1.17/1.22	YES
1.17/1.22	
1.17/1.22	Problem 1: 
1.17/1.22	
1.17/1.22	(VAR v_NonEmpty:S I:S P:S V:S V1:S V2:S X:S X1:S X2:S Y:S Z:S)
1.17/1.22	(RULES
1.17/1.22	a__U11(tt) -> tt
1.17/1.22	a__U11(X:S) -> U11(X:S)
1.17/1.22	a__U21(tt,V2:S) -> a__U22(a__isList(V2:S))
1.17/1.22	a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.17/1.22	a__U22(tt) -> tt
1.17/1.22	a__U22(X:S) -> U22(X:S)
1.17/1.22	a__U31(tt) -> tt
1.17/1.22	a__U31(X:S) -> U31(X:S)
1.17/1.22	a__U41(tt,V2:S) -> a__U42(a__isNeList(V2:S))
1.17/1.22	a__U41(X1:S,X2:S) -> U41(X1:S,X2:S)
1.17/1.22	a__U42(tt) -> tt
1.17/1.22	a__U42(X:S) -> U42(X:S)
1.17/1.22	a__U51(tt,V2:S) -> a__U52(a__isList(V2:S))
1.17/1.22	a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.17/1.22	a__U52(tt) -> tt
1.17/1.22	a__U52(X:S) -> U52(X:S)
1.17/1.22	a__U61(tt) -> tt
1.17/1.22	a__U61(X:S) -> U61(X:S)
1.17/1.22	a__U71(tt,P:S) -> a__U72(a__isPal(P:S))
1.17/1.22	a__U71(X1:S,X2:S) -> U71(X1:S,X2:S)
1.17/1.22	a__U72(tt) -> tt
1.17/1.22	a__U72(X:S) -> U72(X:S)
1.17/1.22	a__U81(tt) -> tt
1.17/1.22	a__U81(X:S) -> U81(X:S)
1.17/1.22	a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
1.17/1.22	a____(nil,X:S) -> mark(X:S)
1.17/1.22	a____(X:S,nil) -> mark(X:S)
1.17/1.22	a____(X1:S,X2:S) -> __(X1:S,X2:S)
1.17/1.22	a__isList(__(V1:S,V2:S)) -> a__U21(a__isList(V1:S),V2:S)
1.17/1.22	a__isList(nil) -> tt
1.17/1.22	a__isList(V:S) -> a__U11(a__isNeList(V:S))
1.17/1.22	a__isList(X:S) -> isList(X:S)
1.17/1.22	a__isNeList(__(V1:S,V2:S)) -> a__U41(a__isList(V1:S),V2:S)
1.17/1.22	a__isNeList(__(V1:S,V2:S)) -> a__U51(a__isNeList(V1:S),V2:S)
1.17/1.22	a__isNeList(V:S) -> a__U31(a__isQid(V:S))
1.17/1.22	a__isNeList(X:S) -> isNeList(X:S)
1.17/1.22	a__isNePal(__(I:S,__(P:S,I:S))) -> a__U71(a__isQid(I:S),P:S)
1.17/1.22	a__isNePal(V:S) -> a__U61(a__isQid(V:S))
1.17/1.22	a__isNePal(X:S) -> isNePal(X:S)
1.17/1.22	a__isPal(nil) -> tt
1.17/1.22	a__isPal(V:S) -> a__U81(a__isNePal(V:S))
1.17/1.22	a__isPal(X:S) -> isPal(X:S)
1.17/1.22	a__isQid(a) -> tt
1.17/1.22	a__isQid(e) -> tt
1.17/1.22	a__isQid(i) -> tt
1.17/1.22	a__isQid(o) -> tt
1.17/1.22	a__isQid(u) -> tt
1.17/1.22	a__isQid(X:S) -> isQid(X:S)
1.17/1.22	mark(U11(X:S)) -> a__U11(mark(X:S))
1.17/1.22	mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.17/1.22	mark(U22(X:S)) -> a__U22(mark(X:S))
1.17/1.22	mark(U31(X:S)) -> a__U31(mark(X:S))
1.17/1.22	mark(U41(X1:S,X2:S)) -> a__U41(mark(X1:S),X2:S)
1.17/1.22	mark(U42(X:S)) -> a__U42(mark(X:S))
1.17/1.22	mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.17/1.22	mark(U52(X:S)) -> a__U52(mark(X:S))
1.17/1.22	mark(U61(X:S)) -> a__U61(mark(X:S))
1.17/1.22	mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S)
1.17/1.22	mark(U72(X:S)) -> a__U72(mark(X:S))
1.17/1.22	mark(U81(X:S)) -> a__U81(mark(X:S))
1.17/1.22	mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
1.17/1.22	mark(a) -> a
1.17/1.22	mark(e) -> e
1.17/1.22	mark(i) -> i
1.17/1.22	mark(isList(X:S)) -> a__isList(X:S)
1.17/1.22	mark(isNeList(X:S)) -> a__isNeList(X:S)
1.17/1.22	mark(isNePal(X:S)) -> a__isNePal(X:S)
1.17/1.22	mark(isPal(X:S)) -> a__isPal(X:S)
1.17/1.22	mark(isQid(X:S)) -> a__isQid(X:S)
1.17/1.22	mark(nil) -> nil
1.17/1.22	mark(o) -> o
1.17/1.22	mark(tt) -> tt
1.17/1.22	mark(u) -> u
1.17/1.22	) 
1.17/1.22	(STRATEGY INNERMOST)
1.17/1.22	
1.17/1.22	Problem 1: 
1.17/1.22	
1.17/1.22	Dependency Pairs Processor:
1.17/1.22	-> Pairs:
1.17/1.22	 A__U21(tt,V2:S) -> A__U22(a__isList(V2:S))
1.17/1.22	 A__U21(tt,V2:S) -> A__ISLIST(V2:S)
1.17/1.22	 A__U41(tt,V2:S) -> A__U42(a__isNeList(V2:S))
1.17/1.22	 A__U41(tt,V2:S) -> A__ISNELIST(V2:S)
1.17/1.22	 A__U51(tt,V2:S) -> A__U52(a__isList(V2:S))
1.17/1.22	 A__U51(tt,V2:S) -> A__ISLIST(V2:S)
1.17/1.22	 A__U71(tt,P:S) -> A__U72(a__isPal(P:S))
1.17/1.22	 A__U71(tt,P:S) -> A__ISPAL(P:S)
1.17/1.22	 A____(__(X:S,Y:S),Z:S) -> A____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
1.17/1.22	 A____(__(X:S,Y:S),Z:S) -> A____(mark(Y:S),mark(Z:S))
1.17/1.22	 A____(__(X:S,Y:S),Z:S) -> MARK(X:S)
1.17/1.22	 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S)
1.17/1.22	 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S)
1.17/1.22	 A____(nil,X:S) -> MARK(X:S)
1.17/1.22	 A____(X:S,nil) -> MARK(X:S)
1.17/1.22	 A__ISLIST(__(V1:S,V2:S)) -> A__U21(a__isList(V1:S),V2:S)
1.17/1.22	 A__ISLIST(__(V1:S,V2:S)) -> A__ISLIST(V1:S)
1.17/1.22	 A__ISLIST(V:S) -> A__U11(a__isNeList(V:S))
1.17/1.22	 A__ISLIST(V:S) -> A__ISNELIST(V:S)
1.17/1.22	 A__ISNELIST(__(V1:S,V2:S)) -> A__U41(a__isList(V1:S),V2:S)
1.17/1.22	 A__ISNELIST(__(V1:S,V2:S)) -> A__U51(a__isNeList(V1:S),V2:S)
1.17/1.22	 A__ISNELIST(__(V1:S,V2:S)) -> A__ISLIST(V1:S)
1.17/1.22	 A__ISNELIST(__(V1:S,V2:S)) -> A__ISNELIST(V1:S)
1.17/1.22	 A__ISNELIST(V:S) -> A__U31(a__isQid(V:S))
1.17/1.22	 A__ISNELIST(V:S) -> A__ISQID(V:S)
1.17/1.22	 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__U71(a__isQid(I:S),P:S)
1.17/1.22	 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__ISQID(I:S)
1.17/1.22	 A__ISNEPAL(V:S) -> A__U61(a__isQid(V:S))
1.17/1.22	 A__ISNEPAL(V:S) -> A__ISQID(V:S)
1.17/1.22	 A__ISPAL(V:S) -> A__U81(a__isNePal(V:S))
1.17/1.22	 A__ISPAL(V:S) -> A__ISNEPAL(V:S)
1.17/1.22	 MARK(U11(X:S)) -> A__U11(mark(X:S))
1.17/1.22	 MARK(U11(X:S)) -> MARK(X:S)
1.17/1.22	 MARK(U21(X1:S,X2:S)) -> A__U21(mark(X1:S),X2:S)
1.17/1.22	 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.22	 MARK(U22(X:S)) -> A__U22(mark(X:S))
1.17/1.22	 MARK(U22(X:S)) -> MARK(X:S)
1.17/1.22	 MARK(U31(X:S)) -> A__U31(mark(X:S))
1.17/1.22	 MARK(U31(X:S)) -> MARK(X:S)
1.17/1.22	 MARK(U41(X1:S,X2:S)) -> A__U41(mark(X1:S),X2:S)
1.17/1.22	 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.22	 MARK(U42(X:S)) -> A__U42(mark(X:S))
1.17/1.22	 MARK(U42(X:S)) -> MARK(X:S)
1.17/1.22	 MARK(U51(X1:S,X2:S)) -> A__U51(mark(X1:S),X2:S)
1.17/1.22	 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.22	 MARK(U52(X:S)) -> A__U52(mark(X:S))
1.17/1.22	 MARK(U52(X:S)) -> MARK(X:S)
1.17/1.22	 MARK(U61(X:S)) -> A__U61(mark(X:S))
1.17/1.22	 MARK(U61(X:S)) -> MARK(X:S)
1.17/1.22	 MARK(U71(X1:S,X2:S)) -> A__U71(mark(X1:S),X2:S)
1.17/1.22	 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.22	 MARK(U72(X:S)) -> A__U72(mark(X:S))
1.17/1.22	 MARK(U72(X:S)) -> MARK(X:S)
1.17/1.22	 MARK(U81(X:S)) -> A__U81(mark(X:S))
1.17/1.22	 MARK(U81(X:S)) -> MARK(X:S)
1.17/1.22	 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S))
1.17/1.22	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.22	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.17/1.22	 MARK(isList(X:S)) -> A__ISLIST(X:S)
1.17/1.22	 MARK(isNeList(X:S)) -> A__ISNELIST(X:S)
1.17/1.22	 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S)
1.17/1.22	 MARK(isPal(X:S)) -> A__ISPAL(X:S)
1.17/1.22	 MARK(isQid(X:S)) -> A__ISQID(X:S)
1.17/1.22	-> Rules:
1.17/1.22	 a__U11(tt) -> tt
1.17/1.22	 a__U11(X:S) -> U11(X:S)
1.17/1.22	 a__U21(tt,V2:S) -> a__U22(a__isList(V2:S))
1.17/1.22	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.17/1.22	 a__U22(tt) -> tt
1.17/1.22	 a__U22(X:S) -> U22(X:S)
1.17/1.22	 a__U31(tt) -> tt
1.17/1.22	 a__U31(X:S) -> U31(X:S)
1.17/1.22	 a__U41(tt,V2:S) -> a__U42(a__isNeList(V2:S))
1.17/1.22	 a__U41(X1:S,X2:S) -> U41(X1:S,X2:S)
1.17/1.22	 a__U42(tt) -> tt
1.17/1.22	 a__U42(X:S) -> U42(X:S)
1.17/1.22	 a__U51(tt,V2:S) -> a__U52(a__isList(V2:S))
1.17/1.22	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.17/1.22	 a__U52(tt) -> tt
1.17/1.22	 a__U52(X:S) -> U52(X:S)
1.17/1.22	 a__U61(tt) -> tt
1.17/1.22	 a__U61(X:S) -> U61(X:S)
1.17/1.22	 a__U71(tt,P:S) -> a__U72(a__isPal(P:S))
1.17/1.22	 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S)
1.17/1.22	 a__U72(tt) -> tt
1.17/1.22	 a__U72(X:S) -> U72(X:S)
1.17/1.22	 a__U81(tt) -> tt
1.17/1.22	 a__U81(X:S) -> U81(X:S)
1.17/1.22	 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
1.17/1.22	 a____(nil,X:S) -> mark(X:S)
1.17/1.22	 a____(X:S,nil) -> mark(X:S)
1.17/1.22	 a____(X1:S,X2:S) -> __(X1:S,X2:S)
1.17/1.22	 a__isList(__(V1:S,V2:S)) -> a__U21(a__isList(V1:S),V2:S)
1.17/1.22	 a__isList(nil) -> tt
1.17/1.22	 a__isList(V:S) -> a__U11(a__isNeList(V:S))
1.17/1.22	 a__isList(X:S) -> isList(X:S)
1.17/1.22	 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__isList(V1:S),V2:S)
1.17/1.22	 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__isNeList(V1:S),V2:S)
1.17/1.22	 a__isNeList(V:S) -> a__U31(a__isQid(V:S))
1.17/1.23	 a__isNeList(X:S) -> isNeList(X:S)
1.17/1.23	 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U71(a__isQid(I:S),P:S)
1.17/1.23	 a__isNePal(V:S) -> a__U61(a__isQid(V:S))
1.17/1.23	 a__isNePal(X:S) -> isNePal(X:S)
1.17/1.23	 a__isPal(nil) -> tt
1.17/1.23	 a__isPal(V:S) -> a__U81(a__isNePal(V:S))
1.17/1.23	 a__isPal(X:S) -> isPal(X:S)
1.17/1.23	 a__isQid(a) -> tt
1.17/1.23	 a__isQid(e) -> tt
1.17/1.23	 a__isQid(i) -> tt
1.17/1.23	 a__isQid(o) -> tt
1.17/1.23	 a__isQid(u) -> tt
1.17/1.23	 a__isQid(X:S) -> isQid(X:S)
1.17/1.23	 mark(U11(X:S)) -> a__U11(mark(X:S))
1.17/1.23	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.17/1.23	 mark(U22(X:S)) -> a__U22(mark(X:S))
1.17/1.23	 mark(U31(X:S)) -> a__U31(mark(X:S))
1.17/1.23	 mark(U41(X1:S,X2:S)) -> a__U41(mark(X1:S),X2:S)
1.17/1.23	 mark(U42(X:S)) -> a__U42(mark(X:S))
1.17/1.23	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.17/1.23	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.17/1.23	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.17/1.23	 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S)
1.17/1.23	 mark(U72(X:S)) -> a__U72(mark(X:S))
1.17/1.23	 mark(U81(X:S)) -> a__U81(mark(X:S))
1.17/1.23	 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
1.17/1.23	 mark(a) -> a
1.17/1.23	 mark(e) -> e
1.17/1.23	 mark(i) -> i
1.17/1.23	 mark(isList(X:S)) -> a__isList(X:S)
1.17/1.23	 mark(isNeList(X:S)) -> a__isNeList(X:S)
1.17/1.23	 mark(isNePal(X:S)) -> a__isNePal(X:S)
1.17/1.23	 mark(isPal(X:S)) -> a__isPal(X:S)
1.17/1.23	 mark(isQid(X:S)) -> a__isQid(X:S)
1.17/1.23	 mark(nil) -> nil
1.17/1.23	 mark(o) -> o
1.17/1.23	 mark(tt) -> tt
1.17/1.23	 mark(u) -> u
1.17/1.23	
1.17/1.23	Problem 1: 
1.17/1.23	
1.17/1.23	SCC Processor:
1.17/1.23	-> Pairs:
1.17/1.23	 A__U21(tt,V2:S) -> A__U22(a__isList(V2:S))
1.17/1.23	 A__U21(tt,V2:S) -> A__ISLIST(V2:S)
1.17/1.23	 A__U41(tt,V2:S) -> A__U42(a__isNeList(V2:S))
1.17/1.23	 A__U41(tt,V2:S) -> A__ISNELIST(V2:S)
1.17/1.23	 A__U51(tt,V2:S) -> A__U52(a__isList(V2:S))
1.17/1.23	 A__U51(tt,V2:S) -> A__ISLIST(V2:S)
1.17/1.23	 A__U71(tt,P:S) -> A__U72(a__isPal(P:S))
1.17/1.23	 A__U71(tt,P:S) -> A__ISPAL(P:S)
1.17/1.23	 A____(__(X:S,Y:S),Z:S) -> A____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
1.17/1.23	 A____(__(X:S,Y:S),Z:S) -> A____(mark(Y:S),mark(Z:S))
1.17/1.23	 A____(__(X:S,Y:S),Z:S) -> MARK(X:S)
1.17/1.23	 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S)
1.17/1.23	 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S)
1.17/1.23	 A____(nil,X:S) -> MARK(X:S)
1.17/1.23	 A____(X:S,nil) -> MARK(X:S)
1.17/1.23	 A__ISLIST(__(V1:S,V2:S)) -> A__U21(a__isList(V1:S),V2:S)
1.17/1.23	 A__ISLIST(__(V1:S,V2:S)) -> A__ISLIST(V1:S)
1.17/1.23	 A__ISLIST(V:S) -> A__U11(a__isNeList(V:S))
1.17/1.23	 A__ISLIST(V:S) -> A__ISNELIST(V:S)
1.17/1.23	 A__ISNELIST(__(V1:S,V2:S)) -> A__U41(a__isList(V1:S),V2:S)
1.17/1.23	 A__ISNELIST(__(V1:S,V2:S)) -> A__U51(a__isNeList(V1:S),V2:S)
1.17/1.23	 A__ISNELIST(__(V1:S,V2:S)) -> A__ISLIST(V1:S)
1.17/1.23	 A__ISNELIST(__(V1:S,V2:S)) -> A__ISNELIST(V1:S)
1.17/1.23	 A__ISNELIST(V:S) -> A__U31(a__isQid(V:S))
1.17/1.23	 A__ISNELIST(V:S) -> A__ISQID(V:S)
1.17/1.23	 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__U71(a__isQid(I:S),P:S)
1.17/1.23	 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__ISQID(I:S)
1.17/1.23	 A__ISNEPAL(V:S) -> A__U61(a__isQid(V:S))
1.17/1.23	 A__ISNEPAL(V:S) -> A__ISQID(V:S)
1.17/1.23	 A__ISPAL(V:S) -> A__U81(a__isNePal(V:S))
1.17/1.23	 A__ISPAL(V:S) -> A__ISNEPAL(V:S)
1.17/1.23	 MARK(U11(X:S)) -> A__U11(mark(X:S))
1.17/1.23	 MARK(U11(X:S)) -> MARK(X:S)
1.17/1.23	 MARK(U21(X1:S,X2:S)) -> A__U21(mark(X1:S),X2:S)
1.17/1.23	 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.23	 MARK(U22(X:S)) -> A__U22(mark(X:S))
1.17/1.23	 MARK(U22(X:S)) -> MARK(X:S)
1.17/1.23	 MARK(U31(X:S)) -> A__U31(mark(X:S))
1.17/1.23	 MARK(U31(X:S)) -> MARK(X:S)
1.17/1.23	 MARK(U41(X1:S,X2:S)) -> A__U41(mark(X1:S),X2:S)
1.17/1.23	 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.23	 MARK(U42(X:S)) -> A__U42(mark(X:S))
1.17/1.23	 MARK(U42(X:S)) -> MARK(X:S)
1.17/1.23	 MARK(U51(X1:S,X2:S)) -> A__U51(mark(X1:S),X2:S)
1.17/1.23	 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.23	 MARK(U52(X:S)) -> A__U52(mark(X:S))
1.17/1.23	 MARK(U52(X:S)) -> MARK(X:S)
1.17/1.23	 MARK(U61(X:S)) -> A__U61(mark(X:S))
1.17/1.23	 MARK(U61(X:S)) -> MARK(X:S)
1.17/1.23	 MARK(U71(X1:S,X2:S)) -> A__U71(mark(X1:S),X2:S)
1.17/1.23	 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.23	 MARK(U72(X:S)) -> A__U72(mark(X:S))
1.17/1.23	 MARK(U72(X:S)) -> MARK(X:S)
1.17/1.23	 MARK(U81(X:S)) -> A__U81(mark(X:S))
1.17/1.23	 MARK(U81(X:S)) -> MARK(X:S)
1.17/1.23	 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S))
1.17/1.23	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.23	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.17/1.23	 MARK(isList(X:S)) -> A__ISLIST(X:S)
1.17/1.23	 MARK(isNeList(X:S)) -> A__ISNELIST(X:S)
1.17/1.23	 MARK(isNePal(X:S)) -> A__ISNEPAL(X:S)
1.17/1.23	 MARK(isPal(X:S)) -> A__ISPAL(X:S)
1.17/1.23	 MARK(isQid(X:S)) -> A__ISQID(X:S)
1.17/1.23	-> Rules:
1.17/1.23	 a__U11(tt) -> tt
1.17/1.23	 a__U11(X:S) -> U11(X:S)
1.17/1.23	 a__U21(tt,V2:S) -> a__U22(a__isList(V2:S))
1.17/1.23	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.17/1.23	 a__U22(tt) -> tt
1.17/1.23	 a__U22(X:S) -> U22(X:S)
1.17/1.23	 a__U31(tt) -> tt
1.17/1.23	 a__U31(X:S) -> U31(X:S)
1.17/1.23	 a__U41(tt,V2:S) -> a__U42(a__isNeList(V2:S))
1.17/1.23	 a__U41(X1:S,X2:S) -> U41(X1:S,X2:S)
1.17/1.23	 a__U42(tt) -> tt
1.17/1.23	 a__U42(X:S) -> U42(X:S)
1.17/1.23	 a__U51(tt,V2:S) -> a__U52(a__isList(V2:S))
1.17/1.23	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.17/1.23	 a__U52(tt) -> tt
1.17/1.23	 a__U52(X:S) -> U52(X:S)
1.17/1.23	 a__U61(tt) -> tt
1.17/1.23	 a__U61(X:S) -> U61(X:S)
1.17/1.23	 a__U71(tt,P:S) -> a__U72(a__isPal(P:S))
1.17/1.23	 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S)
1.17/1.23	 a__U72(tt) -> tt
1.17/1.23	 a__U72(X:S) -> U72(X:S)
1.17/1.23	 a__U81(tt) -> tt
1.17/1.23	 a__U81(X:S) -> U81(X:S)
1.17/1.23	 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
1.17/1.23	 a____(nil,X:S) -> mark(X:S)
1.17/1.23	 a____(X:S,nil) -> mark(X:S)
1.17/1.23	 a____(X1:S,X2:S) -> __(X1:S,X2:S)
1.17/1.23	 a__isList(__(V1:S,V2:S)) -> a__U21(a__isList(V1:S),V2:S)
1.17/1.23	 a__isList(nil) -> tt
1.17/1.23	 a__isList(V:S) -> a__U11(a__isNeList(V:S))
1.17/1.23	 a__isList(X:S) -> isList(X:S)
1.17/1.23	 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__isList(V1:S),V2:S)
1.17/1.23	 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__isNeList(V1:S),V2:S)
1.17/1.23	 a__isNeList(V:S) -> a__U31(a__isQid(V:S))
1.17/1.23	 a__isNeList(X:S) -> isNeList(X:S)
1.17/1.23	 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U71(a__isQid(I:S),P:S)
1.17/1.23	 a__isNePal(V:S) -> a__U61(a__isQid(V:S))
1.17/1.23	 a__isNePal(X:S) -> isNePal(X:S)
1.17/1.23	 a__isPal(nil) -> tt
1.17/1.23	 a__isPal(V:S) -> a__U81(a__isNePal(V:S))
1.17/1.23	 a__isPal(X:S) -> isPal(X:S)
1.17/1.23	 a__isQid(a) -> tt
1.17/1.23	 a__isQid(e) -> tt
1.17/1.23	 a__isQid(i) -> tt
1.17/1.23	 a__isQid(o) -> tt
1.17/1.23	 a__isQid(u) -> tt
1.17/1.23	 a__isQid(X:S) -> isQid(X:S)
1.17/1.23	 mark(U11(X:S)) -> a__U11(mark(X:S))
1.17/1.23	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.17/1.23	 mark(U22(X:S)) -> a__U22(mark(X:S))
1.17/1.23	 mark(U31(X:S)) -> a__U31(mark(X:S))
1.17/1.23	 mark(U41(X1:S,X2:S)) -> a__U41(mark(X1:S),X2:S)
1.17/1.23	 mark(U42(X:S)) -> a__U42(mark(X:S))
1.17/1.23	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.17/1.23	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.17/1.23	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.17/1.23	 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S)
1.17/1.23	 mark(U72(X:S)) -> a__U72(mark(X:S))
1.17/1.23	 mark(U81(X:S)) -> a__U81(mark(X:S))
1.17/1.23	 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
1.17/1.23	 mark(a) -> a
1.17/1.23	 mark(e) -> e
1.17/1.23	 mark(i) -> i
1.17/1.23	 mark(isList(X:S)) -> a__isList(X:S)
1.17/1.23	 mark(isNeList(X:S)) -> a__isNeList(X:S)
1.17/1.23	 mark(isNePal(X:S)) -> a__isNePal(X:S)
1.17/1.23	 mark(isPal(X:S)) -> a__isPal(X:S)
1.17/1.23	 mark(isQid(X:S)) -> a__isQid(X:S)
1.17/1.23	 mark(nil) -> nil
1.17/1.23	 mark(o) -> o
1.17/1.23	 mark(tt) -> tt
1.17/1.23	 mark(u) -> u
1.17/1.23	->Strongly Connected Components:
1.17/1.23	->->Cycle:
1.17/1.23	->->-> Pairs:
1.17/1.23	 A__U71(tt,P:S) -> A__ISPAL(P:S)
1.17/1.23	 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__U71(a__isQid(I:S),P:S)
1.17/1.23	 A__ISPAL(V:S) -> A__ISNEPAL(V:S)
1.17/1.23	->->-> Rules:
1.17/1.23	 a__U11(tt) -> tt
1.17/1.23	 a__U11(X:S) -> U11(X:S)
1.17/1.23	 a__U21(tt,V2:S) -> a__U22(a__isList(V2:S))
1.17/1.23	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.17/1.23	 a__U22(tt) -> tt
1.17/1.23	 a__U22(X:S) -> U22(X:S)
1.17/1.23	 a__U31(tt) -> tt
1.17/1.23	 a__U31(X:S) -> U31(X:S)
1.17/1.23	 a__U41(tt,V2:S) -> a__U42(a__isNeList(V2:S))
1.17/1.23	 a__U41(X1:S,X2:S) -> U41(X1:S,X2:S)
1.17/1.23	 a__U42(tt) -> tt
1.17/1.23	 a__U42(X:S) -> U42(X:S)
1.17/1.23	 a__U51(tt,V2:S) -> a__U52(a__isList(V2:S))
1.17/1.23	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.17/1.23	 a__U52(tt) -> tt
1.17/1.23	 a__U52(X:S) -> U52(X:S)
1.17/1.23	 a__U61(tt) -> tt
1.17/1.23	 a__U61(X:S) -> U61(X:S)
1.17/1.23	 a__U71(tt,P:S) -> a__U72(a__isPal(P:S))
1.17/1.23	 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S)
1.17/1.23	 a__U72(tt) -> tt
1.17/1.23	 a__U72(X:S) -> U72(X:S)
1.17/1.23	 a__U81(tt) -> tt
1.17/1.23	 a__U81(X:S) -> U81(X:S)
1.17/1.23	 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
1.17/1.23	 a____(nil,X:S) -> mark(X:S)
1.17/1.23	 a____(X:S,nil) -> mark(X:S)
1.17/1.23	 a____(X1:S,X2:S) -> __(X1:S,X2:S)
1.17/1.23	 a__isList(__(V1:S,V2:S)) -> a__U21(a__isList(V1:S),V2:S)
1.17/1.23	 a__isList(nil) -> tt
1.17/1.23	 a__isList(V:S) -> a__U11(a__isNeList(V:S))
1.17/1.23	 a__isList(X:S) -> isList(X:S)
1.17/1.23	 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__isList(V1:S),V2:S)
1.17/1.23	 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__isNeList(V1:S),V2:S)
1.17/1.23	 a__isNeList(V:S) -> a__U31(a__isQid(V:S))
1.17/1.23	 a__isNeList(X:S) -> isNeList(X:S)
1.17/1.23	 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U71(a__isQid(I:S),P:S)
1.17/1.23	 a__isNePal(V:S) -> a__U61(a__isQid(V:S))
1.17/1.23	 a__isNePal(X:S) -> isNePal(X:S)
1.17/1.23	 a__isPal(nil) -> tt
1.17/1.23	 a__isPal(V:S) -> a__U81(a__isNePal(V:S))
1.17/1.23	 a__isPal(X:S) -> isPal(X:S)
1.17/1.23	 a__isQid(a) -> tt
1.17/1.23	 a__isQid(e) -> tt
1.17/1.23	 a__isQid(i) -> tt
1.17/1.23	 a__isQid(o) -> tt
1.17/1.23	 a__isQid(u) -> tt
1.17/1.23	 a__isQid(X:S) -> isQid(X:S)
1.17/1.23	 mark(U11(X:S)) -> a__U11(mark(X:S))
1.17/1.23	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.17/1.23	 mark(U22(X:S)) -> a__U22(mark(X:S))
1.17/1.23	 mark(U31(X:S)) -> a__U31(mark(X:S))
1.17/1.23	 mark(U41(X1:S,X2:S)) -> a__U41(mark(X1:S),X2:S)
1.17/1.23	 mark(U42(X:S)) -> a__U42(mark(X:S))
1.17/1.23	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.17/1.23	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.17/1.23	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.17/1.23	 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S)
1.17/1.23	 mark(U72(X:S)) -> a__U72(mark(X:S))
1.17/1.23	 mark(U81(X:S)) -> a__U81(mark(X:S))
1.17/1.23	 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
1.17/1.23	 mark(a) -> a
1.17/1.23	 mark(e) -> e
1.17/1.23	 mark(i) -> i
1.17/1.23	 mark(isList(X:S)) -> a__isList(X:S)
1.17/1.23	 mark(isNeList(X:S)) -> a__isNeList(X:S)
1.17/1.23	 mark(isNePal(X:S)) -> a__isNePal(X:S)
1.17/1.23	 mark(isPal(X:S)) -> a__isPal(X:S)
1.17/1.23	 mark(isQid(X:S)) -> a__isQid(X:S)
1.17/1.23	 mark(nil) -> nil
1.17/1.23	 mark(o) -> o
1.17/1.23	 mark(tt) -> tt
1.17/1.23	 mark(u) -> u
1.17/1.23	->->Cycle:
1.17/1.23	->->-> Pairs:
1.17/1.23	 A__U21(tt,V2:S) -> A__ISLIST(V2:S)
1.17/1.23	 A__U41(tt,V2:S) -> A__ISNELIST(V2:S)
1.17/1.23	 A__U51(tt,V2:S) -> A__ISLIST(V2:S)
1.17/1.23	 A__ISLIST(__(V1:S,V2:S)) -> A__U21(a__isList(V1:S),V2:S)
1.17/1.23	 A__ISLIST(__(V1:S,V2:S)) -> A__ISLIST(V1:S)
1.17/1.23	 A__ISLIST(V:S) -> A__ISNELIST(V:S)
1.17/1.23	 A__ISNELIST(__(V1:S,V2:S)) -> A__U41(a__isList(V1:S),V2:S)
1.17/1.23	 A__ISNELIST(__(V1:S,V2:S)) -> A__U51(a__isNeList(V1:S),V2:S)
1.17/1.23	 A__ISNELIST(__(V1:S,V2:S)) -> A__ISLIST(V1:S)
1.17/1.23	 A__ISNELIST(__(V1:S,V2:S)) -> A__ISNELIST(V1:S)
1.17/1.23	->->-> Rules:
1.17/1.23	 a__U11(tt) -> tt
1.17/1.23	 a__U11(X:S) -> U11(X:S)
1.17/1.23	 a__U21(tt,V2:S) -> a__U22(a__isList(V2:S))
1.17/1.23	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.17/1.23	 a__U22(tt) -> tt
1.17/1.23	 a__U22(X:S) -> U22(X:S)
1.17/1.23	 a__U31(tt) -> tt
1.17/1.23	 a__U31(X:S) -> U31(X:S)
1.17/1.23	 a__U41(tt,V2:S) -> a__U42(a__isNeList(V2:S))
1.17/1.23	 a__U41(X1:S,X2:S) -> U41(X1:S,X2:S)
1.17/1.23	 a__U42(tt) -> tt
1.17/1.23	 a__U42(X:S) -> U42(X:S)
1.17/1.23	 a__U51(tt,V2:S) -> a__U52(a__isList(V2:S))
1.17/1.23	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.17/1.23	 a__U52(tt) -> tt
1.17/1.23	 a__U52(X:S) -> U52(X:S)
1.17/1.23	 a__U61(tt) -> tt
1.17/1.23	 a__U61(X:S) -> U61(X:S)
1.17/1.23	 a__U71(tt,P:S) -> a__U72(a__isPal(P:S))
1.17/1.23	 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S)
1.17/1.23	 a__U72(tt) -> tt
1.17/1.23	 a__U72(X:S) -> U72(X:S)
1.17/1.23	 a__U81(tt) -> tt
1.17/1.23	 a__U81(X:S) -> U81(X:S)
1.17/1.23	 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
1.17/1.23	 a____(nil,X:S) -> mark(X:S)
1.17/1.23	 a____(X:S,nil) -> mark(X:S)
1.17/1.23	 a____(X1:S,X2:S) -> __(X1:S,X2:S)
1.17/1.23	 a__isList(__(V1:S,V2:S)) -> a__U21(a__isList(V1:S),V2:S)
1.17/1.23	 a__isList(nil) -> tt
1.17/1.23	 a__isList(V:S) -> a__U11(a__isNeList(V:S))
1.17/1.23	 a__isList(X:S) -> isList(X:S)
1.17/1.23	 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__isList(V1:S),V2:S)
1.17/1.23	 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__isNeList(V1:S),V2:S)
1.17/1.23	 a__isNeList(V:S) -> a__U31(a__isQid(V:S))
1.17/1.23	 a__isNeList(X:S) -> isNeList(X:S)
1.17/1.23	 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U71(a__isQid(I:S),P:S)
1.17/1.23	 a__isNePal(V:S) -> a__U61(a__isQid(V:S))
1.17/1.23	 a__isNePal(X:S) -> isNePal(X:S)
1.17/1.23	 a__isPal(nil) -> tt
1.17/1.23	 a__isPal(V:S) -> a__U81(a__isNePal(V:S))
1.17/1.23	 a__isPal(X:S) -> isPal(X:S)
1.17/1.23	 a__isQid(a) -> tt
1.17/1.23	 a__isQid(e) -> tt
1.17/1.23	 a__isQid(i) -> tt
1.17/1.23	 a__isQid(o) -> tt
1.17/1.23	 a__isQid(u) -> tt
1.17/1.23	 a__isQid(X:S) -> isQid(X:S)
1.17/1.23	 mark(U11(X:S)) -> a__U11(mark(X:S))
1.17/1.23	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.17/1.23	 mark(U22(X:S)) -> a__U22(mark(X:S))
1.17/1.23	 mark(U31(X:S)) -> a__U31(mark(X:S))
1.17/1.23	 mark(U41(X1:S,X2:S)) -> a__U41(mark(X1:S),X2:S)
1.17/1.23	 mark(U42(X:S)) -> a__U42(mark(X:S))
1.17/1.23	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.17/1.23	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.17/1.23	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.17/1.23	 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S)
1.17/1.23	 mark(U72(X:S)) -> a__U72(mark(X:S))
1.17/1.23	 mark(U81(X:S)) -> a__U81(mark(X:S))
1.17/1.23	 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
1.17/1.23	 mark(a) -> a
1.17/1.23	 mark(e) -> e
1.17/1.23	 mark(i) -> i
1.17/1.23	 mark(isList(X:S)) -> a__isList(X:S)
1.17/1.23	 mark(isNeList(X:S)) -> a__isNeList(X:S)
1.17/1.23	 mark(isNePal(X:S)) -> a__isNePal(X:S)
1.17/1.23	 mark(isPal(X:S)) -> a__isPal(X:S)
1.17/1.23	 mark(isQid(X:S)) -> a__isQid(X:S)
1.17/1.23	 mark(nil) -> nil
1.17/1.23	 mark(o) -> o
1.17/1.23	 mark(tt) -> tt
1.17/1.23	 mark(u) -> u
1.17/1.23	->->Cycle:
1.17/1.23	->->-> Pairs:
1.17/1.23	 A____(__(X:S,Y:S),Z:S) -> A____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
1.17/1.23	 A____(__(X:S,Y:S),Z:S) -> A____(mark(Y:S),mark(Z:S))
1.17/1.23	 A____(__(X:S,Y:S),Z:S) -> MARK(X:S)
1.17/1.23	 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S)
1.17/1.23	 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S)
1.17/1.23	 A____(nil,X:S) -> MARK(X:S)
1.17/1.23	 A____(X:S,nil) -> MARK(X:S)
1.17/1.23	 MARK(U11(X:S)) -> MARK(X:S)
1.17/1.23	 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.23	 MARK(U22(X:S)) -> MARK(X:S)
1.17/1.23	 MARK(U31(X:S)) -> MARK(X:S)
1.17/1.23	 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.23	 MARK(U42(X:S)) -> MARK(X:S)
1.17/1.23	 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.23	 MARK(U52(X:S)) -> MARK(X:S)
1.17/1.23	 MARK(U61(X:S)) -> MARK(X:S)
1.17/1.23	 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.23	 MARK(U72(X:S)) -> MARK(X:S)
1.17/1.23	 MARK(U81(X:S)) -> MARK(X:S)
1.17/1.23	 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S))
1.17/1.23	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.23	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.17/1.23	->->-> Rules:
1.17/1.23	 a__U11(tt) -> tt
1.17/1.23	 a__U11(X:S) -> U11(X:S)
1.17/1.23	 a__U21(tt,V2:S) -> a__U22(a__isList(V2:S))
1.17/1.23	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.17/1.23	 a__U22(tt) -> tt
1.17/1.23	 a__U22(X:S) -> U22(X:S)
1.17/1.23	 a__U31(tt) -> tt
1.17/1.23	 a__U31(X:S) -> U31(X:S)
1.17/1.23	 a__U41(tt,V2:S) -> a__U42(a__isNeList(V2:S))
1.17/1.23	 a__U41(X1:S,X2:S) -> U41(X1:S,X2:S)
1.17/1.23	 a__U42(tt) -> tt
1.17/1.23	 a__U42(X:S) -> U42(X:S)
1.17/1.23	 a__U51(tt,V2:S) -> a__U52(a__isList(V2:S))
1.17/1.23	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.17/1.23	 a__U52(tt) -> tt
1.17/1.23	 a__U52(X:S) -> U52(X:S)
1.17/1.23	 a__U61(tt) -> tt
1.17/1.23	 a__U61(X:S) -> U61(X:S)
1.17/1.23	 a__U71(tt,P:S) -> a__U72(a__isPal(P:S))
1.17/1.23	 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S)
1.17/1.23	 a__U72(tt) -> tt
1.17/1.23	 a__U72(X:S) -> U72(X:S)
1.17/1.23	 a__U81(tt) -> tt
1.17/1.23	 a__U81(X:S) -> U81(X:S)
1.17/1.23	 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
1.17/1.23	 a____(nil,X:S) -> mark(X:S)
1.17/1.23	 a____(X:S,nil) -> mark(X:S)
1.17/1.23	 a____(X1:S,X2:S) -> __(X1:S,X2:S)
1.17/1.23	 a__isList(__(V1:S,V2:S)) -> a__U21(a__isList(V1:S),V2:S)
1.17/1.23	 a__isList(nil) -> tt
1.17/1.23	 a__isList(V:S) -> a__U11(a__isNeList(V:S))
1.17/1.23	 a__isList(X:S) -> isList(X:S)
1.17/1.23	 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__isList(V1:S),V2:S)
1.17/1.23	 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__isNeList(V1:S),V2:S)
1.17/1.23	 a__isNeList(V:S) -> a__U31(a__isQid(V:S))
1.17/1.23	 a__isNeList(X:S) -> isNeList(X:S)
1.17/1.23	 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U71(a__isQid(I:S),P:S)
1.17/1.23	 a__isNePal(V:S) -> a__U61(a__isQid(V:S))
1.17/1.23	 a__isNePal(X:S) -> isNePal(X:S)
1.17/1.23	 a__isPal(nil) -> tt
1.17/1.23	 a__isPal(V:S) -> a__U81(a__isNePal(V:S))
1.17/1.23	 a__isPal(X:S) -> isPal(X:S)
1.17/1.23	 a__isQid(a) -> tt
1.17/1.23	 a__isQid(e) -> tt
1.17/1.23	 a__isQid(i) -> tt
1.17/1.23	 a__isQid(o) -> tt
1.17/1.23	 a__isQid(u) -> tt
1.17/1.23	 a__isQid(X:S) -> isQid(X:S)
1.17/1.23	 mark(U11(X:S)) -> a__U11(mark(X:S))
1.17/1.23	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.17/1.23	 mark(U22(X:S)) -> a__U22(mark(X:S))
1.17/1.23	 mark(U31(X:S)) -> a__U31(mark(X:S))
1.17/1.23	 mark(U41(X1:S,X2:S)) -> a__U41(mark(X1:S),X2:S)
1.17/1.23	 mark(U42(X:S)) -> a__U42(mark(X:S))
1.17/1.23	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.17/1.23	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.17/1.23	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.17/1.23	 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S)
1.17/1.23	 mark(U72(X:S)) -> a__U72(mark(X:S))
1.17/1.23	 mark(U81(X:S)) -> a__U81(mark(X:S))
1.17/1.23	 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
1.17/1.23	 mark(a) -> a
1.17/1.23	 mark(e) -> e
1.17/1.23	 mark(i) -> i
1.17/1.23	 mark(isList(X:S)) -> a__isList(X:S)
1.17/1.23	 mark(isNeList(X:S)) -> a__isNeList(X:S)
1.17/1.23	 mark(isNePal(X:S)) -> a__isNePal(X:S)
1.17/1.23	 mark(isPal(X:S)) -> a__isPal(X:S)
1.17/1.23	 mark(isQid(X:S)) -> a__isQid(X:S)
1.17/1.23	 mark(nil) -> nil
1.17/1.23	 mark(o) -> o
1.17/1.23	 mark(tt) -> tt
1.17/1.23	 mark(u) -> u
1.17/1.23	
1.17/1.23	
1.17/1.23	The problem is decomposed in 3 subproblems.
1.17/1.23	
1.17/1.23	Problem 1.1: 
1.17/1.23	
1.17/1.23	Subterm Processor:
1.17/1.23	-> Pairs:
1.17/1.23	 A__U71(tt,P:S) -> A__ISPAL(P:S)
1.17/1.23	 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__U71(a__isQid(I:S),P:S)
1.17/1.23	 A__ISPAL(V:S) -> A__ISNEPAL(V:S)
1.17/1.23	-> Rules:
1.17/1.23	 a__U11(tt) -> tt
1.17/1.23	 a__U11(X:S) -> U11(X:S)
1.17/1.23	 a__U21(tt,V2:S) -> a__U22(a__isList(V2:S))
1.17/1.23	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.17/1.23	 a__U22(tt) -> tt
1.17/1.23	 a__U22(X:S) -> U22(X:S)
1.17/1.23	 a__U31(tt) -> tt
1.17/1.23	 a__U31(X:S) -> U31(X:S)
1.17/1.23	 a__U41(tt,V2:S) -> a__U42(a__isNeList(V2:S))
1.17/1.23	 a__U41(X1:S,X2:S) -> U41(X1:S,X2:S)
1.17/1.23	 a__U42(tt) -> tt
1.17/1.23	 a__U42(X:S) -> U42(X:S)
1.17/1.23	 a__U51(tt,V2:S) -> a__U52(a__isList(V2:S))
1.17/1.23	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.17/1.23	 a__U52(tt) -> tt
1.17/1.23	 a__U52(X:S) -> U52(X:S)
1.17/1.23	 a__U61(tt) -> tt
1.17/1.23	 a__U61(X:S) -> U61(X:S)
1.17/1.23	 a__U71(tt,P:S) -> a__U72(a__isPal(P:S))
1.17/1.23	 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S)
1.17/1.23	 a__U72(tt) -> tt
1.17/1.23	 a__U72(X:S) -> U72(X:S)
1.17/1.23	 a__U81(tt) -> tt
1.17/1.23	 a__U81(X:S) -> U81(X:S)
1.17/1.23	 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
1.17/1.23	 a____(nil,X:S) -> mark(X:S)
1.17/1.23	 a____(X:S,nil) -> mark(X:S)
1.17/1.23	 a____(X1:S,X2:S) -> __(X1:S,X2:S)
1.17/1.23	 a__isList(__(V1:S,V2:S)) -> a__U21(a__isList(V1:S),V2:S)
1.17/1.23	 a__isList(nil) -> tt
1.17/1.23	 a__isList(V:S) -> a__U11(a__isNeList(V:S))
1.17/1.23	 a__isList(X:S) -> isList(X:S)
1.17/1.23	 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__isList(V1:S),V2:S)
1.17/1.23	 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__isNeList(V1:S),V2:S)
1.17/1.23	 a__isNeList(V:S) -> a__U31(a__isQid(V:S))
1.17/1.23	 a__isNeList(X:S) -> isNeList(X:S)
1.17/1.23	 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U71(a__isQid(I:S),P:S)
1.17/1.23	 a__isNePal(V:S) -> a__U61(a__isQid(V:S))
1.17/1.23	 a__isNePal(X:S) -> isNePal(X:S)
1.17/1.23	 a__isPal(nil) -> tt
1.17/1.23	 a__isPal(V:S) -> a__U81(a__isNePal(V:S))
1.17/1.23	 a__isPal(X:S) -> isPal(X:S)
1.17/1.23	 a__isQid(a) -> tt
1.17/1.23	 a__isQid(e) -> tt
1.17/1.23	 a__isQid(i) -> tt
1.17/1.23	 a__isQid(o) -> tt
1.17/1.23	 a__isQid(u) -> tt
1.17/1.23	 a__isQid(X:S) -> isQid(X:S)
1.17/1.23	 mark(U11(X:S)) -> a__U11(mark(X:S))
1.17/1.23	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.17/1.23	 mark(U22(X:S)) -> a__U22(mark(X:S))
1.17/1.23	 mark(U31(X:S)) -> a__U31(mark(X:S))
1.17/1.23	 mark(U41(X1:S,X2:S)) -> a__U41(mark(X1:S),X2:S)
1.17/1.23	 mark(U42(X:S)) -> a__U42(mark(X:S))
1.17/1.23	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.17/1.23	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.17/1.23	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.17/1.23	 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S)
1.17/1.23	 mark(U72(X:S)) -> a__U72(mark(X:S))
1.17/1.23	 mark(U81(X:S)) -> a__U81(mark(X:S))
1.17/1.23	 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
1.17/1.23	 mark(a) -> a
1.17/1.23	 mark(e) -> e
1.17/1.23	 mark(i) -> i
1.17/1.23	 mark(isList(X:S)) -> a__isList(X:S)
1.17/1.23	 mark(isNeList(X:S)) -> a__isNeList(X:S)
1.17/1.23	 mark(isNePal(X:S)) -> a__isNePal(X:S)
1.17/1.23	 mark(isPal(X:S)) -> a__isPal(X:S)
1.17/1.23	 mark(isQid(X:S)) -> a__isQid(X:S)
1.17/1.23	 mark(nil) -> nil
1.17/1.23	 mark(o) -> o
1.17/1.23	 mark(tt) -> tt
1.17/1.23	 mark(u) -> u
1.17/1.23	->Projection:
1.17/1.23	 pi(A__U71) = 2
1.17/1.23	 pi(A__ISNEPAL) = 1
1.17/1.23	 pi(A__ISPAL) = 1
1.17/1.23	
1.17/1.23	Problem 1.1: 
1.17/1.23	
1.17/1.23	SCC Processor:
1.17/1.23	-> Pairs:
1.17/1.23	 A__U71(tt,P:S) -> A__ISPAL(P:S)
1.17/1.23	 A__ISPAL(V:S) -> A__ISNEPAL(V:S)
1.17/1.23	-> Rules:
1.17/1.23	 a__U11(tt) -> tt
1.17/1.23	 a__U11(X:S) -> U11(X:S)
1.17/1.23	 a__U21(tt,V2:S) -> a__U22(a__isList(V2:S))
1.17/1.23	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.17/1.23	 a__U22(tt) -> tt
1.17/1.23	 a__U22(X:S) -> U22(X:S)
1.17/1.23	 a__U31(tt) -> tt
1.17/1.23	 a__U31(X:S) -> U31(X:S)
1.17/1.23	 a__U41(tt,V2:S) -> a__U42(a__isNeList(V2:S))
1.17/1.23	 a__U41(X1:S,X2:S) -> U41(X1:S,X2:S)
1.17/1.23	 a__U42(tt) -> tt
1.17/1.23	 a__U42(X:S) -> U42(X:S)
1.17/1.23	 a__U51(tt,V2:S) -> a__U52(a__isList(V2:S))
1.17/1.23	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.17/1.23	 a__U52(tt) -> tt
1.17/1.23	 a__U52(X:S) -> U52(X:S)
1.17/1.23	 a__U61(tt) -> tt
1.17/1.23	 a__U61(X:S) -> U61(X:S)
1.17/1.23	 a__U71(tt,P:S) -> a__U72(a__isPal(P:S))
1.17/1.23	 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S)
1.17/1.23	 a__U72(tt) -> tt
1.17/1.23	 a__U72(X:S) -> U72(X:S)
1.17/1.23	 a__U81(tt) -> tt
1.17/1.23	 a__U81(X:S) -> U81(X:S)
1.17/1.23	 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
1.17/1.23	 a____(nil,X:S) -> mark(X:S)
1.17/1.23	 a____(X:S,nil) -> mark(X:S)
1.17/1.23	 a____(X1:S,X2:S) -> __(X1:S,X2:S)
1.17/1.23	 a__isList(__(V1:S,V2:S)) -> a__U21(a__isList(V1:S),V2:S)
1.17/1.23	 a__isList(nil) -> tt
1.17/1.23	 a__isList(V:S) -> a__U11(a__isNeList(V:S))
1.17/1.23	 a__isList(X:S) -> isList(X:S)
1.17/1.23	 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__isList(V1:S),V2:S)
1.17/1.23	 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__isNeList(V1:S),V2:S)
1.17/1.23	 a__isNeList(V:S) -> a__U31(a__isQid(V:S))
1.17/1.23	 a__isNeList(X:S) -> isNeList(X:S)
1.17/1.23	 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U71(a__isQid(I:S),P:S)
1.17/1.23	 a__isNePal(V:S) -> a__U61(a__isQid(V:S))
1.17/1.23	 a__isNePal(X:S) -> isNePal(X:S)
1.17/1.23	 a__isPal(nil) -> tt
1.17/1.23	 a__isPal(V:S) -> a__U81(a__isNePal(V:S))
1.17/1.23	 a__isPal(X:S) -> isPal(X:S)
1.17/1.23	 a__isQid(a) -> tt
1.17/1.23	 a__isQid(e) -> tt
1.17/1.23	 a__isQid(i) -> tt
1.17/1.23	 a__isQid(o) -> tt
1.17/1.23	 a__isQid(u) -> tt
1.17/1.23	 a__isQid(X:S) -> isQid(X:S)
1.17/1.23	 mark(U11(X:S)) -> a__U11(mark(X:S))
1.17/1.23	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.17/1.23	 mark(U22(X:S)) -> a__U22(mark(X:S))
1.17/1.23	 mark(U31(X:S)) -> a__U31(mark(X:S))
1.17/1.23	 mark(U41(X1:S,X2:S)) -> a__U41(mark(X1:S),X2:S)
1.17/1.23	 mark(U42(X:S)) -> a__U42(mark(X:S))
1.17/1.23	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.17/1.23	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.17/1.23	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.17/1.23	 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S)
1.17/1.23	 mark(U72(X:S)) -> a__U72(mark(X:S))
1.17/1.23	 mark(U81(X:S)) -> a__U81(mark(X:S))
1.17/1.23	 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
1.17/1.23	 mark(a) -> a
1.17/1.23	 mark(e) -> e
1.17/1.23	 mark(i) -> i
1.17/1.23	 mark(isList(X:S)) -> a__isList(X:S)
1.17/1.23	 mark(isNeList(X:S)) -> a__isNeList(X:S)
1.17/1.23	 mark(isNePal(X:S)) -> a__isNePal(X:S)
1.17/1.23	 mark(isPal(X:S)) -> a__isPal(X:S)
1.17/1.23	 mark(isQid(X:S)) -> a__isQid(X:S)
1.17/1.23	 mark(nil) -> nil
1.17/1.23	 mark(o) -> o
1.17/1.23	 mark(tt) -> tt
1.17/1.23	 mark(u) -> u
1.17/1.23	->Strongly Connected Components:
1.17/1.23	 There is no strongly connected component
1.17/1.23	
1.17/1.23	The problem is finite.
1.17/1.23	
1.17/1.23	Problem 1.2: 
1.17/1.23	
1.17/1.23	Subterm Processor:
1.17/1.23	-> Pairs:
1.17/1.23	 A__U21(tt,V2:S) -> A__ISLIST(V2:S)
1.17/1.23	 A__U41(tt,V2:S) -> A__ISNELIST(V2:S)
1.17/1.23	 A__U51(tt,V2:S) -> A__ISLIST(V2:S)
1.17/1.23	 A__ISLIST(__(V1:S,V2:S)) -> A__U21(a__isList(V1:S),V2:S)
1.17/1.23	 A__ISLIST(__(V1:S,V2:S)) -> A__ISLIST(V1:S)
1.17/1.23	 A__ISLIST(V:S) -> A__ISNELIST(V:S)
1.17/1.23	 A__ISNELIST(__(V1:S,V2:S)) -> A__U41(a__isList(V1:S),V2:S)
1.17/1.23	 A__ISNELIST(__(V1:S,V2:S)) -> A__U51(a__isNeList(V1:S),V2:S)
1.17/1.23	 A__ISNELIST(__(V1:S,V2:S)) -> A__ISLIST(V1:S)
1.17/1.23	 A__ISNELIST(__(V1:S,V2:S)) -> A__ISNELIST(V1:S)
1.17/1.23	-> Rules:
1.17/1.23	 a__U11(tt) -> tt
1.17/1.23	 a__U11(X:S) -> U11(X:S)
1.17/1.23	 a__U21(tt,V2:S) -> a__U22(a__isList(V2:S))
1.17/1.23	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.17/1.23	 a__U22(tt) -> tt
1.17/1.23	 a__U22(X:S) -> U22(X:S)
1.17/1.23	 a__U31(tt) -> tt
1.17/1.23	 a__U31(X:S) -> U31(X:S)
1.17/1.23	 a__U41(tt,V2:S) -> a__U42(a__isNeList(V2:S))
1.17/1.23	 a__U41(X1:S,X2:S) -> U41(X1:S,X2:S)
1.17/1.23	 a__U42(tt) -> tt
1.17/1.23	 a__U42(X:S) -> U42(X:S)
1.17/1.23	 a__U51(tt,V2:S) -> a__U52(a__isList(V2:S))
1.17/1.23	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.17/1.23	 a__U52(tt) -> tt
1.17/1.23	 a__U52(X:S) -> U52(X:S)
1.17/1.23	 a__U61(tt) -> tt
1.17/1.23	 a__U61(X:S) -> U61(X:S)
1.17/1.23	 a__U71(tt,P:S) -> a__U72(a__isPal(P:S))
1.17/1.23	 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S)
1.17/1.23	 a__U72(tt) -> tt
1.17/1.23	 a__U72(X:S) -> U72(X:S)
1.17/1.23	 a__U81(tt) -> tt
1.17/1.23	 a__U81(X:S) -> U81(X:S)
1.17/1.23	 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
1.17/1.23	 a____(nil,X:S) -> mark(X:S)
1.17/1.23	 a____(X:S,nil) -> mark(X:S)
1.17/1.23	 a____(X1:S,X2:S) -> __(X1:S,X2:S)
1.17/1.23	 a__isList(__(V1:S,V2:S)) -> a__U21(a__isList(V1:S),V2:S)
1.17/1.23	 a__isList(nil) -> tt
1.17/1.23	 a__isList(V:S) -> a__U11(a__isNeList(V:S))
1.17/1.23	 a__isList(X:S) -> isList(X:S)
1.17/1.23	 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__isList(V1:S),V2:S)
1.17/1.23	 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__isNeList(V1:S),V2:S)
1.17/1.23	 a__isNeList(V:S) -> a__U31(a__isQid(V:S))
1.17/1.23	 a__isNeList(X:S) -> isNeList(X:S)
1.17/1.23	 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U71(a__isQid(I:S),P:S)
1.17/1.23	 a__isNePal(V:S) -> a__U61(a__isQid(V:S))
1.17/1.23	 a__isNePal(X:S) -> isNePal(X:S)
1.17/1.23	 a__isPal(nil) -> tt
1.17/1.23	 a__isPal(V:S) -> a__U81(a__isNePal(V:S))
1.17/1.23	 a__isPal(X:S) -> isPal(X:S)
1.17/1.23	 a__isQid(a) -> tt
1.17/1.23	 a__isQid(e) -> tt
1.17/1.23	 a__isQid(i) -> tt
1.17/1.23	 a__isQid(o) -> tt
1.17/1.23	 a__isQid(u) -> tt
1.17/1.23	 a__isQid(X:S) -> isQid(X:S)
1.17/1.23	 mark(U11(X:S)) -> a__U11(mark(X:S))
1.17/1.23	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.17/1.23	 mark(U22(X:S)) -> a__U22(mark(X:S))
1.17/1.23	 mark(U31(X:S)) -> a__U31(mark(X:S))
1.17/1.23	 mark(U41(X1:S,X2:S)) -> a__U41(mark(X1:S),X2:S)
1.17/1.23	 mark(U42(X:S)) -> a__U42(mark(X:S))
1.17/1.23	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.17/1.23	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.17/1.23	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.17/1.23	 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S)
1.17/1.23	 mark(U72(X:S)) -> a__U72(mark(X:S))
1.17/1.23	 mark(U81(X:S)) -> a__U81(mark(X:S))
1.17/1.23	 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
1.17/1.23	 mark(a) -> a
1.17/1.23	 mark(e) -> e
1.17/1.23	 mark(i) -> i
1.17/1.23	 mark(isList(X:S)) -> a__isList(X:S)
1.17/1.23	 mark(isNeList(X:S)) -> a__isNeList(X:S)
1.17/1.23	 mark(isNePal(X:S)) -> a__isNePal(X:S)
1.17/1.23	 mark(isPal(X:S)) -> a__isPal(X:S)
1.17/1.23	 mark(isQid(X:S)) -> a__isQid(X:S)
1.17/1.23	 mark(nil) -> nil
1.17/1.23	 mark(o) -> o
1.17/1.23	 mark(tt) -> tt
1.17/1.23	 mark(u) -> u
1.17/1.23	->Projection:
1.17/1.23	 pi(A__U21) = 2
1.17/1.23	 pi(A__U41) = 2
1.17/1.23	 pi(A__U51) = 2
1.17/1.23	 pi(A__ISLIST) = 1
1.17/1.23	 pi(A__ISNELIST) = 1
1.17/1.23	
1.17/1.23	Problem 1.2: 
1.17/1.23	
1.17/1.23	SCC Processor:
1.17/1.23	-> Pairs:
1.17/1.23	 A__U21(tt,V2:S) -> A__ISLIST(V2:S)
1.17/1.23	 A__U41(tt,V2:S) -> A__ISNELIST(V2:S)
1.17/1.23	 A__U51(tt,V2:S) -> A__ISLIST(V2:S)
1.17/1.23	 A__ISLIST(V:S) -> A__ISNELIST(V:S)
1.17/1.23	-> Rules:
1.17/1.23	 a__U11(tt) -> tt
1.17/1.23	 a__U11(X:S) -> U11(X:S)
1.17/1.23	 a__U21(tt,V2:S) -> a__U22(a__isList(V2:S))
1.17/1.23	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.17/1.23	 a__U22(tt) -> tt
1.17/1.23	 a__U22(X:S) -> U22(X:S)
1.17/1.23	 a__U31(tt) -> tt
1.17/1.23	 a__U31(X:S) -> U31(X:S)
1.17/1.23	 a__U41(tt,V2:S) -> a__U42(a__isNeList(V2:S))
1.18/1.23	 a__U41(X1:S,X2:S) -> U41(X1:S,X2:S)
1.18/1.23	 a__U42(tt) -> tt
1.18/1.23	 a__U42(X:S) -> U42(X:S)
1.18/1.23	 a__U51(tt,V2:S) -> a__U52(a__isList(V2:S))
1.18/1.23	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.18/1.23	 a__U52(tt) -> tt
1.18/1.23	 a__U52(X:S) -> U52(X:S)
1.18/1.23	 a__U61(tt) -> tt
1.18/1.23	 a__U61(X:S) -> U61(X:S)
1.18/1.23	 a__U71(tt,P:S) -> a__U72(a__isPal(P:S))
1.18/1.23	 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S)
1.18/1.23	 a__U72(tt) -> tt
1.18/1.23	 a__U72(X:S) -> U72(X:S)
1.18/1.23	 a__U81(tt) -> tt
1.18/1.23	 a__U81(X:S) -> U81(X:S)
1.18/1.23	 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
1.18/1.23	 a____(nil,X:S) -> mark(X:S)
1.18/1.23	 a____(X:S,nil) -> mark(X:S)
1.18/1.23	 a____(X1:S,X2:S) -> __(X1:S,X2:S)
1.18/1.23	 a__isList(__(V1:S,V2:S)) -> a__U21(a__isList(V1:S),V2:S)
1.18/1.23	 a__isList(nil) -> tt
1.18/1.23	 a__isList(V:S) -> a__U11(a__isNeList(V:S))
1.18/1.23	 a__isList(X:S) -> isList(X:S)
1.18/1.23	 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__isList(V1:S),V2:S)
1.18/1.23	 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__isNeList(V1:S),V2:S)
1.18/1.23	 a__isNeList(V:S) -> a__U31(a__isQid(V:S))
1.18/1.23	 a__isNeList(X:S) -> isNeList(X:S)
1.18/1.23	 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U71(a__isQid(I:S),P:S)
1.18/1.23	 a__isNePal(V:S) -> a__U61(a__isQid(V:S))
1.18/1.23	 a__isNePal(X:S) -> isNePal(X:S)
1.18/1.23	 a__isPal(nil) -> tt
1.18/1.23	 a__isPal(V:S) -> a__U81(a__isNePal(V:S))
1.18/1.23	 a__isPal(X:S) -> isPal(X:S)
1.18/1.23	 a__isQid(a) -> tt
1.18/1.23	 a__isQid(e) -> tt
1.18/1.23	 a__isQid(i) -> tt
1.18/1.23	 a__isQid(o) -> tt
1.18/1.23	 a__isQid(u) -> tt
1.18/1.23	 a__isQid(X:S) -> isQid(X:S)
1.18/1.23	 mark(U11(X:S)) -> a__U11(mark(X:S))
1.18/1.23	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.18/1.23	 mark(U22(X:S)) -> a__U22(mark(X:S))
1.18/1.23	 mark(U31(X:S)) -> a__U31(mark(X:S))
1.18/1.23	 mark(U41(X1:S,X2:S)) -> a__U41(mark(X1:S),X2:S)
1.18/1.23	 mark(U42(X:S)) -> a__U42(mark(X:S))
1.18/1.23	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.18/1.23	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.18/1.23	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.18/1.23	 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S)
1.18/1.23	 mark(U72(X:S)) -> a__U72(mark(X:S))
1.18/1.23	 mark(U81(X:S)) -> a__U81(mark(X:S))
1.18/1.23	 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
1.18/1.23	 mark(a) -> a
1.18/1.23	 mark(e) -> e
1.18/1.23	 mark(i) -> i
1.18/1.23	 mark(isList(X:S)) -> a__isList(X:S)
1.18/1.23	 mark(isNeList(X:S)) -> a__isNeList(X:S)
1.18/1.23	 mark(isNePal(X:S)) -> a__isNePal(X:S)
1.18/1.23	 mark(isPal(X:S)) -> a__isPal(X:S)
1.18/1.23	 mark(isQid(X:S)) -> a__isQid(X:S)
1.18/1.23	 mark(nil) -> nil
1.18/1.23	 mark(o) -> o
1.18/1.23	 mark(tt) -> tt
1.18/1.23	 mark(u) -> u
1.18/1.23	->Strongly Connected Components:
1.18/1.23	 There is no strongly connected component
1.18/1.23	
1.18/1.23	The problem is finite.
1.18/1.23	
1.18/1.23	Problem 1.3: 
1.18/1.23	
1.18/1.23	Reduction Pairs Processor:
1.18/1.23	-> Pairs:
1.18/1.23	 A____(__(X:S,Y:S),Z:S) -> A____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
1.18/1.23	 A____(__(X:S,Y:S),Z:S) -> A____(mark(Y:S),mark(Z:S))
1.18/1.23	 A____(__(X:S,Y:S),Z:S) -> MARK(X:S)
1.18/1.23	 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S)
1.18/1.23	 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S)
1.18/1.23	 A____(nil,X:S) -> MARK(X:S)
1.18/1.23	 A____(X:S,nil) -> MARK(X:S)
1.18/1.23	 MARK(U11(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.23	 MARK(U22(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U31(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.23	 MARK(U42(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.23	 MARK(U52(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U61(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.23	 MARK(U72(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U81(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S))
1.18/1.23	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.23	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.18/1.23	-> Rules:
1.18/1.23	 a__U11(tt) -> tt
1.18/1.23	 a__U11(X:S) -> U11(X:S)
1.18/1.23	 a__U21(tt,V2:S) -> a__U22(a__isList(V2:S))
1.18/1.23	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.18/1.23	 a__U22(tt) -> tt
1.18/1.23	 a__U22(X:S) -> U22(X:S)
1.18/1.23	 a__U31(tt) -> tt
1.18/1.23	 a__U31(X:S) -> U31(X:S)
1.18/1.23	 a__U41(tt,V2:S) -> a__U42(a__isNeList(V2:S))
1.18/1.23	 a__U41(X1:S,X2:S) -> U41(X1:S,X2:S)
1.18/1.23	 a__U42(tt) -> tt
1.18/1.23	 a__U42(X:S) -> U42(X:S)
1.18/1.23	 a__U51(tt,V2:S) -> a__U52(a__isList(V2:S))
1.18/1.23	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.18/1.23	 a__U52(tt) -> tt
1.18/1.23	 a__U52(X:S) -> U52(X:S)
1.18/1.23	 a__U61(tt) -> tt
1.18/1.23	 a__U61(X:S) -> U61(X:S)
1.18/1.23	 a__U71(tt,P:S) -> a__U72(a__isPal(P:S))
1.18/1.23	 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S)
1.18/1.23	 a__U72(tt) -> tt
1.18/1.23	 a__U72(X:S) -> U72(X:S)
1.18/1.23	 a__U81(tt) -> tt
1.18/1.23	 a__U81(X:S) -> U81(X:S)
1.18/1.23	 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
1.18/1.23	 a____(nil,X:S) -> mark(X:S)
1.18/1.23	 a____(X:S,nil) -> mark(X:S)
1.18/1.23	 a____(X1:S,X2:S) -> __(X1:S,X2:S)
1.18/1.23	 a__isList(__(V1:S,V2:S)) -> a__U21(a__isList(V1:S),V2:S)
1.18/1.23	 a__isList(nil) -> tt
1.18/1.23	 a__isList(V:S) -> a__U11(a__isNeList(V:S))
1.18/1.23	 a__isList(X:S) -> isList(X:S)
1.18/1.23	 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__isList(V1:S),V2:S)
1.18/1.23	 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__isNeList(V1:S),V2:S)
1.18/1.23	 a__isNeList(V:S) -> a__U31(a__isQid(V:S))
1.18/1.23	 a__isNeList(X:S) -> isNeList(X:S)
1.18/1.23	 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U71(a__isQid(I:S),P:S)
1.18/1.23	 a__isNePal(V:S) -> a__U61(a__isQid(V:S))
1.18/1.23	 a__isNePal(X:S) -> isNePal(X:S)
1.18/1.23	 a__isPal(nil) -> tt
1.18/1.23	 a__isPal(V:S) -> a__U81(a__isNePal(V:S))
1.18/1.23	 a__isPal(X:S) -> isPal(X:S)
1.18/1.23	 a__isQid(a) -> tt
1.18/1.23	 a__isQid(e) -> tt
1.18/1.23	 a__isQid(i) -> tt
1.18/1.23	 a__isQid(o) -> tt
1.18/1.23	 a__isQid(u) -> tt
1.18/1.23	 a__isQid(X:S) -> isQid(X:S)
1.18/1.23	 mark(U11(X:S)) -> a__U11(mark(X:S))
1.18/1.23	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.18/1.23	 mark(U22(X:S)) -> a__U22(mark(X:S))
1.18/1.23	 mark(U31(X:S)) -> a__U31(mark(X:S))
1.18/1.23	 mark(U41(X1:S,X2:S)) -> a__U41(mark(X1:S),X2:S)
1.18/1.23	 mark(U42(X:S)) -> a__U42(mark(X:S))
1.18/1.23	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.18/1.23	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.18/1.23	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.18/1.23	 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S)
1.18/1.23	 mark(U72(X:S)) -> a__U72(mark(X:S))
1.18/1.23	 mark(U81(X:S)) -> a__U81(mark(X:S))
1.18/1.23	 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
1.18/1.23	 mark(a) -> a
1.18/1.23	 mark(e) -> e
1.18/1.23	 mark(i) -> i
1.18/1.23	 mark(isList(X:S)) -> a__isList(X:S)
1.18/1.23	 mark(isNeList(X:S)) -> a__isNeList(X:S)
1.18/1.23	 mark(isNePal(X:S)) -> a__isNePal(X:S)
1.18/1.23	 mark(isPal(X:S)) -> a__isPal(X:S)
1.18/1.23	 mark(isQid(X:S)) -> a__isQid(X:S)
1.18/1.23	 mark(nil) -> nil
1.18/1.23	 mark(o) -> o
1.18/1.23	 mark(tt) -> tt
1.18/1.23	 mark(u) -> u
1.18/1.23	-> Usable rules:
1.18/1.23	 a__U11(tt) -> tt
1.18/1.23	 a__U11(X:S) -> U11(X:S)
1.18/1.23	 a__U21(tt,V2:S) -> a__U22(a__isList(V2:S))
1.18/1.23	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.18/1.23	 a__U22(tt) -> tt
1.18/1.23	 a__U22(X:S) -> U22(X:S)
1.18/1.23	 a__U31(tt) -> tt
1.18/1.23	 a__U31(X:S) -> U31(X:S)
1.18/1.23	 a__U41(tt,V2:S) -> a__U42(a__isNeList(V2:S))
1.18/1.23	 a__U41(X1:S,X2:S) -> U41(X1:S,X2:S)
1.18/1.23	 a__U42(tt) -> tt
1.18/1.23	 a__U42(X:S) -> U42(X:S)
1.18/1.23	 a__U51(tt,V2:S) -> a__U52(a__isList(V2:S))
1.18/1.23	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.18/1.23	 a__U52(tt) -> tt
1.18/1.23	 a__U52(X:S) -> U52(X:S)
1.18/1.23	 a__U61(tt) -> tt
1.18/1.23	 a__U61(X:S) -> U61(X:S)
1.18/1.23	 a__U71(tt,P:S) -> a__U72(a__isPal(P:S))
1.18/1.23	 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S)
1.18/1.23	 a__U72(tt) -> tt
1.18/1.23	 a__U72(X:S) -> U72(X:S)
1.18/1.23	 a__U81(tt) -> tt
1.18/1.23	 a__U81(X:S) -> U81(X:S)
1.18/1.23	 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
1.18/1.23	 a____(nil,X:S) -> mark(X:S)
1.18/1.23	 a____(X:S,nil) -> mark(X:S)
1.18/1.23	 a____(X1:S,X2:S) -> __(X1:S,X2:S)
1.18/1.23	 a__isList(__(V1:S,V2:S)) -> a__U21(a__isList(V1:S),V2:S)
1.18/1.23	 a__isList(nil) -> tt
1.18/1.23	 a__isList(V:S) -> a__U11(a__isNeList(V:S))
1.18/1.23	 a__isList(X:S) -> isList(X:S)
1.18/1.23	 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__isList(V1:S),V2:S)
1.18/1.23	 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__isNeList(V1:S),V2:S)
1.18/1.23	 a__isNeList(V:S) -> a__U31(a__isQid(V:S))
1.18/1.23	 a__isNeList(X:S) -> isNeList(X:S)
1.18/1.23	 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U71(a__isQid(I:S),P:S)
1.18/1.23	 a__isNePal(V:S) -> a__U61(a__isQid(V:S))
1.18/1.23	 a__isNePal(X:S) -> isNePal(X:S)
1.18/1.23	 a__isPal(nil) -> tt
1.18/1.23	 a__isPal(V:S) -> a__U81(a__isNePal(V:S))
1.18/1.23	 a__isPal(X:S) -> isPal(X:S)
1.18/1.23	 a__isQid(a) -> tt
1.18/1.23	 a__isQid(e) -> tt
1.18/1.23	 a__isQid(i) -> tt
1.18/1.23	 a__isQid(o) -> tt
1.18/1.23	 a__isQid(u) -> tt
1.18/1.23	 a__isQid(X:S) -> isQid(X:S)
1.18/1.23	 mark(U11(X:S)) -> a__U11(mark(X:S))
1.18/1.23	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.18/1.23	 mark(U22(X:S)) -> a__U22(mark(X:S))
1.18/1.23	 mark(U31(X:S)) -> a__U31(mark(X:S))
1.18/1.23	 mark(U41(X1:S,X2:S)) -> a__U41(mark(X1:S),X2:S)
1.18/1.23	 mark(U42(X:S)) -> a__U42(mark(X:S))
1.18/1.23	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.18/1.23	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.18/1.23	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.18/1.23	 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S)
1.18/1.23	 mark(U72(X:S)) -> a__U72(mark(X:S))
1.18/1.23	 mark(U81(X:S)) -> a__U81(mark(X:S))
1.18/1.23	 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
1.18/1.23	 mark(a) -> a
1.18/1.23	 mark(e) -> e
1.18/1.23	 mark(i) -> i
1.18/1.23	 mark(isList(X:S)) -> a__isList(X:S)
1.18/1.23	 mark(isNeList(X:S)) -> a__isNeList(X:S)
1.18/1.23	 mark(isNePal(X:S)) -> a__isNePal(X:S)
1.18/1.23	 mark(isPal(X:S)) -> a__isPal(X:S)
1.18/1.23	 mark(isQid(X:S)) -> a__isQid(X:S)
1.18/1.23	 mark(nil) -> nil
1.18/1.23	 mark(o) -> o
1.18/1.23	 mark(tt) -> tt
1.18/1.23	 mark(u) -> u
1.18/1.23	->Interpretation type:
1.18/1.23	 Linear
1.18/1.23	->Coefficients:
1.18/1.23	 Natural Numbers
1.18/1.23	->Dimension:
1.18/1.23	 1
1.18/1.23	->Bound:
1.18/1.23	 2
1.18/1.23	->Interpretation:
1.18/1.23	 
1.18/1.23	[a__U11](X) = 2.X
1.18/1.23	[a__U21](X1,X2) = 2.X1
1.18/1.23	[a__U22](X) = X
1.18/1.23	[a__U31](X) = 2.X
1.18/1.23	[a__U41](X1,X2) = 2.X1
1.18/1.23	[a__U42](X) = 2.X
1.18/1.23	[a__U51](X1,X2) = 2.X1
1.18/1.23	[a__U52](X) = 2.X
1.18/1.23	[a__U61](X) = 2.X + 1
1.18/1.23	[a__U71](X1,X2) = 2.X1 + 2.X2 + 2
1.18/1.23	[a__U72](X) = X
1.18/1.23	[a__U81](X) = 2.X
1.18/1.23	[a____](X1,X2) = 2.X1 + X2 + 2
1.18/1.23	[a__isList](X) = 0
1.18/1.23	[a__isNeList](X) = 0
1.18/1.23	[a__isNePal](X) = X + 1
1.18/1.23	[a__isPal](X) = 2.X + 2
1.18/1.23	[a__isQid](X) = 0
1.18/1.23	[mark](X) = X
1.18/1.23	[U11](X) = 2.X
1.18/1.23	[U21](X1,X2) = 2.X1
1.18/1.23	[U22](X) = X
1.18/1.23	[U31](X) = 2.X
1.18/1.23	[U41](X1,X2) = 2.X1
1.18/1.23	[U42](X) = 2.X
1.18/1.23	[U51](X1,X2) = 2.X1
1.18/1.23	[U52](X) = 2.X
1.18/1.23	[U61](X) = 2.X + 1
1.18/1.23	[U71](X1,X2) = 2.X1 + 2.X2 + 2
1.18/1.23	[U72](X) = X
1.18/1.23	[U81](X) = 2.X
1.18/1.23	[__](X1,X2) = 2.X1 + X2 + 2
1.18/1.23	[a] = 1
1.18/1.23	[e] = 1
1.18/1.23	[fSNonEmpty] = 0
1.18/1.23	[i] = 1
1.18/1.23	[isList](X) = 0
1.18/1.23	[isNeList](X) = 0
1.18/1.23	[isNePal](X) = X + 1
1.18/1.23	[isPal](X) = 2.X + 2
1.18/1.23	[isQid](X) = 0
1.18/1.23	[nil] = 2
1.18/1.23	[o] = 1
1.18/1.23	[tt] = 0
1.18/1.23	[u] = 1
1.18/1.23	[A__U11](X) = 0
1.18/1.23	[A__U21](X1,X2) = 0
1.18/1.23	[A__U22](X) = 0
1.18/1.23	[A__U31](X) = 0
1.18/1.23	[A__U41](X1,X2) = 0
1.18/1.23	[A__U42](X) = 0
1.18/1.23	[A__U51](X1,X2) = 0
1.18/1.23	[A__U52](X) = 0
1.18/1.23	[A__U61](X) = 0
1.18/1.23	[A__U71](X1,X2) = 0
1.18/1.23	[A__U72](X) = 0
1.18/1.23	[A__U81](X) = 0
1.18/1.23	[A____](X1,X2) = 2.X1 + X2
1.18/1.23	[A__ISLIST](X) = 0
1.18/1.23	[A__ISNELIST](X) = 0
1.18/1.23	[A__ISNEPAL](X) = 0
1.18/1.23	[A__ISPAL](X) = 0
1.18/1.23	[A__ISQID](X) = 0
1.18/1.23	[MARK](X) = X + 2
1.18/1.23	
1.18/1.23	Problem 1.3: 
1.18/1.23	
1.18/1.23	SCC Processor:
1.18/1.23	-> Pairs:
1.18/1.23	 A____(__(X:S,Y:S),Z:S) -> A____(mark(Y:S),mark(Z:S))
1.18/1.23	 A____(__(X:S,Y:S),Z:S) -> MARK(X:S)
1.18/1.23	 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S)
1.18/1.23	 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S)
1.18/1.23	 A____(nil,X:S) -> MARK(X:S)
1.18/1.23	 A____(X:S,nil) -> MARK(X:S)
1.18/1.23	 MARK(U11(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.23	 MARK(U22(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U31(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.23	 MARK(U42(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.23	 MARK(U52(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U61(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.23	 MARK(U72(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U81(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S))
1.18/1.23	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.23	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.18/1.23	-> Rules:
1.18/1.23	 a__U11(tt) -> tt
1.18/1.23	 a__U11(X:S) -> U11(X:S)
1.18/1.23	 a__U21(tt,V2:S) -> a__U22(a__isList(V2:S))
1.18/1.23	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.18/1.23	 a__U22(tt) -> tt
1.18/1.23	 a__U22(X:S) -> U22(X:S)
1.18/1.23	 a__U31(tt) -> tt
1.18/1.23	 a__U31(X:S) -> U31(X:S)
1.18/1.23	 a__U41(tt,V2:S) -> a__U42(a__isNeList(V2:S))
1.18/1.23	 a__U41(X1:S,X2:S) -> U41(X1:S,X2:S)
1.18/1.23	 a__U42(tt) -> tt
1.18/1.23	 a__U42(X:S) -> U42(X:S)
1.18/1.23	 a__U51(tt,V2:S) -> a__U52(a__isList(V2:S))
1.18/1.23	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.18/1.23	 a__U52(tt) -> tt
1.18/1.23	 a__U52(X:S) -> U52(X:S)
1.18/1.23	 a__U61(tt) -> tt
1.18/1.23	 a__U61(X:S) -> U61(X:S)
1.18/1.23	 a__U71(tt,P:S) -> a__U72(a__isPal(P:S))
1.18/1.23	 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S)
1.18/1.23	 a__U72(tt) -> tt
1.18/1.23	 a__U72(X:S) -> U72(X:S)
1.18/1.23	 a__U81(tt) -> tt
1.18/1.23	 a__U81(X:S) -> U81(X:S)
1.18/1.23	 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
1.18/1.23	 a____(nil,X:S) -> mark(X:S)
1.18/1.23	 a____(X:S,nil) -> mark(X:S)
1.18/1.23	 a____(X1:S,X2:S) -> __(X1:S,X2:S)
1.18/1.23	 a__isList(__(V1:S,V2:S)) -> a__U21(a__isList(V1:S),V2:S)
1.18/1.23	 a__isList(nil) -> tt
1.18/1.23	 a__isList(V:S) -> a__U11(a__isNeList(V:S))
1.18/1.23	 a__isList(X:S) -> isList(X:S)
1.18/1.23	 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__isList(V1:S),V2:S)
1.18/1.23	 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__isNeList(V1:S),V2:S)
1.18/1.23	 a__isNeList(V:S) -> a__U31(a__isQid(V:S))
1.18/1.23	 a__isNeList(X:S) -> isNeList(X:S)
1.18/1.23	 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U71(a__isQid(I:S),P:S)
1.18/1.23	 a__isNePal(V:S) -> a__U61(a__isQid(V:S))
1.18/1.23	 a__isNePal(X:S) -> isNePal(X:S)
1.18/1.23	 a__isPal(nil) -> tt
1.18/1.23	 a__isPal(V:S) -> a__U81(a__isNePal(V:S))
1.18/1.23	 a__isPal(X:S) -> isPal(X:S)
1.18/1.23	 a__isQid(a) -> tt
1.18/1.23	 a__isQid(e) -> tt
1.18/1.23	 a__isQid(i) -> tt
1.18/1.23	 a__isQid(o) -> tt
1.18/1.23	 a__isQid(u) -> tt
1.18/1.23	 a__isQid(X:S) -> isQid(X:S)
1.18/1.23	 mark(U11(X:S)) -> a__U11(mark(X:S))
1.18/1.23	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.18/1.23	 mark(U22(X:S)) -> a__U22(mark(X:S))
1.18/1.23	 mark(U31(X:S)) -> a__U31(mark(X:S))
1.18/1.23	 mark(U41(X1:S,X2:S)) -> a__U41(mark(X1:S),X2:S)
1.18/1.23	 mark(U42(X:S)) -> a__U42(mark(X:S))
1.18/1.23	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.18/1.23	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.18/1.23	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.18/1.23	 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S)
1.18/1.23	 mark(U72(X:S)) -> a__U72(mark(X:S))
1.18/1.23	 mark(U81(X:S)) -> a__U81(mark(X:S))
1.18/1.23	 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
1.18/1.23	 mark(a) -> a
1.18/1.23	 mark(e) -> e
1.18/1.23	 mark(i) -> i
1.18/1.23	 mark(isList(X:S)) -> a__isList(X:S)
1.18/1.23	 mark(isNeList(X:S)) -> a__isNeList(X:S)
1.18/1.23	 mark(isNePal(X:S)) -> a__isNePal(X:S)
1.18/1.23	 mark(isPal(X:S)) -> a__isPal(X:S)
1.18/1.23	 mark(isQid(X:S)) -> a__isQid(X:S)
1.18/1.23	 mark(nil) -> nil
1.18/1.23	 mark(o) -> o
1.18/1.23	 mark(tt) -> tt
1.18/1.23	 mark(u) -> u
1.18/1.23	->Strongly Connected Components:
1.18/1.23	->->Cycle:
1.18/1.23	->->-> Pairs:
1.18/1.23	 A____(__(X:S,Y:S),Z:S) -> A____(mark(Y:S),mark(Z:S))
1.18/1.23	 A____(__(X:S,Y:S),Z:S) -> MARK(X:S)
1.18/1.23	 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S)
1.18/1.23	 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S)
1.18/1.23	 A____(nil,X:S) -> MARK(X:S)
1.18/1.23	 A____(X:S,nil) -> MARK(X:S)
1.18/1.23	 MARK(U11(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.23	 MARK(U22(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U31(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.23	 MARK(U42(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.23	 MARK(U52(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U61(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.23	 MARK(U72(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U81(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S))
1.18/1.23	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.23	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.18/1.23	->->-> Rules:
1.18/1.23	 a__U11(tt) -> tt
1.18/1.23	 a__U11(X:S) -> U11(X:S)
1.18/1.23	 a__U21(tt,V2:S) -> a__U22(a__isList(V2:S))
1.18/1.23	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.18/1.23	 a__U22(tt) -> tt
1.18/1.23	 a__U22(X:S) -> U22(X:S)
1.18/1.23	 a__U31(tt) -> tt
1.18/1.23	 a__U31(X:S) -> U31(X:S)
1.18/1.23	 a__U41(tt,V2:S) -> a__U42(a__isNeList(V2:S))
1.18/1.23	 a__U41(X1:S,X2:S) -> U41(X1:S,X2:S)
1.18/1.23	 a__U42(tt) -> tt
1.18/1.23	 a__U42(X:S) -> U42(X:S)
1.18/1.23	 a__U51(tt,V2:S) -> a__U52(a__isList(V2:S))
1.18/1.23	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.18/1.23	 a__U52(tt) -> tt
1.18/1.23	 a__U52(X:S) -> U52(X:S)
1.18/1.23	 a__U61(tt) -> tt
1.18/1.23	 a__U61(X:S) -> U61(X:S)
1.18/1.23	 a__U71(tt,P:S) -> a__U72(a__isPal(P:S))
1.18/1.23	 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S)
1.18/1.23	 a__U72(tt) -> tt
1.18/1.23	 a__U72(X:S) -> U72(X:S)
1.18/1.23	 a__U81(tt) -> tt
1.18/1.23	 a__U81(X:S) -> U81(X:S)
1.18/1.23	 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
1.18/1.23	 a____(nil,X:S) -> mark(X:S)
1.18/1.23	 a____(X:S,nil) -> mark(X:S)
1.18/1.23	 a____(X1:S,X2:S) -> __(X1:S,X2:S)
1.18/1.23	 a__isList(__(V1:S,V2:S)) -> a__U21(a__isList(V1:S),V2:S)
1.18/1.23	 a__isList(nil) -> tt
1.18/1.23	 a__isList(V:S) -> a__U11(a__isNeList(V:S))
1.18/1.23	 a__isList(X:S) -> isList(X:S)
1.18/1.23	 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__isList(V1:S),V2:S)
1.18/1.23	 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__isNeList(V1:S),V2:S)
1.18/1.23	 a__isNeList(V:S) -> a__U31(a__isQid(V:S))
1.18/1.23	 a__isNeList(X:S) -> isNeList(X:S)
1.18/1.23	 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U71(a__isQid(I:S),P:S)
1.18/1.23	 a__isNePal(V:S) -> a__U61(a__isQid(V:S))
1.18/1.23	 a__isNePal(X:S) -> isNePal(X:S)
1.18/1.23	 a__isPal(nil) -> tt
1.18/1.23	 a__isPal(V:S) -> a__U81(a__isNePal(V:S))
1.18/1.23	 a__isPal(X:S) -> isPal(X:S)
1.18/1.23	 a__isQid(a) -> tt
1.18/1.23	 a__isQid(e) -> tt
1.18/1.23	 a__isQid(i) -> tt
1.18/1.23	 a__isQid(o) -> tt
1.18/1.23	 a__isQid(u) -> tt
1.18/1.23	 a__isQid(X:S) -> isQid(X:S)
1.18/1.23	 mark(U11(X:S)) -> a__U11(mark(X:S))
1.18/1.23	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.18/1.23	 mark(U22(X:S)) -> a__U22(mark(X:S))
1.18/1.23	 mark(U31(X:S)) -> a__U31(mark(X:S))
1.18/1.23	 mark(U41(X1:S,X2:S)) -> a__U41(mark(X1:S),X2:S)
1.18/1.23	 mark(U42(X:S)) -> a__U42(mark(X:S))
1.18/1.23	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.18/1.23	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.18/1.23	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.18/1.23	 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S)
1.18/1.23	 mark(U72(X:S)) -> a__U72(mark(X:S))
1.18/1.23	 mark(U81(X:S)) -> a__U81(mark(X:S))
1.18/1.23	 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
1.18/1.23	 mark(a) -> a
1.18/1.23	 mark(e) -> e
1.18/1.23	 mark(i) -> i
1.18/1.23	 mark(isList(X:S)) -> a__isList(X:S)
1.18/1.23	 mark(isNeList(X:S)) -> a__isNeList(X:S)
1.18/1.23	 mark(isNePal(X:S)) -> a__isNePal(X:S)
1.18/1.23	 mark(isPal(X:S)) -> a__isPal(X:S)
1.18/1.23	 mark(isQid(X:S)) -> a__isQid(X:S)
1.18/1.23	 mark(nil) -> nil
1.18/1.23	 mark(o) -> o
1.18/1.23	 mark(tt) -> tt
1.18/1.23	 mark(u) -> u
1.18/1.23	
1.18/1.23	Problem 1.3: 
1.18/1.23	
1.18/1.23	Reduction Pairs Processor:
1.18/1.23	-> Pairs:
1.18/1.23	 A____(__(X:S,Y:S),Z:S) -> A____(mark(Y:S),mark(Z:S))
1.18/1.23	 A____(__(X:S,Y:S),Z:S) -> MARK(X:S)
1.18/1.23	 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S)
1.18/1.23	 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S)
1.18/1.23	 A____(nil,X:S) -> MARK(X:S)
1.18/1.23	 A____(X:S,nil) -> MARK(X:S)
1.18/1.23	 MARK(U11(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.23	 MARK(U22(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U31(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.23	 MARK(U42(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.23	 MARK(U52(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U61(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.23	 MARK(U72(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U81(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S))
1.18/1.23	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.23	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.18/1.23	-> Rules:
1.18/1.23	 a__U11(tt) -> tt
1.18/1.23	 a__U11(X:S) -> U11(X:S)
1.18/1.23	 a__U21(tt,V2:S) -> a__U22(a__isList(V2:S))
1.18/1.23	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.18/1.23	 a__U22(tt) -> tt
1.18/1.23	 a__U22(X:S) -> U22(X:S)
1.18/1.23	 a__U31(tt) -> tt
1.18/1.23	 a__U31(X:S) -> U31(X:S)
1.18/1.23	 a__U41(tt,V2:S) -> a__U42(a__isNeList(V2:S))
1.18/1.23	 a__U41(X1:S,X2:S) -> U41(X1:S,X2:S)
1.18/1.23	 a__U42(tt) -> tt
1.18/1.23	 a__U42(X:S) -> U42(X:S)
1.18/1.23	 a__U51(tt,V2:S) -> a__U52(a__isList(V2:S))
1.18/1.23	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.18/1.23	 a__U52(tt) -> tt
1.18/1.23	 a__U52(X:S) -> U52(X:S)
1.18/1.23	 a__U61(tt) -> tt
1.18/1.23	 a__U61(X:S) -> U61(X:S)
1.18/1.23	 a__U71(tt,P:S) -> a__U72(a__isPal(P:S))
1.18/1.23	 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S)
1.18/1.23	 a__U72(tt) -> tt
1.18/1.23	 a__U72(X:S) -> U72(X:S)
1.18/1.23	 a__U81(tt) -> tt
1.18/1.23	 a__U81(X:S) -> U81(X:S)
1.18/1.23	 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
1.18/1.23	 a____(nil,X:S) -> mark(X:S)
1.18/1.23	 a____(X:S,nil) -> mark(X:S)
1.18/1.23	 a____(X1:S,X2:S) -> __(X1:S,X2:S)
1.18/1.23	 a__isList(__(V1:S,V2:S)) -> a__U21(a__isList(V1:S),V2:S)
1.18/1.23	 a__isList(nil) -> tt
1.18/1.23	 a__isList(V:S) -> a__U11(a__isNeList(V:S))
1.18/1.23	 a__isList(X:S) -> isList(X:S)
1.18/1.23	 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__isList(V1:S),V2:S)
1.18/1.23	 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__isNeList(V1:S),V2:S)
1.18/1.23	 a__isNeList(V:S) -> a__U31(a__isQid(V:S))
1.18/1.23	 a__isNeList(X:S) -> isNeList(X:S)
1.18/1.23	 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U71(a__isQid(I:S),P:S)
1.18/1.23	 a__isNePal(V:S) -> a__U61(a__isQid(V:S))
1.18/1.23	 a__isNePal(X:S) -> isNePal(X:S)
1.18/1.23	 a__isPal(nil) -> tt
1.18/1.23	 a__isPal(V:S) -> a__U81(a__isNePal(V:S))
1.18/1.23	 a__isPal(X:S) -> isPal(X:S)
1.18/1.23	 a__isQid(a) -> tt
1.18/1.23	 a__isQid(e) -> tt
1.18/1.23	 a__isQid(i) -> tt
1.18/1.23	 a__isQid(o) -> tt
1.18/1.23	 a__isQid(u) -> tt
1.18/1.23	 a__isQid(X:S) -> isQid(X:S)
1.18/1.23	 mark(U11(X:S)) -> a__U11(mark(X:S))
1.18/1.23	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.18/1.23	 mark(U22(X:S)) -> a__U22(mark(X:S))
1.18/1.23	 mark(U31(X:S)) -> a__U31(mark(X:S))
1.18/1.23	 mark(U41(X1:S,X2:S)) -> a__U41(mark(X1:S),X2:S)
1.18/1.23	 mark(U42(X:S)) -> a__U42(mark(X:S))
1.18/1.23	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.18/1.23	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.18/1.23	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.18/1.23	 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S)
1.18/1.23	 mark(U72(X:S)) -> a__U72(mark(X:S))
1.18/1.23	 mark(U81(X:S)) -> a__U81(mark(X:S))
1.18/1.23	 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
1.18/1.23	 mark(a) -> a
1.18/1.23	 mark(e) -> e
1.18/1.23	 mark(i) -> i
1.18/1.23	 mark(isList(X:S)) -> a__isList(X:S)
1.18/1.23	 mark(isNeList(X:S)) -> a__isNeList(X:S)
1.18/1.23	 mark(isNePal(X:S)) -> a__isNePal(X:S)
1.18/1.23	 mark(isPal(X:S)) -> a__isPal(X:S)
1.18/1.23	 mark(isQid(X:S)) -> a__isQid(X:S)
1.18/1.23	 mark(nil) -> nil
1.18/1.23	 mark(o) -> o
1.18/1.23	 mark(tt) -> tt
1.18/1.23	 mark(u) -> u
1.18/1.23	-> Usable rules:
1.18/1.23	 a__U11(tt) -> tt
1.18/1.23	 a__U11(X:S) -> U11(X:S)
1.18/1.23	 a__U21(tt,V2:S) -> a__U22(a__isList(V2:S))
1.18/1.23	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.18/1.23	 a__U22(tt) -> tt
1.18/1.23	 a__U22(X:S) -> U22(X:S)
1.18/1.23	 a__U31(tt) -> tt
1.18/1.23	 a__U31(X:S) -> U31(X:S)
1.18/1.23	 a__U41(tt,V2:S) -> a__U42(a__isNeList(V2:S))
1.18/1.23	 a__U41(X1:S,X2:S) -> U41(X1:S,X2:S)
1.18/1.23	 a__U42(tt) -> tt
1.18/1.23	 a__U42(X:S) -> U42(X:S)
1.18/1.23	 a__U51(tt,V2:S) -> a__U52(a__isList(V2:S))
1.18/1.23	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.18/1.23	 a__U52(tt) -> tt
1.18/1.23	 a__U52(X:S) -> U52(X:S)
1.18/1.23	 a__U61(tt) -> tt
1.18/1.23	 a__U61(X:S) -> U61(X:S)
1.18/1.23	 a__U71(tt,P:S) -> a__U72(a__isPal(P:S))
1.18/1.23	 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S)
1.18/1.23	 a__U72(tt) -> tt
1.18/1.23	 a__U72(X:S) -> U72(X:S)
1.18/1.23	 a__U81(tt) -> tt
1.18/1.23	 a__U81(X:S) -> U81(X:S)
1.18/1.23	 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
1.18/1.23	 a____(nil,X:S) -> mark(X:S)
1.18/1.23	 a____(X:S,nil) -> mark(X:S)
1.18/1.23	 a____(X1:S,X2:S) -> __(X1:S,X2:S)
1.18/1.23	 a__isList(__(V1:S,V2:S)) -> a__U21(a__isList(V1:S),V2:S)
1.18/1.23	 a__isList(nil) -> tt
1.18/1.23	 a__isList(V:S) -> a__U11(a__isNeList(V:S))
1.18/1.23	 a__isList(X:S) -> isList(X:S)
1.18/1.23	 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__isList(V1:S),V2:S)
1.18/1.23	 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__isNeList(V1:S),V2:S)
1.18/1.23	 a__isNeList(V:S) -> a__U31(a__isQid(V:S))
1.18/1.23	 a__isNeList(X:S) -> isNeList(X:S)
1.18/1.23	 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U71(a__isQid(I:S),P:S)
1.18/1.23	 a__isNePal(V:S) -> a__U61(a__isQid(V:S))
1.18/1.23	 a__isNePal(X:S) -> isNePal(X:S)
1.18/1.23	 a__isPal(nil) -> tt
1.18/1.23	 a__isPal(V:S) -> a__U81(a__isNePal(V:S))
1.18/1.23	 a__isPal(X:S) -> isPal(X:S)
1.18/1.23	 a__isQid(a) -> tt
1.18/1.23	 a__isQid(e) -> tt
1.18/1.23	 a__isQid(i) -> tt
1.18/1.23	 a__isQid(o) -> tt
1.18/1.23	 a__isQid(u) -> tt
1.18/1.23	 a__isQid(X:S) -> isQid(X:S)
1.18/1.23	 mark(U11(X:S)) -> a__U11(mark(X:S))
1.18/1.23	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.18/1.23	 mark(U22(X:S)) -> a__U22(mark(X:S))
1.18/1.23	 mark(U31(X:S)) -> a__U31(mark(X:S))
1.18/1.23	 mark(U41(X1:S,X2:S)) -> a__U41(mark(X1:S),X2:S)
1.18/1.23	 mark(U42(X:S)) -> a__U42(mark(X:S))
1.18/1.23	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.18/1.23	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.18/1.23	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.18/1.23	 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S)
1.18/1.23	 mark(U72(X:S)) -> a__U72(mark(X:S))
1.18/1.23	 mark(U81(X:S)) -> a__U81(mark(X:S))
1.18/1.23	 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
1.18/1.23	 mark(a) -> a
1.18/1.23	 mark(e) -> e
1.18/1.23	 mark(i) -> i
1.18/1.23	 mark(isList(X:S)) -> a__isList(X:S)
1.18/1.23	 mark(isNeList(X:S)) -> a__isNeList(X:S)
1.18/1.23	 mark(isNePal(X:S)) -> a__isNePal(X:S)
1.18/1.23	 mark(isPal(X:S)) -> a__isPal(X:S)
1.18/1.23	 mark(isQid(X:S)) -> a__isQid(X:S)
1.18/1.23	 mark(nil) -> nil
1.18/1.23	 mark(o) -> o
1.18/1.23	 mark(tt) -> tt
1.18/1.23	 mark(u) -> u
1.18/1.23	->Interpretation type:
1.18/1.23	 Linear
1.18/1.23	->Coefficients:
1.18/1.23	 Natural Numbers
1.18/1.23	->Dimension:
1.18/1.23	 1
1.18/1.23	->Bound:
1.18/1.23	 2
1.18/1.23	->Interpretation:
1.18/1.23	 
1.18/1.23	[a__U11](X) = X
1.18/1.23	[a__U21](X1,X2) = 2.X1 + 2.X2 + 2
1.18/1.23	[a__U22](X) = X + 2
1.18/1.23	[a__U31](X) = 2.X
1.18/1.23	[a__U41](X1,X2) = 2.X1 + 2.X2 + 2
1.18/1.23	[a__U42](X) = X
1.18/1.23	[a__U51](X1,X2) = X1 + 2.X2 + 2
1.18/1.23	[a__U52](X) = X + 1
1.18/1.23	[a__U61](X) = X
1.18/1.23	[a__U71](X1,X2) = 2.X1 + 2.X2 + 2
1.18/1.23	[a__U72](X) = X + 1
1.18/1.23	[a__U81](X) = 2.X
1.18/1.23	[a____](X1,X2) = 2.X1 + X2 + 2
1.18/1.23	[a__isList](X) = 2.X + 2
1.18/1.23	[a__isNeList](X) = 2.X + 2
1.18/1.23	[a__isNePal](X) = X + 1
1.18/1.23	[a__isPal](X) = 2.X + 2
1.18/1.23	[a__isQid](X) = X + 1
1.18/1.23	[mark](X) = X
1.18/1.23	[U11](X) = X
1.18/1.23	[U21](X1,X2) = 2.X1 + 2.X2 + 2
1.18/1.23	[U22](X) = X + 2
1.18/1.23	[U31](X) = 2.X
1.18/1.23	[U41](X1,X2) = 2.X1 + 2.X2 + 2
1.18/1.23	[U42](X) = X
1.18/1.23	[U51](X1,X2) = X1 + 2.X2 + 2
1.18/1.23	[U52](X) = X + 1
1.18/1.23	[U61](X) = X
1.18/1.23	[U71](X1,X2) = 2.X1 + 2.X2 + 2
1.18/1.23	[U72](X) = X + 1
1.18/1.23	[U81](X) = 2.X
1.18/1.23	[__](X1,X2) = 2.X1 + X2 + 2
1.18/1.23	[a] = 1
1.18/1.23	[e] = 1
1.18/1.23	[fSNonEmpty] = 0
1.18/1.23	[i] = 1
1.18/1.23	[isList](X) = 2.X + 2
1.18/1.23	[isNeList](X) = 2.X + 2
1.18/1.23	[isNePal](X) = X + 1
1.18/1.23	[isPal](X) = 2.X + 2
1.18/1.23	[isQid](X) = X + 1
1.18/1.23	[nil] = 2
1.18/1.23	[o] = 1
1.18/1.23	[tt] = 2
1.18/1.23	[u] = 1
1.18/1.23	[A__U11](X) = 0
1.18/1.23	[A__U21](X1,X2) = 0
1.18/1.23	[A__U22](X) = 0
1.18/1.23	[A__U31](X) = 0
1.18/1.23	[A__U41](X1,X2) = 0
1.18/1.23	[A__U42](X) = 0
1.18/1.23	[A__U51](X1,X2) = 0
1.18/1.23	[A__U52](X) = 0
1.18/1.23	[A__U61](X) = 0
1.18/1.23	[A__U71](X1,X2) = 0
1.18/1.23	[A__U72](X) = 0
1.18/1.23	[A__U81](X) = 0
1.18/1.23	[A____](X1,X2) = 2.X1 + 2.X2 + 2
1.18/1.23	[A__ISLIST](X) = 0
1.18/1.23	[A__ISNELIST](X) = 0
1.18/1.23	[A__ISNEPAL](X) = 0
1.18/1.23	[A__ISPAL](X) = 0
1.18/1.23	[A__ISQID](X) = 0
1.18/1.23	[MARK](X) = 2.X
1.18/1.23	
1.18/1.23	Problem 1.3: 
1.18/1.23	
1.18/1.23	SCC Processor:
1.18/1.23	-> Pairs:
1.18/1.23	 A____(__(X:S,Y:S),Z:S) -> MARK(X:S)
1.18/1.23	 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S)
1.18/1.23	 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S)
1.18/1.23	 A____(nil,X:S) -> MARK(X:S)
1.18/1.23	 A____(X:S,nil) -> MARK(X:S)
1.18/1.23	 MARK(U11(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.23	 MARK(U22(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U31(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.23	 MARK(U42(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.23	 MARK(U52(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U61(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.23	 MARK(U72(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U81(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S))
1.18/1.23	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.23	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.18/1.23	-> Rules:
1.18/1.23	 a__U11(tt) -> tt
1.18/1.23	 a__U11(X:S) -> U11(X:S)
1.18/1.23	 a__U21(tt,V2:S) -> a__U22(a__isList(V2:S))
1.18/1.23	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.18/1.23	 a__U22(tt) -> tt
1.18/1.23	 a__U22(X:S) -> U22(X:S)
1.18/1.23	 a__U31(tt) -> tt
1.18/1.23	 a__U31(X:S) -> U31(X:S)
1.18/1.23	 a__U41(tt,V2:S) -> a__U42(a__isNeList(V2:S))
1.18/1.23	 a__U41(X1:S,X2:S) -> U41(X1:S,X2:S)
1.18/1.23	 a__U42(tt) -> tt
1.18/1.23	 a__U42(X:S) -> U42(X:S)
1.18/1.23	 a__U51(tt,V2:S) -> a__U52(a__isList(V2:S))
1.18/1.23	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.18/1.23	 a__U52(tt) -> tt
1.18/1.23	 a__U52(X:S) -> U52(X:S)
1.18/1.23	 a__U61(tt) -> tt
1.18/1.23	 a__U61(X:S) -> U61(X:S)
1.18/1.23	 a__U71(tt,P:S) -> a__U72(a__isPal(P:S))
1.18/1.23	 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S)
1.18/1.23	 a__U72(tt) -> tt
1.18/1.23	 a__U72(X:S) -> U72(X:S)
1.18/1.23	 a__U81(tt) -> tt
1.18/1.23	 a__U81(X:S) -> U81(X:S)
1.18/1.23	 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
1.18/1.23	 a____(nil,X:S) -> mark(X:S)
1.18/1.23	 a____(X:S,nil) -> mark(X:S)
1.18/1.23	 a____(X1:S,X2:S) -> __(X1:S,X2:S)
1.18/1.23	 a__isList(__(V1:S,V2:S)) -> a__U21(a__isList(V1:S),V2:S)
1.18/1.23	 a__isList(nil) -> tt
1.18/1.23	 a__isList(V:S) -> a__U11(a__isNeList(V:S))
1.18/1.23	 a__isList(X:S) -> isList(X:S)
1.18/1.23	 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__isList(V1:S),V2:S)
1.18/1.23	 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__isNeList(V1:S),V2:S)
1.18/1.23	 a__isNeList(V:S) -> a__U31(a__isQid(V:S))
1.18/1.23	 a__isNeList(X:S) -> isNeList(X:S)
1.18/1.23	 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U71(a__isQid(I:S),P:S)
1.18/1.23	 a__isNePal(V:S) -> a__U61(a__isQid(V:S))
1.18/1.23	 a__isNePal(X:S) -> isNePal(X:S)
1.18/1.23	 a__isPal(nil) -> tt
1.18/1.23	 a__isPal(V:S) -> a__U81(a__isNePal(V:S))
1.18/1.23	 a__isPal(X:S) -> isPal(X:S)
1.18/1.23	 a__isQid(a) -> tt
1.18/1.23	 a__isQid(e) -> tt
1.18/1.23	 a__isQid(i) -> tt
1.18/1.23	 a__isQid(o) -> tt
1.18/1.23	 a__isQid(u) -> tt
1.18/1.23	 a__isQid(X:S) -> isQid(X:S)
1.18/1.23	 mark(U11(X:S)) -> a__U11(mark(X:S))
1.18/1.23	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.18/1.23	 mark(U22(X:S)) -> a__U22(mark(X:S))
1.18/1.23	 mark(U31(X:S)) -> a__U31(mark(X:S))
1.18/1.23	 mark(U41(X1:S,X2:S)) -> a__U41(mark(X1:S),X2:S)
1.18/1.23	 mark(U42(X:S)) -> a__U42(mark(X:S))
1.18/1.23	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.18/1.23	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.18/1.23	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.18/1.23	 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S)
1.18/1.23	 mark(U72(X:S)) -> a__U72(mark(X:S))
1.18/1.23	 mark(U81(X:S)) -> a__U81(mark(X:S))
1.18/1.23	 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
1.18/1.23	 mark(a) -> a
1.18/1.23	 mark(e) -> e
1.18/1.23	 mark(i) -> i
1.18/1.23	 mark(isList(X:S)) -> a__isList(X:S)
1.18/1.23	 mark(isNeList(X:S)) -> a__isNeList(X:S)
1.18/1.23	 mark(isNePal(X:S)) -> a__isNePal(X:S)
1.18/1.23	 mark(isPal(X:S)) -> a__isPal(X:S)
1.18/1.23	 mark(isQid(X:S)) -> a__isQid(X:S)
1.18/1.23	 mark(nil) -> nil
1.18/1.23	 mark(o) -> o
1.18/1.23	 mark(tt) -> tt
1.18/1.23	 mark(u) -> u
1.18/1.23	->Strongly Connected Components:
1.18/1.23	->->Cycle:
1.18/1.23	->->-> Pairs:
1.18/1.23	 A____(__(X:S,Y:S),Z:S) -> MARK(X:S)
1.18/1.23	 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S)
1.18/1.23	 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S)
1.18/1.23	 A____(nil,X:S) -> MARK(X:S)
1.18/1.23	 A____(X:S,nil) -> MARK(X:S)
1.18/1.23	 MARK(U11(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.23	 MARK(U22(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U31(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.23	 MARK(U42(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.23	 MARK(U52(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U61(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.23	 MARK(U72(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U81(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S))
1.18/1.23	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.23	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.18/1.23	->->-> Rules:
1.18/1.23	 a__U11(tt) -> tt
1.18/1.23	 a__U11(X:S) -> U11(X:S)
1.18/1.23	 a__U21(tt,V2:S) -> a__U22(a__isList(V2:S))
1.18/1.23	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.18/1.23	 a__U22(tt) -> tt
1.18/1.23	 a__U22(X:S) -> U22(X:S)
1.18/1.23	 a__U31(tt) -> tt
1.18/1.23	 a__U31(X:S) -> U31(X:S)
1.18/1.23	 a__U41(tt,V2:S) -> a__U42(a__isNeList(V2:S))
1.18/1.23	 a__U41(X1:S,X2:S) -> U41(X1:S,X2:S)
1.18/1.23	 a__U42(tt) -> tt
1.18/1.23	 a__U42(X:S) -> U42(X:S)
1.18/1.23	 a__U51(tt,V2:S) -> a__U52(a__isList(V2:S))
1.18/1.23	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.18/1.23	 a__U52(tt) -> tt
1.18/1.23	 a__U52(X:S) -> U52(X:S)
1.18/1.23	 a__U61(tt) -> tt
1.18/1.23	 a__U61(X:S) -> U61(X:S)
1.18/1.23	 a__U71(tt,P:S) -> a__U72(a__isPal(P:S))
1.18/1.23	 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S)
1.18/1.23	 a__U72(tt) -> tt
1.18/1.23	 a__U72(X:S) -> U72(X:S)
1.18/1.23	 a__U81(tt) -> tt
1.18/1.23	 a__U81(X:S) -> U81(X:S)
1.18/1.23	 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
1.18/1.23	 a____(nil,X:S) -> mark(X:S)
1.18/1.23	 a____(X:S,nil) -> mark(X:S)
1.18/1.23	 a____(X1:S,X2:S) -> __(X1:S,X2:S)
1.18/1.23	 a__isList(__(V1:S,V2:S)) -> a__U21(a__isList(V1:S),V2:S)
1.18/1.23	 a__isList(nil) -> tt
1.18/1.23	 a__isList(V:S) -> a__U11(a__isNeList(V:S))
1.18/1.23	 a__isList(X:S) -> isList(X:S)
1.18/1.23	 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__isList(V1:S),V2:S)
1.18/1.23	 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__isNeList(V1:S),V2:S)
1.18/1.23	 a__isNeList(V:S) -> a__U31(a__isQid(V:S))
1.18/1.23	 a__isNeList(X:S) -> isNeList(X:S)
1.18/1.23	 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U71(a__isQid(I:S),P:S)
1.18/1.23	 a__isNePal(V:S) -> a__U61(a__isQid(V:S))
1.18/1.23	 a__isNePal(X:S) -> isNePal(X:S)
1.18/1.23	 a__isPal(nil) -> tt
1.18/1.23	 a__isPal(V:S) -> a__U81(a__isNePal(V:S))
1.18/1.23	 a__isPal(X:S) -> isPal(X:S)
1.18/1.23	 a__isQid(a) -> tt
1.18/1.23	 a__isQid(e) -> tt
1.18/1.23	 a__isQid(i) -> tt
1.18/1.23	 a__isQid(o) -> tt
1.18/1.23	 a__isQid(u) -> tt
1.18/1.23	 a__isQid(X:S) -> isQid(X:S)
1.18/1.23	 mark(U11(X:S)) -> a__U11(mark(X:S))
1.18/1.23	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.18/1.23	 mark(U22(X:S)) -> a__U22(mark(X:S))
1.18/1.23	 mark(U31(X:S)) -> a__U31(mark(X:S))
1.18/1.23	 mark(U41(X1:S,X2:S)) -> a__U41(mark(X1:S),X2:S)
1.18/1.23	 mark(U42(X:S)) -> a__U42(mark(X:S))
1.18/1.23	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.18/1.23	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.18/1.23	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.18/1.23	 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S)
1.18/1.23	 mark(U72(X:S)) -> a__U72(mark(X:S))
1.18/1.23	 mark(U81(X:S)) -> a__U81(mark(X:S))
1.18/1.23	 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
1.18/1.23	 mark(a) -> a
1.18/1.23	 mark(e) -> e
1.18/1.23	 mark(i) -> i
1.18/1.23	 mark(isList(X:S)) -> a__isList(X:S)
1.18/1.23	 mark(isNeList(X:S)) -> a__isNeList(X:S)
1.18/1.23	 mark(isNePal(X:S)) -> a__isNePal(X:S)
1.18/1.23	 mark(isPal(X:S)) -> a__isPal(X:S)
1.18/1.23	 mark(isQid(X:S)) -> a__isQid(X:S)
1.18/1.23	 mark(nil) -> nil
1.18/1.23	 mark(o) -> o
1.18/1.23	 mark(tt) -> tt
1.18/1.23	 mark(u) -> u
1.18/1.23	
1.18/1.23	Problem 1.3: 
1.18/1.23	
1.18/1.23	Reduction Pairs Processor:
1.18/1.23	-> Pairs:
1.18/1.23	 A____(__(X:S,Y:S),Z:S) -> MARK(X:S)
1.18/1.23	 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S)
1.18/1.23	 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S)
1.18/1.23	 A____(nil,X:S) -> MARK(X:S)
1.18/1.23	 A____(X:S,nil) -> MARK(X:S)
1.18/1.23	 MARK(U11(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.23	 MARK(U22(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U31(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.23	 MARK(U42(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.23	 MARK(U52(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U61(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.23	 MARK(U72(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U81(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S))
1.18/1.23	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.23	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.18/1.23	-> Rules:
1.18/1.23	 a__U11(tt) -> tt
1.18/1.23	 a__U11(X:S) -> U11(X:S)
1.18/1.23	 a__U21(tt,V2:S) -> a__U22(a__isList(V2:S))
1.18/1.23	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.18/1.23	 a__U22(tt) -> tt
1.18/1.23	 a__U22(X:S) -> U22(X:S)
1.18/1.23	 a__U31(tt) -> tt
1.18/1.23	 a__U31(X:S) -> U31(X:S)
1.18/1.23	 a__U41(tt,V2:S) -> a__U42(a__isNeList(V2:S))
1.18/1.23	 a__U41(X1:S,X2:S) -> U41(X1:S,X2:S)
1.18/1.23	 a__U42(tt) -> tt
1.18/1.23	 a__U42(X:S) -> U42(X:S)
1.18/1.23	 a__U51(tt,V2:S) -> a__U52(a__isList(V2:S))
1.18/1.23	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.18/1.23	 a__U52(tt) -> tt
1.18/1.23	 a__U52(X:S) -> U52(X:S)
1.18/1.23	 a__U61(tt) -> tt
1.18/1.23	 a__U61(X:S) -> U61(X:S)
1.18/1.23	 a__U71(tt,P:S) -> a__U72(a__isPal(P:S))
1.18/1.23	 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S)
1.18/1.23	 a__U72(tt) -> tt
1.18/1.23	 a__U72(X:S) -> U72(X:S)
1.18/1.23	 a__U81(tt) -> tt
1.18/1.23	 a__U81(X:S) -> U81(X:S)
1.18/1.23	 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
1.18/1.23	 a____(nil,X:S) -> mark(X:S)
1.18/1.23	 a____(X:S,nil) -> mark(X:S)
1.18/1.23	 a____(X1:S,X2:S) -> __(X1:S,X2:S)
1.18/1.23	 a__isList(__(V1:S,V2:S)) -> a__U21(a__isList(V1:S),V2:S)
1.18/1.23	 a__isList(nil) -> tt
1.18/1.23	 a__isList(V:S) -> a__U11(a__isNeList(V:S))
1.18/1.23	 a__isList(X:S) -> isList(X:S)
1.18/1.23	 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__isList(V1:S),V2:S)
1.18/1.23	 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__isNeList(V1:S),V2:S)
1.18/1.23	 a__isNeList(V:S) -> a__U31(a__isQid(V:S))
1.18/1.23	 a__isNeList(X:S) -> isNeList(X:S)
1.18/1.23	 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U71(a__isQid(I:S),P:S)
1.18/1.23	 a__isNePal(V:S) -> a__U61(a__isQid(V:S))
1.18/1.23	 a__isNePal(X:S) -> isNePal(X:S)
1.18/1.23	 a__isPal(nil) -> tt
1.18/1.23	 a__isPal(V:S) -> a__U81(a__isNePal(V:S))
1.18/1.23	 a__isPal(X:S) -> isPal(X:S)
1.18/1.23	 a__isQid(a) -> tt
1.18/1.23	 a__isQid(e) -> tt
1.18/1.23	 a__isQid(i) -> tt
1.18/1.23	 a__isQid(o) -> tt
1.18/1.23	 a__isQid(u) -> tt
1.18/1.23	 a__isQid(X:S) -> isQid(X:S)
1.18/1.23	 mark(U11(X:S)) -> a__U11(mark(X:S))
1.18/1.23	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.18/1.23	 mark(U22(X:S)) -> a__U22(mark(X:S))
1.18/1.23	 mark(U31(X:S)) -> a__U31(mark(X:S))
1.18/1.23	 mark(U41(X1:S,X2:S)) -> a__U41(mark(X1:S),X2:S)
1.18/1.23	 mark(U42(X:S)) -> a__U42(mark(X:S))
1.18/1.23	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.18/1.23	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.18/1.23	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.18/1.23	 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S)
1.18/1.23	 mark(U72(X:S)) -> a__U72(mark(X:S))
1.18/1.23	 mark(U81(X:S)) -> a__U81(mark(X:S))
1.18/1.23	 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
1.18/1.23	 mark(a) -> a
1.18/1.23	 mark(e) -> e
1.18/1.23	 mark(i) -> i
1.18/1.23	 mark(isList(X:S)) -> a__isList(X:S)
1.18/1.23	 mark(isNeList(X:S)) -> a__isNeList(X:S)
1.18/1.23	 mark(isNePal(X:S)) -> a__isNePal(X:S)
1.18/1.23	 mark(isPal(X:S)) -> a__isPal(X:S)
1.18/1.23	 mark(isQid(X:S)) -> a__isQid(X:S)
1.18/1.23	 mark(nil) -> nil
1.18/1.23	 mark(o) -> o
1.18/1.23	 mark(tt) -> tt
1.18/1.23	 mark(u) -> u
1.18/1.23	-> Usable rules:
1.18/1.23	 a__U11(tt) -> tt
1.18/1.23	 a__U11(X:S) -> U11(X:S)
1.18/1.23	 a__U21(tt,V2:S) -> a__U22(a__isList(V2:S))
1.18/1.23	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.18/1.23	 a__U22(tt) -> tt
1.18/1.23	 a__U22(X:S) -> U22(X:S)
1.18/1.23	 a__U31(tt) -> tt
1.18/1.23	 a__U31(X:S) -> U31(X:S)
1.18/1.23	 a__U41(tt,V2:S) -> a__U42(a__isNeList(V2:S))
1.18/1.23	 a__U41(X1:S,X2:S) -> U41(X1:S,X2:S)
1.18/1.23	 a__U42(tt) -> tt
1.18/1.23	 a__U42(X:S) -> U42(X:S)
1.18/1.23	 a__U51(tt,V2:S) -> a__U52(a__isList(V2:S))
1.18/1.23	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.18/1.23	 a__U52(tt) -> tt
1.18/1.23	 a__U52(X:S) -> U52(X:S)
1.18/1.23	 a__U61(tt) -> tt
1.18/1.23	 a__U61(X:S) -> U61(X:S)
1.18/1.23	 a__U71(tt,P:S) -> a__U72(a__isPal(P:S))
1.18/1.23	 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S)
1.18/1.23	 a__U72(tt) -> tt
1.18/1.23	 a__U72(X:S) -> U72(X:S)
1.18/1.23	 a__U81(tt) -> tt
1.18/1.23	 a__U81(X:S) -> U81(X:S)
1.18/1.23	 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
1.18/1.23	 a____(nil,X:S) -> mark(X:S)
1.18/1.23	 a____(X:S,nil) -> mark(X:S)
1.18/1.23	 a____(X1:S,X2:S) -> __(X1:S,X2:S)
1.18/1.23	 a__isList(__(V1:S,V2:S)) -> a__U21(a__isList(V1:S),V2:S)
1.18/1.23	 a__isList(nil) -> tt
1.18/1.23	 a__isList(V:S) -> a__U11(a__isNeList(V:S))
1.18/1.23	 a__isList(X:S) -> isList(X:S)
1.18/1.23	 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__isList(V1:S),V2:S)
1.18/1.23	 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__isNeList(V1:S),V2:S)
1.18/1.23	 a__isNeList(V:S) -> a__U31(a__isQid(V:S))
1.18/1.23	 a__isNeList(X:S) -> isNeList(X:S)
1.18/1.23	 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U71(a__isQid(I:S),P:S)
1.18/1.23	 a__isNePal(V:S) -> a__U61(a__isQid(V:S))
1.18/1.23	 a__isNePal(X:S) -> isNePal(X:S)
1.18/1.23	 a__isPal(nil) -> tt
1.18/1.23	 a__isPal(V:S) -> a__U81(a__isNePal(V:S))
1.18/1.23	 a__isPal(X:S) -> isPal(X:S)
1.18/1.23	 a__isQid(a) -> tt
1.18/1.23	 a__isQid(e) -> tt
1.18/1.23	 a__isQid(i) -> tt
1.18/1.23	 a__isQid(o) -> tt
1.18/1.23	 a__isQid(u) -> tt
1.18/1.23	 a__isQid(X:S) -> isQid(X:S)
1.18/1.23	 mark(U11(X:S)) -> a__U11(mark(X:S))
1.18/1.23	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.18/1.23	 mark(U22(X:S)) -> a__U22(mark(X:S))
1.18/1.23	 mark(U31(X:S)) -> a__U31(mark(X:S))
1.18/1.23	 mark(U41(X1:S,X2:S)) -> a__U41(mark(X1:S),X2:S)
1.18/1.23	 mark(U42(X:S)) -> a__U42(mark(X:S))
1.18/1.23	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.18/1.23	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.18/1.23	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.18/1.23	 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S)
1.18/1.23	 mark(U72(X:S)) -> a__U72(mark(X:S))
1.18/1.23	 mark(U81(X:S)) -> a__U81(mark(X:S))
1.18/1.23	 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
1.18/1.23	 mark(a) -> a
1.18/1.23	 mark(e) -> e
1.18/1.23	 mark(i) -> i
1.18/1.23	 mark(isList(X:S)) -> a__isList(X:S)
1.18/1.23	 mark(isNeList(X:S)) -> a__isNeList(X:S)
1.18/1.23	 mark(isNePal(X:S)) -> a__isNePal(X:S)
1.18/1.23	 mark(isPal(X:S)) -> a__isPal(X:S)
1.18/1.23	 mark(isQid(X:S)) -> a__isQid(X:S)
1.18/1.23	 mark(nil) -> nil
1.18/1.23	 mark(o) -> o
1.18/1.23	 mark(tt) -> tt
1.18/1.23	 mark(u) -> u
1.18/1.23	->Interpretation type:
1.18/1.23	 Linear
1.18/1.23	->Coefficients:
1.18/1.23	 Natural Numbers
1.18/1.23	->Dimension:
1.18/1.23	 1
1.18/1.23	->Bound:
1.18/1.23	 2
1.18/1.23	->Interpretation:
1.18/1.23	 
1.18/1.23	[a__U11](X) = X
1.18/1.23	[a__U21](X1,X2) = 2.X1 + 2.X2 + 2
1.18/1.23	[a__U22](X) = X + 1
1.18/1.23	[a__U31](X) = X
1.18/1.23	[a__U41](X1,X2) = 2.X1 + 2.X2 + 2
1.18/1.23	[a__U42](X) = X + 1
1.18/1.23	[a__U51](X1,X2) = X1 + 2.X2 + 2
1.18/1.23	[a__U52](X) = X + 2
1.18/1.23	[a__U61](X) = X
1.18/1.23	[a__U71](X1,X2) = 2.X1 + 2.X2 + 2
1.18/1.23	[a__U72](X) = X + 2
1.18/1.23	[a__U81](X) = X
1.18/1.23	[a____](X1,X2) = 2.X1 + X2 + 2
1.18/1.23	[a__isList](X) = 2.X + 2
1.18/1.23	[a__isNeList](X) = 2.X + 2
1.18/1.23	[a__isNePal](X) = 2.X + 2
1.18/1.23	[a__isPal](X) = 2.X + 2
1.18/1.23	[a__isQid](X) = 2.X + 2
1.18/1.23	[mark](X) = X
1.18/1.23	[U11](X) = X
1.18/1.23	[U21](X1,X2) = 2.X1 + 2.X2 + 2
1.18/1.23	[U22](X) = X + 1
1.18/1.23	[U31](X) = X
1.18/1.23	[U41](X1,X2) = 2.X1 + 2.X2 + 2
1.18/1.23	[U42](X) = X + 1
1.18/1.23	[U51](X1,X2) = X1 + 2.X2 + 2
1.18/1.23	[U52](X) = X + 2
1.18/1.23	[U61](X) = X
1.18/1.23	[U71](X1,X2) = 2.X1 + 2.X2 + 2
1.18/1.23	[U72](X) = X + 2
1.18/1.23	[U81](X) = X
1.18/1.23	[__](X1,X2) = 2.X1 + X2 + 2
1.18/1.23	[a] = 2
1.18/1.23	[e] = 1
1.18/1.23	[fSNonEmpty] = 0
1.18/1.23	[i] = 2
1.18/1.23	[isList](X) = 2.X + 2
1.18/1.23	[isNeList](X) = 2.X + 2
1.18/1.23	[isNePal](X) = 2.X + 2
1.18/1.23	[isPal](X) = 2.X + 2
1.18/1.23	[isQid](X) = 2.X + 2
1.18/1.23	[nil] = 2
1.18/1.23	[o] = 1
1.18/1.23	[tt] = 2
1.18/1.23	[u] = 1
1.18/1.23	[A__U11](X) = 0
1.18/1.23	[A__U21](X1,X2) = 0
1.18/1.23	[A__U22](X) = 0
1.18/1.23	[A__U31](X) = 0
1.18/1.23	[A__U41](X1,X2) = 0
1.18/1.23	[A__U42](X) = 0
1.18/1.23	[A__U51](X1,X2) = 0
1.18/1.23	[A__U52](X) = 0
1.18/1.23	[A__U61](X) = 0
1.18/1.23	[A__U71](X1,X2) = 0
1.18/1.23	[A__U72](X) = 0
1.18/1.23	[A__U81](X) = 0
1.18/1.23	[A____](X1,X2) = 2.X1 + 2.X2 + 2
1.18/1.23	[A__ISLIST](X) = 0
1.18/1.23	[A__ISNELIST](X) = 0
1.18/1.23	[A__ISNEPAL](X) = 0
1.18/1.23	[A__ISPAL](X) = 0
1.18/1.23	[A__ISQID](X) = 0
1.18/1.23	[MARK](X) = 2.X + 2
1.18/1.23	
1.18/1.23	Problem 1.3: 
1.18/1.23	
1.18/1.23	SCC Processor:
1.18/1.23	-> Pairs:
1.18/1.23	 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S)
1.18/1.23	 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S)
1.18/1.23	 A____(nil,X:S) -> MARK(X:S)
1.18/1.23	 A____(X:S,nil) -> MARK(X:S)
1.18/1.23	 MARK(U11(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.23	 MARK(U22(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U31(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.23	 MARK(U42(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.23	 MARK(U52(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U61(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.23	 MARK(U72(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U81(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S))
1.18/1.23	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.23	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.18/1.23	-> Rules:
1.18/1.23	 a__U11(tt) -> tt
1.18/1.23	 a__U11(X:S) -> U11(X:S)
1.18/1.23	 a__U21(tt,V2:S) -> a__U22(a__isList(V2:S))
1.18/1.23	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.18/1.23	 a__U22(tt) -> tt
1.18/1.23	 a__U22(X:S) -> U22(X:S)
1.18/1.23	 a__U31(tt) -> tt
1.18/1.23	 a__U31(X:S) -> U31(X:S)
1.18/1.23	 a__U41(tt,V2:S) -> a__U42(a__isNeList(V2:S))
1.18/1.23	 a__U41(X1:S,X2:S) -> U41(X1:S,X2:S)
1.18/1.23	 a__U42(tt) -> tt
1.18/1.23	 a__U42(X:S) -> U42(X:S)
1.18/1.23	 a__U51(tt,V2:S) -> a__U52(a__isList(V2:S))
1.18/1.23	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.18/1.23	 a__U52(tt) -> tt
1.18/1.23	 a__U52(X:S) -> U52(X:S)
1.18/1.23	 a__U61(tt) -> tt
1.18/1.23	 a__U61(X:S) -> U61(X:S)
1.18/1.23	 a__U71(tt,P:S) -> a__U72(a__isPal(P:S))
1.18/1.23	 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S)
1.18/1.23	 a__U72(tt) -> tt
1.18/1.23	 a__U72(X:S) -> U72(X:S)
1.18/1.23	 a__U81(tt) -> tt
1.18/1.23	 a__U81(X:S) -> U81(X:S)
1.18/1.23	 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
1.18/1.23	 a____(nil,X:S) -> mark(X:S)
1.18/1.23	 a____(X:S,nil) -> mark(X:S)
1.18/1.23	 a____(X1:S,X2:S) -> __(X1:S,X2:S)
1.18/1.23	 a__isList(__(V1:S,V2:S)) -> a__U21(a__isList(V1:S),V2:S)
1.18/1.23	 a__isList(nil) -> tt
1.18/1.23	 a__isList(V:S) -> a__U11(a__isNeList(V:S))
1.18/1.23	 a__isList(X:S) -> isList(X:S)
1.18/1.23	 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__isList(V1:S),V2:S)
1.18/1.23	 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__isNeList(V1:S),V2:S)
1.18/1.23	 a__isNeList(V:S) -> a__U31(a__isQid(V:S))
1.18/1.23	 a__isNeList(X:S) -> isNeList(X:S)
1.18/1.23	 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U71(a__isQid(I:S),P:S)
1.18/1.23	 a__isNePal(V:S) -> a__U61(a__isQid(V:S))
1.18/1.23	 a__isNePal(X:S) -> isNePal(X:S)
1.18/1.23	 a__isPal(nil) -> tt
1.18/1.23	 a__isPal(V:S) -> a__U81(a__isNePal(V:S))
1.18/1.23	 a__isPal(X:S) -> isPal(X:S)
1.18/1.23	 a__isQid(a) -> tt
1.18/1.23	 a__isQid(e) -> tt
1.18/1.23	 a__isQid(i) -> tt
1.18/1.23	 a__isQid(o) -> tt
1.18/1.23	 a__isQid(u) -> tt
1.18/1.23	 a__isQid(X:S) -> isQid(X:S)
1.18/1.23	 mark(U11(X:S)) -> a__U11(mark(X:S))
1.18/1.23	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.18/1.23	 mark(U22(X:S)) -> a__U22(mark(X:S))
1.18/1.23	 mark(U31(X:S)) -> a__U31(mark(X:S))
1.18/1.23	 mark(U41(X1:S,X2:S)) -> a__U41(mark(X1:S),X2:S)
1.18/1.23	 mark(U42(X:S)) -> a__U42(mark(X:S))
1.18/1.23	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.18/1.23	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.18/1.23	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.18/1.23	 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S)
1.18/1.23	 mark(U72(X:S)) -> a__U72(mark(X:S))
1.18/1.23	 mark(U81(X:S)) -> a__U81(mark(X:S))
1.18/1.23	 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
1.18/1.23	 mark(a) -> a
1.18/1.23	 mark(e) -> e
1.18/1.23	 mark(i) -> i
1.18/1.23	 mark(isList(X:S)) -> a__isList(X:S)
1.18/1.23	 mark(isNeList(X:S)) -> a__isNeList(X:S)
1.18/1.23	 mark(isNePal(X:S)) -> a__isNePal(X:S)
1.18/1.23	 mark(isPal(X:S)) -> a__isPal(X:S)
1.18/1.23	 mark(isQid(X:S)) -> a__isQid(X:S)
1.18/1.23	 mark(nil) -> nil
1.18/1.23	 mark(o) -> o
1.18/1.23	 mark(tt) -> tt
1.18/1.23	 mark(u) -> u
1.18/1.23	->Strongly Connected Components:
1.18/1.23	->->Cycle:
1.18/1.23	->->-> Pairs:
1.18/1.23	 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S)
1.18/1.23	 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S)
1.18/1.23	 A____(nil,X:S) -> MARK(X:S)
1.18/1.23	 A____(X:S,nil) -> MARK(X:S)
1.18/1.23	 MARK(U11(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.23	 MARK(U22(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U31(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.23	 MARK(U42(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.23	 MARK(U52(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U61(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.23	 MARK(U72(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(U81(X:S)) -> MARK(X:S)
1.18/1.23	 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S))
1.18/1.23	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.23	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.18/1.23	->->-> Rules:
1.18/1.23	 a__U11(tt) -> tt
1.18/1.23	 a__U11(X:S) -> U11(X:S)
1.18/1.23	 a__U21(tt,V2:S) -> a__U22(a__isList(V2:S))
1.18/1.23	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.18/1.23	 a__U22(tt) -> tt
1.18/1.23	 a__U22(X:S) -> U22(X:S)
1.18/1.23	 a__U31(tt) -> tt
1.18/1.23	 a__U31(X:S) -> U31(X:S)
1.18/1.23	 a__U41(tt,V2:S) -> a__U42(a__isNeList(V2:S))
1.18/1.23	 a__U41(X1:S,X2:S) -> U41(X1:S,X2:S)
1.18/1.23	 a__U42(tt) -> tt
1.18/1.23	 a__U42(X:S) -> U42(X:S)
1.18/1.23	 a__U51(tt,V2:S) -> a__U52(a__isList(V2:S))
1.18/1.23	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.18/1.23	 a__U52(tt) -> tt
1.18/1.23	 a__U52(X:S) -> U52(X:S)
1.18/1.23	 a__U61(tt) -> tt
1.18/1.23	 a__U61(X:S) -> U61(X:S)
1.18/1.23	 a__U71(tt,P:S) -> a__U72(a__isPal(P:S))
1.18/1.23	 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S)
1.18/1.23	 a__U72(tt) -> tt
1.18/1.23	 a__U72(X:S) -> U72(X:S)
1.18/1.23	 a__U81(tt) -> tt
1.18/1.23	 a__U81(X:S) -> U81(X:S)
1.18/1.23	 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
1.18/1.24	 a____(nil,X:S) -> mark(X:S)
1.18/1.24	 a____(X:S,nil) -> mark(X:S)
1.18/1.24	 a____(X1:S,X2:S) -> __(X1:S,X2:S)
1.18/1.24	 a__isList(__(V1:S,V2:S)) -> a__U21(a__isList(V1:S),V2:S)
1.18/1.24	 a__isList(nil) -> tt
1.18/1.24	 a__isList(V:S) -> a__U11(a__isNeList(V:S))
1.18/1.24	 a__isList(X:S) -> isList(X:S)
1.18/1.24	 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__isList(V1:S),V2:S)
1.18/1.24	 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__isNeList(V1:S),V2:S)
1.18/1.24	 a__isNeList(V:S) -> a__U31(a__isQid(V:S))
1.18/1.24	 a__isNeList(X:S) -> isNeList(X:S)
1.18/1.24	 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U71(a__isQid(I:S),P:S)
1.18/1.24	 a__isNePal(V:S) -> a__U61(a__isQid(V:S))
1.18/1.24	 a__isNePal(X:S) -> isNePal(X:S)
1.18/1.24	 a__isPal(nil) -> tt
1.18/1.24	 a__isPal(V:S) -> a__U81(a__isNePal(V:S))
1.18/1.24	 a__isPal(X:S) -> isPal(X:S)
1.18/1.24	 a__isQid(a) -> tt
1.18/1.24	 a__isQid(e) -> tt
1.18/1.24	 a__isQid(i) -> tt
1.18/1.24	 a__isQid(o) -> tt
1.18/1.24	 a__isQid(u) -> tt
1.18/1.24	 a__isQid(X:S) -> isQid(X:S)
1.18/1.24	 mark(U11(X:S)) -> a__U11(mark(X:S))
1.18/1.24	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.18/1.24	 mark(U22(X:S)) -> a__U22(mark(X:S))
1.18/1.24	 mark(U31(X:S)) -> a__U31(mark(X:S))
1.18/1.24	 mark(U41(X1:S,X2:S)) -> a__U41(mark(X1:S),X2:S)
1.18/1.24	 mark(U42(X:S)) -> a__U42(mark(X:S))
1.18/1.24	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.18/1.24	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.18/1.24	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.18/1.24	 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S)
1.18/1.24	 mark(U72(X:S)) -> a__U72(mark(X:S))
1.18/1.24	 mark(U81(X:S)) -> a__U81(mark(X:S))
1.18/1.24	 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
1.18/1.24	 mark(a) -> a
1.18/1.24	 mark(e) -> e
1.18/1.24	 mark(i) -> i
1.18/1.24	 mark(isList(X:S)) -> a__isList(X:S)
1.18/1.24	 mark(isNeList(X:S)) -> a__isNeList(X:S)
1.18/1.24	 mark(isNePal(X:S)) -> a__isNePal(X:S)
1.18/1.24	 mark(isPal(X:S)) -> a__isPal(X:S)
1.18/1.24	 mark(isQid(X:S)) -> a__isQid(X:S)
1.18/1.24	 mark(nil) -> nil
1.18/1.24	 mark(o) -> o
1.18/1.24	 mark(tt) -> tt
1.18/1.24	 mark(u) -> u
1.18/1.24	
1.18/1.24	Problem 1.3: 
1.18/1.24	
1.18/1.24	Reduction Pairs Processor:
1.18/1.24	-> Pairs:
1.18/1.24	 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S)
1.18/1.24	 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S)
1.18/1.24	 A____(nil,X:S) -> MARK(X:S)
1.18/1.24	 A____(X:S,nil) -> MARK(X:S)
1.18/1.24	 MARK(U11(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(U22(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U31(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(U42(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(U52(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U61(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(U72(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U81(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S))
1.18/1.24	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.18/1.24	-> Rules:
1.18/1.24	 a__U11(tt) -> tt
1.18/1.24	 a__U11(X:S) -> U11(X:S)
1.18/1.24	 a__U21(tt,V2:S) -> a__U22(a__isList(V2:S))
1.18/1.24	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.18/1.24	 a__U22(tt) -> tt
1.18/1.24	 a__U22(X:S) -> U22(X:S)
1.18/1.24	 a__U31(tt) -> tt
1.18/1.24	 a__U31(X:S) -> U31(X:S)
1.18/1.24	 a__U41(tt,V2:S) -> a__U42(a__isNeList(V2:S))
1.18/1.24	 a__U41(X1:S,X2:S) -> U41(X1:S,X2:S)
1.18/1.24	 a__U42(tt) -> tt
1.18/1.24	 a__U42(X:S) -> U42(X:S)
1.18/1.24	 a__U51(tt,V2:S) -> a__U52(a__isList(V2:S))
1.18/1.24	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.18/1.24	 a__U52(tt) -> tt
1.18/1.24	 a__U52(X:S) -> U52(X:S)
1.18/1.24	 a__U61(tt) -> tt
1.18/1.24	 a__U61(X:S) -> U61(X:S)
1.18/1.24	 a__U71(tt,P:S) -> a__U72(a__isPal(P:S))
1.18/1.24	 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S)
1.18/1.24	 a__U72(tt) -> tt
1.18/1.24	 a__U72(X:S) -> U72(X:S)
1.18/1.24	 a__U81(tt) -> tt
1.18/1.24	 a__U81(X:S) -> U81(X:S)
1.18/1.24	 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
1.18/1.24	 a____(nil,X:S) -> mark(X:S)
1.18/1.24	 a____(X:S,nil) -> mark(X:S)
1.18/1.24	 a____(X1:S,X2:S) -> __(X1:S,X2:S)
1.18/1.24	 a__isList(__(V1:S,V2:S)) -> a__U21(a__isList(V1:S),V2:S)
1.18/1.24	 a__isList(nil) -> tt
1.18/1.24	 a__isList(V:S) -> a__U11(a__isNeList(V:S))
1.18/1.24	 a__isList(X:S) -> isList(X:S)
1.18/1.24	 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__isList(V1:S),V2:S)
1.18/1.24	 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__isNeList(V1:S),V2:S)
1.18/1.24	 a__isNeList(V:S) -> a__U31(a__isQid(V:S))
1.18/1.24	 a__isNeList(X:S) -> isNeList(X:S)
1.18/1.24	 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U71(a__isQid(I:S),P:S)
1.18/1.24	 a__isNePal(V:S) -> a__U61(a__isQid(V:S))
1.18/1.24	 a__isNePal(X:S) -> isNePal(X:S)
1.18/1.24	 a__isPal(nil) -> tt
1.18/1.24	 a__isPal(V:S) -> a__U81(a__isNePal(V:S))
1.18/1.24	 a__isPal(X:S) -> isPal(X:S)
1.18/1.24	 a__isQid(a) -> tt
1.18/1.24	 a__isQid(e) -> tt
1.18/1.24	 a__isQid(i) -> tt
1.18/1.24	 a__isQid(o) -> tt
1.18/1.24	 a__isQid(u) -> tt
1.18/1.24	 a__isQid(X:S) -> isQid(X:S)
1.18/1.24	 mark(U11(X:S)) -> a__U11(mark(X:S))
1.18/1.24	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.18/1.24	 mark(U22(X:S)) -> a__U22(mark(X:S))
1.18/1.24	 mark(U31(X:S)) -> a__U31(mark(X:S))
1.18/1.24	 mark(U41(X1:S,X2:S)) -> a__U41(mark(X1:S),X2:S)
1.18/1.24	 mark(U42(X:S)) -> a__U42(mark(X:S))
1.18/1.24	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.18/1.24	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.18/1.24	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.18/1.24	 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S)
1.18/1.24	 mark(U72(X:S)) -> a__U72(mark(X:S))
1.18/1.24	 mark(U81(X:S)) -> a__U81(mark(X:S))
1.18/1.24	 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
1.18/1.24	 mark(a) -> a
1.18/1.24	 mark(e) -> e
1.18/1.24	 mark(i) -> i
1.18/1.24	 mark(isList(X:S)) -> a__isList(X:S)
1.18/1.24	 mark(isNeList(X:S)) -> a__isNeList(X:S)
1.18/1.24	 mark(isNePal(X:S)) -> a__isNePal(X:S)
1.18/1.24	 mark(isPal(X:S)) -> a__isPal(X:S)
1.18/1.24	 mark(isQid(X:S)) -> a__isQid(X:S)
1.18/1.24	 mark(nil) -> nil
1.18/1.24	 mark(o) -> o
1.18/1.24	 mark(tt) -> tt
1.18/1.24	 mark(u) -> u
1.18/1.24	-> Usable rules:
1.18/1.24	 a__U11(tt) -> tt
1.18/1.24	 a__U11(X:S) -> U11(X:S)
1.18/1.24	 a__U21(tt,V2:S) -> a__U22(a__isList(V2:S))
1.18/1.24	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.18/1.24	 a__U22(tt) -> tt
1.18/1.24	 a__U22(X:S) -> U22(X:S)
1.18/1.24	 a__U31(tt) -> tt
1.18/1.24	 a__U31(X:S) -> U31(X:S)
1.18/1.24	 a__U41(tt,V2:S) -> a__U42(a__isNeList(V2:S))
1.18/1.24	 a__U41(X1:S,X2:S) -> U41(X1:S,X2:S)
1.18/1.24	 a__U42(tt) -> tt
1.18/1.24	 a__U42(X:S) -> U42(X:S)
1.18/1.24	 a__U51(tt,V2:S) -> a__U52(a__isList(V2:S))
1.18/1.24	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.18/1.24	 a__U52(tt) -> tt
1.18/1.24	 a__U52(X:S) -> U52(X:S)
1.18/1.24	 a__U61(tt) -> tt
1.18/1.24	 a__U61(X:S) -> U61(X:S)
1.18/1.24	 a__U71(tt,P:S) -> a__U72(a__isPal(P:S))
1.18/1.24	 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S)
1.18/1.24	 a__U72(tt) -> tt
1.18/1.24	 a__U72(X:S) -> U72(X:S)
1.18/1.24	 a__U81(tt) -> tt
1.18/1.24	 a__U81(X:S) -> U81(X:S)
1.18/1.24	 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
1.18/1.24	 a____(nil,X:S) -> mark(X:S)
1.18/1.24	 a____(X:S,nil) -> mark(X:S)
1.18/1.24	 a____(X1:S,X2:S) -> __(X1:S,X2:S)
1.18/1.24	 a__isList(__(V1:S,V2:S)) -> a__U21(a__isList(V1:S),V2:S)
1.18/1.24	 a__isList(nil) -> tt
1.18/1.24	 a__isList(V:S) -> a__U11(a__isNeList(V:S))
1.18/1.24	 a__isList(X:S) -> isList(X:S)
1.18/1.24	 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__isList(V1:S),V2:S)
1.18/1.24	 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__isNeList(V1:S),V2:S)
1.18/1.24	 a__isNeList(V:S) -> a__U31(a__isQid(V:S))
1.18/1.24	 a__isNeList(X:S) -> isNeList(X:S)
1.18/1.24	 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U71(a__isQid(I:S),P:S)
1.18/1.24	 a__isNePal(V:S) -> a__U61(a__isQid(V:S))
1.18/1.24	 a__isNePal(X:S) -> isNePal(X:S)
1.18/1.24	 a__isPal(nil) -> tt
1.18/1.24	 a__isPal(V:S) -> a__U81(a__isNePal(V:S))
1.18/1.24	 a__isPal(X:S) -> isPal(X:S)
1.18/1.24	 a__isQid(a) -> tt
1.18/1.24	 a__isQid(e) -> tt
1.18/1.24	 a__isQid(i) -> tt
1.18/1.24	 a__isQid(o) -> tt
1.18/1.24	 a__isQid(u) -> tt
1.18/1.24	 a__isQid(X:S) -> isQid(X:S)
1.18/1.24	 mark(U11(X:S)) -> a__U11(mark(X:S))
1.18/1.24	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.18/1.24	 mark(U22(X:S)) -> a__U22(mark(X:S))
1.18/1.24	 mark(U31(X:S)) -> a__U31(mark(X:S))
1.18/1.24	 mark(U41(X1:S,X2:S)) -> a__U41(mark(X1:S),X2:S)
1.18/1.24	 mark(U42(X:S)) -> a__U42(mark(X:S))
1.18/1.24	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.18/1.24	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.18/1.24	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.18/1.24	 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S)
1.18/1.24	 mark(U72(X:S)) -> a__U72(mark(X:S))
1.18/1.24	 mark(U81(X:S)) -> a__U81(mark(X:S))
1.18/1.24	 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
1.18/1.24	 mark(a) -> a
1.18/1.24	 mark(e) -> e
1.18/1.24	 mark(i) -> i
1.18/1.24	 mark(isList(X:S)) -> a__isList(X:S)
1.18/1.24	 mark(isNeList(X:S)) -> a__isNeList(X:S)
1.18/1.24	 mark(isNePal(X:S)) -> a__isNePal(X:S)
1.18/1.24	 mark(isPal(X:S)) -> a__isPal(X:S)
1.18/1.24	 mark(isQid(X:S)) -> a__isQid(X:S)
1.18/1.24	 mark(nil) -> nil
1.18/1.24	 mark(o) -> o
1.18/1.24	 mark(tt) -> tt
1.18/1.24	 mark(u) -> u
1.18/1.24	->Interpretation type:
1.18/1.24	 Linear
1.18/1.24	->Coefficients:
1.18/1.24	 Natural Numbers
1.18/1.24	->Dimension:
1.18/1.24	 1
1.18/1.24	->Bound:
1.18/1.24	 2
1.18/1.24	->Interpretation:
1.18/1.24	 
1.18/1.24	[a__U11](X) = 2.X
1.18/1.24	[a__U21](X1,X2) = 2.X1
1.18/1.24	[a__U22](X) = 2.X
1.18/1.24	[a__U31](X) = 2.X
1.18/1.24	[a__U41](X1,X2) = 2.X1
1.18/1.24	[a__U42](X) = 2.X
1.18/1.24	[a__U51](X1,X2) = 2.X1
1.18/1.24	[a__U52](X) = 2.X
1.18/1.24	[a__U61](X) = 2.X
1.18/1.24	[a__U71](X1,X2) = 2.X1 + 2.X2 + 2
1.18/1.24	[a__U72](X) = X
1.18/1.24	[a__U81](X) = 2.X + 2
1.18/1.24	[a____](X1,X2) = 2.X1 + X2 + 2
1.18/1.24	[a__isList](X) = 0
1.18/1.24	[a__isNeList](X) = 0
1.18/1.24	[a__isNePal](X) = X
1.18/1.24	[a__isPal](X) = 2.X + 2
1.18/1.24	[a__isQid](X) = 0
1.18/1.24	[mark](X) = X
1.18/1.24	[U11](X) = 2.X
1.18/1.24	[U21](X1,X2) = 2.X1
1.18/1.24	[U22](X) = 2.X
1.18/1.24	[U31](X) = 2.X
1.18/1.24	[U41](X1,X2) = 2.X1
1.18/1.24	[U42](X) = 2.X
1.18/1.24	[U51](X1,X2) = 2.X1
1.18/1.24	[U52](X) = 2.X
1.18/1.24	[U61](X) = 2.X
1.18/1.24	[U71](X1,X2) = 2.X1 + 2.X2 + 2
1.18/1.24	[U72](X) = X
1.18/1.24	[U81](X) = 2.X + 2
1.18/1.24	[__](X1,X2) = 2.X1 + X2 + 2
1.18/1.24	[a] = 1
1.18/1.24	[e] = 1
1.18/1.24	[fSNonEmpty] = 0
1.18/1.24	[i] = 0
1.18/1.24	[isList](X) = 0
1.18/1.24	[isNeList](X) = 0
1.18/1.24	[isNePal](X) = X
1.18/1.24	[isPal](X) = 2.X + 2
1.18/1.24	[isQid](X) = 0
1.18/1.24	[nil] = 0
1.18/1.24	[o] = 0
1.18/1.24	[tt] = 0
1.18/1.24	[u] = 2
1.18/1.24	[A__U11](X) = 0
1.18/1.24	[A__U21](X1,X2) = 0
1.18/1.24	[A__U22](X) = 0
1.18/1.24	[A__U31](X) = 0
1.18/1.24	[A__U41](X1,X2) = 0
1.18/1.24	[A__U42](X) = 0
1.18/1.24	[A__U51](X1,X2) = 0
1.18/1.24	[A__U52](X) = 0
1.18/1.24	[A__U61](X) = 0
1.18/1.24	[A__U71](X1,X2) = 0
1.18/1.24	[A__U72](X) = 0
1.18/1.24	[A__U81](X) = 0
1.18/1.24	[A____](X1,X2) = 2.X1 + 2.X2 + 1
1.18/1.24	[A__ISLIST](X) = 0
1.18/1.24	[A__ISNELIST](X) = 0
1.18/1.24	[A__ISNEPAL](X) = 0
1.18/1.24	[A__ISPAL](X) = 0
1.18/1.24	[A__ISQID](X) = 0
1.18/1.24	[MARK](X) = 2.X + 1
1.18/1.24	
1.18/1.24	Problem 1.3: 
1.18/1.24	
1.18/1.24	SCC Processor:
1.18/1.24	-> Pairs:
1.18/1.24	 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S)
1.18/1.24	 A____(nil,X:S) -> MARK(X:S)
1.18/1.24	 A____(X:S,nil) -> MARK(X:S)
1.18/1.24	 MARK(U11(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(U22(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U31(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(U42(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(U52(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U61(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(U72(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U81(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S))
1.18/1.24	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.18/1.24	-> Rules:
1.18/1.24	 a__U11(tt) -> tt
1.18/1.24	 a__U11(X:S) -> U11(X:S)
1.18/1.24	 a__U21(tt,V2:S) -> a__U22(a__isList(V2:S))
1.18/1.24	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.18/1.24	 a__U22(tt) -> tt
1.18/1.24	 a__U22(X:S) -> U22(X:S)
1.18/1.24	 a__U31(tt) -> tt
1.18/1.24	 a__U31(X:S) -> U31(X:S)
1.18/1.24	 a__U41(tt,V2:S) -> a__U42(a__isNeList(V2:S))
1.18/1.24	 a__U41(X1:S,X2:S) -> U41(X1:S,X2:S)
1.18/1.24	 a__U42(tt) -> tt
1.18/1.24	 a__U42(X:S) -> U42(X:S)
1.18/1.24	 a__U51(tt,V2:S) -> a__U52(a__isList(V2:S))
1.18/1.24	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.18/1.24	 a__U52(tt) -> tt
1.18/1.24	 a__U52(X:S) -> U52(X:S)
1.18/1.24	 a__U61(tt) -> tt
1.18/1.24	 a__U61(X:S) -> U61(X:S)
1.18/1.24	 a__U71(tt,P:S) -> a__U72(a__isPal(P:S))
1.18/1.24	 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S)
1.18/1.24	 a__U72(tt) -> tt
1.18/1.24	 a__U72(X:S) -> U72(X:S)
1.18/1.24	 a__U81(tt) -> tt
1.18/1.24	 a__U81(X:S) -> U81(X:S)
1.18/1.24	 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
1.18/1.24	 a____(nil,X:S) -> mark(X:S)
1.18/1.24	 a____(X:S,nil) -> mark(X:S)
1.18/1.24	 a____(X1:S,X2:S) -> __(X1:S,X2:S)
1.18/1.24	 a__isList(__(V1:S,V2:S)) -> a__U21(a__isList(V1:S),V2:S)
1.18/1.24	 a__isList(nil) -> tt
1.18/1.24	 a__isList(V:S) -> a__U11(a__isNeList(V:S))
1.18/1.24	 a__isList(X:S) -> isList(X:S)
1.18/1.24	 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__isList(V1:S),V2:S)
1.18/1.24	 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__isNeList(V1:S),V2:S)
1.18/1.24	 a__isNeList(V:S) -> a__U31(a__isQid(V:S))
1.18/1.24	 a__isNeList(X:S) -> isNeList(X:S)
1.18/1.24	 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U71(a__isQid(I:S),P:S)
1.18/1.24	 a__isNePal(V:S) -> a__U61(a__isQid(V:S))
1.18/1.24	 a__isNePal(X:S) -> isNePal(X:S)
1.18/1.24	 a__isPal(nil) -> tt
1.18/1.24	 a__isPal(V:S) -> a__U81(a__isNePal(V:S))
1.18/1.24	 a__isPal(X:S) -> isPal(X:S)
1.18/1.24	 a__isQid(a) -> tt
1.18/1.24	 a__isQid(e) -> tt
1.18/1.24	 a__isQid(i) -> tt
1.18/1.24	 a__isQid(o) -> tt
1.18/1.24	 a__isQid(u) -> tt
1.18/1.24	 a__isQid(X:S) -> isQid(X:S)
1.18/1.24	 mark(U11(X:S)) -> a__U11(mark(X:S))
1.18/1.24	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.18/1.24	 mark(U22(X:S)) -> a__U22(mark(X:S))
1.18/1.24	 mark(U31(X:S)) -> a__U31(mark(X:S))
1.18/1.24	 mark(U41(X1:S,X2:S)) -> a__U41(mark(X1:S),X2:S)
1.18/1.24	 mark(U42(X:S)) -> a__U42(mark(X:S))
1.18/1.24	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.18/1.24	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.18/1.24	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.18/1.24	 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S)
1.18/1.24	 mark(U72(X:S)) -> a__U72(mark(X:S))
1.18/1.24	 mark(U81(X:S)) -> a__U81(mark(X:S))
1.18/1.24	 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
1.18/1.24	 mark(a) -> a
1.18/1.24	 mark(e) -> e
1.18/1.24	 mark(i) -> i
1.18/1.24	 mark(isList(X:S)) -> a__isList(X:S)
1.18/1.24	 mark(isNeList(X:S)) -> a__isNeList(X:S)
1.18/1.24	 mark(isNePal(X:S)) -> a__isNePal(X:S)
1.18/1.24	 mark(isPal(X:S)) -> a__isPal(X:S)
1.18/1.24	 mark(isQid(X:S)) -> a__isQid(X:S)
1.18/1.24	 mark(nil) -> nil
1.18/1.24	 mark(o) -> o
1.18/1.24	 mark(tt) -> tt
1.18/1.24	 mark(u) -> u
1.18/1.24	->Strongly Connected Components:
1.18/1.24	->->Cycle:
1.18/1.24	->->-> Pairs:
1.18/1.24	 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S)
1.18/1.24	 A____(nil,X:S) -> MARK(X:S)
1.18/1.24	 A____(X:S,nil) -> MARK(X:S)
1.18/1.24	 MARK(U11(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(U22(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U31(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(U42(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(U52(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U61(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(U72(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U81(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S))
1.18/1.24	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.18/1.24	->->-> Rules:
1.18/1.24	 a__U11(tt) -> tt
1.18/1.24	 a__U11(X:S) -> U11(X:S)
1.18/1.24	 a__U21(tt,V2:S) -> a__U22(a__isList(V2:S))
1.18/1.24	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.18/1.24	 a__U22(tt) -> tt
1.18/1.24	 a__U22(X:S) -> U22(X:S)
1.18/1.24	 a__U31(tt) -> tt
1.18/1.24	 a__U31(X:S) -> U31(X:S)
1.18/1.24	 a__U41(tt,V2:S) -> a__U42(a__isNeList(V2:S))
1.18/1.24	 a__U41(X1:S,X2:S) -> U41(X1:S,X2:S)
1.18/1.24	 a__U42(tt) -> tt
1.18/1.24	 a__U42(X:S) -> U42(X:S)
1.18/1.24	 a__U51(tt,V2:S) -> a__U52(a__isList(V2:S))
1.18/1.24	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.18/1.24	 a__U52(tt) -> tt
1.18/1.24	 a__U52(X:S) -> U52(X:S)
1.18/1.24	 a__U61(tt) -> tt
1.18/1.24	 a__U61(X:S) -> U61(X:S)
1.18/1.24	 a__U71(tt,P:S) -> a__U72(a__isPal(P:S))
1.18/1.24	 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S)
1.18/1.24	 a__U72(tt) -> tt
1.18/1.24	 a__U72(X:S) -> U72(X:S)
1.18/1.24	 a__U81(tt) -> tt
1.18/1.24	 a__U81(X:S) -> U81(X:S)
1.18/1.24	 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
1.18/1.24	 a____(nil,X:S) -> mark(X:S)
1.18/1.24	 a____(X:S,nil) -> mark(X:S)
1.18/1.24	 a____(X1:S,X2:S) -> __(X1:S,X2:S)
1.18/1.24	 a__isList(__(V1:S,V2:S)) -> a__U21(a__isList(V1:S),V2:S)
1.18/1.24	 a__isList(nil) -> tt
1.18/1.24	 a__isList(V:S) -> a__U11(a__isNeList(V:S))
1.18/1.24	 a__isList(X:S) -> isList(X:S)
1.18/1.24	 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__isList(V1:S),V2:S)
1.18/1.24	 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__isNeList(V1:S),V2:S)
1.18/1.24	 a__isNeList(V:S) -> a__U31(a__isQid(V:S))
1.18/1.24	 a__isNeList(X:S) -> isNeList(X:S)
1.18/1.24	 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U71(a__isQid(I:S),P:S)
1.18/1.24	 a__isNePal(V:S) -> a__U61(a__isQid(V:S))
1.18/1.24	 a__isNePal(X:S) -> isNePal(X:S)
1.18/1.24	 a__isPal(nil) -> tt
1.18/1.24	 a__isPal(V:S) -> a__U81(a__isNePal(V:S))
1.18/1.24	 a__isPal(X:S) -> isPal(X:S)
1.18/1.24	 a__isQid(a) -> tt
1.18/1.24	 a__isQid(e) -> tt
1.18/1.24	 a__isQid(i) -> tt
1.18/1.24	 a__isQid(o) -> tt
1.18/1.24	 a__isQid(u) -> tt
1.18/1.24	 a__isQid(X:S) -> isQid(X:S)
1.18/1.24	 mark(U11(X:S)) -> a__U11(mark(X:S))
1.18/1.24	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.18/1.24	 mark(U22(X:S)) -> a__U22(mark(X:S))
1.18/1.24	 mark(U31(X:S)) -> a__U31(mark(X:S))
1.18/1.24	 mark(U41(X1:S,X2:S)) -> a__U41(mark(X1:S),X2:S)
1.18/1.24	 mark(U42(X:S)) -> a__U42(mark(X:S))
1.18/1.24	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.18/1.24	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.18/1.24	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.18/1.24	 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S)
1.18/1.24	 mark(U72(X:S)) -> a__U72(mark(X:S))
1.18/1.24	 mark(U81(X:S)) -> a__U81(mark(X:S))
1.18/1.24	 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
1.18/1.24	 mark(a) -> a
1.18/1.24	 mark(e) -> e
1.18/1.24	 mark(i) -> i
1.18/1.24	 mark(isList(X:S)) -> a__isList(X:S)
1.18/1.24	 mark(isNeList(X:S)) -> a__isNeList(X:S)
1.18/1.24	 mark(isNePal(X:S)) -> a__isNePal(X:S)
1.18/1.24	 mark(isPal(X:S)) -> a__isPal(X:S)
1.18/1.24	 mark(isQid(X:S)) -> a__isQid(X:S)
1.18/1.24	 mark(nil) -> nil
1.18/1.24	 mark(o) -> o
1.18/1.24	 mark(tt) -> tt
1.18/1.24	 mark(u) -> u
1.18/1.24	
1.18/1.24	Problem 1.3: 
1.18/1.24	
1.18/1.24	Reduction Pairs Processor:
1.18/1.24	-> Pairs:
1.18/1.24	 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S)
1.18/1.24	 A____(nil,X:S) -> MARK(X:S)
1.18/1.24	 A____(X:S,nil) -> MARK(X:S)
1.18/1.24	 MARK(U11(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(U22(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U31(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(U42(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(U52(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U61(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(U72(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U81(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S))
1.18/1.24	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.18/1.24	-> Rules:
1.18/1.24	 a__U11(tt) -> tt
1.18/1.24	 a__U11(X:S) -> U11(X:S)
1.18/1.24	 a__U21(tt,V2:S) -> a__U22(a__isList(V2:S))
1.18/1.24	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.18/1.24	 a__U22(tt) -> tt
1.18/1.24	 a__U22(X:S) -> U22(X:S)
1.18/1.24	 a__U31(tt) -> tt
1.18/1.24	 a__U31(X:S) -> U31(X:S)
1.18/1.24	 a__U41(tt,V2:S) -> a__U42(a__isNeList(V2:S))
1.18/1.24	 a__U41(X1:S,X2:S) -> U41(X1:S,X2:S)
1.18/1.24	 a__U42(tt) -> tt
1.18/1.24	 a__U42(X:S) -> U42(X:S)
1.18/1.24	 a__U51(tt,V2:S) -> a__U52(a__isList(V2:S))
1.18/1.24	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.18/1.24	 a__U52(tt) -> tt
1.18/1.24	 a__U52(X:S) -> U52(X:S)
1.18/1.24	 a__U61(tt) -> tt
1.18/1.24	 a__U61(X:S) -> U61(X:S)
1.18/1.24	 a__U71(tt,P:S) -> a__U72(a__isPal(P:S))
1.18/1.24	 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S)
1.18/1.24	 a__U72(tt) -> tt
1.18/1.24	 a__U72(X:S) -> U72(X:S)
1.18/1.24	 a__U81(tt) -> tt
1.18/1.24	 a__U81(X:S) -> U81(X:S)
1.18/1.24	 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
1.18/1.24	 a____(nil,X:S) -> mark(X:S)
1.18/1.24	 a____(X:S,nil) -> mark(X:S)
1.18/1.24	 a____(X1:S,X2:S) -> __(X1:S,X2:S)
1.18/1.24	 a__isList(__(V1:S,V2:S)) -> a__U21(a__isList(V1:S),V2:S)
1.18/1.24	 a__isList(nil) -> tt
1.18/1.24	 a__isList(V:S) -> a__U11(a__isNeList(V:S))
1.18/1.24	 a__isList(X:S) -> isList(X:S)
1.18/1.24	 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__isList(V1:S),V2:S)
1.18/1.24	 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__isNeList(V1:S),V2:S)
1.18/1.24	 a__isNeList(V:S) -> a__U31(a__isQid(V:S))
1.18/1.24	 a__isNeList(X:S) -> isNeList(X:S)
1.18/1.24	 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U71(a__isQid(I:S),P:S)
1.18/1.24	 a__isNePal(V:S) -> a__U61(a__isQid(V:S))
1.18/1.24	 a__isNePal(X:S) -> isNePal(X:S)
1.18/1.24	 a__isPal(nil) -> tt
1.18/1.24	 a__isPal(V:S) -> a__U81(a__isNePal(V:S))
1.18/1.24	 a__isPal(X:S) -> isPal(X:S)
1.18/1.24	 a__isQid(a) -> tt
1.18/1.24	 a__isQid(e) -> tt
1.18/1.24	 a__isQid(i) -> tt
1.18/1.24	 a__isQid(o) -> tt
1.18/1.24	 a__isQid(u) -> tt
1.18/1.24	 a__isQid(X:S) -> isQid(X:S)
1.18/1.24	 mark(U11(X:S)) -> a__U11(mark(X:S))
1.18/1.24	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.18/1.24	 mark(U22(X:S)) -> a__U22(mark(X:S))
1.18/1.24	 mark(U31(X:S)) -> a__U31(mark(X:S))
1.18/1.24	 mark(U41(X1:S,X2:S)) -> a__U41(mark(X1:S),X2:S)
1.18/1.24	 mark(U42(X:S)) -> a__U42(mark(X:S))
1.18/1.24	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.18/1.24	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.18/1.24	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.18/1.24	 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S)
1.18/1.24	 mark(U72(X:S)) -> a__U72(mark(X:S))
1.18/1.24	 mark(U81(X:S)) -> a__U81(mark(X:S))
1.18/1.24	 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
1.18/1.24	 mark(a) -> a
1.18/1.24	 mark(e) -> e
1.18/1.24	 mark(i) -> i
1.18/1.24	 mark(isList(X:S)) -> a__isList(X:S)
1.18/1.24	 mark(isNeList(X:S)) -> a__isNeList(X:S)
1.18/1.24	 mark(isNePal(X:S)) -> a__isNePal(X:S)
1.18/1.24	 mark(isPal(X:S)) -> a__isPal(X:S)
1.18/1.24	 mark(isQid(X:S)) -> a__isQid(X:S)
1.18/1.24	 mark(nil) -> nil
1.18/1.24	 mark(o) -> o
1.18/1.24	 mark(tt) -> tt
1.18/1.24	 mark(u) -> u
1.18/1.24	-> Usable rules:
1.18/1.24	 a__U11(tt) -> tt
1.18/1.24	 a__U11(X:S) -> U11(X:S)
1.18/1.24	 a__U21(tt,V2:S) -> a__U22(a__isList(V2:S))
1.18/1.24	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.18/1.24	 a__U22(tt) -> tt
1.18/1.24	 a__U22(X:S) -> U22(X:S)
1.18/1.24	 a__U31(tt) -> tt
1.18/1.24	 a__U31(X:S) -> U31(X:S)
1.18/1.24	 a__U41(tt,V2:S) -> a__U42(a__isNeList(V2:S))
1.18/1.24	 a__U41(X1:S,X2:S) -> U41(X1:S,X2:S)
1.18/1.24	 a__U42(tt) -> tt
1.18/1.24	 a__U42(X:S) -> U42(X:S)
1.18/1.24	 a__U51(tt,V2:S) -> a__U52(a__isList(V2:S))
1.18/1.24	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.18/1.24	 a__U52(tt) -> tt
1.18/1.24	 a__U52(X:S) -> U52(X:S)
1.18/1.24	 a__U61(tt) -> tt
1.18/1.24	 a__U61(X:S) -> U61(X:S)
1.18/1.24	 a__U71(tt,P:S) -> a__U72(a__isPal(P:S))
1.18/1.24	 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S)
1.18/1.24	 a__U72(tt) -> tt
1.18/1.24	 a__U72(X:S) -> U72(X:S)
1.18/1.24	 a__U81(tt) -> tt
1.18/1.24	 a__U81(X:S) -> U81(X:S)
1.18/1.24	 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
1.18/1.24	 a____(nil,X:S) -> mark(X:S)
1.18/1.24	 a____(X:S,nil) -> mark(X:S)
1.18/1.24	 a____(X1:S,X2:S) -> __(X1:S,X2:S)
1.18/1.24	 a__isList(__(V1:S,V2:S)) -> a__U21(a__isList(V1:S),V2:S)
1.18/1.24	 a__isList(nil) -> tt
1.18/1.24	 a__isList(V:S) -> a__U11(a__isNeList(V:S))
1.18/1.24	 a__isList(X:S) -> isList(X:S)
1.18/1.24	 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__isList(V1:S),V2:S)
1.18/1.24	 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__isNeList(V1:S),V2:S)
1.18/1.24	 a__isNeList(V:S) -> a__U31(a__isQid(V:S))
1.18/1.24	 a__isNeList(X:S) -> isNeList(X:S)
1.18/1.24	 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U71(a__isQid(I:S),P:S)
1.18/1.24	 a__isNePal(V:S) -> a__U61(a__isQid(V:S))
1.18/1.24	 a__isNePal(X:S) -> isNePal(X:S)
1.18/1.24	 a__isPal(nil) -> tt
1.18/1.24	 a__isPal(V:S) -> a__U81(a__isNePal(V:S))
1.18/1.24	 a__isPal(X:S) -> isPal(X:S)
1.18/1.24	 a__isQid(a) -> tt
1.18/1.24	 a__isQid(e) -> tt
1.18/1.24	 a__isQid(i) -> tt
1.18/1.24	 a__isQid(o) -> tt
1.18/1.24	 a__isQid(u) -> tt
1.18/1.24	 a__isQid(X:S) -> isQid(X:S)
1.18/1.24	 mark(U11(X:S)) -> a__U11(mark(X:S))
1.18/1.24	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.18/1.24	 mark(U22(X:S)) -> a__U22(mark(X:S))
1.18/1.24	 mark(U31(X:S)) -> a__U31(mark(X:S))
1.18/1.24	 mark(U41(X1:S,X2:S)) -> a__U41(mark(X1:S),X2:S)
1.18/1.24	 mark(U42(X:S)) -> a__U42(mark(X:S))
1.18/1.24	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.18/1.24	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.18/1.24	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.18/1.24	 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S)
1.18/1.24	 mark(U72(X:S)) -> a__U72(mark(X:S))
1.18/1.24	 mark(U81(X:S)) -> a__U81(mark(X:S))
1.18/1.24	 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
1.18/1.24	 mark(a) -> a
1.18/1.24	 mark(e) -> e
1.18/1.24	 mark(i) -> i
1.18/1.24	 mark(isList(X:S)) -> a__isList(X:S)
1.18/1.24	 mark(isNeList(X:S)) -> a__isNeList(X:S)
1.18/1.24	 mark(isNePal(X:S)) -> a__isNePal(X:S)
1.18/1.24	 mark(isPal(X:S)) -> a__isPal(X:S)
1.18/1.24	 mark(isQid(X:S)) -> a__isQid(X:S)
1.18/1.24	 mark(nil) -> nil
1.18/1.24	 mark(o) -> o
1.18/1.24	 mark(tt) -> tt
1.18/1.24	 mark(u) -> u
1.18/1.24	->Interpretation type:
1.18/1.24	 Linear
1.18/1.24	->Coefficients:
1.18/1.24	 Natural Numbers
1.18/1.24	->Dimension:
1.18/1.24	 1
1.18/1.24	->Bound:
1.18/1.24	 2
1.18/1.24	->Interpretation:
1.18/1.24	 
1.18/1.24	[a__U11](X) = X
1.18/1.24	[a__U21](X1,X2) = 2.X1 + 2.X2 + 2
1.18/1.24	[a__U22](X) = X + 2
1.18/1.24	[a__U31](X) = X
1.18/1.24	[a__U41](X1,X2) = 2.X1 + 2.X2 + 1
1.18/1.24	[a__U42](X) = X + 2
1.18/1.24	[a__U51](X1,X2) = X1 + 2.X2 + 2
1.18/1.24	[a__U52](X) = X + 2
1.18/1.24	[a__U61](X) = 2.X + 1
1.18/1.24	[a__U71](X1,X2) = 2.X1 + 2.X2 + 2
1.18/1.24	[a__U72](X) = X + 2
1.18/1.24	[a__U81](X) = X
1.18/1.24	[a____](X1,X2) = 2.X1 + X2 + 2
1.18/1.24	[a__isList](X) = 2.X
1.18/1.24	[a__isNeList](X) = 2.X
1.18/1.24	[a__isNePal](X) = 2.X + 2
1.18/1.24	[a__isPal](X) = 2.X + 2
1.18/1.24	[a__isQid](X) = X
1.18/1.24	[mark](X) = X
1.18/1.24	[U11](X) = X
1.18/1.24	[U21](X1,X2) = 2.X1 + 2.X2 + 2
1.18/1.24	[U22](X) = X + 2
1.18/1.24	[U31](X) = X
1.18/1.24	[U41](X1,X2) = 2.X1 + 2.X2 + 1
1.18/1.24	[U42](X) = X + 2
1.18/1.24	[U51](X1,X2) = X1 + 2.X2 + 2
1.18/1.24	[U52](X) = X + 2
1.18/1.24	[U61](X) = 2.X + 1
1.18/1.24	[U71](X1,X2) = 2.X1 + 2.X2 + 2
1.18/1.24	[U72](X) = X + 2
1.18/1.24	[U81](X) = X
1.18/1.24	[__](X1,X2) = 2.X1 + X2 + 2
1.18/1.24	[a] = 2
1.18/1.24	[e] = 2
1.18/1.24	[fSNonEmpty] = 0
1.18/1.24	[i] = 2
1.18/1.24	[isList](X) = 2.X
1.18/1.24	[isNeList](X) = 2.X
1.18/1.24	[isNePal](X) = 2.X + 2
1.18/1.24	[isPal](X) = 2.X + 2
1.18/1.24	[isQid](X) = X
1.18/1.24	[nil] = 2
1.18/1.24	[o] = 2
1.18/1.24	[tt] = 2
1.18/1.24	[u] = 2
1.18/1.24	[A__U11](X) = 0
1.18/1.24	[A__U21](X1,X2) = 0
1.18/1.24	[A__U22](X) = 0
1.18/1.24	[A__U31](X) = 0
1.18/1.24	[A__U41](X1,X2) = 0
1.18/1.24	[A__U42](X) = 0
1.18/1.24	[A__U51](X1,X2) = 0
1.18/1.24	[A__U52](X) = 0
1.18/1.24	[A__U61](X) = 0
1.18/1.24	[A__U71](X1,X2) = 0
1.18/1.24	[A__U72](X) = 0
1.18/1.24	[A__U81](X) = 0
1.18/1.24	[A____](X1,X2) = 2.X1 + 2.X2
1.18/1.24	[A__ISLIST](X) = 0
1.18/1.24	[A__ISNELIST](X) = 0
1.18/1.24	[A__ISNEPAL](X) = 0
1.18/1.24	[A__ISPAL](X) = 0
1.18/1.24	[A__ISQID](X) = 0
1.18/1.24	[MARK](X) = 2.X + 2
1.18/1.24	
1.18/1.24	Problem 1.3: 
1.18/1.24	
1.18/1.24	SCC Processor:
1.18/1.24	-> Pairs:
1.18/1.24	 A____(nil,X:S) -> MARK(X:S)
1.18/1.24	 A____(X:S,nil) -> MARK(X:S)
1.18/1.24	 MARK(U11(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(U22(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U31(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(U42(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(U52(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U61(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(U72(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U81(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S))
1.18/1.24	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.18/1.24	-> Rules:
1.18/1.24	 a__U11(tt) -> tt
1.18/1.24	 a__U11(X:S) -> U11(X:S)
1.18/1.24	 a__U21(tt,V2:S) -> a__U22(a__isList(V2:S))
1.18/1.24	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.18/1.24	 a__U22(tt) -> tt
1.18/1.24	 a__U22(X:S) -> U22(X:S)
1.18/1.24	 a__U31(tt) -> tt
1.18/1.24	 a__U31(X:S) -> U31(X:S)
1.18/1.24	 a__U41(tt,V2:S) -> a__U42(a__isNeList(V2:S))
1.18/1.24	 a__U41(X1:S,X2:S) -> U41(X1:S,X2:S)
1.18/1.24	 a__U42(tt) -> tt
1.18/1.24	 a__U42(X:S) -> U42(X:S)
1.18/1.24	 a__U51(tt,V2:S) -> a__U52(a__isList(V2:S))
1.18/1.24	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.18/1.24	 a__U52(tt) -> tt
1.18/1.24	 a__U52(X:S) -> U52(X:S)
1.18/1.24	 a__U61(tt) -> tt
1.18/1.24	 a__U61(X:S) -> U61(X:S)
1.18/1.24	 a__U71(tt,P:S) -> a__U72(a__isPal(P:S))
1.18/1.24	 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S)
1.18/1.24	 a__U72(tt) -> tt
1.18/1.24	 a__U72(X:S) -> U72(X:S)
1.18/1.24	 a__U81(tt) -> tt
1.18/1.24	 a__U81(X:S) -> U81(X:S)
1.18/1.24	 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
1.18/1.24	 a____(nil,X:S) -> mark(X:S)
1.18/1.24	 a____(X:S,nil) -> mark(X:S)
1.18/1.24	 a____(X1:S,X2:S) -> __(X1:S,X2:S)
1.18/1.24	 a__isList(__(V1:S,V2:S)) -> a__U21(a__isList(V1:S),V2:S)
1.18/1.24	 a__isList(nil) -> tt
1.18/1.24	 a__isList(V:S) -> a__U11(a__isNeList(V:S))
1.18/1.24	 a__isList(X:S) -> isList(X:S)
1.18/1.24	 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__isList(V1:S),V2:S)
1.18/1.24	 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__isNeList(V1:S),V2:S)
1.18/1.24	 a__isNeList(V:S) -> a__U31(a__isQid(V:S))
1.18/1.24	 a__isNeList(X:S) -> isNeList(X:S)
1.18/1.24	 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U71(a__isQid(I:S),P:S)
1.18/1.24	 a__isNePal(V:S) -> a__U61(a__isQid(V:S))
1.18/1.24	 a__isNePal(X:S) -> isNePal(X:S)
1.18/1.24	 a__isPal(nil) -> tt
1.18/1.24	 a__isPal(V:S) -> a__U81(a__isNePal(V:S))
1.18/1.24	 a__isPal(X:S) -> isPal(X:S)
1.18/1.24	 a__isQid(a) -> tt
1.18/1.24	 a__isQid(e) -> tt
1.18/1.24	 a__isQid(i) -> tt
1.18/1.24	 a__isQid(o) -> tt
1.18/1.24	 a__isQid(u) -> tt
1.18/1.24	 a__isQid(X:S) -> isQid(X:S)
1.18/1.24	 mark(U11(X:S)) -> a__U11(mark(X:S))
1.18/1.24	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.18/1.24	 mark(U22(X:S)) -> a__U22(mark(X:S))
1.18/1.24	 mark(U31(X:S)) -> a__U31(mark(X:S))
1.18/1.24	 mark(U41(X1:S,X2:S)) -> a__U41(mark(X1:S),X2:S)
1.18/1.24	 mark(U42(X:S)) -> a__U42(mark(X:S))
1.18/1.24	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.18/1.24	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.18/1.24	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.18/1.24	 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S)
1.18/1.24	 mark(U72(X:S)) -> a__U72(mark(X:S))
1.18/1.24	 mark(U81(X:S)) -> a__U81(mark(X:S))
1.18/1.24	 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
1.18/1.24	 mark(a) -> a
1.18/1.24	 mark(e) -> e
1.18/1.24	 mark(i) -> i
1.18/1.24	 mark(isList(X:S)) -> a__isList(X:S)
1.18/1.24	 mark(isNeList(X:S)) -> a__isNeList(X:S)
1.18/1.24	 mark(isNePal(X:S)) -> a__isNePal(X:S)
1.18/1.24	 mark(isPal(X:S)) -> a__isPal(X:S)
1.18/1.24	 mark(isQid(X:S)) -> a__isQid(X:S)
1.18/1.24	 mark(nil) -> nil
1.18/1.24	 mark(o) -> o
1.18/1.24	 mark(tt) -> tt
1.18/1.24	 mark(u) -> u
1.18/1.24	->Strongly Connected Components:
1.18/1.24	->->Cycle:
1.18/1.24	->->-> Pairs:
1.18/1.24	 A____(nil,X:S) -> MARK(X:S)
1.18/1.24	 A____(X:S,nil) -> MARK(X:S)
1.18/1.24	 MARK(U11(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(U22(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U31(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(U42(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(U52(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U61(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(U72(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U81(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S))
1.18/1.24	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.18/1.24	->->-> Rules:
1.18/1.24	 a__U11(tt) -> tt
1.18/1.24	 a__U11(X:S) -> U11(X:S)
1.18/1.24	 a__U21(tt,V2:S) -> a__U22(a__isList(V2:S))
1.18/1.24	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.18/1.24	 a__U22(tt) -> tt
1.18/1.24	 a__U22(X:S) -> U22(X:S)
1.18/1.24	 a__U31(tt) -> tt
1.18/1.24	 a__U31(X:S) -> U31(X:S)
1.18/1.24	 a__U41(tt,V2:S) -> a__U42(a__isNeList(V2:S))
1.18/1.24	 a__U41(X1:S,X2:S) -> U41(X1:S,X2:S)
1.18/1.24	 a__U42(tt) -> tt
1.18/1.24	 a__U42(X:S) -> U42(X:S)
1.18/1.24	 a__U51(tt,V2:S) -> a__U52(a__isList(V2:S))
1.18/1.24	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.18/1.24	 a__U52(tt) -> tt
1.18/1.24	 a__U52(X:S) -> U52(X:S)
1.18/1.24	 a__U61(tt) -> tt
1.18/1.24	 a__U61(X:S) -> U61(X:S)
1.18/1.24	 a__U71(tt,P:S) -> a__U72(a__isPal(P:S))
1.18/1.24	 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S)
1.18/1.24	 a__U72(tt) -> tt
1.18/1.24	 a__U72(X:S) -> U72(X:S)
1.18/1.24	 a__U81(tt) -> tt
1.18/1.24	 a__U81(X:S) -> U81(X:S)
1.18/1.24	 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
1.18/1.24	 a____(nil,X:S) -> mark(X:S)
1.18/1.24	 a____(X:S,nil) -> mark(X:S)
1.18/1.24	 a____(X1:S,X2:S) -> __(X1:S,X2:S)
1.18/1.24	 a__isList(__(V1:S,V2:S)) -> a__U21(a__isList(V1:S),V2:S)
1.18/1.24	 a__isList(nil) -> tt
1.18/1.24	 a__isList(V:S) -> a__U11(a__isNeList(V:S))
1.18/1.24	 a__isList(X:S) -> isList(X:S)
1.18/1.24	 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__isList(V1:S),V2:S)
1.18/1.24	 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__isNeList(V1:S),V2:S)
1.18/1.24	 a__isNeList(V:S) -> a__U31(a__isQid(V:S))
1.18/1.24	 a__isNeList(X:S) -> isNeList(X:S)
1.18/1.24	 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U71(a__isQid(I:S),P:S)
1.18/1.24	 a__isNePal(V:S) -> a__U61(a__isQid(V:S))
1.18/1.24	 a__isNePal(X:S) -> isNePal(X:S)
1.18/1.24	 a__isPal(nil) -> tt
1.18/1.24	 a__isPal(V:S) -> a__U81(a__isNePal(V:S))
1.18/1.24	 a__isPal(X:S) -> isPal(X:S)
1.18/1.24	 a__isQid(a) -> tt
1.18/1.24	 a__isQid(e) -> tt
1.18/1.24	 a__isQid(i) -> tt
1.18/1.24	 a__isQid(o) -> tt
1.18/1.24	 a__isQid(u) -> tt
1.18/1.24	 a__isQid(X:S) -> isQid(X:S)
1.18/1.24	 mark(U11(X:S)) -> a__U11(mark(X:S))
1.18/1.24	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.18/1.24	 mark(U22(X:S)) -> a__U22(mark(X:S))
1.18/1.24	 mark(U31(X:S)) -> a__U31(mark(X:S))
1.18/1.24	 mark(U41(X1:S,X2:S)) -> a__U41(mark(X1:S),X2:S)
1.18/1.24	 mark(U42(X:S)) -> a__U42(mark(X:S))
1.18/1.24	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.18/1.24	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.18/1.24	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.18/1.24	 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S)
1.18/1.24	 mark(U72(X:S)) -> a__U72(mark(X:S))
1.18/1.24	 mark(U81(X:S)) -> a__U81(mark(X:S))
1.18/1.24	 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
1.18/1.24	 mark(a) -> a
1.18/1.24	 mark(e) -> e
1.18/1.24	 mark(i) -> i
1.18/1.24	 mark(isList(X:S)) -> a__isList(X:S)
1.18/1.24	 mark(isNeList(X:S)) -> a__isNeList(X:S)
1.18/1.24	 mark(isNePal(X:S)) -> a__isNePal(X:S)
1.18/1.24	 mark(isPal(X:S)) -> a__isPal(X:S)
1.18/1.24	 mark(isQid(X:S)) -> a__isQid(X:S)
1.18/1.24	 mark(nil) -> nil
1.18/1.24	 mark(o) -> o
1.18/1.24	 mark(tt) -> tt
1.18/1.24	 mark(u) -> u
1.18/1.24	
1.18/1.24	Problem 1.3: 
1.18/1.24	
1.18/1.24	Reduction Pairs Processor:
1.18/1.24	-> Pairs:
1.18/1.24	 A____(nil,X:S) -> MARK(X:S)
1.18/1.24	 A____(X:S,nil) -> MARK(X:S)
1.18/1.24	 MARK(U11(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(U22(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U31(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(U42(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(U52(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U61(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(U72(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U81(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S))
1.18/1.24	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.18/1.24	-> Rules:
1.18/1.24	 a__U11(tt) -> tt
1.18/1.24	 a__U11(X:S) -> U11(X:S)
1.18/1.24	 a__U21(tt,V2:S) -> a__U22(a__isList(V2:S))
1.18/1.24	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.18/1.24	 a__U22(tt) -> tt
1.18/1.24	 a__U22(X:S) -> U22(X:S)
1.18/1.24	 a__U31(tt) -> tt
1.18/1.24	 a__U31(X:S) -> U31(X:S)
1.18/1.24	 a__U41(tt,V2:S) -> a__U42(a__isNeList(V2:S))
1.18/1.24	 a__U41(X1:S,X2:S) -> U41(X1:S,X2:S)
1.18/1.24	 a__U42(tt) -> tt
1.18/1.24	 a__U42(X:S) -> U42(X:S)
1.18/1.24	 a__U51(tt,V2:S) -> a__U52(a__isList(V2:S))
1.18/1.24	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.18/1.24	 a__U52(tt) -> tt
1.18/1.24	 a__U52(X:S) -> U52(X:S)
1.18/1.24	 a__U61(tt) -> tt
1.18/1.24	 a__U61(X:S) -> U61(X:S)
1.18/1.24	 a__U71(tt,P:S) -> a__U72(a__isPal(P:S))
1.18/1.24	 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S)
1.18/1.24	 a__U72(tt) -> tt
1.18/1.24	 a__U72(X:S) -> U72(X:S)
1.18/1.24	 a__U81(tt) -> tt
1.18/1.24	 a__U81(X:S) -> U81(X:S)
1.18/1.24	 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
1.18/1.24	 a____(nil,X:S) -> mark(X:S)
1.18/1.24	 a____(X:S,nil) -> mark(X:S)
1.18/1.24	 a____(X1:S,X2:S) -> __(X1:S,X2:S)
1.18/1.24	 a__isList(__(V1:S,V2:S)) -> a__U21(a__isList(V1:S),V2:S)
1.18/1.24	 a__isList(nil) -> tt
1.18/1.24	 a__isList(V:S) -> a__U11(a__isNeList(V:S))
1.18/1.24	 a__isList(X:S) -> isList(X:S)
1.18/1.24	 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__isList(V1:S),V2:S)
1.18/1.24	 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__isNeList(V1:S),V2:S)
1.18/1.24	 a__isNeList(V:S) -> a__U31(a__isQid(V:S))
1.18/1.24	 a__isNeList(X:S) -> isNeList(X:S)
1.18/1.24	 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U71(a__isQid(I:S),P:S)
1.18/1.24	 a__isNePal(V:S) -> a__U61(a__isQid(V:S))
1.18/1.24	 a__isNePal(X:S) -> isNePal(X:S)
1.18/1.24	 a__isPal(nil) -> tt
1.18/1.24	 a__isPal(V:S) -> a__U81(a__isNePal(V:S))
1.18/1.24	 a__isPal(X:S) -> isPal(X:S)
1.18/1.24	 a__isQid(a) -> tt
1.18/1.24	 a__isQid(e) -> tt
1.18/1.24	 a__isQid(i) -> tt
1.18/1.24	 a__isQid(o) -> tt
1.18/1.24	 a__isQid(u) -> tt
1.18/1.24	 a__isQid(X:S) -> isQid(X:S)
1.18/1.24	 mark(U11(X:S)) -> a__U11(mark(X:S))
1.18/1.24	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.18/1.24	 mark(U22(X:S)) -> a__U22(mark(X:S))
1.18/1.24	 mark(U31(X:S)) -> a__U31(mark(X:S))
1.18/1.24	 mark(U41(X1:S,X2:S)) -> a__U41(mark(X1:S),X2:S)
1.18/1.24	 mark(U42(X:S)) -> a__U42(mark(X:S))
1.18/1.24	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.18/1.24	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.18/1.24	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.18/1.24	 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S)
1.18/1.24	 mark(U72(X:S)) -> a__U72(mark(X:S))
1.18/1.24	 mark(U81(X:S)) -> a__U81(mark(X:S))
1.18/1.24	 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
1.18/1.24	 mark(a) -> a
1.18/1.24	 mark(e) -> e
1.18/1.24	 mark(i) -> i
1.18/1.24	 mark(isList(X:S)) -> a__isList(X:S)
1.18/1.24	 mark(isNeList(X:S)) -> a__isNeList(X:S)
1.18/1.24	 mark(isNePal(X:S)) -> a__isNePal(X:S)
1.18/1.24	 mark(isPal(X:S)) -> a__isPal(X:S)
1.18/1.24	 mark(isQid(X:S)) -> a__isQid(X:S)
1.18/1.24	 mark(nil) -> nil
1.18/1.24	 mark(o) -> o
1.18/1.24	 mark(tt) -> tt
1.18/1.24	 mark(u) -> u
1.18/1.24	-> Usable rules:
1.18/1.24	 a__U11(tt) -> tt
1.18/1.24	 a__U11(X:S) -> U11(X:S)
1.18/1.24	 a__U21(tt,V2:S) -> a__U22(a__isList(V2:S))
1.18/1.24	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.18/1.24	 a__U22(tt) -> tt
1.18/1.24	 a__U22(X:S) -> U22(X:S)
1.18/1.24	 a__U31(tt) -> tt
1.18/1.24	 a__U31(X:S) -> U31(X:S)
1.18/1.24	 a__U41(tt,V2:S) -> a__U42(a__isNeList(V2:S))
1.18/1.24	 a__U41(X1:S,X2:S) -> U41(X1:S,X2:S)
1.18/1.24	 a__U42(tt) -> tt
1.18/1.24	 a__U42(X:S) -> U42(X:S)
1.18/1.24	 a__U51(tt,V2:S) -> a__U52(a__isList(V2:S))
1.18/1.24	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.18/1.24	 a__U52(tt) -> tt
1.18/1.24	 a__U52(X:S) -> U52(X:S)
1.18/1.24	 a__U61(tt) -> tt
1.18/1.24	 a__U61(X:S) -> U61(X:S)
1.18/1.24	 a__U71(tt,P:S) -> a__U72(a__isPal(P:S))
1.18/1.24	 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S)
1.18/1.24	 a__U72(tt) -> tt
1.18/1.24	 a__U72(X:S) -> U72(X:S)
1.18/1.24	 a__U81(tt) -> tt
1.18/1.24	 a__U81(X:S) -> U81(X:S)
1.18/1.24	 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
1.18/1.24	 a____(nil,X:S) -> mark(X:S)
1.18/1.24	 a____(X:S,nil) -> mark(X:S)
1.18/1.24	 a____(X1:S,X2:S) -> __(X1:S,X2:S)
1.18/1.24	 a__isList(__(V1:S,V2:S)) -> a__U21(a__isList(V1:S),V2:S)
1.18/1.24	 a__isList(nil) -> tt
1.18/1.24	 a__isList(V:S) -> a__U11(a__isNeList(V:S))
1.18/1.24	 a__isList(X:S) -> isList(X:S)
1.18/1.24	 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__isList(V1:S),V2:S)
1.18/1.24	 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__isNeList(V1:S),V2:S)
1.18/1.24	 a__isNeList(V:S) -> a__U31(a__isQid(V:S))
1.18/1.24	 a__isNeList(X:S) -> isNeList(X:S)
1.18/1.24	 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U71(a__isQid(I:S),P:S)
1.18/1.24	 a__isNePal(V:S) -> a__U61(a__isQid(V:S))
1.18/1.24	 a__isNePal(X:S) -> isNePal(X:S)
1.18/1.24	 a__isPal(nil) -> tt
1.18/1.24	 a__isPal(V:S) -> a__U81(a__isNePal(V:S))
1.18/1.24	 a__isPal(X:S) -> isPal(X:S)
1.18/1.24	 a__isQid(a) -> tt
1.18/1.24	 a__isQid(e) -> tt
1.18/1.24	 a__isQid(i) -> tt
1.18/1.24	 a__isQid(o) -> tt
1.18/1.24	 a__isQid(u) -> tt
1.18/1.24	 a__isQid(X:S) -> isQid(X:S)
1.18/1.24	 mark(U11(X:S)) -> a__U11(mark(X:S))
1.18/1.24	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.18/1.24	 mark(U22(X:S)) -> a__U22(mark(X:S))
1.18/1.24	 mark(U31(X:S)) -> a__U31(mark(X:S))
1.18/1.24	 mark(U41(X1:S,X2:S)) -> a__U41(mark(X1:S),X2:S)
1.18/1.24	 mark(U42(X:S)) -> a__U42(mark(X:S))
1.18/1.24	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.18/1.24	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.18/1.24	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.18/1.24	 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S)
1.18/1.24	 mark(U72(X:S)) -> a__U72(mark(X:S))
1.18/1.24	 mark(U81(X:S)) -> a__U81(mark(X:S))
1.18/1.24	 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
1.18/1.24	 mark(a) -> a
1.18/1.24	 mark(e) -> e
1.18/1.24	 mark(i) -> i
1.18/1.24	 mark(isList(X:S)) -> a__isList(X:S)
1.18/1.24	 mark(isNeList(X:S)) -> a__isNeList(X:S)
1.18/1.24	 mark(isNePal(X:S)) -> a__isNePal(X:S)
1.18/1.24	 mark(isPal(X:S)) -> a__isPal(X:S)
1.18/1.24	 mark(isQid(X:S)) -> a__isQid(X:S)
1.18/1.24	 mark(nil) -> nil
1.18/1.24	 mark(o) -> o
1.18/1.24	 mark(tt) -> tt
1.18/1.24	 mark(u) -> u
1.18/1.24	->Interpretation type:
1.18/1.24	 Linear
1.18/1.24	->Coefficients:
1.18/1.24	 Natural Numbers
1.18/1.24	->Dimension:
1.18/1.24	 1
1.18/1.24	->Bound:
1.18/1.24	 2
1.18/1.24	->Interpretation:
1.18/1.24	 
1.18/1.24	[a__U11](X) = X
1.18/1.24	[a__U21](X1,X2) = 2.X1 + 2.X2 + 1
1.18/1.24	[a__U22](X) = X + 2
1.18/1.24	[a__U31](X) = X
1.18/1.24	[a__U41](X1,X2) = 2.X1 + 2.X2 + 2
1.18/1.24	[a__U42](X) = X + 2
1.18/1.24	[a__U51](X1,X2) = 2.X1 + 2.X2 + 2
1.18/1.24	[a__U52](X) = X + 1
1.18/1.24	[a__U61](X) = X
1.18/1.24	[a__U71](X1,X2) = 2.X1 + 2.X2 + 2
1.18/1.24	[a__U72](X) = X + 2
1.18/1.24	[a__U81](X) = X
1.18/1.24	[a____](X1,X2) = 2.X1 + X2 + 2
1.18/1.24	[a__isList](X) = 2.X + 2
1.18/1.24	[a__isNeList](X) = 2.X + 2
1.18/1.24	[a__isNePal](X) = 2.X + 2
1.18/1.24	[a__isPal](X) = 2.X + 2
1.18/1.24	[a__isQid](X) = 2.X + 2
1.18/1.24	[mark](X) = X
1.18/1.24	[U11](X) = X
1.18/1.24	[U21](X1,X2) = 2.X1 + 2.X2 + 1
1.18/1.24	[U22](X) = X + 2
1.18/1.24	[U31](X) = X
1.18/1.24	[U41](X1,X2) = 2.X1 + 2.X2 + 2
1.18/1.24	[U42](X) = X + 2
1.18/1.24	[U51](X1,X2) = 2.X1 + 2.X2 + 2
1.18/1.24	[U52](X) = X + 1
1.18/1.24	[U61](X) = X
1.18/1.24	[U71](X1,X2) = 2.X1 + 2.X2 + 2
1.18/1.24	[U72](X) = X + 2
1.18/1.24	[U81](X) = X
1.18/1.24	[__](X1,X2) = 2.X1 + X2 + 2
1.18/1.24	[a] = 1
1.18/1.24	[e] = 2
1.18/1.24	[fSNonEmpty] = 0
1.18/1.24	[i] = 2
1.18/1.24	[isList](X) = 2.X + 2
1.18/1.24	[isNeList](X) = 2.X + 2
1.18/1.24	[isNePal](X) = 2.X + 2
1.18/1.24	[isPal](X) = 2.X + 2
1.18/1.24	[isQid](X) = 2.X + 2
1.18/1.24	[nil] = 2
1.18/1.24	[o] = 1
1.18/1.24	[tt] = 2
1.18/1.24	[u] = 1
1.18/1.24	[A__U11](X) = 0
1.18/1.24	[A__U21](X1,X2) = 0
1.18/1.24	[A__U22](X) = 0
1.18/1.24	[A__U31](X) = 0
1.18/1.24	[A__U41](X1,X2) = 0
1.18/1.24	[A__U42](X) = 0
1.18/1.24	[A__U51](X1,X2) = 0
1.18/1.24	[A__U52](X) = 0
1.18/1.24	[A__U61](X) = 0
1.18/1.24	[A__U71](X1,X2) = 0
1.18/1.24	[A__U72](X) = 0
1.18/1.24	[A__U81](X) = 0
1.18/1.24	[A____](X1,X2) = 2.X1 + 2.X2
1.18/1.24	[A__ISLIST](X) = 0
1.18/1.24	[A__ISNELIST](X) = 0
1.18/1.24	[A__ISNEPAL](X) = 0
1.18/1.24	[A__ISPAL](X) = 0
1.18/1.24	[A__ISQID](X) = 0
1.18/1.24	[MARK](X) = 2.X + 2
1.18/1.24	
1.18/1.24	Problem 1.3: 
1.18/1.24	
1.18/1.24	SCC Processor:
1.18/1.24	-> Pairs:
1.18/1.24	 A____(X:S,nil) -> MARK(X:S)
1.18/1.24	 MARK(U11(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(U22(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U31(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(U42(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(U52(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U61(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(U72(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U81(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S))
1.18/1.24	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.18/1.24	-> Rules:
1.18/1.24	 a__U11(tt) -> tt
1.18/1.24	 a__U11(X:S) -> U11(X:S)
1.18/1.24	 a__U21(tt,V2:S) -> a__U22(a__isList(V2:S))
1.18/1.24	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.18/1.24	 a__U22(tt) -> tt
1.18/1.24	 a__U22(X:S) -> U22(X:S)
1.18/1.24	 a__U31(tt) -> tt
1.18/1.24	 a__U31(X:S) -> U31(X:S)
1.18/1.24	 a__U41(tt,V2:S) -> a__U42(a__isNeList(V2:S))
1.18/1.24	 a__U41(X1:S,X2:S) -> U41(X1:S,X2:S)
1.18/1.24	 a__U42(tt) -> tt
1.18/1.24	 a__U42(X:S) -> U42(X:S)
1.18/1.24	 a__U51(tt,V2:S) -> a__U52(a__isList(V2:S))
1.18/1.24	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.18/1.24	 a__U52(tt) -> tt
1.18/1.24	 a__U52(X:S) -> U52(X:S)
1.18/1.24	 a__U61(tt) -> tt
1.18/1.24	 a__U61(X:S) -> U61(X:S)
1.18/1.24	 a__U71(tt,P:S) -> a__U72(a__isPal(P:S))
1.18/1.24	 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S)
1.18/1.24	 a__U72(tt) -> tt
1.18/1.24	 a__U72(X:S) -> U72(X:S)
1.18/1.24	 a__U81(tt) -> tt
1.18/1.24	 a__U81(X:S) -> U81(X:S)
1.18/1.24	 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
1.18/1.24	 a____(nil,X:S) -> mark(X:S)
1.18/1.24	 a____(X:S,nil) -> mark(X:S)
1.18/1.24	 a____(X1:S,X2:S) -> __(X1:S,X2:S)
1.18/1.24	 a__isList(__(V1:S,V2:S)) -> a__U21(a__isList(V1:S),V2:S)
1.18/1.24	 a__isList(nil) -> tt
1.18/1.24	 a__isList(V:S) -> a__U11(a__isNeList(V:S))
1.18/1.24	 a__isList(X:S) -> isList(X:S)
1.18/1.24	 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__isList(V1:S),V2:S)
1.18/1.24	 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__isNeList(V1:S),V2:S)
1.18/1.24	 a__isNeList(V:S) -> a__U31(a__isQid(V:S))
1.18/1.24	 a__isNeList(X:S) -> isNeList(X:S)
1.18/1.24	 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U71(a__isQid(I:S),P:S)
1.18/1.24	 a__isNePal(V:S) -> a__U61(a__isQid(V:S))
1.18/1.24	 a__isNePal(X:S) -> isNePal(X:S)
1.18/1.24	 a__isPal(nil) -> tt
1.18/1.24	 a__isPal(V:S) -> a__U81(a__isNePal(V:S))
1.18/1.24	 a__isPal(X:S) -> isPal(X:S)
1.18/1.24	 a__isQid(a) -> tt
1.18/1.24	 a__isQid(e) -> tt
1.18/1.24	 a__isQid(i) -> tt
1.18/1.24	 a__isQid(o) -> tt
1.18/1.24	 a__isQid(u) -> tt
1.18/1.24	 a__isQid(X:S) -> isQid(X:S)
1.18/1.24	 mark(U11(X:S)) -> a__U11(mark(X:S))
1.18/1.24	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.18/1.24	 mark(U22(X:S)) -> a__U22(mark(X:S))
1.18/1.24	 mark(U31(X:S)) -> a__U31(mark(X:S))
1.18/1.24	 mark(U41(X1:S,X2:S)) -> a__U41(mark(X1:S),X2:S)
1.18/1.24	 mark(U42(X:S)) -> a__U42(mark(X:S))
1.18/1.24	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.18/1.24	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.18/1.24	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.18/1.24	 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S)
1.18/1.24	 mark(U72(X:S)) -> a__U72(mark(X:S))
1.18/1.24	 mark(U81(X:S)) -> a__U81(mark(X:S))
1.18/1.24	 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
1.18/1.24	 mark(a) -> a
1.18/1.24	 mark(e) -> e
1.18/1.24	 mark(i) -> i
1.18/1.24	 mark(isList(X:S)) -> a__isList(X:S)
1.18/1.24	 mark(isNeList(X:S)) -> a__isNeList(X:S)
1.18/1.24	 mark(isNePal(X:S)) -> a__isNePal(X:S)
1.18/1.24	 mark(isPal(X:S)) -> a__isPal(X:S)
1.18/1.24	 mark(isQid(X:S)) -> a__isQid(X:S)
1.18/1.24	 mark(nil) -> nil
1.18/1.24	 mark(o) -> o
1.18/1.24	 mark(tt) -> tt
1.18/1.24	 mark(u) -> u
1.18/1.24	->Strongly Connected Components:
1.18/1.24	->->Cycle:
1.18/1.24	->->-> Pairs:
1.18/1.24	 A____(X:S,nil) -> MARK(X:S)
1.18/1.24	 MARK(U11(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(U22(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U31(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(U42(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(U52(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U61(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(U72(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U81(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S))
1.18/1.24	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.18/1.24	->->-> Rules:
1.18/1.24	 a__U11(tt) -> tt
1.18/1.24	 a__U11(X:S) -> U11(X:S)
1.18/1.24	 a__U21(tt,V2:S) -> a__U22(a__isList(V2:S))
1.18/1.24	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.18/1.24	 a__U22(tt) -> tt
1.18/1.24	 a__U22(X:S) -> U22(X:S)
1.18/1.24	 a__U31(tt) -> tt
1.18/1.24	 a__U31(X:S) -> U31(X:S)
1.18/1.24	 a__U41(tt,V2:S) -> a__U42(a__isNeList(V2:S))
1.18/1.24	 a__U41(X1:S,X2:S) -> U41(X1:S,X2:S)
1.18/1.24	 a__U42(tt) -> tt
1.18/1.24	 a__U42(X:S) -> U42(X:S)
1.18/1.24	 a__U51(tt,V2:S) -> a__U52(a__isList(V2:S))
1.18/1.24	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.18/1.24	 a__U52(tt) -> tt
1.18/1.24	 a__U52(X:S) -> U52(X:S)
1.18/1.24	 a__U61(tt) -> tt
1.18/1.24	 a__U61(X:S) -> U61(X:S)
1.18/1.24	 a__U71(tt,P:S) -> a__U72(a__isPal(P:S))
1.18/1.24	 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S)
1.18/1.24	 a__U72(tt) -> tt
1.18/1.24	 a__U72(X:S) -> U72(X:S)
1.18/1.24	 a__U81(tt) -> tt
1.18/1.24	 a__U81(X:S) -> U81(X:S)
1.18/1.24	 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
1.18/1.24	 a____(nil,X:S) -> mark(X:S)
1.18/1.24	 a____(X:S,nil) -> mark(X:S)
1.18/1.24	 a____(X1:S,X2:S) -> __(X1:S,X2:S)
1.18/1.24	 a__isList(__(V1:S,V2:S)) -> a__U21(a__isList(V1:S),V2:S)
1.18/1.24	 a__isList(nil) -> tt
1.18/1.24	 a__isList(V:S) -> a__U11(a__isNeList(V:S))
1.18/1.24	 a__isList(X:S) -> isList(X:S)
1.18/1.24	 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__isList(V1:S),V2:S)
1.18/1.24	 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__isNeList(V1:S),V2:S)
1.18/1.24	 a__isNeList(V:S) -> a__U31(a__isQid(V:S))
1.18/1.24	 a__isNeList(X:S) -> isNeList(X:S)
1.18/1.24	 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U71(a__isQid(I:S),P:S)
1.18/1.24	 a__isNePal(V:S) -> a__U61(a__isQid(V:S))
1.18/1.24	 a__isNePal(X:S) -> isNePal(X:S)
1.18/1.24	 a__isPal(nil) -> tt
1.18/1.24	 a__isPal(V:S) -> a__U81(a__isNePal(V:S))
1.18/1.24	 a__isPal(X:S) -> isPal(X:S)
1.18/1.24	 a__isQid(a) -> tt
1.18/1.24	 a__isQid(e) -> tt
1.18/1.24	 a__isQid(i) -> tt
1.18/1.24	 a__isQid(o) -> tt
1.18/1.24	 a__isQid(u) -> tt
1.18/1.24	 a__isQid(X:S) -> isQid(X:S)
1.18/1.24	 mark(U11(X:S)) -> a__U11(mark(X:S))
1.18/1.24	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.18/1.24	 mark(U22(X:S)) -> a__U22(mark(X:S))
1.18/1.24	 mark(U31(X:S)) -> a__U31(mark(X:S))
1.18/1.24	 mark(U41(X1:S,X2:S)) -> a__U41(mark(X1:S),X2:S)
1.18/1.24	 mark(U42(X:S)) -> a__U42(mark(X:S))
1.18/1.24	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.18/1.24	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.18/1.24	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.18/1.24	 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S)
1.18/1.24	 mark(U72(X:S)) -> a__U72(mark(X:S))
1.18/1.24	 mark(U81(X:S)) -> a__U81(mark(X:S))
1.18/1.24	 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
1.18/1.24	 mark(a) -> a
1.18/1.24	 mark(e) -> e
1.18/1.24	 mark(i) -> i
1.18/1.24	 mark(isList(X:S)) -> a__isList(X:S)
1.18/1.24	 mark(isNeList(X:S)) -> a__isNeList(X:S)
1.18/1.24	 mark(isNePal(X:S)) -> a__isNePal(X:S)
1.18/1.24	 mark(isPal(X:S)) -> a__isPal(X:S)
1.18/1.24	 mark(isQid(X:S)) -> a__isQid(X:S)
1.18/1.24	 mark(nil) -> nil
1.18/1.24	 mark(o) -> o
1.18/1.24	 mark(tt) -> tt
1.18/1.24	 mark(u) -> u
1.18/1.24	
1.18/1.24	Problem 1.3: 
1.18/1.24	
1.18/1.24	Reduction Pairs Processor:
1.18/1.24	-> Pairs:
1.18/1.24	 A____(X:S,nil) -> MARK(X:S)
1.18/1.24	 MARK(U11(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(U22(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U31(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(U42(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(U52(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U61(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(U72(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U81(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S))
1.18/1.24	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.18/1.24	-> Rules:
1.18/1.24	 a__U11(tt) -> tt
1.18/1.24	 a__U11(X:S) -> U11(X:S)
1.18/1.24	 a__U21(tt,V2:S) -> a__U22(a__isList(V2:S))
1.18/1.24	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.18/1.24	 a__U22(tt) -> tt
1.18/1.24	 a__U22(X:S) -> U22(X:S)
1.18/1.24	 a__U31(tt) -> tt
1.18/1.24	 a__U31(X:S) -> U31(X:S)
1.18/1.24	 a__U41(tt,V2:S) -> a__U42(a__isNeList(V2:S))
1.18/1.24	 a__U41(X1:S,X2:S) -> U41(X1:S,X2:S)
1.18/1.24	 a__U42(tt) -> tt
1.18/1.24	 a__U42(X:S) -> U42(X:S)
1.18/1.24	 a__U51(tt,V2:S) -> a__U52(a__isList(V2:S))
1.18/1.24	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.18/1.24	 a__U52(tt) -> tt
1.18/1.24	 a__U52(X:S) -> U52(X:S)
1.18/1.24	 a__U61(tt) -> tt
1.18/1.24	 a__U61(X:S) -> U61(X:S)
1.18/1.24	 a__U71(tt,P:S) -> a__U72(a__isPal(P:S))
1.18/1.24	 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S)
1.18/1.24	 a__U72(tt) -> tt
1.18/1.24	 a__U72(X:S) -> U72(X:S)
1.18/1.24	 a__U81(tt) -> tt
1.18/1.24	 a__U81(X:S) -> U81(X:S)
1.18/1.24	 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
1.18/1.24	 a____(nil,X:S) -> mark(X:S)
1.18/1.24	 a____(X:S,nil) -> mark(X:S)
1.18/1.24	 a____(X1:S,X2:S) -> __(X1:S,X2:S)
1.18/1.24	 a__isList(__(V1:S,V2:S)) -> a__U21(a__isList(V1:S),V2:S)
1.18/1.24	 a__isList(nil) -> tt
1.18/1.24	 a__isList(V:S) -> a__U11(a__isNeList(V:S))
1.18/1.24	 a__isList(X:S) -> isList(X:S)
1.18/1.24	 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__isList(V1:S),V2:S)
1.18/1.24	 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__isNeList(V1:S),V2:S)
1.18/1.24	 a__isNeList(V:S) -> a__U31(a__isQid(V:S))
1.18/1.24	 a__isNeList(X:S) -> isNeList(X:S)
1.18/1.24	 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U71(a__isQid(I:S),P:S)
1.18/1.24	 a__isNePal(V:S) -> a__U61(a__isQid(V:S))
1.18/1.24	 a__isNePal(X:S) -> isNePal(X:S)
1.18/1.24	 a__isPal(nil) -> tt
1.18/1.24	 a__isPal(V:S) -> a__U81(a__isNePal(V:S))
1.18/1.24	 a__isPal(X:S) -> isPal(X:S)
1.18/1.24	 a__isQid(a) -> tt
1.18/1.24	 a__isQid(e) -> tt
1.18/1.24	 a__isQid(i) -> tt
1.18/1.24	 a__isQid(o) -> tt
1.18/1.24	 a__isQid(u) -> tt
1.18/1.24	 a__isQid(X:S) -> isQid(X:S)
1.18/1.24	 mark(U11(X:S)) -> a__U11(mark(X:S))
1.18/1.24	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.18/1.24	 mark(U22(X:S)) -> a__U22(mark(X:S))
1.18/1.24	 mark(U31(X:S)) -> a__U31(mark(X:S))
1.18/1.24	 mark(U41(X1:S,X2:S)) -> a__U41(mark(X1:S),X2:S)
1.18/1.24	 mark(U42(X:S)) -> a__U42(mark(X:S))
1.18/1.24	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.18/1.24	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.18/1.24	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.18/1.24	 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S)
1.18/1.24	 mark(U72(X:S)) -> a__U72(mark(X:S))
1.18/1.24	 mark(U81(X:S)) -> a__U81(mark(X:S))
1.18/1.24	 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
1.18/1.24	 mark(a) -> a
1.18/1.24	 mark(e) -> e
1.18/1.24	 mark(i) -> i
1.18/1.24	 mark(isList(X:S)) -> a__isList(X:S)
1.18/1.24	 mark(isNeList(X:S)) -> a__isNeList(X:S)
1.18/1.24	 mark(isNePal(X:S)) -> a__isNePal(X:S)
1.18/1.24	 mark(isPal(X:S)) -> a__isPal(X:S)
1.18/1.24	 mark(isQid(X:S)) -> a__isQid(X:S)
1.18/1.24	 mark(nil) -> nil
1.18/1.24	 mark(o) -> o
1.18/1.24	 mark(tt) -> tt
1.18/1.24	 mark(u) -> u
1.18/1.24	-> Usable rules:
1.18/1.24	 a__U11(tt) -> tt
1.18/1.24	 a__U11(X:S) -> U11(X:S)
1.18/1.24	 a__U21(tt,V2:S) -> a__U22(a__isList(V2:S))
1.18/1.24	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.18/1.24	 a__U22(tt) -> tt
1.18/1.24	 a__U22(X:S) -> U22(X:S)
1.18/1.24	 a__U31(tt) -> tt
1.18/1.24	 a__U31(X:S) -> U31(X:S)
1.18/1.24	 a__U41(tt,V2:S) -> a__U42(a__isNeList(V2:S))
1.18/1.24	 a__U41(X1:S,X2:S) -> U41(X1:S,X2:S)
1.18/1.24	 a__U42(tt) -> tt
1.18/1.24	 a__U42(X:S) -> U42(X:S)
1.18/1.24	 a__U51(tt,V2:S) -> a__U52(a__isList(V2:S))
1.18/1.24	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.18/1.24	 a__U52(tt) -> tt
1.18/1.24	 a__U52(X:S) -> U52(X:S)
1.18/1.24	 a__U61(tt) -> tt
1.18/1.24	 a__U61(X:S) -> U61(X:S)
1.18/1.24	 a__U71(tt,P:S) -> a__U72(a__isPal(P:S))
1.18/1.24	 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S)
1.18/1.24	 a__U72(tt) -> tt
1.18/1.24	 a__U72(X:S) -> U72(X:S)
1.18/1.24	 a__U81(tt) -> tt
1.18/1.24	 a__U81(X:S) -> U81(X:S)
1.18/1.24	 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
1.18/1.24	 a____(nil,X:S) -> mark(X:S)
1.18/1.24	 a____(X:S,nil) -> mark(X:S)
1.18/1.24	 a____(X1:S,X2:S) -> __(X1:S,X2:S)
1.18/1.24	 a__isList(__(V1:S,V2:S)) -> a__U21(a__isList(V1:S),V2:S)
1.18/1.24	 a__isList(nil) -> tt
1.18/1.24	 a__isList(V:S) -> a__U11(a__isNeList(V:S))
1.18/1.24	 a__isList(X:S) -> isList(X:S)
1.18/1.24	 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__isList(V1:S),V2:S)
1.18/1.24	 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__isNeList(V1:S),V2:S)
1.18/1.24	 a__isNeList(V:S) -> a__U31(a__isQid(V:S))
1.18/1.24	 a__isNeList(X:S) -> isNeList(X:S)
1.18/1.24	 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U71(a__isQid(I:S),P:S)
1.18/1.24	 a__isNePal(V:S) -> a__U61(a__isQid(V:S))
1.18/1.24	 a__isNePal(X:S) -> isNePal(X:S)
1.18/1.24	 a__isPal(nil) -> tt
1.18/1.24	 a__isPal(V:S) -> a__U81(a__isNePal(V:S))
1.18/1.24	 a__isPal(X:S) -> isPal(X:S)
1.18/1.24	 a__isQid(a) -> tt
1.18/1.24	 a__isQid(e) -> tt
1.18/1.24	 a__isQid(i) -> tt
1.18/1.24	 a__isQid(o) -> tt
1.18/1.24	 a__isQid(u) -> tt
1.18/1.24	 a__isQid(X:S) -> isQid(X:S)
1.18/1.24	 mark(U11(X:S)) -> a__U11(mark(X:S))
1.18/1.24	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.18/1.24	 mark(U22(X:S)) -> a__U22(mark(X:S))
1.18/1.24	 mark(U31(X:S)) -> a__U31(mark(X:S))
1.18/1.24	 mark(U41(X1:S,X2:S)) -> a__U41(mark(X1:S),X2:S)
1.18/1.24	 mark(U42(X:S)) -> a__U42(mark(X:S))
1.18/1.24	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.18/1.24	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.18/1.24	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.18/1.24	 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S)
1.18/1.24	 mark(U72(X:S)) -> a__U72(mark(X:S))
1.18/1.24	 mark(U81(X:S)) -> a__U81(mark(X:S))
1.18/1.24	 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
1.18/1.24	 mark(a) -> a
1.18/1.24	 mark(e) -> e
1.18/1.24	 mark(i) -> i
1.18/1.24	 mark(isList(X:S)) -> a__isList(X:S)
1.18/1.24	 mark(isNeList(X:S)) -> a__isNeList(X:S)
1.18/1.24	 mark(isNePal(X:S)) -> a__isNePal(X:S)
1.18/1.24	 mark(isPal(X:S)) -> a__isPal(X:S)
1.18/1.24	 mark(isQid(X:S)) -> a__isQid(X:S)
1.18/1.24	 mark(nil) -> nil
1.18/1.24	 mark(o) -> o
1.18/1.24	 mark(tt) -> tt
1.18/1.24	 mark(u) -> u
1.18/1.24	->Interpretation type:
1.18/1.24	 Linear
1.18/1.24	->Coefficients:
1.18/1.24	 Natural Numbers
1.18/1.24	->Dimension:
1.18/1.24	 1
1.18/1.24	->Bound:
1.18/1.24	 2
1.18/1.24	->Interpretation:
1.18/1.24	 
1.18/1.24	[a__U11](X) = X
1.18/1.24	[a__U21](X1,X2) = X1 + 2.X2 + 1
1.18/1.24	[a__U22](X) = X
1.18/1.24	[a__U31](X) = X
1.18/1.24	[a__U41](X1,X2) = 2.X1 + 2.X2 + 2
1.18/1.24	[a__U42](X) = X + 2
1.18/1.24	[a__U51](X1,X2) = 2.X1 + 2.X2 + 1
1.18/1.24	[a__U52](X) = X + 2
1.18/1.24	[a__U61](X) = X
1.18/1.24	[a__U71](X1,X2) = 2.X1 + 2.X2 + 2
1.18/1.24	[a__U72](X) = X + 2
1.18/1.24	[a__U81](X) = X
1.18/1.24	[a____](X1,X2) = 2.X1 + X2 + 2
1.18/1.24	[a__isList](X) = 2.X + 2
1.18/1.24	[a__isNeList](X) = 2.X + 2
1.18/1.24	[a__isNePal](X) = 2.X + 2
1.18/1.24	[a__isPal](X) = 2.X + 2
1.18/1.24	[a__isQid](X) = 2
1.18/1.24	[mark](X) = X
1.18/1.24	[U11](X) = X
1.18/1.24	[U21](X1,X2) = X1 + 2.X2 + 1
1.18/1.24	[U22](X) = X
1.18/1.24	[U31](X) = X
1.18/1.24	[U41](X1,X2) = 2.X1 + 2.X2 + 2
1.18/1.24	[U42](X) = X + 2
1.18/1.24	[U51](X1,X2) = 2.X1 + 2.X2 + 1
1.18/1.24	[U52](X) = X + 2
1.18/1.24	[U61](X) = X
1.18/1.24	[U71](X1,X2) = 2.X1 + 2.X2 + 2
1.18/1.24	[U72](X) = X + 2
1.18/1.24	[U81](X) = X
1.18/1.24	[__](X1,X2) = 2.X1 + X2 + 2
1.18/1.24	[a] = 0
1.18/1.24	[e] = 2
1.18/1.24	[fSNonEmpty] = 0
1.18/1.24	[i] = 2
1.18/1.24	[isList](X) = 2.X + 2
1.18/1.24	[isNeList](X) = 2.X + 2
1.18/1.24	[isNePal](X) = 2.X + 2
1.18/1.24	[isPal](X) = 2.X + 2
1.18/1.24	[isQid](X) = 2
1.18/1.24	[nil] = 2
1.18/1.24	[o] = 1
1.18/1.24	[tt] = 2
1.18/1.24	[u] = 1
1.18/1.24	[A__U11](X) = 0
1.18/1.24	[A__U21](X1,X2) = 0
1.18/1.24	[A__U22](X) = 0
1.18/1.24	[A__U31](X) = 0
1.18/1.24	[A__U41](X1,X2) = 0
1.18/1.24	[A__U42](X) = 0
1.18/1.24	[A__U51](X1,X2) = 0
1.18/1.24	[A__U52](X) = 0
1.18/1.24	[A__U61](X) = 0
1.18/1.24	[A__U71](X1,X2) = 0
1.18/1.24	[A__U72](X) = 0
1.18/1.24	[A__U81](X) = 0
1.18/1.24	[A____](X1,X2) = 2.X1 + X2
1.18/1.24	[A__ISLIST](X) = 0
1.18/1.24	[A__ISNELIST](X) = 0
1.18/1.24	[A__ISNEPAL](X) = 0
1.18/1.24	[A__ISPAL](X) = 0
1.18/1.24	[A__ISQID](X) = 0
1.18/1.24	[MARK](X) = 2.X
1.18/1.24	
1.18/1.24	Problem 1.3: 
1.18/1.24	
1.18/1.24	SCC Processor:
1.18/1.24	-> Pairs:
1.18/1.24	 MARK(U11(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(U22(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U31(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(U42(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(U52(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U61(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(U72(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U81(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S))
1.18/1.24	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.18/1.24	-> Rules:
1.18/1.24	 a__U11(tt) -> tt
1.18/1.24	 a__U11(X:S) -> U11(X:S)
1.18/1.24	 a__U21(tt,V2:S) -> a__U22(a__isList(V2:S))
1.18/1.24	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.18/1.24	 a__U22(tt) -> tt
1.18/1.24	 a__U22(X:S) -> U22(X:S)
1.18/1.24	 a__U31(tt) -> tt
1.18/1.24	 a__U31(X:S) -> U31(X:S)
1.18/1.24	 a__U41(tt,V2:S) -> a__U42(a__isNeList(V2:S))
1.18/1.24	 a__U41(X1:S,X2:S) -> U41(X1:S,X2:S)
1.18/1.24	 a__U42(tt) -> tt
1.18/1.24	 a__U42(X:S) -> U42(X:S)
1.18/1.24	 a__U51(tt,V2:S) -> a__U52(a__isList(V2:S))
1.18/1.24	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.18/1.24	 a__U52(tt) -> tt
1.18/1.24	 a__U52(X:S) -> U52(X:S)
1.18/1.24	 a__U61(tt) -> tt
1.18/1.24	 a__U61(X:S) -> U61(X:S)
1.18/1.24	 a__U71(tt,P:S) -> a__U72(a__isPal(P:S))
1.18/1.24	 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S)
1.18/1.24	 a__U72(tt) -> tt
1.18/1.24	 a__U72(X:S) -> U72(X:S)
1.18/1.24	 a__U81(tt) -> tt
1.18/1.24	 a__U81(X:S) -> U81(X:S)
1.18/1.24	 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
1.18/1.24	 a____(nil,X:S) -> mark(X:S)
1.18/1.24	 a____(X:S,nil) -> mark(X:S)
1.18/1.24	 a____(X1:S,X2:S) -> __(X1:S,X2:S)
1.18/1.24	 a__isList(__(V1:S,V2:S)) -> a__U21(a__isList(V1:S),V2:S)
1.18/1.24	 a__isList(nil) -> tt
1.18/1.24	 a__isList(V:S) -> a__U11(a__isNeList(V:S))
1.18/1.24	 a__isList(X:S) -> isList(X:S)
1.18/1.24	 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__isList(V1:S),V2:S)
1.18/1.24	 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__isNeList(V1:S),V2:S)
1.18/1.24	 a__isNeList(V:S) -> a__U31(a__isQid(V:S))
1.18/1.24	 a__isNeList(X:S) -> isNeList(X:S)
1.18/1.24	 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U71(a__isQid(I:S),P:S)
1.18/1.24	 a__isNePal(V:S) -> a__U61(a__isQid(V:S))
1.18/1.24	 a__isNePal(X:S) -> isNePal(X:S)
1.18/1.24	 a__isPal(nil) -> tt
1.18/1.24	 a__isPal(V:S) -> a__U81(a__isNePal(V:S))
1.18/1.24	 a__isPal(X:S) -> isPal(X:S)
1.18/1.24	 a__isQid(a) -> tt
1.18/1.24	 a__isQid(e) -> tt
1.18/1.24	 a__isQid(i) -> tt
1.18/1.24	 a__isQid(o) -> tt
1.18/1.24	 a__isQid(u) -> tt
1.18/1.24	 a__isQid(X:S) -> isQid(X:S)
1.18/1.24	 mark(U11(X:S)) -> a__U11(mark(X:S))
1.18/1.24	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.18/1.24	 mark(U22(X:S)) -> a__U22(mark(X:S))
1.18/1.24	 mark(U31(X:S)) -> a__U31(mark(X:S))
1.18/1.24	 mark(U41(X1:S,X2:S)) -> a__U41(mark(X1:S),X2:S)
1.18/1.24	 mark(U42(X:S)) -> a__U42(mark(X:S))
1.18/1.24	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.18/1.24	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.18/1.24	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.18/1.24	 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S)
1.18/1.24	 mark(U72(X:S)) -> a__U72(mark(X:S))
1.18/1.24	 mark(U81(X:S)) -> a__U81(mark(X:S))
1.18/1.24	 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
1.18/1.24	 mark(a) -> a
1.18/1.24	 mark(e) -> e
1.18/1.24	 mark(i) -> i
1.18/1.24	 mark(isList(X:S)) -> a__isList(X:S)
1.18/1.24	 mark(isNeList(X:S)) -> a__isNeList(X:S)
1.18/1.24	 mark(isNePal(X:S)) -> a__isNePal(X:S)
1.18/1.24	 mark(isPal(X:S)) -> a__isPal(X:S)
1.18/1.24	 mark(isQid(X:S)) -> a__isQid(X:S)
1.18/1.24	 mark(nil) -> nil
1.18/1.24	 mark(o) -> o
1.18/1.24	 mark(tt) -> tt
1.18/1.24	 mark(u) -> u
1.18/1.24	->Strongly Connected Components:
1.18/1.24	->->Cycle:
1.18/1.24	->->-> Pairs:
1.18/1.24	 MARK(U11(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(U22(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U31(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(U42(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(U52(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U61(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(U72(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U81(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.18/1.24	->->-> Rules:
1.18/1.24	 a__U11(tt) -> tt
1.18/1.24	 a__U11(X:S) -> U11(X:S)
1.18/1.24	 a__U21(tt,V2:S) -> a__U22(a__isList(V2:S))
1.18/1.24	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.18/1.24	 a__U22(tt) -> tt
1.18/1.24	 a__U22(X:S) -> U22(X:S)
1.18/1.24	 a__U31(tt) -> tt
1.18/1.24	 a__U31(X:S) -> U31(X:S)
1.18/1.24	 a__U41(tt,V2:S) -> a__U42(a__isNeList(V2:S))
1.18/1.24	 a__U41(X1:S,X2:S) -> U41(X1:S,X2:S)
1.18/1.24	 a__U42(tt) -> tt
1.18/1.24	 a__U42(X:S) -> U42(X:S)
1.18/1.24	 a__U51(tt,V2:S) -> a__U52(a__isList(V2:S))
1.18/1.24	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.18/1.24	 a__U52(tt) -> tt
1.18/1.24	 a__U52(X:S) -> U52(X:S)
1.18/1.24	 a__U61(tt) -> tt
1.18/1.24	 a__U61(X:S) -> U61(X:S)
1.18/1.24	 a__U71(tt,P:S) -> a__U72(a__isPal(P:S))
1.18/1.24	 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S)
1.18/1.24	 a__U72(tt) -> tt
1.18/1.24	 a__U72(X:S) -> U72(X:S)
1.18/1.24	 a__U81(tt) -> tt
1.18/1.24	 a__U81(X:S) -> U81(X:S)
1.18/1.24	 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
1.18/1.24	 a____(nil,X:S) -> mark(X:S)
1.18/1.24	 a____(X:S,nil) -> mark(X:S)
1.18/1.24	 a____(X1:S,X2:S) -> __(X1:S,X2:S)
1.18/1.24	 a__isList(__(V1:S,V2:S)) -> a__U21(a__isList(V1:S),V2:S)
1.18/1.24	 a__isList(nil) -> tt
1.18/1.24	 a__isList(V:S) -> a__U11(a__isNeList(V:S))
1.18/1.24	 a__isList(X:S) -> isList(X:S)
1.18/1.24	 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__isList(V1:S),V2:S)
1.18/1.24	 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__isNeList(V1:S),V2:S)
1.18/1.24	 a__isNeList(V:S) -> a__U31(a__isQid(V:S))
1.18/1.24	 a__isNeList(X:S) -> isNeList(X:S)
1.18/1.24	 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U71(a__isQid(I:S),P:S)
1.18/1.24	 a__isNePal(V:S) -> a__U61(a__isQid(V:S))
1.18/1.24	 a__isNePal(X:S) -> isNePal(X:S)
1.18/1.24	 a__isPal(nil) -> tt
1.18/1.24	 a__isPal(V:S) -> a__U81(a__isNePal(V:S))
1.18/1.24	 a__isPal(X:S) -> isPal(X:S)
1.18/1.24	 a__isQid(a) -> tt
1.18/1.24	 a__isQid(e) -> tt
1.18/1.24	 a__isQid(i) -> tt
1.18/1.24	 a__isQid(o) -> tt
1.18/1.24	 a__isQid(u) -> tt
1.18/1.24	 a__isQid(X:S) -> isQid(X:S)
1.18/1.24	 mark(U11(X:S)) -> a__U11(mark(X:S))
1.18/1.24	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.18/1.24	 mark(U22(X:S)) -> a__U22(mark(X:S))
1.18/1.24	 mark(U31(X:S)) -> a__U31(mark(X:S))
1.18/1.24	 mark(U41(X1:S,X2:S)) -> a__U41(mark(X1:S),X2:S)
1.18/1.24	 mark(U42(X:S)) -> a__U42(mark(X:S))
1.18/1.24	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.18/1.24	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.18/1.24	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.18/1.24	 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S)
1.18/1.24	 mark(U72(X:S)) -> a__U72(mark(X:S))
1.18/1.24	 mark(U81(X:S)) -> a__U81(mark(X:S))
1.18/1.24	 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
1.18/1.24	 mark(a) -> a
1.18/1.24	 mark(e) -> e
1.18/1.24	 mark(i) -> i
1.18/1.24	 mark(isList(X:S)) -> a__isList(X:S)
1.18/1.24	 mark(isNeList(X:S)) -> a__isNeList(X:S)
1.18/1.24	 mark(isNePal(X:S)) -> a__isNePal(X:S)
1.18/1.24	 mark(isPal(X:S)) -> a__isPal(X:S)
1.18/1.24	 mark(isQid(X:S)) -> a__isQid(X:S)
1.18/1.24	 mark(nil) -> nil
1.18/1.24	 mark(o) -> o
1.18/1.24	 mark(tt) -> tt
1.18/1.24	 mark(u) -> u
1.18/1.24	
1.18/1.24	Problem 1.3: 
1.18/1.24	
1.18/1.24	Subterm Processor:
1.18/1.24	-> Pairs:
1.18/1.24	 MARK(U11(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(U22(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U31(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U41(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(U42(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(U52(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U61(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U71(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(U72(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(U81(X:S)) -> MARK(X:S)
1.18/1.24	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.24	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.18/1.24	-> Rules:
1.18/1.24	 a__U11(tt) -> tt
1.18/1.24	 a__U11(X:S) -> U11(X:S)
1.18/1.24	 a__U21(tt,V2:S) -> a__U22(a__isList(V2:S))
1.18/1.24	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.18/1.24	 a__U22(tt) -> tt
1.18/1.24	 a__U22(X:S) -> U22(X:S)
1.18/1.24	 a__U31(tt) -> tt
1.18/1.24	 a__U31(X:S) -> U31(X:S)
1.18/1.24	 a__U41(tt,V2:S) -> a__U42(a__isNeList(V2:S))
1.18/1.24	 a__U41(X1:S,X2:S) -> U41(X1:S,X2:S)
1.18/1.24	 a__U42(tt) -> tt
1.18/1.24	 a__U42(X:S) -> U42(X:S)
1.18/1.24	 a__U51(tt,V2:S) -> a__U52(a__isList(V2:S))
1.18/1.24	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.18/1.24	 a__U52(tt) -> tt
1.18/1.24	 a__U52(X:S) -> U52(X:S)
1.18/1.24	 a__U61(tt) -> tt
1.18/1.24	 a__U61(X:S) -> U61(X:S)
1.18/1.24	 a__U71(tt,P:S) -> a__U72(a__isPal(P:S))
1.18/1.24	 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S)
1.18/1.24	 a__U72(tt) -> tt
1.18/1.24	 a__U72(X:S) -> U72(X:S)
1.18/1.24	 a__U81(tt) -> tt
1.18/1.24	 a__U81(X:S) -> U81(X:S)
1.18/1.24	 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
1.18/1.24	 a____(nil,X:S) -> mark(X:S)
1.18/1.24	 a____(X:S,nil) -> mark(X:S)
1.18/1.24	 a____(X1:S,X2:S) -> __(X1:S,X2:S)
1.18/1.24	 a__isList(__(V1:S,V2:S)) -> a__U21(a__isList(V1:S),V2:S)
1.18/1.24	 a__isList(nil) -> tt
1.18/1.24	 a__isList(V:S) -> a__U11(a__isNeList(V:S))
1.18/1.24	 a__isList(X:S) -> isList(X:S)
1.18/1.24	 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__isList(V1:S),V2:S)
1.18/1.24	 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__isNeList(V1:S),V2:S)
1.18/1.24	 a__isNeList(V:S) -> a__U31(a__isQid(V:S))
1.18/1.24	 a__isNeList(X:S) -> isNeList(X:S)
1.18/1.24	 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U71(a__isQid(I:S),P:S)
1.18/1.24	 a__isNePal(V:S) -> a__U61(a__isQid(V:S))
1.18/1.24	 a__isNePal(X:S) -> isNePal(X:S)
1.18/1.24	 a__isPal(nil) -> tt
1.18/1.24	 a__isPal(V:S) -> a__U81(a__isNePal(V:S))
1.18/1.24	 a__isPal(X:S) -> isPal(X:S)
1.18/1.24	 a__isQid(a) -> tt
1.18/1.24	 a__isQid(e) -> tt
1.18/1.24	 a__isQid(i) -> tt
1.18/1.24	 a__isQid(o) -> tt
1.18/1.24	 a__isQid(u) -> tt
1.18/1.24	 a__isQid(X:S) -> isQid(X:S)
1.18/1.24	 mark(U11(X:S)) -> a__U11(mark(X:S))
1.18/1.24	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.18/1.24	 mark(U22(X:S)) -> a__U22(mark(X:S))
1.18/1.24	 mark(U31(X:S)) -> a__U31(mark(X:S))
1.18/1.24	 mark(U41(X1:S,X2:S)) -> a__U41(mark(X1:S),X2:S)
1.18/1.24	 mark(U42(X:S)) -> a__U42(mark(X:S))
1.18/1.24	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.18/1.24	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.18/1.24	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.18/1.24	 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S)
1.18/1.24	 mark(U72(X:S)) -> a__U72(mark(X:S))
1.18/1.24	 mark(U81(X:S)) -> a__U81(mark(X:S))
1.18/1.24	 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
1.18/1.24	 mark(a) -> a
1.18/1.24	 mark(e) -> e
1.18/1.24	 mark(i) -> i
1.18/1.24	 mark(isList(X:S)) -> a__isList(X:S)
1.18/1.24	 mark(isNeList(X:S)) -> a__isNeList(X:S)
1.18/1.24	 mark(isNePal(X:S)) -> a__isNePal(X:S)
1.18/1.24	 mark(isPal(X:S)) -> a__isPal(X:S)
1.18/1.24	 mark(isQid(X:S)) -> a__isQid(X:S)
1.18/1.24	 mark(nil) -> nil
1.18/1.24	 mark(o) -> o
1.18/1.24	 mark(tt) -> tt
1.18/1.24	 mark(u) -> u
1.18/1.24	->Projection:
1.18/1.24	 pi(MARK) = 1
1.18/1.24	
1.18/1.24	Problem 1.3: 
1.18/1.24	
1.18/1.24	SCC Processor:
1.18/1.24	-> Pairs:
1.18/1.24	 Empty
1.18/1.24	-> Rules:
1.18/1.24	 a__U11(tt) -> tt
1.18/1.24	 a__U11(X:S) -> U11(X:S)
1.18/1.24	 a__U21(tt,V2:S) -> a__U22(a__isList(V2:S))
1.18/1.24	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.18/1.24	 a__U22(tt) -> tt
1.18/1.24	 a__U22(X:S) -> U22(X:S)
1.18/1.24	 a__U31(tt) -> tt
1.18/1.24	 a__U31(X:S) -> U31(X:S)
1.18/1.24	 a__U41(tt,V2:S) -> a__U42(a__isNeList(V2:S))
1.18/1.24	 a__U41(X1:S,X2:S) -> U41(X1:S,X2:S)
1.18/1.24	 a__U42(tt) -> tt
1.18/1.24	 a__U42(X:S) -> U42(X:S)
1.18/1.24	 a__U51(tt,V2:S) -> a__U52(a__isList(V2:S))
1.18/1.24	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.18/1.24	 a__U52(tt) -> tt
1.18/1.24	 a__U52(X:S) -> U52(X:S)
1.18/1.24	 a__U61(tt) -> tt
1.18/1.24	 a__U61(X:S) -> U61(X:S)
1.18/1.24	 a__U71(tt,P:S) -> a__U72(a__isPal(P:S))
1.18/1.24	 a__U71(X1:S,X2:S) -> U71(X1:S,X2:S)
1.18/1.24	 a__U72(tt) -> tt
1.18/1.24	 a__U72(X:S) -> U72(X:S)
1.18/1.24	 a__U81(tt) -> tt
1.18/1.24	 a__U81(X:S) -> U81(X:S)
1.18/1.24	 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
1.18/1.24	 a____(nil,X:S) -> mark(X:S)
1.18/1.24	 a____(X:S,nil) -> mark(X:S)
1.18/1.24	 a____(X1:S,X2:S) -> __(X1:S,X2:S)
1.18/1.24	 a__isList(__(V1:S,V2:S)) -> a__U21(a__isList(V1:S),V2:S)
1.18/1.24	 a__isList(nil) -> tt
1.18/1.24	 a__isList(V:S) -> a__U11(a__isNeList(V:S))
1.18/1.24	 a__isList(X:S) -> isList(X:S)
1.18/1.24	 a__isNeList(__(V1:S,V2:S)) -> a__U41(a__isList(V1:S),V2:S)
1.18/1.24	 a__isNeList(__(V1:S,V2:S)) -> a__U51(a__isNeList(V1:S),V2:S)
1.18/1.24	 a__isNeList(V:S) -> a__U31(a__isQid(V:S))
1.18/1.24	 a__isNeList(X:S) -> isNeList(X:S)
1.18/1.24	 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U71(a__isQid(I:S),P:S)
1.18/1.24	 a__isNePal(V:S) -> a__U61(a__isQid(V:S))
1.18/1.24	 a__isNePal(X:S) -> isNePal(X:S)
1.18/1.24	 a__isPal(nil) -> tt
1.18/1.24	 a__isPal(V:S) -> a__U81(a__isNePal(V:S))
1.18/1.24	 a__isPal(X:S) -> isPal(X:S)
1.18/1.24	 a__isQid(a) -> tt
1.18/1.24	 a__isQid(e) -> tt
1.18/1.24	 a__isQid(i) -> tt
1.18/1.24	 a__isQid(o) -> tt
1.18/1.24	 a__isQid(u) -> tt
1.18/1.24	 a__isQid(X:S) -> isQid(X:S)
1.18/1.24	 mark(U11(X:S)) -> a__U11(mark(X:S))
1.18/1.24	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.18/1.24	 mark(U22(X:S)) -> a__U22(mark(X:S))
1.18/1.24	 mark(U31(X:S)) -> a__U31(mark(X:S))
1.18/1.24	 mark(U41(X1:S,X2:S)) -> a__U41(mark(X1:S),X2:S)
1.18/1.24	 mark(U42(X:S)) -> a__U42(mark(X:S))
1.18/1.24	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.18/1.24	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.18/1.24	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.18/1.24	 mark(U71(X1:S,X2:S)) -> a__U71(mark(X1:S),X2:S)
1.18/1.24	 mark(U72(X:S)) -> a__U72(mark(X:S))
1.18/1.24	 mark(U81(X:S)) -> a__U81(mark(X:S))
1.18/1.24	 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
1.18/1.24	 mark(a) -> a
1.18/1.24	 mark(e) -> e
1.18/1.24	 mark(i) -> i
1.18/1.24	 mark(isList(X:S)) -> a__isList(X:S)
1.18/1.24	 mark(isNeList(X:S)) -> a__isNeList(X:S)
1.18/1.24	 mark(isNePal(X:S)) -> a__isNePal(X:S)
1.18/1.24	 mark(isPal(X:S)) -> a__isPal(X:S)
1.18/1.24	 mark(isQid(X:S)) -> a__isQid(X:S)
1.18/1.24	 mark(nil) -> nil
1.18/1.24	 mark(o) -> o
1.18/1.24	 mark(tt) -> tt
1.18/1.24	 mark(u) -> u
1.18/1.24	->Strongly Connected Components:
1.18/1.24	 There is no strongly connected component
1.18/1.24	
1.18/1.24	The problem is finite.
1.18/1.24	EOF