1.03/1.09	YES
1.03/1.09	
1.03/1.09	Problem 1: 
1.03/1.09	
1.03/1.09	(VAR v_NonEmpty:S I:S P:S V:S V1:S V2:S X:S X1:S X2:S Y:S Z:S)
1.03/1.09	(RULES
1.03/1.09	U11(mark(X:S)) -> mark(U11(X:S))
1.03/1.09	U11(ok(X:S)) -> ok(U11(X:S))
1.03/1.09	U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.03/1.09	U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.03/1.09	U22(mark(X:S)) -> mark(U22(X:S))
1.03/1.09	U22(ok(X:S)) -> ok(U22(X:S))
1.03/1.09	U31(mark(X:S)) -> mark(U31(X:S))
1.03/1.09	U31(ok(X:S)) -> ok(U31(X:S))
1.03/1.09	U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.03/1.09	U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.03/1.09	U42(mark(X:S)) -> mark(U42(X:S))
1.03/1.09	U42(ok(X:S)) -> ok(U42(X:S))
1.03/1.09	U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.03/1.09	U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.03/1.09	U52(mark(X:S)) -> mark(U52(X:S))
1.03/1.09	U52(ok(X:S)) -> ok(U52(X:S))
1.03/1.09	U61(mark(X:S)) -> mark(U61(X:S))
1.03/1.09	U61(ok(X:S)) -> ok(U61(X:S))
1.03/1.09	U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.03/1.09	U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.03/1.09	U72(mark(X:S)) -> mark(U72(X:S))
1.03/1.09	U72(ok(X:S)) -> ok(U72(X:S))
1.03/1.09	U81(mark(X:S)) -> mark(U81(X:S))
1.03/1.09	U81(ok(X:S)) -> ok(U81(X:S))
1.03/1.09	__(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.03/1.09	__(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.03/1.09	__(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.03/1.09	active(U11(tt)) -> mark(tt)
1.03/1.09	active(U11(X:S)) -> U11(active(X:S))
1.03/1.09	active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.03/1.09	active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.03/1.09	active(U22(tt)) -> mark(tt)
1.03/1.09	active(U22(X:S)) -> U22(active(X:S))
1.03/1.09	active(U31(tt)) -> mark(tt)
1.03/1.09	active(U31(X:S)) -> U31(active(X:S))
1.03/1.09	active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.03/1.09	active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.03/1.09	active(U42(tt)) -> mark(tt)
1.03/1.09	active(U42(X:S)) -> U42(active(X:S))
1.03/1.09	active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.03/1.09	active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.03/1.09	active(U52(tt)) -> mark(tt)
1.03/1.09	active(U52(X:S)) -> U52(active(X:S))
1.03/1.09	active(U61(tt)) -> mark(tt)
1.03/1.09	active(U61(X:S)) -> U61(active(X:S))
1.03/1.09	active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.03/1.09	active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.03/1.09	active(U72(tt)) -> mark(tt)
1.03/1.09	active(U72(X:S)) -> U72(active(X:S))
1.03/1.09	active(U81(tt)) -> mark(tt)
1.03/1.09	active(U81(X:S)) -> U81(active(X:S))
1.03/1.09	active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.03/1.09	active(__(nil,X:S)) -> mark(X:S)
1.03/1.09	active(__(X:S,nil)) -> mark(X:S)
1.03/1.09	active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.03/1.09	active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.03/1.09	active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.03/1.09	active(isList(nil)) -> mark(tt)
1.03/1.09	active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.03/1.09	active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.03/1.09	active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.03/1.09	active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.03/1.09	active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.03/1.09	active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.03/1.09	active(isPal(nil)) -> mark(tt)
1.03/1.09	active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.03/1.09	active(isQid(a)) -> mark(tt)
1.03/1.09	active(isQid(e)) -> mark(tt)
1.03/1.09	active(isQid(i)) -> mark(tt)
1.03/1.09	active(isQid(o)) -> mark(tt)
1.03/1.09	active(isQid(u)) -> mark(tt)
1.03/1.09	isList(ok(X:S)) -> ok(isList(X:S))
1.03/1.09	isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.03/1.09	isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.03/1.09	isPal(ok(X:S)) -> ok(isPal(X:S))
1.03/1.09	isQid(ok(X:S)) -> ok(isQid(X:S))
1.03/1.09	proper(U11(X:S)) -> U11(proper(X:S))
1.03/1.09	proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.03/1.09	proper(U22(X:S)) -> U22(proper(X:S))
1.03/1.09	proper(U31(X:S)) -> U31(proper(X:S))
1.03/1.09	proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.03/1.09	proper(U42(X:S)) -> U42(proper(X:S))
1.03/1.09	proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.03/1.09	proper(U52(X:S)) -> U52(proper(X:S))
1.03/1.09	proper(U61(X:S)) -> U61(proper(X:S))
1.03/1.09	proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.03/1.09	proper(U72(X:S)) -> U72(proper(X:S))
1.03/1.09	proper(U81(X:S)) -> U81(proper(X:S))
1.03/1.09	proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.03/1.09	proper(isList(X:S)) -> isList(proper(X:S))
1.03/1.09	proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.03/1.09	proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.03/1.09	proper(isPal(X:S)) -> isPal(proper(X:S))
1.03/1.09	proper(isQid(X:S)) -> isQid(proper(X:S))
1.03/1.09	proper(a) -> ok(a)
1.03/1.09	proper(e) -> ok(e)
1.03/1.09	proper(i) -> ok(i)
1.03/1.09	proper(nil) -> ok(nil)
1.03/1.09	proper(o) -> ok(o)
1.03/1.09	proper(tt) -> ok(tt)
1.03/1.09	proper(u) -> ok(u)
1.03/1.09	top(mark(X:S)) -> top(proper(X:S))
1.03/1.09	top(ok(X:S)) -> top(active(X:S))
1.03/1.09	) 
1.03/1.09	(STRATEGY INNERMOST)
1.03/1.09	
1.03/1.09	Problem 1: 
1.03/1.09	
1.03/1.09	Dependency Pairs Processor:
1.03/1.09	-> Pairs:
1.03/1.09	 U11#(mark(X:S)) -> U11#(X:S)
1.03/1.09	 U11#(ok(X:S)) -> U11#(X:S)
1.03/1.09	 U21#(mark(X1:S),X2:S) -> U21#(X1:S,X2:S)
1.03/1.09	 U21#(ok(X1:S),ok(X2:S)) -> U21#(X1:S,X2:S)
1.03/1.09	 U22#(mark(X:S)) -> U22#(X:S)
1.03/1.09	 U22#(ok(X:S)) -> U22#(X:S)
1.03/1.09	 U31#(mark(X:S)) -> U31#(X:S)
1.03/1.09	 U31#(ok(X:S)) -> U31#(X:S)
1.03/1.09	 U41#(mark(X1:S),X2:S) -> U41#(X1:S,X2:S)
1.03/1.09	 U41#(ok(X1:S),ok(X2:S)) -> U41#(X1:S,X2:S)
1.03/1.09	 U42#(mark(X:S)) -> U42#(X:S)
1.03/1.09	 U42#(ok(X:S)) -> U42#(X:S)
1.03/1.09	 U51#(mark(X1:S),X2:S) -> U51#(X1:S,X2:S)
1.03/1.09	 U51#(ok(X1:S),ok(X2:S)) -> U51#(X1:S,X2:S)
1.03/1.09	 U52#(mark(X:S)) -> U52#(X:S)
1.03/1.09	 U52#(ok(X:S)) -> U52#(X:S)
1.03/1.09	 U61#(mark(X:S)) -> U61#(X:S)
1.03/1.09	 U61#(ok(X:S)) -> U61#(X:S)
1.03/1.09	 U71#(mark(X1:S),X2:S) -> U71#(X1:S,X2:S)
1.03/1.09	 U71#(ok(X1:S),ok(X2:S)) -> U71#(X1:S,X2:S)
1.03/1.09	 U72#(mark(X:S)) -> U72#(X:S)
1.03/1.09	 U72#(ok(X:S)) -> U72#(X:S)
1.03/1.09	 U81#(mark(X:S)) -> U81#(X:S)
1.03/1.09	 U81#(ok(X:S)) -> U81#(X:S)
1.03/1.09	 __#(mark(X1:S),X2:S) -> __#(X1:S,X2:S)
1.03/1.09	 __#(ok(X1:S),ok(X2:S)) -> __#(X1:S,X2:S)
1.03/1.09	 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S)
1.03/1.09	 ACTIVE(U11(X:S)) -> U11#(active(X:S))
1.03/1.09	 ACTIVE(U11(X:S)) -> ACTIVE(X:S)
1.03/1.09	 ACTIVE(U21(tt,V2:S)) -> U22#(isList(V2:S))
1.03/1.09	 ACTIVE(U21(tt,V2:S)) -> ISLIST(V2:S)
1.03/1.09	 ACTIVE(U21(X1:S,X2:S)) -> U21#(active(X1:S),X2:S)
1.03/1.09	 ACTIVE(U21(X1:S,X2:S)) -> ACTIVE(X1:S)
1.03/1.09	 ACTIVE(U22(X:S)) -> U22#(active(X:S))
1.03/1.09	 ACTIVE(U22(X:S)) -> ACTIVE(X:S)
1.03/1.09	 ACTIVE(U31(X:S)) -> U31#(active(X:S))
1.03/1.09	 ACTIVE(U31(X:S)) -> ACTIVE(X:S)
1.03/1.09	 ACTIVE(U41(tt,V2:S)) -> U42#(isNeList(V2:S))
1.03/1.09	 ACTIVE(U41(tt,V2:S)) -> ISNELIST(V2:S)
1.03/1.09	 ACTIVE(U41(X1:S,X2:S)) -> U41#(active(X1:S),X2:S)
1.03/1.09	 ACTIVE(U41(X1:S,X2:S)) -> ACTIVE(X1:S)
1.03/1.09	 ACTIVE(U42(X:S)) -> U42#(active(X:S))
1.03/1.09	 ACTIVE(U42(X:S)) -> ACTIVE(X:S)
1.03/1.09	 ACTIVE(U51(tt,V2:S)) -> U52#(isList(V2:S))
1.03/1.09	 ACTIVE(U51(tt,V2:S)) -> ISLIST(V2:S)
1.03/1.09	 ACTIVE(U51(X1:S,X2:S)) -> U51#(active(X1:S),X2:S)
1.03/1.09	 ACTIVE(U51(X1:S,X2:S)) -> ACTIVE(X1:S)
1.03/1.09	 ACTIVE(U52(X:S)) -> U52#(active(X:S))
1.03/1.09	 ACTIVE(U52(X:S)) -> ACTIVE(X:S)
1.03/1.09	 ACTIVE(U61(X:S)) -> U61#(active(X:S))
1.03/1.09	 ACTIVE(U61(X:S)) -> ACTIVE(X:S)
1.03/1.09	 ACTIVE(U71(tt,P:S)) -> U72#(isPal(P:S))
1.03/1.09	 ACTIVE(U71(tt,P:S)) -> ISPAL(P:S)
1.03/1.09	 ACTIVE(U71(X1:S,X2:S)) -> U71#(active(X1:S),X2:S)
1.03/1.09	 ACTIVE(U71(X1:S,X2:S)) -> ACTIVE(X1:S)
1.03/1.09	 ACTIVE(U72(X:S)) -> U72#(active(X:S))
1.03/1.09	 ACTIVE(U72(X:S)) -> ACTIVE(X:S)
1.03/1.09	 ACTIVE(U81(X:S)) -> U81#(active(X:S))
1.03/1.09	 ACTIVE(U81(X:S)) -> ACTIVE(X:S)
1.03/1.09	 ACTIVE(__(__(X:S,Y:S),Z:S)) -> __#(X:S,__(Y:S,Z:S))
1.03/1.09	 ACTIVE(__(__(X:S,Y:S),Z:S)) -> __#(Y:S,Z:S)
1.03/1.09	 ACTIVE(__(X1:S,X2:S)) -> __#(active(X1:S),X2:S)
1.03/1.09	 ACTIVE(__(X1:S,X2:S)) -> __#(X1:S,active(X2:S))
1.03/1.09	 ACTIVE(__(X1:S,X2:S)) -> ACTIVE(X1:S)
1.03/1.09	 ACTIVE(__(X1:S,X2:S)) -> ACTIVE(X2:S)
1.03/1.09	 ACTIVE(isList(__(V1:S,V2:S))) -> U21#(isList(V1:S),V2:S)
1.03/1.09	 ACTIVE(isList(__(V1:S,V2:S))) -> ISLIST(V1:S)
1.03/1.09	 ACTIVE(isList(V:S)) -> U11#(isNeList(V:S))
1.03/1.09	 ACTIVE(isList(V:S)) -> ISNELIST(V:S)
1.03/1.09	 ACTIVE(isNeList(__(V1:S,V2:S))) -> U41#(isList(V1:S),V2:S)
1.03/1.09	 ACTIVE(isNeList(__(V1:S,V2:S))) -> U51#(isNeList(V1:S),V2:S)
1.03/1.09	 ACTIVE(isNeList(__(V1:S,V2:S))) -> ISLIST(V1:S)
1.03/1.09	 ACTIVE(isNeList(__(V1:S,V2:S))) -> ISNELIST(V1:S)
1.03/1.09	 ACTIVE(isNeList(V:S)) -> U31#(isQid(V:S))
1.03/1.09	 ACTIVE(isNeList(V:S)) -> ISQID(V:S)
1.03/1.09	 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> U71#(isQid(I:S),P:S)
1.03/1.09	 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> ISQID(I:S)
1.03/1.09	 ACTIVE(isNePal(V:S)) -> U61#(isQid(V:S))
1.03/1.09	 ACTIVE(isNePal(V:S)) -> ISQID(V:S)
1.03/1.09	 ACTIVE(isPal(V:S)) -> U81#(isNePal(V:S))
1.03/1.09	 ACTIVE(isPal(V:S)) -> ISNEPAL(V:S)
1.03/1.09	 ISLIST(ok(X:S)) -> ISLIST(X:S)
1.03/1.09	 ISNELIST(ok(X:S)) -> ISNELIST(X:S)
1.03/1.09	 ISNEPAL(ok(X:S)) -> ISNEPAL(X:S)
1.03/1.09	 ISPAL(ok(X:S)) -> ISPAL(X:S)
1.03/1.09	 ISQID(ok(X:S)) -> ISQID(X:S)
1.03/1.09	 PROPER(U11(X:S)) -> U11#(proper(X:S))
1.03/1.09	 PROPER(U11(X:S)) -> PROPER(X:S)
1.03/1.09	 PROPER(U21(X1:S,X2:S)) -> U21#(proper(X1:S),proper(X2:S))
1.03/1.09	 PROPER(U21(X1:S,X2:S)) -> PROPER(X1:S)
1.03/1.09	 PROPER(U21(X1:S,X2:S)) -> PROPER(X2:S)
1.03/1.09	 PROPER(U22(X:S)) -> U22#(proper(X:S))
1.03/1.09	 PROPER(U22(X:S)) -> PROPER(X:S)
1.03/1.09	 PROPER(U31(X:S)) -> U31#(proper(X:S))
1.03/1.09	 PROPER(U31(X:S)) -> PROPER(X:S)
1.03/1.09	 PROPER(U41(X1:S,X2:S)) -> U41#(proper(X1:S),proper(X2:S))
1.03/1.09	 PROPER(U41(X1:S,X2:S)) -> PROPER(X1:S)
1.03/1.09	 PROPER(U41(X1:S,X2:S)) -> PROPER(X2:S)
1.03/1.09	 PROPER(U42(X:S)) -> U42#(proper(X:S))
1.03/1.09	 PROPER(U42(X:S)) -> PROPER(X:S)
1.03/1.09	 PROPER(U51(X1:S,X2:S)) -> U51#(proper(X1:S),proper(X2:S))
1.03/1.09	 PROPER(U51(X1:S,X2:S)) -> PROPER(X1:S)
1.03/1.09	 PROPER(U51(X1:S,X2:S)) -> PROPER(X2:S)
1.03/1.09	 PROPER(U52(X:S)) -> U52#(proper(X:S))
1.03/1.09	 PROPER(U52(X:S)) -> PROPER(X:S)
1.03/1.09	 PROPER(U61(X:S)) -> U61#(proper(X:S))
1.03/1.09	 PROPER(U61(X:S)) -> PROPER(X:S)
1.03/1.09	 PROPER(U71(X1:S,X2:S)) -> U71#(proper(X1:S),proper(X2:S))
1.03/1.09	 PROPER(U71(X1:S,X2:S)) -> PROPER(X1:S)
1.03/1.09	 PROPER(U71(X1:S,X2:S)) -> PROPER(X2:S)
1.03/1.09	 PROPER(U72(X:S)) -> U72#(proper(X:S))
1.03/1.09	 PROPER(U72(X:S)) -> PROPER(X:S)
1.03/1.09	 PROPER(U81(X:S)) -> U81#(proper(X:S))
1.03/1.09	 PROPER(U81(X:S)) -> PROPER(X:S)
1.03/1.09	 PROPER(__(X1:S,X2:S)) -> __#(proper(X1:S),proper(X2:S))
1.03/1.09	 PROPER(__(X1:S,X2:S)) -> PROPER(X1:S)
1.03/1.09	 PROPER(__(X1:S,X2:S)) -> PROPER(X2:S)
1.03/1.09	 PROPER(isList(X:S)) -> ISLIST(proper(X:S))
1.03/1.09	 PROPER(isList(X:S)) -> PROPER(X:S)
1.03/1.09	 PROPER(isNeList(X:S)) -> ISNELIST(proper(X:S))
1.03/1.09	 PROPER(isNeList(X:S)) -> PROPER(X:S)
1.03/1.09	 PROPER(isNePal(X:S)) -> ISNEPAL(proper(X:S))
1.03/1.09	 PROPER(isNePal(X:S)) -> PROPER(X:S)
1.03/1.09	 PROPER(isPal(X:S)) -> ISPAL(proper(X:S))
1.03/1.09	 PROPER(isPal(X:S)) -> PROPER(X:S)
1.03/1.09	 PROPER(isQid(X:S)) -> ISQID(proper(X:S))
1.03/1.09	 PROPER(isQid(X:S)) -> PROPER(X:S)
1.03/1.09	 TOP(mark(X:S)) -> PROPER(X:S)
1.03/1.09	 TOP(mark(X:S)) -> TOP(proper(X:S))
1.03/1.09	 TOP(ok(X:S)) -> ACTIVE(X:S)
1.03/1.09	 TOP(ok(X:S)) -> TOP(active(X:S))
1.03/1.09	-> Rules:
1.03/1.09	 U11(mark(X:S)) -> mark(U11(X:S))
1.03/1.09	 U11(ok(X:S)) -> ok(U11(X:S))
1.03/1.09	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.03/1.09	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.03/1.09	 U22(mark(X:S)) -> mark(U22(X:S))
1.03/1.09	 U22(ok(X:S)) -> ok(U22(X:S))
1.03/1.09	 U31(mark(X:S)) -> mark(U31(X:S))
1.03/1.09	 U31(ok(X:S)) -> ok(U31(X:S))
1.03/1.09	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.03/1.09	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.03/1.09	 U42(mark(X:S)) -> mark(U42(X:S))
1.03/1.09	 U42(ok(X:S)) -> ok(U42(X:S))
1.03/1.09	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.03/1.09	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.03/1.09	 U52(mark(X:S)) -> mark(U52(X:S))
1.03/1.09	 U52(ok(X:S)) -> ok(U52(X:S))
1.03/1.09	 U61(mark(X:S)) -> mark(U61(X:S))
1.03/1.09	 U61(ok(X:S)) -> ok(U61(X:S))
1.03/1.09	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.03/1.09	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.03/1.09	 U72(mark(X:S)) -> mark(U72(X:S))
1.03/1.09	 U72(ok(X:S)) -> ok(U72(X:S))
1.03/1.09	 U81(mark(X:S)) -> mark(U81(X:S))
1.03/1.09	 U81(ok(X:S)) -> ok(U81(X:S))
1.03/1.09	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.03/1.09	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.03/1.09	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.03/1.09	 active(U11(tt)) -> mark(tt)
1.03/1.09	 active(U11(X:S)) -> U11(active(X:S))
1.03/1.09	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.03/1.09	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.03/1.09	 active(U22(tt)) -> mark(tt)
1.03/1.09	 active(U22(X:S)) -> U22(active(X:S))
1.03/1.09	 active(U31(tt)) -> mark(tt)
1.03/1.09	 active(U31(X:S)) -> U31(active(X:S))
1.03/1.09	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.03/1.09	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.03/1.09	 active(U42(tt)) -> mark(tt)
1.03/1.09	 active(U42(X:S)) -> U42(active(X:S))
1.03/1.09	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.03/1.09	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.03/1.09	 active(U52(tt)) -> mark(tt)
1.03/1.09	 active(U52(X:S)) -> U52(active(X:S))
1.03/1.09	 active(U61(tt)) -> mark(tt)
1.03/1.09	 active(U61(X:S)) -> U61(active(X:S))
1.03/1.09	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.03/1.09	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.03/1.09	 active(U72(tt)) -> mark(tt)
1.03/1.09	 active(U72(X:S)) -> U72(active(X:S))
1.03/1.09	 active(U81(tt)) -> mark(tt)
1.03/1.09	 active(U81(X:S)) -> U81(active(X:S))
1.03/1.09	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.03/1.09	 active(__(nil,X:S)) -> mark(X:S)
1.03/1.09	 active(__(X:S,nil)) -> mark(X:S)
1.03/1.09	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.03/1.09	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.03/1.09	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.03/1.09	 active(isList(nil)) -> mark(tt)
1.03/1.09	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.03/1.09	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.03/1.09	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.03/1.09	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.03/1.09	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.03/1.09	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.03/1.09	 active(isPal(nil)) -> mark(tt)
1.03/1.09	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.03/1.09	 active(isQid(a)) -> mark(tt)
1.03/1.09	 active(isQid(e)) -> mark(tt)
1.03/1.09	 active(isQid(i)) -> mark(tt)
1.03/1.09	 active(isQid(o)) -> mark(tt)
1.03/1.09	 active(isQid(u)) -> mark(tt)
1.03/1.09	 isList(ok(X:S)) -> ok(isList(X:S))
1.03/1.09	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.03/1.09	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.03/1.09	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.03/1.09	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.03/1.09	 proper(U11(X:S)) -> U11(proper(X:S))
1.03/1.09	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.03/1.09	 proper(U22(X:S)) -> U22(proper(X:S))
1.03/1.09	 proper(U31(X:S)) -> U31(proper(X:S))
1.03/1.09	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.03/1.09	 proper(U42(X:S)) -> U42(proper(X:S))
1.03/1.09	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.03/1.09	 proper(U52(X:S)) -> U52(proper(X:S))
1.03/1.09	 proper(U61(X:S)) -> U61(proper(X:S))
1.03/1.09	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.03/1.09	 proper(U72(X:S)) -> U72(proper(X:S))
1.03/1.09	 proper(U81(X:S)) -> U81(proper(X:S))
1.03/1.09	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.03/1.09	 proper(isList(X:S)) -> isList(proper(X:S))
1.03/1.09	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.03/1.09	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.03/1.09	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.03/1.09	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.03/1.09	 proper(a) -> ok(a)
1.03/1.09	 proper(e) -> ok(e)
1.03/1.09	 proper(i) -> ok(i)
1.03/1.09	 proper(nil) -> ok(nil)
1.03/1.09	 proper(o) -> ok(o)
1.03/1.09	 proper(tt) -> ok(tt)
1.03/1.09	 proper(u) -> ok(u)
1.03/1.09	 top(mark(X:S)) -> top(proper(X:S))
1.03/1.09	 top(ok(X:S)) -> top(active(X:S))
1.03/1.09	
1.03/1.09	Problem 1: 
1.03/1.09	
1.03/1.09	SCC Processor:
1.03/1.09	-> Pairs:
1.03/1.09	 U11#(mark(X:S)) -> U11#(X:S)
1.03/1.09	 U11#(ok(X:S)) -> U11#(X:S)
1.03/1.09	 U21#(mark(X1:S),X2:S) -> U21#(X1:S,X2:S)
1.03/1.09	 U21#(ok(X1:S),ok(X2:S)) -> U21#(X1:S,X2:S)
1.03/1.09	 U22#(mark(X:S)) -> U22#(X:S)
1.03/1.09	 U22#(ok(X:S)) -> U22#(X:S)
1.03/1.09	 U31#(mark(X:S)) -> U31#(X:S)
1.03/1.09	 U31#(ok(X:S)) -> U31#(X:S)
1.03/1.09	 U41#(mark(X1:S),X2:S) -> U41#(X1:S,X2:S)
1.03/1.09	 U41#(ok(X1:S),ok(X2:S)) -> U41#(X1:S,X2:S)
1.03/1.09	 U42#(mark(X:S)) -> U42#(X:S)
1.03/1.09	 U42#(ok(X:S)) -> U42#(X:S)
1.03/1.09	 U51#(mark(X1:S),X2:S) -> U51#(X1:S,X2:S)
1.03/1.09	 U51#(ok(X1:S),ok(X2:S)) -> U51#(X1:S,X2:S)
1.03/1.09	 U52#(mark(X:S)) -> U52#(X:S)
1.03/1.09	 U52#(ok(X:S)) -> U52#(X:S)
1.03/1.09	 U61#(mark(X:S)) -> U61#(X:S)
1.03/1.09	 U61#(ok(X:S)) -> U61#(X:S)
1.03/1.09	 U71#(mark(X1:S),X2:S) -> U71#(X1:S,X2:S)
1.03/1.09	 U71#(ok(X1:S),ok(X2:S)) -> U71#(X1:S,X2:S)
1.03/1.09	 U72#(mark(X:S)) -> U72#(X:S)
1.03/1.09	 U72#(ok(X:S)) -> U72#(X:S)
1.03/1.09	 U81#(mark(X:S)) -> U81#(X:S)
1.03/1.09	 U81#(ok(X:S)) -> U81#(X:S)
1.03/1.09	 __#(mark(X1:S),X2:S) -> __#(X1:S,X2:S)
1.03/1.09	 __#(ok(X1:S),ok(X2:S)) -> __#(X1:S,X2:S)
1.03/1.09	 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S)
1.03/1.09	 ACTIVE(U11(X:S)) -> U11#(active(X:S))
1.03/1.09	 ACTIVE(U11(X:S)) -> ACTIVE(X:S)
1.03/1.09	 ACTIVE(U21(tt,V2:S)) -> U22#(isList(V2:S))
1.03/1.09	 ACTIVE(U21(tt,V2:S)) -> ISLIST(V2:S)
1.03/1.09	 ACTIVE(U21(X1:S,X2:S)) -> U21#(active(X1:S),X2:S)
1.03/1.09	 ACTIVE(U21(X1:S,X2:S)) -> ACTIVE(X1:S)
1.03/1.09	 ACTIVE(U22(X:S)) -> U22#(active(X:S))
1.03/1.09	 ACTIVE(U22(X:S)) -> ACTIVE(X:S)
1.03/1.09	 ACTIVE(U31(X:S)) -> U31#(active(X:S))
1.03/1.09	 ACTIVE(U31(X:S)) -> ACTIVE(X:S)
1.03/1.09	 ACTIVE(U41(tt,V2:S)) -> U42#(isNeList(V2:S))
1.03/1.09	 ACTIVE(U41(tt,V2:S)) -> ISNELIST(V2:S)
1.03/1.09	 ACTIVE(U41(X1:S,X2:S)) -> U41#(active(X1:S),X2:S)
1.03/1.09	 ACTIVE(U41(X1:S,X2:S)) -> ACTIVE(X1:S)
1.03/1.09	 ACTIVE(U42(X:S)) -> U42#(active(X:S))
1.03/1.09	 ACTIVE(U42(X:S)) -> ACTIVE(X:S)
1.03/1.09	 ACTIVE(U51(tt,V2:S)) -> U52#(isList(V2:S))
1.03/1.09	 ACTIVE(U51(tt,V2:S)) -> ISLIST(V2:S)
1.03/1.09	 ACTIVE(U51(X1:S,X2:S)) -> U51#(active(X1:S),X2:S)
1.03/1.09	 ACTIVE(U51(X1:S,X2:S)) -> ACTIVE(X1:S)
1.03/1.09	 ACTIVE(U52(X:S)) -> U52#(active(X:S))
1.03/1.09	 ACTIVE(U52(X:S)) -> ACTIVE(X:S)
1.03/1.09	 ACTIVE(U61(X:S)) -> U61#(active(X:S))
1.03/1.09	 ACTIVE(U61(X:S)) -> ACTIVE(X:S)
1.03/1.09	 ACTIVE(U71(tt,P:S)) -> U72#(isPal(P:S))
1.03/1.09	 ACTIVE(U71(tt,P:S)) -> ISPAL(P:S)
1.03/1.09	 ACTIVE(U71(X1:S,X2:S)) -> U71#(active(X1:S),X2:S)
1.03/1.09	 ACTIVE(U71(X1:S,X2:S)) -> ACTIVE(X1:S)
1.03/1.09	 ACTIVE(U72(X:S)) -> U72#(active(X:S))
1.03/1.09	 ACTIVE(U72(X:S)) -> ACTIVE(X:S)
1.03/1.09	 ACTIVE(U81(X:S)) -> U81#(active(X:S))
1.03/1.09	 ACTIVE(U81(X:S)) -> ACTIVE(X:S)
1.03/1.09	 ACTIVE(__(__(X:S,Y:S),Z:S)) -> __#(X:S,__(Y:S,Z:S))
1.03/1.09	 ACTIVE(__(__(X:S,Y:S),Z:S)) -> __#(Y:S,Z:S)
1.03/1.09	 ACTIVE(__(X1:S,X2:S)) -> __#(active(X1:S),X2:S)
1.03/1.09	 ACTIVE(__(X1:S,X2:S)) -> __#(X1:S,active(X2:S))
1.03/1.09	 ACTIVE(__(X1:S,X2:S)) -> ACTIVE(X1:S)
1.03/1.09	 ACTIVE(__(X1:S,X2:S)) -> ACTIVE(X2:S)
1.03/1.09	 ACTIVE(isList(__(V1:S,V2:S))) -> U21#(isList(V1:S),V2:S)
1.03/1.09	 ACTIVE(isList(__(V1:S,V2:S))) -> ISLIST(V1:S)
1.03/1.09	 ACTIVE(isList(V:S)) -> U11#(isNeList(V:S))
1.03/1.09	 ACTIVE(isList(V:S)) -> ISNELIST(V:S)
1.03/1.09	 ACTIVE(isNeList(__(V1:S,V2:S))) -> U41#(isList(V1:S),V2:S)
1.03/1.09	 ACTIVE(isNeList(__(V1:S,V2:S))) -> U51#(isNeList(V1:S),V2:S)
1.03/1.09	 ACTIVE(isNeList(__(V1:S,V2:S))) -> ISLIST(V1:S)
1.03/1.09	 ACTIVE(isNeList(__(V1:S,V2:S))) -> ISNELIST(V1:S)
1.03/1.09	 ACTIVE(isNeList(V:S)) -> U31#(isQid(V:S))
1.03/1.09	 ACTIVE(isNeList(V:S)) -> ISQID(V:S)
1.03/1.09	 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> U71#(isQid(I:S),P:S)
1.03/1.09	 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> ISQID(I:S)
1.03/1.09	 ACTIVE(isNePal(V:S)) -> U61#(isQid(V:S))
1.03/1.09	 ACTIVE(isNePal(V:S)) -> ISQID(V:S)
1.03/1.09	 ACTIVE(isPal(V:S)) -> U81#(isNePal(V:S))
1.03/1.09	 ACTIVE(isPal(V:S)) -> ISNEPAL(V:S)
1.03/1.09	 ISLIST(ok(X:S)) -> ISLIST(X:S)
1.03/1.09	 ISNELIST(ok(X:S)) -> ISNELIST(X:S)
1.03/1.09	 ISNEPAL(ok(X:S)) -> ISNEPAL(X:S)
1.03/1.09	 ISPAL(ok(X:S)) -> ISPAL(X:S)
1.03/1.09	 ISQID(ok(X:S)) -> ISQID(X:S)
1.03/1.09	 PROPER(U11(X:S)) -> U11#(proper(X:S))
1.03/1.09	 PROPER(U11(X:S)) -> PROPER(X:S)
1.03/1.09	 PROPER(U21(X1:S,X2:S)) -> U21#(proper(X1:S),proper(X2:S))
1.03/1.09	 PROPER(U21(X1:S,X2:S)) -> PROPER(X1:S)
1.03/1.09	 PROPER(U21(X1:S,X2:S)) -> PROPER(X2:S)
1.03/1.09	 PROPER(U22(X:S)) -> U22#(proper(X:S))
1.03/1.09	 PROPER(U22(X:S)) -> PROPER(X:S)
1.03/1.09	 PROPER(U31(X:S)) -> U31#(proper(X:S))
1.03/1.09	 PROPER(U31(X:S)) -> PROPER(X:S)
1.03/1.09	 PROPER(U41(X1:S,X2:S)) -> U41#(proper(X1:S),proper(X2:S))
1.03/1.09	 PROPER(U41(X1:S,X2:S)) -> PROPER(X1:S)
1.03/1.09	 PROPER(U41(X1:S,X2:S)) -> PROPER(X2:S)
1.03/1.09	 PROPER(U42(X:S)) -> U42#(proper(X:S))
1.03/1.09	 PROPER(U42(X:S)) -> PROPER(X:S)
1.03/1.09	 PROPER(U51(X1:S,X2:S)) -> U51#(proper(X1:S),proper(X2:S))
1.03/1.09	 PROPER(U51(X1:S,X2:S)) -> PROPER(X1:S)
1.03/1.09	 PROPER(U51(X1:S,X2:S)) -> PROPER(X2:S)
1.03/1.09	 PROPER(U52(X:S)) -> U52#(proper(X:S))
1.03/1.09	 PROPER(U52(X:S)) -> PROPER(X:S)
1.03/1.09	 PROPER(U61(X:S)) -> U61#(proper(X:S))
1.03/1.09	 PROPER(U61(X:S)) -> PROPER(X:S)
1.03/1.09	 PROPER(U71(X1:S,X2:S)) -> U71#(proper(X1:S),proper(X2:S))
1.03/1.09	 PROPER(U71(X1:S,X2:S)) -> PROPER(X1:S)
1.03/1.09	 PROPER(U71(X1:S,X2:S)) -> PROPER(X2:S)
1.03/1.09	 PROPER(U72(X:S)) -> U72#(proper(X:S))
1.03/1.09	 PROPER(U72(X:S)) -> PROPER(X:S)
1.03/1.09	 PROPER(U81(X:S)) -> U81#(proper(X:S))
1.03/1.09	 PROPER(U81(X:S)) -> PROPER(X:S)
1.03/1.09	 PROPER(__(X1:S,X2:S)) -> __#(proper(X1:S),proper(X2:S))
1.03/1.09	 PROPER(__(X1:S,X2:S)) -> PROPER(X1:S)
1.03/1.09	 PROPER(__(X1:S,X2:S)) -> PROPER(X2:S)
1.03/1.09	 PROPER(isList(X:S)) -> ISLIST(proper(X:S))
1.03/1.09	 PROPER(isList(X:S)) -> PROPER(X:S)
1.03/1.09	 PROPER(isNeList(X:S)) -> ISNELIST(proper(X:S))
1.03/1.09	 PROPER(isNeList(X:S)) -> PROPER(X:S)
1.03/1.09	 PROPER(isNePal(X:S)) -> ISNEPAL(proper(X:S))
1.03/1.09	 PROPER(isNePal(X:S)) -> PROPER(X:S)
1.03/1.09	 PROPER(isPal(X:S)) -> ISPAL(proper(X:S))
1.03/1.09	 PROPER(isPal(X:S)) -> PROPER(X:S)
1.03/1.09	 PROPER(isQid(X:S)) -> ISQID(proper(X:S))
1.03/1.09	 PROPER(isQid(X:S)) -> PROPER(X:S)
1.03/1.09	 TOP(mark(X:S)) -> PROPER(X:S)
1.03/1.09	 TOP(mark(X:S)) -> TOP(proper(X:S))
1.03/1.09	 TOP(ok(X:S)) -> ACTIVE(X:S)
1.03/1.09	 TOP(ok(X:S)) -> TOP(active(X:S))
1.03/1.09	-> Rules:
1.03/1.09	 U11(mark(X:S)) -> mark(U11(X:S))
1.03/1.09	 U11(ok(X:S)) -> ok(U11(X:S))
1.03/1.09	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.03/1.09	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.03/1.09	 U22(mark(X:S)) -> mark(U22(X:S))
1.03/1.09	 U22(ok(X:S)) -> ok(U22(X:S))
1.03/1.09	 U31(mark(X:S)) -> mark(U31(X:S))
1.03/1.09	 U31(ok(X:S)) -> ok(U31(X:S))
1.03/1.09	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.03/1.09	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.03/1.09	 U42(mark(X:S)) -> mark(U42(X:S))
1.03/1.09	 U42(ok(X:S)) -> ok(U42(X:S))
1.03/1.09	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.03/1.09	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.03/1.09	 U52(mark(X:S)) -> mark(U52(X:S))
1.03/1.09	 U52(ok(X:S)) -> ok(U52(X:S))
1.03/1.09	 U61(mark(X:S)) -> mark(U61(X:S))
1.03/1.09	 U61(ok(X:S)) -> ok(U61(X:S))
1.03/1.09	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.03/1.09	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.03/1.09	 U72(mark(X:S)) -> mark(U72(X:S))
1.03/1.09	 U72(ok(X:S)) -> ok(U72(X:S))
1.03/1.09	 U81(mark(X:S)) -> mark(U81(X:S))
1.03/1.09	 U81(ok(X:S)) -> ok(U81(X:S))
1.03/1.09	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.03/1.09	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.03/1.09	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.03/1.09	 active(U11(tt)) -> mark(tt)
1.03/1.09	 active(U11(X:S)) -> U11(active(X:S))
1.03/1.09	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.03/1.09	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.03/1.09	 active(U22(tt)) -> mark(tt)
1.03/1.09	 active(U22(X:S)) -> U22(active(X:S))
1.03/1.09	 active(U31(tt)) -> mark(tt)
1.03/1.09	 active(U31(X:S)) -> U31(active(X:S))
1.03/1.09	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.03/1.09	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.03/1.09	 active(U42(tt)) -> mark(tt)
1.03/1.09	 active(U42(X:S)) -> U42(active(X:S))
1.03/1.09	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.03/1.09	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.03/1.09	 active(U52(tt)) -> mark(tt)
1.03/1.09	 active(U52(X:S)) -> U52(active(X:S))
1.03/1.09	 active(U61(tt)) -> mark(tt)
1.03/1.09	 active(U61(X:S)) -> U61(active(X:S))
1.03/1.09	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.03/1.09	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.03/1.09	 active(U72(tt)) -> mark(tt)
1.03/1.09	 active(U72(X:S)) -> U72(active(X:S))
1.03/1.09	 active(U81(tt)) -> mark(tt)
1.03/1.09	 active(U81(X:S)) -> U81(active(X:S))
1.03/1.09	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.03/1.09	 active(__(nil,X:S)) -> mark(X:S)
1.03/1.09	 active(__(X:S,nil)) -> mark(X:S)
1.03/1.09	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.03/1.09	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.03/1.09	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.03/1.09	 active(isList(nil)) -> mark(tt)
1.03/1.09	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.03/1.09	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.03/1.09	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.03/1.09	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.03/1.09	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.03/1.09	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.03/1.09	 active(isPal(nil)) -> mark(tt)
1.03/1.09	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.03/1.09	 active(isQid(a)) -> mark(tt)
1.03/1.09	 active(isQid(e)) -> mark(tt)
1.03/1.09	 active(isQid(i)) -> mark(tt)
1.03/1.09	 active(isQid(o)) -> mark(tt)
1.03/1.09	 active(isQid(u)) -> mark(tt)
1.03/1.09	 isList(ok(X:S)) -> ok(isList(X:S))
1.03/1.09	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.03/1.09	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.03/1.09	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.03/1.09	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.03/1.09	 proper(U11(X:S)) -> U11(proper(X:S))
1.03/1.09	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.03/1.09	 proper(U22(X:S)) -> U22(proper(X:S))
1.03/1.09	 proper(U31(X:S)) -> U31(proper(X:S))
1.03/1.09	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.03/1.09	 proper(U42(X:S)) -> U42(proper(X:S))
1.03/1.09	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.03/1.09	 proper(U52(X:S)) -> U52(proper(X:S))
1.03/1.09	 proper(U61(X:S)) -> U61(proper(X:S))
1.03/1.09	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.03/1.09	 proper(U72(X:S)) -> U72(proper(X:S))
1.03/1.09	 proper(U81(X:S)) -> U81(proper(X:S))
1.03/1.09	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.03/1.09	 proper(isList(X:S)) -> isList(proper(X:S))
1.03/1.09	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.03/1.09	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.03/1.09	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.03/1.09	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.03/1.09	 proper(a) -> ok(a)
1.03/1.09	 proper(e) -> ok(e)
1.03/1.09	 proper(i) -> ok(i)
1.03/1.09	 proper(nil) -> ok(nil)
1.03/1.09	 proper(o) -> ok(o)
1.03/1.09	 proper(tt) -> ok(tt)
1.03/1.09	 proper(u) -> ok(u)
1.03/1.09	 top(mark(X:S)) -> top(proper(X:S))
1.03/1.09	 top(ok(X:S)) -> top(active(X:S))
1.03/1.09	->Strongly Connected Components:
1.03/1.09	->->Cycle:
1.03/1.09	->->-> Pairs:
1.03/1.09	 ISQID(ok(X:S)) -> ISQID(X:S)
1.03/1.09	->->-> Rules:
1.03/1.09	 U11(mark(X:S)) -> mark(U11(X:S))
1.03/1.09	 U11(ok(X:S)) -> ok(U11(X:S))
1.03/1.09	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.03/1.09	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.03/1.09	 U22(mark(X:S)) -> mark(U22(X:S))
1.03/1.09	 U22(ok(X:S)) -> ok(U22(X:S))
1.03/1.09	 U31(mark(X:S)) -> mark(U31(X:S))
1.03/1.09	 U31(ok(X:S)) -> ok(U31(X:S))
1.03/1.09	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.03/1.09	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.03/1.09	 U42(mark(X:S)) -> mark(U42(X:S))
1.03/1.09	 U42(ok(X:S)) -> ok(U42(X:S))
1.03/1.09	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.03/1.09	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.03/1.09	 U52(mark(X:S)) -> mark(U52(X:S))
1.03/1.09	 U52(ok(X:S)) -> ok(U52(X:S))
1.03/1.09	 U61(mark(X:S)) -> mark(U61(X:S))
1.03/1.09	 U61(ok(X:S)) -> ok(U61(X:S))
1.03/1.09	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.03/1.09	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.03/1.09	 U72(mark(X:S)) -> mark(U72(X:S))
1.03/1.09	 U72(ok(X:S)) -> ok(U72(X:S))
1.03/1.09	 U81(mark(X:S)) -> mark(U81(X:S))
1.03/1.09	 U81(ok(X:S)) -> ok(U81(X:S))
1.03/1.09	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.03/1.09	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.03/1.09	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.03/1.09	 active(U11(tt)) -> mark(tt)
1.03/1.09	 active(U11(X:S)) -> U11(active(X:S))
1.03/1.09	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.03/1.09	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.03/1.09	 active(U22(tt)) -> mark(tt)
1.03/1.09	 active(U22(X:S)) -> U22(active(X:S))
1.03/1.09	 active(U31(tt)) -> mark(tt)
1.03/1.09	 active(U31(X:S)) -> U31(active(X:S))
1.03/1.09	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.03/1.09	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.03/1.09	 active(U42(tt)) -> mark(tt)
1.03/1.09	 active(U42(X:S)) -> U42(active(X:S))
1.03/1.09	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.03/1.09	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.03/1.09	 active(U52(tt)) -> mark(tt)
1.03/1.09	 active(U52(X:S)) -> U52(active(X:S))
1.03/1.09	 active(U61(tt)) -> mark(tt)
1.03/1.09	 active(U61(X:S)) -> U61(active(X:S))
1.03/1.09	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.03/1.09	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.03/1.09	 active(U72(tt)) -> mark(tt)
1.03/1.09	 active(U72(X:S)) -> U72(active(X:S))
1.03/1.09	 active(U81(tt)) -> mark(tt)
1.03/1.09	 active(U81(X:S)) -> U81(active(X:S))
1.03/1.09	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.03/1.09	 active(__(nil,X:S)) -> mark(X:S)
1.03/1.09	 active(__(X:S,nil)) -> mark(X:S)
1.03/1.09	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.03/1.09	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.03/1.09	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.03/1.09	 active(isList(nil)) -> mark(tt)
1.03/1.09	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.03/1.09	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.03/1.09	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.03/1.09	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.03/1.09	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.03/1.09	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.03/1.09	 active(isPal(nil)) -> mark(tt)
1.03/1.09	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.03/1.09	 active(isQid(a)) -> mark(tt)
1.03/1.09	 active(isQid(e)) -> mark(tt)
1.03/1.09	 active(isQid(i)) -> mark(tt)
1.03/1.09	 active(isQid(o)) -> mark(tt)
1.03/1.09	 active(isQid(u)) -> mark(tt)
1.03/1.09	 isList(ok(X:S)) -> ok(isList(X:S))
1.03/1.09	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.03/1.09	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.03/1.09	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.03/1.09	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.03/1.09	 proper(U11(X:S)) -> U11(proper(X:S))
1.03/1.09	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.03/1.09	 proper(U22(X:S)) -> U22(proper(X:S))
1.03/1.09	 proper(U31(X:S)) -> U31(proper(X:S))
1.03/1.09	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.03/1.09	 proper(U42(X:S)) -> U42(proper(X:S))
1.03/1.09	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.03/1.09	 proper(U52(X:S)) -> U52(proper(X:S))
1.03/1.09	 proper(U61(X:S)) -> U61(proper(X:S))
1.03/1.09	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.03/1.09	 proper(U72(X:S)) -> U72(proper(X:S))
1.03/1.09	 proper(U81(X:S)) -> U81(proper(X:S))
1.03/1.09	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.03/1.09	 proper(isList(X:S)) -> isList(proper(X:S))
1.03/1.09	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.03/1.09	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.03/1.09	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.03/1.09	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.03/1.09	 proper(a) -> ok(a)
1.03/1.09	 proper(e) -> ok(e)
1.03/1.09	 proper(i) -> ok(i)
1.03/1.09	 proper(nil) -> ok(nil)
1.03/1.09	 proper(o) -> ok(o)
1.03/1.09	 proper(tt) -> ok(tt)
1.03/1.09	 proper(u) -> ok(u)
1.03/1.09	 top(mark(X:S)) -> top(proper(X:S))
1.03/1.09	 top(ok(X:S)) -> top(active(X:S))
1.03/1.09	->->Cycle:
1.03/1.09	->->-> Pairs:
1.03/1.09	 ISPAL(ok(X:S)) -> ISPAL(X:S)
1.03/1.09	->->-> Rules:
1.03/1.09	 U11(mark(X:S)) -> mark(U11(X:S))
1.03/1.09	 U11(ok(X:S)) -> ok(U11(X:S))
1.03/1.09	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.03/1.09	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.03/1.09	 U22(mark(X:S)) -> mark(U22(X:S))
1.03/1.09	 U22(ok(X:S)) -> ok(U22(X:S))
1.03/1.09	 U31(mark(X:S)) -> mark(U31(X:S))
1.03/1.09	 U31(ok(X:S)) -> ok(U31(X:S))
1.03/1.09	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.03/1.09	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.03/1.09	 U42(mark(X:S)) -> mark(U42(X:S))
1.03/1.09	 U42(ok(X:S)) -> ok(U42(X:S))
1.03/1.09	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.03/1.09	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.03/1.09	 U52(mark(X:S)) -> mark(U52(X:S))
1.03/1.09	 U52(ok(X:S)) -> ok(U52(X:S))
1.03/1.09	 U61(mark(X:S)) -> mark(U61(X:S))
1.03/1.09	 U61(ok(X:S)) -> ok(U61(X:S))
1.03/1.09	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.03/1.09	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.03/1.09	 U72(mark(X:S)) -> mark(U72(X:S))
1.03/1.09	 U72(ok(X:S)) -> ok(U72(X:S))
1.03/1.09	 U81(mark(X:S)) -> mark(U81(X:S))
1.03/1.09	 U81(ok(X:S)) -> ok(U81(X:S))
1.03/1.09	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.03/1.09	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.03/1.09	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.03/1.09	 active(U11(tt)) -> mark(tt)
1.03/1.09	 active(U11(X:S)) -> U11(active(X:S))
1.03/1.09	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.03/1.09	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.03/1.09	 active(U22(tt)) -> mark(tt)
1.03/1.09	 active(U22(X:S)) -> U22(active(X:S))
1.03/1.09	 active(U31(tt)) -> mark(tt)
1.03/1.09	 active(U31(X:S)) -> U31(active(X:S))
1.03/1.09	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.03/1.09	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.03/1.09	 active(U42(tt)) -> mark(tt)
1.03/1.09	 active(U42(X:S)) -> U42(active(X:S))
1.03/1.09	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.03/1.09	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.03/1.09	 active(U52(tt)) -> mark(tt)
1.03/1.09	 active(U52(X:S)) -> U52(active(X:S))
1.03/1.09	 active(U61(tt)) -> mark(tt)
1.03/1.09	 active(U61(X:S)) -> U61(active(X:S))
1.03/1.09	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.03/1.09	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.03/1.09	 active(U72(tt)) -> mark(tt)
1.03/1.09	 active(U72(X:S)) -> U72(active(X:S))
1.03/1.09	 active(U81(tt)) -> mark(tt)
1.03/1.09	 active(U81(X:S)) -> U81(active(X:S))
1.03/1.09	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.03/1.09	 active(__(nil,X:S)) -> mark(X:S)
1.03/1.09	 active(__(X:S,nil)) -> mark(X:S)
1.03/1.09	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.03/1.09	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.03/1.09	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.03/1.09	 active(isList(nil)) -> mark(tt)
1.03/1.09	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.03/1.09	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.03/1.09	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.03/1.09	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.03/1.09	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.03/1.09	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.03/1.09	 active(isPal(nil)) -> mark(tt)
1.03/1.09	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.03/1.09	 active(isQid(a)) -> mark(tt)
1.03/1.09	 active(isQid(e)) -> mark(tt)
1.03/1.09	 active(isQid(i)) -> mark(tt)
1.03/1.09	 active(isQid(o)) -> mark(tt)
1.03/1.09	 active(isQid(u)) -> mark(tt)
1.03/1.09	 isList(ok(X:S)) -> ok(isList(X:S))
1.03/1.09	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.03/1.09	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.03/1.09	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.03/1.09	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.03/1.09	 proper(U11(X:S)) -> U11(proper(X:S))
1.03/1.09	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.03/1.09	 proper(U22(X:S)) -> U22(proper(X:S))
1.03/1.09	 proper(U31(X:S)) -> U31(proper(X:S))
1.03/1.09	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.03/1.09	 proper(U42(X:S)) -> U42(proper(X:S))
1.03/1.09	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.03/1.09	 proper(U52(X:S)) -> U52(proper(X:S))
1.03/1.09	 proper(U61(X:S)) -> U61(proper(X:S))
1.03/1.09	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.03/1.09	 proper(U72(X:S)) -> U72(proper(X:S))
1.03/1.09	 proper(U81(X:S)) -> U81(proper(X:S))
1.03/1.09	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.03/1.09	 proper(isList(X:S)) -> isList(proper(X:S))
1.03/1.09	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.03/1.09	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.03/1.09	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.03/1.09	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.03/1.09	 proper(a) -> ok(a)
1.03/1.09	 proper(e) -> ok(e)
1.03/1.09	 proper(i) -> ok(i)
1.03/1.09	 proper(nil) -> ok(nil)
1.03/1.09	 proper(o) -> ok(o)
1.03/1.09	 proper(tt) -> ok(tt)
1.03/1.09	 proper(u) -> ok(u)
1.03/1.09	 top(mark(X:S)) -> top(proper(X:S))
1.03/1.09	 top(ok(X:S)) -> top(active(X:S))
1.03/1.09	->->Cycle:
1.03/1.09	->->-> Pairs:
1.03/1.09	 ISNEPAL(ok(X:S)) -> ISNEPAL(X:S)
1.03/1.09	->->-> Rules:
1.03/1.09	 U11(mark(X:S)) -> mark(U11(X:S))
1.03/1.09	 U11(ok(X:S)) -> ok(U11(X:S))
1.03/1.09	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.03/1.09	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.03/1.09	 U22(mark(X:S)) -> mark(U22(X:S))
1.03/1.09	 U22(ok(X:S)) -> ok(U22(X:S))
1.03/1.09	 U31(mark(X:S)) -> mark(U31(X:S))
1.03/1.09	 U31(ok(X:S)) -> ok(U31(X:S))
1.03/1.09	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.03/1.09	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.03/1.09	 U42(mark(X:S)) -> mark(U42(X:S))
1.03/1.09	 U42(ok(X:S)) -> ok(U42(X:S))
1.03/1.09	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.03/1.09	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.03/1.09	 U52(mark(X:S)) -> mark(U52(X:S))
1.03/1.09	 U52(ok(X:S)) -> ok(U52(X:S))
1.03/1.09	 U61(mark(X:S)) -> mark(U61(X:S))
1.03/1.09	 U61(ok(X:S)) -> ok(U61(X:S))
1.03/1.09	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.03/1.09	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.03/1.09	 U72(mark(X:S)) -> mark(U72(X:S))
1.03/1.09	 U72(ok(X:S)) -> ok(U72(X:S))
1.03/1.09	 U81(mark(X:S)) -> mark(U81(X:S))
1.03/1.09	 U81(ok(X:S)) -> ok(U81(X:S))
1.03/1.09	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.03/1.09	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.03/1.09	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.03/1.09	 active(U11(tt)) -> mark(tt)
1.03/1.09	 active(U11(X:S)) -> U11(active(X:S))
1.03/1.09	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.03/1.09	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.03/1.09	 active(U22(tt)) -> mark(tt)
1.03/1.09	 active(U22(X:S)) -> U22(active(X:S))
1.03/1.09	 active(U31(tt)) -> mark(tt)
1.03/1.09	 active(U31(X:S)) -> U31(active(X:S))
1.03/1.09	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.03/1.09	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.03/1.09	 active(U42(tt)) -> mark(tt)
1.03/1.09	 active(U42(X:S)) -> U42(active(X:S))
1.03/1.09	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.03/1.09	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.03/1.09	 active(U52(tt)) -> mark(tt)
1.03/1.09	 active(U52(X:S)) -> U52(active(X:S))
1.03/1.09	 active(U61(tt)) -> mark(tt)
1.03/1.09	 active(U61(X:S)) -> U61(active(X:S))
1.03/1.09	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.03/1.09	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.03/1.09	 active(U72(tt)) -> mark(tt)
1.03/1.09	 active(U72(X:S)) -> U72(active(X:S))
1.03/1.09	 active(U81(tt)) -> mark(tt)
1.03/1.09	 active(U81(X:S)) -> U81(active(X:S))
1.03/1.09	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.03/1.09	 active(__(nil,X:S)) -> mark(X:S)
1.03/1.09	 active(__(X:S,nil)) -> mark(X:S)
1.03/1.09	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.03/1.09	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.03/1.09	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.03/1.09	 active(isList(nil)) -> mark(tt)
1.03/1.09	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.03/1.09	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.03/1.09	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.03/1.09	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.03/1.09	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.03/1.09	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.03/1.09	 active(isPal(nil)) -> mark(tt)
1.03/1.09	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.03/1.09	 active(isQid(a)) -> mark(tt)
1.03/1.09	 active(isQid(e)) -> mark(tt)
1.03/1.09	 active(isQid(i)) -> mark(tt)
1.03/1.09	 active(isQid(o)) -> mark(tt)
1.03/1.09	 active(isQid(u)) -> mark(tt)
1.03/1.09	 isList(ok(X:S)) -> ok(isList(X:S))
1.03/1.09	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.03/1.09	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.03/1.09	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.03/1.09	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.03/1.09	 proper(U11(X:S)) -> U11(proper(X:S))
1.03/1.09	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.03/1.09	 proper(U22(X:S)) -> U22(proper(X:S))
1.03/1.09	 proper(U31(X:S)) -> U31(proper(X:S))
1.03/1.09	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.03/1.09	 proper(U42(X:S)) -> U42(proper(X:S))
1.03/1.09	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.03/1.09	 proper(U52(X:S)) -> U52(proper(X:S))
1.03/1.09	 proper(U61(X:S)) -> U61(proper(X:S))
1.03/1.09	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.03/1.09	 proper(U72(X:S)) -> U72(proper(X:S))
1.03/1.09	 proper(U81(X:S)) -> U81(proper(X:S))
1.03/1.09	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.03/1.09	 proper(isList(X:S)) -> isList(proper(X:S))
1.03/1.09	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.03/1.09	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.03/1.09	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.03/1.09	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.03/1.09	 proper(a) -> ok(a)
1.03/1.09	 proper(e) -> ok(e)
1.03/1.09	 proper(i) -> ok(i)
1.03/1.09	 proper(nil) -> ok(nil)
1.03/1.09	 proper(o) -> ok(o)
1.03/1.09	 proper(tt) -> ok(tt)
1.03/1.09	 proper(u) -> ok(u)
1.03/1.09	 top(mark(X:S)) -> top(proper(X:S))
1.03/1.09	 top(ok(X:S)) -> top(active(X:S))
1.03/1.09	->->Cycle:
1.03/1.09	->->-> Pairs:
1.03/1.09	 ISNELIST(ok(X:S)) -> ISNELIST(X:S)
1.03/1.09	->->-> Rules:
1.03/1.09	 U11(mark(X:S)) -> mark(U11(X:S))
1.03/1.09	 U11(ok(X:S)) -> ok(U11(X:S))
1.03/1.09	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.03/1.09	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.03/1.09	 U22(mark(X:S)) -> mark(U22(X:S))
1.03/1.09	 U22(ok(X:S)) -> ok(U22(X:S))
1.03/1.09	 U31(mark(X:S)) -> mark(U31(X:S))
1.03/1.09	 U31(ok(X:S)) -> ok(U31(X:S))
1.03/1.09	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.03/1.09	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.03/1.09	 U42(mark(X:S)) -> mark(U42(X:S))
1.03/1.09	 U42(ok(X:S)) -> ok(U42(X:S))
1.03/1.09	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.03/1.09	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.03/1.09	 U52(mark(X:S)) -> mark(U52(X:S))
1.03/1.09	 U52(ok(X:S)) -> ok(U52(X:S))
1.03/1.09	 U61(mark(X:S)) -> mark(U61(X:S))
1.03/1.09	 U61(ok(X:S)) -> ok(U61(X:S))
1.03/1.09	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.03/1.09	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.03/1.09	 U72(mark(X:S)) -> mark(U72(X:S))
1.03/1.09	 U72(ok(X:S)) -> ok(U72(X:S))
1.03/1.09	 U81(mark(X:S)) -> mark(U81(X:S))
1.03/1.09	 U81(ok(X:S)) -> ok(U81(X:S))
1.03/1.09	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.03/1.09	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.03/1.09	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.03/1.09	 active(U11(tt)) -> mark(tt)
1.03/1.09	 active(U11(X:S)) -> U11(active(X:S))
1.03/1.09	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.03/1.09	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.03/1.09	 active(U22(tt)) -> mark(tt)
1.03/1.09	 active(U22(X:S)) -> U22(active(X:S))
1.03/1.09	 active(U31(tt)) -> mark(tt)
1.03/1.09	 active(U31(X:S)) -> U31(active(X:S))
1.03/1.09	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.03/1.09	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.03/1.09	 active(U42(tt)) -> mark(tt)
1.03/1.09	 active(U42(X:S)) -> U42(active(X:S))
1.03/1.09	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.03/1.09	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.03/1.09	 active(U52(tt)) -> mark(tt)
1.03/1.09	 active(U52(X:S)) -> U52(active(X:S))
1.03/1.09	 active(U61(tt)) -> mark(tt)
1.03/1.09	 active(U61(X:S)) -> U61(active(X:S))
1.03/1.09	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.03/1.09	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.03/1.09	 active(U72(tt)) -> mark(tt)
1.03/1.09	 active(U72(X:S)) -> U72(active(X:S))
1.03/1.09	 active(U81(tt)) -> mark(tt)
1.03/1.09	 active(U81(X:S)) -> U81(active(X:S))
1.03/1.09	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.03/1.09	 active(__(nil,X:S)) -> mark(X:S)
1.03/1.09	 active(__(X:S,nil)) -> mark(X:S)
1.03/1.09	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.03/1.09	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.03/1.09	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.03/1.09	 active(isList(nil)) -> mark(tt)
1.03/1.09	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.03/1.09	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.03/1.09	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.03/1.09	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.03/1.09	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.03/1.09	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.03/1.09	 active(isPal(nil)) -> mark(tt)
1.03/1.09	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.03/1.09	 active(isQid(a)) -> mark(tt)
1.03/1.09	 active(isQid(e)) -> mark(tt)
1.03/1.09	 active(isQid(i)) -> mark(tt)
1.03/1.09	 active(isQid(o)) -> mark(tt)
1.03/1.10	 active(isQid(u)) -> mark(tt)
1.03/1.10	 isList(ok(X:S)) -> ok(isList(X:S))
1.03/1.10	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.03/1.10	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.03/1.10	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.03/1.10	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.03/1.10	 proper(U11(X:S)) -> U11(proper(X:S))
1.03/1.10	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U22(X:S)) -> U22(proper(X:S))
1.03/1.10	 proper(U31(X:S)) -> U31(proper(X:S))
1.03/1.10	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U42(X:S)) -> U42(proper(X:S))
1.03/1.10	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U52(X:S)) -> U52(proper(X:S))
1.03/1.10	 proper(U61(X:S)) -> U61(proper(X:S))
1.03/1.10	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U72(X:S)) -> U72(proper(X:S))
1.03/1.10	 proper(U81(X:S)) -> U81(proper(X:S))
1.03/1.10	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(isList(X:S)) -> isList(proper(X:S))
1.03/1.10	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.03/1.10	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.03/1.10	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.03/1.10	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.03/1.10	 proper(a) -> ok(a)
1.03/1.10	 proper(e) -> ok(e)
1.03/1.10	 proper(i) -> ok(i)
1.03/1.10	 proper(nil) -> ok(nil)
1.03/1.10	 proper(o) -> ok(o)
1.03/1.10	 proper(tt) -> ok(tt)
1.03/1.10	 proper(u) -> ok(u)
1.03/1.10	 top(mark(X:S)) -> top(proper(X:S))
1.03/1.10	 top(ok(X:S)) -> top(active(X:S))
1.03/1.10	->->Cycle:
1.03/1.10	->->-> Pairs:
1.03/1.10	 ISLIST(ok(X:S)) -> ISLIST(X:S)
1.03/1.10	->->-> Rules:
1.03/1.10	 U11(mark(X:S)) -> mark(U11(X:S))
1.03/1.10	 U11(ok(X:S)) -> ok(U11(X:S))
1.03/1.10	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.03/1.10	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.03/1.10	 U22(mark(X:S)) -> mark(U22(X:S))
1.03/1.10	 U22(ok(X:S)) -> ok(U22(X:S))
1.03/1.10	 U31(mark(X:S)) -> mark(U31(X:S))
1.03/1.10	 U31(ok(X:S)) -> ok(U31(X:S))
1.03/1.10	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.03/1.10	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.03/1.10	 U42(mark(X:S)) -> mark(U42(X:S))
1.03/1.10	 U42(ok(X:S)) -> ok(U42(X:S))
1.03/1.10	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.03/1.10	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.03/1.10	 U52(mark(X:S)) -> mark(U52(X:S))
1.03/1.10	 U52(ok(X:S)) -> ok(U52(X:S))
1.03/1.10	 U61(mark(X:S)) -> mark(U61(X:S))
1.03/1.10	 U61(ok(X:S)) -> ok(U61(X:S))
1.03/1.10	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.03/1.10	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.03/1.10	 U72(mark(X:S)) -> mark(U72(X:S))
1.03/1.10	 U72(ok(X:S)) -> ok(U72(X:S))
1.03/1.10	 U81(mark(X:S)) -> mark(U81(X:S))
1.03/1.10	 U81(ok(X:S)) -> ok(U81(X:S))
1.03/1.10	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.03/1.10	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.03/1.10	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.03/1.10	 active(U11(tt)) -> mark(tt)
1.03/1.10	 active(U11(X:S)) -> U11(active(X:S))
1.03/1.10	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.03/1.10	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.03/1.10	 active(U22(tt)) -> mark(tt)
1.03/1.10	 active(U22(X:S)) -> U22(active(X:S))
1.03/1.10	 active(U31(tt)) -> mark(tt)
1.03/1.10	 active(U31(X:S)) -> U31(active(X:S))
1.03/1.10	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.03/1.10	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.03/1.10	 active(U42(tt)) -> mark(tt)
1.03/1.10	 active(U42(X:S)) -> U42(active(X:S))
1.03/1.10	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.03/1.10	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.03/1.10	 active(U52(tt)) -> mark(tt)
1.03/1.10	 active(U52(X:S)) -> U52(active(X:S))
1.03/1.10	 active(U61(tt)) -> mark(tt)
1.03/1.10	 active(U61(X:S)) -> U61(active(X:S))
1.03/1.10	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.03/1.10	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.03/1.10	 active(U72(tt)) -> mark(tt)
1.03/1.10	 active(U72(X:S)) -> U72(active(X:S))
1.03/1.10	 active(U81(tt)) -> mark(tt)
1.03/1.10	 active(U81(X:S)) -> U81(active(X:S))
1.03/1.10	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.03/1.10	 active(__(nil,X:S)) -> mark(X:S)
1.03/1.10	 active(__(X:S,nil)) -> mark(X:S)
1.03/1.10	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.03/1.10	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.03/1.10	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.03/1.10	 active(isList(nil)) -> mark(tt)
1.03/1.10	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.03/1.10	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.03/1.10	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.03/1.10	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.03/1.10	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.03/1.10	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.03/1.10	 active(isPal(nil)) -> mark(tt)
1.03/1.10	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.03/1.10	 active(isQid(a)) -> mark(tt)
1.03/1.10	 active(isQid(e)) -> mark(tt)
1.03/1.10	 active(isQid(i)) -> mark(tt)
1.03/1.10	 active(isQid(o)) -> mark(tt)
1.03/1.10	 active(isQid(u)) -> mark(tt)
1.03/1.10	 isList(ok(X:S)) -> ok(isList(X:S))
1.03/1.10	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.03/1.10	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.03/1.10	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.03/1.10	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.03/1.10	 proper(U11(X:S)) -> U11(proper(X:S))
1.03/1.10	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U22(X:S)) -> U22(proper(X:S))
1.03/1.10	 proper(U31(X:S)) -> U31(proper(X:S))
1.03/1.10	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U42(X:S)) -> U42(proper(X:S))
1.03/1.10	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U52(X:S)) -> U52(proper(X:S))
1.03/1.10	 proper(U61(X:S)) -> U61(proper(X:S))
1.03/1.10	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U72(X:S)) -> U72(proper(X:S))
1.03/1.10	 proper(U81(X:S)) -> U81(proper(X:S))
1.03/1.10	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(isList(X:S)) -> isList(proper(X:S))
1.03/1.10	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.03/1.10	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.03/1.10	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.03/1.10	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.03/1.10	 proper(a) -> ok(a)
1.03/1.10	 proper(e) -> ok(e)
1.03/1.10	 proper(i) -> ok(i)
1.03/1.10	 proper(nil) -> ok(nil)
1.03/1.10	 proper(o) -> ok(o)
1.03/1.10	 proper(tt) -> ok(tt)
1.03/1.10	 proper(u) -> ok(u)
1.03/1.10	 top(mark(X:S)) -> top(proper(X:S))
1.03/1.10	 top(ok(X:S)) -> top(active(X:S))
1.03/1.10	->->Cycle:
1.03/1.10	->->-> Pairs:
1.03/1.10	 __#(mark(X1:S),X2:S) -> __#(X1:S,X2:S)
1.03/1.10	 __#(ok(X1:S),ok(X2:S)) -> __#(X1:S,X2:S)
1.03/1.10	 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S)
1.03/1.10	->->-> Rules:
1.03/1.10	 U11(mark(X:S)) -> mark(U11(X:S))
1.03/1.10	 U11(ok(X:S)) -> ok(U11(X:S))
1.03/1.10	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.03/1.10	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.03/1.10	 U22(mark(X:S)) -> mark(U22(X:S))
1.03/1.10	 U22(ok(X:S)) -> ok(U22(X:S))
1.03/1.10	 U31(mark(X:S)) -> mark(U31(X:S))
1.03/1.10	 U31(ok(X:S)) -> ok(U31(X:S))
1.03/1.10	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.03/1.10	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.03/1.10	 U42(mark(X:S)) -> mark(U42(X:S))
1.03/1.10	 U42(ok(X:S)) -> ok(U42(X:S))
1.03/1.10	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.03/1.10	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.03/1.10	 U52(mark(X:S)) -> mark(U52(X:S))
1.03/1.10	 U52(ok(X:S)) -> ok(U52(X:S))
1.03/1.10	 U61(mark(X:S)) -> mark(U61(X:S))
1.03/1.10	 U61(ok(X:S)) -> ok(U61(X:S))
1.03/1.10	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.03/1.10	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.03/1.10	 U72(mark(X:S)) -> mark(U72(X:S))
1.03/1.10	 U72(ok(X:S)) -> ok(U72(X:S))
1.03/1.10	 U81(mark(X:S)) -> mark(U81(X:S))
1.03/1.10	 U81(ok(X:S)) -> ok(U81(X:S))
1.03/1.10	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.03/1.10	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.03/1.10	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.03/1.10	 active(U11(tt)) -> mark(tt)
1.03/1.10	 active(U11(X:S)) -> U11(active(X:S))
1.03/1.10	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.03/1.10	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.03/1.10	 active(U22(tt)) -> mark(tt)
1.03/1.10	 active(U22(X:S)) -> U22(active(X:S))
1.03/1.10	 active(U31(tt)) -> mark(tt)
1.03/1.10	 active(U31(X:S)) -> U31(active(X:S))
1.03/1.10	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.03/1.10	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.03/1.10	 active(U42(tt)) -> mark(tt)
1.03/1.10	 active(U42(X:S)) -> U42(active(X:S))
1.03/1.10	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.03/1.10	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.03/1.10	 active(U52(tt)) -> mark(tt)
1.03/1.10	 active(U52(X:S)) -> U52(active(X:S))
1.03/1.10	 active(U61(tt)) -> mark(tt)
1.03/1.10	 active(U61(X:S)) -> U61(active(X:S))
1.03/1.10	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.03/1.10	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.03/1.10	 active(U72(tt)) -> mark(tt)
1.03/1.10	 active(U72(X:S)) -> U72(active(X:S))
1.03/1.10	 active(U81(tt)) -> mark(tt)
1.03/1.10	 active(U81(X:S)) -> U81(active(X:S))
1.03/1.10	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.03/1.10	 active(__(nil,X:S)) -> mark(X:S)
1.03/1.10	 active(__(X:S,nil)) -> mark(X:S)
1.03/1.10	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.03/1.10	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.03/1.10	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.03/1.10	 active(isList(nil)) -> mark(tt)
1.03/1.10	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.03/1.10	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.03/1.10	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.03/1.10	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.03/1.10	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.03/1.10	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.03/1.10	 active(isPal(nil)) -> mark(tt)
1.03/1.10	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.03/1.10	 active(isQid(a)) -> mark(tt)
1.03/1.10	 active(isQid(e)) -> mark(tt)
1.03/1.10	 active(isQid(i)) -> mark(tt)
1.03/1.10	 active(isQid(o)) -> mark(tt)
1.03/1.10	 active(isQid(u)) -> mark(tt)
1.03/1.10	 isList(ok(X:S)) -> ok(isList(X:S))
1.03/1.10	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.03/1.10	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.03/1.10	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.03/1.10	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.03/1.10	 proper(U11(X:S)) -> U11(proper(X:S))
1.03/1.10	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U22(X:S)) -> U22(proper(X:S))
1.03/1.10	 proper(U31(X:S)) -> U31(proper(X:S))
1.03/1.10	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U42(X:S)) -> U42(proper(X:S))
1.03/1.10	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U52(X:S)) -> U52(proper(X:S))
1.03/1.10	 proper(U61(X:S)) -> U61(proper(X:S))
1.03/1.10	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U72(X:S)) -> U72(proper(X:S))
1.03/1.10	 proper(U81(X:S)) -> U81(proper(X:S))
1.03/1.10	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(isList(X:S)) -> isList(proper(X:S))
1.03/1.10	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.03/1.10	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.03/1.10	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.03/1.10	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.03/1.10	 proper(a) -> ok(a)
1.03/1.10	 proper(e) -> ok(e)
1.03/1.10	 proper(i) -> ok(i)
1.03/1.10	 proper(nil) -> ok(nil)
1.03/1.10	 proper(o) -> ok(o)
1.03/1.10	 proper(tt) -> ok(tt)
1.03/1.10	 proper(u) -> ok(u)
1.03/1.10	 top(mark(X:S)) -> top(proper(X:S))
1.03/1.10	 top(ok(X:S)) -> top(active(X:S))
1.03/1.10	->->Cycle:
1.03/1.10	->->-> Pairs:
1.03/1.10	 U81#(mark(X:S)) -> U81#(X:S)
1.03/1.10	 U81#(ok(X:S)) -> U81#(X:S)
1.03/1.10	->->-> Rules:
1.03/1.10	 U11(mark(X:S)) -> mark(U11(X:S))
1.03/1.10	 U11(ok(X:S)) -> ok(U11(X:S))
1.03/1.10	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.03/1.10	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.03/1.10	 U22(mark(X:S)) -> mark(U22(X:S))
1.03/1.10	 U22(ok(X:S)) -> ok(U22(X:S))
1.03/1.10	 U31(mark(X:S)) -> mark(U31(X:S))
1.03/1.10	 U31(ok(X:S)) -> ok(U31(X:S))
1.03/1.10	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.03/1.10	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.03/1.10	 U42(mark(X:S)) -> mark(U42(X:S))
1.03/1.10	 U42(ok(X:S)) -> ok(U42(X:S))
1.03/1.10	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.03/1.10	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.03/1.10	 U52(mark(X:S)) -> mark(U52(X:S))
1.03/1.10	 U52(ok(X:S)) -> ok(U52(X:S))
1.03/1.10	 U61(mark(X:S)) -> mark(U61(X:S))
1.03/1.10	 U61(ok(X:S)) -> ok(U61(X:S))
1.03/1.10	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.03/1.10	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.03/1.10	 U72(mark(X:S)) -> mark(U72(X:S))
1.03/1.10	 U72(ok(X:S)) -> ok(U72(X:S))
1.03/1.10	 U81(mark(X:S)) -> mark(U81(X:S))
1.03/1.10	 U81(ok(X:S)) -> ok(U81(X:S))
1.03/1.10	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.03/1.10	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.03/1.10	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.03/1.10	 active(U11(tt)) -> mark(tt)
1.03/1.10	 active(U11(X:S)) -> U11(active(X:S))
1.03/1.10	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.03/1.10	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.03/1.10	 active(U22(tt)) -> mark(tt)
1.03/1.10	 active(U22(X:S)) -> U22(active(X:S))
1.03/1.10	 active(U31(tt)) -> mark(tt)
1.03/1.10	 active(U31(X:S)) -> U31(active(X:S))
1.03/1.10	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.03/1.10	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.03/1.10	 active(U42(tt)) -> mark(tt)
1.03/1.10	 active(U42(X:S)) -> U42(active(X:S))
1.03/1.10	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.03/1.10	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.03/1.10	 active(U52(tt)) -> mark(tt)
1.03/1.10	 active(U52(X:S)) -> U52(active(X:S))
1.03/1.10	 active(U61(tt)) -> mark(tt)
1.03/1.10	 active(U61(X:S)) -> U61(active(X:S))
1.03/1.10	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.03/1.10	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.03/1.10	 active(U72(tt)) -> mark(tt)
1.03/1.10	 active(U72(X:S)) -> U72(active(X:S))
1.03/1.10	 active(U81(tt)) -> mark(tt)
1.03/1.10	 active(U81(X:S)) -> U81(active(X:S))
1.03/1.10	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.03/1.10	 active(__(nil,X:S)) -> mark(X:S)
1.03/1.10	 active(__(X:S,nil)) -> mark(X:S)
1.03/1.10	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.03/1.10	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.03/1.10	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.03/1.10	 active(isList(nil)) -> mark(tt)
1.03/1.10	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.03/1.10	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.03/1.10	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.03/1.10	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.03/1.10	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.03/1.10	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.03/1.10	 active(isPal(nil)) -> mark(tt)
1.03/1.10	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.03/1.10	 active(isQid(a)) -> mark(tt)
1.03/1.10	 active(isQid(e)) -> mark(tt)
1.03/1.10	 active(isQid(i)) -> mark(tt)
1.03/1.10	 active(isQid(o)) -> mark(tt)
1.03/1.10	 active(isQid(u)) -> mark(tt)
1.03/1.10	 isList(ok(X:S)) -> ok(isList(X:S))
1.03/1.10	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.03/1.10	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.03/1.10	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.03/1.10	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.03/1.10	 proper(U11(X:S)) -> U11(proper(X:S))
1.03/1.10	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U22(X:S)) -> U22(proper(X:S))
1.03/1.10	 proper(U31(X:S)) -> U31(proper(X:S))
1.03/1.10	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U42(X:S)) -> U42(proper(X:S))
1.03/1.10	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U52(X:S)) -> U52(proper(X:S))
1.03/1.10	 proper(U61(X:S)) -> U61(proper(X:S))
1.03/1.10	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U72(X:S)) -> U72(proper(X:S))
1.03/1.10	 proper(U81(X:S)) -> U81(proper(X:S))
1.03/1.10	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(isList(X:S)) -> isList(proper(X:S))
1.03/1.10	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.03/1.10	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.03/1.10	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.03/1.10	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.03/1.10	 proper(a) -> ok(a)
1.03/1.10	 proper(e) -> ok(e)
1.03/1.10	 proper(i) -> ok(i)
1.03/1.10	 proper(nil) -> ok(nil)
1.03/1.10	 proper(o) -> ok(o)
1.03/1.10	 proper(tt) -> ok(tt)
1.03/1.10	 proper(u) -> ok(u)
1.03/1.10	 top(mark(X:S)) -> top(proper(X:S))
1.03/1.10	 top(ok(X:S)) -> top(active(X:S))
1.03/1.10	->->Cycle:
1.03/1.10	->->-> Pairs:
1.03/1.10	 U72#(mark(X:S)) -> U72#(X:S)
1.03/1.10	 U72#(ok(X:S)) -> U72#(X:S)
1.03/1.10	->->-> Rules:
1.03/1.10	 U11(mark(X:S)) -> mark(U11(X:S))
1.03/1.10	 U11(ok(X:S)) -> ok(U11(X:S))
1.03/1.10	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.03/1.10	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.03/1.10	 U22(mark(X:S)) -> mark(U22(X:S))
1.03/1.10	 U22(ok(X:S)) -> ok(U22(X:S))
1.03/1.10	 U31(mark(X:S)) -> mark(U31(X:S))
1.03/1.10	 U31(ok(X:S)) -> ok(U31(X:S))
1.03/1.10	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.03/1.10	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.03/1.10	 U42(mark(X:S)) -> mark(U42(X:S))
1.03/1.10	 U42(ok(X:S)) -> ok(U42(X:S))
1.03/1.10	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.03/1.10	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.03/1.10	 U52(mark(X:S)) -> mark(U52(X:S))
1.03/1.10	 U52(ok(X:S)) -> ok(U52(X:S))
1.03/1.10	 U61(mark(X:S)) -> mark(U61(X:S))
1.03/1.10	 U61(ok(X:S)) -> ok(U61(X:S))
1.03/1.10	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.03/1.10	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.03/1.10	 U72(mark(X:S)) -> mark(U72(X:S))
1.03/1.10	 U72(ok(X:S)) -> ok(U72(X:S))
1.03/1.10	 U81(mark(X:S)) -> mark(U81(X:S))
1.03/1.10	 U81(ok(X:S)) -> ok(U81(X:S))
1.03/1.10	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.03/1.10	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.03/1.10	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.03/1.10	 active(U11(tt)) -> mark(tt)
1.03/1.10	 active(U11(X:S)) -> U11(active(X:S))
1.03/1.10	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.03/1.10	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.03/1.10	 active(U22(tt)) -> mark(tt)
1.03/1.10	 active(U22(X:S)) -> U22(active(X:S))
1.03/1.10	 active(U31(tt)) -> mark(tt)
1.03/1.10	 active(U31(X:S)) -> U31(active(X:S))
1.03/1.10	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.03/1.10	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.03/1.10	 active(U42(tt)) -> mark(tt)
1.03/1.10	 active(U42(X:S)) -> U42(active(X:S))
1.03/1.10	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.03/1.10	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.03/1.10	 active(U52(tt)) -> mark(tt)
1.03/1.10	 active(U52(X:S)) -> U52(active(X:S))
1.03/1.10	 active(U61(tt)) -> mark(tt)
1.03/1.10	 active(U61(X:S)) -> U61(active(X:S))
1.03/1.10	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.03/1.10	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.03/1.10	 active(U72(tt)) -> mark(tt)
1.03/1.10	 active(U72(X:S)) -> U72(active(X:S))
1.03/1.10	 active(U81(tt)) -> mark(tt)
1.03/1.10	 active(U81(X:S)) -> U81(active(X:S))
1.03/1.10	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.03/1.10	 active(__(nil,X:S)) -> mark(X:S)
1.03/1.10	 active(__(X:S,nil)) -> mark(X:S)
1.03/1.10	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.03/1.10	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.03/1.10	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.03/1.10	 active(isList(nil)) -> mark(tt)
1.03/1.10	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.03/1.10	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.03/1.10	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.03/1.10	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.03/1.10	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.03/1.10	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.03/1.10	 active(isPal(nil)) -> mark(tt)
1.03/1.10	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.03/1.10	 active(isQid(a)) -> mark(tt)
1.03/1.10	 active(isQid(e)) -> mark(tt)
1.03/1.10	 active(isQid(i)) -> mark(tt)
1.03/1.10	 active(isQid(o)) -> mark(tt)
1.03/1.10	 active(isQid(u)) -> mark(tt)
1.03/1.10	 isList(ok(X:S)) -> ok(isList(X:S))
1.03/1.10	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.03/1.10	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.03/1.10	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.03/1.10	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.03/1.10	 proper(U11(X:S)) -> U11(proper(X:S))
1.03/1.10	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U22(X:S)) -> U22(proper(X:S))
1.03/1.10	 proper(U31(X:S)) -> U31(proper(X:S))
1.03/1.10	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U42(X:S)) -> U42(proper(X:S))
1.03/1.10	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U52(X:S)) -> U52(proper(X:S))
1.03/1.10	 proper(U61(X:S)) -> U61(proper(X:S))
1.03/1.10	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U72(X:S)) -> U72(proper(X:S))
1.03/1.10	 proper(U81(X:S)) -> U81(proper(X:S))
1.03/1.10	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(isList(X:S)) -> isList(proper(X:S))
1.03/1.10	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.03/1.10	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.03/1.10	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.03/1.10	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.03/1.10	 proper(a) -> ok(a)
1.03/1.10	 proper(e) -> ok(e)
1.03/1.10	 proper(i) -> ok(i)
1.03/1.10	 proper(nil) -> ok(nil)
1.03/1.10	 proper(o) -> ok(o)
1.03/1.10	 proper(tt) -> ok(tt)
1.03/1.10	 proper(u) -> ok(u)
1.03/1.10	 top(mark(X:S)) -> top(proper(X:S))
1.03/1.10	 top(ok(X:S)) -> top(active(X:S))
1.03/1.10	->->Cycle:
1.03/1.10	->->-> Pairs:
1.03/1.10	 U71#(mark(X1:S),X2:S) -> U71#(X1:S,X2:S)
1.03/1.10	 U71#(ok(X1:S),ok(X2:S)) -> U71#(X1:S,X2:S)
1.03/1.10	->->-> Rules:
1.03/1.10	 U11(mark(X:S)) -> mark(U11(X:S))
1.03/1.10	 U11(ok(X:S)) -> ok(U11(X:S))
1.03/1.10	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.03/1.10	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.03/1.10	 U22(mark(X:S)) -> mark(U22(X:S))
1.03/1.10	 U22(ok(X:S)) -> ok(U22(X:S))
1.03/1.10	 U31(mark(X:S)) -> mark(U31(X:S))
1.03/1.10	 U31(ok(X:S)) -> ok(U31(X:S))
1.03/1.10	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.03/1.10	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.03/1.10	 U42(mark(X:S)) -> mark(U42(X:S))
1.03/1.10	 U42(ok(X:S)) -> ok(U42(X:S))
1.03/1.10	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.03/1.10	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.03/1.10	 U52(mark(X:S)) -> mark(U52(X:S))
1.03/1.10	 U52(ok(X:S)) -> ok(U52(X:S))
1.03/1.10	 U61(mark(X:S)) -> mark(U61(X:S))
1.03/1.10	 U61(ok(X:S)) -> ok(U61(X:S))
1.03/1.10	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.03/1.10	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.03/1.10	 U72(mark(X:S)) -> mark(U72(X:S))
1.03/1.10	 U72(ok(X:S)) -> ok(U72(X:S))
1.03/1.10	 U81(mark(X:S)) -> mark(U81(X:S))
1.03/1.10	 U81(ok(X:S)) -> ok(U81(X:S))
1.03/1.10	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.03/1.10	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.03/1.10	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.03/1.10	 active(U11(tt)) -> mark(tt)
1.03/1.10	 active(U11(X:S)) -> U11(active(X:S))
1.03/1.10	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.03/1.10	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.03/1.10	 active(U22(tt)) -> mark(tt)
1.03/1.10	 active(U22(X:S)) -> U22(active(X:S))
1.03/1.10	 active(U31(tt)) -> mark(tt)
1.03/1.10	 active(U31(X:S)) -> U31(active(X:S))
1.03/1.10	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.03/1.10	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.03/1.10	 active(U42(tt)) -> mark(tt)
1.03/1.10	 active(U42(X:S)) -> U42(active(X:S))
1.03/1.10	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.03/1.10	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.03/1.10	 active(U52(tt)) -> mark(tt)
1.03/1.10	 active(U52(X:S)) -> U52(active(X:S))
1.03/1.10	 active(U61(tt)) -> mark(tt)
1.03/1.10	 active(U61(X:S)) -> U61(active(X:S))
1.03/1.10	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.03/1.10	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.03/1.10	 active(U72(tt)) -> mark(tt)
1.03/1.10	 active(U72(X:S)) -> U72(active(X:S))
1.03/1.10	 active(U81(tt)) -> mark(tt)
1.03/1.10	 active(U81(X:S)) -> U81(active(X:S))
1.03/1.10	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.03/1.10	 active(__(nil,X:S)) -> mark(X:S)
1.03/1.10	 active(__(X:S,nil)) -> mark(X:S)
1.03/1.10	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.03/1.10	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.03/1.10	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.03/1.10	 active(isList(nil)) -> mark(tt)
1.03/1.10	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.03/1.10	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.03/1.10	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.03/1.10	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.03/1.10	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.03/1.10	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.03/1.10	 active(isPal(nil)) -> mark(tt)
1.03/1.10	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.03/1.10	 active(isQid(a)) -> mark(tt)
1.03/1.10	 active(isQid(e)) -> mark(tt)
1.03/1.10	 active(isQid(i)) -> mark(tt)
1.03/1.10	 active(isQid(o)) -> mark(tt)
1.03/1.10	 active(isQid(u)) -> mark(tt)
1.03/1.10	 isList(ok(X:S)) -> ok(isList(X:S))
1.03/1.10	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.03/1.10	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.03/1.10	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.03/1.10	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.03/1.10	 proper(U11(X:S)) -> U11(proper(X:S))
1.03/1.10	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U22(X:S)) -> U22(proper(X:S))
1.03/1.10	 proper(U31(X:S)) -> U31(proper(X:S))
1.03/1.10	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U42(X:S)) -> U42(proper(X:S))
1.03/1.10	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U52(X:S)) -> U52(proper(X:S))
1.03/1.10	 proper(U61(X:S)) -> U61(proper(X:S))
1.03/1.10	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U72(X:S)) -> U72(proper(X:S))
1.03/1.10	 proper(U81(X:S)) -> U81(proper(X:S))
1.03/1.10	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(isList(X:S)) -> isList(proper(X:S))
1.03/1.10	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.03/1.10	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.03/1.10	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.03/1.10	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.03/1.10	 proper(a) -> ok(a)
1.03/1.10	 proper(e) -> ok(e)
1.03/1.10	 proper(i) -> ok(i)
1.03/1.10	 proper(nil) -> ok(nil)
1.03/1.10	 proper(o) -> ok(o)
1.03/1.10	 proper(tt) -> ok(tt)
1.03/1.10	 proper(u) -> ok(u)
1.03/1.10	 top(mark(X:S)) -> top(proper(X:S))
1.03/1.10	 top(ok(X:S)) -> top(active(X:S))
1.03/1.10	->->Cycle:
1.03/1.10	->->-> Pairs:
1.03/1.10	 U61#(mark(X:S)) -> U61#(X:S)
1.03/1.10	 U61#(ok(X:S)) -> U61#(X:S)
1.03/1.10	->->-> Rules:
1.03/1.10	 U11(mark(X:S)) -> mark(U11(X:S))
1.03/1.10	 U11(ok(X:S)) -> ok(U11(X:S))
1.03/1.10	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.03/1.10	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.03/1.10	 U22(mark(X:S)) -> mark(U22(X:S))
1.03/1.10	 U22(ok(X:S)) -> ok(U22(X:S))
1.03/1.10	 U31(mark(X:S)) -> mark(U31(X:S))
1.03/1.10	 U31(ok(X:S)) -> ok(U31(X:S))
1.03/1.10	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.03/1.10	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.03/1.10	 U42(mark(X:S)) -> mark(U42(X:S))
1.03/1.10	 U42(ok(X:S)) -> ok(U42(X:S))
1.03/1.10	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.03/1.10	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.03/1.10	 U52(mark(X:S)) -> mark(U52(X:S))
1.03/1.10	 U52(ok(X:S)) -> ok(U52(X:S))
1.03/1.10	 U61(mark(X:S)) -> mark(U61(X:S))
1.03/1.10	 U61(ok(X:S)) -> ok(U61(X:S))
1.03/1.10	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.03/1.10	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.03/1.10	 U72(mark(X:S)) -> mark(U72(X:S))
1.03/1.10	 U72(ok(X:S)) -> ok(U72(X:S))
1.03/1.10	 U81(mark(X:S)) -> mark(U81(X:S))
1.03/1.10	 U81(ok(X:S)) -> ok(U81(X:S))
1.03/1.10	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.03/1.10	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.03/1.10	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.03/1.10	 active(U11(tt)) -> mark(tt)
1.03/1.10	 active(U11(X:S)) -> U11(active(X:S))
1.03/1.10	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.03/1.10	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.03/1.10	 active(U22(tt)) -> mark(tt)
1.03/1.10	 active(U22(X:S)) -> U22(active(X:S))
1.03/1.10	 active(U31(tt)) -> mark(tt)
1.03/1.10	 active(U31(X:S)) -> U31(active(X:S))
1.03/1.10	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.03/1.10	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.03/1.10	 active(U42(tt)) -> mark(tt)
1.03/1.10	 active(U42(X:S)) -> U42(active(X:S))
1.03/1.10	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.03/1.10	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.03/1.10	 active(U52(tt)) -> mark(tt)
1.03/1.10	 active(U52(X:S)) -> U52(active(X:S))
1.03/1.10	 active(U61(tt)) -> mark(tt)
1.03/1.10	 active(U61(X:S)) -> U61(active(X:S))
1.03/1.10	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.03/1.10	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.03/1.10	 active(U72(tt)) -> mark(tt)
1.03/1.10	 active(U72(X:S)) -> U72(active(X:S))
1.03/1.10	 active(U81(tt)) -> mark(tt)
1.03/1.10	 active(U81(X:S)) -> U81(active(X:S))
1.03/1.10	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.03/1.10	 active(__(nil,X:S)) -> mark(X:S)
1.03/1.10	 active(__(X:S,nil)) -> mark(X:S)
1.03/1.10	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.03/1.10	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.03/1.10	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.03/1.10	 active(isList(nil)) -> mark(tt)
1.03/1.10	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.03/1.10	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.03/1.10	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.03/1.10	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.03/1.10	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.03/1.10	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.03/1.10	 active(isPal(nil)) -> mark(tt)
1.03/1.10	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.03/1.10	 active(isQid(a)) -> mark(tt)
1.03/1.10	 active(isQid(e)) -> mark(tt)
1.03/1.10	 active(isQid(i)) -> mark(tt)
1.03/1.10	 active(isQid(o)) -> mark(tt)
1.03/1.10	 active(isQid(u)) -> mark(tt)
1.03/1.10	 isList(ok(X:S)) -> ok(isList(X:S))
1.03/1.10	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.03/1.10	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.03/1.10	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.03/1.10	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.03/1.10	 proper(U11(X:S)) -> U11(proper(X:S))
1.03/1.10	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U22(X:S)) -> U22(proper(X:S))
1.03/1.10	 proper(U31(X:S)) -> U31(proper(X:S))
1.03/1.10	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U42(X:S)) -> U42(proper(X:S))
1.03/1.10	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U52(X:S)) -> U52(proper(X:S))
1.03/1.10	 proper(U61(X:S)) -> U61(proper(X:S))
1.03/1.10	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U72(X:S)) -> U72(proper(X:S))
1.03/1.10	 proper(U81(X:S)) -> U81(proper(X:S))
1.03/1.10	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(isList(X:S)) -> isList(proper(X:S))
1.03/1.10	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.03/1.10	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.03/1.10	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.03/1.10	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.03/1.10	 proper(a) -> ok(a)
1.03/1.10	 proper(e) -> ok(e)
1.03/1.10	 proper(i) -> ok(i)
1.03/1.10	 proper(nil) -> ok(nil)
1.03/1.10	 proper(o) -> ok(o)
1.03/1.10	 proper(tt) -> ok(tt)
1.03/1.10	 proper(u) -> ok(u)
1.03/1.10	 top(mark(X:S)) -> top(proper(X:S))
1.03/1.10	 top(ok(X:S)) -> top(active(X:S))
1.03/1.10	->->Cycle:
1.03/1.10	->->-> Pairs:
1.03/1.10	 U52#(mark(X:S)) -> U52#(X:S)
1.03/1.10	 U52#(ok(X:S)) -> U52#(X:S)
1.03/1.10	->->-> Rules:
1.03/1.10	 U11(mark(X:S)) -> mark(U11(X:S))
1.03/1.10	 U11(ok(X:S)) -> ok(U11(X:S))
1.03/1.10	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.03/1.10	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.03/1.10	 U22(mark(X:S)) -> mark(U22(X:S))
1.03/1.10	 U22(ok(X:S)) -> ok(U22(X:S))
1.03/1.10	 U31(mark(X:S)) -> mark(U31(X:S))
1.03/1.10	 U31(ok(X:S)) -> ok(U31(X:S))
1.03/1.10	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.03/1.10	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.03/1.10	 U42(mark(X:S)) -> mark(U42(X:S))
1.03/1.10	 U42(ok(X:S)) -> ok(U42(X:S))
1.03/1.10	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.03/1.10	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.03/1.10	 U52(mark(X:S)) -> mark(U52(X:S))
1.03/1.10	 U52(ok(X:S)) -> ok(U52(X:S))
1.03/1.10	 U61(mark(X:S)) -> mark(U61(X:S))
1.03/1.10	 U61(ok(X:S)) -> ok(U61(X:S))
1.03/1.10	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.03/1.10	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.03/1.10	 U72(mark(X:S)) -> mark(U72(X:S))
1.03/1.10	 U72(ok(X:S)) -> ok(U72(X:S))
1.03/1.10	 U81(mark(X:S)) -> mark(U81(X:S))
1.03/1.10	 U81(ok(X:S)) -> ok(U81(X:S))
1.03/1.10	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.03/1.10	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.03/1.10	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.03/1.10	 active(U11(tt)) -> mark(tt)
1.03/1.10	 active(U11(X:S)) -> U11(active(X:S))
1.03/1.10	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.03/1.10	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.03/1.10	 active(U22(tt)) -> mark(tt)
1.03/1.10	 active(U22(X:S)) -> U22(active(X:S))
1.03/1.10	 active(U31(tt)) -> mark(tt)
1.03/1.10	 active(U31(X:S)) -> U31(active(X:S))
1.03/1.10	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.03/1.10	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.03/1.10	 active(U42(tt)) -> mark(tt)
1.03/1.10	 active(U42(X:S)) -> U42(active(X:S))
1.03/1.10	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.03/1.10	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.03/1.10	 active(U52(tt)) -> mark(tt)
1.03/1.10	 active(U52(X:S)) -> U52(active(X:S))
1.03/1.10	 active(U61(tt)) -> mark(tt)
1.03/1.10	 active(U61(X:S)) -> U61(active(X:S))
1.03/1.10	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.03/1.10	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.03/1.10	 active(U72(tt)) -> mark(tt)
1.03/1.10	 active(U72(X:S)) -> U72(active(X:S))
1.03/1.10	 active(U81(tt)) -> mark(tt)
1.03/1.10	 active(U81(X:S)) -> U81(active(X:S))
1.03/1.10	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.03/1.10	 active(__(nil,X:S)) -> mark(X:S)
1.03/1.10	 active(__(X:S,nil)) -> mark(X:S)
1.03/1.10	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.03/1.10	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.03/1.10	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.03/1.10	 active(isList(nil)) -> mark(tt)
1.03/1.10	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.03/1.10	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.03/1.10	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.03/1.10	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.03/1.10	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.03/1.10	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.03/1.10	 active(isPal(nil)) -> mark(tt)
1.03/1.10	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.03/1.10	 active(isQid(a)) -> mark(tt)
1.03/1.10	 active(isQid(e)) -> mark(tt)
1.03/1.10	 active(isQid(i)) -> mark(tt)
1.03/1.10	 active(isQid(o)) -> mark(tt)
1.03/1.10	 active(isQid(u)) -> mark(tt)
1.03/1.10	 isList(ok(X:S)) -> ok(isList(X:S))
1.03/1.10	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.03/1.10	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.03/1.10	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.03/1.10	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.03/1.10	 proper(U11(X:S)) -> U11(proper(X:S))
1.03/1.10	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U22(X:S)) -> U22(proper(X:S))
1.03/1.10	 proper(U31(X:S)) -> U31(proper(X:S))
1.03/1.10	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U42(X:S)) -> U42(proper(X:S))
1.03/1.10	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U52(X:S)) -> U52(proper(X:S))
1.03/1.10	 proper(U61(X:S)) -> U61(proper(X:S))
1.03/1.10	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U72(X:S)) -> U72(proper(X:S))
1.03/1.10	 proper(U81(X:S)) -> U81(proper(X:S))
1.03/1.10	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(isList(X:S)) -> isList(proper(X:S))
1.03/1.10	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.03/1.10	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.03/1.10	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.03/1.10	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.03/1.10	 proper(a) -> ok(a)
1.03/1.10	 proper(e) -> ok(e)
1.03/1.10	 proper(i) -> ok(i)
1.03/1.10	 proper(nil) -> ok(nil)
1.03/1.10	 proper(o) -> ok(o)
1.03/1.10	 proper(tt) -> ok(tt)
1.03/1.10	 proper(u) -> ok(u)
1.03/1.10	 top(mark(X:S)) -> top(proper(X:S))
1.03/1.10	 top(ok(X:S)) -> top(active(X:S))
1.03/1.10	->->Cycle:
1.03/1.10	->->-> Pairs:
1.03/1.10	 U51#(mark(X1:S),X2:S) -> U51#(X1:S,X2:S)
1.03/1.10	 U51#(ok(X1:S),ok(X2:S)) -> U51#(X1:S,X2:S)
1.03/1.10	->->-> Rules:
1.03/1.10	 U11(mark(X:S)) -> mark(U11(X:S))
1.03/1.10	 U11(ok(X:S)) -> ok(U11(X:S))
1.03/1.10	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.03/1.10	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.03/1.10	 U22(mark(X:S)) -> mark(U22(X:S))
1.03/1.10	 U22(ok(X:S)) -> ok(U22(X:S))
1.03/1.10	 U31(mark(X:S)) -> mark(U31(X:S))
1.03/1.10	 U31(ok(X:S)) -> ok(U31(X:S))
1.03/1.10	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.03/1.10	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.03/1.10	 U42(mark(X:S)) -> mark(U42(X:S))
1.03/1.10	 U42(ok(X:S)) -> ok(U42(X:S))
1.03/1.10	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.03/1.10	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.03/1.10	 U52(mark(X:S)) -> mark(U52(X:S))
1.03/1.10	 U52(ok(X:S)) -> ok(U52(X:S))
1.03/1.10	 U61(mark(X:S)) -> mark(U61(X:S))
1.03/1.10	 U61(ok(X:S)) -> ok(U61(X:S))
1.03/1.10	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.03/1.10	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.03/1.10	 U72(mark(X:S)) -> mark(U72(X:S))
1.03/1.10	 U72(ok(X:S)) -> ok(U72(X:S))
1.03/1.10	 U81(mark(X:S)) -> mark(U81(X:S))
1.03/1.10	 U81(ok(X:S)) -> ok(U81(X:S))
1.03/1.10	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.03/1.10	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.03/1.10	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.03/1.10	 active(U11(tt)) -> mark(tt)
1.03/1.10	 active(U11(X:S)) -> U11(active(X:S))
1.03/1.10	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.03/1.10	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.03/1.10	 active(U22(tt)) -> mark(tt)
1.03/1.10	 active(U22(X:S)) -> U22(active(X:S))
1.03/1.10	 active(U31(tt)) -> mark(tt)
1.03/1.10	 active(U31(X:S)) -> U31(active(X:S))
1.03/1.10	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.03/1.10	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.03/1.10	 active(U42(tt)) -> mark(tt)
1.03/1.10	 active(U42(X:S)) -> U42(active(X:S))
1.03/1.10	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.03/1.10	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.03/1.10	 active(U52(tt)) -> mark(tt)
1.03/1.10	 active(U52(X:S)) -> U52(active(X:S))
1.03/1.10	 active(U61(tt)) -> mark(tt)
1.03/1.10	 active(U61(X:S)) -> U61(active(X:S))
1.03/1.10	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.03/1.10	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.03/1.10	 active(U72(tt)) -> mark(tt)
1.03/1.10	 active(U72(X:S)) -> U72(active(X:S))
1.03/1.10	 active(U81(tt)) -> mark(tt)
1.03/1.10	 active(U81(X:S)) -> U81(active(X:S))
1.03/1.10	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.03/1.10	 active(__(nil,X:S)) -> mark(X:S)
1.03/1.10	 active(__(X:S,nil)) -> mark(X:S)
1.03/1.10	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.03/1.10	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.03/1.10	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.03/1.10	 active(isList(nil)) -> mark(tt)
1.03/1.10	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.03/1.10	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.03/1.10	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.03/1.10	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.03/1.10	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.03/1.10	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.03/1.10	 active(isPal(nil)) -> mark(tt)
1.03/1.10	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.03/1.10	 active(isQid(a)) -> mark(tt)
1.03/1.10	 active(isQid(e)) -> mark(tt)
1.03/1.10	 active(isQid(i)) -> mark(tt)
1.03/1.10	 active(isQid(o)) -> mark(tt)
1.03/1.10	 active(isQid(u)) -> mark(tt)
1.03/1.10	 isList(ok(X:S)) -> ok(isList(X:S))
1.03/1.10	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.03/1.10	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.03/1.10	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.03/1.10	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.03/1.10	 proper(U11(X:S)) -> U11(proper(X:S))
1.03/1.10	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U22(X:S)) -> U22(proper(X:S))
1.03/1.10	 proper(U31(X:S)) -> U31(proper(X:S))
1.03/1.10	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U42(X:S)) -> U42(proper(X:S))
1.03/1.10	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U52(X:S)) -> U52(proper(X:S))
1.03/1.10	 proper(U61(X:S)) -> U61(proper(X:S))
1.03/1.10	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U72(X:S)) -> U72(proper(X:S))
1.03/1.10	 proper(U81(X:S)) -> U81(proper(X:S))
1.03/1.10	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(isList(X:S)) -> isList(proper(X:S))
1.03/1.10	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.03/1.10	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.03/1.10	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.03/1.10	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.03/1.10	 proper(a) -> ok(a)
1.03/1.10	 proper(e) -> ok(e)
1.03/1.10	 proper(i) -> ok(i)
1.03/1.10	 proper(nil) -> ok(nil)
1.03/1.10	 proper(o) -> ok(o)
1.03/1.10	 proper(tt) -> ok(tt)
1.03/1.10	 proper(u) -> ok(u)
1.03/1.10	 top(mark(X:S)) -> top(proper(X:S))
1.03/1.10	 top(ok(X:S)) -> top(active(X:S))
1.03/1.10	->->Cycle:
1.03/1.10	->->-> Pairs:
1.03/1.10	 U42#(mark(X:S)) -> U42#(X:S)
1.03/1.10	 U42#(ok(X:S)) -> U42#(X:S)
1.03/1.10	->->-> Rules:
1.03/1.10	 U11(mark(X:S)) -> mark(U11(X:S))
1.03/1.10	 U11(ok(X:S)) -> ok(U11(X:S))
1.03/1.10	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.03/1.10	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.03/1.10	 U22(mark(X:S)) -> mark(U22(X:S))
1.03/1.10	 U22(ok(X:S)) -> ok(U22(X:S))
1.03/1.10	 U31(mark(X:S)) -> mark(U31(X:S))
1.03/1.10	 U31(ok(X:S)) -> ok(U31(X:S))
1.03/1.10	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.03/1.10	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.03/1.10	 U42(mark(X:S)) -> mark(U42(X:S))
1.03/1.10	 U42(ok(X:S)) -> ok(U42(X:S))
1.03/1.10	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.03/1.10	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.03/1.10	 U52(mark(X:S)) -> mark(U52(X:S))
1.03/1.10	 U52(ok(X:S)) -> ok(U52(X:S))
1.03/1.10	 U61(mark(X:S)) -> mark(U61(X:S))
1.03/1.10	 U61(ok(X:S)) -> ok(U61(X:S))
1.03/1.10	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.03/1.10	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.03/1.10	 U72(mark(X:S)) -> mark(U72(X:S))
1.03/1.10	 U72(ok(X:S)) -> ok(U72(X:S))
1.03/1.10	 U81(mark(X:S)) -> mark(U81(X:S))
1.03/1.10	 U81(ok(X:S)) -> ok(U81(X:S))
1.03/1.10	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.03/1.10	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.03/1.10	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.03/1.10	 active(U11(tt)) -> mark(tt)
1.03/1.10	 active(U11(X:S)) -> U11(active(X:S))
1.03/1.10	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.03/1.10	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.03/1.10	 active(U22(tt)) -> mark(tt)
1.03/1.10	 active(U22(X:S)) -> U22(active(X:S))
1.03/1.10	 active(U31(tt)) -> mark(tt)
1.03/1.10	 active(U31(X:S)) -> U31(active(X:S))
1.03/1.10	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.03/1.10	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.03/1.10	 active(U42(tt)) -> mark(tt)
1.03/1.10	 active(U42(X:S)) -> U42(active(X:S))
1.03/1.10	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.03/1.10	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.03/1.10	 active(U52(tt)) -> mark(tt)
1.03/1.10	 active(U52(X:S)) -> U52(active(X:S))
1.03/1.10	 active(U61(tt)) -> mark(tt)
1.03/1.10	 active(U61(X:S)) -> U61(active(X:S))
1.03/1.10	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.03/1.10	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.03/1.10	 active(U72(tt)) -> mark(tt)
1.03/1.10	 active(U72(X:S)) -> U72(active(X:S))
1.03/1.10	 active(U81(tt)) -> mark(tt)
1.03/1.10	 active(U81(X:S)) -> U81(active(X:S))
1.03/1.10	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.03/1.10	 active(__(nil,X:S)) -> mark(X:S)
1.03/1.10	 active(__(X:S,nil)) -> mark(X:S)
1.03/1.10	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.03/1.10	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.03/1.10	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.03/1.10	 active(isList(nil)) -> mark(tt)
1.03/1.10	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.03/1.10	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.03/1.10	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.03/1.10	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.03/1.10	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.03/1.10	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.03/1.10	 active(isPal(nil)) -> mark(tt)
1.03/1.10	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.03/1.10	 active(isQid(a)) -> mark(tt)
1.03/1.10	 active(isQid(e)) -> mark(tt)
1.03/1.10	 active(isQid(i)) -> mark(tt)
1.03/1.10	 active(isQid(o)) -> mark(tt)
1.03/1.10	 active(isQid(u)) -> mark(tt)
1.03/1.10	 isList(ok(X:S)) -> ok(isList(X:S))
1.03/1.10	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.03/1.10	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.03/1.10	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.03/1.10	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.03/1.10	 proper(U11(X:S)) -> U11(proper(X:S))
1.03/1.10	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U22(X:S)) -> U22(proper(X:S))
1.03/1.10	 proper(U31(X:S)) -> U31(proper(X:S))
1.03/1.10	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U42(X:S)) -> U42(proper(X:S))
1.03/1.10	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U52(X:S)) -> U52(proper(X:S))
1.03/1.10	 proper(U61(X:S)) -> U61(proper(X:S))
1.03/1.10	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U72(X:S)) -> U72(proper(X:S))
1.03/1.10	 proper(U81(X:S)) -> U81(proper(X:S))
1.03/1.10	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(isList(X:S)) -> isList(proper(X:S))
1.03/1.10	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.03/1.10	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.03/1.10	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.03/1.10	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.03/1.10	 proper(a) -> ok(a)
1.03/1.10	 proper(e) -> ok(e)
1.03/1.10	 proper(i) -> ok(i)
1.03/1.10	 proper(nil) -> ok(nil)
1.03/1.10	 proper(o) -> ok(o)
1.03/1.10	 proper(tt) -> ok(tt)
1.03/1.10	 proper(u) -> ok(u)
1.03/1.10	 top(mark(X:S)) -> top(proper(X:S))
1.03/1.10	 top(ok(X:S)) -> top(active(X:S))
1.03/1.10	->->Cycle:
1.03/1.10	->->-> Pairs:
1.03/1.10	 U41#(mark(X1:S),X2:S) -> U41#(X1:S,X2:S)
1.03/1.10	 U41#(ok(X1:S),ok(X2:S)) -> U41#(X1:S,X2:S)
1.03/1.10	->->-> Rules:
1.03/1.10	 U11(mark(X:S)) -> mark(U11(X:S))
1.03/1.10	 U11(ok(X:S)) -> ok(U11(X:S))
1.03/1.10	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.03/1.10	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.03/1.10	 U22(mark(X:S)) -> mark(U22(X:S))
1.03/1.10	 U22(ok(X:S)) -> ok(U22(X:S))
1.03/1.10	 U31(mark(X:S)) -> mark(U31(X:S))
1.03/1.10	 U31(ok(X:S)) -> ok(U31(X:S))
1.03/1.10	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.03/1.10	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.03/1.10	 U42(mark(X:S)) -> mark(U42(X:S))
1.03/1.10	 U42(ok(X:S)) -> ok(U42(X:S))
1.03/1.10	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.03/1.10	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.03/1.10	 U52(mark(X:S)) -> mark(U52(X:S))
1.03/1.10	 U52(ok(X:S)) -> ok(U52(X:S))
1.03/1.10	 U61(mark(X:S)) -> mark(U61(X:S))
1.03/1.10	 U61(ok(X:S)) -> ok(U61(X:S))
1.03/1.10	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.03/1.10	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.03/1.10	 U72(mark(X:S)) -> mark(U72(X:S))
1.03/1.10	 U72(ok(X:S)) -> ok(U72(X:S))
1.03/1.10	 U81(mark(X:S)) -> mark(U81(X:S))
1.03/1.10	 U81(ok(X:S)) -> ok(U81(X:S))
1.03/1.10	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.03/1.10	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.03/1.10	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.03/1.10	 active(U11(tt)) -> mark(tt)
1.03/1.10	 active(U11(X:S)) -> U11(active(X:S))
1.03/1.10	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.03/1.10	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.03/1.10	 active(U22(tt)) -> mark(tt)
1.03/1.10	 active(U22(X:S)) -> U22(active(X:S))
1.03/1.10	 active(U31(tt)) -> mark(tt)
1.03/1.10	 active(U31(X:S)) -> U31(active(X:S))
1.03/1.10	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.03/1.10	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.03/1.10	 active(U42(tt)) -> mark(tt)
1.03/1.10	 active(U42(X:S)) -> U42(active(X:S))
1.03/1.10	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.03/1.10	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.03/1.10	 active(U52(tt)) -> mark(tt)
1.03/1.10	 active(U52(X:S)) -> U52(active(X:S))
1.03/1.10	 active(U61(tt)) -> mark(tt)
1.03/1.10	 active(U61(X:S)) -> U61(active(X:S))
1.03/1.10	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.03/1.10	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.03/1.10	 active(U72(tt)) -> mark(tt)
1.03/1.10	 active(U72(X:S)) -> U72(active(X:S))
1.03/1.10	 active(U81(tt)) -> mark(tt)
1.03/1.10	 active(U81(X:S)) -> U81(active(X:S))
1.03/1.10	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.03/1.10	 active(__(nil,X:S)) -> mark(X:S)
1.03/1.10	 active(__(X:S,nil)) -> mark(X:S)
1.03/1.10	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.03/1.10	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.03/1.10	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.03/1.10	 active(isList(nil)) -> mark(tt)
1.03/1.10	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.03/1.10	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.03/1.10	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.03/1.10	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.03/1.10	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.03/1.10	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.03/1.10	 active(isPal(nil)) -> mark(tt)
1.03/1.10	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.03/1.10	 active(isQid(a)) -> mark(tt)
1.03/1.10	 active(isQid(e)) -> mark(tt)
1.03/1.10	 active(isQid(i)) -> mark(tt)
1.03/1.10	 active(isQid(o)) -> mark(tt)
1.03/1.10	 active(isQid(u)) -> mark(tt)
1.03/1.10	 isList(ok(X:S)) -> ok(isList(X:S))
1.03/1.10	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.03/1.10	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.03/1.10	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.03/1.10	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.03/1.10	 proper(U11(X:S)) -> U11(proper(X:S))
1.03/1.10	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U22(X:S)) -> U22(proper(X:S))
1.03/1.10	 proper(U31(X:S)) -> U31(proper(X:S))
1.03/1.10	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U42(X:S)) -> U42(proper(X:S))
1.03/1.10	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U52(X:S)) -> U52(proper(X:S))
1.03/1.10	 proper(U61(X:S)) -> U61(proper(X:S))
1.03/1.10	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U72(X:S)) -> U72(proper(X:S))
1.03/1.10	 proper(U81(X:S)) -> U81(proper(X:S))
1.03/1.10	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(isList(X:S)) -> isList(proper(X:S))
1.03/1.10	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.03/1.10	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.03/1.10	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.03/1.10	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.03/1.10	 proper(a) -> ok(a)
1.03/1.10	 proper(e) -> ok(e)
1.03/1.10	 proper(i) -> ok(i)
1.03/1.10	 proper(nil) -> ok(nil)
1.03/1.10	 proper(o) -> ok(o)
1.03/1.10	 proper(tt) -> ok(tt)
1.03/1.10	 proper(u) -> ok(u)
1.03/1.10	 top(mark(X:S)) -> top(proper(X:S))
1.03/1.10	 top(ok(X:S)) -> top(active(X:S))
1.03/1.10	->->Cycle:
1.03/1.10	->->-> Pairs:
1.03/1.10	 U31#(mark(X:S)) -> U31#(X:S)
1.03/1.10	 U31#(ok(X:S)) -> U31#(X:S)
1.03/1.10	->->-> Rules:
1.03/1.10	 U11(mark(X:S)) -> mark(U11(X:S))
1.03/1.10	 U11(ok(X:S)) -> ok(U11(X:S))
1.03/1.10	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.03/1.10	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.03/1.10	 U22(mark(X:S)) -> mark(U22(X:S))
1.03/1.10	 U22(ok(X:S)) -> ok(U22(X:S))
1.03/1.10	 U31(mark(X:S)) -> mark(U31(X:S))
1.03/1.10	 U31(ok(X:S)) -> ok(U31(X:S))
1.03/1.10	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.03/1.10	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.03/1.10	 U42(mark(X:S)) -> mark(U42(X:S))
1.03/1.10	 U42(ok(X:S)) -> ok(U42(X:S))
1.03/1.10	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.03/1.10	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.03/1.10	 U52(mark(X:S)) -> mark(U52(X:S))
1.03/1.10	 U52(ok(X:S)) -> ok(U52(X:S))
1.03/1.10	 U61(mark(X:S)) -> mark(U61(X:S))
1.03/1.10	 U61(ok(X:S)) -> ok(U61(X:S))
1.03/1.10	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.03/1.10	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.03/1.10	 U72(mark(X:S)) -> mark(U72(X:S))
1.03/1.10	 U72(ok(X:S)) -> ok(U72(X:S))
1.03/1.10	 U81(mark(X:S)) -> mark(U81(X:S))
1.03/1.10	 U81(ok(X:S)) -> ok(U81(X:S))
1.03/1.10	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.03/1.10	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.03/1.10	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.03/1.10	 active(U11(tt)) -> mark(tt)
1.03/1.10	 active(U11(X:S)) -> U11(active(X:S))
1.03/1.10	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.03/1.10	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.03/1.10	 active(U22(tt)) -> mark(tt)
1.03/1.10	 active(U22(X:S)) -> U22(active(X:S))
1.03/1.10	 active(U31(tt)) -> mark(tt)
1.03/1.10	 active(U31(X:S)) -> U31(active(X:S))
1.03/1.10	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.03/1.10	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.03/1.10	 active(U42(tt)) -> mark(tt)
1.03/1.10	 active(U42(X:S)) -> U42(active(X:S))
1.03/1.10	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.03/1.10	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.03/1.10	 active(U52(tt)) -> mark(tt)
1.03/1.10	 active(U52(X:S)) -> U52(active(X:S))
1.03/1.10	 active(U61(tt)) -> mark(tt)
1.03/1.10	 active(U61(X:S)) -> U61(active(X:S))
1.03/1.10	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.03/1.10	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.03/1.10	 active(U72(tt)) -> mark(tt)
1.03/1.10	 active(U72(X:S)) -> U72(active(X:S))
1.03/1.10	 active(U81(tt)) -> mark(tt)
1.03/1.10	 active(U81(X:S)) -> U81(active(X:S))
1.03/1.10	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.03/1.10	 active(__(nil,X:S)) -> mark(X:S)
1.03/1.10	 active(__(X:S,nil)) -> mark(X:S)
1.03/1.10	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.03/1.10	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.03/1.10	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.03/1.10	 active(isList(nil)) -> mark(tt)
1.03/1.10	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.03/1.10	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.03/1.10	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.03/1.10	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.03/1.10	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.03/1.10	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.03/1.10	 active(isPal(nil)) -> mark(tt)
1.03/1.10	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.03/1.10	 active(isQid(a)) -> mark(tt)
1.03/1.10	 active(isQid(e)) -> mark(tt)
1.03/1.10	 active(isQid(i)) -> mark(tt)
1.03/1.10	 active(isQid(o)) -> mark(tt)
1.03/1.10	 active(isQid(u)) -> mark(tt)
1.03/1.10	 isList(ok(X:S)) -> ok(isList(X:S))
1.03/1.10	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.03/1.10	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.03/1.10	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.03/1.10	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.03/1.10	 proper(U11(X:S)) -> U11(proper(X:S))
1.03/1.10	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U22(X:S)) -> U22(proper(X:S))
1.03/1.10	 proper(U31(X:S)) -> U31(proper(X:S))
1.03/1.10	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U42(X:S)) -> U42(proper(X:S))
1.03/1.10	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U52(X:S)) -> U52(proper(X:S))
1.03/1.10	 proper(U61(X:S)) -> U61(proper(X:S))
1.03/1.10	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U72(X:S)) -> U72(proper(X:S))
1.03/1.10	 proper(U81(X:S)) -> U81(proper(X:S))
1.03/1.10	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(isList(X:S)) -> isList(proper(X:S))
1.03/1.10	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.03/1.10	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.03/1.10	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.03/1.10	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.03/1.10	 proper(a) -> ok(a)
1.03/1.10	 proper(e) -> ok(e)
1.03/1.10	 proper(i) -> ok(i)
1.03/1.10	 proper(nil) -> ok(nil)
1.03/1.10	 proper(o) -> ok(o)
1.03/1.10	 proper(tt) -> ok(tt)
1.03/1.10	 proper(u) -> ok(u)
1.03/1.10	 top(mark(X:S)) -> top(proper(X:S))
1.03/1.10	 top(ok(X:S)) -> top(active(X:S))
1.03/1.10	->->Cycle:
1.03/1.10	->->-> Pairs:
1.03/1.10	 U22#(mark(X:S)) -> U22#(X:S)
1.03/1.10	 U22#(ok(X:S)) -> U22#(X:S)
1.03/1.10	->->-> Rules:
1.03/1.10	 U11(mark(X:S)) -> mark(U11(X:S))
1.03/1.10	 U11(ok(X:S)) -> ok(U11(X:S))
1.03/1.10	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.03/1.10	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.03/1.10	 U22(mark(X:S)) -> mark(U22(X:S))
1.03/1.10	 U22(ok(X:S)) -> ok(U22(X:S))
1.03/1.10	 U31(mark(X:S)) -> mark(U31(X:S))
1.03/1.10	 U31(ok(X:S)) -> ok(U31(X:S))
1.03/1.10	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.03/1.10	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.03/1.10	 U42(mark(X:S)) -> mark(U42(X:S))
1.03/1.10	 U42(ok(X:S)) -> ok(U42(X:S))
1.03/1.10	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.03/1.10	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.03/1.10	 U52(mark(X:S)) -> mark(U52(X:S))
1.03/1.10	 U52(ok(X:S)) -> ok(U52(X:S))
1.03/1.10	 U61(mark(X:S)) -> mark(U61(X:S))
1.03/1.10	 U61(ok(X:S)) -> ok(U61(X:S))
1.03/1.10	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.03/1.10	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.03/1.10	 U72(mark(X:S)) -> mark(U72(X:S))
1.03/1.10	 U72(ok(X:S)) -> ok(U72(X:S))
1.03/1.10	 U81(mark(X:S)) -> mark(U81(X:S))
1.03/1.10	 U81(ok(X:S)) -> ok(U81(X:S))
1.03/1.10	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.03/1.10	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.03/1.10	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.03/1.10	 active(U11(tt)) -> mark(tt)
1.03/1.10	 active(U11(X:S)) -> U11(active(X:S))
1.03/1.10	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.03/1.10	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.03/1.10	 active(U22(tt)) -> mark(tt)
1.03/1.10	 active(U22(X:S)) -> U22(active(X:S))
1.03/1.10	 active(U31(tt)) -> mark(tt)
1.03/1.10	 active(U31(X:S)) -> U31(active(X:S))
1.03/1.10	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.03/1.10	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.03/1.10	 active(U42(tt)) -> mark(tt)
1.03/1.10	 active(U42(X:S)) -> U42(active(X:S))
1.03/1.10	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.03/1.10	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.03/1.10	 active(U52(tt)) -> mark(tt)
1.03/1.10	 active(U52(X:S)) -> U52(active(X:S))
1.03/1.10	 active(U61(tt)) -> mark(tt)
1.03/1.10	 active(U61(X:S)) -> U61(active(X:S))
1.03/1.10	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.03/1.10	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.03/1.10	 active(U72(tt)) -> mark(tt)
1.03/1.10	 active(U72(X:S)) -> U72(active(X:S))
1.03/1.10	 active(U81(tt)) -> mark(tt)
1.03/1.10	 active(U81(X:S)) -> U81(active(X:S))
1.03/1.10	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.03/1.10	 active(__(nil,X:S)) -> mark(X:S)
1.03/1.10	 active(__(X:S,nil)) -> mark(X:S)
1.03/1.10	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.03/1.10	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.03/1.10	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.03/1.10	 active(isList(nil)) -> mark(tt)
1.03/1.10	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.03/1.10	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.03/1.10	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.03/1.10	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.03/1.10	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.03/1.10	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.03/1.10	 active(isPal(nil)) -> mark(tt)
1.03/1.10	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.03/1.10	 active(isQid(a)) -> mark(tt)
1.03/1.10	 active(isQid(e)) -> mark(tt)
1.03/1.10	 active(isQid(i)) -> mark(tt)
1.03/1.10	 active(isQid(o)) -> mark(tt)
1.03/1.10	 active(isQid(u)) -> mark(tt)
1.03/1.10	 isList(ok(X:S)) -> ok(isList(X:S))
1.03/1.10	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.03/1.10	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.03/1.10	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.03/1.10	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.03/1.10	 proper(U11(X:S)) -> U11(proper(X:S))
1.03/1.10	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U22(X:S)) -> U22(proper(X:S))
1.03/1.10	 proper(U31(X:S)) -> U31(proper(X:S))
1.03/1.10	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U42(X:S)) -> U42(proper(X:S))
1.03/1.10	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U52(X:S)) -> U52(proper(X:S))
1.03/1.10	 proper(U61(X:S)) -> U61(proper(X:S))
1.03/1.10	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U72(X:S)) -> U72(proper(X:S))
1.03/1.10	 proper(U81(X:S)) -> U81(proper(X:S))
1.03/1.10	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(isList(X:S)) -> isList(proper(X:S))
1.03/1.10	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.03/1.10	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.03/1.10	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.03/1.10	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.03/1.10	 proper(a) -> ok(a)
1.03/1.10	 proper(e) -> ok(e)
1.03/1.10	 proper(i) -> ok(i)
1.03/1.10	 proper(nil) -> ok(nil)
1.03/1.10	 proper(o) -> ok(o)
1.03/1.10	 proper(tt) -> ok(tt)
1.03/1.10	 proper(u) -> ok(u)
1.03/1.10	 top(mark(X:S)) -> top(proper(X:S))
1.03/1.10	 top(ok(X:S)) -> top(active(X:S))
1.03/1.10	->->Cycle:
1.03/1.10	->->-> Pairs:
1.03/1.10	 U21#(mark(X1:S),X2:S) -> U21#(X1:S,X2:S)
1.03/1.10	 U21#(ok(X1:S),ok(X2:S)) -> U21#(X1:S,X2:S)
1.03/1.10	->->-> Rules:
1.03/1.10	 U11(mark(X:S)) -> mark(U11(X:S))
1.03/1.10	 U11(ok(X:S)) -> ok(U11(X:S))
1.03/1.10	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.03/1.10	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.03/1.10	 U22(mark(X:S)) -> mark(U22(X:S))
1.03/1.10	 U22(ok(X:S)) -> ok(U22(X:S))
1.03/1.10	 U31(mark(X:S)) -> mark(U31(X:S))
1.03/1.10	 U31(ok(X:S)) -> ok(U31(X:S))
1.03/1.10	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.03/1.10	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.03/1.10	 U42(mark(X:S)) -> mark(U42(X:S))
1.03/1.10	 U42(ok(X:S)) -> ok(U42(X:S))
1.03/1.10	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.03/1.10	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.03/1.10	 U52(mark(X:S)) -> mark(U52(X:S))
1.03/1.10	 U52(ok(X:S)) -> ok(U52(X:S))
1.03/1.10	 U61(mark(X:S)) -> mark(U61(X:S))
1.03/1.10	 U61(ok(X:S)) -> ok(U61(X:S))
1.03/1.10	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.03/1.10	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.03/1.10	 U72(mark(X:S)) -> mark(U72(X:S))
1.03/1.10	 U72(ok(X:S)) -> ok(U72(X:S))
1.03/1.10	 U81(mark(X:S)) -> mark(U81(X:S))
1.03/1.10	 U81(ok(X:S)) -> ok(U81(X:S))
1.03/1.10	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.03/1.10	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.03/1.10	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.03/1.10	 active(U11(tt)) -> mark(tt)
1.03/1.10	 active(U11(X:S)) -> U11(active(X:S))
1.03/1.10	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.03/1.10	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.03/1.10	 active(U22(tt)) -> mark(tt)
1.03/1.10	 active(U22(X:S)) -> U22(active(X:S))
1.03/1.10	 active(U31(tt)) -> mark(tt)
1.03/1.10	 active(U31(X:S)) -> U31(active(X:S))
1.03/1.10	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.03/1.10	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.03/1.10	 active(U42(tt)) -> mark(tt)
1.03/1.10	 active(U42(X:S)) -> U42(active(X:S))
1.03/1.10	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.03/1.10	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.03/1.10	 active(U52(tt)) -> mark(tt)
1.03/1.10	 active(U52(X:S)) -> U52(active(X:S))
1.03/1.10	 active(U61(tt)) -> mark(tt)
1.03/1.10	 active(U61(X:S)) -> U61(active(X:S))
1.03/1.10	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.03/1.10	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.03/1.10	 active(U72(tt)) -> mark(tt)
1.03/1.10	 active(U72(X:S)) -> U72(active(X:S))
1.03/1.10	 active(U81(tt)) -> mark(tt)
1.03/1.10	 active(U81(X:S)) -> U81(active(X:S))
1.03/1.10	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.03/1.10	 active(__(nil,X:S)) -> mark(X:S)
1.03/1.10	 active(__(X:S,nil)) -> mark(X:S)
1.03/1.10	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.03/1.10	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.03/1.10	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.03/1.10	 active(isList(nil)) -> mark(tt)
1.03/1.10	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.03/1.10	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.03/1.10	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.03/1.10	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.03/1.10	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.03/1.10	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.03/1.10	 active(isPal(nil)) -> mark(tt)
1.03/1.10	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.03/1.10	 active(isQid(a)) -> mark(tt)
1.03/1.10	 active(isQid(e)) -> mark(tt)
1.03/1.10	 active(isQid(i)) -> mark(tt)
1.03/1.10	 active(isQid(o)) -> mark(tt)
1.03/1.10	 active(isQid(u)) -> mark(tt)
1.03/1.10	 isList(ok(X:S)) -> ok(isList(X:S))
1.03/1.10	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.03/1.10	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.03/1.10	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.03/1.10	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.03/1.10	 proper(U11(X:S)) -> U11(proper(X:S))
1.03/1.10	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U22(X:S)) -> U22(proper(X:S))
1.03/1.10	 proper(U31(X:S)) -> U31(proper(X:S))
1.03/1.10	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U42(X:S)) -> U42(proper(X:S))
1.03/1.10	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U52(X:S)) -> U52(proper(X:S))
1.03/1.10	 proper(U61(X:S)) -> U61(proper(X:S))
1.03/1.10	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U72(X:S)) -> U72(proper(X:S))
1.03/1.10	 proper(U81(X:S)) -> U81(proper(X:S))
1.03/1.10	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(isList(X:S)) -> isList(proper(X:S))
1.03/1.10	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.03/1.10	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.03/1.10	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.03/1.10	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.03/1.10	 proper(a) -> ok(a)
1.03/1.10	 proper(e) -> ok(e)
1.03/1.10	 proper(i) -> ok(i)
1.03/1.10	 proper(nil) -> ok(nil)
1.03/1.10	 proper(o) -> ok(o)
1.03/1.10	 proper(tt) -> ok(tt)
1.03/1.10	 proper(u) -> ok(u)
1.03/1.10	 top(mark(X:S)) -> top(proper(X:S))
1.03/1.10	 top(ok(X:S)) -> top(active(X:S))
1.03/1.10	->->Cycle:
1.03/1.10	->->-> Pairs:
1.03/1.10	 U11#(mark(X:S)) -> U11#(X:S)
1.03/1.10	 U11#(ok(X:S)) -> U11#(X:S)
1.03/1.10	->->-> Rules:
1.03/1.10	 U11(mark(X:S)) -> mark(U11(X:S))
1.03/1.10	 U11(ok(X:S)) -> ok(U11(X:S))
1.03/1.10	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.03/1.10	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.03/1.10	 U22(mark(X:S)) -> mark(U22(X:S))
1.03/1.10	 U22(ok(X:S)) -> ok(U22(X:S))
1.03/1.10	 U31(mark(X:S)) -> mark(U31(X:S))
1.03/1.10	 U31(ok(X:S)) -> ok(U31(X:S))
1.03/1.10	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.03/1.10	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.03/1.10	 U42(mark(X:S)) -> mark(U42(X:S))
1.03/1.10	 U42(ok(X:S)) -> ok(U42(X:S))
1.03/1.10	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.03/1.10	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.03/1.10	 U52(mark(X:S)) -> mark(U52(X:S))
1.03/1.10	 U52(ok(X:S)) -> ok(U52(X:S))
1.03/1.10	 U61(mark(X:S)) -> mark(U61(X:S))
1.03/1.10	 U61(ok(X:S)) -> ok(U61(X:S))
1.03/1.10	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.03/1.10	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.03/1.10	 U72(mark(X:S)) -> mark(U72(X:S))
1.03/1.10	 U72(ok(X:S)) -> ok(U72(X:S))
1.03/1.10	 U81(mark(X:S)) -> mark(U81(X:S))
1.03/1.10	 U81(ok(X:S)) -> ok(U81(X:S))
1.03/1.10	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.03/1.10	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.03/1.10	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.03/1.10	 active(U11(tt)) -> mark(tt)
1.03/1.10	 active(U11(X:S)) -> U11(active(X:S))
1.03/1.10	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.03/1.10	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.03/1.10	 active(U22(tt)) -> mark(tt)
1.03/1.10	 active(U22(X:S)) -> U22(active(X:S))
1.03/1.10	 active(U31(tt)) -> mark(tt)
1.03/1.10	 active(U31(X:S)) -> U31(active(X:S))
1.03/1.10	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.03/1.10	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.03/1.10	 active(U42(tt)) -> mark(tt)
1.03/1.10	 active(U42(X:S)) -> U42(active(X:S))
1.03/1.10	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.03/1.10	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.03/1.10	 active(U52(tt)) -> mark(tt)
1.03/1.10	 active(U52(X:S)) -> U52(active(X:S))
1.03/1.10	 active(U61(tt)) -> mark(tt)
1.03/1.10	 active(U61(X:S)) -> U61(active(X:S))
1.03/1.10	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.03/1.10	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.03/1.10	 active(U72(tt)) -> mark(tt)
1.03/1.10	 active(U72(X:S)) -> U72(active(X:S))
1.03/1.10	 active(U81(tt)) -> mark(tt)
1.03/1.10	 active(U81(X:S)) -> U81(active(X:S))
1.03/1.10	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.03/1.10	 active(__(nil,X:S)) -> mark(X:S)
1.03/1.10	 active(__(X:S,nil)) -> mark(X:S)
1.03/1.10	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.03/1.10	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.03/1.10	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.03/1.10	 active(isList(nil)) -> mark(tt)
1.03/1.10	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.03/1.10	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.03/1.10	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.03/1.10	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.03/1.10	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.03/1.10	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.03/1.10	 active(isPal(nil)) -> mark(tt)
1.03/1.10	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.03/1.10	 active(isQid(a)) -> mark(tt)
1.03/1.10	 active(isQid(e)) -> mark(tt)
1.03/1.10	 active(isQid(i)) -> mark(tt)
1.03/1.10	 active(isQid(o)) -> mark(tt)
1.03/1.10	 active(isQid(u)) -> mark(tt)
1.03/1.10	 isList(ok(X:S)) -> ok(isList(X:S))
1.03/1.10	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.03/1.10	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.03/1.10	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.03/1.10	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.03/1.10	 proper(U11(X:S)) -> U11(proper(X:S))
1.03/1.10	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U22(X:S)) -> U22(proper(X:S))
1.03/1.10	 proper(U31(X:S)) -> U31(proper(X:S))
1.03/1.10	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U42(X:S)) -> U42(proper(X:S))
1.03/1.10	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U52(X:S)) -> U52(proper(X:S))
1.03/1.10	 proper(U61(X:S)) -> U61(proper(X:S))
1.03/1.10	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U72(X:S)) -> U72(proper(X:S))
1.03/1.10	 proper(U81(X:S)) -> U81(proper(X:S))
1.03/1.10	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(isList(X:S)) -> isList(proper(X:S))
1.03/1.10	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.03/1.10	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.03/1.10	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.03/1.10	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.03/1.10	 proper(a) -> ok(a)
1.03/1.10	 proper(e) -> ok(e)
1.03/1.10	 proper(i) -> ok(i)
1.03/1.10	 proper(nil) -> ok(nil)
1.03/1.10	 proper(o) -> ok(o)
1.03/1.10	 proper(tt) -> ok(tt)
1.03/1.10	 proper(u) -> ok(u)
1.03/1.10	 top(mark(X:S)) -> top(proper(X:S))
1.03/1.10	 top(ok(X:S)) -> top(active(X:S))
1.03/1.10	->->Cycle:
1.03/1.10	->->-> Pairs:
1.03/1.10	 ACTIVE(U11(X:S)) -> ACTIVE(X:S)
1.03/1.10	 ACTIVE(U21(X1:S,X2:S)) -> ACTIVE(X1:S)
1.03/1.10	 ACTIVE(U22(X:S)) -> ACTIVE(X:S)
1.03/1.10	 ACTIVE(U31(X:S)) -> ACTIVE(X:S)
1.03/1.10	 ACTIVE(U41(X1:S,X2:S)) -> ACTIVE(X1:S)
1.03/1.10	 ACTIVE(U42(X:S)) -> ACTIVE(X:S)
1.03/1.10	 ACTIVE(U51(X1:S,X2:S)) -> ACTIVE(X1:S)
1.03/1.10	 ACTIVE(U52(X:S)) -> ACTIVE(X:S)
1.03/1.10	 ACTIVE(U61(X:S)) -> ACTIVE(X:S)
1.03/1.10	 ACTIVE(U71(X1:S,X2:S)) -> ACTIVE(X1:S)
1.03/1.10	 ACTIVE(U72(X:S)) -> ACTIVE(X:S)
1.03/1.10	 ACTIVE(U81(X:S)) -> ACTIVE(X:S)
1.03/1.10	 ACTIVE(__(X1:S,X2:S)) -> ACTIVE(X1:S)
1.03/1.10	 ACTIVE(__(X1:S,X2:S)) -> ACTIVE(X2:S)
1.03/1.10	->->-> Rules:
1.03/1.10	 U11(mark(X:S)) -> mark(U11(X:S))
1.03/1.10	 U11(ok(X:S)) -> ok(U11(X:S))
1.03/1.10	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.03/1.10	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.03/1.10	 U22(mark(X:S)) -> mark(U22(X:S))
1.03/1.10	 U22(ok(X:S)) -> ok(U22(X:S))
1.03/1.10	 U31(mark(X:S)) -> mark(U31(X:S))
1.03/1.10	 U31(ok(X:S)) -> ok(U31(X:S))
1.03/1.10	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.03/1.10	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.03/1.10	 U42(mark(X:S)) -> mark(U42(X:S))
1.03/1.10	 U42(ok(X:S)) -> ok(U42(X:S))
1.03/1.10	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.03/1.10	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.03/1.10	 U52(mark(X:S)) -> mark(U52(X:S))
1.03/1.10	 U52(ok(X:S)) -> ok(U52(X:S))
1.03/1.10	 U61(mark(X:S)) -> mark(U61(X:S))
1.03/1.10	 U61(ok(X:S)) -> ok(U61(X:S))
1.03/1.10	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.03/1.10	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.03/1.10	 U72(mark(X:S)) -> mark(U72(X:S))
1.03/1.10	 U72(ok(X:S)) -> ok(U72(X:S))
1.03/1.10	 U81(mark(X:S)) -> mark(U81(X:S))
1.03/1.10	 U81(ok(X:S)) -> ok(U81(X:S))
1.03/1.10	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.03/1.10	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.03/1.10	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.03/1.10	 active(U11(tt)) -> mark(tt)
1.03/1.10	 active(U11(X:S)) -> U11(active(X:S))
1.03/1.10	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.03/1.10	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.03/1.10	 active(U22(tt)) -> mark(tt)
1.03/1.10	 active(U22(X:S)) -> U22(active(X:S))
1.03/1.10	 active(U31(tt)) -> mark(tt)
1.03/1.10	 active(U31(X:S)) -> U31(active(X:S))
1.03/1.10	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.03/1.10	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.03/1.10	 active(U42(tt)) -> mark(tt)
1.03/1.10	 active(U42(X:S)) -> U42(active(X:S))
1.03/1.10	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.03/1.10	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.03/1.10	 active(U52(tt)) -> mark(tt)
1.03/1.10	 active(U52(X:S)) -> U52(active(X:S))
1.03/1.10	 active(U61(tt)) -> mark(tt)
1.03/1.10	 active(U61(X:S)) -> U61(active(X:S))
1.03/1.10	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.03/1.10	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.03/1.10	 active(U72(tt)) -> mark(tt)
1.03/1.10	 active(U72(X:S)) -> U72(active(X:S))
1.03/1.10	 active(U81(tt)) -> mark(tt)
1.03/1.10	 active(U81(X:S)) -> U81(active(X:S))
1.03/1.10	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.03/1.10	 active(__(nil,X:S)) -> mark(X:S)
1.03/1.10	 active(__(X:S,nil)) -> mark(X:S)
1.03/1.10	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.03/1.10	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.03/1.10	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.03/1.10	 active(isList(nil)) -> mark(tt)
1.03/1.10	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.03/1.10	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.03/1.10	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.03/1.10	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.03/1.10	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.03/1.10	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.03/1.10	 active(isPal(nil)) -> mark(tt)
1.03/1.10	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.03/1.10	 active(isQid(a)) -> mark(tt)
1.03/1.10	 active(isQid(e)) -> mark(tt)
1.03/1.10	 active(isQid(i)) -> mark(tt)
1.03/1.10	 active(isQid(o)) -> mark(tt)
1.03/1.10	 active(isQid(u)) -> mark(tt)
1.03/1.10	 isList(ok(X:S)) -> ok(isList(X:S))
1.03/1.10	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.03/1.10	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.03/1.10	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.03/1.10	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.03/1.10	 proper(U11(X:S)) -> U11(proper(X:S))
1.03/1.10	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U22(X:S)) -> U22(proper(X:S))
1.03/1.10	 proper(U31(X:S)) -> U31(proper(X:S))
1.03/1.10	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U42(X:S)) -> U42(proper(X:S))
1.03/1.10	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U52(X:S)) -> U52(proper(X:S))
1.03/1.10	 proper(U61(X:S)) -> U61(proper(X:S))
1.03/1.10	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U72(X:S)) -> U72(proper(X:S))
1.03/1.10	 proper(U81(X:S)) -> U81(proper(X:S))
1.03/1.10	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(isList(X:S)) -> isList(proper(X:S))
1.03/1.10	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.03/1.10	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.03/1.10	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.03/1.10	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.03/1.10	 proper(a) -> ok(a)
1.03/1.10	 proper(e) -> ok(e)
1.03/1.10	 proper(i) -> ok(i)
1.03/1.10	 proper(nil) -> ok(nil)
1.03/1.10	 proper(o) -> ok(o)
1.03/1.10	 proper(tt) -> ok(tt)
1.03/1.10	 proper(u) -> ok(u)
1.03/1.10	 top(mark(X:S)) -> top(proper(X:S))
1.03/1.10	 top(ok(X:S)) -> top(active(X:S))
1.03/1.10	->->Cycle:
1.03/1.10	->->-> Pairs:
1.03/1.10	 PROPER(U11(X:S)) -> PROPER(X:S)
1.03/1.10	 PROPER(U21(X1:S,X2:S)) -> PROPER(X1:S)
1.03/1.10	 PROPER(U21(X1:S,X2:S)) -> PROPER(X2:S)
1.03/1.10	 PROPER(U22(X:S)) -> PROPER(X:S)
1.03/1.10	 PROPER(U31(X:S)) -> PROPER(X:S)
1.03/1.10	 PROPER(U41(X1:S,X2:S)) -> PROPER(X1:S)
1.03/1.10	 PROPER(U41(X1:S,X2:S)) -> PROPER(X2:S)
1.03/1.10	 PROPER(U42(X:S)) -> PROPER(X:S)
1.03/1.10	 PROPER(U51(X1:S,X2:S)) -> PROPER(X1:S)
1.03/1.10	 PROPER(U51(X1:S,X2:S)) -> PROPER(X2:S)
1.03/1.10	 PROPER(U52(X:S)) -> PROPER(X:S)
1.03/1.10	 PROPER(U61(X:S)) -> PROPER(X:S)
1.03/1.10	 PROPER(U71(X1:S,X2:S)) -> PROPER(X1:S)
1.03/1.10	 PROPER(U71(X1:S,X2:S)) -> PROPER(X2:S)
1.03/1.10	 PROPER(U72(X:S)) -> PROPER(X:S)
1.03/1.10	 PROPER(U81(X:S)) -> PROPER(X:S)
1.03/1.10	 PROPER(__(X1:S,X2:S)) -> PROPER(X1:S)
1.03/1.10	 PROPER(__(X1:S,X2:S)) -> PROPER(X2:S)
1.03/1.10	 PROPER(isList(X:S)) -> PROPER(X:S)
1.03/1.10	 PROPER(isNeList(X:S)) -> PROPER(X:S)
1.03/1.10	 PROPER(isNePal(X:S)) -> PROPER(X:S)
1.03/1.10	 PROPER(isPal(X:S)) -> PROPER(X:S)
1.03/1.10	 PROPER(isQid(X:S)) -> PROPER(X:S)
1.03/1.10	->->-> Rules:
1.03/1.10	 U11(mark(X:S)) -> mark(U11(X:S))
1.03/1.10	 U11(ok(X:S)) -> ok(U11(X:S))
1.03/1.10	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.03/1.10	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.03/1.10	 U22(mark(X:S)) -> mark(U22(X:S))
1.03/1.10	 U22(ok(X:S)) -> ok(U22(X:S))
1.03/1.10	 U31(mark(X:S)) -> mark(U31(X:S))
1.03/1.10	 U31(ok(X:S)) -> ok(U31(X:S))
1.03/1.10	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.03/1.10	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.03/1.10	 U42(mark(X:S)) -> mark(U42(X:S))
1.03/1.10	 U42(ok(X:S)) -> ok(U42(X:S))
1.03/1.10	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.03/1.10	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.03/1.10	 U52(mark(X:S)) -> mark(U52(X:S))
1.03/1.10	 U52(ok(X:S)) -> ok(U52(X:S))
1.03/1.10	 U61(mark(X:S)) -> mark(U61(X:S))
1.03/1.10	 U61(ok(X:S)) -> ok(U61(X:S))
1.03/1.10	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.03/1.10	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.03/1.10	 U72(mark(X:S)) -> mark(U72(X:S))
1.03/1.10	 U72(ok(X:S)) -> ok(U72(X:S))
1.03/1.10	 U81(mark(X:S)) -> mark(U81(X:S))
1.03/1.10	 U81(ok(X:S)) -> ok(U81(X:S))
1.03/1.10	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.03/1.10	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.03/1.10	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.03/1.10	 active(U11(tt)) -> mark(tt)
1.03/1.10	 active(U11(X:S)) -> U11(active(X:S))
1.03/1.10	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.03/1.10	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.03/1.10	 active(U22(tt)) -> mark(tt)
1.03/1.10	 active(U22(X:S)) -> U22(active(X:S))
1.03/1.10	 active(U31(tt)) -> mark(tt)
1.03/1.10	 active(U31(X:S)) -> U31(active(X:S))
1.03/1.10	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.03/1.10	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.03/1.10	 active(U42(tt)) -> mark(tt)
1.03/1.10	 active(U42(X:S)) -> U42(active(X:S))
1.03/1.10	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.03/1.10	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.03/1.10	 active(U52(tt)) -> mark(tt)
1.03/1.10	 active(U52(X:S)) -> U52(active(X:S))
1.03/1.10	 active(U61(tt)) -> mark(tt)
1.03/1.10	 active(U61(X:S)) -> U61(active(X:S))
1.03/1.10	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.03/1.10	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.03/1.10	 active(U72(tt)) -> mark(tt)
1.03/1.10	 active(U72(X:S)) -> U72(active(X:S))
1.03/1.10	 active(U81(tt)) -> mark(tt)
1.03/1.10	 active(U81(X:S)) -> U81(active(X:S))
1.03/1.10	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.03/1.10	 active(__(nil,X:S)) -> mark(X:S)
1.03/1.10	 active(__(X:S,nil)) -> mark(X:S)
1.03/1.10	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.03/1.10	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.03/1.10	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.03/1.10	 active(isList(nil)) -> mark(tt)
1.03/1.10	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.03/1.10	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.03/1.10	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.03/1.10	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.03/1.10	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.03/1.10	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.03/1.10	 active(isPal(nil)) -> mark(tt)
1.03/1.10	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.03/1.10	 active(isQid(a)) -> mark(tt)
1.03/1.10	 active(isQid(e)) -> mark(tt)
1.03/1.10	 active(isQid(i)) -> mark(tt)
1.03/1.10	 active(isQid(o)) -> mark(tt)
1.03/1.10	 active(isQid(u)) -> mark(tt)
1.03/1.10	 isList(ok(X:S)) -> ok(isList(X:S))
1.03/1.10	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.03/1.10	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.03/1.10	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.03/1.10	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.03/1.10	 proper(U11(X:S)) -> U11(proper(X:S))
1.03/1.10	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U22(X:S)) -> U22(proper(X:S))
1.03/1.10	 proper(U31(X:S)) -> U31(proper(X:S))
1.03/1.10	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U42(X:S)) -> U42(proper(X:S))
1.03/1.10	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U52(X:S)) -> U52(proper(X:S))
1.03/1.10	 proper(U61(X:S)) -> U61(proper(X:S))
1.03/1.10	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U72(X:S)) -> U72(proper(X:S))
1.03/1.10	 proper(U81(X:S)) -> U81(proper(X:S))
1.03/1.10	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(isList(X:S)) -> isList(proper(X:S))
1.03/1.10	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.03/1.10	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.03/1.10	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.03/1.10	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.03/1.10	 proper(a) -> ok(a)
1.03/1.10	 proper(e) -> ok(e)
1.03/1.10	 proper(i) -> ok(i)
1.03/1.10	 proper(nil) -> ok(nil)
1.03/1.10	 proper(o) -> ok(o)
1.03/1.10	 proper(tt) -> ok(tt)
1.03/1.10	 proper(u) -> ok(u)
1.03/1.10	 top(mark(X:S)) -> top(proper(X:S))
1.03/1.10	 top(ok(X:S)) -> top(active(X:S))
1.03/1.10	->->Cycle:
1.03/1.10	->->-> Pairs:
1.03/1.10	 TOP(mark(X:S)) -> TOP(proper(X:S))
1.03/1.10	 TOP(ok(X:S)) -> TOP(active(X:S))
1.03/1.10	->->-> Rules:
1.03/1.10	 U11(mark(X:S)) -> mark(U11(X:S))
1.03/1.10	 U11(ok(X:S)) -> ok(U11(X:S))
1.03/1.10	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.03/1.10	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.03/1.10	 U22(mark(X:S)) -> mark(U22(X:S))
1.03/1.10	 U22(ok(X:S)) -> ok(U22(X:S))
1.03/1.10	 U31(mark(X:S)) -> mark(U31(X:S))
1.03/1.10	 U31(ok(X:S)) -> ok(U31(X:S))
1.03/1.10	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.03/1.10	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.03/1.10	 U42(mark(X:S)) -> mark(U42(X:S))
1.03/1.10	 U42(ok(X:S)) -> ok(U42(X:S))
1.03/1.10	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.03/1.10	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.03/1.10	 U52(mark(X:S)) -> mark(U52(X:S))
1.03/1.10	 U52(ok(X:S)) -> ok(U52(X:S))
1.03/1.10	 U61(mark(X:S)) -> mark(U61(X:S))
1.03/1.10	 U61(ok(X:S)) -> ok(U61(X:S))
1.03/1.10	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.03/1.10	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.03/1.10	 U72(mark(X:S)) -> mark(U72(X:S))
1.03/1.10	 U72(ok(X:S)) -> ok(U72(X:S))
1.03/1.10	 U81(mark(X:S)) -> mark(U81(X:S))
1.03/1.10	 U81(ok(X:S)) -> ok(U81(X:S))
1.03/1.10	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.03/1.10	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.03/1.10	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.03/1.10	 active(U11(tt)) -> mark(tt)
1.03/1.10	 active(U11(X:S)) -> U11(active(X:S))
1.03/1.10	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.03/1.10	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.03/1.10	 active(U22(tt)) -> mark(tt)
1.03/1.10	 active(U22(X:S)) -> U22(active(X:S))
1.03/1.10	 active(U31(tt)) -> mark(tt)
1.03/1.10	 active(U31(X:S)) -> U31(active(X:S))
1.03/1.10	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.03/1.10	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.03/1.10	 active(U42(tt)) -> mark(tt)
1.03/1.10	 active(U42(X:S)) -> U42(active(X:S))
1.03/1.10	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.03/1.10	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.03/1.10	 active(U52(tt)) -> mark(tt)
1.03/1.10	 active(U52(X:S)) -> U52(active(X:S))
1.03/1.10	 active(U61(tt)) -> mark(tt)
1.03/1.10	 active(U61(X:S)) -> U61(active(X:S))
1.03/1.10	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.03/1.10	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.03/1.10	 active(U72(tt)) -> mark(tt)
1.03/1.10	 active(U72(X:S)) -> U72(active(X:S))
1.03/1.10	 active(U81(tt)) -> mark(tt)
1.03/1.10	 active(U81(X:S)) -> U81(active(X:S))
1.03/1.10	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.03/1.10	 active(__(nil,X:S)) -> mark(X:S)
1.03/1.10	 active(__(X:S,nil)) -> mark(X:S)
1.03/1.10	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.03/1.10	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.03/1.10	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.03/1.10	 active(isList(nil)) -> mark(tt)
1.03/1.10	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.03/1.10	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.03/1.10	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.03/1.10	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.03/1.10	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.03/1.10	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.03/1.10	 active(isPal(nil)) -> mark(tt)
1.03/1.10	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.03/1.10	 active(isQid(a)) -> mark(tt)
1.03/1.10	 active(isQid(e)) -> mark(tt)
1.03/1.10	 active(isQid(i)) -> mark(tt)
1.03/1.10	 active(isQid(o)) -> mark(tt)
1.03/1.10	 active(isQid(u)) -> mark(tt)
1.03/1.10	 isList(ok(X:S)) -> ok(isList(X:S))
1.03/1.10	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.03/1.10	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.03/1.10	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.03/1.10	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.03/1.10	 proper(U11(X:S)) -> U11(proper(X:S))
1.03/1.10	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U22(X:S)) -> U22(proper(X:S))
1.03/1.10	 proper(U31(X:S)) -> U31(proper(X:S))
1.03/1.10	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U42(X:S)) -> U42(proper(X:S))
1.03/1.10	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U52(X:S)) -> U52(proper(X:S))
1.03/1.10	 proper(U61(X:S)) -> U61(proper(X:S))
1.03/1.10	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U72(X:S)) -> U72(proper(X:S))
1.03/1.10	 proper(U81(X:S)) -> U81(proper(X:S))
1.03/1.10	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(isList(X:S)) -> isList(proper(X:S))
1.03/1.10	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.03/1.10	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.03/1.10	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.03/1.10	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.03/1.10	 proper(a) -> ok(a)
1.03/1.10	 proper(e) -> ok(e)
1.03/1.10	 proper(i) -> ok(i)
1.03/1.10	 proper(nil) -> ok(nil)
1.03/1.10	 proper(o) -> ok(o)
1.03/1.10	 proper(tt) -> ok(tt)
1.03/1.10	 proper(u) -> ok(u)
1.03/1.10	 top(mark(X:S)) -> top(proper(X:S))
1.03/1.10	 top(ok(X:S)) -> top(active(X:S))
1.03/1.10	
1.03/1.10	
1.03/1.10	The problem is decomposed in 21 subproblems.
1.03/1.10	
1.03/1.10	Problem 1.1: 
1.03/1.10	
1.03/1.10	Subterm Processor:
1.03/1.10	-> Pairs:
1.03/1.10	 ISQID(ok(X:S)) -> ISQID(X:S)
1.03/1.10	-> Rules:
1.03/1.10	 U11(mark(X:S)) -> mark(U11(X:S))
1.03/1.10	 U11(ok(X:S)) -> ok(U11(X:S))
1.03/1.10	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.03/1.10	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.03/1.10	 U22(mark(X:S)) -> mark(U22(X:S))
1.03/1.10	 U22(ok(X:S)) -> ok(U22(X:S))
1.03/1.10	 U31(mark(X:S)) -> mark(U31(X:S))
1.03/1.10	 U31(ok(X:S)) -> ok(U31(X:S))
1.03/1.10	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.03/1.10	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.03/1.10	 U42(mark(X:S)) -> mark(U42(X:S))
1.03/1.10	 U42(ok(X:S)) -> ok(U42(X:S))
1.03/1.10	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.03/1.10	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.03/1.10	 U52(mark(X:S)) -> mark(U52(X:S))
1.03/1.10	 U52(ok(X:S)) -> ok(U52(X:S))
1.03/1.10	 U61(mark(X:S)) -> mark(U61(X:S))
1.03/1.10	 U61(ok(X:S)) -> ok(U61(X:S))
1.03/1.10	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.03/1.10	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.03/1.10	 U72(mark(X:S)) -> mark(U72(X:S))
1.03/1.10	 U72(ok(X:S)) -> ok(U72(X:S))
1.03/1.10	 U81(mark(X:S)) -> mark(U81(X:S))
1.03/1.10	 U81(ok(X:S)) -> ok(U81(X:S))
1.03/1.10	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.03/1.10	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.03/1.10	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.03/1.10	 active(U11(tt)) -> mark(tt)
1.03/1.10	 active(U11(X:S)) -> U11(active(X:S))
1.03/1.10	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.03/1.10	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.03/1.10	 active(U22(tt)) -> mark(tt)
1.03/1.10	 active(U22(X:S)) -> U22(active(X:S))
1.03/1.10	 active(U31(tt)) -> mark(tt)
1.03/1.10	 active(U31(X:S)) -> U31(active(X:S))
1.03/1.10	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.03/1.10	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.03/1.10	 active(U42(tt)) -> mark(tt)
1.03/1.10	 active(U42(X:S)) -> U42(active(X:S))
1.03/1.10	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.03/1.10	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.03/1.10	 active(U52(tt)) -> mark(tt)
1.03/1.10	 active(U52(X:S)) -> U52(active(X:S))
1.03/1.10	 active(U61(tt)) -> mark(tt)
1.03/1.10	 active(U61(X:S)) -> U61(active(X:S))
1.03/1.10	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.03/1.10	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.03/1.10	 active(U72(tt)) -> mark(tt)
1.03/1.10	 active(U72(X:S)) -> U72(active(X:S))
1.03/1.10	 active(U81(tt)) -> mark(tt)
1.03/1.10	 active(U81(X:S)) -> U81(active(X:S))
1.03/1.10	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.03/1.10	 active(__(nil,X:S)) -> mark(X:S)
1.03/1.10	 active(__(X:S,nil)) -> mark(X:S)
1.03/1.10	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.03/1.10	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.03/1.10	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.03/1.10	 active(isList(nil)) -> mark(tt)
1.03/1.10	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.03/1.10	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.03/1.10	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.03/1.10	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.03/1.10	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.03/1.10	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.03/1.10	 active(isPal(nil)) -> mark(tt)
1.03/1.10	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.03/1.10	 active(isQid(a)) -> mark(tt)
1.03/1.10	 active(isQid(e)) -> mark(tt)
1.03/1.10	 active(isQid(i)) -> mark(tt)
1.03/1.10	 active(isQid(o)) -> mark(tt)
1.03/1.10	 active(isQid(u)) -> mark(tt)
1.03/1.10	 isList(ok(X:S)) -> ok(isList(X:S))
1.03/1.10	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.03/1.10	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.03/1.10	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.03/1.10	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.03/1.10	 proper(U11(X:S)) -> U11(proper(X:S))
1.03/1.10	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U22(X:S)) -> U22(proper(X:S))
1.03/1.10	 proper(U31(X:S)) -> U31(proper(X:S))
1.03/1.10	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U42(X:S)) -> U42(proper(X:S))
1.03/1.10	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U52(X:S)) -> U52(proper(X:S))
1.03/1.10	 proper(U61(X:S)) -> U61(proper(X:S))
1.03/1.10	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U72(X:S)) -> U72(proper(X:S))
1.03/1.10	 proper(U81(X:S)) -> U81(proper(X:S))
1.03/1.10	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(isList(X:S)) -> isList(proper(X:S))
1.03/1.10	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.03/1.10	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.03/1.10	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.03/1.10	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.03/1.10	 proper(a) -> ok(a)
1.03/1.10	 proper(e) -> ok(e)
1.03/1.10	 proper(i) -> ok(i)
1.03/1.10	 proper(nil) -> ok(nil)
1.03/1.10	 proper(o) -> ok(o)
1.03/1.10	 proper(tt) -> ok(tt)
1.03/1.10	 proper(u) -> ok(u)
1.03/1.10	 top(mark(X:S)) -> top(proper(X:S))
1.03/1.10	 top(ok(X:S)) -> top(active(X:S))
1.03/1.10	->Projection:
1.03/1.10	 pi(ISQID) = 1
1.03/1.10	
1.03/1.10	Problem 1.1: 
1.03/1.10	
1.03/1.10	SCC Processor:
1.03/1.10	-> Pairs:
1.03/1.10	 Empty
1.03/1.10	-> Rules:
1.03/1.10	 U11(mark(X:S)) -> mark(U11(X:S))
1.03/1.10	 U11(ok(X:S)) -> ok(U11(X:S))
1.03/1.10	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.03/1.10	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.03/1.10	 U22(mark(X:S)) -> mark(U22(X:S))
1.03/1.10	 U22(ok(X:S)) -> ok(U22(X:S))
1.03/1.10	 U31(mark(X:S)) -> mark(U31(X:S))
1.03/1.10	 U31(ok(X:S)) -> ok(U31(X:S))
1.03/1.10	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.03/1.10	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.03/1.10	 U42(mark(X:S)) -> mark(U42(X:S))
1.03/1.10	 U42(ok(X:S)) -> ok(U42(X:S))
1.03/1.10	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.03/1.10	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.03/1.10	 U52(mark(X:S)) -> mark(U52(X:S))
1.03/1.10	 U52(ok(X:S)) -> ok(U52(X:S))
1.03/1.10	 U61(mark(X:S)) -> mark(U61(X:S))
1.03/1.10	 U61(ok(X:S)) -> ok(U61(X:S))
1.03/1.10	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.03/1.10	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.03/1.10	 U72(mark(X:S)) -> mark(U72(X:S))
1.03/1.10	 U72(ok(X:S)) -> ok(U72(X:S))
1.03/1.10	 U81(mark(X:S)) -> mark(U81(X:S))
1.03/1.10	 U81(ok(X:S)) -> ok(U81(X:S))
1.03/1.10	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.03/1.10	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.03/1.10	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.03/1.10	 active(U11(tt)) -> mark(tt)
1.03/1.10	 active(U11(X:S)) -> U11(active(X:S))
1.03/1.10	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.03/1.10	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.03/1.10	 active(U22(tt)) -> mark(tt)
1.03/1.10	 active(U22(X:S)) -> U22(active(X:S))
1.03/1.10	 active(U31(tt)) -> mark(tt)
1.03/1.10	 active(U31(X:S)) -> U31(active(X:S))
1.03/1.10	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.03/1.10	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.03/1.10	 active(U42(tt)) -> mark(tt)
1.03/1.10	 active(U42(X:S)) -> U42(active(X:S))
1.03/1.10	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.03/1.10	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.03/1.10	 active(U52(tt)) -> mark(tt)
1.03/1.10	 active(U52(X:S)) -> U52(active(X:S))
1.03/1.10	 active(U61(tt)) -> mark(tt)
1.03/1.10	 active(U61(X:S)) -> U61(active(X:S))
1.03/1.10	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.03/1.10	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.03/1.10	 active(U72(tt)) -> mark(tt)
1.03/1.10	 active(U72(X:S)) -> U72(active(X:S))
1.03/1.10	 active(U81(tt)) -> mark(tt)
1.03/1.10	 active(U81(X:S)) -> U81(active(X:S))
1.03/1.10	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.03/1.10	 active(__(nil,X:S)) -> mark(X:S)
1.03/1.10	 active(__(X:S,nil)) -> mark(X:S)
1.03/1.10	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.03/1.10	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.03/1.10	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.03/1.10	 active(isList(nil)) -> mark(tt)
1.03/1.10	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.03/1.10	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.03/1.10	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.03/1.10	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.03/1.10	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.03/1.10	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.03/1.10	 active(isPal(nil)) -> mark(tt)
1.03/1.10	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.03/1.10	 active(isQid(a)) -> mark(tt)
1.03/1.10	 active(isQid(e)) -> mark(tt)
1.03/1.10	 active(isQid(i)) -> mark(tt)
1.03/1.10	 active(isQid(o)) -> mark(tt)
1.03/1.10	 active(isQid(u)) -> mark(tt)
1.03/1.10	 isList(ok(X:S)) -> ok(isList(X:S))
1.03/1.10	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.03/1.10	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.03/1.10	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.03/1.10	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.03/1.10	 proper(U11(X:S)) -> U11(proper(X:S))
1.03/1.10	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U22(X:S)) -> U22(proper(X:S))
1.03/1.10	 proper(U31(X:S)) -> U31(proper(X:S))
1.03/1.10	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U42(X:S)) -> U42(proper(X:S))
1.03/1.10	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U52(X:S)) -> U52(proper(X:S))
1.03/1.10	 proper(U61(X:S)) -> U61(proper(X:S))
1.03/1.10	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.03/1.10	 proper(U72(X:S)) -> U72(proper(X:S))
1.03/1.10	 proper(U81(X:S)) -> U81(proper(X:S))
1.03/1.10	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.03/1.11	 proper(isList(X:S)) -> isList(proper(X:S))
1.03/1.11	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.03/1.11	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.03/1.11	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.03/1.11	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.03/1.11	 proper(a) -> ok(a)
1.03/1.11	 proper(e) -> ok(e)
1.03/1.11	 proper(i) -> ok(i)
1.03/1.11	 proper(nil) -> ok(nil)
1.03/1.11	 proper(o) -> ok(o)
1.03/1.11	 proper(tt) -> ok(tt)
1.03/1.11	 proper(u) -> ok(u)
1.03/1.11	 top(mark(X:S)) -> top(proper(X:S))
1.03/1.11	 top(ok(X:S)) -> top(active(X:S))
1.03/1.11	->Strongly Connected Components:
1.03/1.11	 There is no strongly connected component
1.03/1.11	
1.03/1.11	The problem is finite.
1.03/1.11	
1.03/1.11	Problem 1.2: 
1.03/1.11	
1.03/1.11	Subterm Processor:
1.03/1.11	-> Pairs:
1.03/1.11	 ISPAL(ok(X:S)) -> ISPAL(X:S)
1.03/1.11	-> Rules:
1.03/1.11	 U11(mark(X:S)) -> mark(U11(X:S))
1.03/1.11	 U11(ok(X:S)) -> ok(U11(X:S))
1.03/1.11	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.03/1.11	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.03/1.11	 U22(mark(X:S)) -> mark(U22(X:S))
1.03/1.11	 U22(ok(X:S)) -> ok(U22(X:S))
1.03/1.11	 U31(mark(X:S)) -> mark(U31(X:S))
1.03/1.11	 U31(ok(X:S)) -> ok(U31(X:S))
1.03/1.11	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.03/1.11	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.03/1.11	 U42(mark(X:S)) -> mark(U42(X:S))
1.03/1.11	 U42(ok(X:S)) -> ok(U42(X:S))
1.03/1.11	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.03/1.11	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.03/1.11	 U52(mark(X:S)) -> mark(U52(X:S))
1.03/1.11	 U52(ok(X:S)) -> ok(U52(X:S))
1.03/1.11	 U61(mark(X:S)) -> mark(U61(X:S))
1.03/1.11	 U61(ok(X:S)) -> ok(U61(X:S))
1.03/1.11	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.03/1.11	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.03/1.11	 U72(mark(X:S)) -> mark(U72(X:S))
1.03/1.11	 U72(ok(X:S)) -> ok(U72(X:S))
1.03/1.11	 U81(mark(X:S)) -> mark(U81(X:S))
1.03/1.11	 U81(ok(X:S)) -> ok(U81(X:S))
1.03/1.11	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.03/1.11	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.03/1.11	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.03/1.11	 active(U11(tt)) -> mark(tt)
1.03/1.11	 active(U11(X:S)) -> U11(active(X:S))
1.03/1.11	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.03/1.11	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.03/1.11	 active(U22(tt)) -> mark(tt)
1.03/1.11	 active(U22(X:S)) -> U22(active(X:S))
1.03/1.11	 active(U31(tt)) -> mark(tt)
1.03/1.11	 active(U31(X:S)) -> U31(active(X:S))
1.03/1.11	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.03/1.11	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.03/1.11	 active(U42(tt)) -> mark(tt)
1.03/1.11	 active(U42(X:S)) -> U42(active(X:S))
1.03/1.11	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.03/1.11	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.03/1.11	 active(U52(tt)) -> mark(tt)
1.03/1.11	 active(U52(X:S)) -> U52(active(X:S))
1.03/1.11	 active(U61(tt)) -> mark(tt)
1.03/1.11	 active(U61(X:S)) -> U61(active(X:S))
1.03/1.11	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.03/1.11	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.03/1.11	 active(U72(tt)) -> mark(tt)
1.03/1.11	 active(U72(X:S)) -> U72(active(X:S))
1.03/1.11	 active(U81(tt)) -> mark(tt)
1.03/1.11	 active(U81(X:S)) -> U81(active(X:S))
1.03/1.11	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.03/1.11	 active(__(nil,X:S)) -> mark(X:S)
1.03/1.11	 active(__(X:S,nil)) -> mark(X:S)
1.03/1.11	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.03/1.11	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.03/1.11	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.03/1.11	 active(isList(nil)) -> mark(tt)
1.03/1.11	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.03/1.11	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.03/1.11	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.03/1.11	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.03/1.11	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.03/1.11	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.03/1.11	 active(isPal(nil)) -> mark(tt)
1.03/1.11	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.03/1.11	 active(isQid(a)) -> mark(tt)
1.03/1.11	 active(isQid(e)) -> mark(tt)
1.03/1.11	 active(isQid(i)) -> mark(tt)
1.03/1.11	 active(isQid(o)) -> mark(tt)
1.03/1.11	 active(isQid(u)) -> mark(tt)
1.03/1.11	 isList(ok(X:S)) -> ok(isList(X:S))
1.03/1.11	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.03/1.11	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.03/1.11	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.03/1.11	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.03/1.11	 proper(U11(X:S)) -> U11(proper(X:S))
1.03/1.11	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.03/1.11	 proper(U22(X:S)) -> U22(proper(X:S))
1.03/1.11	 proper(U31(X:S)) -> U31(proper(X:S))
1.03/1.11	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.03/1.11	 proper(U42(X:S)) -> U42(proper(X:S))
1.03/1.11	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.03/1.11	 proper(U52(X:S)) -> U52(proper(X:S))
1.03/1.11	 proper(U61(X:S)) -> U61(proper(X:S))
1.03/1.11	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.03/1.11	 proper(U72(X:S)) -> U72(proper(X:S))
1.03/1.11	 proper(U81(X:S)) -> U81(proper(X:S))
1.03/1.11	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.03/1.11	 proper(isList(X:S)) -> isList(proper(X:S))
1.03/1.11	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.03/1.11	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.03/1.11	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.03/1.11	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.03/1.11	 proper(a) -> ok(a)
1.03/1.11	 proper(e) -> ok(e)
1.03/1.11	 proper(i) -> ok(i)
1.03/1.11	 proper(nil) -> ok(nil)
1.03/1.11	 proper(o) -> ok(o)
1.03/1.11	 proper(tt) -> ok(tt)
1.03/1.11	 proper(u) -> ok(u)
1.03/1.11	 top(mark(X:S)) -> top(proper(X:S))
1.03/1.11	 top(ok(X:S)) -> top(active(X:S))
1.03/1.11	->Projection:
1.03/1.11	 pi(ISPAL) = 1
1.03/1.11	
1.03/1.11	Problem 1.2: 
1.03/1.11	
1.03/1.11	SCC Processor:
1.03/1.11	-> Pairs:
1.03/1.11	 Empty
1.03/1.11	-> Rules:
1.03/1.11	 U11(mark(X:S)) -> mark(U11(X:S))
1.03/1.11	 U11(ok(X:S)) -> ok(U11(X:S))
1.03/1.11	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.03/1.11	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.03/1.11	 U22(mark(X:S)) -> mark(U22(X:S))
1.03/1.11	 U22(ok(X:S)) -> ok(U22(X:S))
1.03/1.11	 U31(mark(X:S)) -> mark(U31(X:S))
1.03/1.11	 U31(ok(X:S)) -> ok(U31(X:S))
1.03/1.11	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.03/1.11	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.03/1.11	 U42(mark(X:S)) -> mark(U42(X:S))
1.03/1.11	 U42(ok(X:S)) -> ok(U42(X:S))
1.03/1.11	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.03/1.11	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.03/1.11	 U52(mark(X:S)) -> mark(U52(X:S))
1.03/1.11	 U52(ok(X:S)) -> ok(U52(X:S))
1.03/1.11	 U61(mark(X:S)) -> mark(U61(X:S))
1.03/1.11	 U61(ok(X:S)) -> ok(U61(X:S))
1.03/1.11	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.03/1.11	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.03/1.11	 U72(mark(X:S)) -> mark(U72(X:S))
1.03/1.11	 U72(ok(X:S)) -> ok(U72(X:S))
1.03/1.11	 U81(mark(X:S)) -> mark(U81(X:S))
1.03/1.11	 U81(ok(X:S)) -> ok(U81(X:S))
1.03/1.11	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.03/1.11	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.03/1.11	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.03/1.11	 active(U11(tt)) -> mark(tt)
1.03/1.11	 active(U11(X:S)) -> U11(active(X:S))
1.03/1.11	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.03/1.11	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.03/1.11	 active(U22(tt)) -> mark(tt)
1.03/1.11	 active(U22(X:S)) -> U22(active(X:S))
1.03/1.11	 active(U31(tt)) -> mark(tt)
1.03/1.11	 active(U31(X:S)) -> U31(active(X:S))
1.03/1.11	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.03/1.11	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.03/1.11	 active(U42(tt)) -> mark(tt)
1.03/1.11	 active(U42(X:S)) -> U42(active(X:S))
1.03/1.11	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.03/1.11	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.03/1.11	 active(U52(tt)) -> mark(tt)
1.03/1.11	 active(U52(X:S)) -> U52(active(X:S))
1.03/1.11	 active(U61(tt)) -> mark(tt)
1.03/1.11	 active(U61(X:S)) -> U61(active(X:S))
1.03/1.11	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.03/1.11	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.03/1.11	 active(U72(tt)) -> mark(tt)
1.03/1.11	 active(U72(X:S)) -> U72(active(X:S))
1.03/1.11	 active(U81(tt)) -> mark(tt)
1.03/1.11	 active(U81(X:S)) -> U81(active(X:S))
1.03/1.11	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.03/1.11	 active(__(nil,X:S)) -> mark(X:S)
1.03/1.11	 active(__(X:S,nil)) -> mark(X:S)
1.03/1.11	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.03/1.11	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.03/1.11	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.03/1.11	 active(isList(nil)) -> mark(tt)
1.03/1.11	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.03/1.11	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.03/1.11	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.03/1.11	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.03/1.11	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.03/1.11	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.03/1.11	 active(isPal(nil)) -> mark(tt)
1.03/1.11	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.03/1.11	 active(isQid(a)) -> mark(tt)
1.03/1.11	 active(isQid(e)) -> mark(tt)
1.03/1.11	 active(isQid(i)) -> mark(tt)
1.03/1.11	 active(isQid(o)) -> mark(tt)
1.03/1.11	 active(isQid(u)) -> mark(tt)
1.03/1.11	 isList(ok(X:S)) -> ok(isList(X:S))
1.03/1.11	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.03/1.11	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.03/1.11	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.03/1.11	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.03/1.11	 proper(U11(X:S)) -> U11(proper(X:S))
1.03/1.11	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.03/1.11	 proper(U22(X:S)) -> U22(proper(X:S))
1.03/1.11	 proper(U31(X:S)) -> U31(proper(X:S))
1.03/1.11	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.03/1.11	 proper(U42(X:S)) -> U42(proper(X:S))
1.03/1.11	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.03/1.11	 proper(U52(X:S)) -> U52(proper(X:S))
1.03/1.11	 proper(U61(X:S)) -> U61(proper(X:S))
1.03/1.11	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.03/1.11	 proper(U72(X:S)) -> U72(proper(X:S))
1.03/1.11	 proper(U81(X:S)) -> U81(proper(X:S))
1.03/1.11	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.03/1.11	 proper(isList(X:S)) -> isList(proper(X:S))
1.03/1.11	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.03/1.11	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.03/1.11	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.03/1.11	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.03/1.11	 proper(a) -> ok(a)
1.03/1.11	 proper(e) -> ok(e)
1.03/1.11	 proper(i) -> ok(i)
1.03/1.11	 proper(nil) -> ok(nil)
1.03/1.11	 proper(o) -> ok(o)
1.03/1.11	 proper(tt) -> ok(tt)
1.03/1.11	 proper(u) -> ok(u)
1.03/1.11	 top(mark(X:S)) -> top(proper(X:S))
1.03/1.11	 top(ok(X:S)) -> top(active(X:S))
1.03/1.11	->Strongly Connected Components:
1.03/1.11	 There is no strongly connected component
1.03/1.11	
1.03/1.11	The problem is finite.
1.03/1.11	
1.03/1.11	Problem 1.3: 
1.03/1.11	
1.03/1.11	Subterm Processor:
1.03/1.11	-> Pairs:
1.03/1.11	 ISNEPAL(ok(X:S)) -> ISNEPAL(X:S)
1.03/1.11	-> Rules:
1.03/1.11	 U11(mark(X:S)) -> mark(U11(X:S))
1.03/1.11	 U11(ok(X:S)) -> ok(U11(X:S))
1.03/1.11	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.03/1.11	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.03/1.11	 U22(mark(X:S)) -> mark(U22(X:S))
1.03/1.11	 U22(ok(X:S)) -> ok(U22(X:S))
1.03/1.11	 U31(mark(X:S)) -> mark(U31(X:S))
1.03/1.11	 U31(ok(X:S)) -> ok(U31(X:S))
1.03/1.11	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.03/1.11	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.03/1.11	 U42(mark(X:S)) -> mark(U42(X:S))
1.03/1.11	 U42(ok(X:S)) -> ok(U42(X:S))
1.03/1.11	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.03/1.11	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.03/1.11	 U52(mark(X:S)) -> mark(U52(X:S))
1.03/1.11	 U52(ok(X:S)) -> ok(U52(X:S))
1.03/1.11	 U61(mark(X:S)) -> mark(U61(X:S))
1.03/1.11	 U61(ok(X:S)) -> ok(U61(X:S))
1.03/1.11	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.03/1.11	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.03/1.11	 U72(mark(X:S)) -> mark(U72(X:S))
1.03/1.11	 U72(ok(X:S)) -> ok(U72(X:S))
1.03/1.11	 U81(mark(X:S)) -> mark(U81(X:S))
1.03/1.11	 U81(ok(X:S)) -> ok(U81(X:S))
1.03/1.11	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.03/1.11	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.03/1.11	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.03/1.11	 active(U11(tt)) -> mark(tt)
1.03/1.11	 active(U11(X:S)) -> U11(active(X:S))
1.03/1.11	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.03/1.11	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.03/1.11	 active(U22(tt)) -> mark(tt)
1.03/1.11	 active(U22(X:S)) -> U22(active(X:S))
1.03/1.11	 active(U31(tt)) -> mark(tt)
1.03/1.11	 active(U31(X:S)) -> U31(active(X:S))
1.03/1.11	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.03/1.11	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.03/1.11	 active(U42(tt)) -> mark(tt)
1.03/1.11	 active(U42(X:S)) -> U42(active(X:S))
1.03/1.11	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.03/1.11	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.03/1.11	 active(U52(tt)) -> mark(tt)
1.03/1.11	 active(U52(X:S)) -> U52(active(X:S))
1.03/1.11	 active(U61(tt)) -> mark(tt)
1.03/1.11	 active(U61(X:S)) -> U61(active(X:S))
1.03/1.11	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.03/1.11	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.03/1.11	 active(U72(tt)) -> mark(tt)
1.03/1.11	 active(U72(X:S)) -> U72(active(X:S))
1.03/1.11	 active(U81(tt)) -> mark(tt)
1.03/1.11	 active(U81(X:S)) -> U81(active(X:S))
1.03/1.11	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.03/1.11	 active(__(nil,X:S)) -> mark(X:S)
1.03/1.11	 active(__(X:S,nil)) -> mark(X:S)
1.03/1.11	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.03/1.11	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.03/1.11	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.03/1.11	 active(isList(nil)) -> mark(tt)
1.03/1.11	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.03/1.11	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.03/1.11	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.03/1.11	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.03/1.11	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.03/1.11	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.03/1.11	 active(isPal(nil)) -> mark(tt)
1.03/1.11	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.03/1.11	 active(isQid(a)) -> mark(tt)
1.03/1.11	 active(isQid(e)) -> mark(tt)
1.03/1.11	 active(isQid(i)) -> mark(tt)
1.03/1.11	 active(isQid(o)) -> mark(tt)
1.03/1.11	 active(isQid(u)) -> mark(tt)
1.03/1.11	 isList(ok(X:S)) -> ok(isList(X:S))
1.03/1.11	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.03/1.11	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.03/1.11	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.03/1.11	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.03/1.11	 proper(U11(X:S)) -> U11(proper(X:S))
1.03/1.11	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.03/1.11	 proper(U22(X:S)) -> U22(proper(X:S))
1.03/1.11	 proper(U31(X:S)) -> U31(proper(X:S))
1.03/1.11	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.03/1.11	 proper(U42(X:S)) -> U42(proper(X:S))
1.03/1.11	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.03/1.11	 proper(U52(X:S)) -> U52(proper(X:S))
1.03/1.11	 proper(U61(X:S)) -> U61(proper(X:S))
1.03/1.11	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.03/1.11	 proper(U72(X:S)) -> U72(proper(X:S))
1.03/1.11	 proper(U81(X:S)) -> U81(proper(X:S))
1.03/1.11	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.03/1.11	 proper(isList(X:S)) -> isList(proper(X:S))
1.03/1.11	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.03/1.11	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.03/1.11	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.03/1.11	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.03/1.11	 proper(a) -> ok(a)
1.03/1.11	 proper(e) -> ok(e)
1.03/1.11	 proper(i) -> ok(i)
1.03/1.11	 proper(nil) -> ok(nil)
1.03/1.11	 proper(o) -> ok(o)
1.03/1.11	 proper(tt) -> ok(tt)
1.03/1.11	 proper(u) -> ok(u)
1.03/1.11	 top(mark(X:S)) -> top(proper(X:S))
1.03/1.11	 top(ok(X:S)) -> top(active(X:S))
1.03/1.11	->Projection:
1.03/1.11	 pi(ISNEPAL) = 1
1.03/1.11	
1.03/1.11	Problem 1.3: 
1.03/1.11	
1.03/1.11	SCC Processor:
1.03/1.11	-> Pairs:
1.03/1.11	 Empty
1.03/1.11	-> Rules:
1.03/1.11	 U11(mark(X:S)) -> mark(U11(X:S))
1.03/1.11	 U11(ok(X:S)) -> ok(U11(X:S))
1.03/1.11	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.03/1.11	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.03/1.11	 U22(mark(X:S)) -> mark(U22(X:S))
1.03/1.11	 U22(ok(X:S)) -> ok(U22(X:S))
1.03/1.11	 U31(mark(X:S)) -> mark(U31(X:S))
1.03/1.11	 U31(ok(X:S)) -> ok(U31(X:S))
1.03/1.11	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.03/1.11	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.03/1.11	 U42(mark(X:S)) -> mark(U42(X:S))
1.03/1.11	 U42(ok(X:S)) -> ok(U42(X:S))
1.03/1.11	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.03/1.11	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.03/1.11	 U52(mark(X:S)) -> mark(U52(X:S))
1.03/1.11	 U52(ok(X:S)) -> ok(U52(X:S))
1.03/1.11	 U61(mark(X:S)) -> mark(U61(X:S))
1.03/1.11	 U61(ok(X:S)) -> ok(U61(X:S))
1.03/1.11	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.03/1.11	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.03/1.11	 U72(mark(X:S)) -> mark(U72(X:S))
1.03/1.11	 U72(ok(X:S)) -> ok(U72(X:S))
1.03/1.11	 U81(mark(X:S)) -> mark(U81(X:S))
1.03/1.11	 U81(ok(X:S)) -> ok(U81(X:S))
1.03/1.11	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.03/1.11	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.03/1.11	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.03/1.11	 active(U11(tt)) -> mark(tt)
1.03/1.11	 active(U11(X:S)) -> U11(active(X:S))
1.03/1.11	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.03/1.11	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.03/1.11	 active(U22(tt)) -> mark(tt)
1.03/1.11	 active(U22(X:S)) -> U22(active(X:S))
1.03/1.11	 active(U31(tt)) -> mark(tt)
1.03/1.11	 active(U31(X:S)) -> U31(active(X:S))
1.03/1.11	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.03/1.11	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.03/1.11	 active(U42(tt)) -> mark(tt)
1.03/1.11	 active(U42(X:S)) -> U42(active(X:S))
1.03/1.11	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.03/1.11	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.03/1.11	 active(U52(tt)) -> mark(tt)
1.03/1.11	 active(U52(X:S)) -> U52(active(X:S))
1.03/1.11	 active(U61(tt)) -> mark(tt)
1.03/1.11	 active(U61(X:S)) -> U61(active(X:S))
1.03/1.11	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.03/1.11	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.03/1.11	 active(U72(tt)) -> mark(tt)
1.03/1.11	 active(U72(X:S)) -> U72(active(X:S))
1.03/1.11	 active(U81(tt)) -> mark(tt)
1.03/1.11	 active(U81(X:S)) -> U81(active(X:S))
1.03/1.11	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.03/1.11	 active(__(nil,X:S)) -> mark(X:S)
1.03/1.11	 active(__(X:S,nil)) -> mark(X:S)
1.03/1.11	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.03/1.11	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.03/1.11	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.03/1.11	 active(isList(nil)) -> mark(tt)
1.03/1.11	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.03/1.11	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.03/1.11	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.03/1.11	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.03/1.11	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.03/1.11	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.03/1.11	 active(isPal(nil)) -> mark(tt)
1.03/1.11	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.03/1.11	 active(isQid(a)) -> mark(tt)
1.03/1.11	 active(isQid(e)) -> mark(tt)
1.03/1.11	 active(isQid(i)) -> mark(tt)
1.03/1.11	 active(isQid(o)) -> mark(tt)
1.03/1.11	 active(isQid(u)) -> mark(tt)
1.03/1.11	 isList(ok(X:S)) -> ok(isList(X:S))
1.03/1.11	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.03/1.11	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.03/1.11	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.03/1.11	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.03/1.11	 proper(U11(X:S)) -> U11(proper(X:S))
1.03/1.11	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.03/1.11	 proper(U22(X:S)) -> U22(proper(X:S))
1.03/1.11	 proper(U31(X:S)) -> U31(proper(X:S))
1.03/1.11	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.03/1.11	 proper(U42(X:S)) -> U42(proper(X:S))
1.03/1.11	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.03/1.11	 proper(U52(X:S)) -> U52(proper(X:S))
1.03/1.11	 proper(U61(X:S)) -> U61(proper(X:S))
1.03/1.11	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.03/1.11	 proper(U72(X:S)) -> U72(proper(X:S))
1.03/1.11	 proper(U81(X:S)) -> U81(proper(X:S))
1.03/1.11	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.03/1.11	 proper(isList(X:S)) -> isList(proper(X:S))
1.03/1.11	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.03/1.11	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.03/1.11	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.03/1.11	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.03/1.11	 proper(a) -> ok(a)
1.03/1.11	 proper(e) -> ok(e)
1.03/1.11	 proper(i) -> ok(i)
1.03/1.11	 proper(nil) -> ok(nil)
1.03/1.11	 proper(o) -> ok(o)
1.03/1.11	 proper(tt) -> ok(tt)
1.03/1.11	 proper(u) -> ok(u)
1.03/1.11	 top(mark(X:S)) -> top(proper(X:S))
1.03/1.11	 top(ok(X:S)) -> top(active(X:S))
1.03/1.11	->Strongly Connected Components:
1.03/1.11	 There is no strongly connected component
1.03/1.11	
1.03/1.11	The problem is finite.
1.03/1.11	
1.03/1.11	Problem 1.4: 
1.03/1.11	
1.03/1.11	Subterm Processor:
1.03/1.11	-> Pairs:
1.03/1.11	 ISNELIST(ok(X:S)) -> ISNELIST(X:S)
1.03/1.11	-> Rules:
1.03/1.11	 U11(mark(X:S)) -> mark(U11(X:S))
1.03/1.11	 U11(ok(X:S)) -> ok(U11(X:S))
1.03/1.11	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.03/1.11	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.03/1.11	 U22(mark(X:S)) -> mark(U22(X:S))
1.03/1.11	 U22(ok(X:S)) -> ok(U22(X:S))
1.03/1.11	 U31(mark(X:S)) -> mark(U31(X:S))
1.03/1.11	 U31(ok(X:S)) -> ok(U31(X:S))
1.03/1.11	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.03/1.11	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.03/1.11	 U42(mark(X:S)) -> mark(U42(X:S))
1.03/1.11	 U42(ok(X:S)) -> ok(U42(X:S))
1.03/1.11	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.03/1.11	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.03/1.11	 U52(mark(X:S)) -> mark(U52(X:S))
1.03/1.11	 U52(ok(X:S)) -> ok(U52(X:S))
1.03/1.11	 U61(mark(X:S)) -> mark(U61(X:S))
1.03/1.11	 U61(ok(X:S)) -> ok(U61(X:S))
1.03/1.11	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.03/1.11	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.03/1.11	 U72(mark(X:S)) -> mark(U72(X:S))
1.03/1.11	 U72(ok(X:S)) -> ok(U72(X:S))
1.03/1.11	 U81(mark(X:S)) -> mark(U81(X:S))
1.03/1.11	 U81(ok(X:S)) -> ok(U81(X:S))
1.03/1.11	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.03/1.11	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.03/1.11	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.03/1.11	 active(U11(tt)) -> mark(tt)
1.03/1.11	 active(U11(X:S)) -> U11(active(X:S))
1.03/1.11	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.03/1.11	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.03/1.11	 active(U22(tt)) -> mark(tt)
1.03/1.11	 active(U22(X:S)) -> U22(active(X:S))
1.03/1.11	 active(U31(tt)) -> mark(tt)
1.03/1.11	 active(U31(X:S)) -> U31(active(X:S))
1.03/1.11	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.03/1.11	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.03/1.11	 active(U42(tt)) -> mark(tt)
1.03/1.11	 active(U42(X:S)) -> U42(active(X:S))
1.03/1.11	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.03/1.11	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.03/1.11	 active(U52(tt)) -> mark(tt)
1.03/1.11	 active(U52(X:S)) -> U52(active(X:S))
1.03/1.11	 active(U61(tt)) -> mark(tt)
1.03/1.11	 active(U61(X:S)) -> U61(active(X:S))
1.03/1.11	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.03/1.11	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.03/1.11	 active(U72(tt)) -> mark(tt)
1.03/1.11	 active(U72(X:S)) -> U72(active(X:S))
1.03/1.11	 active(U81(tt)) -> mark(tt)
1.03/1.11	 active(U81(X:S)) -> U81(active(X:S))
1.03/1.11	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.03/1.11	 active(__(nil,X:S)) -> mark(X:S)
1.03/1.11	 active(__(X:S,nil)) -> mark(X:S)
1.03/1.11	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.03/1.11	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.03/1.11	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.03/1.11	 active(isList(nil)) -> mark(tt)
1.03/1.11	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.03/1.11	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.03/1.11	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.03/1.11	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.03/1.11	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.03/1.11	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.03/1.11	 active(isPal(nil)) -> mark(tt)
1.03/1.11	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.03/1.11	 active(isQid(a)) -> mark(tt)
1.03/1.11	 active(isQid(e)) -> mark(tt)
1.03/1.11	 active(isQid(i)) -> mark(tt)
1.03/1.11	 active(isQid(o)) -> mark(tt)
1.03/1.11	 active(isQid(u)) -> mark(tt)
1.03/1.11	 isList(ok(X:S)) -> ok(isList(X:S))
1.03/1.11	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.03/1.11	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.03/1.11	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.03/1.11	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.03/1.11	 proper(U11(X:S)) -> U11(proper(X:S))
1.03/1.11	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.03/1.11	 proper(U22(X:S)) -> U22(proper(X:S))
1.03/1.11	 proper(U31(X:S)) -> U31(proper(X:S))
1.03/1.11	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.03/1.11	 proper(U42(X:S)) -> U42(proper(X:S))
1.03/1.11	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.03/1.11	 proper(U52(X:S)) -> U52(proper(X:S))
1.03/1.11	 proper(U61(X:S)) -> U61(proper(X:S))
1.03/1.11	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.03/1.11	 proper(U72(X:S)) -> U72(proper(X:S))
1.03/1.11	 proper(U81(X:S)) -> U81(proper(X:S))
1.03/1.11	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.03/1.11	 proper(isList(X:S)) -> isList(proper(X:S))
1.03/1.11	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.03/1.11	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.03/1.11	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.03/1.11	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.03/1.11	 proper(a) -> ok(a)
1.03/1.11	 proper(e) -> ok(e)
1.03/1.11	 proper(i) -> ok(i)
1.03/1.11	 proper(nil) -> ok(nil)
1.03/1.11	 proper(o) -> ok(o)
1.03/1.11	 proper(tt) -> ok(tt)
1.03/1.11	 proper(u) -> ok(u)
1.03/1.11	 top(mark(X:S)) -> top(proper(X:S))
1.03/1.11	 top(ok(X:S)) -> top(active(X:S))
1.03/1.11	->Projection:
1.03/1.11	 pi(ISNELIST) = 1
1.03/1.11	
1.03/1.11	Problem 1.4: 
1.03/1.11	
1.03/1.11	SCC Processor:
1.03/1.11	-> Pairs:
1.03/1.11	 Empty
1.03/1.11	-> Rules:
1.03/1.11	 U11(mark(X:S)) -> mark(U11(X:S))
1.03/1.11	 U11(ok(X:S)) -> ok(U11(X:S))
1.03/1.11	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.03/1.11	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.03/1.11	 U22(mark(X:S)) -> mark(U22(X:S))
1.03/1.11	 U22(ok(X:S)) -> ok(U22(X:S))
1.03/1.11	 U31(mark(X:S)) -> mark(U31(X:S))
1.03/1.11	 U31(ok(X:S)) -> ok(U31(X:S))
1.03/1.11	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.03/1.11	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.03/1.11	 U42(mark(X:S)) -> mark(U42(X:S))
1.03/1.11	 U42(ok(X:S)) -> ok(U42(X:S))
1.03/1.11	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.03/1.11	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.03/1.11	 U52(mark(X:S)) -> mark(U52(X:S))
1.03/1.11	 U52(ok(X:S)) -> ok(U52(X:S))
1.03/1.11	 U61(mark(X:S)) -> mark(U61(X:S))
1.03/1.11	 U61(ok(X:S)) -> ok(U61(X:S))
1.03/1.11	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.03/1.11	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.03/1.11	 U72(mark(X:S)) -> mark(U72(X:S))
1.03/1.11	 U72(ok(X:S)) -> ok(U72(X:S))
1.03/1.11	 U81(mark(X:S)) -> mark(U81(X:S))
1.03/1.11	 U81(ok(X:S)) -> ok(U81(X:S))
1.03/1.11	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.03/1.11	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.03/1.11	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.03/1.11	 active(U11(tt)) -> mark(tt)
1.03/1.11	 active(U11(X:S)) -> U11(active(X:S))
1.03/1.11	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.03/1.11	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.03/1.11	 active(U22(tt)) -> mark(tt)
1.03/1.11	 active(U22(X:S)) -> U22(active(X:S))
1.03/1.11	 active(U31(tt)) -> mark(tt)
1.03/1.11	 active(U31(X:S)) -> U31(active(X:S))
1.03/1.11	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.03/1.11	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.03/1.11	 active(U42(tt)) -> mark(tt)
1.03/1.11	 active(U42(X:S)) -> U42(active(X:S))
1.03/1.11	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.03/1.11	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.03/1.11	 active(U52(tt)) -> mark(tt)
1.03/1.11	 active(U52(X:S)) -> U52(active(X:S))
1.03/1.11	 active(U61(tt)) -> mark(tt)
1.03/1.11	 active(U61(X:S)) -> U61(active(X:S))
1.03/1.11	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.03/1.11	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.03/1.11	 active(U72(tt)) -> mark(tt)
1.03/1.11	 active(U72(X:S)) -> U72(active(X:S))
1.03/1.11	 active(U81(tt)) -> mark(tt)
1.03/1.11	 active(U81(X:S)) -> U81(active(X:S))
1.03/1.11	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.03/1.11	 active(__(nil,X:S)) -> mark(X:S)
1.03/1.11	 active(__(X:S,nil)) -> mark(X:S)
1.03/1.11	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.03/1.11	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.03/1.11	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.03/1.11	 active(isList(nil)) -> mark(tt)
1.03/1.11	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.03/1.11	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.03/1.11	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.03/1.11	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.03/1.11	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.03/1.11	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.03/1.11	 active(isPal(nil)) -> mark(tt)
1.03/1.11	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.03/1.11	 active(isQid(a)) -> mark(tt)
1.03/1.11	 active(isQid(e)) -> mark(tt)
1.03/1.11	 active(isQid(i)) -> mark(tt)
1.03/1.11	 active(isQid(o)) -> mark(tt)
1.03/1.11	 active(isQid(u)) -> mark(tt)
1.03/1.11	 isList(ok(X:S)) -> ok(isList(X:S))
1.03/1.11	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.03/1.11	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.03/1.11	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.03/1.11	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.03/1.11	 proper(U11(X:S)) -> U11(proper(X:S))
1.03/1.11	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.03/1.11	 proper(U22(X:S)) -> U22(proper(X:S))
1.03/1.11	 proper(U31(X:S)) -> U31(proper(X:S))
1.03/1.11	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.03/1.11	 proper(U42(X:S)) -> U42(proper(X:S))
1.03/1.11	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.03/1.11	 proper(U52(X:S)) -> U52(proper(X:S))
1.03/1.11	 proper(U61(X:S)) -> U61(proper(X:S))
1.03/1.11	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.03/1.11	 proper(U72(X:S)) -> U72(proper(X:S))
1.03/1.11	 proper(U81(X:S)) -> U81(proper(X:S))
1.03/1.11	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.03/1.11	 proper(isList(X:S)) -> isList(proper(X:S))
1.03/1.11	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.03/1.11	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.03/1.11	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.03/1.11	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.03/1.11	 proper(a) -> ok(a)
1.03/1.11	 proper(e) -> ok(e)
1.03/1.11	 proper(i) -> ok(i)
1.03/1.11	 proper(nil) -> ok(nil)
1.03/1.11	 proper(o) -> ok(o)
1.03/1.11	 proper(tt) -> ok(tt)
1.03/1.11	 proper(u) -> ok(u)
1.03/1.11	 top(mark(X:S)) -> top(proper(X:S))
1.03/1.11	 top(ok(X:S)) -> top(active(X:S))
1.03/1.11	->Strongly Connected Components:
1.03/1.11	 There is no strongly connected component
1.03/1.11	
1.03/1.11	The problem is finite.
1.03/1.11	
1.03/1.11	Problem 1.5: 
1.03/1.11	
1.03/1.11	Subterm Processor:
1.03/1.11	-> Pairs:
1.03/1.11	 ISLIST(ok(X:S)) -> ISLIST(X:S)
1.03/1.11	-> Rules:
1.03/1.11	 U11(mark(X:S)) -> mark(U11(X:S))
1.03/1.11	 U11(ok(X:S)) -> ok(U11(X:S))
1.03/1.11	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.03/1.11	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.03/1.11	 U22(mark(X:S)) -> mark(U22(X:S))
1.03/1.11	 U22(ok(X:S)) -> ok(U22(X:S))
1.03/1.11	 U31(mark(X:S)) -> mark(U31(X:S))
1.03/1.11	 U31(ok(X:S)) -> ok(U31(X:S))
1.03/1.11	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.03/1.11	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.03/1.11	 U42(mark(X:S)) -> mark(U42(X:S))
1.03/1.11	 U42(ok(X:S)) -> ok(U42(X:S))
1.03/1.11	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.03/1.11	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.03/1.11	 U52(mark(X:S)) -> mark(U52(X:S))
1.03/1.11	 U52(ok(X:S)) -> ok(U52(X:S))
1.03/1.11	 U61(mark(X:S)) -> mark(U61(X:S))
1.03/1.11	 U61(ok(X:S)) -> ok(U61(X:S))
1.03/1.11	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.03/1.11	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.03/1.11	 U72(mark(X:S)) -> mark(U72(X:S))
1.03/1.11	 U72(ok(X:S)) -> ok(U72(X:S))
1.03/1.11	 U81(mark(X:S)) -> mark(U81(X:S))
1.03/1.11	 U81(ok(X:S)) -> ok(U81(X:S))
1.03/1.11	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.03/1.11	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.03/1.11	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.03/1.11	 active(U11(tt)) -> mark(tt)
1.03/1.11	 active(U11(X:S)) -> U11(active(X:S))
1.03/1.11	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.03/1.11	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.03/1.11	 active(U22(tt)) -> mark(tt)
1.03/1.11	 active(U22(X:S)) -> U22(active(X:S))
1.03/1.11	 active(U31(tt)) -> mark(tt)
1.03/1.11	 active(U31(X:S)) -> U31(active(X:S))
1.03/1.11	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.03/1.11	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.03/1.11	 active(U42(tt)) -> mark(tt)
1.03/1.11	 active(U42(X:S)) -> U42(active(X:S))
1.03/1.11	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.03/1.11	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.03/1.11	 active(U52(tt)) -> mark(tt)
1.03/1.11	 active(U52(X:S)) -> U52(active(X:S))
1.03/1.11	 active(U61(tt)) -> mark(tt)
1.03/1.11	 active(U61(X:S)) -> U61(active(X:S))
1.03/1.11	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.03/1.11	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.03/1.11	 active(U72(tt)) -> mark(tt)
1.03/1.11	 active(U72(X:S)) -> U72(active(X:S))
1.03/1.11	 active(U81(tt)) -> mark(tt)
1.03/1.11	 active(U81(X:S)) -> U81(active(X:S))
1.03/1.11	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.03/1.11	 active(__(nil,X:S)) -> mark(X:S)
1.03/1.11	 active(__(X:S,nil)) -> mark(X:S)
1.03/1.11	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.03/1.11	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.03/1.11	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.03/1.11	 active(isList(nil)) -> mark(tt)
1.03/1.11	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.03/1.11	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.03/1.11	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.03/1.11	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.03/1.11	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.03/1.11	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.03/1.11	 active(isPal(nil)) -> mark(tt)
1.03/1.11	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.03/1.11	 active(isQid(a)) -> mark(tt)
1.03/1.11	 active(isQid(e)) -> mark(tt)
1.03/1.11	 active(isQid(i)) -> mark(tt)
1.03/1.11	 active(isQid(o)) -> mark(tt)
1.03/1.11	 active(isQid(u)) -> mark(tt)
1.03/1.11	 isList(ok(X:S)) -> ok(isList(X:S))
1.03/1.11	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.03/1.11	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.03/1.11	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.03/1.11	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.03/1.11	 proper(U11(X:S)) -> U11(proper(X:S))
1.03/1.11	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.03/1.11	 proper(U22(X:S)) -> U22(proper(X:S))
1.03/1.11	 proper(U31(X:S)) -> U31(proper(X:S))
1.03/1.11	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.03/1.11	 proper(U42(X:S)) -> U42(proper(X:S))
1.03/1.11	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.03/1.11	 proper(U52(X:S)) -> U52(proper(X:S))
1.03/1.11	 proper(U61(X:S)) -> U61(proper(X:S))
1.03/1.11	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.03/1.11	 proper(U72(X:S)) -> U72(proper(X:S))
1.03/1.11	 proper(U81(X:S)) -> U81(proper(X:S))
1.03/1.11	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.03/1.11	 proper(isList(X:S)) -> isList(proper(X:S))
1.03/1.11	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.03/1.11	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.03/1.11	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.03/1.11	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.03/1.11	 proper(a) -> ok(a)
1.03/1.11	 proper(e) -> ok(e)
1.03/1.11	 proper(i) -> ok(i)
1.03/1.11	 proper(nil) -> ok(nil)
1.03/1.11	 proper(o) -> ok(o)
1.03/1.11	 proper(tt) -> ok(tt)
1.03/1.11	 proper(u) -> ok(u)
1.03/1.11	 top(mark(X:S)) -> top(proper(X:S))
1.03/1.11	 top(ok(X:S)) -> top(active(X:S))
1.03/1.11	->Projection:
1.03/1.11	 pi(ISLIST) = 1
1.03/1.11	
1.03/1.11	Problem 1.5: 
1.03/1.11	
1.03/1.11	SCC Processor:
1.03/1.11	-> Pairs:
1.03/1.11	 Empty
1.03/1.11	-> Rules:
1.03/1.11	 U11(mark(X:S)) -> mark(U11(X:S))
1.03/1.11	 U11(ok(X:S)) -> ok(U11(X:S))
1.03/1.11	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.03/1.11	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.03/1.11	 U22(mark(X:S)) -> mark(U22(X:S))
1.03/1.11	 U22(ok(X:S)) -> ok(U22(X:S))
1.03/1.11	 U31(mark(X:S)) -> mark(U31(X:S))
1.03/1.11	 U31(ok(X:S)) -> ok(U31(X:S))
1.03/1.11	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.03/1.11	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.03/1.11	 U42(mark(X:S)) -> mark(U42(X:S))
1.03/1.11	 U42(ok(X:S)) -> ok(U42(X:S))
1.03/1.11	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.03/1.11	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.03/1.11	 U52(mark(X:S)) -> mark(U52(X:S))
1.03/1.11	 U52(ok(X:S)) -> ok(U52(X:S))
1.03/1.11	 U61(mark(X:S)) -> mark(U61(X:S))
1.03/1.11	 U61(ok(X:S)) -> ok(U61(X:S))
1.03/1.11	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.03/1.11	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.03/1.11	 U72(mark(X:S)) -> mark(U72(X:S))
1.03/1.11	 U72(ok(X:S)) -> ok(U72(X:S))
1.03/1.11	 U81(mark(X:S)) -> mark(U81(X:S))
1.03/1.11	 U81(ok(X:S)) -> ok(U81(X:S))
1.03/1.11	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.03/1.11	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.03/1.11	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.03/1.11	 active(U11(tt)) -> mark(tt)
1.03/1.11	 active(U11(X:S)) -> U11(active(X:S))
1.03/1.11	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.03/1.11	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.03/1.11	 active(U22(tt)) -> mark(tt)
1.03/1.11	 active(U22(X:S)) -> U22(active(X:S))
1.03/1.11	 active(U31(tt)) -> mark(tt)
1.03/1.11	 active(U31(X:S)) -> U31(active(X:S))
1.03/1.11	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.03/1.11	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.03/1.11	 active(U42(tt)) -> mark(tt)
1.03/1.11	 active(U42(X:S)) -> U42(active(X:S))
1.03/1.11	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.03/1.11	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.03/1.11	 active(U52(tt)) -> mark(tt)
1.03/1.11	 active(U52(X:S)) -> U52(active(X:S))
1.03/1.11	 active(U61(tt)) -> mark(tt)
1.03/1.11	 active(U61(X:S)) -> U61(active(X:S))
1.03/1.11	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.03/1.11	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.03/1.11	 active(U72(tt)) -> mark(tt)
1.03/1.11	 active(U72(X:S)) -> U72(active(X:S))
1.03/1.11	 active(U81(tt)) -> mark(tt)
1.03/1.11	 active(U81(X:S)) -> U81(active(X:S))
1.03/1.11	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.03/1.11	 active(__(nil,X:S)) -> mark(X:S)
1.03/1.11	 active(__(X:S,nil)) -> mark(X:S)
1.03/1.11	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.03/1.11	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.03/1.11	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.03/1.11	 active(isList(nil)) -> mark(tt)
1.03/1.11	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.03/1.11	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.03/1.11	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.03/1.11	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.03/1.11	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.03/1.11	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.03/1.11	 active(isPal(nil)) -> mark(tt)
1.03/1.11	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.03/1.11	 active(isQid(a)) -> mark(tt)
1.03/1.11	 active(isQid(e)) -> mark(tt)
1.03/1.11	 active(isQid(i)) -> mark(tt)
1.03/1.11	 active(isQid(o)) -> mark(tt)
1.03/1.11	 active(isQid(u)) -> mark(tt)
1.03/1.11	 isList(ok(X:S)) -> ok(isList(X:S))
1.03/1.11	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.03/1.11	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.03/1.11	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.03/1.11	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.03/1.11	 proper(U11(X:S)) -> U11(proper(X:S))
1.03/1.11	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.03/1.11	 proper(U22(X:S)) -> U22(proper(X:S))
1.03/1.11	 proper(U31(X:S)) -> U31(proper(X:S))
1.03/1.11	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.03/1.11	 proper(U42(X:S)) -> U42(proper(X:S))
1.03/1.11	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.03/1.11	 proper(U52(X:S)) -> U52(proper(X:S))
1.03/1.11	 proper(U61(X:S)) -> U61(proper(X:S))
1.03/1.11	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.03/1.11	 proper(U72(X:S)) -> U72(proper(X:S))
1.03/1.11	 proper(U81(X:S)) -> U81(proper(X:S))
1.03/1.11	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.03/1.11	 proper(isList(X:S)) -> isList(proper(X:S))
1.03/1.11	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.03/1.11	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.03/1.11	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.03/1.11	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.03/1.11	 proper(a) -> ok(a)
1.03/1.11	 proper(e) -> ok(e)
1.03/1.11	 proper(i) -> ok(i)
1.03/1.11	 proper(nil) -> ok(nil)
1.03/1.11	 proper(o) -> ok(o)
1.03/1.11	 proper(tt) -> ok(tt)
1.03/1.11	 proper(u) -> ok(u)
1.03/1.11	 top(mark(X:S)) -> top(proper(X:S))
1.03/1.11	 top(ok(X:S)) -> top(active(X:S))
1.03/1.11	->Strongly Connected Components:
1.03/1.11	 There is no strongly connected component
1.03/1.11	
1.03/1.11	The problem is finite.
1.03/1.11	
1.03/1.11	Problem 1.6: 
1.03/1.11	
1.03/1.11	Subterm Processor:
1.03/1.11	-> Pairs:
1.03/1.11	 __#(mark(X1:S),X2:S) -> __#(X1:S,X2:S)
1.03/1.11	 __#(ok(X1:S),ok(X2:S)) -> __#(X1:S,X2:S)
1.03/1.11	 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S)
1.03/1.11	-> Rules:
1.03/1.11	 U11(mark(X:S)) -> mark(U11(X:S))
1.03/1.11	 U11(ok(X:S)) -> ok(U11(X:S))
1.03/1.11	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.03/1.11	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.03/1.11	 U22(mark(X:S)) -> mark(U22(X:S))
1.03/1.11	 U22(ok(X:S)) -> ok(U22(X:S))
1.03/1.11	 U31(mark(X:S)) -> mark(U31(X:S))
1.03/1.11	 U31(ok(X:S)) -> ok(U31(X:S))
1.03/1.11	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.03/1.11	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.03/1.11	 U42(mark(X:S)) -> mark(U42(X:S))
1.03/1.11	 U42(ok(X:S)) -> ok(U42(X:S))
1.03/1.11	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.03/1.11	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.03/1.11	 U52(mark(X:S)) -> mark(U52(X:S))
1.03/1.11	 U52(ok(X:S)) -> ok(U52(X:S))
1.03/1.11	 U61(mark(X:S)) -> mark(U61(X:S))
1.03/1.11	 U61(ok(X:S)) -> ok(U61(X:S))
1.03/1.11	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.03/1.11	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.03/1.11	 U72(mark(X:S)) -> mark(U72(X:S))
1.03/1.11	 U72(ok(X:S)) -> ok(U72(X:S))
1.03/1.11	 U81(mark(X:S)) -> mark(U81(X:S))
1.03/1.11	 U81(ok(X:S)) -> ok(U81(X:S))
1.03/1.11	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.03/1.11	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.03/1.11	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.03/1.11	 active(U11(tt)) -> mark(tt)
1.03/1.11	 active(U11(X:S)) -> U11(active(X:S))
1.03/1.11	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.03/1.11	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.03/1.11	 active(U22(tt)) -> mark(tt)
1.03/1.11	 active(U22(X:S)) -> U22(active(X:S))
1.03/1.11	 active(U31(tt)) -> mark(tt)
1.03/1.11	 active(U31(X:S)) -> U31(active(X:S))
1.03/1.11	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.03/1.11	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.03/1.11	 active(U42(tt)) -> mark(tt)
1.03/1.11	 active(U42(X:S)) -> U42(active(X:S))
1.03/1.11	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.03/1.11	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.03/1.11	 active(U52(tt)) -> mark(tt)
1.03/1.11	 active(U52(X:S)) -> U52(active(X:S))
1.03/1.11	 active(U61(tt)) -> mark(tt)
1.03/1.11	 active(U61(X:S)) -> U61(active(X:S))
1.03/1.11	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.03/1.11	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.03/1.11	 active(U72(tt)) -> mark(tt)
1.03/1.11	 active(U72(X:S)) -> U72(active(X:S))
1.03/1.11	 active(U81(tt)) -> mark(tt)
1.03/1.11	 active(U81(X:S)) -> U81(active(X:S))
1.03/1.11	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.03/1.11	 active(__(nil,X:S)) -> mark(X:S)
1.03/1.11	 active(__(X:S,nil)) -> mark(X:S)
1.03/1.11	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.03/1.11	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.03/1.11	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.03/1.11	 active(isList(nil)) -> mark(tt)
1.03/1.11	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.03/1.11	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.03/1.11	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.03/1.11	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.03/1.11	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.03/1.11	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.03/1.11	 active(isPal(nil)) -> mark(tt)
1.03/1.11	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.03/1.11	 active(isQid(a)) -> mark(tt)
1.03/1.11	 active(isQid(e)) -> mark(tt)
1.03/1.11	 active(isQid(i)) -> mark(tt)
1.03/1.11	 active(isQid(o)) -> mark(tt)
1.03/1.11	 active(isQid(u)) -> mark(tt)
1.03/1.11	 isList(ok(X:S)) -> ok(isList(X:S))
1.03/1.11	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.03/1.11	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.03/1.11	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.03/1.11	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.03/1.11	 proper(U11(X:S)) -> U11(proper(X:S))
1.03/1.11	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.03/1.11	 proper(U22(X:S)) -> U22(proper(X:S))
1.03/1.11	 proper(U31(X:S)) -> U31(proper(X:S))
1.03/1.11	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.03/1.11	 proper(U42(X:S)) -> U42(proper(X:S))
1.03/1.11	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.03/1.11	 proper(U52(X:S)) -> U52(proper(X:S))
1.03/1.11	 proper(U61(X:S)) -> U61(proper(X:S))
1.03/1.11	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.03/1.11	 proper(U72(X:S)) -> U72(proper(X:S))
1.03/1.11	 proper(U81(X:S)) -> U81(proper(X:S))
1.03/1.11	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.03/1.11	 proper(isList(X:S)) -> isList(proper(X:S))
1.03/1.11	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.03/1.11	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.03/1.11	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.03/1.11	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.03/1.11	 proper(a) -> ok(a)
1.03/1.11	 proper(e) -> ok(e)
1.03/1.11	 proper(i) -> ok(i)
1.03/1.11	 proper(nil) -> ok(nil)
1.03/1.11	 proper(o) -> ok(o)
1.03/1.11	 proper(tt) -> ok(tt)
1.03/1.11	 proper(u) -> ok(u)
1.03/1.11	 top(mark(X:S)) -> top(proper(X:S))
1.03/1.11	 top(ok(X:S)) -> top(active(X:S))
1.03/1.11	->Projection:
1.03/1.11	 pi(__#) = 1
1.03/1.11	
1.03/1.11	Problem 1.6: 
1.03/1.11	
1.03/1.11	SCC Processor:
1.03/1.11	-> Pairs:
1.03/1.11	 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S)
1.03/1.11	-> Rules:
1.03/1.11	 U11(mark(X:S)) -> mark(U11(X:S))
1.03/1.11	 U11(ok(X:S)) -> ok(U11(X:S))
1.03/1.11	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.03/1.11	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.03/1.11	 U22(mark(X:S)) -> mark(U22(X:S))
1.03/1.11	 U22(ok(X:S)) -> ok(U22(X:S))
1.03/1.11	 U31(mark(X:S)) -> mark(U31(X:S))
1.03/1.11	 U31(ok(X:S)) -> ok(U31(X:S))
1.03/1.11	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.03/1.11	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.03/1.11	 U42(mark(X:S)) -> mark(U42(X:S))
1.03/1.11	 U42(ok(X:S)) -> ok(U42(X:S))
1.03/1.11	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.03/1.11	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.03/1.11	 U52(mark(X:S)) -> mark(U52(X:S))
1.03/1.11	 U52(ok(X:S)) -> ok(U52(X:S))
1.03/1.11	 U61(mark(X:S)) -> mark(U61(X:S))
1.03/1.11	 U61(ok(X:S)) -> ok(U61(X:S))
1.03/1.11	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.03/1.11	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.03/1.11	 U72(mark(X:S)) -> mark(U72(X:S))
1.03/1.11	 U72(ok(X:S)) -> ok(U72(X:S))
1.03/1.11	 U81(mark(X:S)) -> mark(U81(X:S))
1.03/1.11	 U81(ok(X:S)) -> ok(U81(X:S))
1.03/1.11	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.03/1.11	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.03/1.11	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.03/1.11	 active(U11(tt)) -> mark(tt)
1.03/1.11	 active(U11(X:S)) -> U11(active(X:S))
1.03/1.11	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.03/1.11	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.03/1.11	 active(U22(tt)) -> mark(tt)
1.03/1.11	 active(U22(X:S)) -> U22(active(X:S))
1.03/1.11	 active(U31(tt)) -> mark(tt)
1.03/1.11	 active(U31(X:S)) -> U31(active(X:S))
1.03/1.11	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.03/1.11	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.03/1.11	 active(U42(tt)) -> mark(tt)
1.03/1.11	 active(U42(X:S)) -> U42(active(X:S))
1.03/1.11	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.03/1.11	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.03/1.11	 active(U52(tt)) -> mark(tt)
1.03/1.11	 active(U52(X:S)) -> U52(active(X:S))
1.03/1.11	 active(U61(tt)) -> mark(tt)
1.03/1.11	 active(U61(X:S)) -> U61(active(X:S))
1.03/1.11	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.03/1.11	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.03/1.11	 active(U72(tt)) -> mark(tt)
1.03/1.11	 active(U72(X:S)) -> U72(active(X:S))
1.03/1.11	 active(U81(tt)) -> mark(tt)
1.03/1.11	 active(U81(X:S)) -> U81(active(X:S))
1.03/1.11	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.03/1.11	 active(__(nil,X:S)) -> mark(X:S)
1.03/1.11	 active(__(X:S,nil)) -> mark(X:S)
1.03/1.11	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.03/1.11	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.03/1.11	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.03/1.11	 active(isList(nil)) -> mark(tt)
1.03/1.11	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.03/1.11	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.03/1.11	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.03/1.11	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.03/1.11	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.03/1.11	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.03/1.11	 active(isPal(nil)) -> mark(tt)
1.03/1.11	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.03/1.11	 active(isQid(a)) -> mark(tt)
1.03/1.11	 active(isQid(e)) -> mark(tt)
1.03/1.11	 active(isQid(i)) -> mark(tt)
1.03/1.11	 active(isQid(o)) -> mark(tt)
1.03/1.11	 active(isQid(u)) -> mark(tt)
1.03/1.11	 isList(ok(X:S)) -> ok(isList(X:S))
1.03/1.11	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.03/1.11	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.03/1.11	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.03/1.11	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.03/1.11	 proper(U11(X:S)) -> U11(proper(X:S))
1.03/1.11	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.03/1.11	 proper(U22(X:S)) -> U22(proper(X:S))
1.03/1.11	 proper(U31(X:S)) -> U31(proper(X:S))
1.03/1.11	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.03/1.11	 proper(U42(X:S)) -> U42(proper(X:S))
1.03/1.11	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.03/1.11	 proper(U52(X:S)) -> U52(proper(X:S))
1.03/1.11	 proper(U61(X:S)) -> U61(proper(X:S))
1.03/1.11	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.03/1.11	 proper(U72(X:S)) -> U72(proper(X:S))
1.03/1.11	 proper(U81(X:S)) -> U81(proper(X:S))
1.03/1.11	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.03/1.11	 proper(isList(X:S)) -> isList(proper(X:S))
1.03/1.11	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.03/1.11	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.03/1.11	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.03/1.11	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.03/1.11	 proper(a) -> ok(a)
1.03/1.11	 proper(e) -> ok(e)
1.03/1.11	 proper(i) -> ok(i)
1.03/1.11	 proper(nil) -> ok(nil)
1.03/1.11	 proper(o) -> ok(o)
1.03/1.11	 proper(tt) -> ok(tt)
1.03/1.11	 proper(u) -> ok(u)
1.03/1.11	 top(mark(X:S)) -> top(proper(X:S))
1.03/1.11	 top(ok(X:S)) -> top(active(X:S))
1.03/1.11	->Strongly Connected Components:
1.03/1.11	->->Cycle:
1.03/1.11	->->-> Pairs:
1.03/1.11	 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S)
1.03/1.11	->->-> Rules:
1.03/1.11	 U11(mark(X:S)) -> mark(U11(X:S))
1.03/1.11	 U11(ok(X:S)) -> ok(U11(X:S))
1.03/1.11	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.03/1.11	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.03/1.11	 U22(mark(X:S)) -> mark(U22(X:S))
1.03/1.11	 U22(ok(X:S)) -> ok(U22(X:S))
1.03/1.11	 U31(mark(X:S)) -> mark(U31(X:S))
1.03/1.11	 U31(ok(X:S)) -> ok(U31(X:S))
1.03/1.11	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.03/1.11	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.03/1.11	 U42(mark(X:S)) -> mark(U42(X:S))
1.03/1.11	 U42(ok(X:S)) -> ok(U42(X:S))
1.03/1.11	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.03/1.11	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.03/1.11	 U52(mark(X:S)) -> mark(U52(X:S))
1.03/1.11	 U52(ok(X:S)) -> ok(U52(X:S))
1.03/1.11	 U61(mark(X:S)) -> mark(U61(X:S))
1.03/1.11	 U61(ok(X:S)) -> ok(U61(X:S))
1.03/1.11	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.03/1.11	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.03/1.11	 U72(mark(X:S)) -> mark(U72(X:S))
1.03/1.11	 U72(ok(X:S)) -> ok(U72(X:S))
1.03/1.11	 U81(mark(X:S)) -> mark(U81(X:S))
1.03/1.11	 U81(ok(X:S)) -> ok(U81(X:S))
1.03/1.11	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.03/1.11	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.03/1.11	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.03/1.11	 active(U11(tt)) -> mark(tt)
1.03/1.11	 active(U11(X:S)) -> U11(active(X:S))
1.03/1.11	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.03/1.11	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.03/1.11	 active(U22(tt)) -> mark(tt)
1.03/1.11	 active(U22(X:S)) -> U22(active(X:S))
1.03/1.11	 active(U31(tt)) -> mark(tt)
1.03/1.11	 active(U31(X:S)) -> U31(active(X:S))
1.03/1.11	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.03/1.11	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.03/1.11	 active(U42(tt)) -> mark(tt)
1.03/1.11	 active(U42(X:S)) -> U42(active(X:S))
1.03/1.11	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.05/1.11	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.05/1.11	 active(U52(tt)) -> mark(tt)
1.05/1.11	 active(U52(X:S)) -> U52(active(X:S))
1.05/1.11	 active(U61(tt)) -> mark(tt)
1.05/1.11	 active(U61(X:S)) -> U61(active(X:S))
1.05/1.11	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.05/1.11	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.05/1.11	 active(U72(tt)) -> mark(tt)
1.05/1.11	 active(U72(X:S)) -> U72(active(X:S))
1.05/1.11	 active(U81(tt)) -> mark(tt)
1.05/1.11	 active(U81(X:S)) -> U81(active(X:S))
1.05/1.11	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.05/1.11	 active(__(nil,X:S)) -> mark(X:S)
1.05/1.11	 active(__(X:S,nil)) -> mark(X:S)
1.05/1.11	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.05/1.11	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.05/1.11	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.05/1.11	 active(isList(nil)) -> mark(tt)
1.05/1.11	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.05/1.11	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.05/1.11	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.05/1.11	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.05/1.11	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.05/1.11	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.05/1.11	 active(isPal(nil)) -> mark(tt)
1.05/1.11	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.05/1.11	 active(isQid(a)) -> mark(tt)
1.05/1.11	 active(isQid(e)) -> mark(tt)
1.05/1.11	 active(isQid(i)) -> mark(tt)
1.05/1.11	 active(isQid(o)) -> mark(tt)
1.05/1.11	 active(isQid(u)) -> mark(tt)
1.05/1.11	 isList(ok(X:S)) -> ok(isList(X:S))
1.05/1.11	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.05/1.11	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.05/1.11	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.05/1.11	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.05/1.11	 proper(U11(X:S)) -> U11(proper(X:S))
1.05/1.11	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.05/1.11	 proper(U22(X:S)) -> U22(proper(X:S))
1.05/1.11	 proper(U31(X:S)) -> U31(proper(X:S))
1.05/1.11	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.05/1.11	 proper(U42(X:S)) -> U42(proper(X:S))
1.05/1.11	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.05/1.11	 proper(U52(X:S)) -> U52(proper(X:S))
1.05/1.11	 proper(U61(X:S)) -> U61(proper(X:S))
1.05/1.11	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.05/1.11	 proper(U72(X:S)) -> U72(proper(X:S))
1.05/1.11	 proper(U81(X:S)) -> U81(proper(X:S))
1.05/1.11	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.05/1.11	 proper(isList(X:S)) -> isList(proper(X:S))
1.05/1.11	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.05/1.11	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.05/1.11	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.05/1.11	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.05/1.11	 proper(a) -> ok(a)
1.05/1.11	 proper(e) -> ok(e)
1.05/1.11	 proper(i) -> ok(i)
1.05/1.11	 proper(nil) -> ok(nil)
1.05/1.11	 proper(o) -> ok(o)
1.05/1.11	 proper(tt) -> ok(tt)
1.05/1.11	 proper(u) -> ok(u)
1.05/1.11	 top(mark(X:S)) -> top(proper(X:S))
1.05/1.11	 top(ok(X:S)) -> top(active(X:S))
1.05/1.11	
1.05/1.11	Problem 1.6: 
1.05/1.11	
1.05/1.11	Subterm Processor:
1.05/1.11	-> Pairs:
1.05/1.11	 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S)
1.05/1.11	-> Rules:
1.05/1.11	 U11(mark(X:S)) -> mark(U11(X:S))
1.05/1.11	 U11(ok(X:S)) -> ok(U11(X:S))
1.05/1.11	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.05/1.11	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.05/1.11	 U22(mark(X:S)) -> mark(U22(X:S))
1.05/1.11	 U22(ok(X:S)) -> ok(U22(X:S))
1.05/1.11	 U31(mark(X:S)) -> mark(U31(X:S))
1.05/1.11	 U31(ok(X:S)) -> ok(U31(X:S))
1.05/1.11	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.05/1.11	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.05/1.11	 U42(mark(X:S)) -> mark(U42(X:S))
1.05/1.11	 U42(ok(X:S)) -> ok(U42(X:S))
1.05/1.11	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.05/1.11	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.05/1.11	 U52(mark(X:S)) -> mark(U52(X:S))
1.05/1.11	 U52(ok(X:S)) -> ok(U52(X:S))
1.05/1.11	 U61(mark(X:S)) -> mark(U61(X:S))
1.05/1.11	 U61(ok(X:S)) -> ok(U61(X:S))
1.05/1.11	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.05/1.11	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.05/1.11	 U72(mark(X:S)) -> mark(U72(X:S))
1.05/1.11	 U72(ok(X:S)) -> ok(U72(X:S))
1.05/1.11	 U81(mark(X:S)) -> mark(U81(X:S))
1.05/1.11	 U81(ok(X:S)) -> ok(U81(X:S))
1.05/1.11	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.05/1.11	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.05/1.11	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.05/1.11	 active(U11(tt)) -> mark(tt)
1.05/1.11	 active(U11(X:S)) -> U11(active(X:S))
1.05/1.11	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.05/1.11	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.05/1.11	 active(U22(tt)) -> mark(tt)
1.05/1.11	 active(U22(X:S)) -> U22(active(X:S))
1.05/1.11	 active(U31(tt)) -> mark(tt)
1.05/1.11	 active(U31(X:S)) -> U31(active(X:S))
1.05/1.11	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.05/1.11	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.05/1.11	 active(U42(tt)) -> mark(tt)
1.05/1.11	 active(U42(X:S)) -> U42(active(X:S))
1.05/1.11	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.05/1.11	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.05/1.11	 active(U52(tt)) -> mark(tt)
1.05/1.11	 active(U52(X:S)) -> U52(active(X:S))
1.05/1.11	 active(U61(tt)) -> mark(tt)
1.05/1.11	 active(U61(X:S)) -> U61(active(X:S))
1.05/1.11	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.05/1.11	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.05/1.11	 active(U72(tt)) -> mark(tt)
1.05/1.11	 active(U72(X:S)) -> U72(active(X:S))
1.05/1.11	 active(U81(tt)) -> mark(tt)
1.05/1.11	 active(U81(X:S)) -> U81(active(X:S))
1.05/1.11	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.05/1.11	 active(__(nil,X:S)) -> mark(X:S)
1.05/1.11	 active(__(X:S,nil)) -> mark(X:S)
1.05/1.11	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.05/1.11	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.05/1.11	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.05/1.11	 active(isList(nil)) -> mark(tt)
1.05/1.11	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.05/1.11	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.05/1.11	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.05/1.11	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.05/1.11	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.05/1.11	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.05/1.11	 active(isPal(nil)) -> mark(tt)
1.05/1.11	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.05/1.11	 active(isQid(a)) -> mark(tt)
1.05/1.11	 active(isQid(e)) -> mark(tt)
1.05/1.11	 active(isQid(i)) -> mark(tt)
1.05/1.11	 active(isQid(o)) -> mark(tt)
1.05/1.11	 active(isQid(u)) -> mark(tt)
1.05/1.11	 isList(ok(X:S)) -> ok(isList(X:S))
1.05/1.11	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.05/1.11	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.05/1.11	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.05/1.11	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.05/1.11	 proper(U11(X:S)) -> U11(proper(X:S))
1.05/1.11	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.05/1.11	 proper(U22(X:S)) -> U22(proper(X:S))
1.05/1.11	 proper(U31(X:S)) -> U31(proper(X:S))
1.05/1.11	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.05/1.11	 proper(U42(X:S)) -> U42(proper(X:S))
1.05/1.11	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.05/1.11	 proper(U52(X:S)) -> U52(proper(X:S))
1.05/1.11	 proper(U61(X:S)) -> U61(proper(X:S))
1.05/1.11	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.05/1.11	 proper(U72(X:S)) -> U72(proper(X:S))
1.05/1.11	 proper(U81(X:S)) -> U81(proper(X:S))
1.05/1.11	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.05/1.11	 proper(isList(X:S)) -> isList(proper(X:S))
1.05/1.11	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.05/1.11	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.05/1.11	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.05/1.11	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.05/1.11	 proper(a) -> ok(a)
1.05/1.11	 proper(e) -> ok(e)
1.05/1.11	 proper(i) -> ok(i)
1.05/1.11	 proper(nil) -> ok(nil)
1.05/1.11	 proper(o) -> ok(o)
1.05/1.11	 proper(tt) -> ok(tt)
1.05/1.11	 proper(u) -> ok(u)
1.05/1.11	 top(mark(X:S)) -> top(proper(X:S))
1.05/1.11	 top(ok(X:S)) -> top(active(X:S))
1.05/1.11	->Projection:
1.05/1.11	 pi(__#) = 2
1.05/1.11	
1.05/1.11	Problem 1.6: 
1.05/1.11	
1.05/1.11	SCC Processor:
1.05/1.11	-> Pairs:
1.05/1.11	 Empty
1.05/1.11	-> Rules:
1.05/1.11	 U11(mark(X:S)) -> mark(U11(X:S))
1.05/1.11	 U11(ok(X:S)) -> ok(U11(X:S))
1.05/1.11	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.05/1.11	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.05/1.11	 U22(mark(X:S)) -> mark(U22(X:S))
1.05/1.11	 U22(ok(X:S)) -> ok(U22(X:S))
1.05/1.11	 U31(mark(X:S)) -> mark(U31(X:S))
1.05/1.11	 U31(ok(X:S)) -> ok(U31(X:S))
1.05/1.11	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.05/1.11	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.05/1.11	 U42(mark(X:S)) -> mark(U42(X:S))
1.05/1.11	 U42(ok(X:S)) -> ok(U42(X:S))
1.05/1.11	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.05/1.11	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.05/1.11	 U52(mark(X:S)) -> mark(U52(X:S))
1.05/1.11	 U52(ok(X:S)) -> ok(U52(X:S))
1.05/1.11	 U61(mark(X:S)) -> mark(U61(X:S))
1.05/1.11	 U61(ok(X:S)) -> ok(U61(X:S))
1.05/1.11	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.05/1.11	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.05/1.11	 U72(mark(X:S)) -> mark(U72(X:S))
1.05/1.11	 U72(ok(X:S)) -> ok(U72(X:S))
1.05/1.11	 U81(mark(X:S)) -> mark(U81(X:S))
1.05/1.11	 U81(ok(X:S)) -> ok(U81(X:S))
1.05/1.11	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.05/1.11	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.05/1.11	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.05/1.11	 active(U11(tt)) -> mark(tt)
1.05/1.11	 active(U11(X:S)) -> U11(active(X:S))
1.05/1.11	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.05/1.11	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.05/1.11	 active(U22(tt)) -> mark(tt)
1.05/1.11	 active(U22(X:S)) -> U22(active(X:S))
1.05/1.11	 active(U31(tt)) -> mark(tt)
1.05/1.11	 active(U31(X:S)) -> U31(active(X:S))
1.05/1.11	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.05/1.11	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.05/1.11	 active(U42(tt)) -> mark(tt)
1.05/1.11	 active(U42(X:S)) -> U42(active(X:S))
1.05/1.11	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.05/1.11	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.05/1.11	 active(U52(tt)) -> mark(tt)
1.05/1.11	 active(U52(X:S)) -> U52(active(X:S))
1.05/1.11	 active(U61(tt)) -> mark(tt)
1.05/1.11	 active(U61(X:S)) -> U61(active(X:S))
1.05/1.11	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.05/1.11	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.05/1.11	 active(U72(tt)) -> mark(tt)
1.05/1.11	 active(U72(X:S)) -> U72(active(X:S))
1.05/1.11	 active(U81(tt)) -> mark(tt)
1.05/1.11	 active(U81(X:S)) -> U81(active(X:S))
1.05/1.11	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.05/1.11	 active(__(nil,X:S)) -> mark(X:S)
1.05/1.11	 active(__(X:S,nil)) -> mark(X:S)
1.05/1.11	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.05/1.11	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.05/1.11	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.05/1.11	 active(isList(nil)) -> mark(tt)
1.05/1.11	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.05/1.11	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.05/1.11	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.05/1.11	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.05/1.11	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.05/1.11	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.05/1.11	 active(isPal(nil)) -> mark(tt)
1.05/1.11	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.05/1.11	 active(isQid(a)) -> mark(tt)
1.05/1.11	 active(isQid(e)) -> mark(tt)
1.05/1.11	 active(isQid(i)) -> mark(tt)
1.05/1.11	 active(isQid(o)) -> mark(tt)
1.05/1.11	 active(isQid(u)) -> mark(tt)
1.05/1.11	 isList(ok(X:S)) -> ok(isList(X:S))
1.05/1.11	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.05/1.11	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.05/1.11	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.05/1.11	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.05/1.11	 proper(U11(X:S)) -> U11(proper(X:S))
1.05/1.11	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.05/1.11	 proper(U22(X:S)) -> U22(proper(X:S))
1.05/1.11	 proper(U31(X:S)) -> U31(proper(X:S))
1.05/1.11	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.05/1.11	 proper(U42(X:S)) -> U42(proper(X:S))
1.05/1.11	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.05/1.11	 proper(U52(X:S)) -> U52(proper(X:S))
1.05/1.11	 proper(U61(X:S)) -> U61(proper(X:S))
1.05/1.11	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.05/1.11	 proper(U72(X:S)) -> U72(proper(X:S))
1.05/1.11	 proper(U81(X:S)) -> U81(proper(X:S))
1.05/1.11	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.05/1.11	 proper(isList(X:S)) -> isList(proper(X:S))
1.05/1.11	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.05/1.11	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.05/1.11	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.05/1.11	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.05/1.11	 proper(a) -> ok(a)
1.05/1.11	 proper(e) -> ok(e)
1.05/1.11	 proper(i) -> ok(i)
1.05/1.11	 proper(nil) -> ok(nil)
1.05/1.11	 proper(o) -> ok(o)
1.05/1.11	 proper(tt) -> ok(tt)
1.05/1.11	 proper(u) -> ok(u)
1.05/1.11	 top(mark(X:S)) -> top(proper(X:S))
1.05/1.11	 top(ok(X:S)) -> top(active(X:S))
1.05/1.11	->Strongly Connected Components:
1.05/1.11	 There is no strongly connected component
1.05/1.11	
1.05/1.11	The problem is finite.
1.05/1.11	
1.05/1.11	Problem 1.7: 
1.05/1.11	
1.05/1.11	Subterm Processor:
1.05/1.11	-> Pairs:
1.05/1.11	 U81#(mark(X:S)) -> U81#(X:S)
1.05/1.11	 U81#(ok(X:S)) -> U81#(X:S)
1.05/1.11	-> Rules:
1.05/1.11	 U11(mark(X:S)) -> mark(U11(X:S))
1.05/1.11	 U11(ok(X:S)) -> ok(U11(X:S))
1.05/1.11	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.05/1.11	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.05/1.11	 U22(mark(X:S)) -> mark(U22(X:S))
1.05/1.11	 U22(ok(X:S)) -> ok(U22(X:S))
1.05/1.11	 U31(mark(X:S)) -> mark(U31(X:S))
1.05/1.11	 U31(ok(X:S)) -> ok(U31(X:S))
1.05/1.11	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.05/1.11	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.05/1.11	 U42(mark(X:S)) -> mark(U42(X:S))
1.05/1.11	 U42(ok(X:S)) -> ok(U42(X:S))
1.05/1.11	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.05/1.11	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.05/1.11	 U52(mark(X:S)) -> mark(U52(X:S))
1.05/1.11	 U52(ok(X:S)) -> ok(U52(X:S))
1.05/1.11	 U61(mark(X:S)) -> mark(U61(X:S))
1.05/1.11	 U61(ok(X:S)) -> ok(U61(X:S))
1.05/1.11	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.05/1.11	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.05/1.11	 U72(mark(X:S)) -> mark(U72(X:S))
1.05/1.11	 U72(ok(X:S)) -> ok(U72(X:S))
1.05/1.11	 U81(mark(X:S)) -> mark(U81(X:S))
1.05/1.11	 U81(ok(X:S)) -> ok(U81(X:S))
1.05/1.11	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.05/1.11	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.05/1.11	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.05/1.11	 active(U11(tt)) -> mark(tt)
1.05/1.11	 active(U11(X:S)) -> U11(active(X:S))
1.05/1.11	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.05/1.11	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.05/1.11	 active(U22(tt)) -> mark(tt)
1.05/1.11	 active(U22(X:S)) -> U22(active(X:S))
1.05/1.11	 active(U31(tt)) -> mark(tt)
1.05/1.11	 active(U31(X:S)) -> U31(active(X:S))
1.05/1.11	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.05/1.11	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.05/1.11	 active(U42(tt)) -> mark(tt)
1.05/1.11	 active(U42(X:S)) -> U42(active(X:S))
1.05/1.11	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.05/1.11	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.05/1.11	 active(U52(tt)) -> mark(tt)
1.05/1.11	 active(U52(X:S)) -> U52(active(X:S))
1.05/1.11	 active(U61(tt)) -> mark(tt)
1.05/1.11	 active(U61(X:S)) -> U61(active(X:S))
1.05/1.11	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.05/1.11	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.05/1.11	 active(U72(tt)) -> mark(tt)
1.05/1.11	 active(U72(X:S)) -> U72(active(X:S))
1.05/1.11	 active(U81(tt)) -> mark(tt)
1.05/1.11	 active(U81(X:S)) -> U81(active(X:S))
1.05/1.11	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.05/1.11	 active(__(nil,X:S)) -> mark(X:S)
1.05/1.11	 active(__(X:S,nil)) -> mark(X:S)
1.05/1.11	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.05/1.11	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.05/1.11	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.05/1.11	 active(isList(nil)) -> mark(tt)
1.05/1.11	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.05/1.11	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.05/1.11	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.05/1.11	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.05/1.11	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.05/1.11	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.05/1.11	 active(isPal(nil)) -> mark(tt)
1.05/1.11	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.05/1.11	 active(isQid(a)) -> mark(tt)
1.05/1.11	 active(isQid(e)) -> mark(tt)
1.05/1.11	 active(isQid(i)) -> mark(tt)
1.05/1.11	 active(isQid(o)) -> mark(tt)
1.05/1.11	 active(isQid(u)) -> mark(tt)
1.05/1.11	 isList(ok(X:S)) -> ok(isList(X:S))
1.05/1.11	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.05/1.11	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.05/1.11	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.05/1.11	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.05/1.11	 proper(U11(X:S)) -> U11(proper(X:S))
1.05/1.11	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.05/1.11	 proper(U22(X:S)) -> U22(proper(X:S))
1.05/1.11	 proper(U31(X:S)) -> U31(proper(X:S))
1.05/1.11	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.05/1.11	 proper(U42(X:S)) -> U42(proper(X:S))
1.05/1.11	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.05/1.11	 proper(U52(X:S)) -> U52(proper(X:S))
1.05/1.11	 proper(U61(X:S)) -> U61(proper(X:S))
1.05/1.11	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.05/1.11	 proper(U72(X:S)) -> U72(proper(X:S))
1.05/1.11	 proper(U81(X:S)) -> U81(proper(X:S))
1.05/1.11	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.05/1.11	 proper(isList(X:S)) -> isList(proper(X:S))
1.05/1.11	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.05/1.11	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.05/1.11	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.05/1.11	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.05/1.11	 proper(a) -> ok(a)
1.05/1.11	 proper(e) -> ok(e)
1.05/1.11	 proper(i) -> ok(i)
1.05/1.11	 proper(nil) -> ok(nil)
1.05/1.11	 proper(o) -> ok(o)
1.05/1.11	 proper(tt) -> ok(tt)
1.05/1.11	 proper(u) -> ok(u)
1.05/1.11	 top(mark(X:S)) -> top(proper(X:S))
1.05/1.11	 top(ok(X:S)) -> top(active(X:S))
1.05/1.11	->Projection:
1.05/1.11	 pi(U81#) = 1
1.05/1.11	
1.05/1.11	Problem 1.7: 
1.05/1.11	
1.05/1.11	SCC Processor:
1.05/1.11	-> Pairs:
1.05/1.11	 Empty
1.05/1.11	-> Rules:
1.05/1.11	 U11(mark(X:S)) -> mark(U11(X:S))
1.05/1.11	 U11(ok(X:S)) -> ok(U11(X:S))
1.05/1.11	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.05/1.11	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.05/1.11	 U22(mark(X:S)) -> mark(U22(X:S))
1.05/1.11	 U22(ok(X:S)) -> ok(U22(X:S))
1.05/1.11	 U31(mark(X:S)) -> mark(U31(X:S))
1.05/1.11	 U31(ok(X:S)) -> ok(U31(X:S))
1.05/1.11	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.05/1.11	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.05/1.11	 U42(mark(X:S)) -> mark(U42(X:S))
1.05/1.11	 U42(ok(X:S)) -> ok(U42(X:S))
1.05/1.11	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.05/1.11	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.05/1.11	 U52(mark(X:S)) -> mark(U52(X:S))
1.05/1.11	 U52(ok(X:S)) -> ok(U52(X:S))
1.05/1.11	 U61(mark(X:S)) -> mark(U61(X:S))
1.05/1.11	 U61(ok(X:S)) -> ok(U61(X:S))
1.05/1.11	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.05/1.11	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.05/1.11	 U72(mark(X:S)) -> mark(U72(X:S))
1.05/1.11	 U72(ok(X:S)) -> ok(U72(X:S))
1.05/1.11	 U81(mark(X:S)) -> mark(U81(X:S))
1.05/1.11	 U81(ok(X:S)) -> ok(U81(X:S))
1.05/1.11	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.05/1.11	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.05/1.11	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.05/1.11	 active(U11(tt)) -> mark(tt)
1.05/1.11	 active(U11(X:S)) -> U11(active(X:S))
1.05/1.11	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.05/1.11	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.05/1.11	 active(U22(tt)) -> mark(tt)
1.05/1.11	 active(U22(X:S)) -> U22(active(X:S))
1.05/1.11	 active(U31(tt)) -> mark(tt)
1.05/1.11	 active(U31(X:S)) -> U31(active(X:S))
1.05/1.11	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.05/1.11	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.05/1.11	 active(U42(tt)) -> mark(tt)
1.05/1.11	 active(U42(X:S)) -> U42(active(X:S))
1.05/1.11	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.05/1.11	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.05/1.11	 active(U52(tt)) -> mark(tt)
1.05/1.11	 active(U52(X:S)) -> U52(active(X:S))
1.05/1.11	 active(U61(tt)) -> mark(tt)
1.05/1.11	 active(U61(X:S)) -> U61(active(X:S))
1.05/1.11	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.05/1.11	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.05/1.11	 active(U72(tt)) -> mark(tt)
1.05/1.11	 active(U72(X:S)) -> U72(active(X:S))
1.05/1.11	 active(U81(tt)) -> mark(tt)
1.05/1.11	 active(U81(X:S)) -> U81(active(X:S))
1.05/1.11	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.05/1.11	 active(__(nil,X:S)) -> mark(X:S)
1.05/1.11	 active(__(X:S,nil)) -> mark(X:S)
1.05/1.11	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.05/1.11	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.05/1.11	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.05/1.11	 active(isList(nil)) -> mark(tt)
1.05/1.11	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.05/1.11	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.05/1.11	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.05/1.11	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.05/1.11	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.05/1.11	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.05/1.11	 active(isPal(nil)) -> mark(tt)
1.05/1.11	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.05/1.11	 active(isQid(a)) -> mark(tt)
1.05/1.11	 active(isQid(e)) -> mark(tt)
1.05/1.11	 active(isQid(i)) -> mark(tt)
1.05/1.11	 active(isQid(o)) -> mark(tt)
1.05/1.11	 active(isQid(u)) -> mark(tt)
1.05/1.11	 isList(ok(X:S)) -> ok(isList(X:S))
1.05/1.11	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.05/1.11	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.05/1.11	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.05/1.11	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.05/1.11	 proper(U11(X:S)) -> U11(proper(X:S))
1.05/1.11	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.05/1.11	 proper(U22(X:S)) -> U22(proper(X:S))
1.05/1.11	 proper(U31(X:S)) -> U31(proper(X:S))
1.05/1.11	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.05/1.11	 proper(U42(X:S)) -> U42(proper(X:S))
1.05/1.11	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.05/1.11	 proper(U52(X:S)) -> U52(proper(X:S))
1.05/1.11	 proper(U61(X:S)) -> U61(proper(X:S))
1.05/1.11	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.05/1.11	 proper(U72(X:S)) -> U72(proper(X:S))
1.05/1.11	 proper(U81(X:S)) -> U81(proper(X:S))
1.05/1.11	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.05/1.11	 proper(isList(X:S)) -> isList(proper(X:S))
1.05/1.11	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.05/1.11	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.05/1.11	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.05/1.11	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.05/1.11	 proper(a) -> ok(a)
1.05/1.11	 proper(e) -> ok(e)
1.05/1.11	 proper(i) -> ok(i)
1.05/1.11	 proper(nil) -> ok(nil)
1.05/1.11	 proper(o) -> ok(o)
1.05/1.11	 proper(tt) -> ok(tt)
1.05/1.11	 proper(u) -> ok(u)
1.05/1.11	 top(mark(X:S)) -> top(proper(X:S))
1.05/1.11	 top(ok(X:S)) -> top(active(X:S))
1.05/1.11	->Strongly Connected Components:
1.05/1.11	 There is no strongly connected component
1.05/1.11	
1.05/1.11	The problem is finite.
1.05/1.11	
1.05/1.11	Problem 1.8: 
1.05/1.11	
1.05/1.11	Subterm Processor:
1.05/1.11	-> Pairs:
1.05/1.11	 U72#(mark(X:S)) -> U72#(X:S)
1.05/1.11	 U72#(ok(X:S)) -> U72#(X:S)
1.05/1.11	-> Rules:
1.05/1.11	 U11(mark(X:S)) -> mark(U11(X:S))
1.05/1.11	 U11(ok(X:S)) -> ok(U11(X:S))
1.05/1.11	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.05/1.11	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.05/1.11	 U22(mark(X:S)) -> mark(U22(X:S))
1.05/1.11	 U22(ok(X:S)) -> ok(U22(X:S))
1.05/1.11	 U31(mark(X:S)) -> mark(U31(X:S))
1.05/1.11	 U31(ok(X:S)) -> ok(U31(X:S))
1.05/1.11	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.05/1.11	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.05/1.11	 U42(mark(X:S)) -> mark(U42(X:S))
1.05/1.11	 U42(ok(X:S)) -> ok(U42(X:S))
1.05/1.11	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.05/1.11	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.05/1.11	 U52(mark(X:S)) -> mark(U52(X:S))
1.05/1.11	 U52(ok(X:S)) -> ok(U52(X:S))
1.05/1.11	 U61(mark(X:S)) -> mark(U61(X:S))
1.05/1.11	 U61(ok(X:S)) -> ok(U61(X:S))
1.05/1.11	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.05/1.11	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.05/1.11	 U72(mark(X:S)) -> mark(U72(X:S))
1.05/1.11	 U72(ok(X:S)) -> ok(U72(X:S))
1.05/1.11	 U81(mark(X:S)) -> mark(U81(X:S))
1.05/1.11	 U81(ok(X:S)) -> ok(U81(X:S))
1.05/1.11	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.05/1.11	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.05/1.11	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.05/1.11	 active(U11(tt)) -> mark(tt)
1.05/1.11	 active(U11(X:S)) -> U11(active(X:S))
1.05/1.11	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.05/1.11	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.05/1.11	 active(U22(tt)) -> mark(tt)
1.05/1.11	 active(U22(X:S)) -> U22(active(X:S))
1.05/1.11	 active(U31(tt)) -> mark(tt)
1.05/1.11	 active(U31(X:S)) -> U31(active(X:S))
1.05/1.11	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.05/1.11	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.05/1.11	 active(U42(tt)) -> mark(tt)
1.05/1.11	 active(U42(X:S)) -> U42(active(X:S))
1.05/1.11	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.05/1.11	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.05/1.11	 active(U52(tt)) -> mark(tt)
1.05/1.11	 active(U52(X:S)) -> U52(active(X:S))
1.05/1.11	 active(U61(tt)) -> mark(tt)
1.05/1.11	 active(U61(X:S)) -> U61(active(X:S))
1.05/1.11	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.05/1.11	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.05/1.11	 active(U72(tt)) -> mark(tt)
1.05/1.11	 active(U72(X:S)) -> U72(active(X:S))
1.05/1.11	 active(U81(tt)) -> mark(tt)
1.05/1.11	 active(U81(X:S)) -> U81(active(X:S))
1.05/1.11	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.05/1.11	 active(__(nil,X:S)) -> mark(X:S)
1.05/1.11	 active(__(X:S,nil)) -> mark(X:S)
1.05/1.11	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.05/1.11	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.05/1.11	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.05/1.11	 active(isList(nil)) -> mark(tt)
1.05/1.11	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.05/1.11	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.05/1.11	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.05/1.11	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.05/1.11	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.05/1.11	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.05/1.11	 active(isPal(nil)) -> mark(tt)
1.05/1.11	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.05/1.11	 active(isQid(a)) -> mark(tt)
1.05/1.11	 active(isQid(e)) -> mark(tt)
1.05/1.11	 active(isQid(i)) -> mark(tt)
1.05/1.11	 active(isQid(o)) -> mark(tt)
1.05/1.11	 active(isQid(u)) -> mark(tt)
1.05/1.11	 isList(ok(X:S)) -> ok(isList(X:S))
1.05/1.11	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.05/1.11	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.05/1.11	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.05/1.11	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.05/1.11	 proper(U11(X:S)) -> U11(proper(X:S))
1.05/1.11	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.05/1.11	 proper(U22(X:S)) -> U22(proper(X:S))
1.05/1.11	 proper(U31(X:S)) -> U31(proper(X:S))
1.05/1.11	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.05/1.11	 proper(U42(X:S)) -> U42(proper(X:S))
1.05/1.11	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.05/1.11	 proper(U52(X:S)) -> U52(proper(X:S))
1.05/1.11	 proper(U61(X:S)) -> U61(proper(X:S))
1.05/1.11	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.05/1.11	 proper(U72(X:S)) -> U72(proper(X:S))
1.05/1.11	 proper(U81(X:S)) -> U81(proper(X:S))
1.05/1.11	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.05/1.11	 proper(isList(X:S)) -> isList(proper(X:S))
1.05/1.11	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.05/1.11	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.05/1.11	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.05/1.11	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.05/1.11	 proper(a) -> ok(a)
1.05/1.11	 proper(e) -> ok(e)
1.05/1.11	 proper(i) -> ok(i)
1.05/1.11	 proper(nil) -> ok(nil)
1.05/1.11	 proper(o) -> ok(o)
1.05/1.11	 proper(tt) -> ok(tt)
1.05/1.11	 proper(u) -> ok(u)
1.05/1.11	 top(mark(X:S)) -> top(proper(X:S))
1.05/1.11	 top(ok(X:S)) -> top(active(X:S))
1.05/1.11	->Projection:
1.05/1.11	 pi(U72#) = 1
1.05/1.11	
1.05/1.11	Problem 1.8: 
1.05/1.11	
1.05/1.11	SCC Processor:
1.05/1.11	-> Pairs:
1.05/1.11	 Empty
1.05/1.11	-> Rules:
1.05/1.11	 U11(mark(X:S)) -> mark(U11(X:S))
1.05/1.11	 U11(ok(X:S)) -> ok(U11(X:S))
1.05/1.11	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.05/1.11	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.05/1.11	 U22(mark(X:S)) -> mark(U22(X:S))
1.05/1.11	 U22(ok(X:S)) -> ok(U22(X:S))
1.05/1.11	 U31(mark(X:S)) -> mark(U31(X:S))
1.05/1.11	 U31(ok(X:S)) -> ok(U31(X:S))
1.05/1.11	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.05/1.11	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.05/1.11	 U42(mark(X:S)) -> mark(U42(X:S))
1.05/1.11	 U42(ok(X:S)) -> ok(U42(X:S))
1.05/1.11	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.05/1.11	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.05/1.11	 U52(mark(X:S)) -> mark(U52(X:S))
1.05/1.11	 U52(ok(X:S)) -> ok(U52(X:S))
1.05/1.11	 U61(mark(X:S)) -> mark(U61(X:S))
1.05/1.11	 U61(ok(X:S)) -> ok(U61(X:S))
1.05/1.11	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.05/1.11	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.05/1.11	 U72(mark(X:S)) -> mark(U72(X:S))
1.05/1.11	 U72(ok(X:S)) -> ok(U72(X:S))
1.05/1.11	 U81(mark(X:S)) -> mark(U81(X:S))
1.05/1.11	 U81(ok(X:S)) -> ok(U81(X:S))
1.05/1.11	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.05/1.11	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.05/1.11	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.05/1.11	 active(U11(tt)) -> mark(tt)
1.05/1.11	 active(U11(X:S)) -> U11(active(X:S))
1.05/1.11	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.05/1.11	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.05/1.11	 active(U22(tt)) -> mark(tt)
1.05/1.11	 active(U22(X:S)) -> U22(active(X:S))
1.05/1.11	 active(U31(tt)) -> mark(tt)
1.05/1.11	 active(U31(X:S)) -> U31(active(X:S))
1.05/1.11	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.05/1.11	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.05/1.11	 active(U42(tt)) -> mark(tt)
1.05/1.11	 active(U42(X:S)) -> U42(active(X:S))
1.05/1.11	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.05/1.11	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.05/1.11	 active(U52(tt)) -> mark(tt)
1.05/1.11	 active(U52(X:S)) -> U52(active(X:S))
1.05/1.11	 active(U61(tt)) -> mark(tt)
1.05/1.11	 active(U61(X:S)) -> U61(active(X:S))
1.05/1.11	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.05/1.11	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.05/1.11	 active(U72(tt)) -> mark(tt)
1.05/1.11	 active(U72(X:S)) -> U72(active(X:S))
1.05/1.11	 active(U81(tt)) -> mark(tt)
1.05/1.11	 active(U81(X:S)) -> U81(active(X:S))
1.05/1.11	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.05/1.11	 active(__(nil,X:S)) -> mark(X:S)
1.05/1.11	 active(__(X:S,nil)) -> mark(X:S)
1.05/1.11	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.05/1.11	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.05/1.11	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.05/1.11	 active(isList(nil)) -> mark(tt)
1.05/1.11	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.05/1.11	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.05/1.11	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.05/1.11	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.05/1.11	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.05/1.11	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.05/1.11	 active(isPal(nil)) -> mark(tt)
1.05/1.11	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.05/1.11	 active(isQid(a)) -> mark(tt)
1.05/1.11	 active(isQid(e)) -> mark(tt)
1.05/1.11	 active(isQid(i)) -> mark(tt)
1.05/1.11	 active(isQid(o)) -> mark(tt)
1.05/1.11	 active(isQid(u)) -> mark(tt)
1.05/1.11	 isList(ok(X:S)) -> ok(isList(X:S))
1.05/1.11	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.05/1.11	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.05/1.11	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.05/1.11	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.05/1.11	 proper(U11(X:S)) -> U11(proper(X:S))
1.05/1.11	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.05/1.11	 proper(U22(X:S)) -> U22(proper(X:S))
1.05/1.11	 proper(U31(X:S)) -> U31(proper(X:S))
1.05/1.11	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.05/1.11	 proper(U42(X:S)) -> U42(proper(X:S))
1.05/1.11	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.05/1.11	 proper(U52(X:S)) -> U52(proper(X:S))
1.05/1.11	 proper(U61(X:S)) -> U61(proper(X:S))
1.05/1.11	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.05/1.11	 proper(U72(X:S)) -> U72(proper(X:S))
1.05/1.11	 proper(U81(X:S)) -> U81(proper(X:S))
1.05/1.11	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.05/1.11	 proper(isList(X:S)) -> isList(proper(X:S))
1.05/1.11	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.05/1.11	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.05/1.11	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.05/1.11	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.05/1.11	 proper(a) -> ok(a)
1.05/1.11	 proper(e) -> ok(e)
1.05/1.11	 proper(i) -> ok(i)
1.05/1.11	 proper(nil) -> ok(nil)
1.05/1.11	 proper(o) -> ok(o)
1.05/1.11	 proper(tt) -> ok(tt)
1.05/1.11	 proper(u) -> ok(u)
1.05/1.11	 top(mark(X:S)) -> top(proper(X:S))
1.05/1.11	 top(ok(X:S)) -> top(active(X:S))
1.05/1.11	->Strongly Connected Components:
1.05/1.11	 There is no strongly connected component
1.05/1.11	
1.05/1.11	The problem is finite.
1.05/1.11	
1.05/1.11	Problem 1.9: 
1.05/1.11	
1.05/1.11	Subterm Processor:
1.05/1.11	-> Pairs:
1.05/1.11	 U71#(mark(X1:S),X2:S) -> U71#(X1:S,X2:S)
1.05/1.11	 U71#(ok(X1:S),ok(X2:S)) -> U71#(X1:S,X2:S)
1.05/1.11	-> Rules:
1.05/1.11	 U11(mark(X:S)) -> mark(U11(X:S))
1.05/1.11	 U11(ok(X:S)) -> ok(U11(X:S))
1.05/1.11	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.05/1.11	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.05/1.11	 U22(mark(X:S)) -> mark(U22(X:S))
1.05/1.11	 U22(ok(X:S)) -> ok(U22(X:S))
1.05/1.11	 U31(mark(X:S)) -> mark(U31(X:S))
1.05/1.11	 U31(ok(X:S)) -> ok(U31(X:S))
1.05/1.11	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.05/1.11	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.05/1.11	 U42(mark(X:S)) -> mark(U42(X:S))
1.05/1.11	 U42(ok(X:S)) -> ok(U42(X:S))
1.05/1.11	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.05/1.11	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.05/1.11	 U52(mark(X:S)) -> mark(U52(X:S))
1.05/1.11	 U52(ok(X:S)) -> ok(U52(X:S))
1.05/1.11	 U61(mark(X:S)) -> mark(U61(X:S))
1.05/1.11	 U61(ok(X:S)) -> ok(U61(X:S))
1.05/1.11	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.05/1.11	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.05/1.11	 U72(mark(X:S)) -> mark(U72(X:S))
1.05/1.11	 U72(ok(X:S)) -> ok(U72(X:S))
1.05/1.11	 U81(mark(X:S)) -> mark(U81(X:S))
1.05/1.11	 U81(ok(X:S)) -> ok(U81(X:S))
1.05/1.11	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.05/1.11	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.05/1.11	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.05/1.11	 active(U11(tt)) -> mark(tt)
1.05/1.11	 active(U11(X:S)) -> U11(active(X:S))
1.05/1.11	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.05/1.11	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.05/1.11	 active(U22(tt)) -> mark(tt)
1.05/1.11	 active(U22(X:S)) -> U22(active(X:S))
1.05/1.11	 active(U31(tt)) -> mark(tt)
1.05/1.11	 active(U31(X:S)) -> U31(active(X:S))
1.05/1.11	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.05/1.11	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.05/1.11	 active(U42(tt)) -> mark(tt)
1.05/1.11	 active(U42(X:S)) -> U42(active(X:S))
1.05/1.11	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.05/1.11	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.05/1.11	 active(U52(tt)) -> mark(tt)
1.05/1.11	 active(U52(X:S)) -> U52(active(X:S))
1.05/1.11	 active(U61(tt)) -> mark(tt)
1.05/1.11	 active(U61(X:S)) -> U61(active(X:S))
1.05/1.11	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.05/1.11	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.05/1.11	 active(U72(tt)) -> mark(tt)
1.05/1.11	 active(U72(X:S)) -> U72(active(X:S))
1.05/1.11	 active(U81(tt)) -> mark(tt)
1.05/1.11	 active(U81(X:S)) -> U81(active(X:S))
1.05/1.11	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.05/1.11	 active(__(nil,X:S)) -> mark(X:S)
1.05/1.11	 active(__(X:S,nil)) -> mark(X:S)
1.05/1.11	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.05/1.11	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.05/1.11	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.05/1.11	 active(isList(nil)) -> mark(tt)
1.05/1.11	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.05/1.11	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.05/1.11	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.05/1.11	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.05/1.11	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.05/1.11	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.05/1.11	 active(isPal(nil)) -> mark(tt)
1.05/1.11	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.05/1.11	 active(isQid(a)) -> mark(tt)
1.05/1.11	 active(isQid(e)) -> mark(tt)
1.05/1.11	 active(isQid(i)) -> mark(tt)
1.05/1.11	 active(isQid(o)) -> mark(tt)
1.05/1.11	 active(isQid(u)) -> mark(tt)
1.05/1.11	 isList(ok(X:S)) -> ok(isList(X:S))
1.05/1.11	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.05/1.11	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.05/1.11	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.05/1.11	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.05/1.11	 proper(U11(X:S)) -> U11(proper(X:S))
1.05/1.11	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.05/1.11	 proper(U22(X:S)) -> U22(proper(X:S))
1.05/1.11	 proper(U31(X:S)) -> U31(proper(X:S))
1.05/1.11	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.05/1.11	 proper(U42(X:S)) -> U42(proper(X:S))
1.05/1.11	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.05/1.11	 proper(U52(X:S)) -> U52(proper(X:S))
1.05/1.11	 proper(U61(X:S)) -> U61(proper(X:S))
1.05/1.11	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.05/1.11	 proper(U72(X:S)) -> U72(proper(X:S))
1.05/1.11	 proper(U81(X:S)) -> U81(proper(X:S))
1.05/1.11	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.05/1.11	 proper(isList(X:S)) -> isList(proper(X:S))
1.05/1.11	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.05/1.11	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.05/1.11	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.05/1.11	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.05/1.11	 proper(a) -> ok(a)
1.05/1.11	 proper(e) -> ok(e)
1.05/1.11	 proper(i) -> ok(i)
1.05/1.11	 proper(nil) -> ok(nil)
1.05/1.11	 proper(o) -> ok(o)
1.05/1.11	 proper(tt) -> ok(tt)
1.05/1.11	 proper(u) -> ok(u)
1.05/1.11	 top(mark(X:S)) -> top(proper(X:S))
1.05/1.11	 top(ok(X:S)) -> top(active(X:S))
1.05/1.11	->Projection:
1.05/1.11	 pi(U71#) = 1
1.05/1.11	
1.05/1.11	Problem 1.9: 
1.05/1.11	
1.05/1.11	SCC Processor:
1.05/1.11	-> Pairs:
1.05/1.11	 Empty
1.05/1.11	-> Rules:
1.05/1.11	 U11(mark(X:S)) -> mark(U11(X:S))
1.05/1.11	 U11(ok(X:S)) -> ok(U11(X:S))
1.05/1.11	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.05/1.11	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.05/1.11	 U22(mark(X:S)) -> mark(U22(X:S))
1.05/1.11	 U22(ok(X:S)) -> ok(U22(X:S))
1.05/1.11	 U31(mark(X:S)) -> mark(U31(X:S))
1.05/1.11	 U31(ok(X:S)) -> ok(U31(X:S))
1.05/1.11	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.05/1.11	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.05/1.11	 U42(mark(X:S)) -> mark(U42(X:S))
1.05/1.11	 U42(ok(X:S)) -> ok(U42(X:S))
1.05/1.11	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.05/1.11	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.05/1.11	 U52(mark(X:S)) -> mark(U52(X:S))
1.05/1.11	 U52(ok(X:S)) -> ok(U52(X:S))
1.05/1.11	 U61(mark(X:S)) -> mark(U61(X:S))
1.05/1.11	 U61(ok(X:S)) -> ok(U61(X:S))
1.05/1.11	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.05/1.11	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.05/1.11	 U72(mark(X:S)) -> mark(U72(X:S))
1.05/1.11	 U72(ok(X:S)) -> ok(U72(X:S))
1.05/1.11	 U81(mark(X:S)) -> mark(U81(X:S))
1.05/1.11	 U81(ok(X:S)) -> ok(U81(X:S))
1.05/1.11	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.05/1.11	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.05/1.11	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.05/1.11	 active(U11(tt)) -> mark(tt)
1.05/1.11	 active(U11(X:S)) -> U11(active(X:S))
1.05/1.11	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.05/1.11	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.05/1.11	 active(U22(tt)) -> mark(tt)
1.05/1.11	 active(U22(X:S)) -> U22(active(X:S))
1.05/1.11	 active(U31(tt)) -> mark(tt)
1.05/1.11	 active(U31(X:S)) -> U31(active(X:S))
1.05/1.11	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.05/1.11	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.05/1.11	 active(U42(tt)) -> mark(tt)
1.05/1.11	 active(U42(X:S)) -> U42(active(X:S))
1.05/1.11	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.05/1.11	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.05/1.11	 active(U52(tt)) -> mark(tt)
1.05/1.11	 active(U52(X:S)) -> U52(active(X:S))
1.05/1.11	 active(U61(tt)) -> mark(tt)
1.05/1.11	 active(U61(X:S)) -> U61(active(X:S))
1.05/1.11	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.05/1.11	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.05/1.11	 active(U72(tt)) -> mark(tt)
1.05/1.11	 active(U72(X:S)) -> U72(active(X:S))
1.05/1.11	 active(U81(tt)) -> mark(tt)
1.05/1.11	 active(U81(X:S)) -> U81(active(X:S))
1.05/1.11	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.05/1.11	 active(__(nil,X:S)) -> mark(X:S)
1.05/1.11	 active(__(X:S,nil)) -> mark(X:S)
1.05/1.11	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.05/1.11	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.05/1.11	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.05/1.11	 active(isList(nil)) -> mark(tt)
1.05/1.11	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.05/1.11	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.05/1.11	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.05/1.11	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.05/1.11	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.05/1.11	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.05/1.11	 active(isPal(nil)) -> mark(tt)
1.05/1.11	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.05/1.11	 active(isQid(a)) -> mark(tt)
1.05/1.11	 active(isQid(e)) -> mark(tt)
1.05/1.11	 active(isQid(i)) -> mark(tt)
1.05/1.11	 active(isQid(o)) -> mark(tt)
1.05/1.11	 active(isQid(u)) -> mark(tt)
1.05/1.11	 isList(ok(X:S)) -> ok(isList(X:S))
1.05/1.12	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.05/1.12	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.05/1.12	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.05/1.12	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.05/1.12	 proper(U11(X:S)) -> U11(proper(X:S))
1.05/1.12	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U22(X:S)) -> U22(proper(X:S))
1.05/1.12	 proper(U31(X:S)) -> U31(proper(X:S))
1.05/1.12	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U42(X:S)) -> U42(proper(X:S))
1.05/1.12	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U52(X:S)) -> U52(proper(X:S))
1.05/1.12	 proper(U61(X:S)) -> U61(proper(X:S))
1.05/1.12	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U72(X:S)) -> U72(proper(X:S))
1.05/1.12	 proper(U81(X:S)) -> U81(proper(X:S))
1.05/1.12	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(isList(X:S)) -> isList(proper(X:S))
1.05/1.12	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.05/1.12	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.05/1.12	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.05/1.12	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.05/1.12	 proper(a) -> ok(a)
1.05/1.12	 proper(e) -> ok(e)
1.05/1.12	 proper(i) -> ok(i)
1.05/1.12	 proper(nil) -> ok(nil)
1.05/1.12	 proper(o) -> ok(o)
1.05/1.12	 proper(tt) -> ok(tt)
1.05/1.12	 proper(u) -> ok(u)
1.05/1.12	 top(mark(X:S)) -> top(proper(X:S))
1.05/1.12	 top(ok(X:S)) -> top(active(X:S))
1.05/1.12	->Strongly Connected Components:
1.05/1.12	 There is no strongly connected component
1.05/1.12	
1.05/1.12	The problem is finite.
1.05/1.12	
1.05/1.12	Problem 1.10: 
1.05/1.12	
1.05/1.12	Subterm Processor:
1.05/1.12	-> Pairs:
1.05/1.12	 U61#(mark(X:S)) -> U61#(X:S)
1.05/1.12	 U61#(ok(X:S)) -> U61#(X:S)
1.05/1.12	-> Rules:
1.05/1.12	 U11(mark(X:S)) -> mark(U11(X:S))
1.05/1.12	 U11(ok(X:S)) -> ok(U11(X:S))
1.05/1.12	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.05/1.12	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.05/1.12	 U22(mark(X:S)) -> mark(U22(X:S))
1.05/1.12	 U22(ok(X:S)) -> ok(U22(X:S))
1.05/1.12	 U31(mark(X:S)) -> mark(U31(X:S))
1.05/1.12	 U31(ok(X:S)) -> ok(U31(X:S))
1.05/1.12	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.05/1.12	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.05/1.12	 U42(mark(X:S)) -> mark(U42(X:S))
1.05/1.12	 U42(ok(X:S)) -> ok(U42(X:S))
1.05/1.12	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.05/1.12	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.05/1.12	 U52(mark(X:S)) -> mark(U52(X:S))
1.05/1.12	 U52(ok(X:S)) -> ok(U52(X:S))
1.05/1.12	 U61(mark(X:S)) -> mark(U61(X:S))
1.05/1.12	 U61(ok(X:S)) -> ok(U61(X:S))
1.05/1.12	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.05/1.12	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.05/1.12	 U72(mark(X:S)) -> mark(U72(X:S))
1.05/1.12	 U72(ok(X:S)) -> ok(U72(X:S))
1.05/1.12	 U81(mark(X:S)) -> mark(U81(X:S))
1.05/1.12	 U81(ok(X:S)) -> ok(U81(X:S))
1.05/1.12	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.05/1.12	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.05/1.12	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.05/1.12	 active(U11(tt)) -> mark(tt)
1.05/1.12	 active(U11(X:S)) -> U11(active(X:S))
1.05/1.12	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.05/1.12	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.05/1.12	 active(U22(tt)) -> mark(tt)
1.05/1.12	 active(U22(X:S)) -> U22(active(X:S))
1.05/1.12	 active(U31(tt)) -> mark(tt)
1.05/1.12	 active(U31(X:S)) -> U31(active(X:S))
1.05/1.12	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.05/1.12	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.05/1.12	 active(U42(tt)) -> mark(tt)
1.05/1.12	 active(U42(X:S)) -> U42(active(X:S))
1.05/1.12	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.05/1.12	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.05/1.12	 active(U52(tt)) -> mark(tt)
1.05/1.12	 active(U52(X:S)) -> U52(active(X:S))
1.05/1.12	 active(U61(tt)) -> mark(tt)
1.05/1.12	 active(U61(X:S)) -> U61(active(X:S))
1.05/1.12	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.05/1.12	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.05/1.12	 active(U72(tt)) -> mark(tt)
1.05/1.12	 active(U72(X:S)) -> U72(active(X:S))
1.05/1.12	 active(U81(tt)) -> mark(tt)
1.05/1.12	 active(U81(X:S)) -> U81(active(X:S))
1.05/1.12	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.05/1.12	 active(__(nil,X:S)) -> mark(X:S)
1.05/1.12	 active(__(X:S,nil)) -> mark(X:S)
1.05/1.12	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.05/1.12	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.05/1.12	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.05/1.12	 active(isList(nil)) -> mark(tt)
1.05/1.12	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.05/1.12	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.05/1.12	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.05/1.12	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.05/1.12	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.05/1.12	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.05/1.12	 active(isPal(nil)) -> mark(tt)
1.05/1.12	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.05/1.12	 active(isQid(a)) -> mark(tt)
1.05/1.12	 active(isQid(e)) -> mark(tt)
1.05/1.12	 active(isQid(i)) -> mark(tt)
1.05/1.12	 active(isQid(o)) -> mark(tt)
1.05/1.12	 active(isQid(u)) -> mark(tt)
1.05/1.12	 isList(ok(X:S)) -> ok(isList(X:S))
1.05/1.12	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.05/1.12	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.05/1.12	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.05/1.12	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.05/1.12	 proper(U11(X:S)) -> U11(proper(X:S))
1.05/1.12	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U22(X:S)) -> U22(proper(X:S))
1.05/1.12	 proper(U31(X:S)) -> U31(proper(X:S))
1.05/1.12	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U42(X:S)) -> U42(proper(X:S))
1.05/1.12	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U52(X:S)) -> U52(proper(X:S))
1.05/1.12	 proper(U61(X:S)) -> U61(proper(X:S))
1.05/1.12	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U72(X:S)) -> U72(proper(X:S))
1.05/1.12	 proper(U81(X:S)) -> U81(proper(X:S))
1.05/1.12	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(isList(X:S)) -> isList(proper(X:S))
1.05/1.12	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.05/1.12	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.05/1.12	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.05/1.12	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.05/1.12	 proper(a) -> ok(a)
1.05/1.12	 proper(e) -> ok(e)
1.05/1.12	 proper(i) -> ok(i)
1.05/1.12	 proper(nil) -> ok(nil)
1.05/1.12	 proper(o) -> ok(o)
1.05/1.12	 proper(tt) -> ok(tt)
1.05/1.12	 proper(u) -> ok(u)
1.05/1.12	 top(mark(X:S)) -> top(proper(X:S))
1.05/1.12	 top(ok(X:S)) -> top(active(X:S))
1.05/1.12	->Projection:
1.05/1.12	 pi(U61#) = 1
1.05/1.12	
1.05/1.12	Problem 1.10: 
1.05/1.12	
1.05/1.12	SCC Processor:
1.05/1.12	-> Pairs:
1.05/1.12	 Empty
1.05/1.12	-> Rules:
1.05/1.12	 U11(mark(X:S)) -> mark(U11(X:S))
1.05/1.12	 U11(ok(X:S)) -> ok(U11(X:S))
1.05/1.12	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.05/1.12	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.05/1.12	 U22(mark(X:S)) -> mark(U22(X:S))
1.05/1.12	 U22(ok(X:S)) -> ok(U22(X:S))
1.05/1.12	 U31(mark(X:S)) -> mark(U31(X:S))
1.05/1.12	 U31(ok(X:S)) -> ok(U31(X:S))
1.05/1.12	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.05/1.12	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.05/1.12	 U42(mark(X:S)) -> mark(U42(X:S))
1.05/1.12	 U42(ok(X:S)) -> ok(U42(X:S))
1.05/1.12	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.05/1.12	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.05/1.12	 U52(mark(X:S)) -> mark(U52(X:S))
1.05/1.12	 U52(ok(X:S)) -> ok(U52(X:S))
1.05/1.12	 U61(mark(X:S)) -> mark(U61(X:S))
1.05/1.12	 U61(ok(X:S)) -> ok(U61(X:S))
1.05/1.12	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.05/1.12	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.05/1.12	 U72(mark(X:S)) -> mark(U72(X:S))
1.05/1.12	 U72(ok(X:S)) -> ok(U72(X:S))
1.05/1.12	 U81(mark(X:S)) -> mark(U81(X:S))
1.05/1.12	 U81(ok(X:S)) -> ok(U81(X:S))
1.05/1.12	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.05/1.12	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.05/1.12	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.05/1.12	 active(U11(tt)) -> mark(tt)
1.05/1.12	 active(U11(X:S)) -> U11(active(X:S))
1.05/1.12	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.05/1.12	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.05/1.12	 active(U22(tt)) -> mark(tt)
1.05/1.12	 active(U22(X:S)) -> U22(active(X:S))
1.05/1.12	 active(U31(tt)) -> mark(tt)
1.05/1.12	 active(U31(X:S)) -> U31(active(X:S))
1.05/1.12	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.05/1.12	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.05/1.12	 active(U42(tt)) -> mark(tt)
1.05/1.12	 active(U42(X:S)) -> U42(active(X:S))
1.05/1.12	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.05/1.12	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.05/1.12	 active(U52(tt)) -> mark(tt)
1.05/1.12	 active(U52(X:S)) -> U52(active(X:S))
1.05/1.12	 active(U61(tt)) -> mark(tt)
1.05/1.12	 active(U61(X:S)) -> U61(active(X:S))
1.05/1.12	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.05/1.12	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.05/1.12	 active(U72(tt)) -> mark(tt)
1.05/1.12	 active(U72(X:S)) -> U72(active(X:S))
1.05/1.12	 active(U81(tt)) -> mark(tt)
1.05/1.12	 active(U81(X:S)) -> U81(active(X:S))
1.05/1.12	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.05/1.12	 active(__(nil,X:S)) -> mark(X:S)
1.05/1.12	 active(__(X:S,nil)) -> mark(X:S)
1.05/1.12	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.05/1.12	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.05/1.12	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.05/1.12	 active(isList(nil)) -> mark(tt)
1.05/1.12	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.05/1.12	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.05/1.12	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.05/1.12	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.05/1.12	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.05/1.12	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.05/1.12	 active(isPal(nil)) -> mark(tt)
1.05/1.12	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.05/1.12	 active(isQid(a)) -> mark(tt)
1.05/1.12	 active(isQid(e)) -> mark(tt)
1.05/1.12	 active(isQid(i)) -> mark(tt)
1.05/1.12	 active(isQid(o)) -> mark(tt)
1.05/1.12	 active(isQid(u)) -> mark(tt)
1.05/1.12	 isList(ok(X:S)) -> ok(isList(X:S))
1.05/1.12	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.05/1.12	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.05/1.12	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.05/1.12	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.05/1.12	 proper(U11(X:S)) -> U11(proper(X:S))
1.05/1.12	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U22(X:S)) -> U22(proper(X:S))
1.05/1.12	 proper(U31(X:S)) -> U31(proper(X:S))
1.05/1.12	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U42(X:S)) -> U42(proper(X:S))
1.05/1.12	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U52(X:S)) -> U52(proper(X:S))
1.05/1.12	 proper(U61(X:S)) -> U61(proper(X:S))
1.05/1.12	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U72(X:S)) -> U72(proper(X:S))
1.05/1.12	 proper(U81(X:S)) -> U81(proper(X:S))
1.05/1.12	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(isList(X:S)) -> isList(proper(X:S))
1.05/1.12	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.05/1.12	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.05/1.12	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.05/1.12	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.05/1.12	 proper(a) -> ok(a)
1.05/1.12	 proper(e) -> ok(e)
1.05/1.12	 proper(i) -> ok(i)
1.05/1.12	 proper(nil) -> ok(nil)
1.05/1.12	 proper(o) -> ok(o)
1.05/1.12	 proper(tt) -> ok(tt)
1.05/1.12	 proper(u) -> ok(u)
1.05/1.12	 top(mark(X:S)) -> top(proper(X:S))
1.05/1.12	 top(ok(X:S)) -> top(active(X:S))
1.05/1.12	->Strongly Connected Components:
1.05/1.12	 There is no strongly connected component
1.05/1.12	
1.05/1.12	The problem is finite.
1.05/1.12	
1.05/1.12	Problem 1.11: 
1.05/1.12	
1.05/1.12	Subterm Processor:
1.05/1.12	-> Pairs:
1.05/1.12	 U52#(mark(X:S)) -> U52#(X:S)
1.05/1.12	 U52#(ok(X:S)) -> U52#(X:S)
1.05/1.12	-> Rules:
1.05/1.12	 U11(mark(X:S)) -> mark(U11(X:S))
1.05/1.12	 U11(ok(X:S)) -> ok(U11(X:S))
1.05/1.12	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.05/1.12	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.05/1.12	 U22(mark(X:S)) -> mark(U22(X:S))
1.05/1.12	 U22(ok(X:S)) -> ok(U22(X:S))
1.05/1.12	 U31(mark(X:S)) -> mark(U31(X:S))
1.05/1.12	 U31(ok(X:S)) -> ok(U31(X:S))
1.05/1.12	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.05/1.12	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.05/1.12	 U42(mark(X:S)) -> mark(U42(X:S))
1.05/1.12	 U42(ok(X:S)) -> ok(U42(X:S))
1.05/1.12	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.05/1.12	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.05/1.12	 U52(mark(X:S)) -> mark(U52(X:S))
1.05/1.12	 U52(ok(X:S)) -> ok(U52(X:S))
1.05/1.12	 U61(mark(X:S)) -> mark(U61(X:S))
1.05/1.12	 U61(ok(X:S)) -> ok(U61(X:S))
1.05/1.12	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.05/1.12	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.05/1.12	 U72(mark(X:S)) -> mark(U72(X:S))
1.05/1.12	 U72(ok(X:S)) -> ok(U72(X:S))
1.05/1.12	 U81(mark(X:S)) -> mark(U81(X:S))
1.05/1.12	 U81(ok(X:S)) -> ok(U81(X:S))
1.05/1.12	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.05/1.12	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.05/1.12	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.05/1.12	 active(U11(tt)) -> mark(tt)
1.05/1.12	 active(U11(X:S)) -> U11(active(X:S))
1.05/1.12	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.05/1.12	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.05/1.12	 active(U22(tt)) -> mark(tt)
1.05/1.12	 active(U22(X:S)) -> U22(active(X:S))
1.05/1.12	 active(U31(tt)) -> mark(tt)
1.05/1.12	 active(U31(X:S)) -> U31(active(X:S))
1.05/1.12	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.05/1.12	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.05/1.12	 active(U42(tt)) -> mark(tt)
1.05/1.12	 active(U42(X:S)) -> U42(active(X:S))
1.05/1.12	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.05/1.12	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.05/1.12	 active(U52(tt)) -> mark(tt)
1.05/1.12	 active(U52(X:S)) -> U52(active(X:S))
1.05/1.12	 active(U61(tt)) -> mark(tt)
1.05/1.12	 active(U61(X:S)) -> U61(active(X:S))
1.05/1.12	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.05/1.12	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.05/1.12	 active(U72(tt)) -> mark(tt)
1.05/1.12	 active(U72(X:S)) -> U72(active(X:S))
1.05/1.12	 active(U81(tt)) -> mark(tt)
1.05/1.12	 active(U81(X:S)) -> U81(active(X:S))
1.05/1.12	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.05/1.12	 active(__(nil,X:S)) -> mark(X:S)
1.05/1.12	 active(__(X:S,nil)) -> mark(X:S)
1.05/1.12	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.05/1.12	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.05/1.12	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.05/1.12	 active(isList(nil)) -> mark(tt)
1.05/1.12	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.05/1.12	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.05/1.12	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.05/1.12	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.05/1.12	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.05/1.12	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.05/1.12	 active(isPal(nil)) -> mark(tt)
1.05/1.12	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.05/1.12	 active(isQid(a)) -> mark(tt)
1.05/1.12	 active(isQid(e)) -> mark(tt)
1.05/1.12	 active(isQid(i)) -> mark(tt)
1.05/1.12	 active(isQid(o)) -> mark(tt)
1.05/1.12	 active(isQid(u)) -> mark(tt)
1.05/1.12	 isList(ok(X:S)) -> ok(isList(X:S))
1.05/1.12	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.05/1.12	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.05/1.12	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.05/1.12	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.05/1.12	 proper(U11(X:S)) -> U11(proper(X:S))
1.05/1.12	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U22(X:S)) -> U22(proper(X:S))
1.05/1.12	 proper(U31(X:S)) -> U31(proper(X:S))
1.05/1.12	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U42(X:S)) -> U42(proper(X:S))
1.05/1.12	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U52(X:S)) -> U52(proper(X:S))
1.05/1.12	 proper(U61(X:S)) -> U61(proper(X:S))
1.05/1.12	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U72(X:S)) -> U72(proper(X:S))
1.05/1.12	 proper(U81(X:S)) -> U81(proper(X:S))
1.05/1.12	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(isList(X:S)) -> isList(proper(X:S))
1.05/1.12	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.05/1.12	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.05/1.12	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.05/1.12	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.05/1.12	 proper(a) -> ok(a)
1.05/1.12	 proper(e) -> ok(e)
1.05/1.12	 proper(i) -> ok(i)
1.05/1.12	 proper(nil) -> ok(nil)
1.05/1.12	 proper(o) -> ok(o)
1.05/1.12	 proper(tt) -> ok(tt)
1.05/1.12	 proper(u) -> ok(u)
1.05/1.12	 top(mark(X:S)) -> top(proper(X:S))
1.05/1.12	 top(ok(X:S)) -> top(active(X:S))
1.05/1.12	->Projection:
1.05/1.12	 pi(U52#) = 1
1.05/1.12	
1.05/1.12	Problem 1.11: 
1.05/1.12	
1.05/1.12	SCC Processor:
1.05/1.12	-> Pairs:
1.05/1.12	 Empty
1.05/1.12	-> Rules:
1.05/1.12	 U11(mark(X:S)) -> mark(U11(X:S))
1.05/1.12	 U11(ok(X:S)) -> ok(U11(X:S))
1.05/1.12	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.05/1.12	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.05/1.12	 U22(mark(X:S)) -> mark(U22(X:S))
1.05/1.12	 U22(ok(X:S)) -> ok(U22(X:S))
1.05/1.12	 U31(mark(X:S)) -> mark(U31(X:S))
1.05/1.12	 U31(ok(X:S)) -> ok(U31(X:S))
1.05/1.12	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.05/1.12	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.05/1.12	 U42(mark(X:S)) -> mark(U42(X:S))
1.05/1.12	 U42(ok(X:S)) -> ok(U42(X:S))
1.05/1.12	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.05/1.12	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.05/1.12	 U52(mark(X:S)) -> mark(U52(X:S))
1.05/1.12	 U52(ok(X:S)) -> ok(U52(X:S))
1.05/1.12	 U61(mark(X:S)) -> mark(U61(X:S))
1.05/1.12	 U61(ok(X:S)) -> ok(U61(X:S))
1.05/1.12	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.05/1.12	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.05/1.12	 U72(mark(X:S)) -> mark(U72(X:S))
1.05/1.12	 U72(ok(X:S)) -> ok(U72(X:S))
1.05/1.12	 U81(mark(X:S)) -> mark(U81(X:S))
1.05/1.12	 U81(ok(X:S)) -> ok(U81(X:S))
1.05/1.12	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.05/1.12	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.05/1.12	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.05/1.12	 active(U11(tt)) -> mark(tt)
1.05/1.12	 active(U11(X:S)) -> U11(active(X:S))
1.05/1.12	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.05/1.12	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.05/1.12	 active(U22(tt)) -> mark(tt)
1.05/1.12	 active(U22(X:S)) -> U22(active(X:S))
1.05/1.12	 active(U31(tt)) -> mark(tt)
1.05/1.12	 active(U31(X:S)) -> U31(active(X:S))
1.05/1.12	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.05/1.12	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.05/1.12	 active(U42(tt)) -> mark(tt)
1.05/1.12	 active(U42(X:S)) -> U42(active(X:S))
1.05/1.12	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.05/1.12	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.05/1.12	 active(U52(tt)) -> mark(tt)
1.05/1.12	 active(U52(X:S)) -> U52(active(X:S))
1.05/1.12	 active(U61(tt)) -> mark(tt)
1.05/1.12	 active(U61(X:S)) -> U61(active(X:S))
1.05/1.12	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.05/1.12	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.05/1.12	 active(U72(tt)) -> mark(tt)
1.05/1.12	 active(U72(X:S)) -> U72(active(X:S))
1.05/1.12	 active(U81(tt)) -> mark(tt)
1.05/1.12	 active(U81(X:S)) -> U81(active(X:S))
1.05/1.12	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.05/1.12	 active(__(nil,X:S)) -> mark(X:S)
1.05/1.12	 active(__(X:S,nil)) -> mark(X:S)
1.05/1.12	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.05/1.12	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.05/1.12	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.05/1.12	 active(isList(nil)) -> mark(tt)
1.05/1.12	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.05/1.12	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.05/1.12	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.05/1.12	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.05/1.12	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.05/1.12	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.05/1.12	 active(isPal(nil)) -> mark(tt)
1.05/1.12	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.05/1.12	 active(isQid(a)) -> mark(tt)
1.05/1.12	 active(isQid(e)) -> mark(tt)
1.05/1.12	 active(isQid(i)) -> mark(tt)
1.05/1.12	 active(isQid(o)) -> mark(tt)
1.05/1.12	 active(isQid(u)) -> mark(tt)
1.05/1.12	 isList(ok(X:S)) -> ok(isList(X:S))
1.05/1.12	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.05/1.12	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.05/1.12	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.05/1.12	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.05/1.12	 proper(U11(X:S)) -> U11(proper(X:S))
1.05/1.12	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U22(X:S)) -> U22(proper(X:S))
1.05/1.12	 proper(U31(X:S)) -> U31(proper(X:S))
1.05/1.12	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U42(X:S)) -> U42(proper(X:S))
1.05/1.12	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U52(X:S)) -> U52(proper(X:S))
1.05/1.12	 proper(U61(X:S)) -> U61(proper(X:S))
1.05/1.12	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U72(X:S)) -> U72(proper(X:S))
1.05/1.12	 proper(U81(X:S)) -> U81(proper(X:S))
1.05/1.12	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(isList(X:S)) -> isList(proper(X:S))
1.05/1.12	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.05/1.12	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.05/1.12	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.05/1.12	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.05/1.12	 proper(a) -> ok(a)
1.05/1.12	 proper(e) -> ok(e)
1.05/1.12	 proper(i) -> ok(i)
1.05/1.12	 proper(nil) -> ok(nil)
1.05/1.12	 proper(o) -> ok(o)
1.05/1.12	 proper(tt) -> ok(tt)
1.05/1.12	 proper(u) -> ok(u)
1.05/1.12	 top(mark(X:S)) -> top(proper(X:S))
1.05/1.12	 top(ok(X:S)) -> top(active(X:S))
1.05/1.12	->Strongly Connected Components:
1.05/1.12	 There is no strongly connected component
1.05/1.12	
1.05/1.12	The problem is finite.
1.05/1.12	
1.05/1.12	Problem 1.12: 
1.05/1.12	
1.05/1.12	Subterm Processor:
1.05/1.12	-> Pairs:
1.05/1.12	 U51#(mark(X1:S),X2:S) -> U51#(X1:S,X2:S)
1.05/1.12	 U51#(ok(X1:S),ok(X2:S)) -> U51#(X1:S,X2:S)
1.05/1.12	-> Rules:
1.05/1.12	 U11(mark(X:S)) -> mark(U11(X:S))
1.05/1.12	 U11(ok(X:S)) -> ok(U11(X:S))
1.05/1.12	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.05/1.12	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.05/1.12	 U22(mark(X:S)) -> mark(U22(X:S))
1.05/1.12	 U22(ok(X:S)) -> ok(U22(X:S))
1.05/1.12	 U31(mark(X:S)) -> mark(U31(X:S))
1.05/1.12	 U31(ok(X:S)) -> ok(U31(X:S))
1.05/1.12	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.05/1.12	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.05/1.12	 U42(mark(X:S)) -> mark(U42(X:S))
1.05/1.12	 U42(ok(X:S)) -> ok(U42(X:S))
1.05/1.12	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.05/1.12	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.05/1.12	 U52(mark(X:S)) -> mark(U52(X:S))
1.05/1.12	 U52(ok(X:S)) -> ok(U52(X:S))
1.05/1.12	 U61(mark(X:S)) -> mark(U61(X:S))
1.05/1.12	 U61(ok(X:S)) -> ok(U61(X:S))
1.05/1.12	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.05/1.12	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.05/1.12	 U72(mark(X:S)) -> mark(U72(X:S))
1.05/1.12	 U72(ok(X:S)) -> ok(U72(X:S))
1.05/1.12	 U81(mark(X:S)) -> mark(U81(X:S))
1.05/1.12	 U81(ok(X:S)) -> ok(U81(X:S))
1.05/1.12	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.05/1.12	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.05/1.12	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.05/1.12	 active(U11(tt)) -> mark(tt)
1.05/1.12	 active(U11(X:S)) -> U11(active(X:S))
1.05/1.12	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.05/1.12	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.05/1.12	 active(U22(tt)) -> mark(tt)
1.05/1.12	 active(U22(X:S)) -> U22(active(X:S))
1.05/1.12	 active(U31(tt)) -> mark(tt)
1.05/1.12	 active(U31(X:S)) -> U31(active(X:S))
1.05/1.12	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.05/1.12	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.05/1.12	 active(U42(tt)) -> mark(tt)
1.05/1.12	 active(U42(X:S)) -> U42(active(X:S))
1.05/1.12	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.05/1.12	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.05/1.12	 active(U52(tt)) -> mark(tt)
1.05/1.12	 active(U52(X:S)) -> U52(active(X:S))
1.05/1.12	 active(U61(tt)) -> mark(tt)
1.05/1.12	 active(U61(X:S)) -> U61(active(X:S))
1.05/1.12	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.05/1.12	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.05/1.12	 active(U72(tt)) -> mark(tt)
1.05/1.12	 active(U72(X:S)) -> U72(active(X:S))
1.05/1.12	 active(U81(tt)) -> mark(tt)
1.05/1.12	 active(U81(X:S)) -> U81(active(X:S))
1.05/1.12	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.05/1.12	 active(__(nil,X:S)) -> mark(X:S)
1.05/1.12	 active(__(X:S,nil)) -> mark(X:S)
1.05/1.12	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.05/1.12	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.05/1.12	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.05/1.12	 active(isList(nil)) -> mark(tt)
1.05/1.12	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.05/1.12	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.05/1.12	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.05/1.12	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.05/1.12	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.05/1.12	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.05/1.12	 active(isPal(nil)) -> mark(tt)
1.05/1.12	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.05/1.12	 active(isQid(a)) -> mark(tt)
1.05/1.12	 active(isQid(e)) -> mark(tt)
1.05/1.12	 active(isQid(i)) -> mark(tt)
1.05/1.12	 active(isQid(o)) -> mark(tt)
1.05/1.12	 active(isQid(u)) -> mark(tt)
1.05/1.12	 isList(ok(X:S)) -> ok(isList(X:S))
1.05/1.12	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.05/1.12	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.05/1.12	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.05/1.12	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.05/1.12	 proper(U11(X:S)) -> U11(proper(X:S))
1.05/1.12	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U22(X:S)) -> U22(proper(X:S))
1.05/1.12	 proper(U31(X:S)) -> U31(proper(X:S))
1.05/1.12	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U42(X:S)) -> U42(proper(X:S))
1.05/1.12	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U52(X:S)) -> U52(proper(X:S))
1.05/1.12	 proper(U61(X:S)) -> U61(proper(X:S))
1.05/1.12	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U72(X:S)) -> U72(proper(X:S))
1.05/1.12	 proper(U81(X:S)) -> U81(proper(X:S))
1.05/1.12	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(isList(X:S)) -> isList(proper(X:S))
1.05/1.12	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.05/1.12	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.05/1.12	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.05/1.12	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.05/1.12	 proper(a) -> ok(a)
1.05/1.12	 proper(e) -> ok(e)
1.05/1.12	 proper(i) -> ok(i)
1.05/1.12	 proper(nil) -> ok(nil)
1.05/1.12	 proper(o) -> ok(o)
1.05/1.12	 proper(tt) -> ok(tt)
1.05/1.12	 proper(u) -> ok(u)
1.05/1.12	 top(mark(X:S)) -> top(proper(X:S))
1.05/1.12	 top(ok(X:S)) -> top(active(X:S))
1.05/1.12	->Projection:
1.05/1.12	 pi(U51#) = 1
1.05/1.12	
1.05/1.12	Problem 1.12: 
1.05/1.12	
1.05/1.12	SCC Processor:
1.05/1.12	-> Pairs:
1.05/1.12	 Empty
1.05/1.12	-> Rules:
1.05/1.12	 U11(mark(X:S)) -> mark(U11(X:S))
1.05/1.12	 U11(ok(X:S)) -> ok(U11(X:S))
1.05/1.12	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.05/1.12	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.05/1.12	 U22(mark(X:S)) -> mark(U22(X:S))
1.05/1.12	 U22(ok(X:S)) -> ok(U22(X:S))
1.05/1.12	 U31(mark(X:S)) -> mark(U31(X:S))
1.05/1.12	 U31(ok(X:S)) -> ok(U31(X:S))
1.05/1.12	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.05/1.12	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.05/1.12	 U42(mark(X:S)) -> mark(U42(X:S))
1.05/1.12	 U42(ok(X:S)) -> ok(U42(X:S))
1.05/1.12	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.05/1.12	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.05/1.12	 U52(mark(X:S)) -> mark(U52(X:S))
1.05/1.12	 U52(ok(X:S)) -> ok(U52(X:S))
1.05/1.12	 U61(mark(X:S)) -> mark(U61(X:S))
1.05/1.12	 U61(ok(X:S)) -> ok(U61(X:S))
1.05/1.12	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.05/1.12	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.05/1.12	 U72(mark(X:S)) -> mark(U72(X:S))
1.05/1.12	 U72(ok(X:S)) -> ok(U72(X:S))
1.05/1.12	 U81(mark(X:S)) -> mark(U81(X:S))
1.05/1.12	 U81(ok(X:S)) -> ok(U81(X:S))
1.05/1.12	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.05/1.12	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.05/1.12	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.05/1.12	 active(U11(tt)) -> mark(tt)
1.05/1.12	 active(U11(X:S)) -> U11(active(X:S))
1.05/1.12	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.05/1.12	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.05/1.12	 active(U22(tt)) -> mark(tt)
1.05/1.12	 active(U22(X:S)) -> U22(active(X:S))
1.05/1.12	 active(U31(tt)) -> mark(tt)
1.05/1.12	 active(U31(X:S)) -> U31(active(X:S))
1.05/1.12	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.05/1.12	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.05/1.12	 active(U42(tt)) -> mark(tt)
1.05/1.12	 active(U42(X:S)) -> U42(active(X:S))
1.05/1.12	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.05/1.12	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.05/1.12	 active(U52(tt)) -> mark(tt)
1.05/1.12	 active(U52(X:S)) -> U52(active(X:S))
1.05/1.12	 active(U61(tt)) -> mark(tt)
1.05/1.12	 active(U61(X:S)) -> U61(active(X:S))
1.05/1.12	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.05/1.12	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.05/1.12	 active(U72(tt)) -> mark(tt)
1.05/1.12	 active(U72(X:S)) -> U72(active(X:S))
1.05/1.12	 active(U81(tt)) -> mark(tt)
1.05/1.12	 active(U81(X:S)) -> U81(active(X:S))
1.05/1.12	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.05/1.12	 active(__(nil,X:S)) -> mark(X:S)
1.05/1.12	 active(__(X:S,nil)) -> mark(X:S)
1.05/1.12	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.05/1.12	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.05/1.12	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.05/1.12	 active(isList(nil)) -> mark(tt)
1.05/1.12	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.05/1.12	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.05/1.12	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.05/1.12	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.05/1.12	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.05/1.12	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.05/1.12	 active(isPal(nil)) -> mark(tt)
1.05/1.12	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.05/1.12	 active(isQid(a)) -> mark(tt)
1.05/1.12	 active(isQid(e)) -> mark(tt)
1.05/1.12	 active(isQid(i)) -> mark(tt)
1.05/1.12	 active(isQid(o)) -> mark(tt)
1.05/1.12	 active(isQid(u)) -> mark(tt)
1.05/1.12	 isList(ok(X:S)) -> ok(isList(X:S))
1.05/1.12	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.05/1.12	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.05/1.12	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.05/1.12	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.05/1.12	 proper(U11(X:S)) -> U11(proper(X:S))
1.05/1.12	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U22(X:S)) -> U22(proper(X:S))
1.05/1.12	 proper(U31(X:S)) -> U31(proper(X:S))
1.05/1.12	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U42(X:S)) -> U42(proper(X:S))
1.05/1.12	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U52(X:S)) -> U52(proper(X:S))
1.05/1.12	 proper(U61(X:S)) -> U61(proper(X:S))
1.05/1.12	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U72(X:S)) -> U72(proper(X:S))
1.05/1.12	 proper(U81(X:S)) -> U81(proper(X:S))
1.05/1.12	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(isList(X:S)) -> isList(proper(X:S))
1.05/1.12	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.05/1.12	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.05/1.12	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.05/1.12	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.05/1.12	 proper(a) -> ok(a)
1.05/1.12	 proper(e) -> ok(e)
1.05/1.12	 proper(i) -> ok(i)
1.05/1.12	 proper(nil) -> ok(nil)
1.05/1.12	 proper(o) -> ok(o)
1.05/1.12	 proper(tt) -> ok(tt)
1.05/1.12	 proper(u) -> ok(u)
1.05/1.12	 top(mark(X:S)) -> top(proper(X:S))
1.05/1.12	 top(ok(X:S)) -> top(active(X:S))
1.05/1.12	->Strongly Connected Components:
1.05/1.12	 There is no strongly connected component
1.05/1.12	
1.05/1.12	The problem is finite.
1.05/1.12	
1.05/1.12	Problem 1.13: 
1.05/1.12	
1.05/1.12	Subterm Processor:
1.05/1.12	-> Pairs:
1.05/1.12	 U42#(mark(X:S)) -> U42#(X:S)
1.05/1.12	 U42#(ok(X:S)) -> U42#(X:S)
1.05/1.12	-> Rules:
1.05/1.12	 U11(mark(X:S)) -> mark(U11(X:S))
1.05/1.12	 U11(ok(X:S)) -> ok(U11(X:S))
1.05/1.12	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.05/1.12	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.05/1.12	 U22(mark(X:S)) -> mark(U22(X:S))
1.05/1.12	 U22(ok(X:S)) -> ok(U22(X:S))
1.05/1.12	 U31(mark(X:S)) -> mark(U31(X:S))
1.05/1.12	 U31(ok(X:S)) -> ok(U31(X:S))
1.05/1.12	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.05/1.12	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.05/1.12	 U42(mark(X:S)) -> mark(U42(X:S))
1.05/1.12	 U42(ok(X:S)) -> ok(U42(X:S))
1.05/1.12	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.05/1.12	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.05/1.12	 U52(mark(X:S)) -> mark(U52(X:S))
1.05/1.12	 U52(ok(X:S)) -> ok(U52(X:S))
1.05/1.12	 U61(mark(X:S)) -> mark(U61(X:S))
1.05/1.12	 U61(ok(X:S)) -> ok(U61(X:S))
1.05/1.12	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.05/1.12	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.05/1.12	 U72(mark(X:S)) -> mark(U72(X:S))
1.05/1.12	 U72(ok(X:S)) -> ok(U72(X:S))
1.05/1.12	 U81(mark(X:S)) -> mark(U81(X:S))
1.05/1.12	 U81(ok(X:S)) -> ok(U81(X:S))
1.05/1.12	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.05/1.12	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.05/1.12	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.05/1.12	 active(U11(tt)) -> mark(tt)
1.05/1.12	 active(U11(X:S)) -> U11(active(X:S))
1.05/1.12	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.05/1.12	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.05/1.12	 active(U22(tt)) -> mark(tt)
1.05/1.12	 active(U22(X:S)) -> U22(active(X:S))
1.05/1.12	 active(U31(tt)) -> mark(tt)
1.05/1.12	 active(U31(X:S)) -> U31(active(X:S))
1.05/1.12	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.05/1.12	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.05/1.12	 active(U42(tt)) -> mark(tt)
1.05/1.12	 active(U42(X:S)) -> U42(active(X:S))
1.05/1.12	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.05/1.12	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.05/1.12	 active(U52(tt)) -> mark(tt)
1.05/1.12	 active(U52(X:S)) -> U52(active(X:S))
1.05/1.12	 active(U61(tt)) -> mark(tt)
1.05/1.12	 active(U61(X:S)) -> U61(active(X:S))
1.05/1.12	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.05/1.12	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.05/1.12	 active(U72(tt)) -> mark(tt)
1.05/1.12	 active(U72(X:S)) -> U72(active(X:S))
1.05/1.12	 active(U81(tt)) -> mark(tt)
1.05/1.12	 active(U81(X:S)) -> U81(active(X:S))
1.05/1.12	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.05/1.12	 active(__(nil,X:S)) -> mark(X:S)
1.05/1.12	 active(__(X:S,nil)) -> mark(X:S)
1.05/1.12	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.05/1.12	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.05/1.12	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.05/1.12	 active(isList(nil)) -> mark(tt)
1.05/1.12	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.05/1.12	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.05/1.12	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.05/1.12	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.05/1.12	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.05/1.12	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.05/1.12	 active(isPal(nil)) -> mark(tt)
1.05/1.12	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.05/1.12	 active(isQid(a)) -> mark(tt)
1.05/1.12	 active(isQid(e)) -> mark(tt)
1.05/1.12	 active(isQid(i)) -> mark(tt)
1.05/1.12	 active(isQid(o)) -> mark(tt)
1.05/1.12	 active(isQid(u)) -> mark(tt)
1.05/1.12	 isList(ok(X:S)) -> ok(isList(X:S))
1.05/1.12	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.05/1.12	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.05/1.12	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.05/1.12	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.05/1.12	 proper(U11(X:S)) -> U11(proper(X:S))
1.05/1.12	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U22(X:S)) -> U22(proper(X:S))
1.05/1.12	 proper(U31(X:S)) -> U31(proper(X:S))
1.05/1.12	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U42(X:S)) -> U42(proper(X:S))
1.05/1.12	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U52(X:S)) -> U52(proper(X:S))
1.05/1.12	 proper(U61(X:S)) -> U61(proper(X:S))
1.05/1.12	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U72(X:S)) -> U72(proper(X:S))
1.05/1.12	 proper(U81(X:S)) -> U81(proper(X:S))
1.05/1.12	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(isList(X:S)) -> isList(proper(X:S))
1.05/1.12	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.05/1.12	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.05/1.12	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.05/1.12	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.05/1.12	 proper(a) -> ok(a)
1.05/1.12	 proper(e) -> ok(e)
1.05/1.12	 proper(i) -> ok(i)
1.05/1.12	 proper(nil) -> ok(nil)
1.05/1.12	 proper(o) -> ok(o)
1.05/1.12	 proper(tt) -> ok(tt)
1.05/1.12	 proper(u) -> ok(u)
1.05/1.12	 top(mark(X:S)) -> top(proper(X:S))
1.05/1.12	 top(ok(X:S)) -> top(active(X:S))
1.05/1.12	->Projection:
1.05/1.12	 pi(U42#) = 1
1.05/1.12	
1.05/1.12	Problem 1.13: 
1.05/1.12	
1.05/1.12	SCC Processor:
1.05/1.12	-> Pairs:
1.05/1.12	 Empty
1.05/1.12	-> Rules:
1.05/1.12	 U11(mark(X:S)) -> mark(U11(X:S))
1.05/1.12	 U11(ok(X:S)) -> ok(U11(X:S))
1.05/1.12	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.05/1.12	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.05/1.12	 U22(mark(X:S)) -> mark(U22(X:S))
1.05/1.12	 U22(ok(X:S)) -> ok(U22(X:S))
1.05/1.12	 U31(mark(X:S)) -> mark(U31(X:S))
1.05/1.12	 U31(ok(X:S)) -> ok(U31(X:S))
1.05/1.12	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.05/1.12	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.05/1.12	 U42(mark(X:S)) -> mark(U42(X:S))
1.05/1.12	 U42(ok(X:S)) -> ok(U42(X:S))
1.05/1.12	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.05/1.12	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.05/1.12	 U52(mark(X:S)) -> mark(U52(X:S))
1.05/1.12	 U52(ok(X:S)) -> ok(U52(X:S))
1.05/1.12	 U61(mark(X:S)) -> mark(U61(X:S))
1.05/1.12	 U61(ok(X:S)) -> ok(U61(X:S))
1.05/1.12	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.05/1.12	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.05/1.12	 U72(mark(X:S)) -> mark(U72(X:S))
1.05/1.12	 U72(ok(X:S)) -> ok(U72(X:S))
1.05/1.12	 U81(mark(X:S)) -> mark(U81(X:S))
1.05/1.12	 U81(ok(X:S)) -> ok(U81(X:S))
1.05/1.12	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.05/1.12	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.05/1.12	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.05/1.12	 active(U11(tt)) -> mark(tt)
1.05/1.12	 active(U11(X:S)) -> U11(active(X:S))
1.05/1.12	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.05/1.12	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.05/1.12	 active(U22(tt)) -> mark(tt)
1.05/1.12	 active(U22(X:S)) -> U22(active(X:S))
1.05/1.12	 active(U31(tt)) -> mark(tt)
1.05/1.12	 active(U31(X:S)) -> U31(active(X:S))
1.05/1.12	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.05/1.12	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.05/1.12	 active(U42(tt)) -> mark(tt)
1.05/1.12	 active(U42(X:S)) -> U42(active(X:S))
1.05/1.12	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.05/1.12	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.05/1.12	 active(U52(tt)) -> mark(tt)
1.05/1.12	 active(U52(X:S)) -> U52(active(X:S))
1.05/1.12	 active(U61(tt)) -> mark(tt)
1.05/1.12	 active(U61(X:S)) -> U61(active(X:S))
1.05/1.12	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.05/1.12	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.05/1.12	 active(U72(tt)) -> mark(tt)
1.05/1.12	 active(U72(X:S)) -> U72(active(X:S))
1.05/1.12	 active(U81(tt)) -> mark(tt)
1.05/1.12	 active(U81(X:S)) -> U81(active(X:S))
1.05/1.12	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.05/1.12	 active(__(nil,X:S)) -> mark(X:S)
1.05/1.12	 active(__(X:S,nil)) -> mark(X:S)
1.05/1.12	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.05/1.12	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.05/1.12	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.05/1.12	 active(isList(nil)) -> mark(tt)
1.05/1.12	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.05/1.12	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.05/1.12	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.05/1.12	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.05/1.12	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.05/1.12	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.05/1.12	 active(isPal(nil)) -> mark(tt)
1.05/1.12	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.05/1.12	 active(isQid(a)) -> mark(tt)
1.05/1.12	 active(isQid(e)) -> mark(tt)
1.05/1.12	 active(isQid(i)) -> mark(tt)
1.05/1.12	 active(isQid(o)) -> mark(tt)
1.05/1.12	 active(isQid(u)) -> mark(tt)
1.05/1.12	 isList(ok(X:S)) -> ok(isList(X:S))
1.05/1.12	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.05/1.12	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.05/1.12	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.05/1.12	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.05/1.12	 proper(U11(X:S)) -> U11(proper(X:S))
1.05/1.12	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U22(X:S)) -> U22(proper(X:S))
1.05/1.12	 proper(U31(X:S)) -> U31(proper(X:S))
1.05/1.12	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U42(X:S)) -> U42(proper(X:S))
1.05/1.12	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U52(X:S)) -> U52(proper(X:S))
1.05/1.12	 proper(U61(X:S)) -> U61(proper(X:S))
1.05/1.12	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U72(X:S)) -> U72(proper(X:S))
1.05/1.12	 proper(U81(X:S)) -> U81(proper(X:S))
1.05/1.12	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(isList(X:S)) -> isList(proper(X:S))
1.05/1.12	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.05/1.12	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.05/1.12	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.05/1.12	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.05/1.12	 proper(a) -> ok(a)
1.05/1.12	 proper(e) -> ok(e)
1.05/1.12	 proper(i) -> ok(i)
1.05/1.12	 proper(nil) -> ok(nil)
1.05/1.12	 proper(o) -> ok(o)
1.05/1.12	 proper(tt) -> ok(tt)
1.05/1.12	 proper(u) -> ok(u)
1.05/1.12	 top(mark(X:S)) -> top(proper(X:S))
1.05/1.12	 top(ok(X:S)) -> top(active(X:S))
1.05/1.12	->Strongly Connected Components:
1.05/1.12	 There is no strongly connected component
1.05/1.12	
1.05/1.12	The problem is finite.
1.05/1.12	
1.05/1.12	Problem 1.14: 
1.05/1.12	
1.05/1.12	Subterm Processor:
1.05/1.12	-> Pairs:
1.05/1.12	 U41#(mark(X1:S),X2:S) -> U41#(X1:S,X2:S)
1.05/1.12	 U41#(ok(X1:S),ok(X2:S)) -> U41#(X1:S,X2:S)
1.05/1.12	-> Rules:
1.05/1.12	 U11(mark(X:S)) -> mark(U11(X:S))
1.05/1.12	 U11(ok(X:S)) -> ok(U11(X:S))
1.05/1.12	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.05/1.12	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.05/1.12	 U22(mark(X:S)) -> mark(U22(X:S))
1.05/1.12	 U22(ok(X:S)) -> ok(U22(X:S))
1.05/1.12	 U31(mark(X:S)) -> mark(U31(X:S))
1.05/1.12	 U31(ok(X:S)) -> ok(U31(X:S))
1.05/1.12	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.05/1.12	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.05/1.12	 U42(mark(X:S)) -> mark(U42(X:S))
1.05/1.12	 U42(ok(X:S)) -> ok(U42(X:S))
1.05/1.12	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.05/1.12	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.05/1.12	 U52(mark(X:S)) -> mark(U52(X:S))
1.05/1.12	 U52(ok(X:S)) -> ok(U52(X:S))
1.05/1.12	 U61(mark(X:S)) -> mark(U61(X:S))
1.05/1.12	 U61(ok(X:S)) -> ok(U61(X:S))
1.05/1.12	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.05/1.12	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.05/1.12	 U72(mark(X:S)) -> mark(U72(X:S))
1.05/1.12	 U72(ok(X:S)) -> ok(U72(X:S))
1.05/1.12	 U81(mark(X:S)) -> mark(U81(X:S))
1.05/1.12	 U81(ok(X:S)) -> ok(U81(X:S))
1.05/1.12	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.05/1.12	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.05/1.12	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.05/1.12	 active(U11(tt)) -> mark(tt)
1.05/1.12	 active(U11(X:S)) -> U11(active(X:S))
1.05/1.12	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.05/1.12	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.05/1.12	 active(U22(tt)) -> mark(tt)
1.05/1.12	 active(U22(X:S)) -> U22(active(X:S))
1.05/1.12	 active(U31(tt)) -> mark(tt)
1.05/1.12	 active(U31(X:S)) -> U31(active(X:S))
1.05/1.12	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.05/1.12	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.05/1.12	 active(U42(tt)) -> mark(tt)
1.05/1.12	 active(U42(X:S)) -> U42(active(X:S))
1.05/1.12	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.05/1.12	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.05/1.12	 active(U52(tt)) -> mark(tt)
1.05/1.12	 active(U52(X:S)) -> U52(active(X:S))
1.05/1.12	 active(U61(tt)) -> mark(tt)
1.05/1.12	 active(U61(X:S)) -> U61(active(X:S))
1.05/1.12	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.05/1.12	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.05/1.12	 active(U72(tt)) -> mark(tt)
1.05/1.12	 active(U72(X:S)) -> U72(active(X:S))
1.05/1.12	 active(U81(tt)) -> mark(tt)
1.05/1.12	 active(U81(X:S)) -> U81(active(X:S))
1.05/1.12	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.05/1.12	 active(__(nil,X:S)) -> mark(X:S)
1.05/1.12	 active(__(X:S,nil)) -> mark(X:S)
1.05/1.12	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.05/1.12	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.05/1.12	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.05/1.12	 active(isList(nil)) -> mark(tt)
1.05/1.12	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.05/1.12	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.05/1.12	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.05/1.12	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.05/1.12	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.05/1.12	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.05/1.12	 active(isPal(nil)) -> mark(tt)
1.05/1.12	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.05/1.12	 active(isQid(a)) -> mark(tt)
1.05/1.12	 active(isQid(e)) -> mark(tt)
1.05/1.12	 active(isQid(i)) -> mark(tt)
1.05/1.12	 active(isQid(o)) -> mark(tt)
1.05/1.12	 active(isQid(u)) -> mark(tt)
1.05/1.12	 isList(ok(X:S)) -> ok(isList(X:S))
1.05/1.12	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.05/1.12	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.05/1.12	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.05/1.12	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.05/1.12	 proper(U11(X:S)) -> U11(proper(X:S))
1.05/1.12	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U22(X:S)) -> U22(proper(X:S))
1.05/1.12	 proper(U31(X:S)) -> U31(proper(X:S))
1.05/1.12	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U42(X:S)) -> U42(proper(X:S))
1.05/1.12	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U52(X:S)) -> U52(proper(X:S))
1.05/1.12	 proper(U61(X:S)) -> U61(proper(X:S))
1.05/1.12	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U72(X:S)) -> U72(proper(X:S))
1.05/1.12	 proper(U81(X:S)) -> U81(proper(X:S))
1.05/1.12	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(isList(X:S)) -> isList(proper(X:S))
1.05/1.12	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.05/1.12	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.05/1.12	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.05/1.12	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.05/1.12	 proper(a) -> ok(a)
1.05/1.12	 proper(e) -> ok(e)
1.05/1.12	 proper(i) -> ok(i)
1.05/1.12	 proper(nil) -> ok(nil)
1.05/1.12	 proper(o) -> ok(o)
1.05/1.12	 proper(tt) -> ok(tt)
1.05/1.12	 proper(u) -> ok(u)
1.05/1.12	 top(mark(X:S)) -> top(proper(X:S))
1.05/1.12	 top(ok(X:S)) -> top(active(X:S))
1.05/1.12	->Projection:
1.05/1.12	 pi(U41#) = 1
1.05/1.12	
1.05/1.12	Problem 1.14: 
1.05/1.12	
1.05/1.12	SCC Processor:
1.05/1.12	-> Pairs:
1.05/1.12	 Empty
1.05/1.12	-> Rules:
1.05/1.12	 U11(mark(X:S)) -> mark(U11(X:S))
1.05/1.12	 U11(ok(X:S)) -> ok(U11(X:S))
1.05/1.12	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.05/1.12	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.05/1.12	 U22(mark(X:S)) -> mark(U22(X:S))
1.05/1.12	 U22(ok(X:S)) -> ok(U22(X:S))
1.05/1.12	 U31(mark(X:S)) -> mark(U31(X:S))
1.05/1.12	 U31(ok(X:S)) -> ok(U31(X:S))
1.05/1.12	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.05/1.12	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.05/1.12	 U42(mark(X:S)) -> mark(U42(X:S))
1.05/1.12	 U42(ok(X:S)) -> ok(U42(X:S))
1.05/1.12	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.05/1.12	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.05/1.12	 U52(mark(X:S)) -> mark(U52(X:S))
1.05/1.12	 U52(ok(X:S)) -> ok(U52(X:S))
1.05/1.12	 U61(mark(X:S)) -> mark(U61(X:S))
1.05/1.12	 U61(ok(X:S)) -> ok(U61(X:S))
1.05/1.12	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.05/1.12	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.05/1.12	 U72(mark(X:S)) -> mark(U72(X:S))
1.05/1.12	 U72(ok(X:S)) -> ok(U72(X:S))
1.05/1.12	 U81(mark(X:S)) -> mark(U81(X:S))
1.05/1.12	 U81(ok(X:S)) -> ok(U81(X:S))
1.05/1.12	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.05/1.12	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.05/1.12	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.05/1.12	 active(U11(tt)) -> mark(tt)
1.05/1.12	 active(U11(X:S)) -> U11(active(X:S))
1.05/1.12	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.05/1.12	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.05/1.12	 active(U22(tt)) -> mark(tt)
1.05/1.12	 active(U22(X:S)) -> U22(active(X:S))
1.05/1.12	 active(U31(tt)) -> mark(tt)
1.05/1.12	 active(U31(X:S)) -> U31(active(X:S))
1.05/1.12	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.05/1.12	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.05/1.12	 active(U42(tt)) -> mark(tt)
1.05/1.12	 active(U42(X:S)) -> U42(active(X:S))
1.05/1.12	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.05/1.12	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.05/1.12	 active(U52(tt)) -> mark(tt)
1.05/1.12	 active(U52(X:S)) -> U52(active(X:S))
1.05/1.12	 active(U61(tt)) -> mark(tt)
1.05/1.12	 active(U61(X:S)) -> U61(active(X:S))
1.05/1.12	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.05/1.12	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.05/1.12	 active(U72(tt)) -> mark(tt)
1.05/1.12	 active(U72(X:S)) -> U72(active(X:S))
1.05/1.12	 active(U81(tt)) -> mark(tt)
1.05/1.12	 active(U81(X:S)) -> U81(active(X:S))
1.05/1.12	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.05/1.12	 active(__(nil,X:S)) -> mark(X:S)
1.05/1.12	 active(__(X:S,nil)) -> mark(X:S)
1.05/1.12	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.05/1.12	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.05/1.12	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.05/1.12	 active(isList(nil)) -> mark(tt)
1.05/1.12	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.05/1.12	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.05/1.12	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.05/1.12	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.05/1.12	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.05/1.12	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.05/1.12	 active(isPal(nil)) -> mark(tt)
1.05/1.12	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.05/1.12	 active(isQid(a)) -> mark(tt)
1.05/1.12	 active(isQid(e)) -> mark(tt)
1.05/1.12	 active(isQid(i)) -> mark(tt)
1.05/1.12	 active(isQid(o)) -> mark(tt)
1.05/1.12	 active(isQid(u)) -> mark(tt)
1.05/1.12	 isList(ok(X:S)) -> ok(isList(X:S))
1.05/1.12	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.05/1.12	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.05/1.12	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.05/1.12	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.05/1.12	 proper(U11(X:S)) -> U11(proper(X:S))
1.05/1.12	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U22(X:S)) -> U22(proper(X:S))
1.05/1.12	 proper(U31(X:S)) -> U31(proper(X:S))
1.05/1.12	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U42(X:S)) -> U42(proper(X:S))
1.05/1.12	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U52(X:S)) -> U52(proper(X:S))
1.05/1.12	 proper(U61(X:S)) -> U61(proper(X:S))
1.05/1.12	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U72(X:S)) -> U72(proper(X:S))
1.05/1.12	 proper(U81(X:S)) -> U81(proper(X:S))
1.05/1.12	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(isList(X:S)) -> isList(proper(X:S))
1.05/1.12	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.05/1.12	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.05/1.12	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.05/1.12	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.05/1.12	 proper(a) -> ok(a)
1.05/1.12	 proper(e) -> ok(e)
1.05/1.12	 proper(i) -> ok(i)
1.05/1.12	 proper(nil) -> ok(nil)
1.05/1.12	 proper(o) -> ok(o)
1.05/1.12	 proper(tt) -> ok(tt)
1.05/1.12	 proper(u) -> ok(u)
1.05/1.12	 top(mark(X:S)) -> top(proper(X:S))
1.05/1.12	 top(ok(X:S)) -> top(active(X:S))
1.05/1.12	->Strongly Connected Components:
1.05/1.12	 There is no strongly connected component
1.05/1.12	
1.05/1.12	The problem is finite.
1.05/1.12	
1.05/1.12	Problem 1.15: 
1.05/1.12	
1.05/1.12	Subterm Processor:
1.05/1.12	-> Pairs:
1.05/1.12	 U31#(mark(X:S)) -> U31#(X:S)
1.05/1.12	 U31#(ok(X:S)) -> U31#(X:S)
1.05/1.12	-> Rules:
1.05/1.12	 U11(mark(X:S)) -> mark(U11(X:S))
1.05/1.12	 U11(ok(X:S)) -> ok(U11(X:S))
1.05/1.12	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.05/1.12	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.05/1.12	 U22(mark(X:S)) -> mark(U22(X:S))
1.05/1.12	 U22(ok(X:S)) -> ok(U22(X:S))
1.05/1.12	 U31(mark(X:S)) -> mark(U31(X:S))
1.05/1.12	 U31(ok(X:S)) -> ok(U31(X:S))
1.05/1.12	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.05/1.12	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.05/1.12	 U42(mark(X:S)) -> mark(U42(X:S))
1.05/1.12	 U42(ok(X:S)) -> ok(U42(X:S))
1.05/1.12	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.05/1.12	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.05/1.12	 U52(mark(X:S)) -> mark(U52(X:S))
1.05/1.12	 U52(ok(X:S)) -> ok(U52(X:S))
1.05/1.12	 U61(mark(X:S)) -> mark(U61(X:S))
1.05/1.12	 U61(ok(X:S)) -> ok(U61(X:S))
1.05/1.12	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.05/1.12	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.05/1.12	 U72(mark(X:S)) -> mark(U72(X:S))
1.05/1.12	 U72(ok(X:S)) -> ok(U72(X:S))
1.05/1.12	 U81(mark(X:S)) -> mark(U81(X:S))
1.05/1.12	 U81(ok(X:S)) -> ok(U81(X:S))
1.05/1.12	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.05/1.12	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.05/1.12	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.05/1.12	 active(U11(tt)) -> mark(tt)
1.05/1.12	 active(U11(X:S)) -> U11(active(X:S))
1.05/1.12	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.05/1.12	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.05/1.12	 active(U22(tt)) -> mark(tt)
1.05/1.12	 active(U22(X:S)) -> U22(active(X:S))
1.05/1.12	 active(U31(tt)) -> mark(tt)
1.05/1.12	 active(U31(X:S)) -> U31(active(X:S))
1.05/1.12	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.05/1.12	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.05/1.12	 active(U42(tt)) -> mark(tt)
1.05/1.12	 active(U42(X:S)) -> U42(active(X:S))
1.05/1.12	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.05/1.12	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.05/1.12	 active(U52(tt)) -> mark(tt)
1.05/1.12	 active(U52(X:S)) -> U52(active(X:S))
1.05/1.12	 active(U61(tt)) -> mark(tt)
1.05/1.12	 active(U61(X:S)) -> U61(active(X:S))
1.05/1.12	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.05/1.12	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.05/1.12	 active(U72(tt)) -> mark(tt)
1.05/1.12	 active(U72(X:S)) -> U72(active(X:S))
1.05/1.12	 active(U81(tt)) -> mark(tt)
1.05/1.12	 active(U81(X:S)) -> U81(active(X:S))
1.05/1.12	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.05/1.12	 active(__(nil,X:S)) -> mark(X:S)
1.05/1.12	 active(__(X:S,nil)) -> mark(X:S)
1.05/1.12	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.05/1.12	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.05/1.12	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.05/1.12	 active(isList(nil)) -> mark(tt)
1.05/1.12	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.05/1.12	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.05/1.12	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.05/1.12	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.05/1.12	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.05/1.12	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.05/1.12	 active(isPal(nil)) -> mark(tt)
1.05/1.12	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.05/1.12	 active(isQid(a)) -> mark(tt)
1.05/1.12	 active(isQid(e)) -> mark(tt)
1.05/1.12	 active(isQid(i)) -> mark(tt)
1.05/1.12	 active(isQid(o)) -> mark(tt)
1.05/1.12	 active(isQid(u)) -> mark(tt)
1.05/1.12	 isList(ok(X:S)) -> ok(isList(X:S))
1.05/1.12	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.05/1.12	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.05/1.12	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.05/1.12	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.05/1.12	 proper(U11(X:S)) -> U11(proper(X:S))
1.05/1.12	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U22(X:S)) -> U22(proper(X:S))
1.05/1.12	 proper(U31(X:S)) -> U31(proper(X:S))
1.05/1.12	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U42(X:S)) -> U42(proper(X:S))
1.05/1.12	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U52(X:S)) -> U52(proper(X:S))
1.05/1.12	 proper(U61(X:S)) -> U61(proper(X:S))
1.05/1.12	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U72(X:S)) -> U72(proper(X:S))
1.05/1.12	 proper(U81(X:S)) -> U81(proper(X:S))
1.05/1.12	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(isList(X:S)) -> isList(proper(X:S))
1.05/1.12	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.05/1.12	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.05/1.12	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.05/1.12	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.05/1.12	 proper(a) -> ok(a)
1.05/1.12	 proper(e) -> ok(e)
1.05/1.12	 proper(i) -> ok(i)
1.05/1.12	 proper(nil) -> ok(nil)
1.05/1.12	 proper(o) -> ok(o)
1.05/1.12	 proper(tt) -> ok(tt)
1.05/1.12	 proper(u) -> ok(u)
1.05/1.12	 top(mark(X:S)) -> top(proper(X:S))
1.05/1.12	 top(ok(X:S)) -> top(active(X:S))
1.05/1.12	->Projection:
1.05/1.12	 pi(U31#) = 1
1.05/1.12	
1.05/1.12	Problem 1.15: 
1.05/1.12	
1.05/1.12	SCC Processor:
1.05/1.12	-> Pairs:
1.05/1.12	 Empty
1.05/1.12	-> Rules:
1.05/1.12	 U11(mark(X:S)) -> mark(U11(X:S))
1.05/1.12	 U11(ok(X:S)) -> ok(U11(X:S))
1.05/1.12	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.05/1.12	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.05/1.12	 U22(mark(X:S)) -> mark(U22(X:S))
1.05/1.12	 U22(ok(X:S)) -> ok(U22(X:S))
1.05/1.12	 U31(mark(X:S)) -> mark(U31(X:S))
1.05/1.12	 U31(ok(X:S)) -> ok(U31(X:S))
1.05/1.12	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.05/1.12	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.05/1.12	 U42(mark(X:S)) -> mark(U42(X:S))
1.05/1.12	 U42(ok(X:S)) -> ok(U42(X:S))
1.05/1.12	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.05/1.12	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.05/1.12	 U52(mark(X:S)) -> mark(U52(X:S))
1.05/1.12	 U52(ok(X:S)) -> ok(U52(X:S))
1.05/1.12	 U61(mark(X:S)) -> mark(U61(X:S))
1.05/1.12	 U61(ok(X:S)) -> ok(U61(X:S))
1.05/1.12	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.05/1.12	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.05/1.12	 U72(mark(X:S)) -> mark(U72(X:S))
1.05/1.12	 U72(ok(X:S)) -> ok(U72(X:S))
1.05/1.12	 U81(mark(X:S)) -> mark(U81(X:S))
1.05/1.12	 U81(ok(X:S)) -> ok(U81(X:S))
1.05/1.12	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.05/1.12	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.05/1.12	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.05/1.12	 active(U11(tt)) -> mark(tt)
1.05/1.12	 active(U11(X:S)) -> U11(active(X:S))
1.05/1.12	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.05/1.12	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.05/1.12	 active(U22(tt)) -> mark(tt)
1.05/1.12	 active(U22(X:S)) -> U22(active(X:S))
1.05/1.12	 active(U31(tt)) -> mark(tt)
1.05/1.12	 active(U31(X:S)) -> U31(active(X:S))
1.05/1.12	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.05/1.12	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.05/1.12	 active(U42(tt)) -> mark(tt)
1.05/1.12	 active(U42(X:S)) -> U42(active(X:S))
1.05/1.12	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.05/1.12	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.05/1.12	 active(U52(tt)) -> mark(tt)
1.05/1.12	 active(U52(X:S)) -> U52(active(X:S))
1.05/1.12	 active(U61(tt)) -> mark(tt)
1.05/1.12	 active(U61(X:S)) -> U61(active(X:S))
1.05/1.12	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.05/1.12	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.05/1.12	 active(U72(tt)) -> mark(tt)
1.05/1.12	 active(U72(X:S)) -> U72(active(X:S))
1.05/1.12	 active(U81(tt)) -> mark(tt)
1.05/1.12	 active(U81(X:S)) -> U81(active(X:S))
1.05/1.12	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.05/1.12	 active(__(nil,X:S)) -> mark(X:S)
1.05/1.12	 active(__(X:S,nil)) -> mark(X:S)
1.05/1.12	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.05/1.12	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.05/1.12	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.05/1.12	 active(isList(nil)) -> mark(tt)
1.05/1.12	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.05/1.12	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.05/1.12	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.05/1.12	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.05/1.12	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.05/1.12	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.05/1.12	 active(isPal(nil)) -> mark(tt)
1.05/1.12	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.05/1.12	 active(isQid(a)) -> mark(tt)
1.05/1.12	 active(isQid(e)) -> mark(tt)
1.05/1.12	 active(isQid(i)) -> mark(tt)
1.05/1.12	 active(isQid(o)) -> mark(tt)
1.05/1.12	 active(isQid(u)) -> mark(tt)
1.05/1.12	 isList(ok(X:S)) -> ok(isList(X:S))
1.05/1.12	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.05/1.12	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.05/1.12	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.05/1.12	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.05/1.12	 proper(U11(X:S)) -> U11(proper(X:S))
1.05/1.12	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U22(X:S)) -> U22(proper(X:S))
1.05/1.12	 proper(U31(X:S)) -> U31(proper(X:S))
1.05/1.12	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U42(X:S)) -> U42(proper(X:S))
1.05/1.12	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U52(X:S)) -> U52(proper(X:S))
1.05/1.12	 proper(U61(X:S)) -> U61(proper(X:S))
1.05/1.12	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U72(X:S)) -> U72(proper(X:S))
1.05/1.12	 proper(U81(X:S)) -> U81(proper(X:S))
1.05/1.12	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(isList(X:S)) -> isList(proper(X:S))
1.05/1.12	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.05/1.12	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.05/1.12	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.05/1.12	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.05/1.12	 proper(a) -> ok(a)
1.05/1.12	 proper(e) -> ok(e)
1.05/1.12	 proper(i) -> ok(i)
1.05/1.12	 proper(nil) -> ok(nil)
1.05/1.12	 proper(o) -> ok(o)
1.05/1.12	 proper(tt) -> ok(tt)
1.05/1.12	 proper(u) -> ok(u)
1.05/1.12	 top(mark(X:S)) -> top(proper(X:S))
1.05/1.12	 top(ok(X:S)) -> top(active(X:S))
1.05/1.12	->Strongly Connected Components:
1.05/1.12	 There is no strongly connected component
1.05/1.12	
1.05/1.12	The problem is finite.
1.05/1.12	
1.05/1.12	Problem 1.16: 
1.05/1.12	
1.05/1.12	Subterm Processor:
1.05/1.12	-> Pairs:
1.05/1.12	 U22#(mark(X:S)) -> U22#(X:S)
1.05/1.12	 U22#(ok(X:S)) -> U22#(X:S)
1.05/1.12	-> Rules:
1.05/1.12	 U11(mark(X:S)) -> mark(U11(X:S))
1.05/1.12	 U11(ok(X:S)) -> ok(U11(X:S))
1.05/1.12	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.05/1.12	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.05/1.12	 U22(mark(X:S)) -> mark(U22(X:S))
1.05/1.12	 U22(ok(X:S)) -> ok(U22(X:S))
1.05/1.12	 U31(mark(X:S)) -> mark(U31(X:S))
1.05/1.12	 U31(ok(X:S)) -> ok(U31(X:S))
1.05/1.12	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.05/1.12	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.05/1.12	 U42(mark(X:S)) -> mark(U42(X:S))
1.05/1.12	 U42(ok(X:S)) -> ok(U42(X:S))
1.05/1.12	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.05/1.12	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.05/1.12	 U52(mark(X:S)) -> mark(U52(X:S))
1.05/1.12	 U52(ok(X:S)) -> ok(U52(X:S))
1.05/1.12	 U61(mark(X:S)) -> mark(U61(X:S))
1.05/1.12	 U61(ok(X:S)) -> ok(U61(X:S))
1.05/1.12	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.05/1.12	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.05/1.12	 U72(mark(X:S)) -> mark(U72(X:S))
1.05/1.12	 U72(ok(X:S)) -> ok(U72(X:S))
1.05/1.12	 U81(mark(X:S)) -> mark(U81(X:S))
1.05/1.12	 U81(ok(X:S)) -> ok(U81(X:S))
1.05/1.12	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.05/1.12	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.05/1.12	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.05/1.12	 active(U11(tt)) -> mark(tt)
1.05/1.12	 active(U11(X:S)) -> U11(active(X:S))
1.05/1.12	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.05/1.12	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.05/1.12	 active(U22(tt)) -> mark(tt)
1.05/1.12	 active(U22(X:S)) -> U22(active(X:S))
1.05/1.12	 active(U31(tt)) -> mark(tt)
1.05/1.12	 active(U31(X:S)) -> U31(active(X:S))
1.05/1.12	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.05/1.12	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.05/1.12	 active(U42(tt)) -> mark(tt)
1.05/1.12	 active(U42(X:S)) -> U42(active(X:S))
1.05/1.12	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.05/1.12	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.05/1.12	 active(U52(tt)) -> mark(tt)
1.05/1.12	 active(U52(X:S)) -> U52(active(X:S))
1.05/1.12	 active(U61(tt)) -> mark(tt)
1.05/1.12	 active(U61(X:S)) -> U61(active(X:S))
1.05/1.12	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.05/1.12	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.05/1.12	 active(U72(tt)) -> mark(tt)
1.05/1.12	 active(U72(X:S)) -> U72(active(X:S))
1.05/1.12	 active(U81(tt)) -> mark(tt)
1.05/1.12	 active(U81(X:S)) -> U81(active(X:S))
1.05/1.12	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.05/1.12	 active(__(nil,X:S)) -> mark(X:S)
1.05/1.12	 active(__(X:S,nil)) -> mark(X:S)
1.05/1.12	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.05/1.12	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.05/1.12	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.05/1.12	 active(isList(nil)) -> mark(tt)
1.05/1.12	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.05/1.12	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.05/1.12	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.05/1.12	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.05/1.12	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.05/1.12	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.05/1.12	 active(isPal(nil)) -> mark(tt)
1.05/1.12	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.05/1.12	 active(isQid(a)) -> mark(tt)
1.05/1.12	 active(isQid(e)) -> mark(tt)
1.05/1.12	 active(isQid(i)) -> mark(tt)
1.05/1.12	 active(isQid(o)) -> mark(tt)
1.05/1.12	 active(isQid(u)) -> mark(tt)
1.05/1.12	 isList(ok(X:S)) -> ok(isList(X:S))
1.05/1.12	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.05/1.12	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.05/1.12	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.05/1.12	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.05/1.12	 proper(U11(X:S)) -> U11(proper(X:S))
1.05/1.12	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U22(X:S)) -> U22(proper(X:S))
1.05/1.12	 proper(U31(X:S)) -> U31(proper(X:S))
1.05/1.12	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U42(X:S)) -> U42(proper(X:S))
1.05/1.12	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U52(X:S)) -> U52(proper(X:S))
1.05/1.12	 proper(U61(X:S)) -> U61(proper(X:S))
1.05/1.12	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U72(X:S)) -> U72(proper(X:S))
1.05/1.12	 proper(U81(X:S)) -> U81(proper(X:S))
1.05/1.12	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(isList(X:S)) -> isList(proper(X:S))
1.05/1.12	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.05/1.12	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.05/1.12	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.05/1.12	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.05/1.12	 proper(a) -> ok(a)
1.05/1.12	 proper(e) -> ok(e)
1.05/1.12	 proper(i) -> ok(i)
1.05/1.12	 proper(nil) -> ok(nil)
1.05/1.12	 proper(o) -> ok(o)
1.05/1.12	 proper(tt) -> ok(tt)
1.05/1.12	 proper(u) -> ok(u)
1.05/1.12	 top(mark(X:S)) -> top(proper(X:S))
1.05/1.12	 top(ok(X:S)) -> top(active(X:S))
1.05/1.12	->Projection:
1.05/1.12	 pi(U22#) = 1
1.05/1.12	
1.05/1.12	Problem 1.16: 
1.05/1.12	
1.05/1.12	SCC Processor:
1.05/1.12	-> Pairs:
1.05/1.12	 Empty
1.05/1.12	-> Rules:
1.05/1.12	 U11(mark(X:S)) -> mark(U11(X:S))
1.05/1.12	 U11(ok(X:S)) -> ok(U11(X:S))
1.05/1.12	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.05/1.12	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.05/1.12	 U22(mark(X:S)) -> mark(U22(X:S))
1.05/1.12	 U22(ok(X:S)) -> ok(U22(X:S))
1.05/1.12	 U31(mark(X:S)) -> mark(U31(X:S))
1.05/1.12	 U31(ok(X:S)) -> ok(U31(X:S))
1.05/1.12	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.05/1.12	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.05/1.12	 U42(mark(X:S)) -> mark(U42(X:S))
1.05/1.12	 U42(ok(X:S)) -> ok(U42(X:S))
1.05/1.12	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.05/1.12	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.05/1.12	 U52(mark(X:S)) -> mark(U52(X:S))
1.05/1.12	 U52(ok(X:S)) -> ok(U52(X:S))
1.05/1.12	 U61(mark(X:S)) -> mark(U61(X:S))
1.05/1.12	 U61(ok(X:S)) -> ok(U61(X:S))
1.05/1.12	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.05/1.12	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.05/1.12	 U72(mark(X:S)) -> mark(U72(X:S))
1.05/1.12	 U72(ok(X:S)) -> ok(U72(X:S))
1.05/1.12	 U81(mark(X:S)) -> mark(U81(X:S))
1.05/1.12	 U81(ok(X:S)) -> ok(U81(X:S))
1.05/1.12	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.05/1.12	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.05/1.12	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.05/1.12	 active(U11(tt)) -> mark(tt)
1.05/1.12	 active(U11(X:S)) -> U11(active(X:S))
1.05/1.12	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.05/1.12	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.05/1.12	 active(U22(tt)) -> mark(tt)
1.05/1.12	 active(U22(X:S)) -> U22(active(X:S))
1.05/1.12	 active(U31(tt)) -> mark(tt)
1.05/1.12	 active(U31(X:S)) -> U31(active(X:S))
1.05/1.12	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.05/1.12	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.05/1.12	 active(U42(tt)) -> mark(tt)
1.05/1.12	 active(U42(X:S)) -> U42(active(X:S))
1.05/1.12	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.05/1.12	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.05/1.12	 active(U52(tt)) -> mark(tt)
1.05/1.12	 active(U52(X:S)) -> U52(active(X:S))
1.05/1.12	 active(U61(tt)) -> mark(tt)
1.05/1.12	 active(U61(X:S)) -> U61(active(X:S))
1.05/1.12	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.05/1.12	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.05/1.12	 active(U72(tt)) -> mark(tt)
1.05/1.12	 active(U72(X:S)) -> U72(active(X:S))
1.05/1.12	 active(U81(tt)) -> mark(tt)
1.05/1.12	 active(U81(X:S)) -> U81(active(X:S))
1.05/1.12	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.05/1.12	 active(__(nil,X:S)) -> mark(X:S)
1.05/1.12	 active(__(X:S,nil)) -> mark(X:S)
1.05/1.12	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.05/1.12	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.05/1.12	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.05/1.12	 active(isList(nil)) -> mark(tt)
1.05/1.12	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.05/1.12	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.05/1.12	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.05/1.12	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.05/1.12	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.05/1.12	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.05/1.12	 active(isPal(nil)) -> mark(tt)
1.05/1.12	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.05/1.12	 active(isQid(a)) -> mark(tt)
1.05/1.12	 active(isQid(e)) -> mark(tt)
1.05/1.12	 active(isQid(i)) -> mark(tt)
1.05/1.12	 active(isQid(o)) -> mark(tt)
1.05/1.12	 active(isQid(u)) -> mark(tt)
1.05/1.12	 isList(ok(X:S)) -> ok(isList(X:S))
1.05/1.12	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.05/1.12	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.05/1.12	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.05/1.12	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.05/1.12	 proper(U11(X:S)) -> U11(proper(X:S))
1.05/1.12	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U22(X:S)) -> U22(proper(X:S))
1.05/1.12	 proper(U31(X:S)) -> U31(proper(X:S))
1.05/1.12	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U42(X:S)) -> U42(proper(X:S))
1.05/1.12	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U52(X:S)) -> U52(proper(X:S))
1.05/1.12	 proper(U61(X:S)) -> U61(proper(X:S))
1.05/1.12	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U72(X:S)) -> U72(proper(X:S))
1.05/1.12	 proper(U81(X:S)) -> U81(proper(X:S))
1.05/1.12	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(isList(X:S)) -> isList(proper(X:S))
1.05/1.12	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.05/1.12	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.05/1.12	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.05/1.12	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.05/1.12	 proper(a) -> ok(a)
1.05/1.12	 proper(e) -> ok(e)
1.05/1.12	 proper(i) -> ok(i)
1.05/1.12	 proper(nil) -> ok(nil)
1.05/1.12	 proper(o) -> ok(o)
1.05/1.12	 proper(tt) -> ok(tt)
1.05/1.12	 proper(u) -> ok(u)
1.05/1.12	 top(mark(X:S)) -> top(proper(X:S))
1.05/1.12	 top(ok(X:S)) -> top(active(X:S))
1.05/1.12	->Strongly Connected Components:
1.05/1.12	 There is no strongly connected component
1.05/1.12	
1.05/1.12	The problem is finite.
1.05/1.12	
1.05/1.12	Problem 1.17: 
1.05/1.12	
1.05/1.12	Subterm Processor:
1.05/1.12	-> Pairs:
1.05/1.12	 U21#(mark(X1:S),X2:S) -> U21#(X1:S,X2:S)
1.05/1.12	 U21#(ok(X1:S),ok(X2:S)) -> U21#(X1:S,X2:S)
1.05/1.12	-> Rules:
1.05/1.12	 U11(mark(X:S)) -> mark(U11(X:S))
1.05/1.12	 U11(ok(X:S)) -> ok(U11(X:S))
1.05/1.12	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.05/1.12	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.05/1.12	 U22(mark(X:S)) -> mark(U22(X:S))
1.05/1.12	 U22(ok(X:S)) -> ok(U22(X:S))
1.05/1.12	 U31(mark(X:S)) -> mark(U31(X:S))
1.05/1.12	 U31(ok(X:S)) -> ok(U31(X:S))
1.05/1.12	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.05/1.12	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.05/1.12	 U42(mark(X:S)) -> mark(U42(X:S))
1.05/1.12	 U42(ok(X:S)) -> ok(U42(X:S))
1.05/1.12	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.05/1.12	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.05/1.12	 U52(mark(X:S)) -> mark(U52(X:S))
1.05/1.12	 U52(ok(X:S)) -> ok(U52(X:S))
1.05/1.12	 U61(mark(X:S)) -> mark(U61(X:S))
1.05/1.12	 U61(ok(X:S)) -> ok(U61(X:S))
1.05/1.12	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.05/1.12	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.05/1.12	 U72(mark(X:S)) -> mark(U72(X:S))
1.05/1.12	 U72(ok(X:S)) -> ok(U72(X:S))
1.05/1.12	 U81(mark(X:S)) -> mark(U81(X:S))
1.05/1.12	 U81(ok(X:S)) -> ok(U81(X:S))
1.05/1.12	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.05/1.12	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.05/1.12	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.05/1.12	 active(U11(tt)) -> mark(tt)
1.05/1.12	 active(U11(X:S)) -> U11(active(X:S))
1.05/1.12	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.05/1.12	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.05/1.12	 active(U22(tt)) -> mark(tt)
1.05/1.12	 active(U22(X:S)) -> U22(active(X:S))
1.05/1.12	 active(U31(tt)) -> mark(tt)
1.05/1.12	 active(U31(X:S)) -> U31(active(X:S))
1.05/1.12	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.05/1.12	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.05/1.12	 active(U42(tt)) -> mark(tt)
1.05/1.12	 active(U42(X:S)) -> U42(active(X:S))
1.05/1.12	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.05/1.12	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.05/1.12	 active(U52(tt)) -> mark(tt)
1.05/1.12	 active(U52(X:S)) -> U52(active(X:S))
1.05/1.12	 active(U61(tt)) -> mark(tt)
1.05/1.12	 active(U61(X:S)) -> U61(active(X:S))
1.05/1.12	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.05/1.12	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.05/1.12	 active(U72(tt)) -> mark(tt)
1.05/1.12	 active(U72(X:S)) -> U72(active(X:S))
1.05/1.12	 active(U81(tt)) -> mark(tt)
1.05/1.12	 active(U81(X:S)) -> U81(active(X:S))
1.05/1.12	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.05/1.12	 active(__(nil,X:S)) -> mark(X:S)
1.05/1.12	 active(__(X:S,nil)) -> mark(X:S)
1.05/1.12	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.05/1.12	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.05/1.12	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.05/1.12	 active(isList(nil)) -> mark(tt)
1.05/1.12	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.05/1.12	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.05/1.12	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.05/1.12	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.05/1.12	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.05/1.12	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.05/1.12	 active(isPal(nil)) -> mark(tt)
1.05/1.12	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.05/1.12	 active(isQid(a)) -> mark(tt)
1.05/1.12	 active(isQid(e)) -> mark(tt)
1.05/1.12	 active(isQid(i)) -> mark(tt)
1.05/1.12	 active(isQid(o)) -> mark(tt)
1.05/1.12	 active(isQid(u)) -> mark(tt)
1.05/1.12	 isList(ok(X:S)) -> ok(isList(X:S))
1.05/1.12	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.05/1.12	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.05/1.12	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.05/1.12	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.05/1.12	 proper(U11(X:S)) -> U11(proper(X:S))
1.05/1.12	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U22(X:S)) -> U22(proper(X:S))
1.05/1.12	 proper(U31(X:S)) -> U31(proper(X:S))
1.05/1.12	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U42(X:S)) -> U42(proper(X:S))
1.05/1.12	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U52(X:S)) -> U52(proper(X:S))
1.05/1.12	 proper(U61(X:S)) -> U61(proper(X:S))
1.05/1.12	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U72(X:S)) -> U72(proper(X:S))
1.05/1.12	 proper(U81(X:S)) -> U81(proper(X:S))
1.05/1.12	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(isList(X:S)) -> isList(proper(X:S))
1.05/1.12	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.05/1.12	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.05/1.12	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.05/1.12	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.05/1.12	 proper(a) -> ok(a)
1.05/1.12	 proper(e) -> ok(e)
1.05/1.12	 proper(i) -> ok(i)
1.05/1.12	 proper(nil) -> ok(nil)
1.05/1.12	 proper(o) -> ok(o)
1.05/1.12	 proper(tt) -> ok(tt)
1.05/1.12	 proper(u) -> ok(u)
1.05/1.12	 top(mark(X:S)) -> top(proper(X:S))
1.05/1.12	 top(ok(X:S)) -> top(active(X:S))
1.05/1.12	->Projection:
1.05/1.12	 pi(U21#) = 1
1.05/1.12	
1.05/1.12	Problem 1.17: 
1.05/1.12	
1.05/1.12	SCC Processor:
1.05/1.12	-> Pairs:
1.05/1.12	 Empty
1.05/1.12	-> Rules:
1.05/1.12	 U11(mark(X:S)) -> mark(U11(X:S))
1.05/1.12	 U11(ok(X:S)) -> ok(U11(X:S))
1.05/1.12	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.05/1.12	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.05/1.12	 U22(mark(X:S)) -> mark(U22(X:S))
1.05/1.12	 U22(ok(X:S)) -> ok(U22(X:S))
1.05/1.12	 U31(mark(X:S)) -> mark(U31(X:S))
1.05/1.12	 U31(ok(X:S)) -> ok(U31(X:S))
1.05/1.12	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.05/1.12	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.05/1.12	 U42(mark(X:S)) -> mark(U42(X:S))
1.05/1.12	 U42(ok(X:S)) -> ok(U42(X:S))
1.05/1.12	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.05/1.12	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.05/1.12	 U52(mark(X:S)) -> mark(U52(X:S))
1.05/1.12	 U52(ok(X:S)) -> ok(U52(X:S))
1.05/1.12	 U61(mark(X:S)) -> mark(U61(X:S))
1.05/1.12	 U61(ok(X:S)) -> ok(U61(X:S))
1.05/1.12	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.05/1.12	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.05/1.12	 U72(mark(X:S)) -> mark(U72(X:S))
1.05/1.12	 U72(ok(X:S)) -> ok(U72(X:S))
1.05/1.12	 U81(mark(X:S)) -> mark(U81(X:S))
1.05/1.12	 U81(ok(X:S)) -> ok(U81(X:S))
1.05/1.12	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.05/1.12	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.05/1.12	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.05/1.12	 active(U11(tt)) -> mark(tt)
1.05/1.12	 active(U11(X:S)) -> U11(active(X:S))
1.05/1.12	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.05/1.12	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.05/1.12	 active(U22(tt)) -> mark(tt)
1.05/1.12	 active(U22(X:S)) -> U22(active(X:S))
1.05/1.12	 active(U31(tt)) -> mark(tt)
1.05/1.12	 active(U31(X:S)) -> U31(active(X:S))
1.05/1.12	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.05/1.12	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.05/1.12	 active(U42(tt)) -> mark(tt)
1.05/1.12	 active(U42(X:S)) -> U42(active(X:S))
1.05/1.12	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.05/1.12	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.05/1.12	 active(U52(tt)) -> mark(tt)
1.05/1.12	 active(U52(X:S)) -> U52(active(X:S))
1.05/1.12	 active(U61(tt)) -> mark(tt)
1.05/1.12	 active(U61(X:S)) -> U61(active(X:S))
1.05/1.12	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.05/1.12	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.05/1.12	 active(U72(tt)) -> mark(tt)
1.05/1.12	 active(U72(X:S)) -> U72(active(X:S))
1.05/1.12	 active(U81(tt)) -> mark(tt)
1.05/1.12	 active(U81(X:S)) -> U81(active(X:S))
1.05/1.12	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.05/1.12	 active(__(nil,X:S)) -> mark(X:S)
1.05/1.12	 active(__(X:S,nil)) -> mark(X:S)
1.05/1.12	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.05/1.12	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.05/1.12	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.05/1.12	 active(isList(nil)) -> mark(tt)
1.05/1.12	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.05/1.12	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.05/1.12	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.05/1.12	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.05/1.12	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.05/1.12	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.05/1.12	 active(isPal(nil)) -> mark(tt)
1.05/1.12	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.05/1.12	 active(isQid(a)) -> mark(tt)
1.05/1.12	 active(isQid(e)) -> mark(tt)
1.05/1.12	 active(isQid(i)) -> mark(tt)
1.05/1.12	 active(isQid(o)) -> mark(tt)
1.05/1.12	 active(isQid(u)) -> mark(tt)
1.05/1.12	 isList(ok(X:S)) -> ok(isList(X:S))
1.05/1.12	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.05/1.12	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.05/1.12	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.05/1.12	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.05/1.12	 proper(U11(X:S)) -> U11(proper(X:S))
1.05/1.12	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U22(X:S)) -> U22(proper(X:S))
1.05/1.12	 proper(U31(X:S)) -> U31(proper(X:S))
1.05/1.12	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U42(X:S)) -> U42(proper(X:S))
1.05/1.12	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U52(X:S)) -> U52(proper(X:S))
1.05/1.12	 proper(U61(X:S)) -> U61(proper(X:S))
1.05/1.12	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U72(X:S)) -> U72(proper(X:S))
1.05/1.12	 proper(U81(X:S)) -> U81(proper(X:S))
1.05/1.12	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(isList(X:S)) -> isList(proper(X:S))
1.05/1.12	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.05/1.12	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.05/1.12	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.05/1.12	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.05/1.12	 proper(a) -> ok(a)
1.05/1.12	 proper(e) -> ok(e)
1.05/1.12	 proper(i) -> ok(i)
1.05/1.12	 proper(nil) -> ok(nil)
1.05/1.12	 proper(o) -> ok(o)
1.05/1.12	 proper(tt) -> ok(tt)
1.05/1.12	 proper(u) -> ok(u)
1.05/1.12	 top(mark(X:S)) -> top(proper(X:S))
1.05/1.12	 top(ok(X:S)) -> top(active(X:S))
1.05/1.12	->Strongly Connected Components:
1.05/1.12	 There is no strongly connected component
1.05/1.12	
1.05/1.12	The problem is finite.
1.05/1.12	
1.05/1.12	Problem 1.18: 
1.05/1.12	
1.05/1.12	Subterm Processor:
1.05/1.12	-> Pairs:
1.05/1.12	 U11#(mark(X:S)) -> U11#(X:S)
1.05/1.12	 U11#(ok(X:S)) -> U11#(X:S)
1.05/1.12	-> Rules:
1.05/1.12	 U11(mark(X:S)) -> mark(U11(X:S))
1.05/1.12	 U11(ok(X:S)) -> ok(U11(X:S))
1.05/1.12	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.05/1.12	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.05/1.12	 U22(mark(X:S)) -> mark(U22(X:S))
1.05/1.12	 U22(ok(X:S)) -> ok(U22(X:S))
1.05/1.12	 U31(mark(X:S)) -> mark(U31(X:S))
1.05/1.12	 U31(ok(X:S)) -> ok(U31(X:S))
1.05/1.12	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.05/1.12	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.05/1.12	 U42(mark(X:S)) -> mark(U42(X:S))
1.05/1.12	 U42(ok(X:S)) -> ok(U42(X:S))
1.05/1.12	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.05/1.12	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.05/1.12	 U52(mark(X:S)) -> mark(U52(X:S))
1.05/1.12	 U52(ok(X:S)) -> ok(U52(X:S))
1.05/1.12	 U61(mark(X:S)) -> mark(U61(X:S))
1.05/1.12	 U61(ok(X:S)) -> ok(U61(X:S))
1.05/1.12	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.05/1.12	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.05/1.12	 U72(mark(X:S)) -> mark(U72(X:S))
1.05/1.12	 U72(ok(X:S)) -> ok(U72(X:S))
1.05/1.12	 U81(mark(X:S)) -> mark(U81(X:S))
1.05/1.12	 U81(ok(X:S)) -> ok(U81(X:S))
1.05/1.12	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.05/1.12	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.05/1.12	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.05/1.12	 active(U11(tt)) -> mark(tt)
1.05/1.12	 active(U11(X:S)) -> U11(active(X:S))
1.05/1.12	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.05/1.12	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.05/1.12	 active(U22(tt)) -> mark(tt)
1.05/1.12	 active(U22(X:S)) -> U22(active(X:S))
1.05/1.12	 active(U31(tt)) -> mark(tt)
1.05/1.12	 active(U31(X:S)) -> U31(active(X:S))
1.05/1.12	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.05/1.12	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.05/1.12	 active(U42(tt)) -> mark(tt)
1.05/1.12	 active(U42(X:S)) -> U42(active(X:S))
1.05/1.12	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.05/1.12	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.05/1.12	 active(U52(tt)) -> mark(tt)
1.05/1.12	 active(U52(X:S)) -> U52(active(X:S))
1.05/1.12	 active(U61(tt)) -> mark(tt)
1.05/1.12	 active(U61(X:S)) -> U61(active(X:S))
1.05/1.12	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.05/1.12	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.05/1.12	 active(U72(tt)) -> mark(tt)
1.05/1.12	 active(U72(X:S)) -> U72(active(X:S))
1.05/1.12	 active(U81(tt)) -> mark(tt)
1.05/1.12	 active(U81(X:S)) -> U81(active(X:S))
1.05/1.12	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.05/1.12	 active(__(nil,X:S)) -> mark(X:S)
1.05/1.12	 active(__(X:S,nil)) -> mark(X:S)
1.05/1.12	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.05/1.12	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.05/1.12	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.05/1.12	 active(isList(nil)) -> mark(tt)
1.05/1.12	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.05/1.12	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.05/1.12	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.05/1.12	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.05/1.12	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.05/1.12	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.05/1.12	 active(isPal(nil)) -> mark(tt)
1.05/1.12	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.05/1.12	 active(isQid(a)) -> mark(tt)
1.05/1.12	 active(isQid(e)) -> mark(tt)
1.05/1.12	 active(isQid(i)) -> mark(tt)
1.05/1.12	 active(isQid(o)) -> mark(tt)
1.05/1.12	 active(isQid(u)) -> mark(tt)
1.05/1.12	 isList(ok(X:S)) -> ok(isList(X:S))
1.05/1.12	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.05/1.12	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.05/1.12	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.05/1.12	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.05/1.12	 proper(U11(X:S)) -> U11(proper(X:S))
1.05/1.12	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U22(X:S)) -> U22(proper(X:S))
1.05/1.12	 proper(U31(X:S)) -> U31(proper(X:S))
1.05/1.12	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U42(X:S)) -> U42(proper(X:S))
1.05/1.12	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U52(X:S)) -> U52(proper(X:S))
1.05/1.12	 proper(U61(X:S)) -> U61(proper(X:S))
1.05/1.12	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U72(X:S)) -> U72(proper(X:S))
1.05/1.12	 proper(U81(X:S)) -> U81(proper(X:S))
1.05/1.12	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(isList(X:S)) -> isList(proper(X:S))
1.05/1.12	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.05/1.12	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.05/1.12	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.05/1.12	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.05/1.12	 proper(a) -> ok(a)
1.05/1.12	 proper(e) -> ok(e)
1.05/1.12	 proper(i) -> ok(i)
1.05/1.12	 proper(nil) -> ok(nil)
1.05/1.12	 proper(o) -> ok(o)
1.05/1.12	 proper(tt) -> ok(tt)
1.05/1.12	 proper(u) -> ok(u)
1.05/1.12	 top(mark(X:S)) -> top(proper(X:S))
1.05/1.12	 top(ok(X:S)) -> top(active(X:S))
1.05/1.12	->Projection:
1.05/1.12	 pi(U11#) = 1
1.05/1.12	
1.05/1.12	Problem 1.18: 
1.05/1.12	
1.05/1.12	SCC Processor:
1.05/1.12	-> Pairs:
1.05/1.12	 Empty
1.05/1.12	-> Rules:
1.05/1.12	 U11(mark(X:S)) -> mark(U11(X:S))
1.05/1.12	 U11(ok(X:S)) -> ok(U11(X:S))
1.05/1.12	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.05/1.12	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.05/1.12	 U22(mark(X:S)) -> mark(U22(X:S))
1.05/1.12	 U22(ok(X:S)) -> ok(U22(X:S))
1.05/1.12	 U31(mark(X:S)) -> mark(U31(X:S))
1.05/1.12	 U31(ok(X:S)) -> ok(U31(X:S))
1.05/1.12	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.05/1.12	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.05/1.12	 U42(mark(X:S)) -> mark(U42(X:S))
1.05/1.12	 U42(ok(X:S)) -> ok(U42(X:S))
1.05/1.12	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.05/1.12	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.05/1.12	 U52(mark(X:S)) -> mark(U52(X:S))
1.05/1.12	 U52(ok(X:S)) -> ok(U52(X:S))
1.05/1.12	 U61(mark(X:S)) -> mark(U61(X:S))
1.05/1.12	 U61(ok(X:S)) -> ok(U61(X:S))
1.05/1.12	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.05/1.12	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.05/1.12	 U72(mark(X:S)) -> mark(U72(X:S))
1.05/1.12	 U72(ok(X:S)) -> ok(U72(X:S))
1.05/1.12	 U81(mark(X:S)) -> mark(U81(X:S))
1.05/1.12	 U81(ok(X:S)) -> ok(U81(X:S))
1.05/1.12	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.05/1.12	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.05/1.12	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.05/1.12	 active(U11(tt)) -> mark(tt)
1.05/1.12	 active(U11(X:S)) -> U11(active(X:S))
1.05/1.12	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.05/1.12	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.05/1.12	 active(U22(tt)) -> mark(tt)
1.05/1.12	 active(U22(X:S)) -> U22(active(X:S))
1.05/1.12	 active(U31(tt)) -> mark(tt)
1.05/1.12	 active(U31(X:S)) -> U31(active(X:S))
1.05/1.12	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.05/1.12	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.05/1.12	 active(U42(tt)) -> mark(tt)
1.05/1.12	 active(U42(X:S)) -> U42(active(X:S))
1.05/1.12	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.05/1.12	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.05/1.12	 active(U52(tt)) -> mark(tt)
1.05/1.12	 active(U52(X:S)) -> U52(active(X:S))
1.05/1.12	 active(U61(tt)) -> mark(tt)
1.05/1.12	 active(U61(X:S)) -> U61(active(X:S))
1.05/1.12	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.05/1.12	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.05/1.12	 active(U72(tt)) -> mark(tt)
1.05/1.12	 active(U72(X:S)) -> U72(active(X:S))
1.05/1.12	 active(U81(tt)) -> mark(tt)
1.05/1.12	 active(U81(X:S)) -> U81(active(X:S))
1.05/1.12	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.05/1.12	 active(__(nil,X:S)) -> mark(X:S)
1.05/1.12	 active(__(X:S,nil)) -> mark(X:S)
1.05/1.12	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.05/1.12	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.05/1.12	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.05/1.12	 active(isList(nil)) -> mark(tt)
1.05/1.12	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.05/1.12	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.05/1.12	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.05/1.12	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.05/1.12	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.05/1.12	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.05/1.12	 active(isPal(nil)) -> mark(tt)
1.05/1.12	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.05/1.12	 active(isQid(a)) -> mark(tt)
1.05/1.12	 active(isQid(e)) -> mark(tt)
1.05/1.12	 active(isQid(i)) -> mark(tt)
1.05/1.12	 active(isQid(o)) -> mark(tt)
1.05/1.12	 active(isQid(u)) -> mark(tt)
1.05/1.12	 isList(ok(X:S)) -> ok(isList(X:S))
1.05/1.12	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.05/1.12	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.05/1.12	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.05/1.12	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.05/1.12	 proper(U11(X:S)) -> U11(proper(X:S))
1.05/1.12	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U22(X:S)) -> U22(proper(X:S))
1.05/1.12	 proper(U31(X:S)) -> U31(proper(X:S))
1.05/1.12	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U42(X:S)) -> U42(proper(X:S))
1.05/1.12	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U52(X:S)) -> U52(proper(X:S))
1.05/1.12	 proper(U61(X:S)) -> U61(proper(X:S))
1.05/1.12	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(U72(X:S)) -> U72(proper(X:S))
1.05/1.12	 proper(U81(X:S)) -> U81(proper(X:S))
1.05/1.12	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.05/1.12	 proper(isList(X:S)) -> isList(proper(X:S))
1.05/1.12	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.05/1.12	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.05/1.12	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.05/1.12	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.05/1.12	 proper(a) -> ok(a)
1.05/1.12	 proper(e) -> ok(e)
1.05/1.12	 proper(i) -> ok(i)
1.05/1.12	 proper(nil) -> ok(nil)
1.05/1.12	 proper(o) -> ok(o)
1.05/1.12	 proper(tt) -> ok(tt)
1.05/1.12	 proper(u) -> ok(u)
1.05/1.12	 top(mark(X:S)) -> top(proper(X:S))
1.05/1.12	 top(ok(X:S)) -> top(active(X:S))
1.05/1.12	->Strongly Connected Components:
1.05/1.12	 There is no strongly connected component
1.05/1.12	
1.05/1.12	The problem is finite.
1.05/1.12	
1.05/1.12	Problem 1.19: 
1.05/1.12	
1.05/1.12	Subterm Processor:
1.05/1.12	-> Pairs:
1.05/1.12	 ACTIVE(U11(X:S)) -> ACTIVE(X:S)
1.05/1.12	 ACTIVE(U21(X1:S,X2:S)) -> ACTIVE(X1:S)
1.05/1.12	 ACTIVE(U22(X:S)) -> ACTIVE(X:S)
1.05/1.12	 ACTIVE(U31(X:S)) -> ACTIVE(X:S)
1.05/1.12	 ACTIVE(U41(X1:S,X2:S)) -> ACTIVE(X1:S)
1.05/1.12	 ACTIVE(U42(X:S)) -> ACTIVE(X:S)
1.05/1.12	 ACTIVE(U51(X1:S,X2:S)) -> ACTIVE(X1:S)
1.05/1.12	 ACTIVE(U52(X:S)) -> ACTIVE(X:S)
1.05/1.12	 ACTIVE(U61(X:S)) -> ACTIVE(X:S)
1.05/1.12	 ACTIVE(U71(X1:S,X2:S)) -> ACTIVE(X1:S)
1.05/1.12	 ACTIVE(U72(X:S)) -> ACTIVE(X:S)
1.05/1.12	 ACTIVE(U81(X:S)) -> ACTIVE(X:S)
1.05/1.12	 ACTIVE(__(X1:S,X2:S)) -> ACTIVE(X1:S)
1.05/1.12	 ACTIVE(__(X1:S,X2:S)) -> ACTIVE(X2:S)
1.05/1.12	-> Rules:
1.05/1.12	 U11(mark(X:S)) -> mark(U11(X:S))
1.05/1.12	 U11(ok(X:S)) -> ok(U11(X:S))
1.05/1.12	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.05/1.12	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.05/1.12	 U22(mark(X:S)) -> mark(U22(X:S))
1.05/1.12	 U22(ok(X:S)) -> ok(U22(X:S))
1.05/1.12	 U31(mark(X:S)) -> mark(U31(X:S))
1.05/1.12	 U31(ok(X:S)) -> ok(U31(X:S))
1.05/1.12	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.05/1.12	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.05/1.12	 U42(mark(X:S)) -> mark(U42(X:S))
1.05/1.13	 U42(ok(X:S)) -> ok(U42(X:S))
1.05/1.13	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.05/1.13	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.05/1.13	 U52(mark(X:S)) -> mark(U52(X:S))
1.05/1.13	 U52(ok(X:S)) -> ok(U52(X:S))
1.05/1.13	 U61(mark(X:S)) -> mark(U61(X:S))
1.05/1.13	 U61(ok(X:S)) -> ok(U61(X:S))
1.05/1.13	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.05/1.13	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.05/1.13	 U72(mark(X:S)) -> mark(U72(X:S))
1.05/1.13	 U72(ok(X:S)) -> ok(U72(X:S))
1.05/1.13	 U81(mark(X:S)) -> mark(U81(X:S))
1.05/1.13	 U81(ok(X:S)) -> ok(U81(X:S))
1.05/1.13	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.05/1.13	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.05/1.13	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.05/1.13	 active(U11(tt)) -> mark(tt)
1.05/1.13	 active(U11(X:S)) -> U11(active(X:S))
1.05/1.13	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.05/1.13	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.05/1.13	 active(U22(tt)) -> mark(tt)
1.05/1.13	 active(U22(X:S)) -> U22(active(X:S))
1.05/1.13	 active(U31(tt)) -> mark(tt)
1.05/1.13	 active(U31(X:S)) -> U31(active(X:S))
1.05/1.13	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.05/1.13	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.05/1.13	 active(U42(tt)) -> mark(tt)
1.05/1.13	 active(U42(X:S)) -> U42(active(X:S))
1.05/1.13	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.05/1.13	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.05/1.13	 active(U52(tt)) -> mark(tt)
1.05/1.13	 active(U52(X:S)) -> U52(active(X:S))
1.05/1.13	 active(U61(tt)) -> mark(tt)
1.05/1.13	 active(U61(X:S)) -> U61(active(X:S))
1.05/1.13	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.05/1.13	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.05/1.13	 active(U72(tt)) -> mark(tt)
1.05/1.13	 active(U72(X:S)) -> U72(active(X:S))
1.05/1.13	 active(U81(tt)) -> mark(tt)
1.05/1.13	 active(U81(X:S)) -> U81(active(X:S))
1.05/1.13	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.05/1.13	 active(__(nil,X:S)) -> mark(X:S)
1.05/1.13	 active(__(X:S,nil)) -> mark(X:S)
1.05/1.13	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.05/1.13	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.05/1.13	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.05/1.13	 active(isList(nil)) -> mark(tt)
1.05/1.13	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.05/1.13	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.05/1.13	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.05/1.13	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.05/1.13	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.05/1.13	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.05/1.13	 active(isPal(nil)) -> mark(tt)
1.05/1.13	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.05/1.13	 active(isQid(a)) -> mark(tt)
1.05/1.13	 active(isQid(e)) -> mark(tt)
1.05/1.13	 active(isQid(i)) -> mark(tt)
1.05/1.13	 active(isQid(o)) -> mark(tt)
1.05/1.13	 active(isQid(u)) -> mark(tt)
1.05/1.13	 isList(ok(X:S)) -> ok(isList(X:S))
1.05/1.13	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.05/1.13	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.05/1.13	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.05/1.13	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.05/1.13	 proper(U11(X:S)) -> U11(proper(X:S))
1.05/1.13	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.05/1.13	 proper(U22(X:S)) -> U22(proper(X:S))
1.05/1.13	 proper(U31(X:S)) -> U31(proper(X:S))
1.05/1.13	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.05/1.13	 proper(U42(X:S)) -> U42(proper(X:S))
1.05/1.13	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.05/1.13	 proper(U52(X:S)) -> U52(proper(X:S))
1.05/1.13	 proper(U61(X:S)) -> U61(proper(X:S))
1.05/1.13	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.05/1.13	 proper(U72(X:S)) -> U72(proper(X:S))
1.05/1.13	 proper(U81(X:S)) -> U81(proper(X:S))
1.05/1.13	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.05/1.13	 proper(isList(X:S)) -> isList(proper(X:S))
1.05/1.13	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.05/1.13	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.05/1.13	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.05/1.13	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.05/1.13	 proper(a) -> ok(a)
1.05/1.13	 proper(e) -> ok(e)
1.05/1.13	 proper(i) -> ok(i)
1.05/1.13	 proper(nil) -> ok(nil)
1.05/1.13	 proper(o) -> ok(o)
1.05/1.13	 proper(tt) -> ok(tt)
1.05/1.13	 proper(u) -> ok(u)
1.05/1.13	 top(mark(X:S)) -> top(proper(X:S))
1.05/1.13	 top(ok(X:S)) -> top(active(X:S))
1.05/1.13	->Projection:
1.05/1.13	 pi(ACTIVE) = 1
1.05/1.13	
1.05/1.13	Problem 1.19: 
1.05/1.13	
1.05/1.13	SCC Processor:
1.05/1.13	-> Pairs:
1.05/1.13	 Empty
1.05/1.13	-> Rules:
1.05/1.13	 U11(mark(X:S)) -> mark(U11(X:S))
1.05/1.13	 U11(ok(X:S)) -> ok(U11(X:S))
1.05/1.13	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.05/1.13	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.05/1.13	 U22(mark(X:S)) -> mark(U22(X:S))
1.05/1.13	 U22(ok(X:S)) -> ok(U22(X:S))
1.05/1.13	 U31(mark(X:S)) -> mark(U31(X:S))
1.05/1.13	 U31(ok(X:S)) -> ok(U31(X:S))
1.05/1.13	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.05/1.13	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.05/1.13	 U42(mark(X:S)) -> mark(U42(X:S))
1.05/1.13	 U42(ok(X:S)) -> ok(U42(X:S))
1.05/1.13	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.05/1.13	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.05/1.13	 U52(mark(X:S)) -> mark(U52(X:S))
1.05/1.13	 U52(ok(X:S)) -> ok(U52(X:S))
1.05/1.13	 U61(mark(X:S)) -> mark(U61(X:S))
1.05/1.13	 U61(ok(X:S)) -> ok(U61(X:S))
1.05/1.13	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.05/1.13	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.05/1.13	 U72(mark(X:S)) -> mark(U72(X:S))
1.05/1.13	 U72(ok(X:S)) -> ok(U72(X:S))
1.05/1.13	 U81(mark(X:S)) -> mark(U81(X:S))
1.05/1.13	 U81(ok(X:S)) -> ok(U81(X:S))
1.05/1.13	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.05/1.13	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.05/1.13	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.05/1.13	 active(U11(tt)) -> mark(tt)
1.05/1.13	 active(U11(X:S)) -> U11(active(X:S))
1.05/1.13	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.05/1.13	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.05/1.13	 active(U22(tt)) -> mark(tt)
1.05/1.13	 active(U22(X:S)) -> U22(active(X:S))
1.05/1.13	 active(U31(tt)) -> mark(tt)
1.05/1.13	 active(U31(X:S)) -> U31(active(X:S))
1.05/1.13	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.05/1.13	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.05/1.13	 active(U42(tt)) -> mark(tt)
1.05/1.13	 active(U42(X:S)) -> U42(active(X:S))
1.05/1.13	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.05/1.13	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.05/1.13	 active(U52(tt)) -> mark(tt)
1.05/1.13	 active(U52(X:S)) -> U52(active(X:S))
1.05/1.13	 active(U61(tt)) -> mark(tt)
1.05/1.13	 active(U61(X:S)) -> U61(active(X:S))
1.05/1.13	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.05/1.13	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.05/1.13	 active(U72(tt)) -> mark(tt)
1.05/1.13	 active(U72(X:S)) -> U72(active(X:S))
1.05/1.13	 active(U81(tt)) -> mark(tt)
1.05/1.13	 active(U81(X:S)) -> U81(active(X:S))
1.05/1.13	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.05/1.13	 active(__(nil,X:S)) -> mark(X:S)
1.05/1.13	 active(__(X:S,nil)) -> mark(X:S)
1.05/1.13	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.05/1.13	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.05/1.13	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.05/1.13	 active(isList(nil)) -> mark(tt)
1.05/1.13	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.05/1.13	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.05/1.13	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.05/1.13	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.05/1.13	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.05/1.13	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.05/1.13	 active(isPal(nil)) -> mark(tt)
1.05/1.13	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.05/1.13	 active(isQid(a)) -> mark(tt)
1.05/1.13	 active(isQid(e)) -> mark(tt)
1.05/1.13	 active(isQid(i)) -> mark(tt)
1.05/1.13	 active(isQid(o)) -> mark(tt)
1.05/1.13	 active(isQid(u)) -> mark(tt)
1.05/1.13	 isList(ok(X:S)) -> ok(isList(X:S))
1.05/1.13	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.05/1.13	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.05/1.13	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.05/1.13	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.05/1.13	 proper(U11(X:S)) -> U11(proper(X:S))
1.05/1.13	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.05/1.13	 proper(U22(X:S)) -> U22(proper(X:S))
1.05/1.13	 proper(U31(X:S)) -> U31(proper(X:S))
1.05/1.13	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.05/1.13	 proper(U42(X:S)) -> U42(proper(X:S))
1.05/1.13	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.05/1.13	 proper(U52(X:S)) -> U52(proper(X:S))
1.05/1.13	 proper(U61(X:S)) -> U61(proper(X:S))
1.05/1.13	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.05/1.13	 proper(U72(X:S)) -> U72(proper(X:S))
1.05/1.13	 proper(U81(X:S)) -> U81(proper(X:S))
1.05/1.13	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.05/1.13	 proper(isList(X:S)) -> isList(proper(X:S))
1.05/1.13	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.05/1.13	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.05/1.13	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.05/1.13	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.05/1.13	 proper(a) -> ok(a)
1.05/1.13	 proper(e) -> ok(e)
1.05/1.13	 proper(i) -> ok(i)
1.05/1.13	 proper(nil) -> ok(nil)
1.05/1.13	 proper(o) -> ok(o)
1.05/1.13	 proper(tt) -> ok(tt)
1.05/1.13	 proper(u) -> ok(u)
1.05/1.13	 top(mark(X:S)) -> top(proper(X:S))
1.05/1.13	 top(ok(X:S)) -> top(active(X:S))
1.05/1.13	->Strongly Connected Components:
1.05/1.13	 There is no strongly connected component
1.05/1.13	
1.05/1.13	The problem is finite.
1.05/1.13	
1.05/1.13	Problem 1.20: 
1.05/1.13	
1.05/1.13	Subterm Processor:
1.05/1.13	-> Pairs:
1.05/1.13	 PROPER(U11(X:S)) -> PROPER(X:S)
1.05/1.13	 PROPER(U21(X1:S,X2:S)) -> PROPER(X1:S)
1.05/1.13	 PROPER(U21(X1:S,X2:S)) -> PROPER(X2:S)
1.05/1.13	 PROPER(U22(X:S)) -> PROPER(X:S)
1.05/1.13	 PROPER(U31(X:S)) -> PROPER(X:S)
1.05/1.13	 PROPER(U41(X1:S,X2:S)) -> PROPER(X1:S)
1.05/1.13	 PROPER(U41(X1:S,X2:S)) -> PROPER(X2:S)
1.05/1.13	 PROPER(U42(X:S)) -> PROPER(X:S)
1.05/1.13	 PROPER(U51(X1:S,X2:S)) -> PROPER(X1:S)
1.05/1.13	 PROPER(U51(X1:S,X2:S)) -> PROPER(X2:S)
1.05/1.13	 PROPER(U52(X:S)) -> PROPER(X:S)
1.05/1.13	 PROPER(U61(X:S)) -> PROPER(X:S)
1.05/1.13	 PROPER(U71(X1:S,X2:S)) -> PROPER(X1:S)
1.05/1.13	 PROPER(U71(X1:S,X2:S)) -> PROPER(X2:S)
1.05/1.13	 PROPER(U72(X:S)) -> PROPER(X:S)
1.05/1.13	 PROPER(U81(X:S)) -> PROPER(X:S)
1.05/1.13	 PROPER(__(X1:S,X2:S)) -> PROPER(X1:S)
1.05/1.13	 PROPER(__(X1:S,X2:S)) -> PROPER(X2:S)
1.05/1.13	 PROPER(isList(X:S)) -> PROPER(X:S)
1.05/1.13	 PROPER(isNeList(X:S)) -> PROPER(X:S)
1.05/1.13	 PROPER(isNePal(X:S)) -> PROPER(X:S)
1.05/1.13	 PROPER(isPal(X:S)) -> PROPER(X:S)
1.05/1.13	 PROPER(isQid(X:S)) -> PROPER(X:S)
1.05/1.13	-> Rules:
1.05/1.13	 U11(mark(X:S)) -> mark(U11(X:S))
1.05/1.13	 U11(ok(X:S)) -> ok(U11(X:S))
1.05/1.13	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.05/1.13	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.05/1.13	 U22(mark(X:S)) -> mark(U22(X:S))
1.05/1.13	 U22(ok(X:S)) -> ok(U22(X:S))
1.05/1.13	 U31(mark(X:S)) -> mark(U31(X:S))
1.05/1.13	 U31(ok(X:S)) -> ok(U31(X:S))
1.05/1.13	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.05/1.13	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.05/1.13	 U42(mark(X:S)) -> mark(U42(X:S))
1.05/1.13	 U42(ok(X:S)) -> ok(U42(X:S))
1.05/1.13	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.05/1.13	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.05/1.13	 U52(mark(X:S)) -> mark(U52(X:S))
1.05/1.13	 U52(ok(X:S)) -> ok(U52(X:S))
1.05/1.13	 U61(mark(X:S)) -> mark(U61(X:S))
1.05/1.13	 U61(ok(X:S)) -> ok(U61(X:S))
1.05/1.13	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.05/1.13	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.05/1.13	 U72(mark(X:S)) -> mark(U72(X:S))
1.05/1.13	 U72(ok(X:S)) -> ok(U72(X:S))
1.05/1.13	 U81(mark(X:S)) -> mark(U81(X:S))
1.05/1.13	 U81(ok(X:S)) -> ok(U81(X:S))
1.05/1.13	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.05/1.13	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.05/1.13	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.05/1.13	 active(U11(tt)) -> mark(tt)
1.05/1.13	 active(U11(X:S)) -> U11(active(X:S))
1.05/1.13	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.05/1.13	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.05/1.13	 active(U22(tt)) -> mark(tt)
1.05/1.13	 active(U22(X:S)) -> U22(active(X:S))
1.05/1.13	 active(U31(tt)) -> mark(tt)
1.05/1.13	 active(U31(X:S)) -> U31(active(X:S))
1.05/1.13	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.05/1.13	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.05/1.13	 active(U42(tt)) -> mark(tt)
1.05/1.13	 active(U42(X:S)) -> U42(active(X:S))
1.05/1.13	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.05/1.13	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.05/1.13	 active(U52(tt)) -> mark(tt)
1.05/1.13	 active(U52(X:S)) -> U52(active(X:S))
1.05/1.13	 active(U61(tt)) -> mark(tt)
1.05/1.13	 active(U61(X:S)) -> U61(active(X:S))
1.05/1.13	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.05/1.13	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.05/1.13	 active(U72(tt)) -> mark(tt)
1.05/1.13	 active(U72(X:S)) -> U72(active(X:S))
1.05/1.13	 active(U81(tt)) -> mark(tt)
1.05/1.13	 active(U81(X:S)) -> U81(active(X:S))
1.05/1.13	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.05/1.13	 active(__(nil,X:S)) -> mark(X:S)
1.05/1.13	 active(__(X:S,nil)) -> mark(X:S)
1.05/1.13	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.05/1.13	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.05/1.13	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.05/1.13	 active(isList(nil)) -> mark(tt)
1.05/1.13	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.05/1.13	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.05/1.13	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.05/1.13	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.05/1.13	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.05/1.13	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.05/1.13	 active(isPal(nil)) -> mark(tt)
1.05/1.13	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.05/1.13	 active(isQid(a)) -> mark(tt)
1.05/1.13	 active(isQid(e)) -> mark(tt)
1.05/1.13	 active(isQid(i)) -> mark(tt)
1.05/1.13	 active(isQid(o)) -> mark(tt)
1.05/1.13	 active(isQid(u)) -> mark(tt)
1.05/1.13	 isList(ok(X:S)) -> ok(isList(X:S))
1.05/1.13	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.05/1.13	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.05/1.13	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.05/1.13	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.05/1.13	 proper(U11(X:S)) -> U11(proper(X:S))
1.05/1.13	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.05/1.13	 proper(U22(X:S)) -> U22(proper(X:S))
1.05/1.13	 proper(U31(X:S)) -> U31(proper(X:S))
1.05/1.13	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.05/1.13	 proper(U42(X:S)) -> U42(proper(X:S))
1.05/1.13	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.05/1.13	 proper(U52(X:S)) -> U52(proper(X:S))
1.05/1.13	 proper(U61(X:S)) -> U61(proper(X:S))
1.05/1.13	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.05/1.13	 proper(U72(X:S)) -> U72(proper(X:S))
1.05/1.13	 proper(U81(X:S)) -> U81(proper(X:S))
1.05/1.13	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.05/1.13	 proper(isList(X:S)) -> isList(proper(X:S))
1.05/1.13	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.05/1.13	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.05/1.13	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.05/1.13	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.05/1.13	 proper(a) -> ok(a)
1.05/1.13	 proper(e) -> ok(e)
1.05/1.13	 proper(i) -> ok(i)
1.05/1.13	 proper(nil) -> ok(nil)
1.05/1.13	 proper(o) -> ok(o)
1.05/1.13	 proper(tt) -> ok(tt)
1.05/1.13	 proper(u) -> ok(u)
1.05/1.13	 top(mark(X:S)) -> top(proper(X:S))
1.05/1.13	 top(ok(X:S)) -> top(active(X:S))
1.05/1.13	->Projection:
1.05/1.13	 pi(PROPER) = 1
1.05/1.13	
1.05/1.13	Problem 1.20: 
1.05/1.13	
1.05/1.13	SCC Processor:
1.05/1.13	-> Pairs:
1.05/1.13	 Empty
1.05/1.13	-> Rules:
1.05/1.13	 U11(mark(X:S)) -> mark(U11(X:S))
1.05/1.13	 U11(ok(X:S)) -> ok(U11(X:S))
1.05/1.13	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.05/1.13	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.05/1.13	 U22(mark(X:S)) -> mark(U22(X:S))
1.05/1.13	 U22(ok(X:S)) -> ok(U22(X:S))
1.05/1.13	 U31(mark(X:S)) -> mark(U31(X:S))
1.05/1.13	 U31(ok(X:S)) -> ok(U31(X:S))
1.05/1.13	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.05/1.13	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.05/1.13	 U42(mark(X:S)) -> mark(U42(X:S))
1.05/1.13	 U42(ok(X:S)) -> ok(U42(X:S))
1.05/1.13	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.05/1.13	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.05/1.13	 U52(mark(X:S)) -> mark(U52(X:S))
1.05/1.13	 U52(ok(X:S)) -> ok(U52(X:S))
1.05/1.13	 U61(mark(X:S)) -> mark(U61(X:S))
1.05/1.13	 U61(ok(X:S)) -> ok(U61(X:S))
1.05/1.13	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.05/1.13	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.05/1.13	 U72(mark(X:S)) -> mark(U72(X:S))
1.05/1.13	 U72(ok(X:S)) -> ok(U72(X:S))
1.05/1.13	 U81(mark(X:S)) -> mark(U81(X:S))
1.05/1.13	 U81(ok(X:S)) -> ok(U81(X:S))
1.05/1.13	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.05/1.13	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.05/1.13	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.05/1.13	 active(U11(tt)) -> mark(tt)
1.05/1.13	 active(U11(X:S)) -> U11(active(X:S))
1.05/1.13	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.05/1.13	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.05/1.13	 active(U22(tt)) -> mark(tt)
1.05/1.13	 active(U22(X:S)) -> U22(active(X:S))
1.05/1.13	 active(U31(tt)) -> mark(tt)
1.05/1.13	 active(U31(X:S)) -> U31(active(X:S))
1.05/1.13	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.05/1.13	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.05/1.13	 active(U42(tt)) -> mark(tt)
1.05/1.13	 active(U42(X:S)) -> U42(active(X:S))
1.05/1.13	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.05/1.13	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.05/1.13	 active(U52(tt)) -> mark(tt)
1.05/1.13	 active(U52(X:S)) -> U52(active(X:S))
1.05/1.13	 active(U61(tt)) -> mark(tt)
1.05/1.13	 active(U61(X:S)) -> U61(active(X:S))
1.05/1.13	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.05/1.13	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.05/1.13	 active(U72(tt)) -> mark(tt)
1.05/1.13	 active(U72(X:S)) -> U72(active(X:S))
1.05/1.13	 active(U81(tt)) -> mark(tt)
1.05/1.13	 active(U81(X:S)) -> U81(active(X:S))
1.05/1.13	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.05/1.13	 active(__(nil,X:S)) -> mark(X:S)
1.05/1.13	 active(__(X:S,nil)) -> mark(X:S)
1.05/1.13	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.05/1.13	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.05/1.13	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.05/1.13	 active(isList(nil)) -> mark(tt)
1.05/1.13	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.05/1.13	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.05/1.13	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.05/1.13	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.05/1.13	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.05/1.13	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.05/1.13	 active(isPal(nil)) -> mark(tt)
1.05/1.13	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.05/1.13	 active(isQid(a)) -> mark(tt)
1.05/1.13	 active(isQid(e)) -> mark(tt)
1.05/1.13	 active(isQid(i)) -> mark(tt)
1.05/1.13	 active(isQid(o)) -> mark(tt)
1.05/1.13	 active(isQid(u)) -> mark(tt)
1.05/1.13	 isList(ok(X:S)) -> ok(isList(X:S))
1.05/1.13	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.05/1.13	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.05/1.13	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.05/1.13	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.05/1.13	 proper(U11(X:S)) -> U11(proper(X:S))
1.05/1.13	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.05/1.13	 proper(U22(X:S)) -> U22(proper(X:S))
1.05/1.13	 proper(U31(X:S)) -> U31(proper(X:S))
1.05/1.13	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.05/1.13	 proper(U42(X:S)) -> U42(proper(X:S))
1.05/1.13	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.05/1.13	 proper(U52(X:S)) -> U52(proper(X:S))
1.05/1.13	 proper(U61(X:S)) -> U61(proper(X:S))
1.05/1.13	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.05/1.13	 proper(U72(X:S)) -> U72(proper(X:S))
1.05/1.13	 proper(U81(X:S)) -> U81(proper(X:S))
1.05/1.13	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.05/1.13	 proper(isList(X:S)) -> isList(proper(X:S))
1.05/1.13	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.05/1.13	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.05/1.13	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.05/1.13	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.05/1.13	 proper(a) -> ok(a)
1.05/1.13	 proper(e) -> ok(e)
1.05/1.13	 proper(i) -> ok(i)
1.05/1.13	 proper(nil) -> ok(nil)
1.05/1.13	 proper(o) -> ok(o)
1.05/1.13	 proper(tt) -> ok(tt)
1.05/1.13	 proper(u) -> ok(u)
1.05/1.13	 top(mark(X:S)) -> top(proper(X:S))
1.05/1.13	 top(ok(X:S)) -> top(active(X:S))
1.05/1.13	->Strongly Connected Components:
1.05/1.13	 There is no strongly connected component
1.05/1.13	
1.05/1.13	The problem is finite.
1.05/1.13	
1.05/1.13	Problem 1.21: 
1.05/1.13	
1.05/1.13	Reduction Pairs Processor:
1.05/1.13	-> Pairs:
1.05/1.13	 TOP(mark(X:S)) -> TOP(proper(X:S))
1.05/1.13	 TOP(ok(X:S)) -> TOP(active(X:S))
1.05/1.13	-> Rules:
1.05/1.13	 U11(mark(X:S)) -> mark(U11(X:S))
1.05/1.13	 U11(ok(X:S)) -> ok(U11(X:S))
1.05/1.13	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.05/1.13	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.05/1.13	 U22(mark(X:S)) -> mark(U22(X:S))
1.05/1.13	 U22(ok(X:S)) -> ok(U22(X:S))
1.05/1.13	 U31(mark(X:S)) -> mark(U31(X:S))
1.05/1.13	 U31(ok(X:S)) -> ok(U31(X:S))
1.05/1.13	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.05/1.13	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.05/1.13	 U42(mark(X:S)) -> mark(U42(X:S))
1.05/1.13	 U42(ok(X:S)) -> ok(U42(X:S))
1.05/1.13	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.05/1.13	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.05/1.13	 U52(mark(X:S)) -> mark(U52(X:S))
1.05/1.13	 U52(ok(X:S)) -> ok(U52(X:S))
1.05/1.13	 U61(mark(X:S)) -> mark(U61(X:S))
1.05/1.13	 U61(ok(X:S)) -> ok(U61(X:S))
1.05/1.13	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.05/1.13	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.05/1.13	 U72(mark(X:S)) -> mark(U72(X:S))
1.05/1.13	 U72(ok(X:S)) -> ok(U72(X:S))
1.05/1.13	 U81(mark(X:S)) -> mark(U81(X:S))
1.05/1.13	 U81(ok(X:S)) -> ok(U81(X:S))
1.05/1.13	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.05/1.13	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.05/1.13	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.05/1.13	 active(U11(tt)) -> mark(tt)
1.05/1.13	 active(U11(X:S)) -> U11(active(X:S))
1.05/1.13	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.05/1.13	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.05/1.13	 active(U22(tt)) -> mark(tt)
1.05/1.13	 active(U22(X:S)) -> U22(active(X:S))
1.05/1.13	 active(U31(tt)) -> mark(tt)
1.05/1.13	 active(U31(X:S)) -> U31(active(X:S))
1.05/1.13	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.05/1.13	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.05/1.13	 active(U42(tt)) -> mark(tt)
1.05/1.13	 active(U42(X:S)) -> U42(active(X:S))
1.05/1.13	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.05/1.13	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.05/1.13	 active(U52(tt)) -> mark(tt)
1.05/1.13	 active(U52(X:S)) -> U52(active(X:S))
1.05/1.13	 active(U61(tt)) -> mark(tt)
1.05/1.13	 active(U61(X:S)) -> U61(active(X:S))
1.05/1.13	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.05/1.13	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.05/1.13	 active(U72(tt)) -> mark(tt)
1.05/1.13	 active(U72(X:S)) -> U72(active(X:S))
1.05/1.13	 active(U81(tt)) -> mark(tt)
1.05/1.13	 active(U81(X:S)) -> U81(active(X:S))
1.05/1.13	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.05/1.13	 active(__(nil,X:S)) -> mark(X:S)
1.05/1.13	 active(__(X:S,nil)) -> mark(X:S)
1.05/1.13	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.05/1.13	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.05/1.13	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.05/1.13	 active(isList(nil)) -> mark(tt)
1.05/1.13	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.05/1.13	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.05/1.13	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.05/1.13	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.05/1.13	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.05/1.13	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.05/1.13	 active(isPal(nil)) -> mark(tt)
1.05/1.13	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.05/1.13	 active(isQid(a)) -> mark(tt)
1.05/1.13	 active(isQid(e)) -> mark(tt)
1.05/1.13	 active(isQid(i)) -> mark(tt)
1.05/1.13	 active(isQid(o)) -> mark(tt)
1.05/1.13	 active(isQid(u)) -> mark(tt)
1.05/1.13	 isList(ok(X:S)) -> ok(isList(X:S))
1.05/1.13	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.05/1.13	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.05/1.13	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.05/1.13	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.05/1.13	 proper(U11(X:S)) -> U11(proper(X:S))
1.05/1.13	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.05/1.13	 proper(U22(X:S)) -> U22(proper(X:S))
1.05/1.13	 proper(U31(X:S)) -> U31(proper(X:S))
1.05/1.13	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.05/1.13	 proper(U42(X:S)) -> U42(proper(X:S))
1.05/1.13	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.05/1.13	 proper(U52(X:S)) -> U52(proper(X:S))
1.05/1.13	 proper(U61(X:S)) -> U61(proper(X:S))
1.05/1.13	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.05/1.13	 proper(U72(X:S)) -> U72(proper(X:S))
1.05/1.13	 proper(U81(X:S)) -> U81(proper(X:S))
1.05/1.13	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.05/1.13	 proper(isList(X:S)) -> isList(proper(X:S))
1.05/1.13	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.05/1.13	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.05/1.13	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.05/1.13	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.05/1.13	 proper(a) -> ok(a)
1.05/1.13	 proper(e) -> ok(e)
1.05/1.13	 proper(i) -> ok(i)
1.05/1.13	 proper(nil) -> ok(nil)
1.05/1.13	 proper(o) -> ok(o)
1.05/1.13	 proper(tt) -> ok(tt)
1.05/1.13	 proper(u) -> ok(u)
1.05/1.13	 top(mark(X:S)) -> top(proper(X:S))
1.05/1.13	 top(ok(X:S)) -> top(active(X:S))
1.05/1.13	-> Usable rules:
1.05/1.13	 U11(mark(X:S)) -> mark(U11(X:S))
1.05/1.13	 U11(ok(X:S)) -> ok(U11(X:S))
1.05/1.13	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.05/1.13	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.05/1.13	 U22(mark(X:S)) -> mark(U22(X:S))
1.05/1.13	 U22(ok(X:S)) -> ok(U22(X:S))
1.05/1.13	 U31(mark(X:S)) -> mark(U31(X:S))
1.05/1.13	 U31(ok(X:S)) -> ok(U31(X:S))
1.05/1.13	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.05/1.13	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.05/1.13	 U42(mark(X:S)) -> mark(U42(X:S))
1.05/1.13	 U42(ok(X:S)) -> ok(U42(X:S))
1.05/1.13	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.05/1.13	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.05/1.13	 U52(mark(X:S)) -> mark(U52(X:S))
1.05/1.13	 U52(ok(X:S)) -> ok(U52(X:S))
1.05/1.13	 U61(mark(X:S)) -> mark(U61(X:S))
1.05/1.13	 U61(ok(X:S)) -> ok(U61(X:S))
1.05/1.13	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.05/1.13	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.05/1.13	 U72(mark(X:S)) -> mark(U72(X:S))
1.05/1.13	 U72(ok(X:S)) -> ok(U72(X:S))
1.05/1.13	 U81(mark(X:S)) -> mark(U81(X:S))
1.05/1.13	 U81(ok(X:S)) -> ok(U81(X:S))
1.05/1.13	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.05/1.13	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.05/1.13	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.05/1.13	 active(U11(tt)) -> mark(tt)
1.05/1.13	 active(U11(X:S)) -> U11(active(X:S))
1.05/1.13	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.05/1.13	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.05/1.13	 active(U22(tt)) -> mark(tt)
1.05/1.13	 active(U22(X:S)) -> U22(active(X:S))
1.05/1.13	 active(U31(tt)) -> mark(tt)
1.05/1.13	 active(U31(X:S)) -> U31(active(X:S))
1.05/1.13	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.05/1.13	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.05/1.13	 active(U42(tt)) -> mark(tt)
1.05/1.13	 active(U42(X:S)) -> U42(active(X:S))
1.05/1.13	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.05/1.13	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.05/1.13	 active(U52(tt)) -> mark(tt)
1.05/1.13	 active(U52(X:S)) -> U52(active(X:S))
1.05/1.13	 active(U61(tt)) -> mark(tt)
1.05/1.13	 active(U61(X:S)) -> U61(active(X:S))
1.05/1.13	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.05/1.13	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.05/1.13	 active(U72(tt)) -> mark(tt)
1.05/1.13	 active(U72(X:S)) -> U72(active(X:S))
1.05/1.13	 active(U81(tt)) -> mark(tt)
1.05/1.13	 active(U81(X:S)) -> U81(active(X:S))
1.05/1.13	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.05/1.13	 active(__(nil,X:S)) -> mark(X:S)
1.05/1.13	 active(__(X:S,nil)) -> mark(X:S)
1.05/1.13	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.05/1.13	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.05/1.13	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.05/1.13	 active(isList(nil)) -> mark(tt)
1.05/1.13	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.05/1.13	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.05/1.13	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.05/1.13	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.05/1.13	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.05/1.13	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.05/1.13	 active(isPal(nil)) -> mark(tt)
1.05/1.13	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.05/1.13	 active(isQid(a)) -> mark(tt)
1.05/1.13	 active(isQid(e)) -> mark(tt)
1.05/1.13	 active(isQid(i)) -> mark(tt)
1.05/1.13	 active(isQid(o)) -> mark(tt)
1.05/1.13	 active(isQid(u)) -> mark(tt)
1.05/1.13	 isList(ok(X:S)) -> ok(isList(X:S))
1.05/1.13	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.05/1.13	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.05/1.13	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.05/1.13	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.05/1.13	 proper(U11(X:S)) -> U11(proper(X:S))
1.05/1.13	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.05/1.13	 proper(U22(X:S)) -> U22(proper(X:S))
1.05/1.13	 proper(U31(X:S)) -> U31(proper(X:S))
1.05/1.13	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.05/1.13	 proper(U42(X:S)) -> U42(proper(X:S))
1.05/1.13	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.05/1.13	 proper(U52(X:S)) -> U52(proper(X:S))
1.05/1.13	 proper(U61(X:S)) -> U61(proper(X:S))
1.05/1.13	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.05/1.13	 proper(U72(X:S)) -> U72(proper(X:S))
1.05/1.13	 proper(U81(X:S)) -> U81(proper(X:S))
1.05/1.13	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.05/1.13	 proper(isList(X:S)) -> isList(proper(X:S))
1.05/1.13	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.05/1.13	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.05/1.13	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.05/1.13	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.05/1.13	 proper(a) -> ok(a)
1.05/1.13	 proper(e) -> ok(e)
1.05/1.13	 proper(i) -> ok(i)
1.05/1.13	 proper(nil) -> ok(nil)
1.05/1.13	 proper(o) -> ok(o)
1.05/1.13	 proper(tt) -> ok(tt)
1.05/1.13	 proper(u) -> ok(u)
1.05/1.13	->Interpretation type:
1.05/1.13	 Linear
1.05/1.13	->Coefficients:
1.05/1.13	 All rationals
1.05/1.13	->Dimension:
1.05/1.13	 1
1.05/1.13	->Bound:
1.05/1.13	 2
1.05/1.13	->Interpretation:
1.05/1.13	 
1.05/1.13	[U11](X) = X + 1
1.05/1.13	[U21](X1,X2) = X1 + 2.X2 + 2
1.05/1.13	[U22](X) = X + 1/2
1.05/1.13	[U31](X) = 2.X
1.05/1.13	[U41](X1,X2) = 2.X1 + 2.X2
1.05/1.13	[U42](X) = X + 1/2
1.05/1.13	[U51](X1,X2) = 2.X1 + 2.X2 + 2
1.05/1.13	[U52](X) = X + 1/2
1.05/1.13	[U61](X) = 2.X + 1/2
1.05/1.13	[U71](X1,X2) = 2.X1 + 2.X2 + 2
1.05/1.13	[U72](X) = X + 1/2
1.05/1.13	[U81](X) = X + 1/2
1.05/1.13	[__](X1,X2) = 2.X1 + X2 + 2
1.05/1.13	[active](X) = X
1.05/1.13	[isList](X) = 2.X + 2
1.05/1.13	[isNeList](X) = 2.X + 1/2
1.05/1.13	[isNePal](X) = 2.X + 1
1.05/1.13	[isPal](X) = 2.X + 2
1.05/1.13	[isQid](X) = X
1.05/1.13	[proper](X) = X
1.05/1.13	[top](X) = 0
1.05/1.13	[a] = 2
1.05/1.13	[e] = 2
1.05/1.13	[fSNonEmpty] = 0
1.05/1.13	[i] = 2
1.05/1.13	[mark](X) = X + 1/2
1.05/1.13	[nil] = 1/2
1.05/1.13	[o] = 2
1.05/1.13	[ok](X) = X
1.05/1.13	[tt] = 1
1.05/1.13	[u] = 2
1.05/1.13	[U11#](X) = 0
1.05/1.13	[U21#](X1,X2) = 0
1.05/1.13	[U22#](X) = 0
1.05/1.13	[U31#](X) = 0
1.05/1.13	[U41#](X1,X2) = 0
1.05/1.13	[U42#](X) = 0
1.05/1.13	[U51#](X1,X2) = 0
1.05/1.13	[U52#](X) = 0
1.05/1.13	[U61#](X) = 0
1.05/1.13	[U71#](X1,X2) = 0
1.05/1.13	[U72#](X) = 0
1.05/1.13	[U81#](X) = 0
1.05/1.13	[__#](X1,X2) = 0
1.05/1.13	[ACTIVE](X) = 0
1.05/1.13	[ISLIST](X) = 0
1.05/1.13	[ISNELIST](X) = 0
1.05/1.13	[ISNEPAL](X) = 0
1.05/1.13	[ISPAL](X) = 0
1.05/1.13	[ISQID](X) = 0
1.05/1.13	[PROPER](X) = 0
1.05/1.13	[TOP](X) = 2.X
1.05/1.13	
1.05/1.13	Problem 1.21: 
1.05/1.13	
1.05/1.13	SCC Processor:
1.05/1.13	-> Pairs:
1.05/1.13	 TOP(ok(X:S)) -> TOP(active(X:S))
1.05/1.13	-> Rules:
1.05/1.13	 U11(mark(X:S)) -> mark(U11(X:S))
1.05/1.13	 U11(ok(X:S)) -> ok(U11(X:S))
1.05/1.13	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.05/1.13	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.05/1.13	 U22(mark(X:S)) -> mark(U22(X:S))
1.05/1.13	 U22(ok(X:S)) -> ok(U22(X:S))
1.05/1.13	 U31(mark(X:S)) -> mark(U31(X:S))
1.05/1.13	 U31(ok(X:S)) -> ok(U31(X:S))
1.05/1.13	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.05/1.13	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.05/1.13	 U42(mark(X:S)) -> mark(U42(X:S))
1.05/1.13	 U42(ok(X:S)) -> ok(U42(X:S))
1.05/1.13	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.05/1.13	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.05/1.13	 U52(mark(X:S)) -> mark(U52(X:S))
1.05/1.13	 U52(ok(X:S)) -> ok(U52(X:S))
1.05/1.13	 U61(mark(X:S)) -> mark(U61(X:S))
1.05/1.13	 U61(ok(X:S)) -> ok(U61(X:S))
1.05/1.13	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.05/1.13	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.05/1.13	 U72(mark(X:S)) -> mark(U72(X:S))
1.05/1.13	 U72(ok(X:S)) -> ok(U72(X:S))
1.05/1.13	 U81(mark(X:S)) -> mark(U81(X:S))
1.05/1.13	 U81(ok(X:S)) -> ok(U81(X:S))
1.05/1.13	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.05/1.13	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.05/1.13	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.05/1.13	 active(U11(tt)) -> mark(tt)
1.05/1.13	 active(U11(X:S)) -> U11(active(X:S))
1.05/1.13	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.05/1.13	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.05/1.13	 active(U22(tt)) -> mark(tt)
1.05/1.13	 active(U22(X:S)) -> U22(active(X:S))
1.05/1.13	 active(U31(tt)) -> mark(tt)
1.05/1.13	 active(U31(X:S)) -> U31(active(X:S))
1.05/1.13	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.05/1.13	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.05/1.13	 active(U42(tt)) -> mark(tt)
1.05/1.13	 active(U42(X:S)) -> U42(active(X:S))
1.05/1.13	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.05/1.13	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.05/1.13	 active(U52(tt)) -> mark(tt)
1.05/1.13	 active(U52(X:S)) -> U52(active(X:S))
1.05/1.13	 active(U61(tt)) -> mark(tt)
1.05/1.13	 active(U61(X:S)) -> U61(active(X:S))
1.05/1.13	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.05/1.13	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.05/1.13	 active(U72(tt)) -> mark(tt)
1.05/1.13	 active(U72(X:S)) -> U72(active(X:S))
1.05/1.13	 active(U81(tt)) -> mark(tt)
1.05/1.13	 active(U81(X:S)) -> U81(active(X:S))
1.05/1.13	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.05/1.13	 active(__(nil,X:S)) -> mark(X:S)
1.05/1.13	 active(__(X:S,nil)) -> mark(X:S)
1.05/1.13	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.05/1.13	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.05/1.13	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.05/1.13	 active(isList(nil)) -> mark(tt)
1.05/1.13	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.05/1.13	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.05/1.13	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.05/1.13	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.05/1.13	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.05/1.13	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.05/1.13	 active(isPal(nil)) -> mark(tt)
1.05/1.13	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.05/1.13	 active(isQid(a)) -> mark(tt)
1.05/1.13	 active(isQid(e)) -> mark(tt)
1.05/1.13	 active(isQid(i)) -> mark(tt)
1.05/1.13	 active(isQid(o)) -> mark(tt)
1.05/1.13	 active(isQid(u)) -> mark(tt)
1.05/1.13	 isList(ok(X:S)) -> ok(isList(X:S))
1.05/1.13	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.05/1.13	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.05/1.13	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.05/1.13	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.05/1.13	 proper(U11(X:S)) -> U11(proper(X:S))
1.05/1.13	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.05/1.13	 proper(U22(X:S)) -> U22(proper(X:S))
1.05/1.13	 proper(U31(X:S)) -> U31(proper(X:S))
1.05/1.13	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.05/1.13	 proper(U42(X:S)) -> U42(proper(X:S))
1.05/1.13	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.05/1.13	 proper(U52(X:S)) -> U52(proper(X:S))
1.05/1.13	 proper(U61(X:S)) -> U61(proper(X:S))
1.05/1.13	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.05/1.13	 proper(U72(X:S)) -> U72(proper(X:S))
1.05/1.13	 proper(U81(X:S)) -> U81(proper(X:S))
1.05/1.13	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.05/1.13	 proper(isList(X:S)) -> isList(proper(X:S))
1.05/1.13	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.05/1.13	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.05/1.13	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.05/1.13	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.05/1.13	 proper(a) -> ok(a)
1.05/1.13	 proper(e) -> ok(e)
1.05/1.13	 proper(i) -> ok(i)
1.05/1.13	 proper(nil) -> ok(nil)
1.05/1.13	 proper(o) -> ok(o)
1.05/1.13	 proper(tt) -> ok(tt)
1.05/1.13	 proper(u) -> ok(u)
1.05/1.13	 top(mark(X:S)) -> top(proper(X:S))
1.05/1.13	 top(ok(X:S)) -> top(active(X:S))
1.05/1.13	->Strongly Connected Components:
1.05/1.13	->->Cycle:
1.05/1.13	->->-> Pairs:
1.05/1.13	 TOP(ok(X:S)) -> TOP(active(X:S))
1.05/1.13	->->-> Rules:
1.05/1.13	 U11(mark(X:S)) -> mark(U11(X:S))
1.05/1.13	 U11(ok(X:S)) -> ok(U11(X:S))
1.05/1.13	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.05/1.13	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.05/1.13	 U22(mark(X:S)) -> mark(U22(X:S))
1.05/1.13	 U22(ok(X:S)) -> ok(U22(X:S))
1.05/1.13	 U31(mark(X:S)) -> mark(U31(X:S))
1.05/1.13	 U31(ok(X:S)) -> ok(U31(X:S))
1.05/1.13	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.05/1.13	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.05/1.13	 U42(mark(X:S)) -> mark(U42(X:S))
1.05/1.13	 U42(ok(X:S)) -> ok(U42(X:S))
1.05/1.13	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.05/1.13	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.05/1.13	 U52(mark(X:S)) -> mark(U52(X:S))
1.05/1.13	 U52(ok(X:S)) -> ok(U52(X:S))
1.05/1.13	 U61(mark(X:S)) -> mark(U61(X:S))
1.05/1.13	 U61(ok(X:S)) -> ok(U61(X:S))
1.05/1.13	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.05/1.13	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.05/1.13	 U72(mark(X:S)) -> mark(U72(X:S))
1.05/1.13	 U72(ok(X:S)) -> ok(U72(X:S))
1.05/1.13	 U81(mark(X:S)) -> mark(U81(X:S))
1.05/1.13	 U81(ok(X:S)) -> ok(U81(X:S))
1.05/1.13	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.05/1.13	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.05/1.13	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.05/1.13	 active(U11(tt)) -> mark(tt)
1.05/1.13	 active(U11(X:S)) -> U11(active(X:S))
1.05/1.13	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.05/1.13	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.05/1.13	 active(U22(tt)) -> mark(tt)
1.05/1.13	 active(U22(X:S)) -> U22(active(X:S))
1.05/1.13	 active(U31(tt)) -> mark(tt)
1.05/1.13	 active(U31(X:S)) -> U31(active(X:S))
1.05/1.13	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.05/1.13	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.05/1.13	 active(U42(tt)) -> mark(tt)
1.05/1.13	 active(U42(X:S)) -> U42(active(X:S))
1.05/1.13	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.05/1.13	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.05/1.13	 active(U52(tt)) -> mark(tt)
1.05/1.13	 active(U52(X:S)) -> U52(active(X:S))
1.05/1.13	 active(U61(tt)) -> mark(tt)
1.05/1.13	 active(U61(X:S)) -> U61(active(X:S))
1.05/1.13	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.05/1.13	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.05/1.13	 active(U72(tt)) -> mark(tt)
1.05/1.13	 active(U72(X:S)) -> U72(active(X:S))
1.05/1.13	 active(U81(tt)) -> mark(tt)
1.05/1.13	 active(U81(X:S)) -> U81(active(X:S))
1.05/1.13	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.05/1.13	 active(__(nil,X:S)) -> mark(X:S)
1.05/1.13	 active(__(X:S,nil)) -> mark(X:S)
1.05/1.13	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.05/1.13	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.05/1.13	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.05/1.13	 active(isList(nil)) -> mark(tt)
1.05/1.13	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.05/1.13	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.05/1.13	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.05/1.13	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.05/1.13	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.05/1.13	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.05/1.13	 active(isPal(nil)) -> mark(tt)
1.05/1.13	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.05/1.13	 active(isQid(a)) -> mark(tt)
1.05/1.13	 active(isQid(e)) -> mark(tt)
1.05/1.13	 active(isQid(i)) -> mark(tt)
1.05/1.13	 active(isQid(o)) -> mark(tt)
1.05/1.13	 active(isQid(u)) -> mark(tt)
1.05/1.13	 isList(ok(X:S)) -> ok(isList(X:S))
1.05/1.13	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.05/1.13	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.05/1.13	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.05/1.13	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.05/1.13	 proper(U11(X:S)) -> U11(proper(X:S))
1.05/1.13	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.05/1.13	 proper(U22(X:S)) -> U22(proper(X:S))
1.05/1.13	 proper(U31(X:S)) -> U31(proper(X:S))
1.05/1.13	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.05/1.13	 proper(U42(X:S)) -> U42(proper(X:S))
1.05/1.13	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.05/1.13	 proper(U52(X:S)) -> U52(proper(X:S))
1.05/1.13	 proper(U61(X:S)) -> U61(proper(X:S))
1.05/1.13	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.05/1.13	 proper(U72(X:S)) -> U72(proper(X:S))
1.05/1.13	 proper(U81(X:S)) -> U81(proper(X:S))
1.05/1.13	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.05/1.13	 proper(isList(X:S)) -> isList(proper(X:S))
1.05/1.13	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.05/1.13	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.05/1.13	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.05/1.13	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.05/1.13	 proper(a) -> ok(a)
1.05/1.13	 proper(e) -> ok(e)
1.05/1.13	 proper(i) -> ok(i)
1.05/1.13	 proper(nil) -> ok(nil)
1.05/1.13	 proper(o) -> ok(o)
1.05/1.13	 proper(tt) -> ok(tt)
1.05/1.13	 proper(u) -> ok(u)
1.05/1.13	 top(mark(X:S)) -> top(proper(X:S))
1.05/1.13	 top(ok(X:S)) -> top(active(X:S))
1.05/1.13	
1.05/1.13	Problem 1.21: 
1.05/1.13	
1.05/1.13	Reduction Pairs Processor:
1.05/1.13	-> Pairs:
1.05/1.13	 TOP(ok(X:S)) -> TOP(active(X:S))
1.05/1.13	-> Rules:
1.05/1.13	 U11(mark(X:S)) -> mark(U11(X:S))
1.05/1.13	 U11(ok(X:S)) -> ok(U11(X:S))
1.05/1.13	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.05/1.13	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.05/1.13	 U22(mark(X:S)) -> mark(U22(X:S))
1.05/1.13	 U22(ok(X:S)) -> ok(U22(X:S))
1.05/1.13	 U31(mark(X:S)) -> mark(U31(X:S))
1.05/1.13	 U31(ok(X:S)) -> ok(U31(X:S))
1.05/1.13	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.05/1.13	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.05/1.13	 U42(mark(X:S)) -> mark(U42(X:S))
1.05/1.13	 U42(ok(X:S)) -> ok(U42(X:S))
1.05/1.13	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.05/1.13	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.05/1.13	 U52(mark(X:S)) -> mark(U52(X:S))
1.05/1.13	 U52(ok(X:S)) -> ok(U52(X:S))
1.05/1.13	 U61(mark(X:S)) -> mark(U61(X:S))
1.05/1.13	 U61(ok(X:S)) -> ok(U61(X:S))
1.05/1.13	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.05/1.13	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.05/1.13	 U72(mark(X:S)) -> mark(U72(X:S))
1.05/1.13	 U72(ok(X:S)) -> ok(U72(X:S))
1.05/1.13	 U81(mark(X:S)) -> mark(U81(X:S))
1.05/1.13	 U81(ok(X:S)) -> ok(U81(X:S))
1.05/1.13	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.05/1.13	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.05/1.13	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.05/1.13	 active(U11(tt)) -> mark(tt)
1.05/1.13	 active(U11(X:S)) -> U11(active(X:S))
1.05/1.13	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.05/1.13	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.05/1.13	 active(U22(tt)) -> mark(tt)
1.05/1.13	 active(U22(X:S)) -> U22(active(X:S))
1.05/1.13	 active(U31(tt)) -> mark(tt)
1.05/1.13	 active(U31(X:S)) -> U31(active(X:S))
1.05/1.13	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.05/1.13	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.05/1.13	 active(U42(tt)) -> mark(tt)
1.05/1.13	 active(U42(X:S)) -> U42(active(X:S))
1.05/1.13	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.05/1.13	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.05/1.13	 active(U52(tt)) -> mark(tt)
1.05/1.13	 active(U52(X:S)) -> U52(active(X:S))
1.05/1.13	 active(U61(tt)) -> mark(tt)
1.05/1.13	 active(U61(X:S)) -> U61(active(X:S))
1.05/1.13	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.05/1.13	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.05/1.13	 active(U72(tt)) -> mark(tt)
1.05/1.13	 active(U72(X:S)) -> U72(active(X:S))
1.05/1.13	 active(U81(tt)) -> mark(tt)
1.05/1.13	 active(U81(X:S)) -> U81(active(X:S))
1.05/1.13	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.05/1.13	 active(__(nil,X:S)) -> mark(X:S)
1.05/1.13	 active(__(X:S,nil)) -> mark(X:S)
1.05/1.13	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.05/1.13	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.05/1.13	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.05/1.13	 active(isList(nil)) -> mark(tt)
1.05/1.13	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.05/1.13	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.05/1.13	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.05/1.13	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.05/1.13	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.05/1.13	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.05/1.13	 active(isPal(nil)) -> mark(tt)
1.05/1.13	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.05/1.13	 active(isQid(a)) -> mark(tt)
1.05/1.13	 active(isQid(e)) -> mark(tt)
1.05/1.13	 active(isQid(i)) -> mark(tt)
1.05/1.13	 active(isQid(o)) -> mark(tt)
1.05/1.13	 active(isQid(u)) -> mark(tt)
1.05/1.13	 isList(ok(X:S)) -> ok(isList(X:S))
1.05/1.13	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.05/1.13	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.05/1.13	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.05/1.13	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.05/1.13	 proper(U11(X:S)) -> U11(proper(X:S))
1.05/1.13	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.05/1.13	 proper(U22(X:S)) -> U22(proper(X:S))
1.05/1.13	 proper(U31(X:S)) -> U31(proper(X:S))
1.05/1.13	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.05/1.13	 proper(U42(X:S)) -> U42(proper(X:S))
1.05/1.13	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.05/1.13	 proper(U52(X:S)) -> U52(proper(X:S))
1.05/1.13	 proper(U61(X:S)) -> U61(proper(X:S))
1.05/1.13	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.05/1.13	 proper(U72(X:S)) -> U72(proper(X:S))
1.05/1.13	 proper(U81(X:S)) -> U81(proper(X:S))
1.05/1.13	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.05/1.13	 proper(isList(X:S)) -> isList(proper(X:S))
1.05/1.13	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.05/1.13	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.05/1.13	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.05/1.13	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.05/1.13	 proper(a) -> ok(a)
1.05/1.13	 proper(e) -> ok(e)
1.05/1.13	 proper(i) -> ok(i)
1.05/1.13	 proper(nil) -> ok(nil)
1.05/1.13	 proper(o) -> ok(o)
1.05/1.13	 proper(tt) -> ok(tt)
1.05/1.13	 proper(u) -> ok(u)
1.05/1.13	 top(mark(X:S)) -> top(proper(X:S))
1.05/1.13	 top(ok(X:S)) -> top(active(X:S))
1.05/1.13	-> Usable rules:
1.05/1.13	 U11(mark(X:S)) -> mark(U11(X:S))
1.05/1.13	 U11(ok(X:S)) -> ok(U11(X:S))
1.05/1.13	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.05/1.13	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.05/1.13	 U22(mark(X:S)) -> mark(U22(X:S))
1.05/1.13	 U22(ok(X:S)) -> ok(U22(X:S))
1.05/1.13	 U31(mark(X:S)) -> mark(U31(X:S))
1.05/1.13	 U31(ok(X:S)) -> ok(U31(X:S))
1.05/1.13	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.05/1.13	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.05/1.13	 U42(mark(X:S)) -> mark(U42(X:S))
1.05/1.13	 U42(ok(X:S)) -> ok(U42(X:S))
1.05/1.13	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.05/1.13	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.05/1.13	 U52(mark(X:S)) -> mark(U52(X:S))
1.05/1.13	 U52(ok(X:S)) -> ok(U52(X:S))
1.05/1.13	 U61(mark(X:S)) -> mark(U61(X:S))
1.05/1.13	 U61(ok(X:S)) -> ok(U61(X:S))
1.05/1.13	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.05/1.13	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.05/1.13	 U72(mark(X:S)) -> mark(U72(X:S))
1.05/1.13	 U72(ok(X:S)) -> ok(U72(X:S))
1.05/1.13	 U81(mark(X:S)) -> mark(U81(X:S))
1.05/1.13	 U81(ok(X:S)) -> ok(U81(X:S))
1.05/1.13	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.05/1.13	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.05/1.13	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.05/1.13	 active(U11(tt)) -> mark(tt)
1.05/1.13	 active(U11(X:S)) -> U11(active(X:S))
1.05/1.13	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.05/1.13	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.05/1.13	 active(U22(tt)) -> mark(tt)
1.05/1.13	 active(U22(X:S)) -> U22(active(X:S))
1.05/1.13	 active(U31(tt)) -> mark(tt)
1.05/1.13	 active(U31(X:S)) -> U31(active(X:S))
1.05/1.13	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.05/1.13	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.05/1.13	 active(U42(tt)) -> mark(tt)
1.05/1.13	 active(U42(X:S)) -> U42(active(X:S))
1.05/1.13	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.05/1.13	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.05/1.13	 active(U52(tt)) -> mark(tt)
1.05/1.13	 active(U52(X:S)) -> U52(active(X:S))
1.05/1.13	 active(U61(tt)) -> mark(tt)
1.05/1.13	 active(U61(X:S)) -> U61(active(X:S))
1.05/1.13	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.05/1.13	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.05/1.13	 active(U72(tt)) -> mark(tt)
1.05/1.13	 active(U72(X:S)) -> U72(active(X:S))
1.05/1.13	 active(U81(tt)) -> mark(tt)
1.05/1.13	 active(U81(X:S)) -> U81(active(X:S))
1.05/1.13	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.05/1.13	 active(__(nil,X:S)) -> mark(X:S)
1.05/1.13	 active(__(X:S,nil)) -> mark(X:S)
1.05/1.13	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.05/1.13	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.05/1.13	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.05/1.13	 active(isList(nil)) -> mark(tt)
1.05/1.13	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.05/1.13	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.05/1.13	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.05/1.13	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.05/1.13	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.05/1.13	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.05/1.13	 active(isPal(nil)) -> mark(tt)
1.05/1.13	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.05/1.13	 active(isQid(a)) -> mark(tt)
1.05/1.13	 active(isQid(e)) -> mark(tt)
1.05/1.13	 active(isQid(i)) -> mark(tt)
1.05/1.13	 active(isQid(o)) -> mark(tt)
1.05/1.13	 active(isQid(u)) -> mark(tt)
1.05/1.13	 isList(ok(X:S)) -> ok(isList(X:S))
1.05/1.13	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.05/1.13	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.05/1.13	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.05/1.13	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.05/1.13	->Interpretation type:
1.05/1.13	 Linear
1.05/1.13	->Coefficients:
1.05/1.13	 Natural Numbers
1.05/1.13	->Dimension:
1.05/1.13	 1
1.05/1.13	->Bound:
1.05/1.13	 2
1.05/1.13	->Interpretation:
1.05/1.13	 
1.05/1.13	[U11](X) = 2.X + 2
1.05/1.13	[U21](X1,X2) = 2.X2 + 2
1.05/1.13	[U22](X) = 2.X + 2
1.05/1.13	[U31](X) = 2.X + 2
1.05/1.13	[U41](X1,X2) = 2.X2 + 2
1.05/1.13	[U42](X) = 2.X + 1
1.05/1.13	[U51](X1,X2) = 2.X1 + 2
1.05/1.13	[U52](X) = 2.X + 1
1.05/1.13	[U61](X) = 2.X + 2
1.05/1.13	[U71](X1,X2) = X1 + 2.X2 + 1
1.05/1.13	[U72](X) = 2.X + 2
1.05/1.13	[U81](X) = 2.X + 2
1.05/1.13	[__](X1,X2) = 2.X2 + 2
1.05/1.13	[active](X) = 2.X + 1
1.05/1.13	[isList](X) = 2.X + 2
1.05/1.13	[isNeList](X) = 2.X + 2
1.05/1.13	[isNePal](X) = 2.X + 1
1.05/1.13	[isPal](X) = 2.X + 2
1.05/1.13	[isQid](X) = X
1.05/1.13	[proper](X) = 0
1.05/1.13	[top](X) = 0
1.05/1.13	[a] = 1
1.05/1.13	[e] = 2
1.05/1.13	[fSNonEmpty] = 0
1.05/1.13	[i] = 2
1.05/1.13	[mark](X) = 2
1.05/1.13	[nil] = 1
1.05/1.13	[o] = 2
1.05/1.13	[ok](X) = 2.X + 2
1.05/1.13	[tt] = 0
1.05/1.13	[u] = 2
1.05/1.13	[U11#](X) = 0
1.05/1.13	[U21#](X1,X2) = 0
1.05/1.13	[U22#](X) = 0
1.05/1.13	[U31#](X) = 0
1.05/1.13	[U41#](X1,X2) = 0
1.05/1.13	[U42#](X) = 0
1.05/1.13	[U51#](X1,X2) = 0
1.05/1.13	[U52#](X) = 0
1.05/1.13	[U61#](X) = 0
1.05/1.13	[U71#](X1,X2) = 0
1.05/1.13	[U72#](X) = 0
1.05/1.13	[U81#](X) = 0
1.05/1.13	[__#](X1,X2) = 0
1.05/1.13	[ACTIVE](X) = 0
1.05/1.13	[ISLIST](X) = 0
1.05/1.13	[ISNELIST](X) = 0
1.05/1.13	[ISNEPAL](X) = 0
1.05/1.13	[ISPAL](X) = 0
1.05/1.13	[ISQID](X) = 0
1.05/1.13	[PROPER](X) = 0
1.05/1.13	[TOP](X) = 2.X
1.05/1.13	
1.05/1.13	Problem 1.21: 
1.05/1.13	
1.05/1.13	SCC Processor:
1.05/1.13	-> Pairs:
1.05/1.13	 Empty
1.05/1.13	-> Rules:
1.05/1.13	 U11(mark(X:S)) -> mark(U11(X:S))
1.05/1.13	 U11(ok(X:S)) -> ok(U11(X:S))
1.05/1.13	 U21(mark(X1:S),X2:S) -> mark(U21(X1:S,X2:S))
1.05/1.13	 U21(ok(X1:S),ok(X2:S)) -> ok(U21(X1:S,X2:S))
1.05/1.13	 U22(mark(X:S)) -> mark(U22(X:S))
1.05/1.13	 U22(ok(X:S)) -> ok(U22(X:S))
1.05/1.13	 U31(mark(X:S)) -> mark(U31(X:S))
1.05/1.13	 U31(ok(X:S)) -> ok(U31(X:S))
1.05/1.13	 U41(mark(X1:S),X2:S) -> mark(U41(X1:S,X2:S))
1.05/1.13	 U41(ok(X1:S),ok(X2:S)) -> ok(U41(X1:S,X2:S))
1.05/1.13	 U42(mark(X:S)) -> mark(U42(X:S))
1.05/1.13	 U42(ok(X:S)) -> ok(U42(X:S))
1.05/1.13	 U51(mark(X1:S),X2:S) -> mark(U51(X1:S,X2:S))
1.05/1.13	 U51(ok(X1:S),ok(X2:S)) -> ok(U51(X1:S,X2:S))
1.05/1.13	 U52(mark(X:S)) -> mark(U52(X:S))
1.05/1.13	 U52(ok(X:S)) -> ok(U52(X:S))
1.05/1.13	 U61(mark(X:S)) -> mark(U61(X:S))
1.05/1.13	 U61(ok(X:S)) -> ok(U61(X:S))
1.05/1.13	 U71(mark(X1:S),X2:S) -> mark(U71(X1:S,X2:S))
1.05/1.13	 U71(ok(X1:S),ok(X2:S)) -> ok(U71(X1:S,X2:S))
1.05/1.13	 U72(mark(X:S)) -> mark(U72(X:S))
1.05/1.13	 U72(ok(X:S)) -> ok(U72(X:S))
1.05/1.13	 U81(mark(X:S)) -> mark(U81(X:S))
1.05/1.13	 U81(ok(X:S)) -> ok(U81(X:S))
1.05/1.13	 __(mark(X1:S),X2:S) -> mark(__(X1:S,X2:S))
1.05/1.13	 __(ok(X1:S),ok(X2:S)) -> ok(__(X1:S,X2:S))
1.05/1.13	 __(X1:S,mark(X2:S)) -> mark(__(X1:S,X2:S))
1.05/1.13	 active(U11(tt)) -> mark(tt)
1.05/1.13	 active(U11(X:S)) -> U11(active(X:S))
1.05/1.13	 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S)))
1.05/1.13	 active(U21(X1:S,X2:S)) -> U21(active(X1:S),X2:S)
1.05/1.13	 active(U22(tt)) -> mark(tt)
1.05/1.13	 active(U22(X:S)) -> U22(active(X:S))
1.05/1.13	 active(U31(tt)) -> mark(tt)
1.05/1.13	 active(U31(X:S)) -> U31(active(X:S))
1.05/1.13	 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S)))
1.05/1.13	 active(U41(X1:S,X2:S)) -> U41(active(X1:S),X2:S)
1.05/1.13	 active(U42(tt)) -> mark(tt)
1.05/1.13	 active(U42(X:S)) -> U42(active(X:S))
1.05/1.13	 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S)))
1.05/1.13	 active(U51(X1:S,X2:S)) -> U51(active(X1:S),X2:S)
1.05/1.13	 active(U52(tt)) -> mark(tt)
1.05/1.13	 active(U52(X:S)) -> U52(active(X:S))
1.05/1.13	 active(U61(tt)) -> mark(tt)
1.05/1.13	 active(U61(X:S)) -> U61(active(X:S))
1.05/1.13	 active(U71(tt,P:S)) -> mark(U72(isPal(P:S)))
1.05/1.13	 active(U71(X1:S,X2:S)) -> U71(active(X1:S),X2:S)
1.05/1.13	 active(U72(tt)) -> mark(tt)
1.05/1.13	 active(U72(X:S)) -> U72(active(X:S))
1.05/1.13	 active(U81(tt)) -> mark(tt)
1.05/1.13	 active(U81(X:S)) -> U81(active(X:S))
1.05/1.13	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.05/1.13	 active(__(nil,X:S)) -> mark(X:S)
1.05/1.13	 active(__(X:S,nil)) -> mark(X:S)
1.05/1.13	 active(__(X1:S,X2:S)) -> __(active(X1:S),X2:S)
1.05/1.13	 active(__(X1:S,X2:S)) -> __(X1:S,active(X2:S))
1.05/1.13	 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S))
1.05/1.13	 active(isList(nil)) -> mark(tt)
1.05/1.13	 active(isList(V:S)) -> mark(U11(isNeList(V:S)))
1.05/1.13	 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S))
1.05/1.13	 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S))
1.05/1.13	 active(isNeList(V:S)) -> mark(U31(isQid(V:S)))
1.05/1.13	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S))
1.05/1.13	 active(isNePal(V:S)) -> mark(U61(isQid(V:S)))
1.05/1.13	 active(isPal(nil)) -> mark(tt)
1.05/1.13	 active(isPal(V:S)) -> mark(U81(isNePal(V:S)))
1.05/1.13	 active(isQid(a)) -> mark(tt)
1.05/1.13	 active(isQid(e)) -> mark(tt)
1.05/1.13	 active(isQid(i)) -> mark(tt)
1.05/1.13	 active(isQid(o)) -> mark(tt)
1.05/1.13	 active(isQid(u)) -> mark(tt)
1.05/1.13	 isList(ok(X:S)) -> ok(isList(X:S))
1.05/1.13	 isNeList(ok(X:S)) -> ok(isNeList(X:S))
1.05/1.13	 isNePal(ok(X:S)) -> ok(isNePal(X:S))
1.05/1.13	 isPal(ok(X:S)) -> ok(isPal(X:S))
1.05/1.13	 isQid(ok(X:S)) -> ok(isQid(X:S))
1.05/1.13	 proper(U11(X:S)) -> U11(proper(X:S))
1.05/1.13	 proper(U21(X1:S,X2:S)) -> U21(proper(X1:S),proper(X2:S))
1.05/1.13	 proper(U22(X:S)) -> U22(proper(X:S))
1.05/1.13	 proper(U31(X:S)) -> U31(proper(X:S))
1.05/1.13	 proper(U41(X1:S,X2:S)) -> U41(proper(X1:S),proper(X2:S))
1.05/1.13	 proper(U42(X:S)) -> U42(proper(X:S))
1.05/1.13	 proper(U51(X1:S,X2:S)) -> U51(proper(X1:S),proper(X2:S))
1.05/1.13	 proper(U52(X:S)) -> U52(proper(X:S))
1.05/1.13	 proper(U61(X:S)) -> U61(proper(X:S))
1.05/1.13	 proper(U71(X1:S,X2:S)) -> U71(proper(X1:S),proper(X2:S))
1.05/1.13	 proper(U72(X:S)) -> U72(proper(X:S))
1.05/1.13	 proper(U81(X:S)) -> U81(proper(X:S))
1.05/1.13	 proper(__(X1:S,X2:S)) -> __(proper(X1:S),proper(X2:S))
1.05/1.13	 proper(isList(X:S)) -> isList(proper(X:S))
1.05/1.13	 proper(isNeList(X:S)) -> isNeList(proper(X:S))
1.05/1.13	 proper(isNePal(X:S)) -> isNePal(proper(X:S))
1.05/1.13	 proper(isPal(X:S)) -> isPal(proper(X:S))
1.05/1.13	 proper(isQid(X:S)) -> isQid(proper(X:S))
1.05/1.13	 proper(a) -> ok(a)
1.05/1.13	 proper(e) -> ok(e)
1.05/1.13	 proper(i) -> ok(i)
1.05/1.13	 proper(nil) -> ok(nil)
1.05/1.13	 proper(o) -> ok(o)
1.05/1.13	 proper(tt) -> ok(tt)
1.05/1.13	 proper(u) -> ok(u)
1.05/1.13	 top(mark(X:S)) -> top(proper(X:S))
1.05/1.13	 top(ok(X:S)) -> top(active(X:S))
1.05/1.13	->Strongly Connected Components:
1.05/1.13	 There is no strongly connected component
1.05/1.13	
1.05/1.13	The problem is finite.
1.05/1.13	EOF