X:S) -> mark(X:S) 20.62/20.96 a____(X:S,nil) -> mark(X:S) 20.62/20.96 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.96 a__and(tt,X:S) -> mark(X:S) 20.62/20.96 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.96 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.96 a__isList(nil) -> tt 20.62/20.96 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.96 a__isList(X:S) -> isList(X:S) 20.62/20.96 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.96 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.96 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.96 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.96 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.96 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.96 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.96 a__isPal(nil) -> tt 20.62/20.96 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.96 a__isPal(X:S) -> isPal(X:S) 20.62/20.96 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.96 a__isPalListKind(a) -> tt 20.62/20.96 a__isPalListKind(e) -> tt 20.62/20.96 a__isPalListKind(i) -> tt 20.62/20.96 a__isPalListKind(nil) -> tt 20.62/20.96 a__isPalListKind(o) -> tt 20.62/20.96 a__isPalListKind(u) -> tt 20.62/20.96 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.96 a__isQid(a) -> tt 20.62/20.96 a__isQid(e) -> tt 20.62/20.96 a__isQid(i) -> tt 20.62/20.96 a__isQid(o) -> tt 20.62/20.96 a__isQid(u) -> tt 20.62/20.96 a__isQid(X:S) -> isQid(X:S) 20.62/20.96 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.96 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.96 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.96 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.96 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.96 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.96 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.96 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.96 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.96 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.96 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.96 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.96 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.96 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.96 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.96 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.96 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.96 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.96 mark(a) -> a 20.62/20.96 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.96 mark(e) -> e 20.62/20.96 mark(i) -> i 20.62/20.96 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.96 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.96 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.96 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.96 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.96 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.96 mark(nil) -> nil 20.62/20.96 mark(o) -> o 20.62/20.96 mark(tt) -> tt 20.62/20.96 mark(u) -> u 20.62/20.96 20.62/20.96 Problem 1: 20.62/20.96 20.62/20.96 Reduction Pairs Processor: 20.62/20.96 -> Pairs: 20.62/20.96 A__AND(tt,X:S) -> MARK(X:S) 20.62/20.96 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.96 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.62/20.96 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.96 MARK(U53(X:S)) -> MARK(X:S) 20.62/20.96 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.96 MARK(U62(X:S)) -> MARK(X:S) 20.62/20.96 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.96 MARK(U72(X:S)) -> MARK(X:S) 20.62/20.96 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.96 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.62/20.96 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.62/20.96 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.96 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.62/20.96 -> Rules: 20.62/20.96 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.96 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.96 a__U12(tt) -> tt 20.62/20.96 a__U12(X:S) -> U12(X:S) 20.62/20.96 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.96 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.96 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.96 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.96 a__U23(tt) -> tt 20.62/20.96 a__U23(X:S) -> U23(X:S) 20.62/20.96 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.96 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.96 a__U32(tt) -> tt 20.62/20.96 a__U32(X:S) -> U32(X:S) 20.62/20.96 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.96 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.96 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.96 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.96 a__U43(tt) -> tt 20.62/20.96 a__U43(X:S) -> U43(X:S) 20.62/20.96 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.96 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.96 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.96 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.96 a__U53(tt) -> tt 20.62/20.96 a__U53(X:S) -> U53(X:S) 20.62/20.96 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.96 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.96 a__U62(tt) -> tt 20.62/20.96 a__U62(X:S) -> U62(X:S) 20.62/20.96 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.96 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.96 a__U72(tt) -> tt 20.62/20.96 a__U72(X:S) -> U72(X:S) 20.62/20.96 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.96 a____(nil,X:S) -> mark(X:S) 20.62/20.96 a____(X:S,nil) -> mark(X:S) 20.62/20.96 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.96 a__and(tt,X:S) -> mark(X:S) 20.62/20.96 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.96 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.96 a__isList(nil) -> tt 20.62/20.96 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.96 a__isList(X:S) -> isList(X:S) 20.62/20.96 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.96 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.96 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.96 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.96 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.96 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.96 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.96 a__isPal(nil) -> tt 20.62/20.96 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.96 a__isPal(X:S) -> isPal(X:S) 20.62/20.96 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.96 a__isPalListKind(a) -> tt 20.62/20.96 a__isPalListKind(e) -> tt 20.62/20.96 a__isPalListKind(i) -> tt 20.62/20.96 a__isPalListKind(nil) -> tt 20.62/20.96 a__isPalListKind(o) -> tt 20.62/20.96 a__isPalListKind(u) -> tt 20.62/20.96 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.96 a__isQid(a) -> tt 20.62/20.96 a__isQid(e) -> tt 20.62/20.96 a__isQid(i) -> tt 20.62/20.96 a__isQid(o) -> tt 20.62/20.96 a__isQid(u) -> tt 20.62/20.96 a__isQid(X:S) -> isQid(X:S) 20.62/20.96 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.96 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.96 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.96 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.96 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.96 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.96 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.96 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.96 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.96 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.96 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.96 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.96 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.96 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.96 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.96 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.96 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.96 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.96 mark(a) -> a 20.62/20.96 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.96 mark(e) -> e 20.62/20.96 mark(i) -> i 20.62/20.96 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.96 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.96 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.96 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.96 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.96 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.96 mark(nil) -> nil 20.62/20.96 mark(o) -> o 20.62/20.96 mark(tt) -> tt 20.62/20.96 mark(u) -> u 20.62/20.96 -> Usable rules: 20.62/20.96 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.96 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.96 a__U12(tt) -> tt 20.62/20.96 a__U12(X:S) -> U12(X:S) 20.62/20.96 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.96 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.96 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.96 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.96 a__U23(tt) -> tt 20.62/20.96 a__U23(X:S) -> U23(X:S) 20.62/20.96 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.96 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.96 a__U32(tt) -> tt 20.62/20.96 a__U32(X:S) -> U32(X:S) 20.62/20.96 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.96 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.96 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.96 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.96 a__U43(tt) -> tt 20.62/20.96 a__U43(X:S) -> U43(X:S) 20.62/20.96 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.96 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.96 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.96 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.96 a__U53(tt) -> tt 20.62/20.96 a__U53(X:S) -> U53(X:S) 20.62/20.96 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.96 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.96 a__U62(tt) -> tt 20.62/20.96 a__U62(X:S) -> U62(X:S) 20.62/20.96 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.96 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.96 a__U72(tt) -> tt 20.62/20.96 a__U72(X:S) -> U72(X:S) 20.62/20.96 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.96 a____(nil,X:S) -> mark(X:S) 20.62/20.96 a____(X:S,nil) -> mark(X:S) 20.62/20.96 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.96 a__and(tt,X:S) -> mark(X:S) 20.62/20.96 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.96 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.96 a__isList(nil) -> tt 20.62/20.96 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.96 a__isList(X:S) -> isList(X:S) 20.62/20.96 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.96 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.96 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.96 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.96 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.96 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.96 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.96 a__isPal(nil) -> tt 20.62/20.96 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.96 a__isPal(X:S) -> isPal(X:S) 20.62/20.96 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.96 a__isPalListKind(a) -> tt 20.62/20.96 a__isPalListKind(e) -> tt 20.62/20.96 a__isPalListKind(i) -> tt 20.62/20.96 a__isPalListKind(nil) -> tt 20.62/20.96 a__isPalListKind(o) -> tt 20.62/20.96 a__isPalListKind(u) -> tt 20.62/20.96 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.96 a__isQid(a) -> tt 20.62/20.96 a__isQid(e) -> tt 20.62/20.96 a__isQid(i) -> tt 20.62/20.96 a__isQid(o) -> tt 20.62/20.96 a__isQid(u) -> tt 20.62/20.96 a__isQid(X:S) -> isQid(X:S) 20.62/20.96 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.96 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.96 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.96 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.96 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.96 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.96 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.96 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.96 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.96 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.96 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.96 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.96 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.96 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.96 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.96 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.96 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.96 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.96 mark(a) -> a 20.62/20.96 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.96 mark(e) -> e 20.62/20.96 mark(i) -> i 20.62/20.96 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.96 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.96 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.96 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.96 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.96 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.96 mark(nil) -> nil 20.62/20.96 mark(o) -> o 20.62/20.96 mark(tt) -> tt 20.62/20.96 mark(u) -> u 20.62/20.96 ->Interpretation type: 20.62/20.96 Linear 20.62/20.96 ->Coefficients: 20.62/20.96 Natural Numbers 20.62/20.96 ->Dimension: 20.62/20.96 1 20.62/20.96 ->Bound: 20.62/20.96 2 20.62/20.96 ->Interpretation: 20.62/20.96 20.62/20.96 [a__U11](X1,X2) = 2.X1 + 2.X2 20.62/20.96 [a__U12](X) = X 20.62/20.96 [a__U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.62/20.96 [a__U22](X1,X2) = X1 + 2.X2 + 2 20.62/20.96 [a__U23](X) = 2 20.62/20.96 [a__U31](X1,X2) = 2.X1 + 2.X2 20.62/20.96 [a__U32](X) = 2.X 20.62/20.96 [a__U41](X1,X2,X3) = 2.X2 + 2.X3 + 2 20.62/20.96 [a__U42](X1,X2) = X1 + 2.X2 + 2 20.62/20.96 [a__U43](X) = 1 20.62/20.96 [a__U51](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 20.62/20.96 [a__U52](X1,X2) = X1 + 2.X2 + 2 20.62/20.96 [a__U53](X) = X 20.62/20.96 [a__U61](X1,X2) = X1 + 2.X2 + 2 20.62/20.96 [a__U62](X) = 2.X + 2 20.62/20.96 [a__U71](X1,X2) = 2.X1 + 2.X2 + 2 20.62/20.96 [a__U72](X) = X 20.62/20.96 [a____](X1,X2) = 2.X1 + X2 + 2 20.62/20.96 [a__and](X1,X2) = 2.X1 + X2 20.62/20.96 [a__isList](X) = 2.X 20.62/20.96 [a__isNeList](X) = 2.X 20.62/20.96 [a__isNePal](X) = 2.X + 2 20.62/20.96 [a__isPal](X) = 2.X + 2 20.62/20.96 [a__isPalListKind](X) = 0 20.62/20.96 [a__isQid](X) = X 20.62/20.96 [mark](X) = X 20.62/20.96 [U11](X1,X2) = 2.X1 + 2.X2 20.62/20.96 [U12](X) = X 20.62/20.96 [U21](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.62/20.96 [U22](X1,X2) = X1 + 2.X2 + 2 20.62/20.96 [U23](X) = 2 20.62/20.96 [U31](X1,X2) = 2.X1 + 2.X2 20.62/20.96 [U32](X) = 2.X 20.62/20.96 [U41](X1,X2,X3) = 2.X2 + 2.X3 + 2 20.62/20.96 [U42](X1,X2) = X1 + 2.X2 + 2 20.62/20.96 [U43](X) = 1 20.62/20.96 [U51](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 20.62/20.96 [U52](X1,X2) = X1 + 2.X2 + 2 20.62/20.96 [U53](X) = X 20.62/20.96 [U61](X1,X2) = X1 + 2.X2 + 2 20.62/20.96 [U62](X) = 2.X + 2 20.62/20.96 [U71](X1,X2) = 2.X1 + 2.X2 + 2 20.62/20.96 [U72](X) = X 20.62/20.96 [__](X1,X2) = 2.X1 + X2 + 2 20.62/20.96 [a] = 1 20.62/20.96 [and](X1,X2) = 2.X1 + X2 20.62/20.96 [e] = 1 20.62/20.96 [fSNonEmpty] = 0 20.62/20.96 [i] = 1 20.62/20.96 [isList](X) = 2.X 20.62/20.96 [isNeList](X) = 2.X 20.62/20.96 [isNePal](X) = 2.X + 2 20.62/20.96 [isPal](X) = 2.X + 2 20.62/20.96 [isPalListKind](X) = 0 20.62/20.96 [isQid](X) = X 20.62/20.96 [nil] = 1 20.62/20.96 [o] = 1 20.62/20.96 [tt] = 0 20.62/20.96 [u] = 0 20.62/20.96 [A__U11](X1,X2) = 0 20.62/20.96 [A__U12](X) = 0 20.62/20.96 [A__U21](X1,X2,X3) = 0 20.62/20.96 [A__U22](X1,X2) = 0 20.62/20.96 [A__U23](X) = 0 20.62/20.96 [A__U31](X1,X2) = 0 20.62/20.96 [A__U32](X) = 0 20.62/20.96 [A__U41](X1,X2,X3) = 0 20.62/20.96 [A__U42](X1,X2) = 0 20.62/20.96 [A__U43](X) = 0 20.62/20.96 [A__U51](X1,X2,X3) = 0 20.62/20.96 [A__U52](X1,X2) = 0 20.62/20.96 [A__U53](X) = 0 20.62/20.96 [A__U61](X1,X2) = 0 20.62/20.96 [A__U62](X) = 0 20.62/20.96 [A__U71](X1,X2) = 0 20.62/20.96 [A__U72](X) = 0 20.62/20.96 [A____](X1,X2) = 0 20.62/20.96 [A__AND](X1,X2) = 2.X2 + 2 20.62/20.96 [A__ISLIST](X) = 0 20.62/20.96 [A__ISNELIST](X) = 0 20.62/20.96 [A__ISNEPAL](X) = 0 20.62/20.96 [A__ISPAL](X) = 0 20.62/20.96 [A__ISPALLISTKIND](X) = 2 20.62/20.96 [A__ISQID](X) = 0 20.62/20.96 [MARK](X) = 2.X + 2 20.62/20.96 20.62/20.96 Problem 1: 20.62/20.96 20.62/20.96 SCC Processor: 20.62/20.96 -> Pairs: 20.62/20.96 A__AND(tt,X:S) -> MARK(X:S) 20.62/20.96 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.96 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.62/20.96 MARK(U53(X:S)) -> MARK(X:S) 20.62/20.96 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.96 MARK(U62(X:S)) -> MARK(X:S) 20.62/20.96 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.96 MARK(U72(X:S)) -> MARK(X:S) 20.62/20.96 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.96 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.62/20.96 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.62/20.96 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.96 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.62/20.96 -> Rules: 20.62/20.96 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.96 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.96 a__U12(tt) -> tt 20.62/20.96 a__U12(X:S) -> U12(X:S) 20.62/20.96 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.96 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.96 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.96 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.96 a__U23(tt) -> tt 20.62/20.96 a__U23(X:S) -> U23(X:S) 20.62/20.96 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.96 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.96 a__U32(tt) -> tt 20.62/20.96 a__U32(X:S) -> U32(X:S) 20.62/20.96 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.96 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.96 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.96 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.96 a__U43(tt) -> tt 20.62/20.96 a__U43(X:S) -> U43(X:S) 20.62/20.96 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.96 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.96 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.96 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.96 a__U53(tt) -> tt 20.62/20.96 a__U53(X:S) -> U53(X:S) 20.62/20.96 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.96 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.96 a__U62(tt) -> tt 20.62/20.96 a__U62(X:S) -> U62(X:S) 20.62/20.96 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.96 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.96 a__U72(tt) -> tt 20.62/20.96 a__U72(X:S) -> U72(X:S) 20.62/20.96 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.96 a____(nil,X:S) -> mark(X:S) 20.62/20.96 a____(X:S,nil) -> mark(X:S) 20.62/20.96 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.96 a__and(tt,X:S) -> mark(X:S) 20.62/20.96 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.96 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.96 a__isList(nil) -> tt 20.62/20.96 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.96 a__isList(X:S) -> isList(X:S) 20.62/20.96 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.96 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.96 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.96 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.96 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.96 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.96 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.96 a__isPal(nil) -> tt 20.62/20.96 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.96 a__isPal(X:S) -> isPal(X:S) 20.62/20.96 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.96 a__isPalListKind(a) -> tt 20.62/20.96 a__isPalListKind(e) -> tt 20.62/20.96 a__isPalListKind(i) -> tt 20.62/20.96 a__isPalListKind(nil) -> tt 20.62/20.96 a__isPalListKind(o) -> tt 20.62/20.96 a__isPalListKind(u) -> tt 20.62/20.96 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.96 a__isQid(a) -> tt 20.62/20.96 a__isQid(e) -> tt 20.62/20.96 a__isQid(i) -> tt 20.62/20.96 a__isQid(o) -> tt 20.62/20.96 a__isQid(u) -> tt 20.62/20.96 a__isQid(X:S) -> isQid(X:S) 20.62/20.96 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.96 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.96 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.96 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.96 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.96 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.96 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.96 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.96 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.96 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.96 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.96 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.96 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.96 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.96 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.96 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.96 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.96 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.96 mark(a) -> a 20.62/20.96 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.96 mark(e) -> e 20.62/20.96 mark(i) -> i 20.62/20.96 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.96 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.96 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.96 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.96 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.96 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.96 mark(nil) -> nil 20.62/20.96 mark(o) -> o 20.62/20.96 mark(tt) -> tt 20.62/20.96 mark(u) -> u 20.62/20.96 ->Strongly Connected Components: 20.62/20.96 ->->Cycle: 20.62/20.96 ->->-> Pairs: 20.62/20.96 A__AND(tt,X:S) -> MARK(X:S) 20.62/20.96 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.96 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.62/20.96 MARK(U53(X:S)) -> MARK(X:S) 20.62/20.96 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.96 MARK(U62(X:S)) -> MARK(X:S) 20.62/20.96 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.96 MARK(U72(X:S)) -> MARK(X:S) 20.62/20.96 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.96 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.62/20.96 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.62/20.96 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.96 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.62/20.96 ->->-> Rules: 20.62/20.96 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.96 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.96 a__U12(tt) -> tt 20.62/20.96 a__U12(X:S) -> U12(X:S) 20.62/20.96 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.96 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.96 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.96 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.96 a__U23(tt) -> tt 20.62/20.96 a__U23(X:S) -> U23(X:S) 20.62/20.96 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.96 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.96 a__U32(tt) -> tt 20.62/20.96 a__U32(X:S) -> U32(X:S) 20.62/20.96 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.96 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.96 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.96 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.96 a__U43(tt) -> tt 20.62/20.96 a__U43(X:S) -> U43(X:S) 20.62/20.96 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.96 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.96 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.96 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.96 a__U53(tt) -> tt 20.62/20.96 a__U53(X:S) -> U53(X:S) 20.62/20.96 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.96 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.96 a__U62(tt) -> tt 20.62/20.96 a__U62(X:S) -> U62(X:S) 20.62/20.96 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.96 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.96 a__U72(tt) -> tt 20.62/20.96 a__U72(X:S) -> U72(X:S) 20.62/20.96 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.96 a____(nil,X:S) -> mark(X:S) 20.62/20.96 a____(X:S,nil) -> mark(X:S) 20.62/20.96 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.96 a__and(tt,X:S) -> mark(X:S) 20.62/20.96 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.96 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.96 a__isList(nil) -> tt 20.62/20.96 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.96 a__isList(X:S) -> isList(X:S) 20.62/20.96 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.96 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.96 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.96 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.96 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.96 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.96 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.96 a__isPal(nil) -> tt 20.62/20.96 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.96 a__isPal(X:S) -> isPal(X:S) 20.62/20.96 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.96 a__isPalListKind(a) -> tt 20.62/20.96 a__isPalListKind(e) -> tt 20.62/20.96 a__isPalListKind(i) -> tt 20.62/20.96 a__isPalListKind(nil) -> tt 20.62/20.96 a__isPalListKind(o) -> tt 20.62/20.96 a__isPalListKind(u) -> tt 20.62/20.96 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.96 a__isQid(a) -> tt 20.62/20.96 a__isQid(e) -> tt 20.62/20.96 a__isQid(i) -> tt 20.62/20.96 a__isQid(o) -> tt 20.62/20.96 a__isQid(u) -> tt 20.62/20.96 a__isQid(X:S) -> isQid(X:S) 20.62/20.96 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.96 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.96 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.96 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.96 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.96 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.96 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.96 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.96 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.96 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.96 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.96 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.96 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.96 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.96 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.96 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.96 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.96 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.96 mark(a) -> a 20.62/20.96 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.96 mark(e) -> e 20.62/20.96 mark(i) -> i 20.62/20.96 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.96 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.96 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.96 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.96 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.96 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.96 mark(nil) -> nil 20.62/20.96 mark(o) -> o 20.62/20.96 mark(tt) -> tt 20.62/20.96 mark(u) -> u 20.62/20.96 20.62/20.96 Problem 1: 20.62/20.96 20.62/20.96 Reduction Pairs Processor: 20.62/20.96 -> Pairs: 20.62/20.96 A__AND(tt,X:S) -> MARK(X:S) 20.62/20.96 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.96 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.62/20.96 MARK(U53(X:S)) -> MARK(X:S) 20.62/20.96 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.96 MARK(U62(X:S)) -> MARK(X:S) 20.62/20.96 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.96 MARK(U72(X:S)) -> MARK(X:S) 20.62/20.96 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.96 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.62/20.96 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.62/20.96 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.96 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.62/20.96 -> Rules: 20.62/20.96 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.96 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.96 a__U12(tt) -> tt 20.62/20.96 a__U12(X:S) -> U12(X:S) 20.62/20.96 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.96 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.96 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.96 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.96 a__U23(tt) -> tt 20.62/20.96 a__U23(X:S) -> U23(X:S) 20.62/20.96 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.96 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.96 a__U32(tt) -> tt 20.62/20.96 a__U32(X:S) -> U32(X:S) 20.62/20.96 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.96 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.96 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.96 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.96 a__U43(tt) -> tt 20.62/20.96 a__U43(X:S) -> U43(X:S) 20.62/20.96 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.96 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.96 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.96 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.96 a__U53(tt) -> tt 20.62/20.96 a__U53(X:S) -> U53(X:S) 20.62/20.96 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.96 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.96 a__U62(tt) -> tt 20.62/20.96 a__U62(X:S) -> U62(X:S) 20.62/20.96 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.96 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.96 a__U72(tt) -> tt 20.62/20.96 a__U72(X:S) -> U72(X:S) 20.62/20.96 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.96 a____(nil,X:S) -> mark(X:S) 20.62/20.96 a____(X:S,nil) -> mark(X:S) 20.62/20.96 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.96 a__and(tt,X:S) -> mark(X:S) 20.62/20.96 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.96 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.96 a__isList(nil) -> tt 20.62/20.96 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.96 a__isList(X:S) -> isList(X:S) 20.62/20.96 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.96 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.96 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.96 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.96 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.96 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.96 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.96 a__isPal(nil) -> tt 20.62/20.96 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.96 a__isPal(X:S) -> isPal(X:S) 20.62/20.96 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.96 a__isPalListKind(a) -> tt 20.62/20.96 a__isPalListKind(e) -> tt 20.62/20.96 a__isPalListKind(i) -> tt 20.62/20.96 a__isPalListKind(nil) -> tt 20.62/20.96 a__isPalListKind(o) -> tt 20.62/20.96 a__isPalListKind(u) -> tt 20.62/20.96 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.96 a__isQid(a) -> tt 20.62/20.96 a__isQid(e) -> tt 20.62/20.96 a__isQid(i) -> tt 20.62/20.96 a__isQid(o) -> tt 20.62/20.96 a__isQid(u) -> tt 20.62/20.96 a__isQid(X:S) -> isQid(X:S) 20.62/20.96 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.96 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.96 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.96 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.96 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.96 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.96 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.96 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.96 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.96 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.96 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.96 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.96 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.96 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.96 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.96 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.96 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.96 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.96 mark(a) -> a 20.62/20.96 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.96 mark(e) -> e 20.62/20.96 mark(i) -> i 20.62/20.96 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.96 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.96 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.96 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.96 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.96 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.96 mark(nil) -> nil 20.62/20.96 mark(o) -> o 20.62/20.96 mark(tt) -> tt 20.62/20.96 mark(u) -> u 20.62/20.96 -> Usable rules: 20.62/20.96 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.96 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.96 a__U12(tt) -> tt 20.62/20.96 a__U12(X:S) -> U12(X:S) 20.62/20.96 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.96 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.96 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.96 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.96 a__U23(tt) -> tt 20.62/20.96 a__U23(X:S) -> U23(X:S) 20.62/20.96 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.96 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.96 a__U32(tt) -> tt 20.62/20.96 a__U32(X:S) -> U32(X:S) 20.62/20.96 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.96 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.96 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.96 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.96 a__U43(tt) -> tt 20.62/20.96 a__U43(X:S) -> U43(X:S) 20.62/20.96 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.96 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.96 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.96 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.96 a__U53(tt) -> tt 20.62/20.96 a__U53(X:S) -> U53(X:S) 20.62/20.96 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.96 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.96 a__U62(tt) -> tt 20.62/20.96 a__U62(X:S) -> U62(X:S) 20.62/20.96 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.96 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.96 a__U72(tt) -> tt 20.62/20.96 a__U72(X:S) -> U72(X:S) 20.62/20.96 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.96 a____(nil,X:S) -> mark(X:S) 20.62/20.96 a____(X:S,nil) -> mark(X:S) 20.62/20.96 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.96 a__and(tt,X:S) -> mark(X:S) 20.62/20.96 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.96 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.96 a__isList(nil) -> tt 20.62/20.96 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.96 a__isList(X:S) -> isList(X:S) 20.62/20.96 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.96 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.96 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.96 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.96 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.96 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.96 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.96 a__isPal(nil) -> tt 20.62/20.96 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.96 a__isPal(X:S) -> isPal(X:S) 20.62/20.96 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.96 a__isPalListKind(a) -> tt 20.62/20.96 a__isPalListKind(e) -> tt 20.62/20.96 a__isPalListKind(i) -> tt 20.62/20.96 a__isPalListKind(nil) -> tt 20.62/20.96 a__isPalListKind(o) -> tt 20.62/20.96 a__isPalListKind(u) -> tt 20.62/20.96 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.96 a__isQid(a) -> tt 20.62/20.96 a__isQid(e) -> tt 20.62/20.96 a__isQid(i) -> tt 20.62/20.96 a__isQid(o) -> tt 20.62/20.96 a__isQid(u) -> tt 20.62/20.96 a__isQid(X:S) -> isQid(X:S) 20.62/20.96 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.96 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.96 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.96 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.96 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.96 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.96 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.96 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.96 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.96 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.96 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.96 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.96 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.96 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.96 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.96 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.96 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.96 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.96 mark(a) -> a 20.62/20.96 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.96 mark(e) -> e 20.62/20.96 mark(i) -> i 20.62/20.96 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.96 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.96 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.96 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.96 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.96 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.96 mark(nil) -> nil 20.62/20.96 mark(o) -> o 20.62/20.96 mark(tt) -> tt 20.62/20.96 mark(u) -> u 20.62/20.96 ->Interpretation type: 20.62/20.96 Linear 20.62/20.96 ->Coefficients: 20.62/20.96 Natural Numbers 20.62/20.96 ->Dimension: 20.62/20.96 1 20.62/20.96 ->Bound: 20.62/20.96 2 20.62/20.96 ->Interpretation: 20.62/20.96 20.62/20.96 [a__U11](X1,X2) = 2.X1 + 2.X2 + 1 20.62/20.96 [a__U12](X) = 0 20.62/20.96 [a__U21](X1,X2,X3) = 2.X1 + X2 + 2.X3 + 2 20.62/20.96 [a__U22](X1,X2) = 2.X2 + 2 20.62/20.96 [a__U23](X) = 2 20.62/20.96 [a__U31](X1,X2) = 2.X1 + 2.X2 + 2 20.62/20.96 [a__U32](X) = 2.X + 2 20.62/20.96 [a__U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.62/20.96 [a__U42](X1,X2) = X1 + 2.X2 20.62/20.96 [a__U43](X) = 0 20.62/20.96 [a__U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.62/20.96 [a__U52](X1,X2) = 2.X2 + 2 20.62/20.96 [a__U53](X) = X + 1 20.62/20.96 [a__U61](X1,X2) = 2.X1 + 2.X2 + 2 20.62/20.96 [a__U62](X) = X + 2 20.62/20.96 [a__U71](X1,X2) = 2.X1 + 2.X2 + 2 20.62/20.96 [a__U72](X) = X 20.62/20.96 [a____](X1,X2) = 2.X1 + X2 + 2 20.62/20.96 [a__and](X1,X2) = X1 + 2.X2 20.62/20.96 [a__isList](X) = 2.X + 1 20.62/20.96 [a__isNeList](X) = 2.X + 2 20.62/20.96 [a__isNePal](X) = 2.X + 2 20.62/20.96 [a__isPal](X) = 2.X + 2 20.62/20.96 [a__isPalListKind](X) = 0 20.62/20.96 [a__isQid](X) = X 20.62/20.96 [mark](X) = X 20.62/20.96 [U11](X1,X2) = 2.X1 + 2.X2 + 1 20.62/20.96 [U12](X) = 0 20.62/20.96 [U21](X1,X2,X3) = 2.X1 + X2 + 2.X3 + 2 20.62/20.96 [U22](X1,X2) = 2.X2 + 2 20.62/20.96 [U23](X) = 2 20.62/20.96 [U31](X1,X2) = 2.X1 + 2.X2 + 2 20.62/20.96 [U32](X) = 2.X + 2 20.62/20.96 [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.62/20.96 [U42](X1,X2) = X1 + 2.X2 20.62/20.96 [U43](X) = 0 20.62/20.96 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.62/20.96 [U52](X1,X2) = 2.X2 + 2 20.62/20.96 [U53](X) = X + 1 20.62/20.96 [U61](X1,X2) = 2.X1 + 2.X2 + 2 20.62/20.96 [U62](X) = X + 2 20.62/20.96 [U71](X1,X2) = 2.X1 + 2.X2 + 2 20.62/20.96 [U72](X) = X 20.62/20.96 [__](X1,X2) = 2.X1 + X2 + 2 20.62/20.96 [a] = 0 20.62/20.96 [and](X1,X2) = X1 + 2.X2 20.62/20.96 [e] = 0 20.62/20.96 [fSNonEmpty] = 0 20.62/20.96 [i] = 0 20.62/20.96 [isList](X) = 2.X + 1 20.62/20.96 [isNeList](X) = 2.X + 2 20.62/20.96 [isNePal](X) = 2.X + 2 20.62/20.96 [isPal](X) = 2.X + 2 20.62/20.96 [isPalListKind](X) = 0 20.62/20.96 [isQid](X) = X 20.62/20.96 [nil] = 0 20.62/20.96 [o] = 0 20.62/20.96 [tt] = 0 20.62/20.96 [u] = 1 20.62/20.96 [A__U11](X1,X2) = 0 20.62/20.96 [A__U12](X) = 0 20.62/20.96 [A__U21](X1,X2,X3) = 0 20.62/20.96 [A__U22](X1,X2) = 0 20.62/20.96 [A__U23](X) = 0 20.62/20.96 [A__U31](X1,X2) = 0 20.62/20.96 [A__U32](X) = 0 20.62/20.96 [A__U41](X1,X2,X3) = 0 20.62/20.96 [A__U42](X1,X2) = 0 20.62/20.96 [A__U43](X) = 0 20.62/20.96 [A__U51](X1,X2,X3) = 0 20.62/20.96 [A__U52](X1,X2) = 0 20.62/20.96 [A__U53](X) = 0 20.62/20.96 [A__U61](X1,X2) = 0 20.62/20.96 [A__U62](X) = 0 20.62/20.96 [A__U71](X1,X2) = 0 20.62/20.96 [A__U72](X) = 0 20.62/20.96 [A____](X1,X2) = 0 20.62/20.96 [A__AND](X1,X2) = 2.X1 + 2.X2 20.62/20.96 [A__ISLIST](X) = 0 20.62/20.96 [A__ISNELIST](X) = 0 20.62/20.96 [A__ISNEPAL](X) = 0 20.62/20.96 [A__ISPAL](X) = 0 20.62/20.96 [A__ISPALLISTKIND](X) = 0 20.62/20.96 [A__ISQID](X) = 0 20.62/20.96 [MARK](X) = 2.X 20.62/20.96 20.62/20.96 Problem 1: 20.62/20.96 20.62/20.96 SCC Processor: 20.62/20.96 -> Pairs: 20.62/20.96 A__AND(tt,X:S) -> MARK(X:S) 20.62/20.96 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.96 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.62/20.96 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.96 MARK(U62(X:S)) -> MARK(X:S) 20.62/20.96 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.96 MARK(U72(X:S)) -> MARK(X:S) 20.62/20.96 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.96 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.62/20.96 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.62/20.96 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.96 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.62/20.96 -> Rules: 20.62/20.96 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.96 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.96 a__U12(tt) -> tt 20.62/20.96 a__U12(X:S) -> U12(X:S) 20.62/20.96 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.96 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.96 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.96 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.96 a__U23(tt) -> tt 20.62/20.96 a__U23(X:S) -> U23(X:S) 20.62/20.96 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.96 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.96 a__U32(tt) -> tt 20.62/20.96 a__U32(X:S) -> U32(X:S) 20.62/20.96 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.96 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.96 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.96 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.96 a__U43(tt) -> tt 20.62/20.96 a__U43(X:S) -> U43(X:S) 20.62/20.96 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.96 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.96 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.96 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.96 a__U53(tt) -> tt 20.62/20.96 a__U53(X:S) -> U53(X:S) 20.62/20.96 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.96 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.96 a__U62(tt) -> tt 20.62/20.96 a__U62(X:S) -> U62(X:S) 20.62/20.96 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.96 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.96 a__U72(tt) -> tt 20.62/20.96 a__U72(X:S) -> U72(X:S) 20.62/20.96 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.96 a____(nil,X:S) -> mark(X:S) 20.62/20.96 a____(X:S,nil) -> mark(X:S) 20.62/20.96 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.96 a__and(tt,X:S) -> mark(X:S) 20.62/20.96 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.96 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.96 a__isList(nil) -> tt 20.62/20.96 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.96 a__isList(X:S) -> isList(X:S) 20.62/20.96 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.96 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.96 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.96 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.96 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.96 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.96 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.96 a__isPal(nil) -> tt 20.62/20.96 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.96 a__isPal(X:S) -> isPal(X:S) 20.62/20.96 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.96 a__isPalListKind(a) -> tt 20.62/20.96 a__isPalListKind(e) -> tt 20.62/20.96 a__isPalListKind(i) -> tt 20.62/20.96 a__isPalListKind(nil) -> tt 20.62/20.96 a__isPalListKind(o) -> tt 20.62/20.96 a__isPalListKind(u) -> tt 20.62/20.96 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.96 a__isQid(a) -> tt 20.62/20.96 a__isQid(e) -> tt 20.62/20.96 a__isQid(i) -> tt 20.62/20.96 a__isQid(o) -> tt 20.62/20.96 a__isQid(u) -> tt 20.62/20.96 a__isQid(X:S) -> isQid(X:S) 20.62/20.96 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.96 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.96 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.96 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.96 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.96 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.96 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.96 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.96 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.96 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.96 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.96 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.96 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.96 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.96 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.96 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.96 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.96 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.96 mark(a) -> a 20.62/20.96 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.96 mark(e) -> e 20.62/20.96 mark(i) -> i 20.62/20.96 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.96 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.96 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.96 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.96 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.96 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.96 mark(nil) -> nil 20.62/20.96 mark(o) -> o 20.62/20.96 mark(tt) -> tt 20.62/20.96 mark(u) -> u 20.62/20.96 ->Strongly Connected Components: 20.62/20.96 ->->Cycle: 20.62/20.96 ->->-> Pairs: 20.62/20.96 A__AND(tt,X:S) -> MARK(X:S) 20.62/20.96 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.96 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.62/20.96 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.96 MARK(U62(X:S)) -> MARK(X:S) 20.62/20.96 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.96 MARK(U72(X:S)) -> MARK(X:S) 20.62/20.96 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.96 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.62/20.96 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.62/20.96 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.96 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.62/20.96 ->->-> Rules: 20.62/20.96 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.96 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.96 a__U12(tt) -> tt 20.62/20.96 a__U12(X:S) -> U12(X:S) 20.62/20.96 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.96 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.96 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.96 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.96 a__U23(tt) -> tt 20.62/20.96 a__U23(X:S) -> U23(X:S) 20.62/20.96 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.96 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.96 a__U32(tt) -> tt 20.62/20.96 a__U32(X:S) -> U32(X:S) 20.62/20.96 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.96 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.96 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.96 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.96 a__U43(tt) -> tt 20.62/20.96 a__U43(X:S) -> U43(X:S) 20.62/20.96 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.96 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.96 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.96 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.96 a__U53(tt) -> tt 20.62/20.96 a__U53(X:S) -> U53(X:S) 20.62/20.96 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.96 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.96 a__U62(tt) -> tt 20.62/20.96 a__U62(X:S) -> U62(X:S) 20.62/20.96 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.96 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.96 a__U72(tt) -> tt 20.62/20.96 a__U72(X:S) -> U72(X:S) 20.62/20.96 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.96 a____(nil,X:S) -> mark(X:S) 20.62/20.96 a____(X:S,nil) -> mark(X:S) 20.62/20.96 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.96 a__and(tt,X:S) -> mark(X:S) 20.62/20.96 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.96 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.96 a__isList(nil) -> tt 20.62/20.96 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.96 a__isList(X:S) -> isList(X:S) 20.62/20.96 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.96 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.96 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.96 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.96 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.96 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.96 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.96 a__isPal(nil) -> tt 20.62/20.96 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.96 a__isPal(X:S) -> isPal(X:S) 20.62/20.96 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.96 a__isPalListKind(a) -> tt 20.62/20.96 a__isPalListKind(e) -> tt 20.62/20.96 a__isPalListKind(i) -> tt 20.62/20.96 a__isPalListKind(nil) -> tt 20.62/20.96 a__isPalListKind(o) -> tt 20.62/20.96 a__isPalListKind(u) -> tt 20.62/20.96 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.96 a__isQid(a) -> tt 20.62/20.96 a__isQid(e) -> tt 20.62/20.96 a__isQid(i) -> tt 20.62/20.96 a__isQid(o) -> tt 20.62/20.96 a__isQid(u) -> tt 20.62/20.96 a__isQid(X:S) -> isQid(X:S) 20.62/20.96 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.96 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.96 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.96 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.96 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.96 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.96 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.96 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.96 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.96 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.96 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.96 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.96 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.96 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.96 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.96 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.96 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.96 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.96 mark(a) -> a 20.62/20.96 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.96 mark(e) -> e 20.62/20.96 mark(i) -> i 20.62/20.96 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.96 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.96 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.96 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.96 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.96 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.96 mark(nil) -> nil 20.62/20.96 mark(o) -> o 20.62/20.96 mark(tt) -> tt 20.62/20.96 mark(u) -> u 20.62/20.96 20.62/20.96 Problem 1: 20.62/20.96 20.62/20.96 Reduction Pairs Processor: 20.62/20.96 -> Pairs: 20.62/20.96 A__AND(tt,X:S) -> MARK(X:S) 20.62/20.96 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.96 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.62/20.96 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.96 MARK(U62(X:S)) -> MARK(X:S) 20.62/20.96 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.96 MARK(U72(X:S)) -> MARK(X:S) 20.62/20.96 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.96 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.62/20.96 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.62/20.96 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.96 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.62/20.96 -> Rules: 20.62/20.96 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.96 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.96 a__U12(tt) -> tt 20.62/20.96 a__U12(X:S) -> U12(X:S) 20.62/20.96 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.96 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.96 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.96 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.96 a__U23(tt) -> tt 20.62/20.96 a__U23(X:S) -> U23(X:S) 20.62/20.96 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.96 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.96 a__U32(tt) -> tt 20.62/20.96 a__U32(X:S) -> U32(X:S) 20.62/20.96 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.96 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.96 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.96 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.96 a__U43(tt) -> tt 20.62/20.96 a__U43(X:S) -> U43(X:S) 20.62/20.96 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.96 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.96 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.96 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.96 a__U53(tt) -> tt 20.62/20.96 a__U53(X:S) -> U53(X:S) 20.62/20.96 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.96 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.96 a__U62(tt) -> tt 20.62/20.96 a__U62(X:S) -> U62(X:S) 20.62/20.96 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.96 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.96 a__U72(tt) -> tt 20.62/20.96 a__U72(X:S) -> U72(X:S) 20.62/20.96 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.96 a____(nil,X:S) -> mark(X:S) 20.62/20.96 a____(X:S,nil) -> mark(X:S) 20.62/20.96 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.96 a__and(tt,X:S) -> mark(X:S) 20.62/20.96 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.96 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.96 a__isList(nil) -> tt 20.62/20.96 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.96 a__isList(X:S) -> isList(X:S) 20.62/20.96 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.96 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.96 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.96 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.96 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.96 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.96 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.96 a__isPal(nil) -> tt 20.62/20.96 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.96 a__isPal(X:S) -> isPal(X:S) 20.62/20.96 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.96 a__isPalListKind(a) -> tt 20.62/20.96 a__isPalListKind(e) -> tt 20.62/20.96 a__isPalListKind(i) -> tt 20.62/20.96 a__isPalListKind(nil) -> tt 20.62/20.96 a__isPalListKind(o) -> tt 20.62/20.96 a__isPalListKind(u) -> tt 20.62/20.96 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.96 a__isQid(a) -> tt 20.62/20.96 a__isQid(e) -> tt 20.62/20.96 a__isQid(i) -> tt 20.62/20.96 a__isQid(o) -> tt 20.62/20.96 a__isQid(u) -> tt 20.62/20.96 a__isQid(X:S) -> isQid(X:S) 20.62/20.96 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.96 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.96 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.96 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.96 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.96 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.96 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.96 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.96 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.96 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.96 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.96 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.96 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.96 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.96 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.96 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.96 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.96 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.96 mark(a) -> a 20.62/20.96 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.96 mark(e) -> e 20.62/20.96 mark(i) -> i 20.62/20.96 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.96 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.96 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.96 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.96 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.96 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.96 mark(nil) -> nil 20.62/20.96 mark(o) -> o 20.62/20.96 mark(tt) -> tt 20.62/20.96 mark(u) -> u 20.62/20.96 -> Usable rules: 20.62/20.96 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.96 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.96 a__U12(tt) -> tt 20.62/20.96 a__U12(X:S) -> U12(X:S) 20.62/20.96 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.96 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.96 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.96 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.96 a__U23(tt) -> tt 20.62/20.96 a__U23(X:S) -> U23(X:S) 20.62/20.96 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.96 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.96 a__U32(tt) -> tt 20.62/20.96 a__U32(X:S) -> U32(X:S) 20.62/20.96 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.96 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.96 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.96 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.96 a__U43(tt) -> tt 20.62/20.96 a__U43(X:S) -> U43(X:S) 20.62/20.96 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.96 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.96 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.96 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.96 a__U53(tt) -> tt 20.62/20.96 a__U53(X:S) -> U53(X:S) 20.62/20.96 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.96 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.96 a__U62(tt) -> tt 20.62/20.96 a__U62(X:S) -> U62(X:S) 20.62/20.96 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.96 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.96 a__U72(tt) -> tt 20.62/20.96 a__U72(X:S) -> U72(X:S) 20.62/20.96 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.96 a____(nil,X:S) -> mark(X:S) 20.62/20.96 a____(X:S,nil) -> mark(X:S) 20.62/20.96 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.96 a__and(tt,X:S) -> mark(X:S) 20.62/20.96 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.96 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.96 a__isList(nil) -> tt 20.62/20.96 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.96 a__isList(X:S) -> isList(X:S) 20.62/20.96 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.96 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.96 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.96 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.96 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.96 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.96 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.96 a__isPal(nil) -> tt 20.62/20.96 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.96 a__isPal(X:S) -> isPal(X:S) 20.62/20.96 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.96 a__isPalListKind(a) -> tt 20.62/20.96 a__isPalListKind(e) -> tt 20.62/20.96 a__isPalListKind(i) -> tt 20.62/20.96 a__isPalListKind(nil) -> tt 20.62/20.96 a__isPalListKind(o) -> tt 20.62/20.96 a__isPalListKind(u) -> tt 20.62/20.96 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.96 a__isQid(a) -> tt 20.62/20.96 a__isQid(e) -> tt 20.62/20.96 a__isQid(i) -> tt 20.62/20.96 a__isQid(o) -> tt 20.62/20.96 a__isQid(u) -> tt 20.62/20.96 a__isQid(X:S) -> isQid(X:S) 20.62/20.96 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.96 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.96 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.96 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.96 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.96 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.96 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.96 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.96 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.96 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.96 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.96 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.96 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.96 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.96 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.96 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.96 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.96 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.96 mark(a) -> a 20.62/20.96 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.96 mark(e) -> e 20.62/20.96 mark(i) -> i 20.62/20.96 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.96 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.96 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.96 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.96 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.96 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.96 mark(nil) -> nil 20.62/20.96 mark(o) -> o 20.62/20.96 mark(tt) -> tt 20.62/20.96 mark(u) -> u 20.62/20.96 ->Interpretation type: 20.62/20.96 Linear 20.62/20.96 ->Coefficients: 20.62/20.96 Natural Numbers 20.62/20.96 ->Dimension: 20.62/20.96 1 20.62/20.96 ->Bound: 20.62/20.96 2 20.62/20.96 ->Interpretation: 20.62/20.96 20.62/20.96 [a__U11](X1,X2) = 2.X1 + 2.X2 + 2 20.62/20.96 [a__U12](X) = 2 20.62/20.96 [a__U21](X1,X2,X3) = 2.X1 + X2 + 2.X3 + 2 20.62/20.96 [a__U22](X1,X2) = 2.X2 + 2 20.62/20.96 [a__U23](X) = 1 20.62/20.96 [a__U31](X1,X2) = 2.X1 + 2.X2 + 2 20.62/20.96 [a__U32](X) = 2.X 20.62/20.96 [a__U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.62/20.96 [a__U42](X1,X2) = 2.X2 + 2 20.62/20.96 [a__U43](X) = 0 20.62/20.96 [a__U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.62/20.96 [a__U52](X1,X2) = 2.X2 + 2 20.62/20.96 [a__U53](X) = X 20.62/20.96 [a__U61](X1,X2) = X1 + X2 + 2 20.62/20.96 [a__U62](X) = 2.X + 2 20.62/20.96 [a__U71](X1,X2) = 2.X1 + 2.X2 + 2 20.62/20.96 [a__U72](X) = X 20.62/20.96 [a____](X1,X2) = 2.X1 + X2 + 2 20.62/20.96 [a__and](X1,X2) = X1 + X2 20.62/20.96 [a__isList](X) = 2.X + 2 20.62/20.96 [a__isNeList](X) = 2.X + 2 20.62/20.96 [a__isNePal](X) = X + 2 20.62/20.96 [a__isPal](X) = 2.X + 2 20.62/20.96 [a__isPalListKind](X) = 0 20.62/20.96 [a__isQid](X) = 0 20.62/20.96 [mark](X) = X 20.62/20.96 [U11](X1,X2) = 2.X1 + 2.X2 + 2 20.62/20.96 [U12](X) = 2 20.62/20.96 [U21](X1,X2,X3) = 2.X1 + X2 + 2.X3 + 2 20.62/20.96 [U22](X1,X2) = 2.X2 + 2 20.62/20.96 [U23](X) = 1 20.62/20.96 [U31](X1,X2) = 2.X1 + 2.X2 + 2 20.62/20.96 [U32](X) = 2.X 20.62/20.96 [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.62/20.96 [U42](X1,X2) = 2.X2 + 2 20.62/20.96 [U43](X) = 0 20.62/20.96 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.62/20.96 [U52](X1,X2) = 2.X2 + 2 20.62/20.96 [U53](X) = X 20.62/20.96 [U61](X1,X2) = X1 + X2 + 2 20.62/20.96 [U62](X) = 2.X + 2 20.62/20.96 [U71](X1,X2) = 2.X1 + 2.X2 + 2 20.62/20.96 [U72](X) = X 20.62/20.96 [__](X1,X2) = 2.X1 + X2 + 2 20.62/20.96 [a] = 0 20.62/20.96 [and](X1,X2) = X1 + X2 20.62/20.96 [e] = 1 20.62/20.96 [fSNonEmpty] = 0 20.62/20.96 [i] = 1 20.62/20.96 [isList](X) = 2.X + 2 20.62/20.96 [isNeList](X) = 2.X + 2 20.62/20.96 [isNePal](X) = X + 2 20.62/20.96 [isPal](X) = 2.X + 2 20.62/20.96 [isPalListKind](X) = 0 20.62/20.96 [isQid](X) = 0 20.62/20.96 [nil] = 1 20.62/20.96 [o] = 1 20.62/20.96 [tt] = 0 20.62/20.96 [u] = 1 20.62/20.96 [A__U11](X1,X2) = 0 20.62/20.96 [A__U12](X) = 0 20.62/20.96 [A__U21](X1,X2,X3) = 0 20.62/20.96 [A__U22](X1,X2) = 0 20.62/20.96 [A__U23](X) = 0 20.62/20.96 [A__U31](X1,X2) = 0 20.62/20.96 [A__U32](X) = 0 20.62/20.96 [A__U41](X1,X2,X3) = 0 20.62/20.96 [A__U42](X1,X2) = 0 20.62/20.96 [A__U43](X) = 0 20.62/20.96 [A__U51](X1,X2,X3) = 0 20.62/20.96 [A__U52](X1,X2) = 0 20.62/20.96 [A__U53](X) = 0 20.62/20.96 [A__U61](X1,X2) = 0 20.62/20.96 [A__U62](X) = 0 20.62/20.96 [A__U71](X1,X2) = 0 20.62/20.96 [A__U72](X) = 0 20.62/20.96 [A____](X1,X2) = 0 20.62/20.96 [A__AND](X1,X2) = 2.X1 + 2.X2 + 2 20.62/20.96 [A__ISLIST](X) = 0 20.62/20.96 [A__ISNELIST](X) = 0 20.62/20.96 [A__ISNEPAL](X) = 0 20.62/20.96 [A__ISPAL](X) = 0 20.62/20.96 [A__ISPALLISTKIND](X) = 2 20.62/20.96 [A__ISQID](X) = 0 20.62/20.96 [MARK](X) = 2.X + 2 20.62/20.96 20.62/20.96 Problem 1: 20.62/20.96 20.62/20.96 SCC Processor: 20.62/20.96 -> Pairs: 20.62/20.96 A__AND(tt,X:S) -> MARK(X:S) 20.62/20.96 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.96 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.62/20.96 MARK(U62(X:S)) -> MARK(X:S) 20.62/20.96 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.96 MARK(U72(X:S)) -> MARK(X:S) 20.62/20.96 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.96 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.62/20.96 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.62/20.96 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.96 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.62/20.96 -> Rules: 20.62/20.96 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.96 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.96 a__U12(tt) -> tt 20.62/20.96 a__U12(X:S) -> U12(X:S) 20.62/20.96 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.96 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.96 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.96 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.96 a__U23(tt) -> tt 20.62/20.96 a__U23(X:S) -> U23(X:S) 20.62/20.96 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.96 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.96 a__U32(tt) -> tt 20.62/20.96 a__U32(X:S) -> U32(X:S) 20.62/20.96 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.96 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.96 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.96 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.96 a__U43(tt) -> tt 20.62/20.96 a__U43(X:S) -> U43(X:S) 20.62/20.96 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.96 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.96 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.96 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.96 a__U53(tt) -> tt 20.62/20.96 a__U53(X:S) -> U53(X:S) 20.62/20.96 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.96 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.96 a__U62(tt) -> tt 20.62/20.96 a__U62(X:S) -> U62(X:S) 20.62/20.96 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.96 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.96 a__U72(tt) -> tt 20.62/20.96 a__U72(X:S) -> U72(X:S) 20.62/20.96 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.96 a____(nil,X:S) -> mark(X:S) 20.62/20.96 a____(X:S,nil) -> mark(X:S) 20.62/20.96 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.96 a__and(tt,X:S) -> mark(X:S) 20.62/20.96 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.96 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.96 a__isList(nil) -> tt 20.62/20.96 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.96 a__isList(X:S) -> isList(X:S) 20.62/20.96 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.96 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.96 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.96 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.96 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.96 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.96 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.96 a__isPal(nil) -> tt 20.62/20.96 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.96 a__isPal(X:S) -> isPal(X:S) 20.62/20.96 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.96 a__isPalListKind(a) -> tt 20.62/20.96 a__isPalListKind(e) -> tt 20.62/20.96 a__isPalListKind(i) -> tt 20.62/20.96 a__isPalListKind(nil) -> tt 20.62/20.96 a__isPalListKind(o) -> tt 20.62/20.96 a__isPalListKind(u) -> tt 20.62/20.96 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.96 a__isQid(a) -> tt 20.62/20.96 a__isQid(e) -> tt 20.62/20.96 a__isQid(i) -> tt 20.62/20.96 a__isQid(o) -> tt 20.62/20.96 a__isQid(u) -> tt 20.62/20.96 a__isQid(X:S) -> isQid(X:S) 20.62/20.96 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.96 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.96 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.96 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.96 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.96 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.96 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.96 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.96 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.96 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.96 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.96 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.96 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.96 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.96 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.96 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.96 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.96 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.96 mark(a) -> a 20.62/20.96 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.96 mark(e) -> e 20.62/20.96 mark(i) -> i 20.62/20.96 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.96 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.96 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.96 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.96 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.96 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.96 mark(nil) -> nil 20.62/20.96 mark(o) -> o 20.62/20.96 mark(tt) -> tt 20.62/20.96 mark(u) -> u 20.62/20.96 ->Strongly Connected Components: 20.62/20.96 ->->Cycle: 20.62/20.96 ->->-> Pairs: 20.62/20.96 A__AND(tt,X:S) -> MARK(X:S) 20.62/20.96 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.96 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.62/20.96 MARK(U62(X:S)) -> MARK(X:S) 20.62/20.96 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.96 MARK(U72(X:S)) -> MARK(X:S) 20.62/20.96 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.96 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.62/20.96 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.62/20.96 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.96 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.62/20.96 ->->-> Rules: 20.62/20.96 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.96 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.96 a__U12(tt) -> tt 20.62/20.96 a__U12(X:S) -> U12(X:S) 20.62/20.96 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.96 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.96 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.96 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.96 a__U23(tt) -> tt 20.62/20.96 a__U23(X:S) -> U23(X:S) 20.62/20.96 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.96 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.96 a__U32(tt) -> tt 20.62/20.96 a__U32(X:S) -> U32(X:S) 20.62/20.96 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.96 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.96 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.96 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.96 a__U43(tt) -> tt 20.62/20.96 a__U43(X:S) -> U43(X:S) 20.62/20.96 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.96 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.96 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.96 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.96 a__U53(tt) -> tt 20.62/20.96 a__U53(X:S) -> U53(X:S) 20.62/20.96 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.96 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.96 a__U62(tt) -> tt 20.62/20.96 a__U62(X:S) -> U62(X:S) 20.62/20.96 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.96 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.96 a__U72(tt) -> tt 20.62/20.96 a__U72(X:S) -> U72(X:S) 20.62/20.96 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.96 a____(nil,X:S) -> mark(X:S) 20.62/20.96 a____(X:S,nil) -> mark(X:S) 20.62/20.96 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.96 a__and(tt,X:S) -> mark(X:S) 20.62/20.96 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.96 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.96 a__isList(nil) -> tt 20.62/20.96 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.96 a__isList(X:S) -> isList(X:S) 20.62/20.96 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.96 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.96 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.96 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.96 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.96 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.96 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.96 a__isPal(nil) -> tt 20.62/20.96 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.96 a__isPal(X:S) -> isPal(X:S) 20.62/20.96 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.96 a__isPalListKind(a) -> tt 20.62/20.96 a__isPalListKind(e) -> tt 20.62/20.96 a__isPalListKind(i) -> tt 20.62/20.96 a__isPalListKind(nil) -> tt 20.62/20.96 a__isPalListKind(o) -> tt 20.62/20.96 a__isPalListKind(u) -> tt 20.62/20.96 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.96 a__isQid(a) -> tt 20.62/20.96 a__isQid(e) -> tt 20.62/20.96 a__isQid(i) -> tt 20.62/20.96 a__isQid(o) -> tt 20.62/20.96 a__isQid(u) -> tt 20.62/20.96 a__isQid(X:S) -> isQid(X:S) 20.62/20.96 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.96 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.96 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.96 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.96 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.96 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.96 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.96 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.96 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.96 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.96 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.96 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.96 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.96 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.96 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.96 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.96 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.96 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.96 mark(a) -> a 20.62/20.96 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.96 mark(e) -> e 20.62/20.96 mark(i) -> i 20.62/20.96 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.96 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.96 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.96 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.96 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.96 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.96 mark(nil) -> nil 20.62/20.96 mark(o) -> o 20.62/20.96 mark(tt) -> tt 20.62/20.96 mark(u) -> u 20.62/20.96 20.62/20.96 Problem 1: 20.62/20.96 20.62/20.96 Reduction Pairs Processor: 20.62/20.96 -> Pairs: 20.62/20.96 A__AND(tt,X:S) -> MARK(X:S) 20.62/20.96 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.96 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.62/20.96 MARK(U62(X:S)) -> MARK(X:S) 20.62/20.96 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.96 MARK(U72(X:S)) -> MARK(X:S) 20.62/20.96 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.96 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.62/20.96 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.62/20.96 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.96 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.62/20.96 -> Rules: 20.62/20.96 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.96 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.96 a__U12(tt) -> tt 20.62/20.96 a__U12(X:S) -> U12(X:S) 20.62/20.96 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.96 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.96 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.96 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.96 a__U23(tt) -> tt 20.62/20.96 a__U23(X:S) -> U23(X:S) 20.62/20.96 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.96 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.96 a__U32(tt) -> tt 20.62/20.96 a__U32(X:S) -> U32(X:S) 20.62/20.96 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.96 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.96 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.96 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.96 a__U43(tt) -> tt 20.62/20.96 a__U43(X:S) -> U43(X:S) 20.62/20.96 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.96 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.97 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.97 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.97 a__U53(tt) -> tt 20.62/20.97 a__U53(X:S) -> U53(X:S) 20.62/20.97 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.97 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.97 a__U62(tt) -> tt 20.62/20.97 a__U62(X:S) -> U62(X:S) 20.62/20.97 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.97 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.97 a__U72(tt) -> tt 20.62/20.97 a__U72(X:S) -> U72(X:S) 20.62/20.97 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.97 a____(nil,X:S) -> mark(X:S) 20.62/20.97 a____(X:S,nil) -> mark(X:S) 20.62/20.97 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.97 a__and(tt,X:S) -> mark(X:S) 20.62/20.97 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.97 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.97 a__isList(nil) -> tt 20.62/20.97 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isList(X:S) -> isList(X:S) 20.62/20.97 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.97 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.97 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.97 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.97 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.97 a__isPal(nil) -> tt 20.62/20.97 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isPal(X:S) -> isPal(X:S) 20.62/20.97 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.97 a__isPalListKind(a) -> tt 20.62/20.97 a__isPalListKind(e) -> tt 20.62/20.97 a__isPalListKind(i) -> tt 20.62/20.97 a__isPalListKind(nil) -> tt 20.62/20.97 a__isPalListKind(o) -> tt 20.62/20.97 a__isPalListKind(u) -> tt 20.62/20.97 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.97 a__isQid(a) -> tt 20.62/20.97 a__isQid(e) -> tt 20.62/20.97 a__isQid(i) -> tt 20.62/20.97 a__isQid(o) -> tt 20.62/20.97 a__isQid(u) -> tt 20.62/20.97 a__isQid(X:S) -> isQid(X:S) 20.62/20.97 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.97 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.97 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.97 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.97 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.97 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.97 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.97 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.97 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.97 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.97 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.97 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.97 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.97 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.97 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.97 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.97 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.97 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.97 mark(a) -> a 20.62/20.97 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.97 mark(e) -> e 20.62/20.97 mark(i) -> i 20.62/20.97 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.97 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.97 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.97 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.97 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.97 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.97 mark(nil) -> nil 20.62/20.97 mark(o) -> o 20.62/20.97 mark(tt) -> tt 20.62/20.97 mark(u) -> u 20.62/20.97 -> Usable rules: 20.62/20.97 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.97 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.97 a__U12(tt) -> tt 20.62/20.97 a__U12(X:S) -> U12(X:S) 20.62/20.97 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.97 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.97 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.97 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.97 a__U23(tt) -> tt 20.62/20.97 a__U23(X:S) -> U23(X:S) 20.62/20.97 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.97 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.97 a__U32(tt) -> tt 20.62/20.97 a__U32(X:S) -> U32(X:S) 20.62/20.97 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.97 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.97 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.97 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.97 a__U43(tt) -> tt 20.62/20.97 a__U43(X:S) -> U43(X:S) 20.62/20.97 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.97 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.97 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.97 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.97 a__U53(tt) -> tt 20.62/20.97 a__U53(X:S) -> U53(X:S) 20.62/20.97 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.97 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.97 a__U62(tt) -> tt 20.62/20.97 a__U62(X:S) -> U62(X:S) 20.62/20.97 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.97 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.97 a__U72(tt) -> tt 20.62/20.97 a__U72(X:S) -> U72(X:S) 20.62/20.97 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.97 a____(nil,X:S) -> mark(X:S) 20.62/20.97 a____(X:S,nil) -> mark(X:S) 20.62/20.97 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.97 a__and(tt,X:S) -> mark(X:S) 20.62/20.97 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.97 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.97 a__isList(nil) -> tt 20.62/20.97 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isList(X:S) -> isList(X:S) 20.62/20.97 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.97 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.97 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.97 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.97 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.97 a__isPal(nil) -> tt 20.62/20.97 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isPal(X:S) -> isPal(X:S) 20.62/20.97 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.97 a__isPalListKind(a) -> tt 20.62/20.97 a__isPalListKind(e) -> tt 20.62/20.97 a__isPalListKind(i) -> tt 20.62/20.97 a__isPalListKind(nil) -> tt 20.62/20.97 a__isPalListKind(o) -> tt 20.62/20.97 a__isPalListKind(u) -> tt 20.62/20.97 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.97 a__isQid(a) -> tt 20.62/20.97 a__isQid(e) -> tt 20.62/20.97 a__isQid(i) -> tt 20.62/20.97 a__isQid(o) -> tt 20.62/20.97 a__isQid(u) -> tt 20.62/20.97 a__isQid(X:S) -> isQid(X:S) 20.62/20.97 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.97 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.97 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.97 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.97 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.97 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.97 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.97 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.97 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.97 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.97 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.97 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.97 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.97 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.97 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.97 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.97 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.97 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.97 mark(a) -> a 20.62/20.97 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.97 mark(e) -> e 20.62/20.97 mark(i) -> i 20.62/20.97 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.97 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.97 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.97 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.97 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.97 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.97 mark(nil) -> nil 20.62/20.97 mark(o) -> o 20.62/20.97 mark(tt) -> tt 20.62/20.97 mark(u) -> u 20.62/20.97 ->Interpretation type: 20.62/20.97 Linear 20.62/20.97 ->Coefficients: 20.62/20.97 Natural Numbers 20.62/20.97 ->Dimension: 20.62/20.97 1 20.62/20.97 ->Bound: 20.62/20.97 2 20.62/20.97 ->Interpretation: 20.62/20.97 20.62/20.97 [a__U11](X1,X2) = X1 + 2.X2 + 2 20.62/20.97 [a__U12](X) = 2 20.62/20.97 [a__U21](X1,X2,X3) = 2.X1 + X2 + 2.X3 + 2 20.62/20.97 [a__U22](X1,X2) = 2.X2 + 2 20.62/20.97 [a__U23](X) = X 20.62/20.97 [a__U31](X1,X2) = X1 + 2.X2 + 1 20.62/20.97 [a__U32](X) = X 20.62/20.97 [a__U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.62/20.97 [a__U42](X1,X2) = X1 + 2.X2 20.62/20.97 [a__U43](X) = 0 20.62/20.97 [a__U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.62/20.97 [a__U52](X1,X2) = X1 + 2.X2 + 1 20.62/20.97 [a__U53](X) = 1 20.62/20.97 [a__U61](X1,X2) = 2.X2 + 2 20.62/20.97 [a__U62](X) = X + 2 20.62/20.97 [a__U71](X1,X2) = 2.X1 + 2.X2 + 2 20.62/20.97 [a__U72](X) = X 20.62/20.97 [a____](X1,X2) = 2.X1 + X2 + 2 20.62/20.97 [a__and](X1,X2) = X1 + 2.X2 20.62/20.97 [a__isList](X) = 2.X + 2 20.62/20.97 [a__isNeList](X) = 2.X + 1 20.62/20.97 [a__isNePal](X) = 2.X + 2 20.62/20.97 [a__isPal](X) = 2.X + 2 20.62/20.97 [a__isPalListKind](X) = 0 20.62/20.97 [a__isQid](X) = 2.X 20.62/20.97 [mark](X) = X 20.62/20.97 [U11](X1,X2) = X1 + 2.X2 + 2 20.62/20.97 [U12](X) = 2 20.62/20.97 [U21](X1,X2,X3) = 2.X1 + X2 + 2.X3 + 2 20.62/20.97 [U22](X1,X2) = 2.X2 + 2 20.62/20.97 [U23](X) = X 20.62/20.97 [U31](X1,X2) = X1 + 2.X2 + 1 20.62/20.97 [U32](X) = X 20.62/20.97 [U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.62/20.97 [U42](X1,X2) = X1 + 2.X2 20.62/20.97 [U43](X) = 0 20.62/20.97 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 20.62/20.97 [U52](X1,X2) = X1 + 2.X2 + 1 20.62/20.97 [U53](X) = 1 20.62/20.97 [U61](X1,X2) = 2.X2 + 2 20.62/20.97 [U62](X) = X + 2 20.62/20.97 [U71](X1,X2) = 2.X1 + 2.X2 + 2 20.62/20.97 [U72](X) = X 20.62/20.97 [__](X1,X2) = 2.X1 + X2 + 2 20.62/20.97 [a] = 1 20.62/20.97 [and](X1,X2) = X1 + 2.X2 20.62/20.97 [e] = 0 20.62/20.97 [fSNonEmpty] = 0 20.62/20.97 [i] = 0 20.62/20.97 [isList](X) = 2.X + 2 20.62/20.97 [isNeList](X) = 2.X + 1 20.62/20.97 [isNePal](X) = 2.X + 2 20.62/20.97 [isPal](X) = 2.X + 2 20.62/20.97 [isPalListKind](X) = 0 20.62/20.97 [isQid](X) = 2.X 20.62/20.97 [nil] = 0 20.62/20.97 [o] = 2 20.62/20.97 [tt] = 0 20.62/20.97 [u] = 0 20.62/20.97 [A__U11](X1,X2) = 0 20.62/20.97 [A__U12](X) = 0 20.62/20.97 [A__U21](X1,X2,X3) = 0 20.62/20.97 [A__U22](X1,X2) = 0 20.62/20.97 [A__U23](X) = 0 20.62/20.97 [A__U31](X1,X2) = 0 20.62/20.97 [A__U32](X) = 0 20.62/20.97 [A__U41](X1,X2,X3) = 0 20.62/20.97 [A__U42](X1,X2) = 0 20.62/20.97 [A__U43](X) = 0 20.62/20.97 [A__U51](X1,X2,X3) = 0 20.62/20.97 [A__U52](X1,X2) = 0 20.62/20.97 [A__U53](X) = 0 20.62/20.97 [A__U61](X1,X2) = 0 20.62/20.97 [A__U62](X) = 0 20.62/20.97 [A__U71](X1,X2) = 0 20.62/20.97 [A__U72](X) = 0 20.62/20.97 [A____](X1,X2) = 0 20.62/20.97 [A__AND](X1,X2) = X1 + 2.X2 + 2 20.62/20.97 [A__ISLIST](X) = 0 20.62/20.97 [A__ISNELIST](X) = 0 20.62/20.97 [A__ISNEPAL](X) = 0 20.62/20.97 [A__ISPAL](X) = 0 20.62/20.97 [A__ISPALLISTKIND](X) = 2 20.62/20.97 [A__ISQID](X) = 0 20.62/20.97 [MARK](X) = 2.X + 2 20.62/20.97 20.62/20.97 Problem 1: 20.62/20.97 20.62/20.97 SCC Processor: 20.62/20.97 -> Pairs: 20.62/20.97 A__AND(tt,X:S) -> MARK(X:S) 20.62/20.97 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.97 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.62/20.97 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.97 MARK(U72(X:S)) -> MARK(X:S) 20.62/20.97 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.97 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.62/20.97 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.62/20.97 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.97 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.62/20.97 -> Rules: 20.62/20.97 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.97 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.97 a__U12(tt) -> tt 20.62/20.97 a__U12(X:S) -> U12(X:S) 20.62/20.97 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.97 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.97 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.97 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.97 a__U23(tt) -> tt 20.62/20.97 a__U23(X:S) -> U23(X:S) 20.62/20.97 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.97 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.97 a__U32(tt) -> tt 20.62/20.97 a__U32(X:S) -> U32(X:S) 20.62/20.97 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.97 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.97 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.97 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.97 a__U43(tt) -> tt 20.62/20.97 a__U43(X:S) -> U43(X:S) 20.62/20.97 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.97 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.97 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.97 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.97 a__U53(tt) -> tt 20.62/20.97 a__U53(X:S) -> U53(X:S) 20.62/20.97 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.97 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.97 a__U62(tt) -> tt 20.62/20.97 a__U62(X:S) -> U62(X:S) 20.62/20.97 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.97 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.97 a__U72(tt) -> tt 20.62/20.97 a__U72(X:S) -> U72(X:S) 20.62/20.97 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.97 a____(nil,X:S) -> mark(X:S) 20.62/20.97 a____(X:S,nil) -> mark(X:S) 20.62/20.97 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.97 a__and(tt,X:S) -> mark(X:S) 20.62/20.97 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.97 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.97 a__isList(nil) -> tt 20.62/20.97 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isList(X:S) -> isList(X:S) 20.62/20.97 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.97 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.97 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.97 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.97 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.97 a__isPal(nil) -> tt 20.62/20.97 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isPal(X:S) -> isPal(X:S) 20.62/20.97 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.97 a__isPalListKind(a) -> tt 20.62/20.97 a__isPalListKind(e) -> tt 20.62/20.97 a__isPalListKind(i) -> tt 20.62/20.97 a__isPalListKind(nil) -> tt 20.62/20.97 a__isPalListKind(o) -> tt 20.62/20.97 a__isPalListKind(u) -> tt 20.62/20.97 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.97 a__isQid(a) -> tt 20.62/20.97 a__isQid(e) -> tt 20.62/20.97 a__isQid(i) -> tt 20.62/20.97 a__isQid(o) -> tt 20.62/20.97 a__isQid(u) -> tt 20.62/20.97 a__isQid(X:S) -> isQid(X:S) 20.62/20.97 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.97 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.97 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.97 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.97 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.97 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.97 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.97 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.97 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.97 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.97 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.97 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.97 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.97 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.97 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.97 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.97 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.97 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.97 mark(a) -> a 20.62/20.97 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.97 mark(e) -> e 20.62/20.97 mark(i) -> i 20.62/20.97 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.97 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.97 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.97 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.97 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.97 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.97 mark(nil) -> nil 20.62/20.97 mark(o) -> o 20.62/20.97 mark(tt) -> tt 20.62/20.97 mark(u) -> u 20.62/20.97 ->Strongly Connected Components: 20.62/20.97 ->->Cycle: 20.62/20.97 ->->-> Pairs: 20.62/20.97 A__AND(tt,X:S) -> MARK(X:S) 20.62/20.97 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.97 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.62/20.97 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.97 MARK(U72(X:S)) -> MARK(X:S) 20.62/20.97 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.97 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.62/20.97 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.62/20.97 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.97 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.62/20.97 ->->-> Rules: 20.62/20.97 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.97 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.97 a__U12(tt) -> tt 20.62/20.97 a__U12(X:S) -> U12(X:S) 20.62/20.97 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.97 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.97 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.97 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.97 a__U23(tt) -> tt 20.62/20.97 a__U23(X:S) -> U23(X:S) 20.62/20.97 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.97 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.97 a__U32(tt) -> tt 20.62/20.97 a__U32(X:S) -> U32(X:S) 20.62/20.97 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.97 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.97 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.97 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.97 a__U43(tt) -> tt 20.62/20.97 a__U43(X:S) -> U43(X:S) 20.62/20.97 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.97 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.97 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.97 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.97 a__U53(tt) -> tt 20.62/20.97 a__U53(X:S) -> U53(X:S) 20.62/20.97 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.97 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.97 a__U62(tt) -> tt 20.62/20.97 a__U62(X:S) -> U62(X:S) 20.62/20.97 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.97 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.97 a__U72(tt) -> tt 20.62/20.97 a__U72(X:S) -> U72(X:S) 20.62/20.97 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.97 a____(nil,X:S) -> mark(X:S) 20.62/20.97 a____(X:S,nil) -> mark(X:S) 20.62/20.97 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.97 a__and(tt,X:S) -> mark(X:S) 20.62/20.97 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.97 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.97 a__isList(nil) -> tt 20.62/20.97 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isList(X:S) -> isList(X:S) 20.62/20.97 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.97 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.97 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.97 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.97 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.97 a__isPal(nil) -> tt 20.62/20.97 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isPal(X:S) -> isPal(X:S) 20.62/20.97 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.97 a__isPalListKind(a) -> tt 20.62/20.97 a__isPalListKind(e) -> tt 20.62/20.97 a__isPalListKind(i) -> tt 20.62/20.97 a__isPalListKind(nil) -> tt 20.62/20.97 a__isPalListKind(o) -> tt 20.62/20.97 a__isPalListKind(u) -> tt 20.62/20.97 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.97 a__isQid(a) -> tt 20.62/20.97 a__isQid(e) -> tt 20.62/20.97 a__isQid(i) -> tt 20.62/20.97 a__isQid(o) -> tt 20.62/20.97 a__isQid(u) -> tt 20.62/20.97 a__isQid(X:S) -> isQid(X:S) 20.62/20.97 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.97 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.97 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.97 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.97 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.97 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.97 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.97 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.97 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.97 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.97 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.97 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.97 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.97 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.97 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.97 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.97 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.97 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.97 mark(a) -> a 20.62/20.97 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.97 mark(e) -> e 20.62/20.97 mark(i) -> i 20.62/20.97 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.97 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.97 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.97 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.97 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.97 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.97 mark(nil) -> nil 20.62/20.97 mark(o) -> o 20.62/20.97 mark(tt) -> tt 20.62/20.97 mark(u) -> u 20.62/20.97 20.62/20.97 Problem 1: 20.62/20.97 20.62/20.97 Reduction Pairs Processor: 20.62/20.97 -> Pairs: 20.62/20.97 A__AND(tt,X:S) -> MARK(X:S) 20.62/20.97 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.97 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.62/20.97 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.97 MARK(U72(X:S)) -> MARK(X:S) 20.62/20.97 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.97 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.62/20.97 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.62/20.97 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.97 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.62/20.97 -> Rules: 20.62/20.97 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.97 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.97 a__U12(tt) -> tt 20.62/20.97 a__U12(X:S) -> U12(X:S) 20.62/20.97 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.97 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.97 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.97 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.97 a__U23(tt) -> tt 20.62/20.97 a__U23(X:S) -> U23(X:S) 20.62/20.97 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.97 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.97 a__U32(tt) -> tt 20.62/20.97 a__U32(X:S) -> U32(X:S) 20.62/20.97 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.97 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.97 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.97 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.97 a__U43(tt) -> tt 20.62/20.97 a__U43(X:S) -> U43(X:S) 20.62/20.97 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.97 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.97 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.97 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.97 a__U53(tt) -> tt 20.62/20.97 a__U53(X:S) -> U53(X:S) 20.62/20.97 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.97 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.97 a__U62(tt) -> tt 20.62/20.97 a__U62(X:S) -> U62(X:S) 20.62/20.97 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.97 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.97 a__U72(tt) -> tt 20.62/20.97 a__U72(X:S) -> U72(X:S) 20.62/20.97 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.97 a____(nil,X:S) -> mark(X:S) 20.62/20.97 a____(X:S,nil) -> mark(X:S) 20.62/20.97 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.97 a__and(tt,X:S) -> mark(X:S) 20.62/20.97 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.97 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.97 a__isList(nil) -> tt 20.62/20.97 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isList(X:S) -> isList(X:S) 20.62/20.97 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.97 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.97 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.97 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.97 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.97 a__isPal(nil) -> tt 20.62/20.97 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isPal(X:S) -> isPal(X:S) 20.62/20.97 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.97 a__isPalListKind(a) -> tt 20.62/20.97 a__isPalListKind(e) -> tt 20.62/20.97 a__isPalListKind(i) -> tt 20.62/20.97 a__isPalListKind(nil) -> tt 20.62/20.97 a__isPalListKind(o) -> tt 20.62/20.97 a__isPalListKind(u) -> tt 20.62/20.97 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.97 a__isQid(a) -> tt 20.62/20.97 a__isQid(e) -> tt 20.62/20.97 a__isQid(i) -> tt 20.62/20.97 a__isQid(o) -> tt 20.62/20.97 a__isQid(u) -> tt 20.62/20.97 a__isQid(X:S) -> isQid(X:S) 20.62/20.97 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.97 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.97 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.97 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.97 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.97 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.97 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.97 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.97 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.97 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.97 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.97 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.97 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.97 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.97 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.97 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.97 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.97 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.97 mark(a) -> a 20.62/20.97 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.97 mark(e) -> e 20.62/20.97 mark(i) -> i 20.62/20.97 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.97 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.97 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.97 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.97 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.97 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.97 mark(nil) -> nil 20.62/20.97 mark(o) -> o 20.62/20.97 mark(tt) -> tt 20.62/20.97 mark(u) -> u 20.62/20.97 -> Usable rules: 20.62/20.97 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.97 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.97 a__U12(tt) -> tt 20.62/20.97 a__U12(X:S) -> U12(X:S) 20.62/20.97 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.97 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.97 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.97 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.97 a__U23(tt) -> tt 20.62/20.97 a__U23(X:S) -> U23(X:S) 20.62/20.97 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.97 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.97 a__U32(tt) -> tt 20.62/20.97 a__U32(X:S) -> U32(X:S) 20.62/20.97 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.97 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.97 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.97 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.97 a__U43(tt) -> tt 20.62/20.97 a__U43(X:S) -> U43(X:S) 20.62/20.97 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.97 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.97 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.97 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.97 a__U53(tt) -> tt 20.62/20.97 a__U53(X:S) -> U53(X:S) 20.62/20.97 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.97 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.97 a__U62(tt) -> tt 20.62/20.97 a__U62(X:S) -> U62(X:S) 20.62/20.97 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.97 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.97 a__U72(tt) -> tt 20.62/20.97 a__U72(X:S) -> U72(X:S) 20.62/20.97 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.97 a____(nil,X:S) -> mark(X:S) 20.62/20.97 a____(X:S,nil) -> mark(X:S) 20.62/20.97 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.97 a__and(tt,X:S) -> mark(X:S) 20.62/20.97 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.97 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.97 a__isList(nil) -> tt 20.62/20.97 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isList(X:S) -> isList(X:S) 20.62/20.97 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.97 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.97 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.97 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.97 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.97 a__isPal(nil) -> tt 20.62/20.97 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isPal(X:S) -> isPal(X:S) 20.62/20.97 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.97 a__isPalListKind(a) -> tt 20.62/20.97 a__isPalListKind(e) -> tt 20.62/20.97 a__isPalListKind(i) -> tt 20.62/20.97 a__isPalListKind(nil) -> tt 20.62/20.97 a__isPalListKind(o) -> tt 20.62/20.97 a__isPalListKind(u) -> tt 20.62/20.97 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.97 a__isQid(a) -> tt 20.62/20.97 a__isQid(e) -> tt 20.62/20.97 a__isQid(i) -> tt 20.62/20.97 a__isQid(o) -> tt 20.62/20.97 a__isQid(u) -> tt 20.62/20.97 a__isQid(X:S) -> isQid(X:S) 20.62/20.97 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.97 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.97 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.97 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.97 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.97 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.97 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.97 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.97 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.97 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.97 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.97 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.97 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.97 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.97 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.97 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.97 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.97 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.97 mark(a) -> a 20.62/20.97 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.97 mark(e) -> e 20.62/20.97 mark(i) -> i 20.62/20.97 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.97 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.97 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.97 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.97 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.97 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.97 mark(nil) -> nil 20.62/20.97 mark(o) -> o 20.62/20.97 mark(tt) -> tt 20.62/20.97 mark(u) -> u 20.62/20.97 ->Interpretation type: 20.62/20.97 Linear 20.62/20.97 ->Coefficients: 20.62/20.97 Natural Numbers 20.62/20.97 ->Dimension: 20.62/20.97 1 20.62/20.97 ->Bound: 20.62/20.97 2 20.62/20.97 ->Interpretation: 20.62/20.97 20.62/20.97 [a__U11](X1,X2) = X1 + 2.X2 + 2 20.62/20.97 [a__U12](X) = 1 20.62/20.97 [a__U21](X1,X2,X3) = 2.X1 + X2 + 2.X3 + 2 20.62/20.97 [a__U22](X1,X2) = 2.X2 + 2 20.62/20.97 [a__U23](X) = X 20.62/20.97 [a__U31](X1,X2) = 2.X1 + 2.X2 + 2 20.62/20.97 [a__U32](X) = X + 1 20.62/20.97 [a__U41](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 20.62/20.97 [a__U42](X1,X2) = 2.X2 + 2 20.62/20.97 [a__U43](X) = 1 20.62/20.97 [a__U51](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 20.62/20.97 [a__U52](X1,X2) = 2.X2 + 2 20.62/20.97 [a__U53](X) = X 20.62/20.97 [a__U61](X1,X2) = 2.X1 + X2 + 2 20.62/20.97 [a__U62](X) = 1 20.62/20.97 [a__U71](X1,X2) = 2.X1 + 2.X2 + 2 20.62/20.97 [a__U72](X) = X 20.62/20.97 [a____](X1,X2) = 2.X1 + X2 + 2 20.62/20.97 [a__and](X1,X2) = X1 + 2.X2 20.62/20.97 [a__isList](X) = 2.X + 2 20.62/20.97 [a__isNeList](X) = 2.X + 2 20.62/20.97 [a__isNePal](X) = 2.X + 2 20.62/20.97 [a__isPal](X) = 2.X + 2 20.62/20.97 [a__isPalListKind](X) = 0 20.62/20.97 [a__isQid](X) = 2.X + 1 20.62/20.97 [mark](X) = X 20.62/20.97 [U11](X1,X2) = X1 + 2.X2 + 2 20.62/20.97 [U12](X) = 1 20.62/20.97 [U21](X1,X2,X3) = 2.X1 + X2 + 2.X3 + 2 20.62/20.97 [U22](X1,X2) = 2.X2 + 2 20.62/20.97 [U23](X) = X 20.62/20.97 [U31](X1,X2) = 2.X1 + 2.X2 + 2 20.62/20.97 [U32](X) = X + 1 20.62/20.97 [U41](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 20.62/20.97 [U42](X1,X2) = 2.X2 + 2 20.62/20.97 [U43](X) = 1 20.62/20.97 [U51](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 20.62/20.97 [U52](X1,X2) = 2.X2 + 2 20.62/20.97 [U53](X) = X 20.62/20.97 [U61](X1,X2) = 2.X1 + X2 + 2 20.62/20.97 [U62](X) = 1 20.62/20.97 [U71](X1,X2) = 2.X1 + 2.X2 + 2 20.62/20.97 [U72](X) = X 20.62/20.97 [__](X1,X2) = 2.X1 + X2 + 2 20.62/20.97 [a] = 2 20.62/20.97 [and](X1,X2) = X1 + 2.X2 20.62/20.97 [e] = 2 20.62/20.97 [fSNonEmpty] = 0 20.62/20.97 [i] = 2 20.62/20.97 [isList](X) = 2.X + 2 20.62/20.97 [isNeList](X) = 2.X + 2 20.62/20.97 [isNePal](X) = 2.X + 2 20.62/20.97 [isPal](X) = 2.X + 2 20.62/20.97 [isPalListKind](X) = 0 20.62/20.97 [isQid](X) = 2.X + 1 20.62/20.97 [nil] = 2 20.62/20.97 [o] = 2 20.62/20.97 [tt] = 0 20.62/20.97 [u] = 0 20.62/20.97 [A__U11](X1,X2) = 0 20.62/20.97 [A__U12](X) = 0 20.62/20.97 [A__U21](X1,X2,X3) = 0 20.62/20.97 [A__U22](X1,X2) = 0 20.62/20.97 [A__U23](X) = 0 20.62/20.97 [A__U31](X1,X2) = 0 20.62/20.97 [A__U32](X) = 0 20.62/20.97 [A__U41](X1,X2,X3) = 0 20.62/20.97 [A__U42](X1,X2) = 0 20.62/20.97 [A__U43](X) = 0 20.62/20.97 [A__U51](X1,X2,X3) = 0 20.62/20.97 [A__U52](X1,X2) = 0 20.62/20.97 [A__U53](X) = 0 20.62/20.97 [A__U61](X1,X2) = 0 20.62/20.97 [A__U62](X) = 0 20.62/20.97 [A__U71](X1,X2) = 0 20.62/20.97 [A__U72](X) = 0 20.62/20.97 [A____](X1,X2) = 0 20.62/20.97 [A__AND](X1,X2) = 2.X1 + 2.X2 + 2 20.62/20.97 [A__ISLIST](X) = 0 20.62/20.97 [A__ISNELIST](X) = 0 20.62/20.97 [A__ISNEPAL](X) = 0 20.62/20.97 [A__ISPAL](X) = 0 20.62/20.97 [A__ISPALLISTKIND](X) = 2 20.62/20.97 [A__ISQID](X) = 0 20.62/20.97 [MARK](X) = 2.X + 2 20.62/20.97 20.62/20.97 Problem 1: 20.62/20.97 20.62/20.97 SCC Processor: 20.62/20.97 -> Pairs: 20.62/20.97 A__AND(tt,X:S) -> MARK(X:S) 20.62/20.97 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.97 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.62/20.97 MARK(U72(X:S)) -> MARK(X:S) 20.62/20.97 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.97 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.62/20.97 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.62/20.97 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.97 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.62/20.97 -> Rules: 20.62/20.97 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.97 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.97 a__U12(tt) -> tt 20.62/20.97 a__U12(X:S) -> U12(X:S) 20.62/20.97 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.97 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.97 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.97 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.97 a__U23(tt) -> tt 20.62/20.97 a__U23(X:S) -> U23(X:S) 20.62/20.97 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.97 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.97 a__U32(tt) -> tt 20.62/20.97 a__U32(X:S) -> U32(X:S) 20.62/20.97 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.97 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.97 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.97 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.97 a__U43(tt) -> tt 20.62/20.97 a__U43(X:S) -> U43(X:S) 20.62/20.97 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.97 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.97 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.97 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.97 a__U53(tt) -> tt 20.62/20.97 a__U53(X:S) -> U53(X:S) 20.62/20.97 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.97 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.97 a__U62(tt) -> tt 20.62/20.97 a__U62(X:S) -> U62(X:S) 20.62/20.97 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.97 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.97 a__U72(tt) -> tt 20.62/20.97 a__U72(X:S) -> U72(X:S) 20.62/20.97 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.97 a____(nil,X:S) -> mark(X:S) 20.62/20.97 a____(X:S,nil) -> mark(X:S) 20.62/20.97 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.97 a__and(tt,X:S) -> mark(X:S) 20.62/20.97 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.97 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.97 a__isList(nil) -> tt 20.62/20.97 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isList(X:S) -> isList(X:S) 20.62/20.97 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.97 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.97 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.97 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.97 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.97 a__isPal(nil) -> tt 20.62/20.97 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isPal(X:S) -> isPal(X:S) 20.62/20.97 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.97 a__isPalListKind(a) -> tt 20.62/20.97 a__isPalListKind(e) -> tt 20.62/20.97 a__isPalListKind(i) -> tt 20.62/20.97 a__isPalListKind(nil) -> tt 20.62/20.97 a__isPalListKind(o) -> tt 20.62/20.97 a__isPalListKind(u) -> tt 20.62/20.97 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.97 a__isQid(a) -> tt 20.62/20.97 a__isQid(e) -> tt 20.62/20.97 a__isQid(i) -> tt 20.62/20.97 a__isQid(o) -> tt 20.62/20.97 a__isQid(u) -> tt 20.62/20.97 a__isQid(X:S) -> isQid(X:S) 20.62/20.97 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.97 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.97 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.97 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.97 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.97 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.97 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.97 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.97 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.97 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.97 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.97 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.97 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.97 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.97 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.97 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.97 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.97 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.97 mark(a) -> a 20.62/20.97 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.97 mark(e) -> e 20.62/20.97 mark(i) -> i 20.62/20.97 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.97 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.97 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.97 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.97 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.97 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.97 mark(nil) -> nil 20.62/20.97 mark(o) -> o 20.62/20.97 mark(tt) -> tt 20.62/20.97 mark(u) -> u 20.62/20.97 ->Strongly Connected Components: 20.62/20.97 ->->Cycle: 20.62/20.97 ->->-> Pairs: 20.62/20.97 A__AND(tt,X:S) -> MARK(X:S) 20.62/20.97 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.97 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.62/20.97 MARK(U72(X:S)) -> MARK(X:S) 20.62/20.97 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.97 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.62/20.97 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.62/20.97 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.97 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.62/20.97 ->->-> Rules: 20.62/20.97 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.97 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.97 a__U12(tt) -> tt 20.62/20.97 a__U12(X:S) -> U12(X:S) 20.62/20.97 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.97 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.97 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.97 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.97 a__U23(tt) -> tt 20.62/20.97 a__U23(X:S) -> U23(X:S) 20.62/20.97 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.97 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.97 a__U32(tt) -> tt 20.62/20.97 a__U32(X:S) -> U32(X:S) 20.62/20.97 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.97 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.97 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.97 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.97 a__U43(tt) -> tt 20.62/20.97 a__U43(X:S) -> U43(X:S) 20.62/20.97 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.97 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.97 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.97 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.97 a__U53(tt) -> tt 20.62/20.97 a__U53(X:S) -> U53(X:S) 20.62/20.97 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.97 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.97 a__U62(tt) -> tt 20.62/20.97 a__U62(X:S) -> U62(X:S) 20.62/20.97 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.97 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.97 a__U72(tt) -> tt 20.62/20.97 a__U72(X:S) -> U72(X:S) 20.62/20.97 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.97 a____(nil,X:S) -> mark(X:S) 20.62/20.97 a____(X:S,nil) -> mark(X:S) 20.62/20.97 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.97 a__and(tt,X:S) -> mark(X:S) 20.62/20.97 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.97 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.97 a__isList(nil) -> tt 20.62/20.97 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isList(X:S) -> isList(X:S) 20.62/20.97 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.97 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.97 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.97 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.97 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.97 a__isPal(nil) -> tt 20.62/20.97 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isPal(X:S) -> isPal(X:S) 20.62/20.97 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.97 a__isPalListKind(a) -> tt 20.62/20.97 a__isPalListKind(e) -> tt 20.62/20.97 a__isPalListKind(i) -> tt 20.62/20.97 a__isPalListKind(nil) -> tt 20.62/20.97 a__isPalListKind(o) -> tt 20.62/20.97 a__isPalListKind(u) -> tt 20.62/20.97 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.97 a__isQid(a) -> tt 20.62/20.97 a__isQid(e) -> tt 20.62/20.97 a__isQid(i) -> tt 20.62/20.97 a__isQid(o) -> tt 20.62/20.97 a__isQid(u) -> tt 20.62/20.97 a__isQid(X:S) -> isQid(X:S) 20.62/20.97 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.97 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.97 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.97 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.97 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.97 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.97 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.97 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.97 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.97 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.97 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.97 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.97 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.97 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.97 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.97 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.97 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.97 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.97 mark(a) -> a 20.62/20.97 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.97 mark(e) -> e 20.62/20.97 mark(i) -> i 20.62/20.97 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.97 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.97 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.97 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.97 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.97 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.97 mark(nil) -> nil 20.62/20.97 mark(o) -> o 20.62/20.97 mark(tt) -> tt 20.62/20.97 mark(u) -> u 20.62/20.97 20.62/20.97 Problem 1: 20.62/20.97 20.62/20.97 Reduction Pairs Processor: 20.62/20.97 -> Pairs: 20.62/20.97 A__AND(tt,X:S) -> MARK(X:S) 20.62/20.97 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.97 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.62/20.97 MARK(U72(X:S)) -> MARK(X:S) 20.62/20.97 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.97 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.62/20.97 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.62/20.97 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.97 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.62/20.97 -> Rules: 20.62/20.97 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.97 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.97 a__U12(tt) -> tt 20.62/20.97 a__U12(X:S) -> U12(X:S) 20.62/20.97 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.97 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.97 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.97 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.97 a__U23(tt) -> tt 20.62/20.97 a__U23(X:S) -> U23(X:S) 20.62/20.97 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.97 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.97 a__U32(tt) -> tt 20.62/20.97 a__U32(X:S) -> U32(X:S) 20.62/20.97 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.97 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.97 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.97 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.97 a__U43(tt) -> tt 20.62/20.97 a__U43(X:S) -> U43(X:S) 20.62/20.97 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.97 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.97 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.97 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.97 a__U53(tt) -> tt 20.62/20.97 a__U53(X:S) -> U53(X:S) 20.62/20.97 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.97 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.97 a__U62(tt) -> tt 20.62/20.97 a__U62(X:S) -> U62(X:S) 20.62/20.97 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.97 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.97 a__U72(tt) -> tt 20.62/20.97 a__U72(X:S) -> U72(X:S) 20.62/20.97 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.97 a____(nil,X:S) -> mark(X:S) 20.62/20.97 a____(X:S,nil) -> mark(X:S) 20.62/20.97 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.97 a__and(tt,X:S) -> mark(X:S) 20.62/20.97 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.97 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.97 a__isList(nil) -> tt 20.62/20.97 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isList(X:S) -> isList(X:S) 20.62/20.97 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.97 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.97 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.97 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.97 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.97 a__isPal(nil) -> tt 20.62/20.97 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isPal(X:S) -> isPal(X:S) 20.62/20.97 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.97 a__isPalListKind(a) -> tt 20.62/20.97 a__isPalListKind(e) -> tt 20.62/20.97 a__isPalListKind(i) -> tt 20.62/20.97 a__isPalListKind(nil) -> tt 20.62/20.97 a__isPalListKind(o) -> tt 20.62/20.97 a__isPalListKind(u) -> tt 20.62/20.97 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.97 a__isQid(a) -> tt 20.62/20.97 a__isQid(e) -> tt 20.62/20.97 a__isQid(i) -> tt 20.62/20.97 a__isQid(o) -> tt 20.62/20.97 a__isQid(u) -> tt 20.62/20.97 a__isQid(X:S) -> isQid(X:S) 20.62/20.97 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.97 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.97 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.97 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.97 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.97 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.97 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.97 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.97 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.97 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.97 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.97 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.97 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.97 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.97 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.97 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.97 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.97 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.97 mark(a) -> a 20.62/20.97 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.97 mark(e) -> e 20.62/20.97 mark(i) -> i 20.62/20.97 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.97 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.97 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.97 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.97 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.97 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.97 mark(nil) -> nil 20.62/20.97 mark(o) -> o 20.62/20.97 mark(tt) -> tt 20.62/20.97 mark(u) -> u 20.62/20.97 -> Usable rules: 20.62/20.97 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.97 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.97 a__U12(tt) -> tt 20.62/20.97 a__U12(X:S) -> U12(X:S) 20.62/20.97 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.97 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.97 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.97 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.97 a__U23(tt) -> tt 20.62/20.97 a__U23(X:S) -> U23(X:S) 20.62/20.97 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.97 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.97 a__U32(tt) -> tt 20.62/20.97 a__U32(X:S) -> U32(X:S) 20.62/20.97 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.97 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.97 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.97 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.97 a__U43(tt) -> tt 20.62/20.97 a__U43(X:S) -> U43(X:S) 20.62/20.97 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.97 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.97 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.97 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.97 a__U53(tt) -> tt 20.62/20.97 a__U53(X:S) -> U53(X:S) 20.62/20.97 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.97 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.97 a__U62(tt) -> tt 20.62/20.97 a__U62(X:S) -> U62(X:S) 20.62/20.97 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.97 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.97 a__U72(tt) -> tt 20.62/20.97 a__U72(X:S) -> U72(X:S) 20.62/20.97 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.97 a____(nil,X:S) -> mark(X:S) 20.62/20.97 a____(X:S,nil) -> mark(X:S) 20.62/20.97 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.97 a__and(tt,X:S) -> mark(X:S) 20.62/20.97 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.97 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.97 a__isList(nil) -> tt 20.62/20.97 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isList(X:S) -> isList(X:S) 20.62/20.97 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.97 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.97 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.97 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.97 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.97 a__isPal(nil) -> tt 20.62/20.97 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isPal(X:S) -> isPal(X:S) 20.62/20.97 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.97 a__isPalListKind(a) -> tt 20.62/20.97 a__isPalListKind(e) -> tt 20.62/20.97 a__isPalListKind(i) -> tt 20.62/20.97 a__isPalListKind(nil) -> tt 20.62/20.97 a__isPalListKind(o) -> tt 20.62/20.97 a__isPalListKind(u) -> tt 20.62/20.97 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.97 a__isQid(a) -> tt 20.62/20.97 a__isQid(e) -> tt 20.62/20.97 a__isQid(i) -> tt 20.62/20.97 a__isQid(o) -> tt 20.62/20.97 a__isQid(u) -> tt 20.62/20.97 a__isQid(X:S) -> isQid(X:S) 20.62/20.97 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.97 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.97 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.97 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.97 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.97 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.97 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.97 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.97 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.97 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.97 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.97 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.97 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.97 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.97 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.97 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.97 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.97 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.97 mark(a) -> a 20.62/20.97 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.97 mark(e) -> e 20.62/20.97 mark(i) -> i 20.62/20.97 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.97 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.97 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.97 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.97 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.97 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.97 mark(nil) -> nil 20.62/20.97 mark(o) -> o 20.62/20.97 mark(tt) -> tt 20.62/20.97 mark(u) -> u 20.62/20.97 ->Interpretation type: 20.62/20.97 Linear 20.62/20.97 ->Coefficients: 20.62/20.97 Natural Numbers 20.62/20.97 ->Dimension: 20.62/20.97 1 20.62/20.97 ->Bound: 20.62/20.97 2 20.62/20.97 ->Interpretation: 20.62/20.97 20.62/20.97 [a__U11](X1,X2) = 2 20.62/20.97 [a__U12](X) = 2 20.62/20.97 [a__U21](X1,X2,X3) = 2 20.62/20.97 [a__U22](X1,X2) = 2 20.62/20.97 [a__U23](X) = 2 20.62/20.97 [a__U31](X1,X2) = X1 + X2 20.62/20.97 [a__U32](X) = 2 20.62/20.97 [a__U41](X1,X2,X3) = X1 + X2 + X3 + 2 20.62/20.97 [a__U42](X1,X2) = X1 + X2 + 2 20.62/20.97 [a__U43](X) = 2 20.62/20.97 [a__U51](X1,X2,X3) = 2.X1 + 2.X2 + 2 20.62/20.97 [a__U52](X1,X2) = X1 + 2 20.62/20.97 [a__U53](X) = 2 20.62/20.97 [a__U61](X1,X2) = X1 + X2 + 2 20.62/20.97 [a__U62](X) = 2 20.62/20.97 [a__U71](X1,X2) = 2.X2 + 2 20.62/20.97 [a__U72](X) = X 20.62/20.97 [a____](X1,X2) = 2.X1 + X2 + 2 20.62/20.97 [a__and](X1,X2) = X1 + X2 + 2 20.62/20.97 [a__isList](X) = 2 20.62/20.97 [a__isNeList](X) = 2.X + 2 20.62/20.97 [a__isNePal](X) = 2.X + 2 20.62/20.97 [a__isPal](X) = 2.X + 2 20.62/20.97 [a__isPalListKind](X) = X 20.62/20.97 [a__isQid](X) = X + 2 20.62/20.97 [mark](X) = X 20.62/20.97 [U11](X1,X2) = 2 20.62/20.97 [U12](X) = 2 20.62/20.97 [U21](X1,X2,X3) = 2 20.62/20.97 [U22](X1,X2) = 2 20.62/20.97 [U23](X) = 2 20.62/20.97 [U31](X1,X2) = X1 + X2 20.62/20.97 [U32](X) = 2 20.62/20.97 [U41](X1,X2,X3) = X1 + X2 + X3 + 2 20.62/20.97 [U42](X1,X2) = X1 + X2 + 2 20.62/20.97 [U43](X) = 2 20.62/20.97 [U51](X1,X2,X3) = 2.X1 + 2.X2 + 2 20.62/20.97 [U52](X1,X2) = X1 + 2 20.62/20.97 [U53](X) = 2 20.62/20.97 [U61](X1,X2) = X1 + X2 + 2 20.62/20.97 [U62](X) = 2 20.62/20.97 [U71](X1,X2) = 2.X2 + 2 20.62/20.97 [U72](X) = X 20.62/20.97 [__](X1,X2) = 2.X1 + X2 + 2 20.62/20.97 [a] = 2 20.62/20.97 [and](X1,X2) = X1 + X2 + 2 20.62/20.97 [e] = 2 20.62/20.97 [fSNonEmpty] = 0 20.62/20.97 [i] = 2 20.62/20.97 [isList](X) = 2 20.62/20.97 [isNeList](X) = 2.X + 2 20.62/20.97 [isNePal](X) = 2.X + 2 20.62/20.97 [isPal](X) = 2.X + 2 20.62/20.97 [isPalListKind](X) = X 20.62/20.97 [isQid](X) = X + 2 20.62/20.97 [nil] = 2 20.62/20.97 [o] = 2 20.62/20.97 [tt] = 2 20.62/20.97 [u] = 2 20.62/20.97 [A__U11](X1,X2) = 0 20.62/20.97 [A__U12](X) = 0 20.62/20.97 [A__U21](X1,X2,X3) = 0 20.62/20.97 [A__U22](X1,X2) = 0 20.62/20.97 [A__U23](X) = 0 20.62/20.97 [A__U31](X1,X2) = 0 20.62/20.97 [A__U32](X) = 0 20.62/20.97 [A__U41](X1,X2,X3) = 0 20.62/20.97 [A__U42](X1,X2) = 0 20.62/20.97 [A__U43](X) = 0 20.62/20.97 [A__U51](X1,X2,X3) = 0 20.62/20.97 [A__U52](X1,X2) = 0 20.62/20.97 [A__U53](X) = 0 20.62/20.97 [A__U61](X1,X2) = 0 20.62/20.97 [A__U62](X) = 0 20.62/20.97 [A__U71](X1,X2) = 0 20.62/20.97 [A__U72](X) = 0 20.62/20.97 [A____](X1,X2) = 0 20.62/20.97 [A__AND](X1,X2) = 2.X1 + 2.X2 + 2 20.62/20.97 [A__ISLIST](X) = 0 20.62/20.97 [A__ISNELIST](X) = 0 20.62/20.97 [A__ISNEPAL](X) = 0 20.62/20.97 [A__ISPAL](X) = 0 20.62/20.97 [A__ISPALLISTKIND](X) = 2.X + 1 20.62/20.97 [A__ISQID](X) = 0 20.62/20.97 [MARK](X) = 2.X + 2 20.62/20.97 20.62/20.97 Problem 1: 20.62/20.97 20.62/20.97 SCC Processor: 20.62/20.97 -> Pairs: 20.62/20.97 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__AND(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.97 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.62/20.97 MARK(U72(X:S)) -> MARK(X:S) 20.62/20.97 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.97 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.62/20.97 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 20.62/20.97 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.97 MARK(isPalListKind(X:S)) -> A__ISPALLISTKIND(X:S) 20.62/20.97 -> Rules: 20.62/20.97 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.97 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.97 a__U12(tt) -> tt 20.62/20.97 a__U12(X:S) -> U12(X:S) 20.62/20.97 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.97 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.97 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.97 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.97 a__U23(tt) -> tt 20.62/20.97 a__U23(X:S) -> U23(X:S) 20.62/20.97 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.97 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.97 a__U32(tt) -> tt 20.62/20.97 a__U32(X:S) -> U32(X:S) 20.62/20.97 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.97 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.97 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.97 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.97 a__U43(tt) -> tt 20.62/20.97 a__U43(X:S) -> U43(X:S) 20.62/20.97 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.97 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.97 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.97 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.97 a__U53(tt) -> tt 20.62/20.97 a__U53(X:S) -> U53(X:S) 20.62/20.97 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.97 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.97 a__U62(tt) -> tt 20.62/20.97 a__U62(X:S) -> U62(X:S) 20.62/20.97 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.97 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.97 a__U72(tt) -> tt 20.62/20.97 a__U72(X:S) -> U72(X:S) 20.62/20.97 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.97 a____(nil,X:S) -> mark(X:S) 20.62/20.97 a____(X:S,nil) -> mark(X:S) 20.62/20.97 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.97 a__and(tt,X:S) -> mark(X:S) 20.62/20.97 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.97 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.97 a__isList(nil) -> tt 20.62/20.97 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isList(X:S) -> isList(X:S) 20.62/20.97 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.97 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.97 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.97 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.97 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.97 a__isPal(nil) -> tt 20.62/20.97 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isPal(X:S) -> isPal(X:S) 20.62/20.97 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.97 a__isPalListKind(a) -> tt 20.62/20.97 a__isPalListKind(e) -> tt 20.62/20.97 a__isPalListKind(i) -> tt 20.62/20.97 a__isPalListKind(nil) -> tt 20.62/20.97 a__isPalListKind(o) -> tt 20.62/20.97 a__isPalListKind(u) -> tt 20.62/20.97 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.97 a__isQid(a) -> tt 20.62/20.97 a__isQid(e) -> tt 20.62/20.97 a__isQid(i) -> tt 20.62/20.97 a__isQid(o) -> tt 20.62/20.97 a__isQid(u) -> tt 20.62/20.97 a__isQid(X:S) -> isQid(X:S) 20.62/20.97 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.97 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.97 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.97 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.97 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.97 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.97 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.97 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.97 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.97 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.97 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.97 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.97 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.97 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.97 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.97 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.97 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.97 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.97 mark(a) -> a 20.62/20.97 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.97 mark(e) -> e 20.62/20.97 mark(i) -> i 20.62/20.97 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.97 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.97 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.97 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.97 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.97 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.97 mark(nil) -> nil 20.62/20.97 mark(o) -> o 20.62/20.97 mark(tt) -> tt 20.62/20.97 mark(u) -> u 20.62/20.97 ->Strongly Connected Components: 20.62/20.97 ->->Cycle: 20.62/20.97 ->->-> Pairs: 20.62/20.97 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.62/20.97 ->->-> Rules: 20.62/20.97 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.97 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.97 a__U12(tt) -> tt 20.62/20.97 a__U12(X:S) -> U12(X:S) 20.62/20.97 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.97 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.97 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.97 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.97 a__U23(tt) -> tt 20.62/20.97 a__U23(X:S) -> U23(X:S) 20.62/20.97 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.97 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.97 a__U32(tt) -> tt 20.62/20.97 a__U32(X:S) -> U32(X:S) 20.62/20.97 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.97 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.97 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.97 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.97 a__U43(tt) -> tt 20.62/20.97 a__U43(X:S) -> U43(X:S) 20.62/20.97 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.97 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.97 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.97 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.97 a__U53(tt) -> tt 20.62/20.97 a__U53(X:S) -> U53(X:S) 20.62/20.97 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.97 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.97 a__U62(tt) -> tt 20.62/20.97 a__U62(X:S) -> U62(X:S) 20.62/20.97 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.97 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.97 a__U72(tt) -> tt 20.62/20.97 a__U72(X:S) -> U72(X:S) 20.62/20.97 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.97 a____(nil,X:S) -> mark(X:S) 20.62/20.97 a____(X:S,nil) -> mark(X:S) 20.62/20.97 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.97 a__and(tt,X:S) -> mark(X:S) 20.62/20.97 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.97 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.97 a__isList(nil) -> tt 20.62/20.97 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isList(X:S) -> isList(X:S) 20.62/20.97 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.97 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.97 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.97 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.97 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.97 a__isPal(nil) -> tt 20.62/20.97 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isPal(X:S) -> isPal(X:S) 20.62/20.97 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.97 a__isPalListKind(a) -> tt 20.62/20.97 a__isPalListKind(e) -> tt 20.62/20.97 a__isPalListKind(i) -> tt 20.62/20.97 a__isPalListKind(nil) -> tt 20.62/20.97 a__isPalListKind(o) -> tt 20.62/20.97 a__isPalListKind(u) -> tt 20.62/20.97 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.97 a__isQid(a) -> tt 20.62/20.97 a__isQid(e) -> tt 20.62/20.97 a__isQid(i) -> tt 20.62/20.97 a__isQid(o) -> tt 20.62/20.97 a__isQid(u) -> tt 20.62/20.97 a__isQid(X:S) -> isQid(X:S) 20.62/20.97 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.97 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.97 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.97 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.97 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.97 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.97 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.97 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.97 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.97 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.97 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.97 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.97 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.97 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.97 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.97 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.97 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.97 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.97 mark(a) -> a 20.62/20.97 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.97 mark(e) -> e 20.62/20.97 mark(i) -> i 20.62/20.97 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.97 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.97 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.97 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.97 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.97 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.97 mark(nil) -> nil 20.62/20.97 mark(o) -> o 20.62/20.97 mark(tt) -> tt 20.62/20.97 mark(u) -> u 20.62/20.97 ->->Cycle: 20.62/20.97 ->->-> Pairs: 20.62/20.97 MARK(U72(X:S)) -> MARK(X:S) 20.62/20.97 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.97 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.62/20.97 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.97 ->->-> Rules: 20.62/20.97 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.97 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.97 a__U12(tt) -> tt 20.62/20.97 a__U12(X:S) -> U12(X:S) 20.62/20.97 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.97 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.97 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.97 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.97 a__U23(tt) -> tt 20.62/20.97 a__U23(X:S) -> U23(X:S) 20.62/20.97 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.97 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.97 a__U32(tt) -> tt 20.62/20.97 a__U32(X:S) -> U32(X:S) 20.62/20.97 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.97 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.97 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.97 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.97 a__U43(tt) -> tt 20.62/20.97 a__U43(X:S) -> U43(X:S) 20.62/20.97 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.97 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.97 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.97 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.97 a__U53(tt) -> tt 20.62/20.97 a__U53(X:S) -> U53(X:S) 20.62/20.97 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.97 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.97 a__U62(tt) -> tt 20.62/20.97 a__U62(X:S) -> U62(X:S) 20.62/20.97 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.97 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.97 a__U72(tt) -> tt 20.62/20.97 a__U72(X:S) -> U72(X:S) 20.62/20.97 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.97 a____(nil,X:S) -> mark(X:S) 20.62/20.97 a____(X:S,nil) -> mark(X:S) 20.62/20.97 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.97 a__and(tt,X:S) -> mark(X:S) 20.62/20.97 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.97 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.97 a__isList(nil) -> tt 20.62/20.97 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isList(X:S) -> isList(X:S) 20.62/20.97 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.97 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.97 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.97 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.97 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.97 a__isPal(nil) -> tt 20.62/20.97 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isPal(X:S) -> isPal(X:S) 20.62/20.97 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.97 a__isPalListKind(a) -> tt 20.62/20.97 a__isPalListKind(e) -> tt 20.62/20.97 a__isPalListKind(i) -> tt 20.62/20.97 a__isPalListKind(nil) -> tt 20.62/20.97 a__isPalListKind(o) -> tt 20.62/20.97 a__isPalListKind(u) -> tt 20.62/20.97 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.97 a__isQid(a) -> tt 20.62/20.97 a__isQid(e) -> tt 20.62/20.97 a__isQid(i) -> tt 20.62/20.97 a__isQid(o) -> tt 20.62/20.97 a__isQid(u) -> tt 20.62/20.97 a__isQid(X:S) -> isQid(X:S) 20.62/20.97 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.97 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.97 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.97 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.97 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.97 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.97 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.97 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.97 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.97 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.97 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.97 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.97 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.97 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.97 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.97 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.97 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.97 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.97 mark(a) -> a 20.62/20.97 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.97 mark(e) -> e 20.62/20.97 mark(i) -> i 20.62/20.97 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.97 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.97 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.97 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.97 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.97 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.97 mark(nil) -> nil 20.62/20.97 mark(o) -> o 20.62/20.97 mark(tt) -> tt 20.62/20.97 mark(u) -> u 20.62/20.97 20.62/20.97 20.62/20.97 The problem is decomposed in 2 subproblems. 20.62/20.97 20.62/20.97 Problem 1.1: 20.62/20.97 20.62/20.97 Subterm Processor: 20.62/20.97 -> Pairs: 20.62/20.97 A__ISPALLISTKIND(__(V1:S,V2:S)) -> A__ISPALLISTKIND(V1:S) 20.62/20.97 -> Rules: 20.62/20.97 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.97 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.97 a__U12(tt) -> tt 20.62/20.97 a__U12(X:S) -> U12(X:S) 20.62/20.97 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.97 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.97 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.97 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.97 a__U23(tt) -> tt 20.62/20.97 a__U23(X:S) -> U23(X:S) 20.62/20.97 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.97 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.97 a__U32(tt) -> tt 20.62/20.97 a__U32(X:S) -> U32(X:S) 20.62/20.97 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.97 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.97 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.97 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.97 a__U43(tt) -> tt 20.62/20.97 a__U43(X:S) -> U43(X:S) 20.62/20.97 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.97 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.97 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.97 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.97 a__U53(tt) -> tt 20.62/20.97 a__U53(X:S) -> U53(X:S) 20.62/20.97 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.97 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.97 a__U62(tt) -> tt 20.62/20.97 a__U62(X:S) -> U62(X:S) 20.62/20.97 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.97 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.97 a__U72(tt) -> tt 20.62/20.97 a__U72(X:S) -> U72(X:S) 20.62/20.97 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.97 a____(nil,X:S) -> mark(X:S) 20.62/20.97 a____(X:S,nil) -> mark(X:S) 20.62/20.97 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.97 a__and(tt,X:S) -> mark(X:S) 20.62/20.97 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.97 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.97 a__isList(nil) -> tt 20.62/20.97 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isList(X:S) -> isList(X:S) 20.62/20.97 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.97 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.97 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.97 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.97 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.97 a__isPal(nil) -> tt 20.62/20.97 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isPal(X:S) -> isPal(X:S) 20.62/20.97 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.97 a__isPalListKind(a) -> tt 20.62/20.97 a__isPalListKind(e) -> tt 20.62/20.97 a__isPalListKind(i) -> tt 20.62/20.97 a__isPalListKind(nil) -> tt 20.62/20.97 a__isPalListKind(o) -> tt 20.62/20.97 a__isPalListKind(u) -> tt 20.62/20.97 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.97 a__isQid(a) -> tt 20.62/20.97 a__isQid(e) -> tt 20.62/20.97 a__isQid(i) -> tt 20.62/20.97 a__isQid(o) -> tt 20.62/20.97 a__isQid(u) -> tt 20.62/20.97 a__isQid(X:S) -> isQid(X:S) 20.62/20.97 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.97 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.97 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.97 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.97 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.97 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.97 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.97 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.97 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.97 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.97 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.97 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.97 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.97 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.97 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.97 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.97 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.97 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.97 mark(a) -> a 20.62/20.97 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.97 mark(e) -> e 20.62/20.97 mark(i) -> i 20.62/20.97 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.97 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.97 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.97 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.97 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.97 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.97 mark(nil) -> nil 20.62/20.97 mark(o) -> o 20.62/20.97 mark(tt) -> tt 20.62/20.97 mark(u) -> u 20.62/20.97 ->Projection: 20.62/20.97 pi(A__ISPALLISTKIND) = 1 20.62/20.97 20.62/20.97 Problem 1.1: 20.62/20.97 20.62/20.97 SCC Processor: 20.62/20.97 -> Pairs: 20.62/20.97 Empty 20.62/20.97 -> Rules: 20.62/20.97 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.97 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.97 a__U12(tt) -> tt 20.62/20.97 a__U12(X:S) -> U12(X:S) 20.62/20.97 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.97 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.97 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.97 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.97 a__U23(tt) -> tt 20.62/20.97 a__U23(X:S) -> U23(X:S) 20.62/20.97 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.97 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.97 a__U32(tt) -> tt 20.62/20.97 a__U32(X:S) -> U32(X:S) 20.62/20.97 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.97 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.97 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.97 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.97 a__U43(tt) -> tt 20.62/20.97 a__U43(X:S) -> U43(X:S) 20.62/20.97 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.97 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.97 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.97 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.97 a__U53(tt) -> tt 20.62/20.97 a__U53(X:S) -> U53(X:S) 20.62/20.97 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.97 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.97 a__U62(tt) -> tt 20.62/20.97 a__U62(X:S) -> U62(X:S) 20.62/20.97 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.97 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.97 a__U72(tt) -> tt 20.62/20.97 a__U72(X:S) -> U72(X:S) 20.62/20.97 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.97 a____(nil,X:S) -> mark(X:S) 20.62/20.97 a____(X:S,nil) -> mark(X:S) 20.62/20.97 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.97 a__and(tt,X:S) -> mark(X:S) 20.62/20.97 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.97 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.97 a__isList(nil) -> tt 20.62/20.97 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isList(X:S) -> isList(X:S) 20.62/20.97 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.97 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.97 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.97 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.97 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.97 a__isPal(nil) -> tt 20.62/20.97 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isPal(X:S) -> isPal(X:S) 20.62/20.97 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.97 a__isPalListKind(a) -> tt 20.62/20.97 a__isPalListKind(e) -> tt 20.62/20.97 a__isPalListKind(i) -> tt 20.62/20.97 a__isPalListKind(nil) -> tt 20.62/20.97 a__isPalListKind(o) -> tt 20.62/20.97 a__isPalListKind(u) -> tt 20.62/20.97 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.97 a__isQid(a) -> tt 20.62/20.97 a__isQid(e) -> tt 20.62/20.97 a__isQid(i) -> tt 20.62/20.97 a__isQid(o) -> tt 20.62/20.97 a__isQid(u) -> tt 20.62/20.97 a__isQid(X:S) -> isQid(X:S) 20.62/20.97 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.97 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.97 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.97 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.97 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.97 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.97 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.97 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.97 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.97 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.97 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.97 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.97 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.97 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.97 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.97 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.97 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.97 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.97 mark(a) -> a 20.62/20.97 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.97 mark(e) -> e 20.62/20.97 mark(i) -> i 20.62/20.97 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.97 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.97 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.97 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.97 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.97 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.97 mark(nil) -> nil 20.62/20.97 mark(o) -> o 20.62/20.97 mark(tt) -> tt 20.62/20.97 mark(u) -> u 20.62/20.97 ->Strongly Connected Components: 20.62/20.97 There is no strongly connected component 20.62/20.97 20.62/20.97 The problem is finite. 20.62/20.97 20.62/20.97 Problem 1.2: 20.62/20.97 20.62/20.97 Subterm Processor: 20.62/20.97 -> Pairs: 20.62/20.97 MARK(U72(X:S)) -> MARK(X:S) 20.62/20.97 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.97 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 20.62/20.97 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 20.62/20.97 -> Rules: 20.62/20.97 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.97 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.97 a__U12(tt) -> tt 20.62/20.97 a__U12(X:S) -> U12(X:S) 20.62/20.97 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.97 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.97 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.97 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.97 a__U23(tt) -> tt 20.62/20.97 a__U23(X:S) -> U23(X:S) 20.62/20.97 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.97 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.97 a__U32(tt) -> tt 20.62/20.97 a__U32(X:S) -> U32(X:S) 20.62/20.97 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.97 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.97 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.97 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.97 a__U43(tt) -> tt 20.62/20.97 a__U43(X:S) -> U43(X:S) 20.62/20.97 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.97 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.97 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.97 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.97 a__U53(tt) -> tt 20.62/20.97 a__U53(X:S) -> U53(X:S) 20.62/20.97 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.97 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.97 a__U62(tt) -> tt 20.62/20.97 a__U62(X:S) -> U62(X:S) 20.62/20.97 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.97 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.97 a__U72(tt) -> tt 20.62/20.97 a__U72(X:S) -> U72(X:S) 20.62/20.97 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.97 a____(nil,X:S) -> mark(X:S) 20.62/20.97 a____(X:S,nil) -> mark(X:S) 20.62/20.97 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.97 a__and(tt,X:S) -> mark(X:S) 20.62/20.97 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.97 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.97 a__isList(nil) -> tt 20.62/20.97 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isList(X:S) -> isList(X:S) 20.62/20.97 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.97 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.97 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.97 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.97 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.97 a__isPal(nil) -> tt 20.62/20.97 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isPal(X:S) -> isPal(X:S) 20.62/20.97 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.97 a__isPalListKind(a) -> tt 20.62/20.97 a__isPalListKind(e) -> tt 20.62/20.97 a__isPalListKind(i) -> tt 20.62/20.97 a__isPalListKind(nil) -> tt 20.62/20.97 a__isPalListKind(o) -> tt 20.62/20.97 a__isPalListKind(u) -> tt 20.62/20.97 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.97 a__isQid(a) -> tt 20.62/20.97 a__isQid(e) -> tt 20.62/20.97 a__isQid(i) -> tt 20.62/20.97 a__isQid(o) -> tt 20.62/20.97 a__isQid(u) -> tt 20.62/20.97 a__isQid(X:S) -> isQid(X:S) 20.62/20.97 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.97 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.97 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.97 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.97 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.97 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.97 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.97 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.97 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.97 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.97 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.97 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.97 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.97 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.97 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.97 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.97 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.97 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.97 mark(a) -> a 20.62/20.97 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.97 mark(e) -> e 20.62/20.97 mark(i) -> i 20.62/20.97 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.97 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.97 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.97 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.97 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.97 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.97 mark(nil) -> nil 20.62/20.97 mark(o) -> o 20.62/20.97 mark(tt) -> tt 20.62/20.97 mark(u) -> u 20.62/20.97 ->Projection: 20.62/20.97 pi(MARK) = 1 20.62/20.97 20.62/20.97 Problem 1.2: 20.62/20.97 20.62/20.97 SCC Processor: 20.62/20.97 -> Pairs: 20.62/20.97 Empty 20.62/20.97 -> Rules: 20.62/20.97 a__U11(tt,V:S) -> a__U12(a__isNeList(V:S)) 20.62/20.97 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 20.62/20.97 a__U12(tt) -> tt 20.62/20.97 a__U12(X:S) -> U12(X:S) 20.62/20.97 a__U21(tt,V1:S,V2:S) -> a__U22(a__isList(V1:S),V2:S) 20.62/20.97 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 20.62/20.97 a__U22(tt,V2:S) -> a__U23(a__isList(V2:S)) 20.62/20.97 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 20.62/20.97 a__U23(tt) -> tt 20.62/20.97 a__U23(X:S) -> U23(X:S) 20.62/20.97 a__U31(tt,V:S) -> a__U32(a__isQid(V:S)) 20.62/20.97 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 20.62/20.97 a__U32(tt) -> tt 20.62/20.97 a__U32(X:S) -> U32(X:S) 20.62/20.97 a__U41(tt,V1:S,V2:S) -> a__U42(a__isList(V1:S),V2:S) 20.62/20.97 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 20.62/20.97 a__U42(tt,V2:S) -> a__U43(a__isNeList(V2:S)) 20.62/20.97 a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) 20.62/20.97 a__U43(tt) -> tt 20.62/20.97 a__U43(X:S) -> U43(X:S) 20.62/20.97 a__U51(tt,V1:S,V2:S) -> a__U52(a__isNeList(V1:S),V2:S) 20.62/20.97 a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) 20.62/20.97 a__U52(tt,V2:S) -> a__U53(a__isList(V2:S)) 20.62/20.97 a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) 20.62/20.97 a__U53(tt) -> tt 20.62/20.97 a__U53(X:S) -> U53(X:S) 20.62/20.97 a__U61(tt,V:S) -> a__U62(a__isQid(V:S)) 20.62/20.97 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 20.62/20.97 a__U62(tt) -> tt 20.62/20.97 a__U62(X:S) -> U62(X:S) 20.62/20.97 a__U71(tt,V:S) -> a__U72(a__isNePal(V:S)) 20.62/20.97 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S) 20.62/20.97 a__U72(tt) -> tt 20.62/20.97 a__U72(X:S) -> U72(X:S) 20.62/20.97 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 20.62/20.97 a____(nil,X:S) -> mark(X:S) 20.62/20.97 a____(X:S,nil) -> mark(X:S) 20.62/20.97 a____(X1:S,X2:S) -> __(X1:S,X2:S) 20.62/20.97 a__and(tt,X:S) -> mark(X:S) 20.62/20.97 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 20.62/20.97 a__isList(__(V1:S,V2:S)) -> a__U21(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.97 a__isList(nil) -> tt 20.62/20.97 a__isList(V:S) -> a__U11(a__isPalListKind(V:S),V:S) 20.62/20.97 a__isList(X:S) -> isList(X:S) 20.62/20.97 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.97 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)),V1:S,V2:S) 20.62/20.97 a__isNeList(V:S) -> a__U31(a__isPalListKind(V:S),V:S) 20.62/20.98 a__isNeList(X:S) -> isNeList(X:S) 20.62/20.98 a__isNePal(__(I:S,__(P:S,I:S))) -> a__and(a__and(a__isQid(I:S),isPalListKind(I:S)),and(isPal(P:S),isPalListKind(P:S))) 20.62/20.98 a__isNePal(V:S) -> a__U61(a__isPalListKind(V:S),V:S) 20.62/20.98 a__isNePal(X:S) -> isNePal(X:S) 20.62/20.98 a__isPal(nil) -> tt 20.62/20.98 a__isPal(V:S) -> a__U71(a__isPalListKind(V:S),V:S) 20.62/20.98 a__isPal(X:S) -> isPal(X:S) 20.62/20.98 a__isPalListKind(__(V1:S,V2:S)) -> a__and(a__isPalListKind(V1:S),isPalListKind(V2:S)) 20.62/20.98 a__isPalListKind(a) -> tt 20.62/20.98 a__isPalListKind(e) -> tt 20.62/20.98 a__isPalListKind(i) -> tt 20.62/20.98 a__isPalListKind(nil) -> tt 20.62/20.98 a__isPalListKind(o) -> tt 20.62/20.98 a__isPalListKind(u) -> tt 20.62/20.98 a__isPalListKind(X:S) -> isPalListKind(X:S) 20.62/20.98 a__isQid(a) -> tt 20.62/20.98 a__isQid(e) -> tt 20.62/20.98 a__isQid(i) -> tt 20.62/20.98 a__isQid(o) -> tt 20.62/20.98 a__isQid(u) -> tt 20.62/20.98 a__isQid(X:S) -> isQid(X:S) 20.62/20.98 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 20.62/20.98 mark(U12(X:S)) -> a__U12(mark(X:S)) 20.62/20.98 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 20.62/20.98 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 20.62/20.98 mark(U23(X:S)) -> a__U23(mark(X:S)) 20.62/20.98 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 20.62/20.98 mark(U32(X:S)) -> a__U32(mark(X:S)) 20.62/20.98 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 20.62/20.98 mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) 20.62/20.98 mark(U43(X:S)) -> a__U43(mark(X:S)) 20.62/20.98 mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) 20.62/20.98 mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) 20.62/20.98 mark(U53(X:S)) -> a__U53(mark(X:S)) 20.62/20.98 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 20.62/20.98 mark(U62(X:S)) -> a__U62(mark(X:S)) 20.62/20.98 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S) 20.62/20.98 mark(U72(X:S)) -> a__U72(mark(X:S)) 20.62/20.98 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 20.62/20.98 mark(a) -> a 20.62/20.98 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 20.62/20.98 mark(e) -> e 20.62/20.98 mark(i) -> i 20.62/20.98 mark(isList(X:S)) -> a__isList(X:S) 20.62/20.98 mark(isNeList(X:S)) -> a__isNeList(X:S) 20.62/20.98 mark(isNePal(X:S)) -> a__isNePal(X:S) 20.62/20.98 mark(isPal(X:S)) -> a__isPal(X:S) 20.62/20.98 mark(isPalListKind(X:S)) -> a__isPalListKind(X:S) 20.62/20.98 mark(isQid(X:S)) -> a__isQid(X:S) 20.62/20.98 mark(nil) -> nil 20.62/20.98 mark(o) -> o 20.62/20.98 mark(tt) -> tt 20.62/20.98 mark(u) -> u 20.62/20.98 ->Strongly Connected Components: 20.62/20.98 There is no strongly connected component 20.62/20.98 20.62/20.98 The problem is finite. 20.62/20.98 EOF