1.15/1.17	YES
1.15/1.17	
1.15/1.17	Problem 1: 
1.15/1.17	
1.15/1.17	(VAR v_NonEmpty:S I:S P:S V:S V1:S V2:S X:S X1:S X2:S Y:S Z:S)
1.15/1.17	(RULES
1.15/1.17	__(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.17	__(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.17	__(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.15/1.17	__(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.15/1.17	active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.15/1.17	active(__(nil,X:S)) -> mark(X:S)
1.15/1.17	active(__(X:S,nil)) -> mark(X:S)
1.15/1.17	active(and(tt,X:S)) -> mark(X:S)
1.15/1.17	active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.15/1.17	active(isList(nil)) -> mark(tt)
1.15/1.17	active(isList(V:S)) -> mark(isNeList(V:S))
1.15/1.17	active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.15/1.17	active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.15/1.17	active(isNeList(V:S)) -> mark(isQid(V:S))
1.15/1.17	active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.15/1.17	active(isNePal(V:S)) -> mark(isQid(V:S))
1.15/1.17	active(isPal(nil)) -> mark(tt)
1.15/1.17	active(isPal(V:S)) -> mark(isNePal(V:S))
1.15/1.17	active(isQid(a)) -> mark(tt)
1.15/1.17	active(isQid(e)) -> mark(tt)
1.15/1.17	active(isQid(i)) -> mark(tt)
1.15/1.17	active(isQid(o)) -> mark(tt)
1.15/1.17	active(isQid(u)) -> mark(tt)
1.15/1.17	and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.17	and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.17	and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.15/1.17	and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.15/1.17	isList(active(X:S)) -> isList(X:S)
1.15/1.17	isList(mark(X:S)) -> isList(X:S)
1.15/1.17	isNeList(active(X:S)) -> isNeList(X:S)
1.15/1.17	isNeList(mark(X:S)) -> isNeList(X:S)
1.15/1.17	isNePal(active(X:S)) -> isNePal(X:S)
1.15/1.17	isNePal(mark(X:S)) -> isNePal(X:S)
1.15/1.17	isPal(active(X:S)) -> isPal(X:S)
1.15/1.17	isPal(mark(X:S)) -> isPal(X:S)
1.15/1.17	isQid(active(X:S)) -> isQid(X:S)
1.15/1.17	isQid(mark(X:S)) -> isQid(X:S)
1.15/1.17	mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.15/1.17	mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.15/1.17	mark(isList(X:S)) -> active(isList(X:S))
1.15/1.17	mark(isNeList(X:S)) -> active(isNeList(X:S))
1.15/1.17	mark(isNePal(X:S)) -> active(isNePal(X:S))
1.15/1.17	mark(isPal(X:S)) -> active(isPal(X:S))
1.15/1.17	mark(isQid(X:S)) -> active(isQid(X:S))
1.15/1.17	mark(a) -> active(a)
1.15/1.17	mark(e) -> active(e)
1.15/1.17	mark(i) -> active(i)
1.15/1.17	mark(nil) -> active(nil)
1.15/1.17	mark(o) -> active(o)
1.15/1.17	mark(tt) -> active(tt)
1.15/1.17	mark(u) -> active(u)
1.15/1.17	) 
1.15/1.17	(STRATEGY INNERMOST)
1.15/1.17	
1.15/1.17	Problem 1: 
1.15/1.17	
1.15/1.17	Dependency Pairs Processor:
1.15/1.17	-> Pairs:
1.15/1.17	 __#(active(X1:S),X2:S) -> __#(X1:S,X2:S)
1.15/1.17	 __#(mark(X1:S),X2:S) -> __#(X1:S,X2:S)
1.15/1.17	 __#(X1:S,active(X2:S)) -> __#(X1:S,X2:S)
1.15/1.17	 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S)
1.15/1.17	 ACTIVE(__(__(X:S,Y:S),Z:S)) -> __#(X:S,__(Y:S,Z:S))
1.15/1.17	 ACTIVE(__(__(X:S,Y:S),Z:S)) -> __#(Y:S,Z:S)
1.15/1.17	 ACTIVE(__(__(X:S,Y:S),Z:S)) -> MARK(__(X:S,__(Y:S,Z:S)))
1.15/1.17	 ACTIVE(__(nil,X:S)) -> MARK(X:S)
1.15/1.17	 ACTIVE(__(X:S,nil)) -> MARK(X:S)
1.15/1.17	 ACTIVE(and(tt,X:S)) -> MARK(X:S)
1.15/1.17	 ACTIVE(isList(__(V1:S,V2:S))) -> AND(isList(V1:S),isList(V2:S))
1.15/1.17	 ACTIVE(isList(__(V1:S,V2:S))) -> ISLIST(V1:S)
1.15/1.17	 ACTIVE(isList(__(V1:S,V2:S))) -> ISLIST(V2:S)
1.15/1.17	 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(and(isList(V1:S),isList(V2:S)))
1.15/1.17	 ACTIVE(isList(nil)) -> MARK(tt)
1.15/1.17	 ACTIVE(isList(V:S)) -> ISNELIST(V:S)
1.15/1.17	 ACTIVE(isList(V:S)) -> MARK(isNeList(V:S))
1.15/1.17	 ACTIVE(isNeList(__(V1:S,V2:S))) -> AND(isList(V1:S),isNeList(V2:S))
1.15/1.17	 ACTIVE(isNeList(__(V1:S,V2:S))) -> AND(isNeList(V1:S),isList(V2:S))
1.15/1.17	 ACTIVE(isNeList(__(V1:S,V2:S))) -> ISLIST(V1:S)
1.15/1.17	 ACTIVE(isNeList(__(V1:S,V2:S))) -> ISLIST(V2:S)
1.15/1.17	 ACTIVE(isNeList(__(V1:S,V2:S))) -> ISNELIST(V1:S)
1.15/1.17	 ACTIVE(isNeList(__(V1:S,V2:S))) -> ISNELIST(V2:S)
1.15/1.17	 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(and(isList(V1:S),isNeList(V2:S)))
1.15/1.17	 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(and(isNeList(V1:S),isList(V2:S)))
1.15/1.17	 ACTIVE(isNeList(V:S)) -> ISQID(V:S)
1.15/1.17	 ACTIVE(isNeList(V:S)) -> MARK(isQid(V:S))
1.15/1.17	 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> AND(isQid(I:S),isPal(P:S))
1.15/1.17	 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> ISPAL(P:S)
1.15/1.17	 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> ISQID(I:S)
1.15/1.17	 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(and(isQid(I:S),isPal(P:S)))
1.15/1.17	 ACTIVE(isNePal(V:S)) -> ISQID(V:S)
1.15/1.17	 ACTIVE(isNePal(V:S)) -> MARK(isQid(V:S))
1.15/1.17	 ACTIVE(isPal(nil)) -> MARK(tt)
1.15/1.17	 ACTIVE(isPal(V:S)) -> ISNEPAL(V:S)
1.15/1.17	 ACTIVE(isPal(V:S)) -> MARK(isNePal(V:S))
1.15/1.17	 ACTIVE(isQid(a)) -> MARK(tt)
1.15/1.17	 ACTIVE(isQid(e)) -> MARK(tt)
1.15/1.17	 ACTIVE(isQid(i)) -> MARK(tt)
1.15/1.17	 ACTIVE(isQid(o)) -> MARK(tt)
1.15/1.17	 ACTIVE(isQid(u)) -> MARK(tt)
1.15/1.17	 AND(active(X1:S),X2:S) -> AND(X1:S,X2:S)
1.15/1.17	 AND(mark(X1:S),X2:S) -> AND(X1:S,X2:S)
1.15/1.17	 AND(X1:S,active(X2:S)) -> AND(X1:S,X2:S)
1.15/1.17	 AND(X1:S,mark(X2:S)) -> AND(X1:S,X2:S)
1.15/1.17	 ISLIST(active(X:S)) -> ISLIST(X:S)
1.15/1.17	 ISLIST(mark(X:S)) -> ISLIST(X:S)
1.15/1.17	 ISNELIST(active(X:S)) -> ISNELIST(X:S)
1.15/1.17	 ISNELIST(mark(X:S)) -> ISNELIST(X:S)
1.15/1.17	 ISNEPAL(active(X:S)) -> ISNEPAL(X:S)
1.15/1.17	 ISNEPAL(mark(X:S)) -> ISNEPAL(X:S)
1.15/1.17	 ISPAL(active(X:S)) -> ISPAL(X:S)
1.15/1.17	 ISPAL(mark(X:S)) -> ISPAL(X:S)
1.15/1.17	 ISQID(active(X:S)) -> ISQID(X:S)
1.15/1.17	 ISQID(mark(X:S)) -> ISQID(X:S)
1.15/1.17	 MARK(__(X1:S,X2:S)) -> __#(mark(X1:S),mark(X2:S))
1.15/1.17	 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
1.15/1.17	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.15/1.17	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.15/1.17	 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S))
1.15/1.17	 MARK(and(X1:S,X2:S)) -> AND(mark(X1:S),X2:S)
1.15/1.17	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
1.15/1.17	 MARK(isList(X:S)) -> ACTIVE(isList(X:S))
1.15/1.17	 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
1.15/1.17	 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
1.15/1.17	 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
1.15/1.17	 MARK(isQid(X:S)) -> ACTIVE(isQid(X:S))
1.15/1.17	-> Rules:
1.15/1.17	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.17	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.17	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.15/1.17	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.15/1.17	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.15/1.17	 active(__(nil,X:S)) -> mark(X:S)
1.15/1.17	 active(__(X:S,nil)) -> mark(X:S)
1.15/1.17	 active(and(tt,X:S)) -> mark(X:S)
1.15/1.17	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.15/1.17	 active(isList(nil)) -> mark(tt)
1.15/1.17	 active(isList(V:S)) -> mark(isNeList(V:S))
1.15/1.17	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.15/1.17	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.15/1.17	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.15/1.17	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.15/1.17	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.15/1.17	 active(isPal(nil)) -> mark(tt)
1.15/1.17	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.15/1.17	 active(isQid(a)) -> mark(tt)
1.15/1.17	 active(isQid(e)) -> mark(tt)
1.15/1.17	 active(isQid(i)) -> mark(tt)
1.15/1.17	 active(isQid(o)) -> mark(tt)
1.15/1.17	 active(isQid(u)) -> mark(tt)
1.15/1.17	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.17	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.17	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.15/1.17	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.15/1.17	 isList(active(X:S)) -> isList(X:S)
1.15/1.17	 isList(mark(X:S)) -> isList(X:S)
1.15/1.17	 isNeList(active(X:S)) -> isNeList(X:S)
1.15/1.17	 isNeList(mark(X:S)) -> isNeList(X:S)
1.15/1.17	 isNePal(active(X:S)) -> isNePal(X:S)
1.15/1.17	 isNePal(mark(X:S)) -> isNePal(X:S)
1.15/1.17	 isPal(active(X:S)) -> isPal(X:S)
1.15/1.17	 isPal(mark(X:S)) -> isPal(X:S)
1.15/1.17	 isQid(active(X:S)) -> isQid(X:S)
1.15/1.17	 isQid(mark(X:S)) -> isQid(X:S)
1.15/1.17	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.15/1.17	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.15/1.17	 mark(isList(X:S)) -> active(isList(X:S))
1.15/1.17	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.15/1.17	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.15/1.17	 mark(isPal(X:S)) -> active(isPal(X:S))
1.15/1.17	 mark(isQid(X:S)) -> active(isQid(X:S))
1.15/1.17	 mark(a) -> active(a)
1.15/1.17	 mark(e) -> active(e)
1.15/1.17	 mark(i) -> active(i)
1.15/1.17	 mark(nil) -> active(nil)
1.15/1.17	 mark(o) -> active(o)
1.15/1.17	 mark(tt) -> active(tt)
1.15/1.17	 mark(u) -> active(u)
1.15/1.17	
1.15/1.17	Problem 1: 
1.15/1.17	
1.15/1.17	SCC Processor:
1.15/1.17	-> Pairs:
1.15/1.17	 __#(active(X1:S),X2:S) -> __#(X1:S,X2:S)
1.15/1.17	 __#(mark(X1:S),X2:S) -> __#(X1:S,X2:S)
1.15/1.17	 __#(X1:S,active(X2:S)) -> __#(X1:S,X2:S)
1.15/1.17	 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S)
1.15/1.17	 ACTIVE(__(__(X:S,Y:S),Z:S)) -> __#(X:S,__(Y:S,Z:S))
1.15/1.17	 ACTIVE(__(__(X:S,Y:S),Z:S)) -> __#(Y:S,Z:S)
1.15/1.17	 ACTIVE(__(__(X:S,Y:S),Z:S)) -> MARK(__(X:S,__(Y:S,Z:S)))
1.15/1.17	 ACTIVE(__(nil,X:S)) -> MARK(X:S)
1.15/1.17	 ACTIVE(__(X:S,nil)) -> MARK(X:S)
1.15/1.17	 ACTIVE(and(tt,X:S)) -> MARK(X:S)
1.15/1.17	 ACTIVE(isList(__(V1:S,V2:S))) -> AND(isList(V1:S),isList(V2:S))
1.15/1.17	 ACTIVE(isList(__(V1:S,V2:S))) -> ISLIST(V1:S)
1.15/1.17	 ACTIVE(isList(__(V1:S,V2:S))) -> ISLIST(V2:S)
1.15/1.17	 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(and(isList(V1:S),isList(V2:S)))
1.15/1.17	 ACTIVE(isList(nil)) -> MARK(tt)
1.15/1.17	 ACTIVE(isList(V:S)) -> ISNELIST(V:S)
1.15/1.17	 ACTIVE(isList(V:S)) -> MARK(isNeList(V:S))
1.15/1.17	 ACTIVE(isNeList(__(V1:S,V2:S))) -> AND(isList(V1:S),isNeList(V2:S))
1.15/1.17	 ACTIVE(isNeList(__(V1:S,V2:S))) -> AND(isNeList(V1:S),isList(V2:S))
1.15/1.17	 ACTIVE(isNeList(__(V1:S,V2:S))) -> ISLIST(V1:S)
1.15/1.17	 ACTIVE(isNeList(__(V1:S,V2:S))) -> ISLIST(V2:S)
1.15/1.17	 ACTIVE(isNeList(__(V1:S,V2:S))) -> ISNELIST(V1:S)
1.15/1.17	 ACTIVE(isNeList(__(V1:S,V2:S))) -> ISNELIST(V2:S)
1.15/1.17	 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(and(isList(V1:S),isNeList(V2:S)))
1.15/1.17	 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(and(isNeList(V1:S),isList(V2:S)))
1.15/1.17	 ACTIVE(isNeList(V:S)) -> ISQID(V:S)
1.15/1.17	 ACTIVE(isNeList(V:S)) -> MARK(isQid(V:S))
1.15/1.17	 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> AND(isQid(I:S),isPal(P:S))
1.15/1.17	 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> ISPAL(P:S)
1.15/1.17	 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> ISQID(I:S)
1.15/1.17	 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(and(isQid(I:S),isPal(P:S)))
1.15/1.17	 ACTIVE(isNePal(V:S)) -> ISQID(V:S)
1.15/1.17	 ACTIVE(isNePal(V:S)) -> MARK(isQid(V:S))
1.15/1.17	 ACTIVE(isPal(nil)) -> MARK(tt)
1.15/1.17	 ACTIVE(isPal(V:S)) -> ISNEPAL(V:S)
1.15/1.17	 ACTIVE(isPal(V:S)) -> MARK(isNePal(V:S))
1.15/1.17	 ACTIVE(isQid(a)) -> MARK(tt)
1.15/1.17	 ACTIVE(isQid(e)) -> MARK(tt)
1.15/1.17	 ACTIVE(isQid(i)) -> MARK(tt)
1.15/1.17	 ACTIVE(isQid(o)) -> MARK(tt)
1.15/1.17	 ACTIVE(isQid(u)) -> MARK(tt)
1.15/1.17	 AND(active(X1:S),X2:S) -> AND(X1:S,X2:S)
1.15/1.17	 AND(mark(X1:S),X2:S) -> AND(X1:S,X2:S)
1.15/1.17	 AND(X1:S,active(X2:S)) -> AND(X1:S,X2:S)
1.15/1.17	 AND(X1:S,mark(X2:S)) -> AND(X1:S,X2:S)
1.15/1.17	 ISLIST(active(X:S)) -> ISLIST(X:S)
1.15/1.17	 ISLIST(mark(X:S)) -> ISLIST(X:S)
1.15/1.17	 ISNELIST(active(X:S)) -> ISNELIST(X:S)
1.15/1.17	 ISNELIST(mark(X:S)) -> ISNELIST(X:S)
1.15/1.17	 ISNEPAL(active(X:S)) -> ISNEPAL(X:S)
1.15/1.17	 ISNEPAL(mark(X:S)) -> ISNEPAL(X:S)
1.15/1.17	 ISPAL(active(X:S)) -> ISPAL(X:S)
1.15/1.17	 ISPAL(mark(X:S)) -> ISPAL(X:S)
1.15/1.17	 ISQID(active(X:S)) -> ISQID(X:S)
1.15/1.17	 ISQID(mark(X:S)) -> ISQID(X:S)
1.15/1.17	 MARK(__(X1:S,X2:S)) -> __#(mark(X1:S),mark(X2:S))
1.15/1.17	 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
1.15/1.17	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.15/1.17	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.15/1.17	 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S))
1.15/1.17	 MARK(and(X1:S,X2:S)) -> AND(mark(X1:S),X2:S)
1.15/1.17	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
1.15/1.17	 MARK(isList(X:S)) -> ACTIVE(isList(X:S))
1.15/1.17	 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
1.15/1.17	 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
1.15/1.17	 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
1.15/1.17	 MARK(isQid(X:S)) -> ACTIVE(isQid(X:S))
1.15/1.17	-> Rules:
1.15/1.17	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.17	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.17	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.15/1.17	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.15/1.17	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.15/1.17	 active(__(nil,X:S)) -> mark(X:S)
1.15/1.17	 active(__(X:S,nil)) -> mark(X:S)
1.15/1.17	 active(and(tt,X:S)) -> mark(X:S)
1.15/1.17	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.15/1.17	 active(isList(nil)) -> mark(tt)
1.15/1.17	 active(isList(V:S)) -> mark(isNeList(V:S))
1.15/1.17	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.15/1.17	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.15/1.17	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.15/1.17	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.15/1.17	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.15/1.17	 active(isPal(nil)) -> mark(tt)
1.15/1.17	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.15/1.17	 active(isQid(a)) -> mark(tt)
1.15/1.17	 active(isQid(e)) -> mark(tt)
1.15/1.17	 active(isQid(i)) -> mark(tt)
1.15/1.17	 active(isQid(o)) -> mark(tt)
1.15/1.17	 active(isQid(u)) -> mark(tt)
1.15/1.17	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.17	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.17	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.15/1.17	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.15/1.17	 isList(active(X:S)) -> isList(X:S)
1.15/1.17	 isList(mark(X:S)) -> isList(X:S)
1.15/1.17	 isNeList(active(X:S)) -> isNeList(X:S)
1.15/1.17	 isNeList(mark(X:S)) -> isNeList(X:S)
1.15/1.17	 isNePal(active(X:S)) -> isNePal(X:S)
1.15/1.17	 isNePal(mark(X:S)) -> isNePal(X:S)
1.15/1.17	 isPal(active(X:S)) -> isPal(X:S)
1.15/1.17	 isPal(mark(X:S)) -> isPal(X:S)
1.15/1.17	 isQid(active(X:S)) -> isQid(X:S)
1.15/1.17	 isQid(mark(X:S)) -> isQid(X:S)
1.15/1.17	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.15/1.17	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.15/1.17	 mark(isList(X:S)) -> active(isList(X:S))
1.15/1.17	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.15/1.17	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.15/1.17	 mark(isPal(X:S)) -> active(isPal(X:S))
1.15/1.17	 mark(isQid(X:S)) -> active(isQid(X:S))
1.15/1.17	 mark(a) -> active(a)
1.15/1.17	 mark(e) -> active(e)
1.15/1.17	 mark(i) -> active(i)
1.15/1.17	 mark(nil) -> active(nil)
1.15/1.17	 mark(o) -> active(o)
1.15/1.17	 mark(tt) -> active(tt)
1.15/1.17	 mark(u) -> active(u)
1.15/1.17	->Strongly Connected Components:
1.15/1.17	->->Cycle:
1.15/1.17	->->-> Pairs:
1.15/1.17	 ISQID(active(X:S)) -> ISQID(X:S)
1.15/1.17	 ISQID(mark(X:S)) -> ISQID(X:S)
1.15/1.17	->->-> Rules:
1.15/1.17	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.17	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.17	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.15/1.17	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.15/1.17	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.15/1.17	 active(__(nil,X:S)) -> mark(X:S)
1.15/1.17	 active(__(X:S,nil)) -> mark(X:S)
1.15/1.17	 active(and(tt,X:S)) -> mark(X:S)
1.15/1.17	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.15/1.17	 active(isList(nil)) -> mark(tt)
1.15/1.17	 active(isList(V:S)) -> mark(isNeList(V:S))
1.15/1.17	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.15/1.17	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.15/1.17	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.15/1.17	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.15/1.17	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.15/1.17	 active(isPal(nil)) -> mark(tt)
1.15/1.17	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.15/1.17	 active(isQid(a)) -> mark(tt)
1.15/1.17	 active(isQid(e)) -> mark(tt)
1.15/1.17	 active(isQid(i)) -> mark(tt)
1.15/1.17	 active(isQid(o)) -> mark(tt)
1.15/1.17	 active(isQid(u)) -> mark(tt)
1.15/1.17	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.17	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.17	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.15/1.17	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.15/1.17	 isList(active(X:S)) -> isList(X:S)
1.15/1.17	 isList(mark(X:S)) -> isList(X:S)
1.15/1.17	 isNeList(active(X:S)) -> isNeList(X:S)
1.15/1.17	 isNeList(mark(X:S)) -> isNeList(X:S)
1.15/1.17	 isNePal(active(X:S)) -> isNePal(X:S)
1.15/1.17	 isNePal(mark(X:S)) -> isNePal(X:S)
1.15/1.17	 isPal(active(X:S)) -> isPal(X:S)
1.15/1.17	 isPal(mark(X:S)) -> isPal(X:S)
1.15/1.17	 isQid(active(X:S)) -> isQid(X:S)
1.15/1.17	 isQid(mark(X:S)) -> isQid(X:S)
1.15/1.17	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.15/1.17	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.15/1.17	 mark(isList(X:S)) -> active(isList(X:S))
1.15/1.17	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.15/1.17	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.15/1.17	 mark(isPal(X:S)) -> active(isPal(X:S))
1.15/1.17	 mark(isQid(X:S)) -> active(isQid(X:S))
1.15/1.17	 mark(a) -> active(a)
1.15/1.17	 mark(e) -> active(e)
1.15/1.17	 mark(i) -> active(i)
1.15/1.17	 mark(nil) -> active(nil)
1.15/1.17	 mark(o) -> active(o)
1.15/1.17	 mark(tt) -> active(tt)
1.15/1.17	 mark(u) -> active(u)
1.15/1.17	->->Cycle:
1.15/1.17	->->-> Pairs:
1.15/1.17	 ISPAL(active(X:S)) -> ISPAL(X:S)
1.15/1.17	 ISPAL(mark(X:S)) -> ISPAL(X:S)
1.15/1.17	->->-> Rules:
1.15/1.17	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.17	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.17	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.15/1.17	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.15/1.17	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.15/1.17	 active(__(nil,X:S)) -> mark(X:S)
1.15/1.17	 active(__(X:S,nil)) -> mark(X:S)
1.15/1.17	 active(and(tt,X:S)) -> mark(X:S)
1.15/1.17	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.15/1.17	 active(isList(nil)) -> mark(tt)
1.15/1.17	 active(isList(V:S)) -> mark(isNeList(V:S))
1.15/1.17	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.15/1.17	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.15/1.17	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.15/1.17	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.15/1.17	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.15/1.17	 active(isPal(nil)) -> mark(tt)
1.15/1.17	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.15/1.17	 active(isQid(a)) -> mark(tt)
1.15/1.17	 active(isQid(e)) -> mark(tt)
1.15/1.17	 active(isQid(i)) -> mark(tt)
1.15/1.17	 active(isQid(o)) -> mark(tt)
1.15/1.17	 active(isQid(u)) -> mark(tt)
1.15/1.17	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.17	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.17	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.15/1.17	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.15/1.17	 isList(active(X:S)) -> isList(X:S)
1.15/1.17	 isList(mark(X:S)) -> isList(X:S)
1.15/1.17	 isNeList(active(X:S)) -> isNeList(X:S)
1.15/1.17	 isNeList(mark(X:S)) -> isNeList(X:S)
1.15/1.17	 isNePal(active(X:S)) -> isNePal(X:S)
1.15/1.17	 isNePal(mark(X:S)) -> isNePal(X:S)
1.15/1.17	 isPal(active(X:S)) -> isPal(X:S)
1.15/1.17	 isPal(mark(X:S)) -> isPal(X:S)
1.15/1.17	 isQid(active(X:S)) -> isQid(X:S)
1.15/1.17	 isQid(mark(X:S)) -> isQid(X:S)
1.15/1.17	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.15/1.17	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.15/1.17	 mark(isList(X:S)) -> active(isList(X:S))
1.15/1.17	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.15/1.17	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.15/1.17	 mark(isPal(X:S)) -> active(isPal(X:S))
1.15/1.17	 mark(isQid(X:S)) -> active(isQid(X:S))
1.15/1.17	 mark(a) -> active(a)
1.15/1.17	 mark(e) -> active(e)
1.15/1.17	 mark(i) -> active(i)
1.15/1.17	 mark(nil) -> active(nil)
1.15/1.17	 mark(o) -> active(o)
1.15/1.17	 mark(tt) -> active(tt)
1.15/1.17	 mark(u) -> active(u)
1.15/1.17	->->Cycle:
1.15/1.17	->->-> Pairs:
1.15/1.17	 ISNEPAL(active(X:S)) -> ISNEPAL(X:S)
1.15/1.17	 ISNEPAL(mark(X:S)) -> ISNEPAL(X:S)
1.15/1.17	->->-> Rules:
1.15/1.17	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.17	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.17	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.15/1.17	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.15/1.17	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.15/1.17	 active(__(nil,X:S)) -> mark(X:S)
1.15/1.17	 active(__(X:S,nil)) -> mark(X:S)
1.15/1.17	 active(and(tt,X:S)) -> mark(X:S)
1.15/1.17	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.15/1.17	 active(isList(nil)) -> mark(tt)
1.15/1.17	 active(isList(V:S)) -> mark(isNeList(V:S))
1.15/1.17	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.15/1.17	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.15/1.17	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.15/1.17	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.15/1.17	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.15/1.17	 active(isPal(nil)) -> mark(tt)
1.15/1.17	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.15/1.17	 active(isQid(a)) -> mark(tt)
1.15/1.17	 active(isQid(e)) -> mark(tt)
1.15/1.17	 active(isQid(i)) -> mark(tt)
1.15/1.17	 active(isQid(o)) -> mark(tt)
1.15/1.17	 active(isQid(u)) -> mark(tt)
1.15/1.17	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.17	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.17	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.15/1.17	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.15/1.17	 isList(active(X:S)) -> isList(X:S)
1.15/1.17	 isList(mark(X:S)) -> isList(X:S)
1.15/1.17	 isNeList(active(X:S)) -> isNeList(X:S)
1.15/1.17	 isNeList(mark(X:S)) -> isNeList(X:S)
1.15/1.17	 isNePal(active(X:S)) -> isNePal(X:S)
1.15/1.17	 isNePal(mark(X:S)) -> isNePal(X:S)
1.15/1.17	 isPal(active(X:S)) -> isPal(X:S)
1.15/1.17	 isPal(mark(X:S)) -> isPal(X:S)
1.15/1.17	 isQid(active(X:S)) -> isQid(X:S)
1.15/1.17	 isQid(mark(X:S)) -> isQid(X:S)
1.15/1.17	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.15/1.17	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.15/1.17	 mark(isList(X:S)) -> active(isList(X:S))
1.15/1.17	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.15/1.17	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.15/1.17	 mark(isPal(X:S)) -> active(isPal(X:S))
1.15/1.17	 mark(isQid(X:S)) -> active(isQid(X:S))
1.15/1.17	 mark(a) -> active(a)
1.15/1.17	 mark(e) -> active(e)
1.15/1.17	 mark(i) -> active(i)
1.15/1.17	 mark(nil) -> active(nil)
1.15/1.17	 mark(o) -> active(o)
1.15/1.17	 mark(tt) -> active(tt)
1.15/1.17	 mark(u) -> active(u)
1.15/1.17	->->Cycle:
1.15/1.17	->->-> Pairs:
1.15/1.17	 ISNELIST(active(X:S)) -> ISNELIST(X:S)
1.15/1.17	 ISNELIST(mark(X:S)) -> ISNELIST(X:S)
1.15/1.17	->->-> Rules:
1.15/1.17	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.17	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.17	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.15/1.17	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.15/1.17	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.15/1.17	 active(__(nil,X:S)) -> mark(X:S)
1.15/1.17	 active(__(X:S,nil)) -> mark(X:S)
1.15/1.17	 active(and(tt,X:S)) -> mark(X:S)
1.15/1.17	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.15/1.17	 active(isList(nil)) -> mark(tt)
1.15/1.17	 active(isList(V:S)) -> mark(isNeList(V:S))
1.15/1.17	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.15/1.17	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.15/1.17	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.15/1.17	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.15/1.17	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.15/1.17	 active(isPal(nil)) -> mark(tt)
1.15/1.17	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.15/1.17	 active(isQid(a)) -> mark(tt)
1.15/1.17	 active(isQid(e)) -> mark(tt)
1.15/1.17	 active(isQid(i)) -> mark(tt)
1.15/1.17	 active(isQid(o)) -> mark(tt)
1.15/1.17	 active(isQid(u)) -> mark(tt)
1.15/1.17	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.17	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.17	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.15/1.17	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.15/1.17	 isList(active(X:S)) -> isList(X:S)
1.15/1.17	 isList(mark(X:S)) -> isList(X:S)
1.15/1.17	 isNeList(active(X:S)) -> isNeList(X:S)
1.15/1.17	 isNeList(mark(X:S)) -> isNeList(X:S)
1.15/1.17	 isNePal(active(X:S)) -> isNePal(X:S)
1.15/1.17	 isNePal(mark(X:S)) -> isNePal(X:S)
1.15/1.17	 isPal(active(X:S)) -> isPal(X:S)
1.15/1.17	 isPal(mark(X:S)) -> isPal(X:S)
1.15/1.17	 isQid(active(X:S)) -> isQid(X:S)
1.15/1.17	 isQid(mark(X:S)) -> isQid(X:S)
1.15/1.17	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.15/1.17	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.15/1.17	 mark(isList(X:S)) -> active(isList(X:S))
1.15/1.17	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.15/1.17	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.15/1.17	 mark(isPal(X:S)) -> active(isPal(X:S))
1.15/1.17	 mark(isQid(X:S)) -> active(isQid(X:S))
1.15/1.17	 mark(a) -> active(a)
1.15/1.17	 mark(e) -> active(e)
1.15/1.17	 mark(i) -> active(i)
1.15/1.17	 mark(nil) -> active(nil)
1.15/1.17	 mark(o) -> active(o)
1.15/1.17	 mark(tt) -> active(tt)
1.15/1.17	 mark(u) -> active(u)
1.15/1.17	->->Cycle:
1.15/1.17	->->-> Pairs:
1.15/1.17	 ISLIST(active(X:S)) -> ISLIST(X:S)
1.15/1.17	 ISLIST(mark(X:S)) -> ISLIST(X:S)
1.15/1.17	->->-> Rules:
1.15/1.17	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.17	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.17	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.15/1.17	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.15/1.17	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.15/1.17	 active(__(nil,X:S)) -> mark(X:S)
1.15/1.17	 active(__(X:S,nil)) -> mark(X:S)
1.15/1.17	 active(and(tt,X:S)) -> mark(X:S)
1.15/1.17	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.15/1.17	 active(isList(nil)) -> mark(tt)
1.15/1.17	 active(isList(V:S)) -> mark(isNeList(V:S))
1.15/1.17	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.15/1.17	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.15/1.17	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.15/1.17	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.15/1.17	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.15/1.17	 active(isPal(nil)) -> mark(tt)
1.15/1.17	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.15/1.17	 active(isQid(a)) -> mark(tt)
1.15/1.17	 active(isQid(e)) -> mark(tt)
1.15/1.17	 active(isQid(i)) -> mark(tt)
1.15/1.17	 active(isQid(o)) -> mark(tt)
1.15/1.17	 active(isQid(u)) -> mark(tt)
1.15/1.17	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.17	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.17	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.15/1.17	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.15/1.17	 isList(active(X:S)) -> isList(X:S)
1.15/1.17	 isList(mark(X:S)) -> isList(X:S)
1.15/1.17	 isNeList(active(X:S)) -> isNeList(X:S)
1.15/1.17	 isNeList(mark(X:S)) -> isNeList(X:S)
1.15/1.17	 isNePal(active(X:S)) -> isNePal(X:S)
1.15/1.17	 isNePal(mark(X:S)) -> isNePal(X:S)
1.15/1.17	 isPal(active(X:S)) -> isPal(X:S)
1.15/1.17	 isPal(mark(X:S)) -> isPal(X:S)
1.15/1.17	 isQid(active(X:S)) -> isQid(X:S)
1.15/1.17	 isQid(mark(X:S)) -> isQid(X:S)
1.15/1.17	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.15/1.17	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.15/1.17	 mark(isList(X:S)) -> active(isList(X:S))
1.15/1.17	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.15/1.17	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.15/1.17	 mark(isPal(X:S)) -> active(isPal(X:S))
1.15/1.17	 mark(isQid(X:S)) -> active(isQid(X:S))
1.15/1.17	 mark(a) -> active(a)
1.15/1.17	 mark(e) -> active(e)
1.15/1.17	 mark(i) -> active(i)
1.15/1.17	 mark(nil) -> active(nil)
1.15/1.17	 mark(o) -> active(o)
1.15/1.17	 mark(tt) -> active(tt)
1.15/1.17	 mark(u) -> active(u)
1.15/1.17	->->Cycle:
1.15/1.17	->->-> Pairs:
1.15/1.17	 AND(active(X1:S),X2:S) -> AND(X1:S,X2:S)
1.15/1.17	 AND(mark(X1:S),X2:S) -> AND(X1:S,X2:S)
1.15/1.17	 AND(X1:S,active(X2:S)) -> AND(X1:S,X2:S)
1.15/1.17	 AND(X1:S,mark(X2:S)) -> AND(X1:S,X2:S)
1.15/1.17	->->-> Rules:
1.15/1.17	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.17	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.17	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.15/1.17	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.15/1.17	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.15/1.17	 active(__(nil,X:S)) -> mark(X:S)
1.15/1.17	 active(__(X:S,nil)) -> mark(X:S)
1.15/1.17	 active(and(tt,X:S)) -> mark(X:S)
1.15/1.17	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.15/1.17	 active(isList(nil)) -> mark(tt)
1.15/1.17	 active(isList(V:S)) -> mark(isNeList(V:S))
1.15/1.17	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.15/1.17	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.15/1.17	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.15/1.17	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.15/1.17	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.15/1.17	 active(isPal(nil)) -> mark(tt)
1.15/1.17	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.15/1.17	 active(isQid(a)) -> mark(tt)
1.15/1.17	 active(isQid(e)) -> mark(tt)
1.15/1.17	 active(isQid(i)) -> mark(tt)
1.15/1.17	 active(isQid(o)) -> mark(tt)
1.15/1.17	 active(isQid(u)) -> mark(tt)
1.15/1.17	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.17	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.17	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.15/1.17	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.15/1.17	 isList(active(X:S)) -> isList(X:S)
1.15/1.17	 isList(mark(X:S)) -> isList(X:S)
1.15/1.17	 isNeList(active(X:S)) -> isNeList(X:S)
1.15/1.17	 isNeList(mark(X:S)) -> isNeList(X:S)
1.15/1.17	 isNePal(active(X:S)) -> isNePal(X:S)
1.15/1.17	 isNePal(mark(X:S)) -> isNePal(X:S)
1.15/1.17	 isPal(active(X:S)) -> isPal(X:S)
1.15/1.17	 isPal(mark(X:S)) -> isPal(X:S)
1.15/1.17	 isQid(active(X:S)) -> isQid(X:S)
1.15/1.17	 isQid(mark(X:S)) -> isQid(X:S)
1.15/1.17	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.15/1.17	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.15/1.17	 mark(isList(X:S)) -> active(isList(X:S))
1.15/1.17	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.15/1.17	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.15/1.17	 mark(isPal(X:S)) -> active(isPal(X:S))
1.15/1.17	 mark(isQid(X:S)) -> active(isQid(X:S))
1.15/1.17	 mark(a) -> active(a)
1.15/1.17	 mark(e) -> active(e)
1.15/1.17	 mark(i) -> active(i)
1.15/1.17	 mark(nil) -> active(nil)
1.15/1.17	 mark(o) -> active(o)
1.15/1.17	 mark(tt) -> active(tt)
1.15/1.17	 mark(u) -> active(u)
1.15/1.17	->->Cycle:
1.15/1.17	->->-> Pairs:
1.15/1.17	 __#(active(X1:S),X2:S) -> __#(X1:S,X2:S)
1.15/1.17	 __#(mark(X1:S),X2:S) -> __#(X1:S,X2:S)
1.15/1.17	 __#(X1:S,active(X2:S)) -> __#(X1:S,X2:S)
1.15/1.17	 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S)
1.15/1.17	->->-> Rules:
1.15/1.17	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.17	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.17	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.15/1.17	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.15/1.17	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.15/1.17	 active(__(nil,X:S)) -> mark(X:S)
1.15/1.17	 active(__(X:S,nil)) -> mark(X:S)
1.15/1.17	 active(and(tt,X:S)) -> mark(X:S)
1.15/1.17	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.15/1.17	 active(isList(nil)) -> mark(tt)
1.15/1.17	 active(isList(V:S)) -> mark(isNeList(V:S))
1.15/1.17	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.15/1.17	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.15/1.17	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.15/1.17	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.15/1.17	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.15/1.17	 active(isPal(nil)) -> mark(tt)
1.15/1.17	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.15/1.17	 active(isQid(a)) -> mark(tt)
1.15/1.17	 active(isQid(e)) -> mark(tt)
1.15/1.17	 active(isQid(i)) -> mark(tt)
1.15/1.17	 active(isQid(o)) -> mark(tt)
1.15/1.17	 active(isQid(u)) -> mark(tt)
1.15/1.17	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.17	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.17	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.15/1.17	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.15/1.17	 isList(active(X:S)) -> isList(X:S)
1.15/1.17	 isList(mark(X:S)) -> isList(X:S)
1.15/1.17	 isNeList(active(X:S)) -> isNeList(X:S)
1.15/1.17	 isNeList(mark(X:S)) -> isNeList(X:S)
1.15/1.17	 isNePal(active(X:S)) -> isNePal(X:S)
1.15/1.17	 isNePal(mark(X:S)) -> isNePal(X:S)
1.15/1.17	 isPal(active(X:S)) -> isPal(X:S)
1.15/1.17	 isPal(mark(X:S)) -> isPal(X:S)
1.15/1.17	 isQid(active(X:S)) -> isQid(X:S)
1.15/1.17	 isQid(mark(X:S)) -> isQid(X:S)
1.15/1.17	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.15/1.17	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.15/1.17	 mark(isList(X:S)) -> active(isList(X:S))
1.15/1.17	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.15/1.17	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.15/1.17	 mark(isPal(X:S)) -> active(isPal(X:S))
1.15/1.17	 mark(isQid(X:S)) -> active(isQid(X:S))
1.15/1.17	 mark(a) -> active(a)
1.15/1.17	 mark(e) -> active(e)
1.15/1.17	 mark(i) -> active(i)
1.15/1.17	 mark(nil) -> active(nil)
1.15/1.17	 mark(o) -> active(o)
1.15/1.17	 mark(tt) -> active(tt)
1.15/1.17	 mark(u) -> active(u)
1.15/1.17	->->Cycle:
1.15/1.17	->->-> Pairs:
1.15/1.17	 ACTIVE(__(__(X:S,Y:S),Z:S)) -> MARK(__(X:S,__(Y:S,Z:S)))
1.15/1.17	 ACTIVE(__(nil,X:S)) -> MARK(X:S)
1.15/1.17	 ACTIVE(__(X:S,nil)) -> MARK(X:S)
1.15/1.17	 ACTIVE(and(tt,X:S)) -> MARK(X:S)
1.15/1.17	 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(and(isList(V1:S),isList(V2:S)))
1.15/1.17	 ACTIVE(isList(V:S)) -> MARK(isNeList(V:S))
1.15/1.17	 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(and(isList(V1:S),isNeList(V2:S)))
1.15/1.17	 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(and(isNeList(V1:S),isList(V2:S)))
1.15/1.17	 ACTIVE(isNeList(V:S)) -> MARK(isQid(V:S))
1.15/1.17	 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(and(isQid(I:S),isPal(P:S)))
1.15/1.17	 ACTIVE(isNePal(V:S)) -> MARK(isQid(V:S))
1.15/1.17	 ACTIVE(isPal(V:S)) -> MARK(isNePal(V:S))
1.15/1.17	 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
1.15/1.17	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.15/1.17	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.15/1.17	 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S))
1.15/1.17	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
1.15/1.17	 MARK(isList(X:S)) -> ACTIVE(isList(X:S))
1.15/1.17	 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
1.15/1.17	 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
1.15/1.17	 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
1.15/1.17	->->-> Rules:
1.15/1.17	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.17	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.17	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.15/1.17	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.15/1.17	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.15/1.17	 active(__(nil,X:S)) -> mark(X:S)
1.15/1.17	 active(__(X:S,nil)) -> mark(X:S)
1.15/1.17	 active(and(tt,X:S)) -> mark(X:S)
1.15/1.17	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.15/1.17	 active(isList(nil)) -> mark(tt)
1.15/1.17	 active(isList(V:S)) -> mark(isNeList(V:S))
1.15/1.17	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.15/1.17	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.15/1.17	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.15/1.17	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.15/1.17	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.15/1.17	 active(isPal(nil)) -> mark(tt)
1.15/1.17	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.15/1.17	 active(isQid(a)) -> mark(tt)
1.15/1.17	 active(isQid(e)) -> mark(tt)
1.15/1.17	 active(isQid(i)) -> mark(tt)
1.15/1.17	 active(isQid(o)) -> mark(tt)
1.15/1.17	 active(isQid(u)) -> mark(tt)
1.15/1.17	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.17	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.17	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.15/1.17	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.15/1.17	 isList(active(X:S)) -> isList(X:S)
1.15/1.17	 isList(mark(X:S)) -> isList(X:S)
1.15/1.17	 isNeList(active(X:S)) -> isNeList(X:S)
1.15/1.17	 isNeList(mark(X:S)) -> isNeList(X:S)
1.15/1.17	 isNePal(active(X:S)) -> isNePal(X:S)
1.15/1.17	 isNePal(mark(X:S)) -> isNePal(X:S)
1.15/1.17	 isPal(active(X:S)) -> isPal(X:S)
1.15/1.17	 isPal(mark(X:S)) -> isPal(X:S)
1.15/1.17	 isQid(active(X:S)) -> isQid(X:S)
1.15/1.17	 isQid(mark(X:S)) -> isQid(X:S)
1.15/1.17	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.15/1.17	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.15/1.17	 mark(isList(X:S)) -> active(isList(X:S))
1.15/1.17	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.15/1.17	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.15/1.17	 mark(isPal(X:S)) -> active(isPal(X:S))
1.15/1.17	 mark(isQid(X:S)) -> active(isQid(X:S))
1.15/1.17	 mark(a) -> active(a)
1.15/1.17	 mark(e) -> active(e)
1.15/1.17	 mark(i) -> active(i)
1.15/1.17	 mark(nil) -> active(nil)
1.15/1.17	 mark(o) -> active(o)
1.15/1.17	 mark(tt) -> active(tt)
1.15/1.17	 mark(u) -> active(u)
1.15/1.17	
1.15/1.17	
1.15/1.17	The problem is decomposed in 8 subproblems.
1.15/1.17	
1.15/1.17	Problem 1.1: 
1.15/1.17	
1.15/1.17	Subterm Processor:
1.15/1.17	-> Pairs:
1.15/1.17	 ISQID(active(X:S)) -> ISQID(X:S)
1.15/1.17	 ISQID(mark(X:S)) -> ISQID(X:S)
1.15/1.17	-> Rules:
1.15/1.17	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.17	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.17	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.15/1.17	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.15/1.17	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.15/1.17	 active(__(nil,X:S)) -> mark(X:S)
1.15/1.17	 active(__(X:S,nil)) -> mark(X:S)
1.15/1.17	 active(and(tt,X:S)) -> mark(X:S)
1.15/1.17	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.15/1.17	 active(isList(nil)) -> mark(tt)
1.15/1.17	 active(isList(V:S)) -> mark(isNeList(V:S))
1.15/1.17	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.15/1.17	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.15/1.17	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.15/1.17	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.15/1.17	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.15/1.17	 active(isPal(nil)) -> mark(tt)
1.15/1.17	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.15/1.17	 active(isQid(a)) -> mark(tt)
1.15/1.17	 active(isQid(e)) -> mark(tt)
1.15/1.17	 active(isQid(i)) -> mark(tt)
1.15/1.17	 active(isQid(o)) -> mark(tt)
1.15/1.17	 active(isQid(u)) -> mark(tt)
1.15/1.17	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.17	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.17	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.15/1.17	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.15/1.17	 isList(active(X:S)) -> isList(X:S)
1.15/1.17	 isList(mark(X:S)) -> isList(X:S)
1.15/1.17	 isNeList(active(X:S)) -> isNeList(X:S)
1.15/1.17	 isNeList(mark(X:S)) -> isNeList(X:S)
1.15/1.17	 isNePal(active(X:S)) -> isNePal(X:S)
1.15/1.17	 isNePal(mark(X:S)) -> isNePal(X:S)
1.15/1.17	 isPal(active(X:S)) -> isPal(X:S)
1.15/1.17	 isPal(mark(X:S)) -> isPal(X:S)
1.15/1.18	 isQid(active(X:S)) -> isQid(X:S)
1.15/1.18	 isQid(mark(X:S)) -> isQid(X:S)
1.15/1.18	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.15/1.18	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.15/1.18	 mark(isList(X:S)) -> active(isList(X:S))
1.15/1.18	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.15/1.18	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.15/1.18	 mark(isPal(X:S)) -> active(isPal(X:S))
1.15/1.18	 mark(isQid(X:S)) -> active(isQid(X:S))
1.15/1.18	 mark(a) -> active(a)
1.15/1.18	 mark(e) -> active(e)
1.15/1.18	 mark(i) -> active(i)
1.15/1.18	 mark(nil) -> active(nil)
1.15/1.18	 mark(o) -> active(o)
1.15/1.18	 mark(tt) -> active(tt)
1.15/1.18	 mark(u) -> active(u)
1.15/1.18	->Projection:
1.15/1.18	 pi(ISQID) = 1
1.15/1.18	
1.15/1.18	Problem 1.1: 
1.15/1.18	
1.15/1.18	SCC Processor:
1.15/1.18	-> Pairs:
1.15/1.18	 Empty
1.15/1.18	-> Rules:
1.15/1.18	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.18	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.18	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.15/1.18	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.15/1.18	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.15/1.18	 active(__(nil,X:S)) -> mark(X:S)
1.15/1.18	 active(__(X:S,nil)) -> mark(X:S)
1.15/1.18	 active(and(tt,X:S)) -> mark(X:S)
1.15/1.18	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.15/1.18	 active(isList(nil)) -> mark(tt)
1.15/1.18	 active(isList(V:S)) -> mark(isNeList(V:S))
1.15/1.18	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.15/1.18	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.15/1.18	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.15/1.18	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.15/1.18	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.15/1.18	 active(isPal(nil)) -> mark(tt)
1.15/1.18	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.15/1.18	 active(isQid(a)) -> mark(tt)
1.15/1.18	 active(isQid(e)) -> mark(tt)
1.15/1.18	 active(isQid(i)) -> mark(tt)
1.15/1.18	 active(isQid(o)) -> mark(tt)
1.15/1.18	 active(isQid(u)) -> mark(tt)
1.15/1.18	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.18	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.18	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.15/1.18	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.15/1.18	 isList(active(X:S)) -> isList(X:S)
1.15/1.18	 isList(mark(X:S)) -> isList(X:S)
1.15/1.18	 isNeList(active(X:S)) -> isNeList(X:S)
1.15/1.18	 isNeList(mark(X:S)) -> isNeList(X:S)
1.15/1.18	 isNePal(active(X:S)) -> isNePal(X:S)
1.15/1.18	 isNePal(mark(X:S)) -> isNePal(X:S)
1.15/1.18	 isPal(active(X:S)) -> isPal(X:S)
1.15/1.18	 isPal(mark(X:S)) -> isPal(X:S)
1.15/1.18	 isQid(active(X:S)) -> isQid(X:S)
1.15/1.18	 isQid(mark(X:S)) -> isQid(X:S)
1.15/1.18	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.15/1.18	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.15/1.18	 mark(isList(X:S)) -> active(isList(X:S))
1.15/1.18	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.15/1.18	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.15/1.18	 mark(isPal(X:S)) -> active(isPal(X:S))
1.15/1.18	 mark(isQid(X:S)) -> active(isQid(X:S))
1.15/1.18	 mark(a) -> active(a)
1.15/1.18	 mark(e) -> active(e)
1.15/1.18	 mark(i) -> active(i)
1.15/1.18	 mark(nil) -> active(nil)
1.15/1.18	 mark(o) -> active(o)
1.15/1.18	 mark(tt) -> active(tt)
1.15/1.18	 mark(u) -> active(u)
1.15/1.18	->Strongly Connected Components:
1.15/1.18	 There is no strongly connected component
1.15/1.18	
1.15/1.18	The problem is finite.
1.15/1.18	
1.15/1.18	Problem 1.2: 
1.15/1.18	
1.15/1.18	Subterm Processor:
1.15/1.18	-> Pairs:
1.15/1.18	 ISPAL(active(X:S)) -> ISPAL(X:S)
1.15/1.18	 ISPAL(mark(X:S)) -> ISPAL(X:S)
1.15/1.18	-> Rules:
1.15/1.18	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.18	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.18	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.15/1.18	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.15/1.18	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.15/1.18	 active(__(nil,X:S)) -> mark(X:S)
1.15/1.18	 active(__(X:S,nil)) -> mark(X:S)
1.15/1.18	 active(and(tt,X:S)) -> mark(X:S)
1.15/1.18	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.15/1.18	 active(isList(nil)) -> mark(tt)
1.15/1.18	 active(isList(V:S)) -> mark(isNeList(V:S))
1.15/1.18	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.15/1.18	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.15/1.18	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.15/1.18	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.15/1.18	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.15/1.18	 active(isPal(nil)) -> mark(tt)
1.15/1.18	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.15/1.18	 active(isQid(a)) -> mark(tt)
1.15/1.18	 active(isQid(e)) -> mark(tt)
1.15/1.18	 active(isQid(i)) -> mark(tt)
1.15/1.18	 active(isQid(o)) -> mark(tt)
1.15/1.18	 active(isQid(u)) -> mark(tt)
1.15/1.18	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.18	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.18	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.15/1.18	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.15/1.18	 isList(active(X:S)) -> isList(X:S)
1.15/1.18	 isList(mark(X:S)) -> isList(X:S)
1.15/1.18	 isNeList(active(X:S)) -> isNeList(X:S)
1.15/1.18	 isNeList(mark(X:S)) -> isNeList(X:S)
1.15/1.18	 isNePal(active(X:S)) -> isNePal(X:S)
1.15/1.18	 isNePal(mark(X:S)) -> isNePal(X:S)
1.15/1.18	 isPal(active(X:S)) -> isPal(X:S)
1.15/1.18	 isPal(mark(X:S)) -> isPal(X:S)
1.15/1.18	 isQid(active(X:S)) -> isQid(X:S)
1.15/1.18	 isQid(mark(X:S)) -> isQid(X:S)
1.15/1.18	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.15/1.18	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.15/1.18	 mark(isList(X:S)) -> active(isList(X:S))
1.15/1.18	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.15/1.18	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.15/1.18	 mark(isPal(X:S)) -> active(isPal(X:S))
1.15/1.18	 mark(isQid(X:S)) -> active(isQid(X:S))
1.15/1.18	 mark(a) -> active(a)
1.15/1.18	 mark(e) -> active(e)
1.15/1.18	 mark(i) -> active(i)
1.15/1.18	 mark(nil) -> active(nil)
1.15/1.18	 mark(o) -> active(o)
1.15/1.18	 mark(tt) -> active(tt)
1.15/1.18	 mark(u) -> active(u)
1.15/1.18	->Projection:
1.15/1.18	 pi(ISPAL) = 1
1.15/1.18	
1.15/1.18	Problem 1.2: 
1.15/1.18	
1.15/1.18	SCC Processor:
1.15/1.18	-> Pairs:
1.15/1.18	 Empty
1.15/1.18	-> Rules:
1.15/1.18	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.18	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.18	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.15/1.18	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.15/1.18	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.15/1.18	 active(__(nil,X:S)) -> mark(X:S)
1.15/1.18	 active(__(X:S,nil)) -> mark(X:S)
1.15/1.18	 active(and(tt,X:S)) -> mark(X:S)
1.15/1.18	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.15/1.18	 active(isList(nil)) -> mark(tt)
1.15/1.18	 active(isList(V:S)) -> mark(isNeList(V:S))
1.15/1.18	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.15/1.18	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.15/1.18	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.15/1.18	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.15/1.18	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.15/1.18	 active(isPal(nil)) -> mark(tt)
1.15/1.18	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.15/1.18	 active(isQid(a)) -> mark(tt)
1.15/1.18	 active(isQid(e)) -> mark(tt)
1.15/1.18	 active(isQid(i)) -> mark(tt)
1.15/1.18	 active(isQid(o)) -> mark(tt)
1.15/1.18	 active(isQid(u)) -> mark(tt)
1.15/1.18	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.18	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.18	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.15/1.18	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.15/1.18	 isList(active(X:S)) -> isList(X:S)
1.15/1.18	 isList(mark(X:S)) -> isList(X:S)
1.15/1.18	 isNeList(active(X:S)) -> isNeList(X:S)
1.15/1.18	 isNeList(mark(X:S)) -> isNeList(X:S)
1.15/1.18	 isNePal(active(X:S)) -> isNePal(X:S)
1.15/1.18	 isNePal(mark(X:S)) -> isNePal(X:S)
1.15/1.18	 isPal(active(X:S)) -> isPal(X:S)
1.15/1.18	 isPal(mark(X:S)) -> isPal(X:S)
1.15/1.18	 isQid(active(X:S)) -> isQid(X:S)
1.15/1.18	 isQid(mark(X:S)) -> isQid(X:S)
1.15/1.18	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.15/1.18	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.15/1.18	 mark(isList(X:S)) -> active(isList(X:S))
1.15/1.18	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.15/1.18	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.15/1.18	 mark(isPal(X:S)) -> active(isPal(X:S))
1.15/1.18	 mark(isQid(X:S)) -> active(isQid(X:S))
1.15/1.18	 mark(a) -> active(a)
1.15/1.18	 mark(e) -> active(e)
1.15/1.18	 mark(i) -> active(i)
1.15/1.18	 mark(nil) -> active(nil)
1.15/1.18	 mark(o) -> active(o)
1.15/1.18	 mark(tt) -> active(tt)
1.15/1.18	 mark(u) -> active(u)
1.15/1.18	->Strongly Connected Components:
1.15/1.18	 There is no strongly connected component
1.15/1.18	
1.15/1.18	The problem is finite.
1.15/1.18	
1.15/1.18	Problem 1.3: 
1.15/1.18	
1.15/1.18	Subterm Processor:
1.15/1.18	-> Pairs:
1.15/1.18	 ISNEPAL(active(X:S)) -> ISNEPAL(X:S)
1.15/1.18	 ISNEPAL(mark(X:S)) -> ISNEPAL(X:S)
1.15/1.18	-> Rules:
1.15/1.18	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.18	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.18	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.15/1.18	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.15/1.18	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.15/1.18	 active(__(nil,X:S)) -> mark(X:S)
1.15/1.18	 active(__(X:S,nil)) -> mark(X:S)
1.15/1.18	 active(and(tt,X:S)) -> mark(X:S)
1.15/1.18	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.15/1.18	 active(isList(nil)) -> mark(tt)
1.15/1.18	 active(isList(V:S)) -> mark(isNeList(V:S))
1.15/1.18	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.15/1.18	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.15/1.18	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.15/1.18	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.15/1.18	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.15/1.18	 active(isPal(nil)) -> mark(tt)
1.15/1.18	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.15/1.18	 active(isQid(a)) -> mark(tt)
1.15/1.18	 active(isQid(e)) -> mark(tt)
1.15/1.18	 active(isQid(i)) -> mark(tt)
1.15/1.18	 active(isQid(o)) -> mark(tt)
1.15/1.18	 active(isQid(u)) -> mark(tt)
1.15/1.18	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.18	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.18	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.15/1.18	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.15/1.18	 isList(active(X:S)) -> isList(X:S)
1.15/1.18	 isList(mark(X:S)) -> isList(X:S)
1.15/1.18	 isNeList(active(X:S)) -> isNeList(X:S)
1.15/1.18	 isNeList(mark(X:S)) -> isNeList(X:S)
1.15/1.18	 isNePal(active(X:S)) -> isNePal(X:S)
1.15/1.18	 isNePal(mark(X:S)) -> isNePal(X:S)
1.15/1.18	 isPal(active(X:S)) -> isPal(X:S)
1.15/1.18	 isPal(mark(X:S)) -> isPal(X:S)
1.15/1.18	 isQid(active(X:S)) -> isQid(X:S)
1.15/1.18	 isQid(mark(X:S)) -> isQid(X:S)
1.15/1.18	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.15/1.18	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.15/1.18	 mark(isList(X:S)) -> active(isList(X:S))
1.15/1.18	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.15/1.18	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.15/1.18	 mark(isPal(X:S)) -> active(isPal(X:S))
1.15/1.18	 mark(isQid(X:S)) -> active(isQid(X:S))
1.15/1.18	 mark(a) -> active(a)
1.15/1.18	 mark(e) -> active(e)
1.15/1.18	 mark(i) -> active(i)
1.15/1.18	 mark(nil) -> active(nil)
1.15/1.18	 mark(o) -> active(o)
1.15/1.18	 mark(tt) -> active(tt)
1.15/1.18	 mark(u) -> active(u)
1.15/1.18	->Projection:
1.15/1.18	 pi(ISNEPAL) = 1
1.15/1.18	
1.15/1.18	Problem 1.3: 
1.15/1.18	
1.15/1.18	SCC Processor:
1.15/1.18	-> Pairs:
1.15/1.18	 Empty
1.15/1.18	-> Rules:
1.15/1.18	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.18	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.18	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.15/1.18	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.15/1.18	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.15/1.18	 active(__(nil,X:S)) -> mark(X:S)
1.15/1.18	 active(__(X:S,nil)) -> mark(X:S)
1.15/1.18	 active(and(tt,X:S)) -> mark(X:S)
1.15/1.18	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.15/1.18	 active(isList(nil)) -> mark(tt)
1.15/1.18	 active(isList(V:S)) -> mark(isNeList(V:S))
1.15/1.18	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.15/1.18	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.15/1.18	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.15/1.18	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.15/1.18	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.15/1.18	 active(isPal(nil)) -> mark(tt)
1.15/1.18	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.15/1.18	 active(isQid(a)) -> mark(tt)
1.15/1.18	 active(isQid(e)) -> mark(tt)
1.15/1.18	 active(isQid(i)) -> mark(tt)
1.15/1.18	 active(isQid(o)) -> mark(tt)
1.15/1.18	 active(isQid(u)) -> mark(tt)
1.15/1.18	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.18	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.18	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.15/1.18	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.15/1.18	 isList(active(X:S)) -> isList(X:S)
1.15/1.18	 isList(mark(X:S)) -> isList(X:S)
1.15/1.18	 isNeList(active(X:S)) -> isNeList(X:S)
1.15/1.18	 isNeList(mark(X:S)) -> isNeList(X:S)
1.15/1.18	 isNePal(active(X:S)) -> isNePal(X:S)
1.15/1.18	 isNePal(mark(X:S)) -> isNePal(X:S)
1.15/1.18	 isPal(active(X:S)) -> isPal(X:S)
1.15/1.18	 isPal(mark(X:S)) -> isPal(X:S)
1.15/1.18	 isQid(active(X:S)) -> isQid(X:S)
1.15/1.18	 isQid(mark(X:S)) -> isQid(X:S)
1.15/1.18	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.15/1.18	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.15/1.18	 mark(isList(X:S)) -> active(isList(X:S))
1.15/1.18	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.15/1.18	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.15/1.18	 mark(isPal(X:S)) -> active(isPal(X:S))
1.15/1.18	 mark(isQid(X:S)) -> active(isQid(X:S))
1.15/1.18	 mark(a) -> active(a)
1.15/1.18	 mark(e) -> active(e)
1.15/1.18	 mark(i) -> active(i)
1.15/1.18	 mark(nil) -> active(nil)
1.15/1.18	 mark(o) -> active(o)
1.15/1.18	 mark(tt) -> active(tt)
1.15/1.18	 mark(u) -> active(u)
1.15/1.18	->Strongly Connected Components:
1.15/1.18	 There is no strongly connected component
1.15/1.18	
1.15/1.18	The problem is finite.
1.15/1.18	
1.15/1.18	Problem 1.4: 
1.15/1.18	
1.15/1.18	Subterm Processor:
1.15/1.18	-> Pairs:
1.15/1.18	 ISNELIST(active(X:S)) -> ISNELIST(X:S)
1.15/1.18	 ISNELIST(mark(X:S)) -> ISNELIST(X:S)
1.15/1.18	-> Rules:
1.15/1.18	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.18	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.18	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.15/1.18	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.15/1.18	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.15/1.18	 active(__(nil,X:S)) -> mark(X:S)
1.15/1.18	 active(__(X:S,nil)) -> mark(X:S)
1.15/1.18	 active(and(tt,X:S)) -> mark(X:S)
1.15/1.18	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.15/1.18	 active(isList(nil)) -> mark(tt)
1.15/1.18	 active(isList(V:S)) -> mark(isNeList(V:S))
1.15/1.18	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.15/1.18	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.15/1.18	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.15/1.18	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.15/1.18	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.15/1.18	 active(isPal(nil)) -> mark(tt)
1.15/1.18	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.15/1.18	 active(isQid(a)) -> mark(tt)
1.15/1.18	 active(isQid(e)) -> mark(tt)
1.15/1.18	 active(isQid(i)) -> mark(tt)
1.15/1.18	 active(isQid(o)) -> mark(tt)
1.15/1.18	 active(isQid(u)) -> mark(tt)
1.15/1.18	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.18	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.18	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.15/1.18	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.15/1.18	 isList(active(X:S)) -> isList(X:S)
1.15/1.18	 isList(mark(X:S)) -> isList(X:S)
1.15/1.18	 isNeList(active(X:S)) -> isNeList(X:S)
1.15/1.18	 isNeList(mark(X:S)) -> isNeList(X:S)
1.15/1.18	 isNePal(active(X:S)) -> isNePal(X:S)
1.15/1.18	 isNePal(mark(X:S)) -> isNePal(X:S)
1.15/1.18	 isPal(active(X:S)) -> isPal(X:S)
1.15/1.18	 isPal(mark(X:S)) -> isPal(X:S)
1.15/1.18	 isQid(active(X:S)) -> isQid(X:S)
1.15/1.18	 isQid(mark(X:S)) -> isQid(X:S)
1.15/1.18	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.15/1.18	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.15/1.18	 mark(isList(X:S)) -> active(isList(X:S))
1.15/1.18	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.15/1.18	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.15/1.18	 mark(isPal(X:S)) -> active(isPal(X:S))
1.15/1.18	 mark(isQid(X:S)) -> active(isQid(X:S))
1.15/1.18	 mark(a) -> active(a)
1.15/1.18	 mark(e) -> active(e)
1.15/1.18	 mark(i) -> active(i)
1.15/1.18	 mark(nil) -> active(nil)
1.15/1.18	 mark(o) -> active(o)
1.15/1.18	 mark(tt) -> active(tt)
1.15/1.18	 mark(u) -> active(u)
1.15/1.18	->Projection:
1.15/1.18	 pi(ISNELIST) = 1
1.15/1.18	
1.15/1.18	Problem 1.4: 
1.15/1.18	
1.15/1.18	SCC Processor:
1.15/1.18	-> Pairs:
1.15/1.18	 Empty
1.15/1.18	-> Rules:
1.15/1.18	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.18	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.18	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.15/1.18	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.15/1.18	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.15/1.18	 active(__(nil,X:S)) -> mark(X:S)
1.15/1.18	 active(__(X:S,nil)) -> mark(X:S)
1.15/1.18	 active(and(tt,X:S)) -> mark(X:S)
1.15/1.18	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.15/1.18	 active(isList(nil)) -> mark(tt)
1.15/1.18	 active(isList(V:S)) -> mark(isNeList(V:S))
1.15/1.18	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.15/1.18	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.15/1.18	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.15/1.18	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.15/1.18	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.15/1.18	 active(isPal(nil)) -> mark(tt)
1.15/1.18	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.15/1.18	 active(isQid(a)) -> mark(tt)
1.15/1.18	 active(isQid(e)) -> mark(tt)
1.15/1.18	 active(isQid(i)) -> mark(tt)
1.15/1.18	 active(isQid(o)) -> mark(tt)
1.15/1.18	 active(isQid(u)) -> mark(tt)
1.15/1.18	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.18	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.18	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.15/1.18	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.15/1.18	 isList(active(X:S)) -> isList(X:S)
1.15/1.18	 isList(mark(X:S)) -> isList(X:S)
1.15/1.18	 isNeList(active(X:S)) -> isNeList(X:S)
1.15/1.18	 isNeList(mark(X:S)) -> isNeList(X:S)
1.15/1.18	 isNePal(active(X:S)) -> isNePal(X:S)
1.15/1.18	 isNePal(mark(X:S)) -> isNePal(X:S)
1.15/1.18	 isPal(active(X:S)) -> isPal(X:S)
1.15/1.18	 isPal(mark(X:S)) -> isPal(X:S)
1.15/1.18	 isQid(active(X:S)) -> isQid(X:S)
1.15/1.18	 isQid(mark(X:S)) -> isQid(X:S)
1.15/1.18	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.15/1.18	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.15/1.18	 mark(isList(X:S)) -> active(isList(X:S))
1.15/1.18	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.15/1.18	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.15/1.18	 mark(isPal(X:S)) -> active(isPal(X:S))
1.15/1.18	 mark(isQid(X:S)) -> active(isQid(X:S))
1.15/1.18	 mark(a) -> active(a)
1.15/1.18	 mark(e) -> active(e)
1.15/1.18	 mark(i) -> active(i)
1.15/1.18	 mark(nil) -> active(nil)
1.15/1.18	 mark(o) -> active(o)
1.15/1.18	 mark(tt) -> active(tt)
1.15/1.18	 mark(u) -> active(u)
1.15/1.18	->Strongly Connected Components:
1.15/1.18	 There is no strongly connected component
1.15/1.18	
1.15/1.18	The problem is finite.
1.15/1.18	
1.15/1.18	Problem 1.5: 
1.15/1.18	
1.15/1.18	Subterm Processor:
1.15/1.18	-> Pairs:
1.15/1.18	 ISLIST(active(X:S)) -> ISLIST(X:S)
1.15/1.18	 ISLIST(mark(X:S)) -> ISLIST(X:S)
1.15/1.18	-> Rules:
1.15/1.18	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.18	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.18	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.15/1.18	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.15/1.18	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.15/1.18	 active(__(nil,X:S)) -> mark(X:S)
1.15/1.18	 active(__(X:S,nil)) -> mark(X:S)
1.15/1.18	 active(and(tt,X:S)) -> mark(X:S)
1.15/1.18	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.15/1.18	 active(isList(nil)) -> mark(tt)
1.15/1.18	 active(isList(V:S)) -> mark(isNeList(V:S))
1.15/1.18	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.15/1.18	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.15/1.18	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.15/1.18	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.15/1.18	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.15/1.18	 active(isPal(nil)) -> mark(tt)
1.15/1.18	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.15/1.18	 active(isQid(a)) -> mark(tt)
1.15/1.18	 active(isQid(e)) -> mark(tt)
1.15/1.18	 active(isQid(i)) -> mark(tt)
1.15/1.18	 active(isQid(o)) -> mark(tt)
1.15/1.18	 active(isQid(u)) -> mark(tt)
1.15/1.18	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.18	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.18	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.15/1.18	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.15/1.18	 isList(active(X:S)) -> isList(X:S)
1.15/1.18	 isList(mark(X:S)) -> isList(X:S)
1.15/1.18	 isNeList(active(X:S)) -> isNeList(X:S)
1.15/1.18	 isNeList(mark(X:S)) -> isNeList(X:S)
1.15/1.18	 isNePal(active(X:S)) -> isNePal(X:S)
1.15/1.18	 isNePal(mark(X:S)) -> isNePal(X:S)
1.15/1.18	 isPal(active(X:S)) -> isPal(X:S)
1.15/1.18	 isPal(mark(X:S)) -> isPal(X:S)
1.15/1.18	 isQid(active(X:S)) -> isQid(X:S)
1.15/1.18	 isQid(mark(X:S)) -> isQid(X:S)
1.15/1.18	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.15/1.18	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.15/1.18	 mark(isList(X:S)) -> active(isList(X:S))
1.15/1.18	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.15/1.18	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.15/1.18	 mark(isPal(X:S)) -> active(isPal(X:S))
1.15/1.18	 mark(isQid(X:S)) -> active(isQid(X:S))
1.15/1.18	 mark(a) -> active(a)
1.15/1.18	 mark(e) -> active(e)
1.15/1.18	 mark(i) -> active(i)
1.15/1.18	 mark(nil) -> active(nil)
1.15/1.18	 mark(o) -> active(o)
1.15/1.18	 mark(tt) -> active(tt)
1.15/1.18	 mark(u) -> active(u)
1.15/1.18	->Projection:
1.15/1.18	 pi(ISLIST) = 1
1.15/1.18	
1.15/1.18	Problem 1.5: 
1.15/1.18	
1.15/1.18	SCC Processor:
1.15/1.18	-> Pairs:
1.15/1.18	 Empty
1.15/1.18	-> Rules:
1.15/1.18	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.18	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.18	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.15/1.18	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.15/1.18	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.15/1.18	 active(__(nil,X:S)) -> mark(X:S)
1.15/1.18	 active(__(X:S,nil)) -> mark(X:S)
1.15/1.18	 active(and(tt,X:S)) -> mark(X:S)
1.15/1.18	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.15/1.18	 active(isList(nil)) -> mark(tt)
1.15/1.18	 active(isList(V:S)) -> mark(isNeList(V:S))
1.15/1.18	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.15/1.18	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.15/1.18	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.15/1.18	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.15/1.18	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.15/1.18	 active(isPal(nil)) -> mark(tt)
1.15/1.18	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.15/1.18	 active(isQid(a)) -> mark(tt)
1.15/1.18	 active(isQid(e)) -> mark(tt)
1.15/1.18	 active(isQid(i)) -> mark(tt)
1.15/1.18	 active(isQid(o)) -> mark(tt)
1.15/1.18	 active(isQid(u)) -> mark(tt)
1.15/1.18	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.18	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.18	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.15/1.18	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.15/1.18	 isList(active(X:S)) -> isList(X:S)
1.15/1.18	 isList(mark(X:S)) -> isList(X:S)
1.15/1.18	 isNeList(active(X:S)) -> isNeList(X:S)
1.15/1.18	 isNeList(mark(X:S)) -> isNeList(X:S)
1.15/1.18	 isNePal(active(X:S)) -> isNePal(X:S)
1.15/1.18	 isNePal(mark(X:S)) -> isNePal(X:S)
1.15/1.18	 isPal(active(X:S)) -> isPal(X:S)
1.15/1.18	 isPal(mark(X:S)) -> isPal(X:S)
1.15/1.18	 isQid(active(X:S)) -> isQid(X:S)
1.15/1.18	 isQid(mark(X:S)) -> isQid(X:S)
1.15/1.18	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.15/1.18	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.15/1.18	 mark(isList(X:S)) -> active(isList(X:S))
1.15/1.18	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.15/1.18	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.15/1.18	 mark(isPal(X:S)) -> active(isPal(X:S))
1.15/1.18	 mark(isQid(X:S)) -> active(isQid(X:S))
1.15/1.18	 mark(a) -> active(a)
1.15/1.18	 mark(e) -> active(e)
1.15/1.18	 mark(i) -> active(i)
1.15/1.18	 mark(nil) -> active(nil)
1.15/1.18	 mark(o) -> active(o)
1.15/1.18	 mark(tt) -> active(tt)
1.15/1.18	 mark(u) -> active(u)
1.15/1.18	->Strongly Connected Components:
1.15/1.18	 There is no strongly connected component
1.15/1.18	
1.15/1.18	The problem is finite.
1.15/1.18	
1.15/1.18	Problem 1.6: 
1.15/1.18	
1.15/1.18	Subterm Processor:
1.15/1.18	-> Pairs:
1.15/1.18	 AND(active(X1:S),X2:S) -> AND(X1:S,X2:S)
1.15/1.18	 AND(mark(X1:S),X2:S) -> AND(X1:S,X2:S)
1.15/1.18	 AND(X1:S,active(X2:S)) -> AND(X1:S,X2:S)
1.15/1.18	 AND(X1:S,mark(X2:S)) -> AND(X1:S,X2:S)
1.15/1.18	-> Rules:
1.15/1.18	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.18	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.18	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.15/1.18	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.15/1.18	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.15/1.18	 active(__(nil,X:S)) -> mark(X:S)
1.15/1.18	 active(__(X:S,nil)) -> mark(X:S)
1.15/1.18	 active(and(tt,X:S)) -> mark(X:S)
1.15/1.18	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.15/1.18	 active(isList(nil)) -> mark(tt)
1.15/1.18	 active(isList(V:S)) -> mark(isNeList(V:S))
1.15/1.18	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.15/1.18	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.15/1.18	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.15/1.18	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.15/1.18	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.15/1.18	 active(isPal(nil)) -> mark(tt)
1.15/1.18	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.15/1.18	 active(isQid(a)) -> mark(tt)
1.15/1.18	 active(isQid(e)) -> mark(tt)
1.15/1.18	 active(isQid(i)) -> mark(tt)
1.15/1.18	 active(isQid(o)) -> mark(tt)
1.15/1.18	 active(isQid(u)) -> mark(tt)
1.15/1.18	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.18	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.18	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.15/1.18	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.15/1.18	 isList(active(X:S)) -> isList(X:S)
1.15/1.18	 isList(mark(X:S)) -> isList(X:S)
1.15/1.18	 isNeList(active(X:S)) -> isNeList(X:S)
1.15/1.18	 isNeList(mark(X:S)) -> isNeList(X:S)
1.15/1.18	 isNePal(active(X:S)) -> isNePal(X:S)
1.15/1.18	 isNePal(mark(X:S)) -> isNePal(X:S)
1.15/1.18	 isPal(active(X:S)) -> isPal(X:S)
1.15/1.18	 isPal(mark(X:S)) -> isPal(X:S)
1.15/1.18	 isQid(active(X:S)) -> isQid(X:S)
1.15/1.18	 isQid(mark(X:S)) -> isQid(X:S)
1.15/1.18	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.15/1.18	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.15/1.18	 mark(isList(X:S)) -> active(isList(X:S))
1.15/1.18	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.15/1.18	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.15/1.18	 mark(isPal(X:S)) -> active(isPal(X:S))
1.15/1.18	 mark(isQid(X:S)) -> active(isQid(X:S))
1.15/1.18	 mark(a) -> active(a)
1.15/1.18	 mark(e) -> active(e)
1.15/1.18	 mark(i) -> active(i)
1.15/1.18	 mark(nil) -> active(nil)
1.15/1.18	 mark(o) -> active(o)
1.15/1.18	 mark(tt) -> active(tt)
1.15/1.18	 mark(u) -> active(u)
1.15/1.18	->Projection:
1.15/1.18	 pi(AND) = 1
1.15/1.18	
1.15/1.18	Problem 1.6: 
1.15/1.18	
1.15/1.18	SCC Processor:
1.15/1.18	-> Pairs:
1.15/1.18	 AND(X1:S,active(X2:S)) -> AND(X1:S,X2:S)
1.15/1.18	 AND(X1:S,mark(X2:S)) -> AND(X1:S,X2:S)
1.15/1.18	-> Rules:
1.15/1.18	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.18	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.18	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.15/1.18	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.15/1.18	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.15/1.18	 active(__(nil,X:S)) -> mark(X:S)
1.15/1.18	 active(__(X:S,nil)) -> mark(X:S)
1.15/1.18	 active(and(tt,X:S)) -> mark(X:S)
1.15/1.18	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.15/1.18	 active(isList(nil)) -> mark(tt)
1.15/1.18	 active(isList(V:S)) -> mark(isNeList(V:S))
1.15/1.18	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.15/1.18	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.15/1.18	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.15/1.18	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.15/1.18	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.15/1.18	 active(isPal(nil)) -> mark(tt)
1.15/1.18	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.15/1.18	 active(isQid(a)) -> mark(tt)
1.15/1.18	 active(isQid(e)) -> mark(tt)
1.15/1.18	 active(isQid(i)) -> mark(tt)
1.15/1.18	 active(isQid(o)) -> mark(tt)
1.15/1.18	 active(isQid(u)) -> mark(tt)
1.15/1.18	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.18	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.18	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.15/1.18	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.15/1.18	 isList(active(X:S)) -> isList(X:S)
1.15/1.18	 isList(mark(X:S)) -> isList(X:S)
1.15/1.18	 isNeList(active(X:S)) -> isNeList(X:S)
1.15/1.18	 isNeList(mark(X:S)) -> isNeList(X:S)
1.15/1.18	 isNePal(active(X:S)) -> isNePal(X:S)
1.15/1.18	 isNePal(mark(X:S)) -> isNePal(X:S)
1.15/1.18	 isPal(active(X:S)) -> isPal(X:S)
1.15/1.18	 isPal(mark(X:S)) -> isPal(X:S)
1.15/1.18	 isQid(active(X:S)) -> isQid(X:S)
1.15/1.18	 isQid(mark(X:S)) -> isQid(X:S)
1.15/1.18	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.15/1.18	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.15/1.18	 mark(isList(X:S)) -> active(isList(X:S))
1.15/1.18	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.15/1.18	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.15/1.18	 mark(isPal(X:S)) -> active(isPal(X:S))
1.15/1.18	 mark(isQid(X:S)) -> active(isQid(X:S))
1.15/1.18	 mark(a) -> active(a)
1.15/1.18	 mark(e) -> active(e)
1.15/1.18	 mark(i) -> active(i)
1.15/1.18	 mark(nil) -> active(nil)
1.15/1.18	 mark(o) -> active(o)
1.15/1.18	 mark(tt) -> active(tt)
1.15/1.18	 mark(u) -> active(u)
1.15/1.18	->Strongly Connected Components:
1.15/1.18	->->Cycle:
1.15/1.18	->->-> Pairs:
1.15/1.18	 AND(X1:S,active(X2:S)) -> AND(X1:S,X2:S)
1.15/1.18	 AND(X1:S,mark(X2:S)) -> AND(X1:S,X2:S)
1.15/1.18	->->-> Rules:
1.15/1.18	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.18	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.18	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.15/1.18	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.15/1.18	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.15/1.18	 active(__(nil,X:S)) -> mark(X:S)
1.15/1.18	 active(__(X:S,nil)) -> mark(X:S)
1.15/1.18	 active(and(tt,X:S)) -> mark(X:S)
1.15/1.18	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.15/1.18	 active(isList(nil)) -> mark(tt)
1.15/1.18	 active(isList(V:S)) -> mark(isNeList(V:S))
1.15/1.18	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.15/1.18	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.15/1.18	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.15/1.18	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.15/1.18	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.15/1.18	 active(isPal(nil)) -> mark(tt)
1.15/1.18	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.15/1.18	 active(isQid(a)) -> mark(tt)
1.15/1.18	 active(isQid(e)) -> mark(tt)
1.15/1.18	 active(isQid(i)) -> mark(tt)
1.15/1.18	 active(isQid(o)) -> mark(tt)
1.15/1.18	 active(isQid(u)) -> mark(tt)
1.15/1.18	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.18	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.18	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.15/1.18	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.15/1.18	 isList(active(X:S)) -> isList(X:S)
1.15/1.18	 isList(mark(X:S)) -> isList(X:S)
1.15/1.18	 isNeList(active(X:S)) -> isNeList(X:S)
1.15/1.18	 isNeList(mark(X:S)) -> isNeList(X:S)
1.15/1.18	 isNePal(active(X:S)) -> isNePal(X:S)
1.15/1.18	 isNePal(mark(X:S)) -> isNePal(X:S)
1.15/1.18	 isPal(active(X:S)) -> isPal(X:S)
1.15/1.18	 isPal(mark(X:S)) -> isPal(X:S)
1.15/1.18	 isQid(active(X:S)) -> isQid(X:S)
1.15/1.18	 isQid(mark(X:S)) -> isQid(X:S)
1.15/1.18	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.15/1.18	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.15/1.18	 mark(isList(X:S)) -> active(isList(X:S))
1.15/1.18	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.15/1.18	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.15/1.18	 mark(isPal(X:S)) -> active(isPal(X:S))
1.15/1.18	 mark(isQid(X:S)) -> active(isQid(X:S))
1.15/1.18	 mark(a) -> active(a)
1.15/1.18	 mark(e) -> active(e)
1.15/1.18	 mark(i) -> active(i)
1.15/1.18	 mark(nil) -> active(nil)
1.15/1.18	 mark(o) -> active(o)
1.15/1.18	 mark(tt) -> active(tt)
1.15/1.18	 mark(u) -> active(u)
1.15/1.18	
1.15/1.18	Problem 1.6: 
1.15/1.18	
1.15/1.18	Subterm Processor:
1.15/1.18	-> Pairs:
1.15/1.18	 AND(X1:S,active(X2:S)) -> AND(X1:S,X2:S)
1.15/1.18	 AND(X1:S,mark(X2:S)) -> AND(X1:S,X2:S)
1.15/1.18	-> Rules:
1.15/1.18	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.18	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.18	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.15/1.18	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.15/1.18	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.15/1.18	 active(__(nil,X:S)) -> mark(X:S)
1.15/1.18	 active(__(X:S,nil)) -> mark(X:S)
1.15/1.18	 active(and(tt,X:S)) -> mark(X:S)
1.15/1.18	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.15/1.18	 active(isList(nil)) -> mark(tt)
1.15/1.18	 active(isList(V:S)) -> mark(isNeList(V:S))
1.15/1.18	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.15/1.18	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.15/1.18	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.15/1.18	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.15/1.18	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.15/1.18	 active(isPal(nil)) -> mark(tt)
1.15/1.18	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.15/1.18	 active(isQid(a)) -> mark(tt)
1.15/1.18	 active(isQid(e)) -> mark(tt)
1.15/1.18	 active(isQid(i)) -> mark(tt)
1.15/1.18	 active(isQid(o)) -> mark(tt)
1.15/1.18	 active(isQid(u)) -> mark(tt)
1.15/1.18	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.18	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.18	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.15/1.18	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.15/1.18	 isList(active(X:S)) -> isList(X:S)
1.15/1.18	 isList(mark(X:S)) -> isList(X:S)
1.15/1.18	 isNeList(active(X:S)) -> isNeList(X:S)
1.15/1.18	 isNeList(mark(X:S)) -> isNeList(X:S)
1.15/1.18	 isNePal(active(X:S)) -> isNePal(X:S)
1.15/1.18	 isNePal(mark(X:S)) -> isNePal(X:S)
1.15/1.18	 isPal(active(X:S)) -> isPal(X:S)
1.15/1.18	 isPal(mark(X:S)) -> isPal(X:S)
1.15/1.18	 isQid(active(X:S)) -> isQid(X:S)
1.15/1.18	 isQid(mark(X:S)) -> isQid(X:S)
1.15/1.18	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.15/1.18	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.15/1.18	 mark(isList(X:S)) -> active(isList(X:S))
1.15/1.18	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.15/1.18	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.15/1.18	 mark(isPal(X:S)) -> active(isPal(X:S))
1.15/1.18	 mark(isQid(X:S)) -> active(isQid(X:S))
1.15/1.18	 mark(a) -> active(a)
1.15/1.18	 mark(e) -> active(e)
1.15/1.18	 mark(i) -> active(i)
1.15/1.18	 mark(nil) -> active(nil)
1.15/1.18	 mark(o) -> active(o)
1.15/1.18	 mark(tt) -> active(tt)
1.15/1.18	 mark(u) -> active(u)
1.15/1.18	->Projection:
1.15/1.18	 pi(AND) = 2
1.15/1.18	
1.15/1.18	Problem 1.6: 
1.15/1.18	
1.15/1.18	SCC Processor:
1.15/1.18	-> Pairs:
1.15/1.18	 Empty
1.15/1.18	-> Rules:
1.15/1.18	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.18	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.18	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.15/1.18	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.15/1.18	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.15/1.18	 active(__(nil,X:S)) -> mark(X:S)
1.15/1.18	 active(__(X:S,nil)) -> mark(X:S)
1.15/1.18	 active(and(tt,X:S)) -> mark(X:S)
1.15/1.18	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.15/1.18	 active(isList(nil)) -> mark(tt)
1.15/1.18	 active(isList(V:S)) -> mark(isNeList(V:S))
1.15/1.18	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.15/1.18	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.15/1.18	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.15/1.18	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.15/1.18	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.15/1.18	 active(isPal(nil)) -> mark(tt)
1.15/1.18	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.15/1.18	 active(isQid(a)) -> mark(tt)
1.15/1.18	 active(isQid(e)) -> mark(tt)
1.15/1.18	 active(isQid(i)) -> mark(tt)
1.15/1.18	 active(isQid(o)) -> mark(tt)
1.15/1.18	 active(isQid(u)) -> mark(tt)
1.15/1.18	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.18	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.18	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.15/1.18	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.15/1.18	 isList(active(X:S)) -> isList(X:S)
1.15/1.18	 isList(mark(X:S)) -> isList(X:S)
1.15/1.18	 isNeList(active(X:S)) -> isNeList(X:S)
1.15/1.18	 isNeList(mark(X:S)) -> isNeList(X:S)
1.15/1.18	 isNePal(active(X:S)) -> isNePal(X:S)
1.15/1.18	 isNePal(mark(X:S)) -> isNePal(X:S)
1.15/1.18	 isPal(active(X:S)) -> isPal(X:S)
1.15/1.18	 isPal(mark(X:S)) -> isPal(X:S)
1.15/1.18	 isQid(active(X:S)) -> isQid(X:S)
1.15/1.18	 isQid(mark(X:S)) -> isQid(X:S)
1.15/1.18	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.15/1.18	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.15/1.18	 mark(isList(X:S)) -> active(isList(X:S))
1.15/1.18	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.15/1.18	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.15/1.18	 mark(isPal(X:S)) -> active(isPal(X:S))
1.15/1.18	 mark(isQid(X:S)) -> active(isQid(X:S))
1.15/1.18	 mark(a) -> active(a)
1.15/1.18	 mark(e) -> active(e)
1.15/1.18	 mark(i) -> active(i)
1.15/1.18	 mark(nil) -> active(nil)
1.15/1.18	 mark(o) -> active(o)
1.15/1.18	 mark(tt) -> active(tt)
1.15/1.18	 mark(u) -> active(u)
1.15/1.18	->Strongly Connected Components:
1.15/1.18	 There is no strongly connected component
1.15/1.18	
1.15/1.18	The problem is finite.
1.15/1.18	
1.15/1.18	Problem 1.7: 
1.15/1.18	
1.15/1.18	Subterm Processor:
1.15/1.18	-> Pairs:
1.15/1.18	 __#(active(X1:S),X2:S) -> __#(X1:S,X2:S)
1.15/1.18	 __#(mark(X1:S),X2:S) -> __#(X1:S,X2:S)
1.15/1.18	 __#(X1:S,active(X2:S)) -> __#(X1:S,X2:S)
1.15/1.18	 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S)
1.15/1.18	-> Rules:
1.15/1.18	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.18	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.18	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.15/1.18	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.15/1.18	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.15/1.18	 active(__(nil,X:S)) -> mark(X:S)
1.15/1.18	 active(__(X:S,nil)) -> mark(X:S)
1.15/1.18	 active(and(tt,X:S)) -> mark(X:S)
1.15/1.18	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.15/1.18	 active(isList(nil)) -> mark(tt)
1.15/1.18	 active(isList(V:S)) -> mark(isNeList(V:S))
1.15/1.18	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.15/1.18	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.15/1.18	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.15/1.18	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.15/1.18	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.15/1.18	 active(isPal(nil)) -> mark(tt)
1.15/1.18	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.15/1.18	 active(isQid(a)) -> mark(tt)
1.15/1.18	 active(isQid(e)) -> mark(tt)
1.15/1.18	 active(isQid(i)) -> mark(tt)
1.15/1.18	 active(isQid(o)) -> mark(tt)
1.15/1.18	 active(isQid(u)) -> mark(tt)
1.15/1.18	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.18	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.18	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.15/1.18	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.15/1.18	 isList(active(X:S)) -> isList(X:S)
1.15/1.18	 isList(mark(X:S)) -> isList(X:S)
1.15/1.18	 isNeList(active(X:S)) -> isNeList(X:S)
1.15/1.18	 isNeList(mark(X:S)) -> isNeList(X:S)
1.15/1.18	 isNePal(active(X:S)) -> isNePal(X:S)
1.15/1.18	 isNePal(mark(X:S)) -> isNePal(X:S)
1.15/1.18	 isPal(active(X:S)) -> isPal(X:S)
1.15/1.18	 isPal(mark(X:S)) -> isPal(X:S)
1.15/1.18	 isQid(active(X:S)) -> isQid(X:S)
1.15/1.18	 isQid(mark(X:S)) -> isQid(X:S)
1.15/1.18	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.15/1.18	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.15/1.18	 mark(isList(X:S)) -> active(isList(X:S))
1.15/1.18	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.15/1.18	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.15/1.18	 mark(isPal(X:S)) -> active(isPal(X:S))
1.15/1.18	 mark(isQid(X:S)) -> active(isQid(X:S))
1.15/1.18	 mark(a) -> active(a)
1.15/1.18	 mark(e) -> active(e)
1.15/1.18	 mark(i) -> active(i)
1.15/1.18	 mark(nil) -> active(nil)
1.15/1.18	 mark(o) -> active(o)
1.15/1.18	 mark(tt) -> active(tt)
1.15/1.18	 mark(u) -> active(u)
1.15/1.18	->Projection:
1.15/1.18	 pi(__#) = 1
1.15/1.18	
1.15/1.18	Problem 1.7: 
1.15/1.18	
1.15/1.18	SCC Processor:
1.15/1.18	-> Pairs:
1.15/1.18	 __#(X1:S,active(X2:S)) -> __#(X1:S,X2:S)
1.15/1.18	 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S)
1.15/1.18	-> Rules:
1.15/1.18	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.18	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.18	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.15/1.18	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.15/1.18	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.15/1.18	 active(__(nil,X:S)) -> mark(X:S)
1.15/1.18	 active(__(X:S,nil)) -> mark(X:S)
1.15/1.18	 active(and(tt,X:S)) -> mark(X:S)
1.15/1.18	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.15/1.18	 active(isList(nil)) -> mark(tt)
1.15/1.18	 active(isList(V:S)) -> mark(isNeList(V:S))
1.15/1.18	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.15/1.18	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.15/1.18	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.15/1.18	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.15/1.18	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.15/1.18	 active(isPal(nil)) -> mark(tt)
1.15/1.18	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.15/1.18	 active(isQid(a)) -> mark(tt)
1.15/1.18	 active(isQid(e)) -> mark(tt)
1.15/1.18	 active(isQid(i)) -> mark(tt)
1.15/1.18	 active(isQid(o)) -> mark(tt)
1.15/1.18	 active(isQid(u)) -> mark(tt)
1.15/1.18	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.18	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.18	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.15/1.18	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.15/1.18	 isList(active(X:S)) -> isList(X:S)
1.15/1.18	 isList(mark(X:S)) -> isList(X:S)
1.15/1.18	 isNeList(active(X:S)) -> isNeList(X:S)
1.15/1.18	 isNeList(mark(X:S)) -> isNeList(X:S)
1.15/1.18	 isNePal(active(X:S)) -> isNePal(X:S)
1.15/1.18	 isNePal(mark(X:S)) -> isNePal(X:S)
1.15/1.18	 isPal(active(X:S)) -> isPal(X:S)
1.15/1.18	 isPal(mark(X:S)) -> isPal(X:S)
1.15/1.18	 isQid(active(X:S)) -> isQid(X:S)
1.15/1.18	 isQid(mark(X:S)) -> isQid(X:S)
1.15/1.18	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.15/1.18	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.15/1.18	 mark(isList(X:S)) -> active(isList(X:S))
1.15/1.18	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.15/1.18	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.15/1.18	 mark(isPal(X:S)) -> active(isPal(X:S))
1.15/1.18	 mark(isQid(X:S)) -> active(isQid(X:S))
1.15/1.18	 mark(a) -> active(a)
1.15/1.18	 mark(e) -> active(e)
1.15/1.18	 mark(i) -> active(i)
1.15/1.18	 mark(nil) -> active(nil)
1.15/1.18	 mark(o) -> active(o)
1.15/1.18	 mark(tt) -> active(tt)
1.15/1.18	 mark(u) -> active(u)
1.15/1.18	->Strongly Connected Components:
1.15/1.18	->->Cycle:
1.15/1.18	->->-> Pairs:
1.15/1.18	 __#(X1:S,active(X2:S)) -> __#(X1:S,X2:S)
1.15/1.18	 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S)
1.15/1.18	->->-> Rules:
1.15/1.18	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.18	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.18	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.15/1.18	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.15/1.18	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.15/1.18	 active(__(nil,X:S)) -> mark(X:S)
1.15/1.18	 active(__(X:S,nil)) -> mark(X:S)
1.15/1.18	 active(and(tt,X:S)) -> mark(X:S)
1.15/1.18	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.15/1.18	 active(isList(nil)) -> mark(tt)
1.15/1.18	 active(isList(V:S)) -> mark(isNeList(V:S))
1.15/1.18	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.15/1.18	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.15/1.18	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.15/1.18	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.15/1.18	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.15/1.18	 active(isPal(nil)) -> mark(tt)
1.15/1.18	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.15/1.18	 active(isQid(a)) -> mark(tt)
1.15/1.18	 active(isQid(e)) -> mark(tt)
1.15/1.18	 active(isQid(i)) -> mark(tt)
1.15/1.18	 active(isQid(o)) -> mark(tt)
1.15/1.18	 active(isQid(u)) -> mark(tt)
1.15/1.18	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.18	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.18	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.15/1.18	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.15/1.18	 isList(active(X:S)) -> isList(X:S)
1.15/1.18	 isList(mark(X:S)) -> isList(X:S)
1.15/1.18	 isNeList(active(X:S)) -> isNeList(X:S)
1.15/1.18	 isNeList(mark(X:S)) -> isNeList(X:S)
1.15/1.18	 isNePal(active(X:S)) -> isNePal(X:S)
1.15/1.18	 isNePal(mark(X:S)) -> isNePal(X:S)
1.15/1.18	 isPal(active(X:S)) -> isPal(X:S)
1.15/1.18	 isPal(mark(X:S)) -> isPal(X:S)
1.15/1.18	 isQid(active(X:S)) -> isQid(X:S)
1.15/1.18	 isQid(mark(X:S)) -> isQid(X:S)
1.15/1.18	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.15/1.18	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.15/1.18	 mark(isList(X:S)) -> active(isList(X:S))
1.15/1.18	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.15/1.18	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.15/1.18	 mark(isPal(X:S)) -> active(isPal(X:S))
1.15/1.18	 mark(isQid(X:S)) -> active(isQid(X:S))
1.15/1.18	 mark(a) -> active(a)
1.15/1.18	 mark(e) -> active(e)
1.15/1.18	 mark(i) -> active(i)
1.15/1.18	 mark(nil) -> active(nil)
1.15/1.18	 mark(o) -> active(o)
1.15/1.18	 mark(tt) -> active(tt)
1.15/1.18	 mark(u) -> active(u)
1.15/1.18	
1.15/1.18	Problem 1.7: 
1.15/1.18	
1.15/1.18	Subterm Processor:
1.15/1.18	-> Pairs:
1.15/1.18	 __#(X1:S,active(X2:S)) -> __#(X1:S,X2:S)
1.15/1.18	 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S)
1.15/1.18	-> Rules:
1.15/1.18	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.18	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.18	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.15/1.18	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.15/1.18	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.15/1.18	 active(__(nil,X:S)) -> mark(X:S)
1.15/1.18	 active(__(X:S,nil)) -> mark(X:S)
1.15/1.18	 active(and(tt,X:S)) -> mark(X:S)
1.15/1.18	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.15/1.18	 active(isList(nil)) -> mark(tt)
1.15/1.18	 active(isList(V:S)) -> mark(isNeList(V:S))
1.15/1.18	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.15/1.18	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.15/1.18	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.15/1.18	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.15/1.18	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.15/1.18	 active(isPal(nil)) -> mark(tt)
1.15/1.18	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.15/1.18	 active(isQid(a)) -> mark(tt)
1.15/1.18	 active(isQid(e)) -> mark(tt)
1.15/1.18	 active(isQid(i)) -> mark(tt)
1.15/1.18	 active(isQid(o)) -> mark(tt)
1.15/1.18	 active(isQid(u)) -> mark(tt)
1.15/1.18	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.18	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.18	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.15/1.18	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.15/1.18	 isList(active(X:S)) -> isList(X:S)
1.15/1.18	 isList(mark(X:S)) -> isList(X:S)
1.15/1.18	 isNeList(active(X:S)) -> isNeList(X:S)
1.15/1.18	 isNeList(mark(X:S)) -> isNeList(X:S)
1.15/1.18	 isNePal(active(X:S)) -> isNePal(X:S)
1.15/1.18	 isNePal(mark(X:S)) -> isNePal(X:S)
1.15/1.18	 isPal(active(X:S)) -> isPal(X:S)
1.15/1.18	 isPal(mark(X:S)) -> isPal(X:S)
1.15/1.18	 isQid(active(X:S)) -> isQid(X:S)
1.15/1.18	 isQid(mark(X:S)) -> isQid(X:S)
1.15/1.18	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.15/1.18	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.15/1.18	 mark(isList(X:S)) -> active(isList(X:S))
1.15/1.18	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.15/1.18	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.15/1.18	 mark(isPal(X:S)) -> active(isPal(X:S))
1.15/1.18	 mark(isQid(X:S)) -> active(isQid(X:S))
1.15/1.18	 mark(a) -> active(a)
1.15/1.18	 mark(e) -> active(e)
1.15/1.18	 mark(i) -> active(i)
1.15/1.18	 mark(nil) -> active(nil)
1.15/1.18	 mark(o) -> active(o)
1.15/1.18	 mark(tt) -> active(tt)
1.15/1.18	 mark(u) -> active(u)
1.15/1.18	->Projection:
1.15/1.18	 pi(__#) = 2
1.15/1.18	
1.15/1.18	Problem 1.7: 
1.15/1.18	
1.15/1.18	SCC Processor:
1.15/1.18	-> Pairs:
1.15/1.18	 Empty
1.15/1.18	-> Rules:
1.15/1.18	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.18	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.18	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.15/1.18	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.15/1.18	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.15/1.18	 active(__(nil,X:S)) -> mark(X:S)
1.15/1.18	 active(__(X:S,nil)) -> mark(X:S)
1.15/1.18	 active(and(tt,X:S)) -> mark(X:S)
1.15/1.18	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.15/1.18	 active(isList(nil)) -> mark(tt)
1.15/1.18	 active(isList(V:S)) -> mark(isNeList(V:S))
1.15/1.18	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.15/1.18	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.15/1.18	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.15/1.18	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.15/1.18	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.15/1.18	 active(isPal(nil)) -> mark(tt)
1.15/1.18	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.15/1.18	 active(isQid(a)) -> mark(tt)
1.15/1.18	 active(isQid(e)) -> mark(tt)
1.15/1.18	 active(isQid(i)) -> mark(tt)
1.15/1.18	 active(isQid(o)) -> mark(tt)
1.15/1.18	 active(isQid(u)) -> mark(tt)
1.15/1.18	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.18	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.18	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.15/1.18	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.15/1.18	 isList(active(X:S)) -> isList(X:S)
1.15/1.18	 isList(mark(X:S)) -> isList(X:S)
1.15/1.18	 isNeList(active(X:S)) -> isNeList(X:S)
1.15/1.18	 isNeList(mark(X:S)) -> isNeList(X:S)
1.15/1.18	 isNePal(active(X:S)) -> isNePal(X:S)
1.15/1.18	 isNePal(mark(X:S)) -> isNePal(X:S)
1.15/1.18	 isPal(active(X:S)) -> isPal(X:S)
1.15/1.18	 isPal(mark(X:S)) -> isPal(X:S)
1.15/1.18	 isQid(active(X:S)) -> isQid(X:S)
1.15/1.18	 isQid(mark(X:S)) -> isQid(X:S)
1.15/1.18	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.15/1.18	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.15/1.18	 mark(isList(X:S)) -> active(isList(X:S))
1.15/1.18	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.15/1.18	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.15/1.18	 mark(isPal(X:S)) -> active(isPal(X:S))
1.15/1.18	 mark(isQid(X:S)) -> active(isQid(X:S))
1.15/1.18	 mark(a) -> active(a)
1.15/1.18	 mark(e) -> active(e)
1.15/1.18	 mark(i) -> active(i)
1.15/1.18	 mark(nil) -> active(nil)
1.15/1.18	 mark(o) -> active(o)
1.15/1.18	 mark(tt) -> active(tt)
1.15/1.18	 mark(u) -> active(u)
1.15/1.18	->Strongly Connected Components:
1.15/1.18	 There is no strongly connected component
1.15/1.18	
1.15/1.18	The problem is finite.
1.15/1.18	
1.15/1.18	Problem 1.8: 
1.15/1.18	
1.15/1.18	Reduction Pairs Processor:
1.15/1.18	-> Pairs:
1.15/1.18	 ACTIVE(__(__(X:S,Y:S),Z:S)) -> MARK(__(X:S,__(Y:S,Z:S)))
1.15/1.18	 ACTIVE(__(nil,X:S)) -> MARK(X:S)
1.15/1.18	 ACTIVE(__(X:S,nil)) -> MARK(X:S)
1.15/1.18	 ACTIVE(and(tt,X:S)) -> MARK(X:S)
1.15/1.18	 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(and(isList(V1:S),isList(V2:S)))
1.15/1.18	 ACTIVE(isList(V:S)) -> MARK(isNeList(V:S))
1.15/1.18	 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(and(isList(V1:S),isNeList(V2:S)))
1.15/1.18	 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(and(isNeList(V1:S),isList(V2:S)))
1.15/1.18	 ACTIVE(isNeList(V:S)) -> MARK(isQid(V:S))
1.15/1.18	 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(and(isQid(I:S),isPal(P:S)))
1.15/1.18	 ACTIVE(isNePal(V:S)) -> MARK(isQid(V:S))
1.15/1.18	 ACTIVE(isPal(V:S)) -> MARK(isNePal(V:S))
1.15/1.18	 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
1.15/1.18	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.15/1.18	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.15/1.18	 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S))
1.15/1.18	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
1.15/1.18	 MARK(isList(X:S)) -> ACTIVE(isList(X:S))
1.15/1.18	 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
1.15/1.18	 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
1.15/1.18	 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
1.15/1.18	-> Rules:
1.15/1.18	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.18	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.18	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.15/1.18	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.15/1.18	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.15/1.18	 active(__(nil,X:S)) -> mark(X:S)
1.15/1.18	 active(__(X:S,nil)) -> mark(X:S)
1.15/1.18	 active(and(tt,X:S)) -> mark(X:S)
1.15/1.18	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.15/1.18	 active(isList(nil)) -> mark(tt)
1.15/1.18	 active(isList(V:S)) -> mark(isNeList(V:S))
1.15/1.18	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.15/1.18	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.15/1.18	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.15/1.18	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.15/1.18	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.15/1.18	 active(isPal(nil)) -> mark(tt)
1.15/1.18	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.15/1.18	 active(isQid(a)) -> mark(tt)
1.15/1.18	 active(isQid(e)) -> mark(tt)
1.15/1.18	 active(isQid(i)) -> mark(tt)
1.15/1.18	 active(isQid(o)) -> mark(tt)
1.15/1.18	 active(isQid(u)) -> mark(tt)
1.15/1.18	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.18	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.18	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.15/1.18	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.15/1.18	 isList(active(X:S)) -> isList(X:S)
1.15/1.18	 isList(mark(X:S)) -> isList(X:S)
1.15/1.18	 isNeList(active(X:S)) -> isNeList(X:S)
1.15/1.18	 isNeList(mark(X:S)) -> isNeList(X:S)
1.15/1.18	 isNePal(active(X:S)) -> isNePal(X:S)
1.15/1.18	 isNePal(mark(X:S)) -> isNePal(X:S)
1.15/1.18	 isPal(active(X:S)) -> isPal(X:S)
1.15/1.18	 isPal(mark(X:S)) -> isPal(X:S)
1.15/1.18	 isQid(active(X:S)) -> isQid(X:S)
1.15/1.18	 isQid(mark(X:S)) -> isQid(X:S)
1.15/1.18	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.15/1.18	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.15/1.18	 mark(isList(X:S)) -> active(isList(X:S))
1.15/1.18	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.15/1.18	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.15/1.18	 mark(isPal(X:S)) -> active(isPal(X:S))
1.15/1.18	 mark(isQid(X:S)) -> active(isQid(X:S))
1.15/1.18	 mark(a) -> active(a)
1.15/1.18	 mark(e) -> active(e)
1.15/1.18	 mark(i) -> active(i)
1.15/1.18	 mark(nil) -> active(nil)
1.15/1.18	 mark(o) -> active(o)
1.15/1.18	 mark(tt) -> active(tt)
1.15/1.18	 mark(u) -> active(u)
1.15/1.18	-> Usable rules:
1.15/1.18	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.18	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.18	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.15/1.18	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.15/1.18	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.15/1.18	 active(__(nil,X:S)) -> mark(X:S)
1.15/1.18	 active(__(X:S,nil)) -> mark(X:S)
1.15/1.18	 active(and(tt,X:S)) -> mark(X:S)
1.15/1.18	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.15/1.18	 active(isList(nil)) -> mark(tt)
1.15/1.18	 active(isList(V:S)) -> mark(isNeList(V:S))
1.15/1.18	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.15/1.18	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.15/1.18	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.15/1.18	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.15/1.18	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.15/1.18	 active(isPal(nil)) -> mark(tt)
1.15/1.18	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.15/1.18	 active(isQid(a)) -> mark(tt)
1.15/1.18	 active(isQid(e)) -> mark(tt)
1.15/1.18	 active(isQid(i)) -> mark(tt)
1.15/1.18	 active(isQid(o)) -> mark(tt)
1.15/1.18	 active(isQid(u)) -> mark(tt)
1.15/1.18	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.18	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.18	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.15/1.18	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.15/1.18	 isList(active(X:S)) -> isList(X:S)
1.15/1.18	 isList(mark(X:S)) -> isList(X:S)
1.15/1.18	 isNeList(active(X:S)) -> isNeList(X:S)
1.15/1.18	 isNeList(mark(X:S)) -> isNeList(X:S)
1.15/1.18	 isNePal(active(X:S)) -> isNePal(X:S)
1.15/1.18	 isNePal(mark(X:S)) -> isNePal(X:S)
1.15/1.18	 isPal(active(X:S)) -> isPal(X:S)
1.15/1.18	 isPal(mark(X:S)) -> isPal(X:S)
1.15/1.18	 isQid(active(X:S)) -> isQid(X:S)
1.15/1.18	 isQid(mark(X:S)) -> isQid(X:S)
1.15/1.18	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.15/1.18	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.15/1.18	 mark(isList(X:S)) -> active(isList(X:S))
1.15/1.18	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.15/1.18	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.15/1.18	 mark(isPal(X:S)) -> active(isPal(X:S))
1.15/1.18	 mark(isQid(X:S)) -> active(isQid(X:S))
1.15/1.18	 mark(a) -> active(a)
1.15/1.18	 mark(e) -> active(e)
1.15/1.18	 mark(i) -> active(i)
1.15/1.18	 mark(nil) -> active(nil)
1.15/1.18	 mark(o) -> active(o)
1.15/1.18	 mark(tt) -> active(tt)
1.15/1.18	 mark(u) -> active(u)
1.15/1.18	->Interpretation type:
1.15/1.18	 Linear
1.15/1.18	->Coefficients:
1.15/1.18	 Natural Numbers
1.15/1.18	->Dimension:
1.15/1.18	 1
1.15/1.18	->Bound:
1.15/1.18	 2
1.15/1.18	->Interpretation:
1.15/1.18	 
1.15/1.18	[__](X1,X2) = 2.X1 + X2 + 2
1.15/1.18	[active](X) = X
1.15/1.18	[and](X1,X2) = X1 + X2 + 2
1.15/1.18	[isList](X) = 2.X + 2
1.15/1.18	[isNeList](X) = 2.X + 2
1.15/1.18	[isNePal](X) = X + 2
1.15/1.18	[isPal](X) = 2.X + 2
1.15/1.18	[isQid](X) = 0
1.15/1.18	[mark](X) = X
1.15/1.18	[a] = 0
1.15/1.18	[e] = 2
1.15/1.18	[fSNonEmpty] = 0
1.15/1.18	[i] = 0
1.15/1.18	[nil] = 2
1.15/1.18	[o] = 0
1.15/1.18	[tt] = 0
1.15/1.18	[u] = 2
1.15/1.18	[__#](X1,X2) = 0
1.15/1.18	[ACTIVE](X) = 2.X + 2
1.15/1.18	[AND](X1,X2) = 0
1.15/1.18	[ISLIST](X) = 0
1.15/1.18	[ISNELIST](X) = 0
1.15/1.18	[ISNEPAL](X) = 0
1.15/1.18	[ISPAL](X) = 0
1.15/1.18	[ISQID](X) = 0
1.15/1.18	[MARK](X) = 2.X + 2
1.15/1.18	
1.15/1.18	Problem 1.8: 
1.15/1.18	
1.15/1.18	SCC Processor:
1.15/1.18	-> Pairs:
1.15/1.18	 ACTIVE(__(nil,X:S)) -> MARK(X:S)
1.15/1.18	 ACTIVE(__(X:S,nil)) -> MARK(X:S)
1.15/1.18	 ACTIVE(and(tt,X:S)) -> MARK(X:S)
1.15/1.18	 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(and(isList(V1:S),isList(V2:S)))
1.15/1.18	 ACTIVE(isList(V:S)) -> MARK(isNeList(V:S))
1.15/1.18	 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(and(isList(V1:S),isNeList(V2:S)))
1.15/1.18	 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(and(isNeList(V1:S),isList(V2:S)))
1.15/1.18	 ACTIVE(isNeList(V:S)) -> MARK(isQid(V:S))
1.15/1.18	 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(and(isQid(I:S),isPal(P:S)))
1.15/1.18	 ACTIVE(isNePal(V:S)) -> MARK(isQid(V:S))
1.15/1.18	 ACTIVE(isPal(V:S)) -> MARK(isNePal(V:S))
1.15/1.18	 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
1.15/1.18	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.15/1.18	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.15/1.18	 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S))
1.15/1.18	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
1.15/1.18	 MARK(isList(X:S)) -> ACTIVE(isList(X:S))
1.15/1.18	 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
1.15/1.18	 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
1.15/1.18	 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
1.15/1.18	-> Rules:
1.15/1.18	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.18	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.18	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.15/1.18	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.15/1.18	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.15/1.18	 active(__(nil,X:S)) -> mark(X:S)
1.15/1.18	 active(__(X:S,nil)) -> mark(X:S)
1.15/1.18	 active(and(tt,X:S)) -> mark(X:S)
1.15/1.18	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.15/1.18	 active(isList(nil)) -> mark(tt)
1.15/1.18	 active(isList(V:S)) -> mark(isNeList(V:S))
1.15/1.18	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.15/1.18	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.15/1.18	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.15/1.18	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.15/1.18	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.15/1.18	 active(isPal(nil)) -> mark(tt)
1.15/1.18	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.15/1.18	 active(isQid(a)) -> mark(tt)
1.15/1.18	 active(isQid(e)) -> mark(tt)
1.15/1.18	 active(isQid(i)) -> mark(tt)
1.15/1.18	 active(isQid(o)) -> mark(tt)
1.15/1.18	 active(isQid(u)) -> mark(tt)
1.15/1.18	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.18	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.18	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.15/1.18	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.15/1.18	 isList(active(X:S)) -> isList(X:S)
1.15/1.18	 isList(mark(X:S)) -> isList(X:S)
1.15/1.18	 isNeList(active(X:S)) -> isNeList(X:S)
1.15/1.18	 isNeList(mark(X:S)) -> isNeList(X:S)
1.15/1.18	 isNePal(active(X:S)) -> isNePal(X:S)
1.15/1.18	 isNePal(mark(X:S)) -> isNePal(X:S)
1.15/1.18	 isPal(active(X:S)) -> isPal(X:S)
1.15/1.18	 isPal(mark(X:S)) -> isPal(X:S)
1.15/1.18	 isQid(active(X:S)) -> isQid(X:S)
1.15/1.18	 isQid(mark(X:S)) -> isQid(X:S)
1.15/1.18	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.15/1.18	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.15/1.18	 mark(isList(X:S)) -> active(isList(X:S))
1.15/1.18	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.15/1.18	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.15/1.18	 mark(isPal(X:S)) -> active(isPal(X:S))
1.15/1.18	 mark(isQid(X:S)) -> active(isQid(X:S))
1.15/1.18	 mark(a) -> active(a)
1.15/1.18	 mark(e) -> active(e)
1.15/1.18	 mark(i) -> active(i)
1.15/1.18	 mark(nil) -> active(nil)
1.15/1.18	 mark(o) -> active(o)
1.15/1.18	 mark(tt) -> active(tt)
1.15/1.18	 mark(u) -> active(u)
1.15/1.18	->Strongly Connected Components:
1.15/1.18	->->Cycle:
1.15/1.18	->->-> Pairs:
1.15/1.18	 ACTIVE(__(nil,X:S)) -> MARK(X:S)
1.15/1.18	 ACTIVE(__(X:S,nil)) -> MARK(X:S)
1.15/1.18	 ACTIVE(and(tt,X:S)) -> MARK(X:S)
1.15/1.18	 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(and(isList(V1:S),isList(V2:S)))
1.15/1.18	 ACTIVE(isList(V:S)) -> MARK(isNeList(V:S))
1.15/1.18	 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(and(isList(V1:S),isNeList(V2:S)))
1.15/1.18	 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(and(isNeList(V1:S),isList(V2:S)))
1.15/1.18	 ACTIVE(isNeList(V:S)) -> MARK(isQid(V:S))
1.15/1.18	 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(and(isQid(I:S),isPal(P:S)))
1.15/1.18	 ACTIVE(isNePal(V:S)) -> MARK(isQid(V:S))
1.15/1.18	 ACTIVE(isPal(V:S)) -> MARK(isNePal(V:S))
1.15/1.18	 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
1.15/1.18	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.15/1.18	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.15/1.18	 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S))
1.15/1.18	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
1.15/1.18	 MARK(isList(X:S)) -> ACTIVE(isList(X:S))
1.15/1.18	 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
1.15/1.18	 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
1.15/1.18	 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
1.15/1.18	->->-> Rules:
1.15/1.18	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.18	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.18	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.15/1.18	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.15/1.18	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.15/1.18	 active(__(nil,X:S)) -> mark(X:S)
1.15/1.18	 active(__(X:S,nil)) -> mark(X:S)
1.15/1.18	 active(and(tt,X:S)) -> mark(X:S)
1.15/1.18	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.15/1.18	 active(isList(nil)) -> mark(tt)
1.15/1.18	 active(isList(V:S)) -> mark(isNeList(V:S))
1.15/1.18	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.15/1.18	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.15/1.18	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.15/1.18	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.15/1.18	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.15/1.18	 active(isPal(nil)) -> mark(tt)
1.15/1.18	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.15/1.18	 active(isQid(a)) -> mark(tt)
1.15/1.18	 active(isQid(e)) -> mark(tt)
1.15/1.18	 active(isQid(i)) -> mark(tt)
1.15/1.18	 active(isQid(o)) -> mark(tt)
1.15/1.18	 active(isQid(u)) -> mark(tt)
1.15/1.18	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.18	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.18	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.15/1.18	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.15/1.18	 isList(active(X:S)) -> isList(X:S)
1.15/1.18	 isList(mark(X:S)) -> isList(X:S)
1.15/1.18	 isNeList(active(X:S)) -> isNeList(X:S)
1.15/1.18	 isNeList(mark(X:S)) -> isNeList(X:S)
1.15/1.18	 isNePal(active(X:S)) -> isNePal(X:S)
1.15/1.18	 isNePal(mark(X:S)) -> isNePal(X:S)
1.15/1.18	 isPal(active(X:S)) -> isPal(X:S)
1.15/1.18	 isPal(mark(X:S)) -> isPal(X:S)
1.15/1.18	 isQid(active(X:S)) -> isQid(X:S)
1.15/1.18	 isQid(mark(X:S)) -> isQid(X:S)
1.15/1.18	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.15/1.18	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.15/1.18	 mark(isList(X:S)) -> active(isList(X:S))
1.15/1.18	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.15/1.18	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.15/1.18	 mark(isPal(X:S)) -> active(isPal(X:S))
1.15/1.18	 mark(isQid(X:S)) -> active(isQid(X:S))
1.15/1.18	 mark(a) -> active(a)
1.15/1.18	 mark(e) -> active(e)
1.15/1.18	 mark(i) -> active(i)
1.15/1.18	 mark(nil) -> active(nil)
1.15/1.18	 mark(o) -> active(o)
1.15/1.18	 mark(tt) -> active(tt)
1.15/1.18	 mark(u) -> active(u)
1.15/1.18	
1.15/1.18	Problem 1.8: 
1.15/1.18	
1.15/1.18	Reduction Pairs Processor:
1.15/1.18	-> Pairs:
1.15/1.18	 ACTIVE(__(nil,X:S)) -> MARK(X:S)
1.15/1.18	 ACTIVE(__(X:S,nil)) -> MARK(X:S)
1.15/1.18	 ACTIVE(and(tt,X:S)) -> MARK(X:S)
1.15/1.18	 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(and(isList(V1:S),isList(V2:S)))
1.15/1.18	 ACTIVE(isList(V:S)) -> MARK(isNeList(V:S))
1.15/1.18	 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(and(isList(V1:S),isNeList(V2:S)))
1.15/1.18	 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(and(isNeList(V1:S),isList(V2:S)))
1.15/1.18	 ACTIVE(isNeList(V:S)) -> MARK(isQid(V:S))
1.15/1.18	 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(and(isQid(I:S),isPal(P:S)))
1.15/1.18	 ACTIVE(isNePal(V:S)) -> MARK(isQid(V:S))
1.15/1.18	 ACTIVE(isPal(V:S)) -> MARK(isNePal(V:S))
1.15/1.18	 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
1.15/1.18	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.15/1.18	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.15/1.18	 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S))
1.15/1.18	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
1.15/1.18	 MARK(isList(X:S)) -> ACTIVE(isList(X:S))
1.15/1.18	 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
1.15/1.18	 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
1.15/1.18	 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
1.15/1.18	-> Rules:
1.15/1.18	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.18	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.18	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.15/1.18	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.15/1.18	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.15/1.18	 active(__(nil,X:S)) -> mark(X:S)
1.15/1.18	 active(__(X:S,nil)) -> mark(X:S)
1.15/1.18	 active(and(tt,X:S)) -> mark(X:S)
1.15/1.18	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.15/1.18	 active(isList(nil)) -> mark(tt)
1.15/1.18	 active(isList(V:S)) -> mark(isNeList(V:S))
1.15/1.18	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.15/1.18	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.15/1.18	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.15/1.18	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.15/1.18	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.15/1.18	 active(isPal(nil)) -> mark(tt)
1.15/1.18	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.15/1.18	 active(isQid(a)) -> mark(tt)
1.15/1.18	 active(isQid(e)) -> mark(tt)
1.15/1.18	 active(isQid(i)) -> mark(tt)
1.15/1.18	 active(isQid(o)) -> mark(tt)
1.15/1.18	 active(isQid(u)) -> mark(tt)
1.15/1.18	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.18	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.18	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.15/1.18	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.15/1.18	 isList(active(X:S)) -> isList(X:S)
1.15/1.18	 isList(mark(X:S)) -> isList(X:S)
1.15/1.18	 isNeList(active(X:S)) -> isNeList(X:S)
1.15/1.18	 isNeList(mark(X:S)) -> isNeList(X:S)
1.15/1.18	 isNePal(active(X:S)) -> isNePal(X:S)
1.15/1.18	 isNePal(mark(X:S)) -> isNePal(X:S)
1.15/1.18	 isPal(active(X:S)) -> isPal(X:S)
1.15/1.18	 isPal(mark(X:S)) -> isPal(X:S)
1.15/1.18	 isQid(active(X:S)) -> isQid(X:S)
1.15/1.18	 isQid(mark(X:S)) -> isQid(X:S)
1.15/1.18	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.15/1.18	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.15/1.18	 mark(isList(X:S)) -> active(isList(X:S))
1.15/1.18	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.15/1.18	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.15/1.18	 mark(isPal(X:S)) -> active(isPal(X:S))
1.15/1.18	 mark(isQid(X:S)) -> active(isQid(X:S))
1.15/1.18	 mark(a) -> active(a)
1.15/1.18	 mark(e) -> active(e)
1.15/1.18	 mark(i) -> active(i)
1.15/1.18	 mark(nil) -> active(nil)
1.15/1.18	 mark(o) -> active(o)
1.15/1.18	 mark(tt) -> active(tt)
1.15/1.18	 mark(u) -> active(u)
1.15/1.18	-> Usable rules:
1.15/1.18	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.18	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.18	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.15/1.18	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.15/1.18	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.15/1.18	 active(__(nil,X:S)) -> mark(X:S)
1.15/1.18	 active(__(X:S,nil)) -> mark(X:S)
1.15/1.18	 active(and(tt,X:S)) -> mark(X:S)
1.15/1.18	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.15/1.18	 active(isList(nil)) -> mark(tt)
1.15/1.18	 active(isList(V:S)) -> mark(isNeList(V:S))
1.15/1.18	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.15/1.18	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.15/1.18	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.15/1.18	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.15/1.18	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.15/1.18	 active(isPal(nil)) -> mark(tt)
1.15/1.18	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.15/1.18	 active(isQid(a)) -> mark(tt)
1.15/1.18	 active(isQid(e)) -> mark(tt)
1.15/1.18	 active(isQid(i)) -> mark(tt)
1.15/1.18	 active(isQid(o)) -> mark(tt)
1.15/1.18	 active(isQid(u)) -> mark(tt)
1.15/1.18	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.18	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.18	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.15/1.18	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.15/1.18	 isList(active(X:S)) -> isList(X:S)
1.15/1.18	 isList(mark(X:S)) -> isList(X:S)
1.15/1.18	 isNeList(active(X:S)) -> isNeList(X:S)
1.15/1.18	 isNeList(mark(X:S)) -> isNeList(X:S)
1.15/1.18	 isNePal(active(X:S)) -> isNePal(X:S)
1.15/1.18	 isNePal(mark(X:S)) -> isNePal(X:S)
1.15/1.18	 isPal(active(X:S)) -> isPal(X:S)
1.15/1.18	 isPal(mark(X:S)) -> isPal(X:S)
1.15/1.18	 isQid(active(X:S)) -> isQid(X:S)
1.15/1.18	 isQid(mark(X:S)) -> isQid(X:S)
1.15/1.18	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.15/1.18	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.15/1.18	 mark(isList(X:S)) -> active(isList(X:S))
1.15/1.18	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.15/1.18	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.15/1.18	 mark(isPal(X:S)) -> active(isPal(X:S))
1.15/1.18	 mark(isQid(X:S)) -> active(isQid(X:S))
1.15/1.18	 mark(a) -> active(a)
1.15/1.18	 mark(e) -> active(e)
1.15/1.18	 mark(i) -> active(i)
1.15/1.18	 mark(nil) -> active(nil)
1.15/1.18	 mark(o) -> active(o)
1.15/1.18	 mark(tt) -> active(tt)
1.15/1.18	 mark(u) -> active(u)
1.15/1.18	->Interpretation type:
1.15/1.18	 Linear
1.15/1.18	->Coefficients:
1.15/1.18	 Natural Numbers
1.15/1.18	->Dimension:
1.15/1.18	 1
1.15/1.18	->Bound:
1.15/1.18	 2
1.15/1.18	->Interpretation:
1.15/1.18	 
1.15/1.18	[__](X1,X2) = 2.X1 + X2 + 2
1.15/1.18	[active](X) = X
1.15/1.18	[and](X1,X2) = 2.X1 + X2 + 2
1.15/1.18	[isList](X) = 2.X + 1
1.15/1.18	[isNeList](X) = 2.X + 1
1.15/1.18	[isNePal](X) = 2.X + 2
1.15/1.18	[isPal](X) = 2.X + 2
1.15/1.18	[isQid](X) = 2.X + 1
1.15/1.18	[mark](X) = X
1.15/1.18	[a] = 1
1.15/1.18	[e] = 0
1.15/1.18	[fSNonEmpty] = 0
1.15/1.18	[i] = 0
1.15/1.18	[nil] = 2
1.15/1.18	[o] = 1
1.15/1.18	[tt] = 0
1.15/1.18	[u] = 1
1.15/1.18	[__#](X1,X2) = 0
1.15/1.18	[ACTIVE](X) = 2.X + 2
1.15/1.18	[AND](X1,X2) = 0
1.15/1.18	[ISLIST](X) = 0
1.15/1.18	[ISNELIST](X) = 0
1.15/1.18	[ISNEPAL](X) = 0
1.15/1.18	[ISPAL](X) = 0
1.15/1.18	[ISQID](X) = 0
1.15/1.18	[MARK](X) = 2.X + 2
1.15/1.18	
1.15/1.18	Problem 1.8: 
1.15/1.18	
1.15/1.18	SCC Processor:
1.15/1.18	-> Pairs:
1.15/1.18	 ACTIVE(__(X:S,nil)) -> MARK(X:S)
1.15/1.18	 ACTIVE(and(tt,X:S)) -> MARK(X:S)
1.15/1.18	 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(and(isList(V1:S),isList(V2:S)))
1.15/1.18	 ACTIVE(isList(V:S)) -> MARK(isNeList(V:S))
1.15/1.18	 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(and(isList(V1:S),isNeList(V2:S)))
1.15/1.18	 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(and(isNeList(V1:S),isList(V2:S)))
1.15/1.18	 ACTIVE(isNeList(V:S)) -> MARK(isQid(V:S))
1.15/1.18	 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(and(isQid(I:S),isPal(P:S)))
1.15/1.18	 ACTIVE(isNePal(V:S)) -> MARK(isQid(V:S))
1.15/1.18	 ACTIVE(isPal(V:S)) -> MARK(isNePal(V:S))
1.15/1.18	 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
1.15/1.18	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.15/1.18	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.15/1.18	 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S))
1.15/1.18	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
1.15/1.18	 MARK(isList(X:S)) -> ACTIVE(isList(X:S))
1.15/1.18	 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
1.15/1.18	 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
1.15/1.18	 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
1.15/1.18	-> Rules:
1.15/1.18	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.18	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.18	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.15/1.18	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.15/1.18	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.15/1.18	 active(__(nil,X:S)) -> mark(X:S)
1.15/1.18	 active(__(X:S,nil)) -> mark(X:S)
1.15/1.18	 active(and(tt,X:S)) -> mark(X:S)
1.15/1.18	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.15/1.18	 active(isList(nil)) -> mark(tt)
1.15/1.18	 active(isList(V:S)) -> mark(isNeList(V:S))
1.15/1.18	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.15/1.18	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.15/1.18	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.15/1.18	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.15/1.18	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.15/1.18	 active(isPal(nil)) -> mark(tt)
1.15/1.18	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.15/1.18	 active(isQid(a)) -> mark(tt)
1.15/1.18	 active(isQid(e)) -> mark(tt)
1.15/1.18	 active(isQid(i)) -> mark(tt)
1.15/1.18	 active(isQid(o)) -> mark(tt)
1.15/1.18	 active(isQid(u)) -> mark(tt)
1.15/1.18	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.18	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.18	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.15/1.18	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.15/1.18	 isList(active(X:S)) -> isList(X:S)
1.15/1.18	 isList(mark(X:S)) -> isList(X:S)
1.15/1.18	 isNeList(active(X:S)) -> isNeList(X:S)
1.15/1.18	 isNeList(mark(X:S)) -> isNeList(X:S)
1.15/1.18	 isNePal(active(X:S)) -> isNePal(X:S)
1.15/1.18	 isNePal(mark(X:S)) -> isNePal(X:S)
1.15/1.18	 isPal(active(X:S)) -> isPal(X:S)
1.15/1.18	 isPal(mark(X:S)) -> isPal(X:S)
1.15/1.18	 isQid(active(X:S)) -> isQid(X:S)
1.15/1.18	 isQid(mark(X:S)) -> isQid(X:S)
1.15/1.18	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.15/1.18	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.15/1.18	 mark(isList(X:S)) -> active(isList(X:S))
1.15/1.18	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.15/1.18	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.15/1.18	 mark(isPal(X:S)) -> active(isPal(X:S))
1.15/1.18	 mark(isQid(X:S)) -> active(isQid(X:S))
1.15/1.18	 mark(a) -> active(a)
1.15/1.18	 mark(e) -> active(e)
1.15/1.18	 mark(i) -> active(i)
1.15/1.18	 mark(nil) -> active(nil)
1.15/1.18	 mark(o) -> active(o)
1.15/1.18	 mark(tt) -> active(tt)
1.15/1.18	 mark(u) -> active(u)
1.15/1.18	->Strongly Connected Components:
1.15/1.18	->->Cycle:
1.15/1.18	->->-> Pairs:
1.15/1.18	 ACTIVE(__(X:S,nil)) -> MARK(X:S)
1.15/1.18	 ACTIVE(and(tt,X:S)) -> MARK(X:S)
1.15/1.18	 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(and(isList(V1:S),isList(V2:S)))
1.15/1.18	 ACTIVE(isList(V:S)) -> MARK(isNeList(V:S))
1.15/1.18	 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(and(isList(V1:S),isNeList(V2:S)))
1.15/1.18	 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(and(isNeList(V1:S),isList(V2:S)))
1.15/1.18	 ACTIVE(isNeList(V:S)) -> MARK(isQid(V:S))
1.15/1.18	 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(and(isQid(I:S),isPal(P:S)))
1.15/1.18	 ACTIVE(isNePal(V:S)) -> MARK(isQid(V:S))
1.15/1.18	 ACTIVE(isPal(V:S)) -> MARK(isNePal(V:S))
1.15/1.18	 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
1.15/1.18	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.15/1.18	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.15/1.18	 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S))
1.15/1.18	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
1.15/1.18	 MARK(isList(X:S)) -> ACTIVE(isList(X:S))
1.15/1.18	 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
1.15/1.18	 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
1.15/1.18	 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
1.15/1.18	->->-> Rules:
1.15/1.18	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.18	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.18	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.15/1.18	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.15/1.18	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.15/1.18	 active(__(nil,X:S)) -> mark(X:S)
1.15/1.18	 active(__(X:S,nil)) -> mark(X:S)
1.15/1.18	 active(and(tt,X:S)) -> mark(X:S)
1.15/1.18	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.15/1.18	 active(isList(nil)) -> mark(tt)
1.15/1.18	 active(isList(V:S)) -> mark(isNeList(V:S))
1.15/1.18	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.15/1.18	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.15/1.18	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.15/1.18	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.15/1.18	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.15/1.18	 active(isPal(nil)) -> mark(tt)
1.15/1.18	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.15/1.18	 active(isQid(a)) -> mark(tt)
1.15/1.18	 active(isQid(e)) -> mark(tt)
1.15/1.18	 active(isQid(i)) -> mark(tt)
1.15/1.18	 active(isQid(o)) -> mark(tt)
1.15/1.18	 active(isQid(u)) -> mark(tt)
1.15/1.18	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.18	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.18	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.15/1.18	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.15/1.18	 isList(active(X:S)) -> isList(X:S)
1.15/1.18	 isList(mark(X:S)) -> isList(X:S)
1.15/1.18	 isNeList(active(X:S)) -> isNeList(X:S)
1.15/1.18	 isNeList(mark(X:S)) -> isNeList(X:S)
1.15/1.18	 isNePal(active(X:S)) -> isNePal(X:S)
1.15/1.18	 isNePal(mark(X:S)) -> isNePal(X:S)
1.15/1.18	 isPal(active(X:S)) -> isPal(X:S)
1.15/1.18	 isPal(mark(X:S)) -> isPal(X:S)
1.15/1.18	 isQid(active(X:S)) -> isQid(X:S)
1.15/1.18	 isQid(mark(X:S)) -> isQid(X:S)
1.15/1.18	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.15/1.18	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.15/1.18	 mark(isList(X:S)) -> active(isList(X:S))
1.15/1.18	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.15/1.18	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.15/1.18	 mark(isPal(X:S)) -> active(isPal(X:S))
1.15/1.18	 mark(isQid(X:S)) -> active(isQid(X:S))
1.15/1.18	 mark(a) -> active(a)
1.15/1.18	 mark(e) -> active(e)
1.15/1.18	 mark(i) -> active(i)
1.15/1.18	 mark(nil) -> active(nil)
1.15/1.18	 mark(o) -> active(o)
1.15/1.18	 mark(tt) -> active(tt)
1.15/1.18	 mark(u) -> active(u)
1.15/1.18	
1.15/1.18	Problem 1.8: 
1.15/1.18	
1.15/1.18	Reduction Pairs Processor:
1.15/1.18	-> Pairs:
1.15/1.18	 ACTIVE(__(X:S,nil)) -> MARK(X:S)
1.15/1.18	 ACTIVE(and(tt,X:S)) -> MARK(X:S)
1.15/1.18	 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(and(isList(V1:S),isList(V2:S)))
1.15/1.18	 ACTIVE(isList(V:S)) -> MARK(isNeList(V:S))
1.15/1.18	 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(and(isList(V1:S),isNeList(V2:S)))
1.15/1.18	 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(and(isNeList(V1:S),isList(V2:S)))
1.15/1.18	 ACTIVE(isNeList(V:S)) -> MARK(isQid(V:S))
1.15/1.18	 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(and(isQid(I:S),isPal(P:S)))
1.15/1.18	 ACTIVE(isNePal(V:S)) -> MARK(isQid(V:S))
1.15/1.18	 ACTIVE(isPal(V:S)) -> MARK(isNePal(V:S))
1.15/1.18	 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
1.15/1.18	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.15/1.18	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.15/1.18	 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S))
1.15/1.18	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
1.15/1.18	 MARK(isList(X:S)) -> ACTIVE(isList(X:S))
1.15/1.18	 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
1.15/1.18	 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
1.15/1.18	 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
1.15/1.18	-> Rules:
1.15/1.18	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.18	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.18	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.15/1.18	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.15/1.18	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.15/1.18	 active(__(nil,X:S)) -> mark(X:S)
1.15/1.18	 active(__(X:S,nil)) -> mark(X:S)
1.15/1.18	 active(and(tt,X:S)) -> mark(X:S)
1.15/1.18	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.15/1.18	 active(isList(nil)) -> mark(tt)
1.15/1.18	 active(isList(V:S)) -> mark(isNeList(V:S))
1.15/1.18	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.15/1.18	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.15/1.18	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.15/1.18	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.15/1.18	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.15/1.18	 active(isPal(nil)) -> mark(tt)
1.15/1.18	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.15/1.18	 active(isQid(a)) -> mark(tt)
1.15/1.18	 active(isQid(e)) -> mark(tt)
1.15/1.18	 active(isQid(i)) -> mark(tt)
1.15/1.18	 active(isQid(o)) -> mark(tt)
1.15/1.18	 active(isQid(u)) -> mark(tt)
1.15/1.18	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.18	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.18	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.15/1.18	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.15/1.18	 isList(active(X:S)) -> isList(X:S)
1.15/1.18	 isList(mark(X:S)) -> isList(X:S)
1.15/1.18	 isNeList(active(X:S)) -> isNeList(X:S)
1.15/1.18	 isNeList(mark(X:S)) -> isNeList(X:S)
1.15/1.18	 isNePal(active(X:S)) -> isNePal(X:S)
1.15/1.18	 isNePal(mark(X:S)) -> isNePal(X:S)
1.15/1.18	 isPal(active(X:S)) -> isPal(X:S)
1.15/1.18	 isPal(mark(X:S)) -> isPal(X:S)
1.15/1.18	 isQid(active(X:S)) -> isQid(X:S)
1.15/1.18	 isQid(mark(X:S)) -> isQid(X:S)
1.15/1.18	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.15/1.18	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.15/1.18	 mark(isList(X:S)) -> active(isList(X:S))
1.15/1.18	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.15/1.18	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.15/1.18	 mark(isPal(X:S)) -> active(isPal(X:S))
1.15/1.18	 mark(isQid(X:S)) -> active(isQid(X:S))
1.15/1.18	 mark(a) -> active(a)
1.15/1.18	 mark(e) -> active(e)
1.15/1.18	 mark(i) -> active(i)
1.15/1.18	 mark(nil) -> active(nil)
1.15/1.18	 mark(o) -> active(o)
1.15/1.18	 mark(tt) -> active(tt)
1.15/1.18	 mark(u) -> active(u)
1.15/1.18	-> Usable rules:
1.15/1.18	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.18	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.18	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.15/1.18	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.15/1.18	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.15/1.18	 active(__(nil,X:S)) -> mark(X:S)
1.15/1.18	 active(__(X:S,nil)) -> mark(X:S)
1.15/1.18	 active(and(tt,X:S)) -> mark(X:S)
1.15/1.18	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.15/1.18	 active(isList(nil)) -> mark(tt)
1.15/1.18	 active(isList(V:S)) -> mark(isNeList(V:S))
1.15/1.18	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.15/1.18	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.15/1.18	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.15/1.18	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.15/1.18	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.15/1.18	 active(isPal(nil)) -> mark(tt)
1.15/1.18	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.15/1.18	 active(isQid(a)) -> mark(tt)
1.15/1.18	 active(isQid(e)) -> mark(tt)
1.15/1.18	 active(isQid(i)) -> mark(tt)
1.15/1.18	 active(isQid(o)) -> mark(tt)
1.15/1.18	 active(isQid(u)) -> mark(tt)
1.15/1.18	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.18	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.18	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.15/1.18	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.15/1.18	 isList(active(X:S)) -> isList(X:S)
1.15/1.18	 isList(mark(X:S)) -> isList(X:S)
1.15/1.18	 isNeList(active(X:S)) -> isNeList(X:S)
1.15/1.18	 isNeList(mark(X:S)) -> isNeList(X:S)
1.15/1.18	 isNePal(active(X:S)) -> isNePal(X:S)
1.15/1.18	 isNePal(mark(X:S)) -> isNePal(X:S)
1.15/1.18	 isPal(active(X:S)) -> isPal(X:S)
1.15/1.18	 isPal(mark(X:S)) -> isPal(X:S)
1.15/1.18	 isQid(active(X:S)) -> isQid(X:S)
1.15/1.18	 isQid(mark(X:S)) -> isQid(X:S)
1.15/1.18	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.15/1.18	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.15/1.18	 mark(isList(X:S)) -> active(isList(X:S))
1.15/1.18	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.15/1.18	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.15/1.18	 mark(isPal(X:S)) -> active(isPal(X:S))
1.15/1.18	 mark(isQid(X:S)) -> active(isQid(X:S))
1.15/1.18	 mark(a) -> active(a)
1.15/1.18	 mark(e) -> active(e)
1.15/1.18	 mark(i) -> active(i)
1.15/1.18	 mark(nil) -> active(nil)
1.15/1.18	 mark(o) -> active(o)
1.15/1.18	 mark(tt) -> active(tt)
1.15/1.18	 mark(u) -> active(u)
1.15/1.18	->Interpretation type:
1.15/1.18	 Linear
1.15/1.18	->Coefficients:
1.15/1.18	 Natural Numbers
1.15/1.18	->Dimension:
1.15/1.18	 1
1.15/1.18	->Bound:
1.15/1.18	 2
1.15/1.18	->Interpretation:
1.15/1.18	 
1.15/1.18	[__](X1,X2) = 2.X1 + X2 + 2
1.15/1.18	[active](X) = X
1.15/1.18	[and](X1,X2) = X1 + X2 + 2
1.15/1.18	[isList](X) = 2.X + 2
1.15/1.18	[isNeList](X) = 2.X + 2
1.15/1.18	[isNePal](X) = 2.X + 2
1.15/1.18	[isPal](X) = 2.X + 2
1.15/1.18	[isQid](X) = X + 1
1.15/1.18	[mark](X) = X
1.15/1.18	[a] = 1
1.15/1.18	[e] = 2
1.15/1.18	[fSNonEmpty] = 0
1.15/1.18	[i] = 2
1.15/1.18	[nil] = 2
1.15/1.18	[o] = 2
1.15/1.18	[tt] = 1
1.15/1.18	[u] = 2
1.15/1.18	[__#](X1,X2) = 0
1.15/1.18	[ACTIVE](X) = 2.X + 2
1.15/1.18	[AND](X1,X2) = 0
1.15/1.18	[ISLIST](X) = 0
1.15/1.18	[ISNELIST](X) = 0
1.15/1.18	[ISNEPAL](X) = 0
1.15/1.18	[ISPAL](X) = 0
1.15/1.18	[ISQID](X) = 0
1.15/1.18	[MARK](X) = 2.X + 2
1.15/1.18	
1.15/1.18	Problem 1.8: 
1.15/1.18	
1.15/1.18	SCC Processor:
1.15/1.18	-> Pairs:
1.15/1.18	 ACTIVE(and(tt,X:S)) -> MARK(X:S)
1.15/1.18	 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(and(isList(V1:S),isList(V2:S)))
1.15/1.18	 ACTIVE(isList(V:S)) -> MARK(isNeList(V:S))
1.15/1.18	 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(and(isList(V1:S),isNeList(V2:S)))
1.15/1.18	 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(and(isNeList(V1:S),isList(V2:S)))
1.15/1.18	 ACTIVE(isNeList(V:S)) -> MARK(isQid(V:S))
1.15/1.18	 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(and(isQid(I:S),isPal(P:S)))
1.15/1.18	 ACTIVE(isNePal(V:S)) -> MARK(isQid(V:S))
1.15/1.18	 ACTIVE(isPal(V:S)) -> MARK(isNePal(V:S))
1.15/1.18	 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
1.15/1.18	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.15/1.18	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.15/1.18	 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S))
1.15/1.18	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
1.15/1.18	 MARK(isList(X:S)) -> ACTIVE(isList(X:S))
1.15/1.18	 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
1.15/1.18	 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
1.15/1.18	 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
1.15/1.18	-> Rules:
1.15/1.18	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.18	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.18	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.15/1.18	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.15/1.18	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.15/1.18	 active(__(nil,X:S)) -> mark(X:S)
1.15/1.18	 active(__(X:S,nil)) -> mark(X:S)
1.15/1.18	 active(and(tt,X:S)) -> mark(X:S)
1.15/1.18	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.15/1.18	 active(isList(nil)) -> mark(tt)
1.15/1.18	 active(isList(V:S)) -> mark(isNeList(V:S))
1.15/1.18	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.15/1.18	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.15/1.18	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.15/1.18	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.15/1.18	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.15/1.18	 active(isPal(nil)) -> mark(tt)
1.15/1.18	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.15/1.18	 active(isQid(a)) -> mark(tt)
1.15/1.18	 active(isQid(e)) -> mark(tt)
1.15/1.18	 active(isQid(i)) -> mark(tt)
1.15/1.18	 active(isQid(o)) -> mark(tt)
1.15/1.18	 active(isQid(u)) -> mark(tt)
1.15/1.18	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.18	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.18	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.15/1.18	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.15/1.18	 isList(active(X:S)) -> isList(X:S)
1.15/1.18	 isList(mark(X:S)) -> isList(X:S)
1.15/1.18	 isNeList(active(X:S)) -> isNeList(X:S)
1.15/1.18	 isNeList(mark(X:S)) -> isNeList(X:S)
1.15/1.18	 isNePal(active(X:S)) -> isNePal(X:S)
1.15/1.18	 isNePal(mark(X:S)) -> isNePal(X:S)
1.15/1.18	 isPal(active(X:S)) -> isPal(X:S)
1.15/1.18	 isPal(mark(X:S)) -> isPal(X:S)
1.15/1.18	 isQid(active(X:S)) -> isQid(X:S)
1.15/1.18	 isQid(mark(X:S)) -> isQid(X:S)
1.15/1.18	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.15/1.18	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.15/1.18	 mark(isList(X:S)) -> active(isList(X:S))
1.15/1.18	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.15/1.18	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.15/1.18	 mark(isPal(X:S)) -> active(isPal(X:S))
1.15/1.18	 mark(isQid(X:S)) -> active(isQid(X:S))
1.15/1.18	 mark(a) -> active(a)
1.15/1.18	 mark(e) -> active(e)
1.15/1.18	 mark(i) -> active(i)
1.15/1.18	 mark(nil) -> active(nil)
1.15/1.18	 mark(o) -> active(o)
1.15/1.18	 mark(tt) -> active(tt)
1.15/1.18	 mark(u) -> active(u)
1.15/1.18	->Strongly Connected Components:
1.15/1.18	->->Cycle:
1.15/1.18	->->-> Pairs:
1.15/1.18	 ACTIVE(and(tt,X:S)) -> MARK(X:S)
1.15/1.18	 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(and(isList(V1:S),isList(V2:S)))
1.15/1.18	 ACTIVE(isList(V:S)) -> MARK(isNeList(V:S))
1.15/1.18	 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(and(isList(V1:S),isNeList(V2:S)))
1.15/1.18	 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(and(isNeList(V1:S),isList(V2:S)))
1.15/1.18	 ACTIVE(isNeList(V:S)) -> MARK(isQid(V:S))
1.15/1.18	 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(and(isQid(I:S),isPal(P:S)))
1.15/1.18	 ACTIVE(isNePal(V:S)) -> MARK(isQid(V:S))
1.15/1.18	 ACTIVE(isPal(V:S)) -> MARK(isNePal(V:S))
1.15/1.18	 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
1.15/1.18	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.15/1.18	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.15/1.18	 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S))
1.15/1.18	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
1.15/1.18	 MARK(isList(X:S)) -> ACTIVE(isList(X:S))
1.15/1.18	 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
1.15/1.18	 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
1.15/1.18	 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
1.15/1.18	->->-> Rules:
1.15/1.18	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.18	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.18	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.15/1.18	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.15/1.18	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.15/1.18	 active(__(nil,X:S)) -> mark(X:S)
1.15/1.18	 active(__(X:S,nil)) -> mark(X:S)
1.15/1.18	 active(and(tt,X:S)) -> mark(X:S)
1.15/1.18	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.15/1.18	 active(isList(nil)) -> mark(tt)
1.15/1.18	 active(isList(V:S)) -> mark(isNeList(V:S))
1.15/1.18	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.15/1.18	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.15/1.18	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.15/1.18	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.15/1.18	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.15/1.18	 active(isPal(nil)) -> mark(tt)
1.15/1.18	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.15/1.18	 active(isQid(a)) -> mark(tt)
1.15/1.18	 active(isQid(e)) -> mark(tt)
1.15/1.18	 active(isQid(i)) -> mark(tt)
1.15/1.18	 active(isQid(o)) -> mark(tt)
1.15/1.18	 active(isQid(u)) -> mark(tt)
1.15/1.18	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.18	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.18	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.15/1.18	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.15/1.18	 isList(active(X:S)) -> isList(X:S)
1.15/1.18	 isList(mark(X:S)) -> isList(X:S)
1.15/1.18	 isNeList(active(X:S)) -> isNeList(X:S)
1.15/1.18	 isNeList(mark(X:S)) -> isNeList(X:S)
1.15/1.18	 isNePal(active(X:S)) -> isNePal(X:S)
1.15/1.18	 isNePal(mark(X:S)) -> isNePal(X:S)
1.15/1.18	 isPal(active(X:S)) -> isPal(X:S)
1.15/1.18	 isPal(mark(X:S)) -> isPal(X:S)
1.15/1.18	 isQid(active(X:S)) -> isQid(X:S)
1.15/1.18	 isQid(mark(X:S)) -> isQid(X:S)
1.15/1.18	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.15/1.18	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.15/1.18	 mark(isList(X:S)) -> active(isList(X:S))
1.15/1.18	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.15/1.18	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.15/1.18	 mark(isPal(X:S)) -> active(isPal(X:S))
1.15/1.18	 mark(isQid(X:S)) -> active(isQid(X:S))
1.15/1.18	 mark(a) -> active(a)
1.15/1.18	 mark(e) -> active(e)
1.15/1.18	 mark(i) -> active(i)
1.15/1.18	 mark(nil) -> active(nil)
1.15/1.18	 mark(o) -> active(o)
1.15/1.18	 mark(tt) -> active(tt)
1.15/1.18	 mark(u) -> active(u)
1.15/1.18	
1.15/1.18	Problem 1.8: 
1.15/1.18	
1.15/1.18	Reduction Pairs Processor:
1.15/1.18	-> Pairs:
1.15/1.18	 ACTIVE(and(tt,X:S)) -> MARK(X:S)
1.15/1.18	 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(and(isList(V1:S),isList(V2:S)))
1.15/1.18	 ACTIVE(isList(V:S)) -> MARK(isNeList(V:S))
1.15/1.18	 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(and(isList(V1:S),isNeList(V2:S)))
1.15/1.18	 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(and(isNeList(V1:S),isList(V2:S)))
1.15/1.18	 ACTIVE(isNeList(V:S)) -> MARK(isQid(V:S))
1.15/1.18	 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(and(isQid(I:S),isPal(P:S)))
1.15/1.19	 ACTIVE(isNePal(V:S)) -> MARK(isQid(V:S))
1.15/1.19	 ACTIVE(isPal(V:S)) -> MARK(isNePal(V:S))
1.15/1.19	 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
1.15/1.19	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.15/1.19	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.15/1.19	 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S))
1.15/1.19	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
1.15/1.19	 MARK(isList(X:S)) -> ACTIVE(isList(X:S))
1.15/1.19	 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
1.15/1.19	 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
1.15/1.19	 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
1.15/1.19	-> Rules:
1.15/1.19	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.19	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.19	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.15/1.19	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.15/1.19	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.15/1.19	 active(__(nil,X:S)) -> mark(X:S)
1.15/1.19	 active(__(X:S,nil)) -> mark(X:S)
1.15/1.19	 active(and(tt,X:S)) -> mark(X:S)
1.15/1.19	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.15/1.19	 active(isList(nil)) -> mark(tt)
1.15/1.19	 active(isList(V:S)) -> mark(isNeList(V:S))
1.15/1.19	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.15/1.19	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.15/1.19	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.15/1.19	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.15/1.19	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.15/1.19	 active(isPal(nil)) -> mark(tt)
1.15/1.19	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.15/1.19	 active(isQid(a)) -> mark(tt)
1.15/1.19	 active(isQid(e)) -> mark(tt)
1.15/1.19	 active(isQid(i)) -> mark(tt)
1.15/1.19	 active(isQid(o)) -> mark(tt)
1.15/1.19	 active(isQid(u)) -> mark(tt)
1.15/1.19	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.19	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.19	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.15/1.19	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.15/1.19	 isList(active(X:S)) -> isList(X:S)
1.15/1.19	 isList(mark(X:S)) -> isList(X:S)
1.15/1.19	 isNeList(active(X:S)) -> isNeList(X:S)
1.15/1.19	 isNeList(mark(X:S)) -> isNeList(X:S)
1.15/1.19	 isNePal(active(X:S)) -> isNePal(X:S)
1.15/1.19	 isNePal(mark(X:S)) -> isNePal(X:S)
1.15/1.19	 isPal(active(X:S)) -> isPal(X:S)
1.15/1.19	 isPal(mark(X:S)) -> isPal(X:S)
1.15/1.19	 isQid(active(X:S)) -> isQid(X:S)
1.15/1.19	 isQid(mark(X:S)) -> isQid(X:S)
1.15/1.19	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.15/1.19	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.15/1.19	 mark(isList(X:S)) -> active(isList(X:S))
1.15/1.19	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.15/1.19	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.15/1.19	 mark(isPal(X:S)) -> active(isPal(X:S))
1.15/1.19	 mark(isQid(X:S)) -> active(isQid(X:S))
1.15/1.19	 mark(a) -> active(a)
1.15/1.19	 mark(e) -> active(e)
1.15/1.19	 mark(i) -> active(i)
1.15/1.19	 mark(nil) -> active(nil)
1.15/1.19	 mark(o) -> active(o)
1.15/1.19	 mark(tt) -> active(tt)
1.15/1.19	 mark(u) -> active(u)
1.15/1.19	-> Usable rules:
1.15/1.19	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.19	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.15/1.19	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.15/1.19	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.15/1.19	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.15/1.19	 active(__(nil,X:S)) -> mark(X:S)
1.15/1.19	 active(__(X:S,nil)) -> mark(X:S)
1.15/1.19	 active(and(tt,X:S)) -> mark(X:S)
1.15/1.19	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.15/1.19	 active(isList(nil)) -> mark(tt)
1.15/1.19	 active(isList(V:S)) -> mark(isNeList(V:S))
1.15/1.19	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.15/1.19	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.15/1.19	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.15/1.19	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.15/1.19	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.15/1.19	 active(isPal(nil)) -> mark(tt)
1.15/1.19	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.15/1.19	 active(isQid(a)) -> mark(tt)
1.15/1.19	 active(isQid(e)) -> mark(tt)
1.15/1.19	 active(isQid(i)) -> mark(tt)
1.15/1.19	 active(isQid(o)) -> mark(tt)
1.15/1.19	 active(isQid(u)) -> mark(tt)
1.15/1.19	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.19	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.15/1.19	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.15/1.19	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.15/1.19	 isList(active(X:S)) -> isList(X:S)
1.15/1.19	 isList(mark(X:S)) -> isList(X:S)
1.15/1.19	 isNeList(active(X:S)) -> isNeList(X:S)
1.15/1.19	 isNeList(mark(X:S)) -> isNeList(X:S)
1.15/1.19	 isNePal(active(X:S)) -> isNePal(X:S)
1.15/1.19	 isNePal(mark(X:S)) -> isNePal(X:S)
1.15/1.19	 isPal(active(X:S)) -> isPal(X:S)
1.15/1.19	 isPal(mark(X:S)) -> isPal(X:S)
1.15/1.19	 isQid(active(X:S)) -> isQid(X:S)
1.15/1.19	 isQid(mark(X:S)) -> isQid(X:S)
1.15/1.19	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.15/1.19	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.15/1.19	 mark(isList(X:S)) -> active(isList(X:S))
1.15/1.19	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.15/1.19	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.15/1.19	 mark(isPal(X:S)) -> active(isPal(X:S))
1.15/1.19	 mark(isQid(X:S)) -> active(isQid(X:S))
1.15/1.19	 mark(a) -> active(a)
1.15/1.19	 mark(e) -> active(e)
1.15/1.19	 mark(i) -> active(i)
1.15/1.19	 mark(nil) -> active(nil)
1.15/1.19	 mark(o) -> active(o)
1.15/1.19	 mark(tt) -> active(tt)
1.15/1.19	 mark(u) -> active(u)
1.15/1.19	->Interpretation type:
1.15/1.19	 Linear
1.15/1.19	->Coefficients:
1.15/1.19	 Natural Numbers
1.15/1.19	->Dimension:
1.15/1.19	 1
1.15/1.19	->Bound:
1.15/1.19	 2
1.15/1.19	->Interpretation:
1.15/1.19	 
1.15/1.19	[__](X1,X2) = X1 + X2 + 2
1.15/1.19	[active](X) = X
1.15/1.19	[and](X1,X2) = X1 + X2 + 2
1.15/1.19	[isList](X) = 2.X + 2
1.15/1.19	[isNeList](X) = 2.X + 1
1.15/1.19	[isNePal](X) = 2.X + 1
1.15/1.19	[isPal](X) = 2.X + 1
1.15/1.19	[isQid](X) = 1
1.15/1.19	[mark](X) = X
1.15/1.19	[a] = 2
1.15/1.19	[e] = 2
1.15/1.19	[fSNonEmpty] = 0
1.15/1.19	[i] = 2
1.15/1.19	[nil] = 2
1.15/1.19	[o] = 0
1.15/1.19	[tt] = 1
1.15/1.19	[u] = 1
1.15/1.19	[__#](X1,X2) = 0
1.15/1.19	[ACTIVE](X) = 2.X + 2
1.15/1.19	[AND](X1,X2) = 0
1.15/1.19	[ISLIST](X) = 0
1.15/1.19	[ISNELIST](X) = 0
1.15/1.19	[ISNEPAL](X) = 0
1.15/1.19	[ISPAL](X) = 0
1.15/1.19	[ISQID](X) = 0
1.15/1.19	[MARK](X) = 2.X + 2
1.15/1.19	
1.15/1.19	Problem 1.8: 
1.15/1.19	
1.15/1.19	SCC Processor:
1.15/1.19	-> Pairs:
1.15/1.19	 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(and(isList(V1:S),isList(V2:S)))
1.17/1.19	 ACTIVE(isList(V:S)) -> MARK(isNeList(V:S))
1.17/1.19	 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(and(isList(V1:S),isNeList(V2:S)))
1.17/1.19	 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(and(isNeList(V1:S),isList(V2:S)))
1.17/1.19	 ACTIVE(isNeList(V:S)) -> MARK(isQid(V:S))
1.17/1.19	 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(and(isQid(I:S),isPal(P:S)))
1.17/1.19	 ACTIVE(isNePal(V:S)) -> MARK(isQid(V:S))
1.17/1.19	 ACTIVE(isPal(V:S)) -> MARK(isNePal(V:S))
1.17/1.19	 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
1.17/1.19	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.19	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.17/1.19	 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S))
1.17/1.19	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.19	 MARK(isList(X:S)) -> ACTIVE(isList(X:S))
1.17/1.19	 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
1.17/1.19	 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
1.17/1.19	 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
1.17/1.19	-> Rules:
1.17/1.19	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.19	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.19	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.17/1.19	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.17/1.19	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.17/1.19	 active(__(nil,X:S)) -> mark(X:S)
1.17/1.19	 active(__(X:S,nil)) -> mark(X:S)
1.17/1.19	 active(and(tt,X:S)) -> mark(X:S)
1.17/1.19	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.17/1.19	 active(isList(nil)) -> mark(tt)
1.17/1.19	 active(isList(V:S)) -> mark(isNeList(V:S))
1.17/1.19	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.17/1.19	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.17/1.19	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.17/1.19	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.17/1.19	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.17/1.19	 active(isPal(nil)) -> mark(tt)
1.17/1.19	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.17/1.19	 active(isQid(a)) -> mark(tt)
1.17/1.19	 active(isQid(e)) -> mark(tt)
1.17/1.19	 active(isQid(i)) -> mark(tt)
1.17/1.19	 active(isQid(o)) -> mark(tt)
1.17/1.19	 active(isQid(u)) -> mark(tt)
1.17/1.19	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.19	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.19	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.17/1.19	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.17/1.19	 isList(active(X:S)) -> isList(X:S)
1.17/1.19	 isList(mark(X:S)) -> isList(X:S)
1.17/1.19	 isNeList(active(X:S)) -> isNeList(X:S)
1.17/1.19	 isNeList(mark(X:S)) -> isNeList(X:S)
1.17/1.19	 isNePal(active(X:S)) -> isNePal(X:S)
1.17/1.19	 isNePal(mark(X:S)) -> isNePal(X:S)
1.17/1.19	 isPal(active(X:S)) -> isPal(X:S)
1.17/1.19	 isPal(mark(X:S)) -> isPal(X:S)
1.17/1.19	 isQid(active(X:S)) -> isQid(X:S)
1.17/1.19	 isQid(mark(X:S)) -> isQid(X:S)
1.17/1.19	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.17/1.19	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.17/1.19	 mark(isList(X:S)) -> active(isList(X:S))
1.17/1.19	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.17/1.19	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.17/1.19	 mark(isPal(X:S)) -> active(isPal(X:S))
1.17/1.19	 mark(isQid(X:S)) -> active(isQid(X:S))
1.17/1.19	 mark(a) -> active(a)
1.17/1.19	 mark(e) -> active(e)
1.17/1.19	 mark(i) -> active(i)
1.17/1.19	 mark(nil) -> active(nil)
1.17/1.19	 mark(o) -> active(o)
1.17/1.19	 mark(tt) -> active(tt)
1.17/1.19	 mark(u) -> active(u)
1.17/1.19	->Strongly Connected Components:
1.17/1.19	->->Cycle:
1.17/1.19	->->-> Pairs:
1.17/1.19	 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(and(isList(V1:S),isList(V2:S)))
1.17/1.19	 ACTIVE(isList(V:S)) -> MARK(isNeList(V:S))
1.17/1.19	 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(and(isList(V1:S),isNeList(V2:S)))
1.17/1.19	 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(and(isNeList(V1:S),isList(V2:S)))
1.17/1.19	 ACTIVE(isNeList(V:S)) -> MARK(isQid(V:S))
1.17/1.19	 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(and(isQid(I:S),isPal(P:S)))
1.17/1.19	 ACTIVE(isNePal(V:S)) -> MARK(isQid(V:S))
1.17/1.19	 ACTIVE(isPal(V:S)) -> MARK(isNePal(V:S))
1.17/1.19	 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
1.17/1.19	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.19	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.17/1.19	 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S))
1.17/1.19	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.19	 MARK(isList(X:S)) -> ACTIVE(isList(X:S))
1.17/1.19	 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
1.17/1.19	 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
1.17/1.19	 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
1.17/1.19	->->-> Rules:
1.17/1.19	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.19	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.19	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.17/1.19	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.17/1.19	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.17/1.19	 active(__(nil,X:S)) -> mark(X:S)
1.17/1.19	 active(__(X:S,nil)) -> mark(X:S)
1.17/1.19	 active(and(tt,X:S)) -> mark(X:S)
1.17/1.19	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.17/1.19	 active(isList(nil)) -> mark(tt)
1.17/1.19	 active(isList(V:S)) -> mark(isNeList(V:S))
1.17/1.19	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.17/1.19	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.17/1.19	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.17/1.19	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.17/1.19	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.17/1.19	 active(isPal(nil)) -> mark(tt)
1.17/1.19	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.17/1.19	 active(isQid(a)) -> mark(tt)
1.17/1.19	 active(isQid(e)) -> mark(tt)
1.17/1.19	 active(isQid(i)) -> mark(tt)
1.17/1.19	 active(isQid(o)) -> mark(tt)
1.17/1.19	 active(isQid(u)) -> mark(tt)
1.17/1.19	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.19	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.19	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.17/1.19	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.17/1.19	 isList(active(X:S)) -> isList(X:S)
1.17/1.19	 isList(mark(X:S)) -> isList(X:S)
1.17/1.19	 isNeList(active(X:S)) -> isNeList(X:S)
1.17/1.19	 isNeList(mark(X:S)) -> isNeList(X:S)
1.17/1.19	 isNePal(active(X:S)) -> isNePal(X:S)
1.17/1.19	 isNePal(mark(X:S)) -> isNePal(X:S)
1.17/1.19	 isPal(active(X:S)) -> isPal(X:S)
1.17/1.19	 isPal(mark(X:S)) -> isPal(X:S)
1.17/1.19	 isQid(active(X:S)) -> isQid(X:S)
1.17/1.19	 isQid(mark(X:S)) -> isQid(X:S)
1.17/1.19	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.17/1.19	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.17/1.19	 mark(isList(X:S)) -> active(isList(X:S))
1.17/1.19	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.17/1.19	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.17/1.19	 mark(isPal(X:S)) -> active(isPal(X:S))
1.17/1.19	 mark(isQid(X:S)) -> active(isQid(X:S))
1.17/1.19	 mark(a) -> active(a)
1.17/1.19	 mark(e) -> active(e)
1.17/1.19	 mark(i) -> active(i)
1.17/1.19	 mark(nil) -> active(nil)
1.17/1.19	 mark(o) -> active(o)
1.17/1.19	 mark(tt) -> active(tt)
1.17/1.19	 mark(u) -> active(u)
1.17/1.19	
1.17/1.19	Problem 1.8: 
1.17/1.19	
1.17/1.19	Reduction Pairs Processor:
1.17/1.19	-> Pairs:
1.17/1.19	 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(and(isList(V1:S),isList(V2:S)))
1.17/1.19	 ACTIVE(isList(V:S)) -> MARK(isNeList(V:S))
1.17/1.19	 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(and(isList(V1:S),isNeList(V2:S)))
1.17/1.19	 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(and(isNeList(V1:S),isList(V2:S)))
1.17/1.19	 ACTIVE(isNeList(V:S)) -> MARK(isQid(V:S))
1.17/1.19	 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(and(isQid(I:S),isPal(P:S)))
1.17/1.19	 ACTIVE(isNePal(V:S)) -> MARK(isQid(V:S))
1.17/1.19	 ACTIVE(isPal(V:S)) -> MARK(isNePal(V:S))
1.17/1.19	 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
1.17/1.19	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.19	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.17/1.19	 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S))
1.17/1.19	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.19	 MARK(isList(X:S)) -> ACTIVE(isList(X:S))
1.17/1.19	 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
1.17/1.19	 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
1.17/1.19	 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
1.17/1.19	-> Rules:
1.17/1.19	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.19	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.19	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.17/1.19	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.17/1.19	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.17/1.19	 active(__(nil,X:S)) -> mark(X:S)
1.17/1.19	 active(__(X:S,nil)) -> mark(X:S)
1.17/1.19	 active(and(tt,X:S)) -> mark(X:S)
1.17/1.19	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.17/1.19	 active(isList(nil)) -> mark(tt)
1.17/1.19	 active(isList(V:S)) -> mark(isNeList(V:S))
1.17/1.19	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.17/1.19	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.17/1.19	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.17/1.19	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.17/1.19	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.17/1.19	 active(isPal(nil)) -> mark(tt)
1.17/1.19	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.17/1.19	 active(isQid(a)) -> mark(tt)
1.17/1.19	 active(isQid(e)) -> mark(tt)
1.17/1.19	 active(isQid(i)) -> mark(tt)
1.17/1.19	 active(isQid(o)) -> mark(tt)
1.17/1.19	 active(isQid(u)) -> mark(tt)
1.17/1.19	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.19	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.19	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.17/1.19	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.17/1.19	 isList(active(X:S)) -> isList(X:S)
1.17/1.19	 isList(mark(X:S)) -> isList(X:S)
1.17/1.19	 isNeList(active(X:S)) -> isNeList(X:S)
1.17/1.19	 isNeList(mark(X:S)) -> isNeList(X:S)
1.17/1.19	 isNePal(active(X:S)) -> isNePal(X:S)
1.17/1.19	 isNePal(mark(X:S)) -> isNePal(X:S)
1.17/1.19	 isPal(active(X:S)) -> isPal(X:S)
1.17/1.19	 isPal(mark(X:S)) -> isPal(X:S)
1.17/1.19	 isQid(active(X:S)) -> isQid(X:S)
1.17/1.19	 isQid(mark(X:S)) -> isQid(X:S)
1.17/1.19	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.17/1.19	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.17/1.19	 mark(isList(X:S)) -> active(isList(X:S))
1.17/1.19	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.17/1.19	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.17/1.19	 mark(isPal(X:S)) -> active(isPal(X:S))
1.17/1.19	 mark(isQid(X:S)) -> active(isQid(X:S))
1.17/1.19	 mark(a) -> active(a)
1.17/1.19	 mark(e) -> active(e)
1.17/1.19	 mark(i) -> active(i)
1.17/1.19	 mark(nil) -> active(nil)
1.17/1.19	 mark(o) -> active(o)
1.17/1.19	 mark(tt) -> active(tt)
1.17/1.19	 mark(u) -> active(u)
1.17/1.19	-> Usable rules:
1.17/1.19	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.19	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.19	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.17/1.19	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.17/1.19	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.17/1.19	 active(__(nil,X:S)) -> mark(X:S)
1.17/1.19	 active(__(X:S,nil)) -> mark(X:S)
1.17/1.19	 active(and(tt,X:S)) -> mark(X:S)
1.17/1.19	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.17/1.19	 active(isList(nil)) -> mark(tt)
1.17/1.19	 active(isList(V:S)) -> mark(isNeList(V:S))
1.17/1.19	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.17/1.19	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.17/1.19	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.17/1.19	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.17/1.19	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.17/1.19	 active(isPal(nil)) -> mark(tt)
1.17/1.19	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.17/1.19	 active(isQid(a)) -> mark(tt)
1.17/1.19	 active(isQid(e)) -> mark(tt)
1.17/1.19	 active(isQid(i)) -> mark(tt)
1.17/1.19	 active(isQid(o)) -> mark(tt)
1.17/1.19	 active(isQid(u)) -> mark(tt)
1.17/1.19	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.19	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.19	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.17/1.19	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.17/1.19	 isList(active(X:S)) -> isList(X:S)
1.17/1.19	 isList(mark(X:S)) -> isList(X:S)
1.17/1.19	 isNeList(active(X:S)) -> isNeList(X:S)
1.17/1.19	 isNeList(mark(X:S)) -> isNeList(X:S)
1.17/1.19	 isNePal(active(X:S)) -> isNePal(X:S)
1.17/1.19	 isNePal(mark(X:S)) -> isNePal(X:S)
1.17/1.19	 isPal(active(X:S)) -> isPal(X:S)
1.17/1.19	 isPal(mark(X:S)) -> isPal(X:S)
1.17/1.19	 isQid(active(X:S)) -> isQid(X:S)
1.17/1.19	 isQid(mark(X:S)) -> isQid(X:S)
1.17/1.19	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.17/1.19	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.17/1.19	 mark(isList(X:S)) -> active(isList(X:S))
1.17/1.19	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.17/1.19	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.17/1.19	 mark(isPal(X:S)) -> active(isPal(X:S))
1.17/1.19	 mark(isQid(X:S)) -> active(isQid(X:S))
1.17/1.19	 mark(a) -> active(a)
1.17/1.19	 mark(e) -> active(e)
1.17/1.19	 mark(i) -> active(i)
1.17/1.19	 mark(nil) -> active(nil)
1.17/1.19	 mark(o) -> active(o)
1.17/1.19	 mark(tt) -> active(tt)
1.17/1.19	 mark(u) -> active(u)
1.17/1.19	->Interpretation type:
1.17/1.19	 Linear
1.17/1.19	->Coefficients:
1.17/1.19	 Natural Numbers
1.17/1.19	->Dimension:
1.17/1.19	 1
1.17/1.19	->Bound:
1.17/1.19	 2
1.17/1.19	->Interpretation:
1.17/1.19	 
1.17/1.19	[__](X1,X2) = X1 + X2 + 2
1.17/1.19	[active](X) = X
1.17/1.19	[and](X1,X2) = X1 + X2 + 1
1.17/1.19	[isList](X) = 2.X + 2
1.17/1.19	[isNeList](X) = 2.X + 2
1.17/1.19	[isNePal](X) = 2.X + 2
1.17/1.19	[isPal](X) = 2.X + 2
1.17/1.19	[isQid](X) = 2.X + 2
1.17/1.19	[mark](X) = X
1.17/1.19	[a] = 1
1.17/1.19	[e] = 0
1.17/1.19	[fSNonEmpty] = 0
1.17/1.19	[i] = 1
1.17/1.19	[nil] = 2
1.17/1.19	[o] = 1
1.17/1.19	[tt] = 2
1.17/1.19	[u] = 2
1.17/1.19	[__#](X1,X2) = 0
1.17/1.19	[ACTIVE](X) = 2.X + 1
1.17/1.19	[AND](X1,X2) = 0
1.17/1.19	[ISLIST](X) = 0
1.17/1.19	[ISNELIST](X) = 0
1.17/1.19	[ISNEPAL](X) = 0
1.17/1.19	[ISPAL](X) = 0
1.17/1.19	[ISQID](X) = 0
1.17/1.19	[MARK](X) = 2.X + 1
1.17/1.19	
1.17/1.19	Problem 1.8: 
1.17/1.19	
1.17/1.19	SCC Processor:
1.17/1.19	-> Pairs:
1.17/1.19	 ACTIVE(isList(V:S)) -> MARK(isNeList(V:S))
1.17/1.19	 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(and(isList(V1:S),isNeList(V2:S)))
1.17/1.19	 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(and(isNeList(V1:S),isList(V2:S)))
1.17/1.19	 ACTIVE(isNeList(V:S)) -> MARK(isQid(V:S))
1.17/1.19	 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(and(isQid(I:S),isPal(P:S)))
1.17/1.19	 ACTIVE(isNePal(V:S)) -> MARK(isQid(V:S))
1.17/1.19	 ACTIVE(isPal(V:S)) -> MARK(isNePal(V:S))
1.17/1.19	 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
1.17/1.19	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.19	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.17/1.19	 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S))
1.17/1.19	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.19	 MARK(isList(X:S)) -> ACTIVE(isList(X:S))
1.17/1.19	 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
1.17/1.19	 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
1.17/1.19	 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
1.17/1.19	-> Rules:
1.17/1.19	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.19	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.19	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.17/1.19	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.17/1.19	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.17/1.19	 active(__(nil,X:S)) -> mark(X:S)
1.17/1.19	 active(__(X:S,nil)) -> mark(X:S)
1.17/1.19	 active(and(tt,X:S)) -> mark(X:S)
1.17/1.19	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.17/1.19	 active(isList(nil)) -> mark(tt)
1.17/1.19	 active(isList(V:S)) -> mark(isNeList(V:S))
1.17/1.19	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.17/1.19	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.17/1.19	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.17/1.19	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.17/1.19	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.17/1.19	 active(isPal(nil)) -> mark(tt)
1.17/1.19	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.17/1.19	 active(isQid(a)) -> mark(tt)
1.17/1.19	 active(isQid(e)) -> mark(tt)
1.17/1.19	 active(isQid(i)) -> mark(tt)
1.17/1.19	 active(isQid(o)) -> mark(tt)
1.17/1.19	 active(isQid(u)) -> mark(tt)
1.17/1.19	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.19	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.19	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.17/1.19	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.17/1.19	 isList(active(X:S)) -> isList(X:S)
1.17/1.19	 isList(mark(X:S)) -> isList(X:S)
1.17/1.19	 isNeList(active(X:S)) -> isNeList(X:S)
1.17/1.19	 isNeList(mark(X:S)) -> isNeList(X:S)
1.17/1.19	 isNePal(active(X:S)) -> isNePal(X:S)
1.17/1.19	 isNePal(mark(X:S)) -> isNePal(X:S)
1.17/1.19	 isPal(active(X:S)) -> isPal(X:S)
1.17/1.19	 isPal(mark(X:S)) -> isPal(X:S)
1.17/1.19	 isQid(active(X:S)) -> isQid(X:S)
1.17/1.19	 isQid(mark(X:S)) -> isQid(X:S)
1.17/1.19	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.17/1.19	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.17/1.19	 mark(isList(X:S)) -> active(isList(X:S))
1.17/1.19	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.17/1.19	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.17/1.19	 mark(isPal(X:S)) -> active(isPal(X:S))
1.17/1.19	 mark(isQid(X:S)) -> active(isQid(X:S))
1.17/1.19	 mark(a) -> active(a)
1.17/1.19	 mark(e) -> active(e)
1.17/1.19	 mark(i) -> active(i)
1.17/1.19	 mark(nil) -> active(nil)
1.17/1.19	 mark(o) -> active(o)
1.17/1.19	 mark(tt) -> active(tt)
1.17/1.19	 mark(u) -> active(u)
1.17/1.19	->Strongly Connected Components:
1.17/1.19	->->Cycle:
1.17/1.19	->->-> Pairs:
1.17/1.19	 ACTIVE(isList(V:S)) -> MARK(isNeList(V:S))
1.17/1.19	 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(and(isList(V1:S),isNeList(V2:S)))
1.17/1.19	 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(and(isNeList(V1:S),isList(V2:S)))
1.17/1.19	 ACTIVE(isNeList(V:S)) -> MARK(isQid(V:S))
1.17/1.19	 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(and(isQid(I:S),isPal(P:S)))
1.17/1.19	 ACTIVE(isNePal(V:S)) -> MARK(isQid(V:S))
1.17/1.19	 ACTIVE(isPal(V:S)) -> MARK(isNePal(V:S))
1.17/1.19	 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
1.17/1.19	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.19	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.17/1.19	 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S))
1.17/1.19	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.19	 MARK(isList(X:S)) -> ACTIVE(isList(X:S))
1.17/1.19	 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
1.17/1.19	 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
1.17/1.19	 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
1.17/1.19	->->-> Rules:
1.17/1.19	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.19	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.19	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.17/1.19	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.17/1.19	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.17/1.19	 active(__(nil,X:S)) -> mark(X:S)
1.17/1.19	 active(__(X:S,nil)) -> mark(X:S)
1.17/1.19	 active(and(tt,X:S)) -> mark(X:S)
1.17/1.19	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.17/1.19	 active(isList(nil)) -> mark(tt)
1.17/1.19	 active(isList(V:S)) -> mark(isNeList(V:S))
1.17/1.19	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.17/1.19	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.17/1.19	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.17/1.19	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.17/1.19	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.17/1.19	 active(isPal(nil)) -> mark(tt)
1.17/1.19	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.17/1.19	 active(isQid(a)) -> mark(tt)
1.17/1.19	 active(isQid(e)) -> mark(tt)
1.17/1.19	 active(isQid(i)) -> mark(tt)
1.17/1.19	 active(isQid(o)) -> mark(tt)
1.17/1.19	 active(isQid(u)) -> mark(tt)
1.17/1.19	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.19	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.19	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.17/1.19	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.17/1.19	 isList(active(X:S)) -> isList(X:S)
1.17/1.19	 isList(mark(X:S)) -> isList(X:S)
1.17/1.19	 isNeList(active(X:S)) -> isNeList(X:S)
1.17/1.19	 isNeList(mark(X:S)) -> isNeList(X:S)
1.17/1.19	 isNePal(active(X:S)) -> isNePal(X:S)
1.17/1.19	 isNePal(mark(X:S)) -> isNePal(X:S)
1.17/1.19	 isPal(active(X:S)) -> isPal(X:S)
1.17/1.19	 isPal(mark(X:S)) -> isPal(X:S)
1.17/1.19	 isQid(active(X:S)) -> isQid(X:S)
1.17/1.19	 isQid(mark(X:S)) -> isQid(X:S)
1.17/1.19	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.17/1.19	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.17/1.19	 mark(isList(X:S)) -> active(isList(X:S))
1.17/1.19	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.17/1.19	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.17/1.19	 mark(isPal(X:S)) -> active(isPal(X:S))
1.17/1.19	 mark(isQid(X:S)) -> active(isQid(X:S))
1.17/1.19	 mark(a) -> active(a)
1.17/1.19	 mark(e) -> active(e)
1.17/1.19	 mark(i) -> active(i)
1.17/1.19	 mark(nil) -> active(nil)
1.17/1.19	 mark(o) -> active(o)
1.17/1.19	 mark(tt) -> active(tt)
1.17/1.19	 mark(u) -> active(u)
1.17/1.19	
1.17/1.19	Problem 1.8: 
1.17/1.19	
1.17/1.19	Reduction Pairs Processor:
1.17/1.19	-> Pairs:
1.17/1.19	 ACTIVE(isList(V:S)) -> MARK(isNeList(V:S))
1.17/1.19	 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(and(isList(V1:S),isNeList(V2:S)))
1.17/1.19	 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(and(isNeList(V1:S),isList(V2:S)))
1.17/1.19	 ACTIVE(isNeList(V:S)) -> MARK(isQid(V:S))
1.17/1.19	 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(and(isQid(I:S),isPal(P:S)))
1.17/1.19	 ACTIVE(isNePal(V:S)) -> MARK(isQid(V:S))
1.17/1.19	 ACTIVE(isPal(V:S)) -> MARK(isNePal(V:S))
1.17/1.19	 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
1.17/1.19	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.19	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.17/1.19	 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S))
1.17/1.19	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.19	 MARK(isList(X:S)) -> ACTIVE(isList(X:S))
1.17/1.19	 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
1.17/1.19	 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
1.17/1.19	 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
1.17/1.19	-> Rules:
1.17/1.19	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.19	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.19	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.17/1.19	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.17/1.19	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.17/1.19	 active(__(nil,X:S)) -> mark(X:S)
1.17/1.19	 active(__(X:S,nil)) -> mark(X:S)
1.17/1.19	 active(and(tt,X:S)) -> mark(X:S)
1.17/1.19	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.17/1.19	 active(isList(nil)) -> mark(tt)
1.17/1.19	 active(isList(V:S)) -> mark(isNeList(V:S))
1.17/1.19	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.17/1.19	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.17/1.19	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.17/1.19	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.17/1.19	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.17/1.19	 active(isPal(nil)) -> mark(tt)
1.17/1.19	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.17/1.19	 active(isQid(a)) -> mark(tt)
1.17/1.19	 active(isQid(e)) -> mark(tt)
1.17/1.19	 active(isQid(i)) -> mark(tt)
1.17/1.19	 active(isQid(o)) -> mark(tt)
1.17/1.19	 active(isQid(u)) -> mark(tt)
1.17/1.19	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.19	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.19	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.17/1.19	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.17/1.19	 isList(active(X:S)) -> isList(X:S)
1.17/1.19	 isList(mark(X:S)) -> isList(X:S)
1.17/1.19	 isNeList(active(X:S)) -> isNeList(X:S)
1.17/1.19	 isNeList(mark(X:S)) -> isNeList(X:S)
1.17/1.19	 isNePal(active(X:S)) -> isNePal(X:S)
1.17/1.19	 isNePal(mark(X:S)) -> isNePal(X:S)
1.17/1.19	 isPal(active(X:S)) -> isPal(X:S)
1.17/1.19	 isPal(mark(X:S)) -> isPal(X:S)
1.17/1.19	 isQid(active(X:S)) -> isQid(X:S)
1.17/1.19	 isQid(mark(X:S)) -> isQid(X:S)
1.17/1.19	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.17/1.19	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.17/1.19	 mark(isList(X:S)) -> active(isList(X:S))
1.17/1.19	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.17/1.19	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.17/1.19	 mark(isPal(X:S)) -> active(isPal(X:S))
1.17/1.19	 mark(isQid(X:S)) -> active(isQid(X:S))
1.17/1.19	 mark(a) -> active(a)
1.17/1.19	 mark(e) -> active(e)
1.17/1.19	 mark(i) -> active(i)
1.17/1.19	 mark(nil) -> active(nil)
1.17/1.19	 mark(o) -> active(o)
1.17/1.19	 mark(tt) -> active(tt)
1.17/1.19	 mark(u) -> active(u)
1.17/1.19	-> Usable rules:
1.17/1.19	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.19	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.19	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.17/1.19	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.17/1.19	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.17/1.19	 active(__(nil,X:S)) -> mark(X:S)
1.17/1.19	 active(__(X:S,nil)) -> mark(X:S)
1.17/1.19	 active(and(tt,X:S)) -> mark(X:S)
1.17/1.19	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.17/1.19	 active(isList(nil)) -> mark(tt)
1.17/1.19	 active(isList(V:S)) -> mark(isNeList(V:S))
1.17/1.19	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.17/1.19	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.17/1.19	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.17/1.19	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.17/1.19	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.17/1.19	 active(isPal(nil)) -> mark(tt)
1.17/1.19	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.17/1.19	 active(isQid(a)) -> mark(tt)
1.17/1.19	 active(isQid(e)) -> mark(tt)
1.17/1.19	 active(isQid(i)) -> mark(tt)
1.17/1.19	 active(isQid(o)) -> mark(tt)
1.17/1.19	 active(isQid(u)) -> mark(tt)
1.17/1.19	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.19	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.19	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.17/1.19	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.17/1.19	 isList(active(X:S)) -> isList(X:S)
1.17/1.19	 isList(mark(X:S)) -> isList(X:S)
1.17/1.19	 isNeList(active(X:S)) -> isNeList(X:S)
1.17/1.19	 isNeList(mark(X:S)) -> isNeList(X:S)
1.17/1.19	 isNePal(active(X:S)) -> isNePal(X:S)
1.17/1.19	 isNePal(mark(X:S)) -> isNePal(X:S)
1.17/1.19	 isPal(active(X:S)) -> isPal(X:S)
1.17/1.19	 isPal(mark(X:S)) -> isPal(X:S)
1.17/1.19	 isQid(active(X:S)) -> isQid(X:S)
1.17/1.19	 isQid(mark(X:S)) -> isQid(X:S)
1.17/1.19	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.17/1.19	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.17/1.19	 mark(isList(X:S)) -> active(isList(X:S))
1.17/1.19	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.17/1.19	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.17/1.19	 mark(isPal(X:S)) -> active(isPal(X:S))
1.17/1.19	 mark(isQid(X:S)) -> active(isQid(X:S))
1.17/1.19	 mark(a) -> active(a)
1.17/1.19	 mark(e) -> active(e)
1.17/1.19	 mark(i) -> active(i)
1.17/1.19	 mark(nil) -> active(nil)
1.17/1.19	 mark(o) -> active(o)
1.17/1.19	 mark(tt) -> active(tt)
1.17/1.19	 mark(u) -> active(u)
1.17/1.19	->Interpretation type:
1.17/1.19	 Linear
1.17/1.19	->Coefficients:
1.17/1.19	 Natural Numbers
1.17/1.19	->Dimension:
1.17/1.19	 1
1.17/1.19	->Bound:
1.17/1.19	 2
1.17/1.19	->Interpretation:
1.17/1.19	 
1.17/1.19	[__](X1,X2) = 2.X1 + X2 + 2
1.17/1.19	[active](X) = X
1.17/1.19	[and](X1,X2) = 2.X1 + X2
1.17/1.19	[isList](X) = 2.X + 2
1.17/1.19	[isNeList](X) = 2.X + 1
1.17/1.19	[isNePal](X) = 2.X + 2
1.17/1.19	[isPal](X) = 2.X + 2
1.17/1.19	[isQid](X) = X + 1
1.17/1.19	[mark](X) = X
1.17/1.19	[a] = 2
1.17/1.19	[e] = 2
1.17/1.19	[fSNonEmpty] = 0
1.17/1.19	[i] = 2
1.17/1.19	[nil] = 1
1.17/1.19	[o] = 2
1.17/1.19	[tt] = 2
1.17/1.19	[u] = 1
1.17/1.19	[__#](X1,X2) = 0
1.17/1.19	[ACTIVE](X) = 2.X + 2
1.17/1.19	[AND](X1,X2) = 0
1.17/1.19	[ISLIST](X) = 0
1.17/1.19	[ISNELIST](X) = 0
1.17/1.19	[ISNEPAL](X) = 0
1.17/1.19	[ISPAL](X) = 0
1.17/1.19	[ISQID](X) = 0
1.17/1.19	[MARK](X) = 2.X + 2
1.17/1.19	
1.17/1.19	Problem 1.8: 
1.17/1.19	
1.17/1.19	SCC Processor:
1.17/1.19	-> Pairs:
1.17/1.19	 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(and(isList(V1:S),isNeList(V2:S)))
1.17/1.19	 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(and(isNeList(V1:S),isList(V2:S)))
1.17/1.19	 ACTIVE(isNeList(V:S)) -> MARK(isQid(V:S))
1.17/1.19	 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(and(isQid(I:S),isPal(P:S)))
1.17/1.19	 ACTIVE(isNePal(V:S)) -> MARK(isQid(V:S))
1.17/1.19	 ACTIVE(isPal(V:S)) -> MARK(isNePal(V:S))
1.17/1.19	 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
1.17/1.19	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.19	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.17/1.19	 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S))
1.17/1.19	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.19	 MARK(isList(X:S)) -> ACTIVE(isList(X:S))
1.17/1.19	 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
1.17/1.19	 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
1.17/1.19	 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
1.17/1.19	-> Rules:
1.17/1.19	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.19	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.19	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.17/1.19	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.17/1.19	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.17/1.19	 active(__(nil,X:S)) -> mark(X:S)
1.17/1.19	 active(__(X:S,nil)) -> mark(X:S)
1.17/1.19	 active(and(tt,X:S)) -> mark(X:S)
1.17/1.19	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.17/1.19	 active(isList(nil)) -> mark(tt)
1.17/1.19	 active(isList(V:S)) -> mark(isNeList(V:S))
1.17/1.19	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.17/1.19	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.17/1.19	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.17/1.19	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.17/1.19	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.17/1.19	 active(isPal(nil)) -> mark(tt)
1.17/1.19	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.17/1.19	 active(isQid(a)) -> mark(tt)
1.17/1.19	 active(isQid(e)) -> mark(tt)
1.17/1.19	 active(isQid(i)) -> mark(tt)
1.17/1.19	 active(isQid(o)) -> mark(tt)
1.17/1.19	 active(isQid(u)) -> mark(tt)
1.17/1.19	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.19	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.19	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.17/1.19	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.17/1.19	 isList(active(X:S)) -> isList(X:S)
1.17/1.19	 isList(mark(X:S)) -> isList(X:S)
1.17/1.19	 isNeList(active(X:S)) -> isNeList(X:S)
1.17/1.19	 isNeList(mark(X:S)) -> isNeList(X:S)
1.17/1.19	 isNePal(active(X:S)) -> isNePal(X:S)
1.17/1.19	 isNePal(mark(X:S)) -> isNePal(X:S)
1.17/1.19	 isPal(active(X:S)) -> isPal(X:S)
1.17/1.19	 isPal(mark(X:S)) -> isPal(X:S)
1.17/1.19	 isQid(active(X:S)) -> isQid(X:S)
1.17/1.19	 isQid(mark(X:S)) -> isQid(X:S)
1.17/1.19	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.17/1.19	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.17/1.19	 mark(isList(X:S)) -> active(isList(X:S))
1.17/1.19	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.17/1.19	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.17/1.19	 mark(isPal(X:S)) -> active(isPal(X:S))
1.17/1.19	 mark(isQid(X:S)) -> active(isQid(X:S))
1.17/1.19	 mark(a) -> active(a)
1.17/1.19	 mark(e) -> active(e)
1.17/1.19	 mark(i) -> active(i)
1.17/1.19	 mark(nil) -> active(nil)
1.17/1.19	 mark(o) -> active(o)
1.17/1.19	 mark(tt) -> active(tt)
1.17/1.19	 mark(u) -> active(u)
1.17/1.19	->Strongly Connected Components:
1.17/1.19	->->Cycle:
1.17/1.19	->->-> Pairs:
1.17/1.19	 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(and(isList(V1:S),isNeList(V2:S)))
1.17/1.19	 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(and(isNeList(V1:S),isList(V2:S)))
1.17/1.19	 ACTIVE(isNeList(V:S)) -> MARK(isQid(V:S))
1.17/1.19	 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(and(isQid(I:S),isPal(P:S)))
1.17/1.19	 ACTIVE(isNePal(V:S)) -> MARK(isQid(V:S))
1.17/1.19	 ACTIVE(isPal(V:S)) -> MARK(isNePal(V:S))
1.17/1.19	 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
1.17/1.19	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.19	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.17/1.19	 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S))
1.17/1.19	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.19	 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
1.17/1.19	 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
1.17/1.19	 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
1.17/1.19	->->-> Rules:
1.17/1.19	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.19	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.19	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.17/1.19	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.17/1.19	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.17/1.19	 active(__(nil,X:S)) -> mark(X:S)
1.17/1.19	 active(__(X:S,nil)) -> mark(X:S)
1.17/1.19	 active(and(tt,X:S)) -> mark(X:S)
1.17/1.19	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.17/1.19	 active(isList(nil)) -> mark(tt)
1.17/1.19	 active(isList(V:S)) -> mark(isNeList(V:S))
1.17/1.19	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.17/1.19	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.17/1.19	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.17/1.19	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.17/1.19	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.17/1.19	 active(isPal(nil)) -> mark(tt)
1.17/1.19	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.17/1.19	 active(isQid(a)) -> mark(tt)
1.17/1.19	 active(isQid(e)) -> mark(tt)
1.17/1.19	 active(isQid(i)) -> mark(tt)
1.17/1.19	 active(isQid(o)) -> mark(tt)
1.17/1.19	 active(isQid(u)) -> mark(tt)
1.17/1.19	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.19	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.19	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.17/1.19	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.17/1.19	 isList(active(X:S)) -> isList(X:S)
1.17/1.19	 isList(mark(X:S)) -> isList(X:S)
1.17/1.19	 isNeList(active(X:S)) -> isNeList(X:S)
1.17/1.19	 isNeList(mark(X:S)) -> isNeList(X:S)
1.17/1.19	 isNePal(active(X:S)) -> isNePal(X:S)
1.17/1.19	 isNePal(mark(X:S)) -> isNePal(X:S)
1.17/1.19	 isPal(active(X:S)) -> isPal(X:S)
1.17/1.19	 isPal(mark(X:S)) -> isPal(X:S)
1.17/1.19	 isQid(active(X:S)) -> isQid(X:S)
1.17/1.19	 isQid(mark(X:S)) -> isQid(X:S)
1.17/1.19	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.17/1.19	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.17/1.19	 mark(isList(X:S)) -> active(isList(X:S))
1.17/1.19	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.17/1.19	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.17/1.19	 mark(isPal(X:S)) -> active(isPal(X:S))
1.17/1.19	 mark(isQid(X:S)) -> active(isQid(X:S))
1.17/1.19	 mark(a) -> active(a)
1.17/1.19	 mark(e) -> active(e)
1.17/1.19	 mark(i) -> active(i)
1.17/1.19	 mark(nil) -> active(nil)
1.17/1.19	 mark(o) -> active(o)
1.17/1.19	 mark(tt) -> active(tt)
1.17/1.19	 mark(u) -> active(u)
1.17/1.19	
1.17/1.19	Problem 1.8: 
1.17/1.19	
1.17/1.19	Reduction Pairs Processor:
1.17/1.19	-> Pairs:
1.17/1.19	 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(and(isList(V1:S),isNeList(V2:S)))
1.17/1.19	 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(and(isNeList(V1:S),isList(V2:S)))
1.17/1.19	 ACTIVE(isNeList(V:S)) -> MARK(isQid(V:S))
1.17/1.19	 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(and(isQid(I:S),isPal(P:S)))
1.17/1.19	 ACTIVE(isNePal(V:S)) -> MARK(isQid(V:S))
1.17/1.19	 ACTIVE(isPal(V:S)) -> MARK(isNePal(V:S))
1.17/1.19	 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
1.17/1.19	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.19	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.17/1.19	 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S))
1.17/1.19	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.19	 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
1.17/1.19	 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
1.17/1.19	 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
1.17/1.19	-> Rules:
1.17/1.19	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.19	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.19	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.17/1.19	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.17/1.19	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.17/1.19	 active(__(nil,X:S)) -> mark(X:S)
1.17/1.19	 active(__(X:S,nil)) -> mark(X:S)
1.17/1.19	 active(and(tt,X:S)) -> mark(X:S)
1.17/1.19	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.17/1.19	 active(isList(nil)) -> mark(tt)
1.17/1.19	 active(isList(V:S)) -> mark(isNeList(V:S))
1.17/1.19	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.17/1.19	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.17/1.19	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.17/1.19	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.17/1.19	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.17/1.19	 active(isPal(nil)) -> mark(tt)
1.17/1.19	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.17/1.19	 active(isQid(a)) -> mark(tt)
1.17/1.19	 active(isQid(e)) -> mark(tt)
1.17/1.19	 active(isQid(i)) -> mark(tt)
1.17/1.19	 active(isQid(o)) -> mark(tt)
1.17/1.19	 active(isQid(u)) -> mark(tt)
1.17/1.19	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.19	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.19	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.17/1.19	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.17/1.19	 isList(active(X:S)) -> isList(X:S)
1.17/1.19	 isList(mark(X:S)) -> isList(X:S)
1.17/1.19	 isNeList(active(X:S)) -> isNeList(X:S)
1.17/1.19	 isNeList(mark(X:S)) -> isNeList(X:S)
1.17/1.19	 isNePal(active(X:S)) -> isNePal(X:S)
1.17/1.19	 isNePal(mark(X:S)) -> isNePal(X:S)
1.17/1.19	 isPal(active(X:S)) -> isPal(X:S)
1.17/1.19	 isPal(mark(X:S)) -> isPal(X:S)
1.17/1.19	 isQid(active(X:S)) -> isQid(X:S)
1.17/1.19	 isQid(mark(X:S)) -> isQid(X:S)
1.17/1.19	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.17/1.19	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.17/1.19	 mark(isList(X:S)) -> active(isList(X:S))
1.17/1.19	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.17/1.19	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.17/1.19	 mark(isPal(X:S)) -> active(isPal(X:S))
1.17/1.19	 mark(isQid(X:S)) -> active(isQid(X:S))
1.17/1.19	 mark(a) -> active(a)
1.17/1.19	 mark(e) -> active(e)
1.17/1.19	 mark(i) -> active(i)
1.17/1.19	 mark(nil) -> active(nil)
1.17/1.19	 mark(o) -> active(o)
1.17/1.19	 mark(tt) -> active(tt)
1.17/1.19	 mark(u) -> active(u)
1.17/1.19	-> Usable rules:
1.17/1.19	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.19	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.19	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.17/1.19	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.17/1.19	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.17/1.19	 active(__(nil,X:S)) -> mark(X:S)
1.17/1.19	 active(__(X:S,nil)) -> mark(X:S)
1.17/1.19	 active(and(tt,X:S)) -> mark(X:S)
1.17/1.19	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.17/1.19	 active(isList(nil)) -> mark(tt)
1.17/1.19	 active(isList(V:S)) -> mark(isNeList(V:S))
1.17/1.19	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.17/1.19	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.17/1.19	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.17/1.19	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.17/1.19	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.17/1.19	 active(isPal(nil)) -> mark(tt)
1.17/1.19	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.17/1.19	 active(isQid(a)) -> mark(tt)
1.17/1.19	 active(isQid(e)) -> mark(tt)
1.17/1.19	 active(isQid(i)) -> mark(tt)
1.17/1.19	 active(isQid(o)) -> mark(tt)
1.17/1.19	 active(isQid(u)) -> mark(tt)
1.17/1.19	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.19	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.19	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.17/1.19	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.17/1.19	 isList(active(X:S)) -> isList(X:S)
1.17/1.19	 isList(mark(X:S)) -> isList(X:S)
1.17/1.19	 isNeList(active(X:S)) -> isNeList(X:S)
1.17/1.19	 isNeList(mark(X:S)) -> isNeList(X:S)
1.17/1.19	 isNePal(active(X:S)) -> isNePal(X:S)
1.17/1.19	 isNePal(mark(X:S)) -> isNePal(X:S)
1.17/1.19	 isPal(active(X:S)) -> isPal(X:S)
1.17/1.19	 isPal(mark(X:S)) -> isPal(X:S)
1.17/1.19	 isQid(active(X:S)) -> isQid(X:S)
1.17/1.19	 isQid(mark(X:S)) -> isQid(X:S)
1.17/1.19	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.17/1.19	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.17/1.19	 mark(isList(X:S)) -> active(isList(X:S))
1.17/1.19	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.17/1.19	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.17/1.19	 mark(isPal(X:S)) -> active(isPal(X:S))
1.17/1.19	 mark(isQid(X:S)) -> active(isQid(X:S))
1.17/1.19	 mark(a) -> active(a)
1.17/1.19	 mark(e) -> active(e)
1.17/1.19	 mark(i) -> active(i)
1.17/1.19	 mark(nil) -> active(nil)
1.17/1.19	 mark(o) -> active(o)
1.17/1.19	 mark(tt) -> active(tt)
1.17/1.19	 mark(u) -> active(u)
1.17/1.19	->Interpretation type:
1.17/1.19	 Linear
1.17/1.19	->Coefficients:
1.17/1.19	 Natural Numbers
1.17/1.19	->Dimension:
1.17/1.19	 1
1.17/1.19	->Bound:
1.17/1.19	 2
1.17/1.19	->Interpretation:
1.17/1.19	 
1.17/1.19	[__](X1,X2) = 2.X1 + X2 + 2
1.17/1.19	[active](X) = X
1.17/1.19	[and](X1,X2) = 2.X1 + X2 + 1
1.17/1.19	[isList](X) = 2.X + 1
1.17/1.19	[isNeList](X) = 2.X
1.17/1.19	[isNePal](X) = 2.X + 2
1.17/1.19	[isPal](X) = 2.X + 2
1.17/1.19	[isQid](X) = 2.X
1.17/1.19	[mark](X) = X
1.17/1.19	[a] = 2
1.17/1.19	[e] = 2
1.17/1.19	[fSNonEmpty] = 0
1.17/1.19	[i] = 0
1.17/1.19	[nil] = 2
1.17/1.19	[o] = 2
1.17/1.19	[tt] = 0
1.17/1.19	[u] = 2
1.17/1.19	[__#](X1,X2) = 0
1.17/1.19	[ACTIVE](X) = 2.X
1.17/1.19	[AND](X1,X2) = 0
1.17/1.19	[ISLIST](X) = 0
1.17/1.19	[ISNELIST](X) = 0
1.17/1.19	[ISNEPAL](X) = 0
1.17/1.19	[ISPAL](X) = 0
1.17/1.19	[ISQID](X) = 0
1.17/1.19	[MARK](X) = 2.X
1.17/1.19	
1.17/1.19	Problem 1.8: 
1.17/1.19	
1.17/1.19	SCC Processor:
1.17/1.19	-> Pairs:
1.17/1.19	 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(and(isNeList(V1:S),isList(V2:S)))
1.17/1.19	 ACTIVE(isNeList(V:S)) -> MARK(isQid(V:S))
1.17/1.19	 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(and(isQid(I:S),isPal(P:S)))
1.17/1.19	 ACTIVE(isNePal(V:S)) -> MARK(isQid(V:S))
1.17/1.19	 ACTIVE(isPal(V:S)) -> MARK(isNePal(V:S))
1.17/1.19	 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
1.17/1.19	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.19	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.17/1.19	 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S))
1.17/1.19	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.19	 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
1.17/1.19	 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
1.17/1.19	 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
1.17/1.19	-> Rules:
1.17/1.19	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.19	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.19	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.17/1.19	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.17/1.19	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.17/1.19	 active(__(nil,X:S)) -> mark(X:S)
1.17/1.19	 active(__(X:S,nil)) -> mark(X:S)
1.17/1.19	 active(and(tt,X:S)) -> mark(X:S)
1.17/1.19	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.17/1.19	 active(isList(nil)) -> mark(tt)
1.17/1.19	 active(isList(V:S)) -> mark(isNeList(V:S))
1.17/1.19	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.17/1.19	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.17/1.19	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.17/1.19	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.17/1.19	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.17/1.19	 active(isPal(nil)) -> mark(tt)
1.17/1.19	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.17/1.19	 active(isQid(a)) -> mark(tt)
1.17/1.19	 active(isQid(e)) -> mark(tt)
1.17/1.19	 active(isQid(i)) -> mark(tt)
1.17/1.19	 active(isQid(o)) -> mark(tt)
1.17/1.19	 active(isQid(u)) -> mark(tt)
1.17/1.19	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.19	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.19	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.17/1.19	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.17/1.19	 isList(active(X:S)) -> isList(X:S)
1.17/1.19	 isList(mark(X:S)) -> isList(X:S)
1.17/1.19	 isNeList(active(X:S)) -> isNeList(X:S)
1.17/1.19	 isNeList(mark(X:S)) -> isNeList(X:S)
1.17/1.19	 isNePal(active(X:S)) -> isNePal(X:S)
1.17/1.19	 isNePal(mark(X:S)) -> isNePal(X:S)
1.17/1.19	 isPal(active(X:S)) -> isPal(X:S)
1.17/1.19	 isPal(mark(X:S)) -> isPal(X:S)
1.17/1.19	 isQid(active(X:S)) -> isQid(X:S)
1.17/1.19	 isQid(mark(X:S)) -> isQid(X:S)
1.17/1.19	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.17/1.19	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.17/1.19	 mark(isList(X:S)) -> active(isList(X:S))
1.17/1.19	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.17/1.19	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.17/1.19	 mark(isPal(X:S)) -> active(isPal(X:S))
1.17/1.19	 mark(isQid(X:S)) -> active(isQid(X:S))
1.17/1.19	 mark(a) -> active(a)
1.17/1.19	 mark(e) -> active(e)
1.17/1.19	 mark(i) -> active(i)
1.17/1.19	 mark(nil) -> active(nil)
1.17/1.19	 mark(o) -> active(o)
1.17/1.19	 mark(tt) -> active(tt)
1.17/1.19	 mark(u) -> active(u)
1.17/1.19	->Strongly Connected Components:
1.17/1.19	->->Cycle:
1.17/1.19	->->-> Pairs:
1.17/1.19	 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(and(isNeList(V1:S),isList(V2:S)))
1.17/1.19	 ACTIVE(isNeList(V:S)) -> MARK(isQid(V:S))
1.17/1.19	 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(and(isQid(I:S),isPal(P:S)))
1.17/1.19	 ACTIVE(isNePal(V:S)) -> MARK(isQid(V:S))
1.17/1.19	 ACTIVE(isPal(V:S)) -> MARK(isNePal(V:S))
1.17/1.19	 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
1.17/1.19	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.19	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.17/1.19	 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S))
1.17/1.19	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.19	 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
1.17/1.19	 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
1.17/1.19	 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
1.17/1.19	->->-> Rules:
1.17/1.19	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.19	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.19	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.17/1.19	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.17/1.19	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.17/1.19	 active(__(nil,X:S)) -> mark(X:S)
1.17/1.19	 active(__(X:S,nil)) -> mark(X:S)
1.17/1.19	 active(and(tt,X:S)) -> mark(X:S)
1.17/1.19	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.17/1.19	 active(isList(nil)) -> mark(tt)
1.17/1.19	 active(isList(V:S)) -> mark(isNeList(V:S))
1.17/1.19	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.17/1.19	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.17/1.19	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.17/1.19	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.17/1.19	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.17/1.19	 active(isPal(nil)) -> mark(tt)
1.17/1.19	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.17/1.19	 active(isQid(a)) -> mark(tt)
1.17/1.19	 active(isQid(e)) -> mark(tt)
1.17/1.19	 active(isQid(i)) -> mark(tt)
1.17/1.19	 active(isQid(o)) -> mark(tt)
1.17/1.19	 active(isQid(u)) -> mark(tt)
1.17/1.19	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.19	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.19	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.17/1.19	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.17/1.19	 isList(active(X:S)) -> isList(X:S)
1.17/1.19	 isList(mark(X:S)) -> isList(X:S)
1.17/1.19	 isNeList(active(X:S)) -> isNeList(X:S)
1.17/1.19	 isNeList(mark(X:S)) -> isNeList(X:S)
1.17/1.19	 isNePal(active(X:S)) -> isNePal(X:S)
1.17/1.19	 isNePal(mark(X:S)) -> isNePal(X:S)
1.17/1.19	 isPal(active(X:S)) -> isPal(X:S)
1.17/1.19	 isPal(mark(X:S)) -> isPal(X:S)
1.17/1.19	 isQid(active(X:S)) -> isQid(X:S)
1.17/1.19	 isQid(mark(X:S)) -> isQid(X:S)
1.17/1.19	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.17/1.19	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.17/1.19	 mark(isList(X:S)) -> active(isList(X:S))
1.17/1.19	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.17/1.19	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.17/1.19	 mark(isPal(X:S)) -> active(isPal(X:S))
1.17/1.19	 mark(isQid(X:S)) -> active(isQid(X:S))
1.17/1.19	 mark(a) -> active(a)
1.17/1.19	 mark(e) -> active(e)
1.17/1.19	 mark(i) -> active(i)
1.17/1.19	 mark(nil) -> active(nil)
1.17/1.19	 mark(o) -> active(o)
1.17/1.19	 mark(tt) -> active(tt)
1.17/1.19	 mark(u) -> active(u)
1.17/1.19	
1.17/1.19	Problem 1.8: 
1.17/1.19	
1.17/1.19	Reduction Pairs Processor:
1.17/1.19	-> Pairs:
1.17/1.19	 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(and(isNeList(V1:S),isList(V2:S)))
1.17/1.19	 ACTIVE(isNeList(V:S)) -> MARK(isQid(V:S))
1.17/1.19	 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(and(isQid(I:S),isPal(P:S)))
1.17/1.19	 ACTIVE(isNePal(V:S)) -> MARK(isQid(V:S))
1.17/1.19	 ACTIVE(isPal(V:S)) -> MARK(isNePal(V:S))
1.17/1.19	 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
1.17/1.19	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.19	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.17/1.19	 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S))
1.17/1.19	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.19	 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
1.17/1.19	 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
1.17/1.19	 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
1.17/1.19	-> Rules:
1.17/1.19	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.19	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.19	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.17/1.19	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.17/1.19	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.17/1.19	 active(__(nil,X:S)) -> mark(X:S)
1.17/1.19	 active(__(X:S,nil)) -> mark(X:S)
1.17/1.19	 active(and(tt,X:S)) -> mark(X:S)
1.17/1.19	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.17/1.19	 active(isList(nil)) -> mark(tt)
1.17/1.19	 active(isList(V:S)) -> mark(isNeList(V:S))
1.17/1.19	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.17/1.19	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.17/1.19	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.17/1.19	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.17/1.19	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.17/1.19	 active(isPal(nil)) -> mark(tt)
1.17/1.19	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.17/1.19	 active(isQid(a)) -> mark(tt)
1.17/1.19	 active(isQid(e)) -> mark(tt)
1.17/1.19	 active(isQid(i)) -> mark(tt)
1.17/1.19	 active(isQid(o)) -> mark(tt)
1.17/1.19	 active(isQid(u)) -> mark(tt)
1.17/1.19	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.19	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.19	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.17/1.19	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.17/1.19	 isList(active(X:S)) -> isList(X:S)
1.17/1.19	 isList(mark(X:S)) -> isList(X:S)
1.17/1.19	 isNeList(active(X:S)) -> isNeList(X:S)
1.17/1.19	 isNeList(mark(X:S)) -> isNeList(X:S)
1.17/1.19	 isNePal(active(X:S)) -> isNePal(X:S)
1.17/1.19	 isNePal(mark(X:S)) -> isNePal(X:S)
1.17/1.19	 isPal(active(X:S)) -> isPal(X:S)
1.17/1.19	 isPal(mark(X:S)) -> isPal(X:S)
1.17/1.19	 isQid(active(X:S)) -> isQid(X:S)
1.17/1.19	 isQid(mark(X:S)) -> isQid(X:S)
1.17/1.19	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.17/1.19	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.17/1.19	 mark(isList(X:S)) -> active(isList(X:S))
1.17/1.19	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.17/1.19	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.17/1.19	 mark(isPal(X:S)) -> active(isPal(X:S))
1.17/1.19	 mark(isQid(X:S)) -> active(isQid(X:S))
1.17/1.19	 mark(a) -> active(a)
1.17/1.19	 mark(e) -> active(e)
1.17/1.19	 mark(i) -> active(i)
1.17/1.19	 mark(nil) -> active(nil)
1.17/1.19	 mark(o) -> active(o)
1.17/1.19	 mark(tt) -> active(tt)
1.17/1.19	 mark(u) -> active(u)
1.17/1.19	-> Usable rules:
1.17/1.19	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.19	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.19	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.17/1.19	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.17/1.19	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.17/1.19	 active(__(nil,X:S)) -> mark(X:S)
1.17/1.19	 active(__(X:S,nil)) -> mark(X:S)
1.17/1.19	 active(and(tt,X:S)) -> mark(X:S)
1.17/1.19	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.17/1.19	 active(isList(nil)) -> mark(tt)
1.17/1.19	 active(isList(V:S)) -> mark(isNeList(V:S))
1.17/1.19	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.17/1.19	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.17/1.19	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.17/1.19	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.17/1.19	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.17/1.19	 active(isPal(nil)) -> mark(tt)
1.17/1.19	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.17/1.19	 active(isQid(a)) -> mark(tt)
1.17/1.19	 active(isQid(e)) -> mark(tt)
1.17/1.19	 active(isQid(i)) -> mark(tt)
1.17/1.19	 active(isQid(o)) -> mark(tt)
1.17/1.19	 active(isQid(u)) -> mark(tt)
1.17/1.19	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.19	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.19	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.17/1.19	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.17/1.19	 isList(active(X:S)) -> isList(X:S)
1.17/1.19	 isList(mark(X:S)) -> isList(X:S)
1.17/1.19	 isNeList(active(X:S)) -> isNeList(X:S)
1.17/1.19	 isNeList(mark(X:S)) -> isNeList(X:S)
1.17/1.19	 isNePal(active(X:S)) -> isNePal(X:S)
1.17/1.19	 isNePal(mark(X:S)) -> isNePal(X:S)
1.17/1.19	 isPal(active(X:S)) -> isPal(X:S)
1.17/1.19	 isPal(mark(X:S)) -> isPal(X:S)
1.17/1.19	 isQid(active(X:S)) -> isQid(X:S)
1.17/1.19	 isQid(mark(X:S)) -> isQid(X:S)
1.17/1.19	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.17/1.19	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.17/1.19	 mark(isList(X:S)) -> active(isList(X:S))
1.17/1.19	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.17/1.19	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.17/1.19	 mark(isPal(X:S)) -> active(isPal(X:S))
1.17/1.19	 mark(isQid(X:S)) -> active(isQid(X:S))
1.17/1.19	 mark(a) -> active(a)
1.17/1.19	 mark(e) -> active(e)
1.17/1.19	 mark(i) -> active(i)
1.17/1.19	 mark(nil) -> active(nil)
1.17/1.19	 mark(o) -> active(o)
1.17/1.19	 mark(tt) -> active(tt)
1.17/1.19	 mark(u) -> active(u)
1.17/1.19	->Interpretation type:
1.17/1.19	 Linear
1.17/1.19	->Coefficients:
1.17/1.19	 Natural Numbers
1.17/1.19	->Dimension:
1.17/1.19	 1
1.17/1.19	->Bound:
1.17/1.19	 2
1.17/1.19	->Interpretation:
1.17/1.19	 
1.17/1.19	[__](X1,X2) = 2.X1 + X2 + 1
1.17/1.19	[active](X) = X
1.17/1.19	[and](X1,X2) = X1 + X2
1.17/1.19	[isList](X) = 2.X + 1
1.17/1.19	[isNeList](X) = 2.X + 1
1.17/1.19	[isNePal](X) = X + 2
1.17/1.19	[isPal](X) = X + 2
1.17/1.19	[isQid](X) = X + 1
1.17/1.19	[mark](X) = X
1.17/1.19	[a] = 1
1.17/1.19	[e] = 2
1.17/1.19	[fSNonEmpty] = 0
1.17/1.19	[i] = 2
1.17/1.19	[nil] = 1
1.17/1.19	[o] = 2
1.17/1.19	[tt] = 1
1.17/1.19	[u] = 2
1.17/1.19	[__#](X1,X2) = 0
1.17/1.19	[ACTIVE](X) = 2.X + 2
1.17/1.19	[AND](X1,X2) = 0
1.17/1.19	[ISLIST](X) = 0
1.17/1.19	[ISNELIST](X) = 0
1.17/1.19	[ISNEPAL](X) = 0
1.17/1.19	[ISPAL](X) = 0
1.17/1.19	[ISQID](X) = 0
1.17/1.19	[MARK](X) = 2.X + 2
1.17/1.19	
1.17/1.19	Problem 1.8: 
1.17/1.19	
1.17/1.19	SCC Processor:
1.17/1.19	-> Pairs:
1.17/1.19	 ACTIVE(isNeList(V:S)) -> MARK(isQid(V:S))
1.17/1.19	 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(and(isQid(I:S),isPal(P:S)))
1.17/1.19	 ACTIVE(isNePal(V:S)) -> MARK(isQid(V:S))
1.17/1.19	 ACTIVE(isPal(V:S)) -> MARK(isNePal(V:S))
1.17/1.19	 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
1.17/1.19	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.19	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.17/1.19	 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S))
1.17/1.19	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.19	 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
1.17/1.19	 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
1.17/1.19	 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
1.17/1.19	-> Rules:
1.17/1.19	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.19	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.19	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.17/1.19	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.17/1.19	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.17/1.19	 active(__(nil,X:S)) -> mark(X:S)
1.17/1.19	 active(__(X:S,nil)) -> mark(X:S)
1.17/1.19	 active(and(tt,X:S)) -> mark(X:S)
1.17/1.19	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.17/1.19	 active(isList(nil)) -> mark(tt)
1.17/1.19	 active(isList(V:S)) -> mark(isNeList(V:S))
1.17/1.19	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.17/1.19	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.17/1.19	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.17/1.19	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.17/1.19	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.17/1.19	 active(isPal(nil)) -> mark(tt)
1.17/1.19	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.17/1.19	 active(isQid(a)) -> mark(tt)
1.17/1.19	 active(isQid(e)) -> mark(tt)
1.17/1.19	 active(isQid(i)) -> mark(tt)
1.17/1.19	 active(isQid(o)) -> mark(tt)
1.17/1.19	 active(isQid(u)) -> mark(tt)
1.17/1.19	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.19	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.19	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.17/1.19	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.17/1.19	 isList(active(X:S)) -> isList(X:S)
1.17/1.19	 isList(mark(X:S)) -> isList(X:S)
1.17/1.19	 isNeList(active(X:S)) -> isNeList(X:S)
1.17/1.19	 isNeList(mark(X:S)) -> isNeList(X:S)
1.17/1.19	 isNePal(active(X:S)) -> isNePal(X:S)
1.17/1.19	 isNePal(mark(X:S)) -> isNePal(X:S)
1.17/1.19	 isPal(active(X:S)) -> isPal(X:S)
1.17/1.19	 isPal(mark(X:S)) -> isPal(X:S)
1.17/1.19	 isQid(active(X:S)) -> isQid(X:S)
1.17/1.19	 isQid(mark(X:S)) -> isQid(X:S)
1.17/1.19	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.17/1.19	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.17/1.19	 mark(isList(X:S)) -> active(isList(X:S))
1.17/1.19	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.17/1.19	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.17/1.19	 mark(isPal(X:S)) -> active(isPal(X:S))
1.17/1.19	 mark(isQid(X:S)) -> active(isQid(X:S))
1.17/1.19	 mark(a) -> active(a)
1.17/1.19	 mark(e) -> active(e)
1.17/1.19	 mark(i) -> active(i)
1.17/1.19	 mark(nil) -> active(nil)
1.17/1.19	 mark(o) -> active(o)
1.17/1.19	 mark(tt) -> active(tt)
1.17/1.19	 mark(u) -> active(u)
1.17/1.19	->Strongly Connected Components:
1.17/1.19	->->Cycle:
1.17/1.19	->->-> Pairs:
1.17/1.19	 ACTIVE(isNeList(V:S)) -> MARK(isQid(V:S))
1.17/1.19	 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(and(isQid(I:S),isPal(P:S)))
1.17/1.19	 ACTIVE(isNePal(V:S)) -> MARK(isQid(V:S))
1.17/1.19	 ACTIVE(isPal(V:S)) -> MARK(isNePal(V:S))
1.17/1.19	 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
1.17/1.19	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.19	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.17/1.19	 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S))
1.17/1.19	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.19	 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
1.17/1.19	 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
1.17/1.19	 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
1.17/1.19	->->-> Rules:
1.17/1.19	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.19	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.19	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.17/1.19	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.17/1.19	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.17/1.19	 active(__(nil,X:S)) -> mark(X:S)
1.17/1.19	 active(__(X:S,nil)) -> mark(X:S)
1.17/1.19	 active(and(tt,X:S)) -> mark(X:S)
1.17/1.19	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.17/1.19	 active(isList(nil)) -> mark(tt)
1.17/1.19	 active(isList(V:S)) -> mark(isNeList(V:S))
1.17/1.19	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.17/1.19	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.17/1.19	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.17/1.19	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.17/1.19	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.17/1.19	 active(isPal(nil)) -> mark(tt)
1.17/1.19	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.17/1.19	 active(isQid(a)) -> mark(tt)
1.17/1.19	 active(isQid(e)) -> mark(tt)
1.17/1.19	 active(isQid(i)) -> mark(tt)
1.17/1.19	 active(isQid(o)) -> mark(tt)
1.17/1.19	 active(isQid(u)) -> mark(tt)
1.17/1.19	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.19	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.19	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.17/1.19	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.17/1.19	 isList(active(X:S)) -> isList(X:S)
1.17/1.19	 isList(mark(X:S)) -> isList(X:S)
1.17/1.19	 isNeList(active(X:S)) -> isNeList(X:S)
1.17/1.19	 isNeList(mark(X:S)) -> isNeList(X:S)
1.17/1.19	 isNePal(active(X:S)) -> isNePal(X:S)
1.17/1.19	 isNePal(mark(X:S)) -> isNePal(X:S)
1.17/1.19	 isPal(active(X:S)) -> isPal(X:S)
1.17/1.19	 isPal(mark(X:S)) -> isPal(X:S)
1.17/1.19	 isQid(active(X:S)) -> isQid(X:S)
1.17/1.19	 isQid(mark(X:S)) -> isQid(X:S)
1.17/1.19	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.17/1.19	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.17/1.19	 mark(isList(X:S)) -> active(isList(X:S))
1.17/1.19	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.17/1.19	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.17/1.19	 mark(isPal(X:S)) -> active(isPal(X:S))
1.17/1.19	 mark(isQid(X:S)) -> active(isQid(X:S))
1.17/1.19	 mark(a) -> active(a)
1.17/1.19	 mark(e) -> active(e)
1.17/1.19	 mark(i) -> active(i)
1.17/1.19	 mark(nil) -> active(nil)
1.17/1.19	 mark(o) -> active(o)
1.17/1.19	 mark(tt) -> active(tt)
1.17/1.19	 mark(u) -> active(u)
1.17/1.19	
1.17/1.19	Problem 1.8: 
1.17/1.19	
1.17/1.19	Reduction Pairs Processor:
1.17/1.19	-> Pairs:
1.17/1.19	 ACTIVE(isNeList(V:S)) -> MARK(isQid(V:S))
1.17/1.19	 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(and(isQid(I:S),isPal(P:S)))
1.17/1.19	 ACTIVE(isNePal(V:S)) -> MARK(isQid(V:S))
1.17/1.19	 ACTIVE(isPal(V:S)) -> MARK(isNePal(V:S))
1.17/1.19	 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
1.17/1.19	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.19	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.17/1.19	 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S))
1.17/1.19	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.19	 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
1.17/1.19	 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
1.17/1.19	 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
1.17/1.19	-> Rules:
1.17/1.19	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.19	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.19	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.17/1.19	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.17/1.19	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.17/1.19	 active(__(nil,X:S)) -> mark(X:S)
1.17/1.19	 active(__(X:S,nil)) -> mark(X:S)
1.17/1.19	 active(and(tt,X:S)) -> mark(X:S)
1.17/1.19	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.17/1.19	 active(isList(nil)) -> mark(tt)
1.17/1.19	 active(isList(V:S)) -> mark(isNeList(V:S))
1.17/1.19	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.17/1.19	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.17/1.19	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.17/1.19	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.17/1.19	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.17/1.19	 active(isPal(nil)) -> mark(tt)
1.17/1.19	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.17/1.19	 active(isQid(a)) -> mark(tt)
1.17/1.19	 active(isQid(e)) -> mark(tt)
1.17/1.19	 active(isQid(i)) -> mark(tt)
1.17/1.19	 active(isQid(o)) -> mark(tt)
1.17/1.19	 active(isQid(u)) -> mark(tt)
1.17/1.19	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.19	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.19	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.17/1.19	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.17/1.19	 isList(active(X:S)) -> isList(X:S)
1.17/1.19	 isList(mark(X:S)) -> isList(X:S)
1.17/1.19	 isNeList(active(X:S)) -> isNeList(X:S)
1.17/1.19	 isNeList(mark(X:S)) -> isNeList(X:S)
1.17/1.19	 isNePal(active(X:S)) -> isNePal(X:S)
1.17/1.19	 isNePal(mark(X:S)) -> isNePal(X:S)
1.17/1.19	 isPal(active(X:S)) -> isPal(X:S)
1.17/1.19	 isPal(mark(X:S)) -> isPal(X:S)
1.17/1.19	 isQid(active(X:S)) -> isQid(X:S)
1.17/1.19	 isQid(mark(X:S)) -> isQid(X:S)
1.17/1.19	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.17/1.19	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.17/1.19	 mark(isList(X:S)) -> active(isList(X:S))
1.17/1.19	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.17/1.19	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.17/1.19	 mark(isPal(X:S)) -> active(isPal(X:S))
1.17/1.19	 mark(isQid(X:S)) -> active(isQid(X:S))
1.17/1.19	 mark(a) -> active(a)
1.17/1.19	 mark(e) -> active(e)
1.17/1.19	 mark(i) -> active(i)
1.17/1.19	 mark(nil) -> active(nil)
1.17/1.19	 mark(o) -> active(o)
1.17/1.19	 mark(tt) -> active(tt)
1.17/1.19	 mark(u) -> active(u)
1.17/1.19	-> Usable rules:
1.17/1.19	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.19	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.19	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.17/1.19	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.17/1.19	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.17/1.19	 active(__(nil,X:S)) -> mark(X:S)
1.17/1.19	 active(__(X:S,nil)) -> mark(X:S)
1.17/1.19	 active(and(tt,X:S)) -> mark(X:S)
1.17/1.19	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.17/1.19	 active(isList(nil)) -> mark(tt)
1.17/1.19	 active(isList(V:S)) -> mark(isNeList(V:S))
1.17/1.19	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.17/1.19	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.17/1.19	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.17/1.19	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.17/1.19	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.17/1.19	 active(isPal(nil)) -> mark(tt)
1.17/1.19	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.17/1.19	 active(isQid(a)) -> mark(tt)
1.17/1.19	 active(isQid(e)) -> mark(tt)
1.17/1.19	 active(isQid(i)) -> mark(tt)
1.17/1.19	 active(isQid(o)) -> mark(tt)
1.17/1.19	 active(isQid(u)) -> mark(tt)
1.17/1.19	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.19	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.19	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.17/1.19	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.17/1.19	 isList(active(X:S)) -> isList(X:S)
1.17/1.19	 isList(mark(X:S)) -> isList(X:S)
1.17/1.19	 isNeList(active(X:S)) -> isNeList(X:S)
1.17/1.19	 isNeList(mark(X:S)) -> isNeList(X:S)
1.17/1.19	 isNePal(active(X:S)) -> isNePal(X:S)
1.17/1.19	 isNePal(mark(X:S)) -> isNePal(X:S)
1.17/1.19	 isPal(active(X:S)) -> isPal(X:S)
1.17/1.19	 isPal(mark(X:S)) -> isPal(X:S)
1.17/1.19	 isQid(active(X:S)) -> isQid(X:S)
1.17/1.19	 isQid(mark(X:S)) -> isQid(X:S)
1.17/1.19	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.17/1.19	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.17/1.19	 mark(isList(X:S)) -> active(isList(X:S))
1.17/1.19	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.17/1.19	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.17/1.19	 mark(isPal(X:S)) -> active(isPal(X:S))
1.17/1.19	 mark(isQid(X:S)) -> active(isQid(X:S))
1.17/1.19	 mark(a) -> active(a)
1.17/1.19	 mark(e) -> active(e)
1.17/1.19	 mark(i) -> active(i)
1.17/1.19	 mark(nil) -> active(nil)
1.17/1.19	 mark(o) -> active(o)
1.17/1.19	 mark(tt) -> active(tt)
1.17/1.19	 mark(u) -> active(u)
1.17/1.19	->Interpretation type:
1.17/1.19	 Linear
1.17/1.19	->Coefficients:
1.17/1.19	 Natural Numbers
1.17/1.19	->Dimension:
1.17/1.19	 1
1.17/1.19	->Bound:
1.17/1.19	 2
1.17/1.19	->Interpretation:
1.17/1.19	 
1.17/1.19	[__](X1,X2) = 2.X1 + X2 + 2
1.17/1.19	[active](X) = X
1.17/1.19	[and](X1,X2) = 2.X1 + X2
1.17/1.19	[isList](X) = 2.X + 2
1.17/1.19	[isNeList](X) = 2.X + 2
1.17/1.19	[isNePal](X) = 2.X + 1
1.17/1.19	[isPal](X) = 2.X + 1
1.17/1.19	[isQid](X) = 2.X + 1
1.17/1.19	[mark](X) = X
1.17/1.19	[a] = 2
1.17/1.19	[e] = 0
1.17/1.19	[fSNonEmpty] = 0
1.17/1.19	[i] = 2
1.17/1.19	[nil] = 2
1.17/1.19	[o] = 2
1.17/1.19	[tt] = 0
1.17/1.19	[u] = 1
1.17/1.19	[__#](X1,X2) = 0
1.17/1.19	[ACTIVE](X) = 2.X + 1
1.17/1.19	[AND](X1,X2) = 0
1.17/1.19	[ISLIST](X) = 0
1.17/1.19	[ISNELIST](X) = 0
1.17/1.19	[ISNEPAL](X) = 0
1.17/1.19	[ISPAL](X) = 0
1.17/1.19	[ISQID](X) = 0
1.17/1.19	[MARK](X) = 2.X + 1
1.17/1.19	
1.17/1.19	Problem 1.8: 
1.17/1.19	
1.17/1.19	SCC Processor:
1.17/1.19	-> Pairs:
1.17/1.19	 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(and(isQid(I:S),isPal(P:S)))
1.17/1.19	 ACTIVE(isNePal(V:S)) -> MARK(isQid(V:S))
1.17/1.19	 ACTIVE(isPal(V:S)) -> MARK(isNePal(V:S))
1.17/1.19	 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
1.17/1.19	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.19	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.17/1.19	 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S))
1.17/1.19	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.19	 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S))
1.17/1.19	 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
1.17/1.19	 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
1.17/1.19	-> Rules:
1.17/1.19	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.19	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.19	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.17/1.19	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.17/1.19	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.17/1.19	 active(__(nil,X:S)) -> mark(X:S)
1.17/1.19	 active(__(X:S,nil)) -> mark(X:S)
1.17/1.19	 active(and(tt,X:S)) -> mark(X:S)
1.17/1.19	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.17/1.19	 active(isList(nil)) -> mark(tt)
1.17/1.19	 active(isList(V:S)) -> mark(isNeList(V:S))
1.17/1.19	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.17/1.19	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.17/1.19	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.17/1.19	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.17/1.19	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.17/1.19	 active(isPal(nil)) -> mark(tt)
1.17/1.19	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.17/1.19	 active(isQid(a)) -> mark(tt)
1.17/1.19	 active(isQid(e)) -> mark(tt)
1.17/1.19	 active(isQid(i)) -> mark(tt)
1.17/1.19	 active(isQid(o)) -> mark(tt)
1.17/1.19	 active(isQid(u)) -> mark(tt)
1.17/1.19	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.19	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.19	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.17/1.19	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.17/1.19	 isList(active(X:S)) -> isList(X:S)
1.17/1.19	 isList(mark(X:S)) -> isList(X:S)
1.17/1.19	 isNeList(active(X:S)) -> isNeList(X:S)
1.17/1.19	 isNeList(mark(X:S)) -> isNeList(X:S)
1.17/1.19	 isNePal(active(X:S)) -> isNePal(X:S)
1.17/1.19	 isNePal(mark(X:S)) -> isNePal(X:S)
1.17/1.19	 isPal(active(X:S)) -> isPal(X:S)
1.17/1.19	 isPal(mark(X:S)) -> isPal(X:S)
1.17/1.19	 isQid(active(X:S)) -> isQid(X:S)
1.17/1.19	 isQid(mark(X:S)) -> isQid(X:S)
1.17/1.19	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.17/1.19	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.17/1.19	 mark(isList(X:S)) -> active(isList(X:S))
1.17/1.19	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.17/1.19	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.17/1.19	 mark(isPal(X:S)) -> active(isPal(X:S))
1.17/1.19	 mark(isQid(X:S)) -> active(isQid(X:S))
1.17/1.19	 mark(a) -> active(a)
1.17/1.19	 mark(e) -> active(e)
1.17/1.19	 mark(i) -> active(i)
1.17/1.19	 mark(nil) -> active(nil)
1.17/1.19	 mark(o) -> active(o)
1.17/1.19	 mark(tt) -> active(tt)
1.17/1.19	 mark(u) -> active(u)
1.17/1.19	->Strongly Connected Components:
1.17/1.19	->->Cycle:
1.17/1.19	->->-> Pairs:
1.17/1.19	 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(and(isQid(I:S),isPal(P:S)))
1.17/1.19	 ACTIVE(isNePal(V:S)) -> MARK(isQid(V:S))
1.17/1.19	 ACTIVE(isPal(V:S)) -> MARK(isNePal(V:S))
1.17/1.19	 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
1.17/1.19	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.19	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.17/1.19	 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S))
1.17/1.19	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.19	 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
1.17/1.19	 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
1.17/1.19	->->-> Rules:
1.17/1.19	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.19	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.19	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.17/1.19	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.17/1.19	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.17/1.19	 active(__(nil,X:S)) -> mark(X:S)
1.17/1.19	 active(__(X:S,nil)) -> mark(X:S)
1.17/1.19	 active(and(tt,X:S)) -> mark(X:S)
1.17/1.19	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.17/1.19	 active(isList(nil)) -> mark(tt)
1.17/1.19	 active(isList(V:S)) -> mark(isNeList(V:S))
1.17/1.19	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.17/1.19	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.17/1.19	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.17/1.19	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.17/1.19	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.17/1.19	 active(isPal(nil)) -> mark(tt)
1.17/1.19	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.17/1.19	 active(isQid(a)) -> mark(tt)
1.17/1.19	 active(isQid(e)) -> mark(tt)
1.17/1.19	 active(isQid(i)) -> mark(tt)
1.17/1.19	 active(isQid(o)) -> mark(tt)
1.17/1.19	 active(isQid(u)) -> mark(tt)
1.17/1.19	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.19	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.19	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.17/1.19	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.17/1.19	 isList(active(X:S)) -> isList(X:S)
1.17/1.19	 isList(mark(X:S)) -> isList(X:S)
1.17/1.19	 isNeList(active(X:S)) -> isNeList(X:S)
1.17/1.19	 isNeList(mark(X:S)) -> isNeList(X:S)
1.17/1.19	 isNePal(active(X:S)) -> isNePal(X:S)
1.17/1.19	 isNePal(mark(X:S)) -> isNePal(X:S)
1.17/1.19	 isPal(active(X:S)) -> isPal(X:S)
1.17/1.19	 isPal(mark(X:S)) -> isPal(X:S)
1.17/1.19	 isQid(active(X:S)) -> isQid(X:S)
1.17/1.19	 isQid(mark(X:S)) -> isQid(X:S)
1.17/1.19	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.17/1.19	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.17/1.19	 mark(isList(X:S)) -> active(isList(X:S))
1.17/1.19	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.17/1.19	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.17/1.19	 mark(isPal(X:S)) -> active(isPal(X:S))
1.17/1.19	 mark(isQid(X:S)) -> active(isQid(X:S))
1.17/1.19	 mark(a) -> active(a)
1.17/1.19	 mark(e) -> active(e)
1.17/1.19	 mark(i) -> active(i)
1.17/1.19	 mark(nil) -> active(nil)
1.17/1.19	 mark(o) -> active(o)
1.17/1.19	 mark(tt) -> active(tt)
1.17/1.19	 mark(u) -> active(u)
1.17/1.19	
1.17/1.19	Problem 1.8: 
1.17/1.19	
1.17/1.19	Reduction Pairs Processor:
1.17/1.19	-> Pairs:
1.17/1.19	 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(and(isQid(I:S),isPal(P:S)))
1.17/1.19	 ACTIVE(isNePal(V:S)) -> MARK(isQid(V:S))
1.17/1.19	 ACTIVE(isPal(V:S)) -> MARK(isNePal(V:S))
1.17/1.19	 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
1.17/1.19	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.19	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.17/1.19	 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S))
1.17/1.19	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.19	 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
1.17/1.19	 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
1.17/1.19	-> Rules:
1.17/1.19	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.19	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.19	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.17/1.19	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.17/1.19	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.17/1.19	 active(__(nil,X:S)) -> mark(X:S)
1.17/1.19	 active(__(X:S,nil)) -> mark(X:S)
1.17/1.19	 active(and(tt,X:S)) -> mark(X:S)
1.17/1.19	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.17/1.19	 active(isList(nil)) -> mark(tt)
1.17/1.19	 active(isList(V:S)) -> mark(isNeList(V:S))
1.17/1.19	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.17/1.19	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.17/1.19	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.17/1.19	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.17/1.19	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.17/1.19	 active(isPal(nil)) -> mark(tt)
1.17/1.19	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.17/1.19	 active(isQid(a)) -> mark(tt)
1.17/1.19	 active(isQid(e)) -> mark(tt)
1.17/1.19	 active(isQid(i)) -> mark(tt)
1.17/1.19	 active(isQid(o)) -> mark(tt)
1.17/1.19	 active(isQid(u)) -> mark(tt)
1.17/1.19	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.19	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.19	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.17/1.19	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.17/1.19	 isList(active(X:S)) -> isList(X:S)
1.17/1.19	 isList(mark(X:S)) -> isList(X:S)
1.17/1.19	 isNeList(active(X:S)) -> isNeList(X:S)
1.17/1.19	 isNeList(mark(X:S)) -> isNeList(X:S)
1.17/1.19	 isNePal(active(X:S)) -> isNePal(X:S)
1.17/1.19	 isNePal(mark(X:S)) -> isNePal(X:S)
1.17/1.19	 isPal(active(X:S)) -> isPal(X:S)
1.17/1.19	 isPal(mark(X:S)) -> isPal(X:S)
1.17/1.19	 isQid(active(X:S)) -> isQid(X:S)
1.17/1.19	 isQid(mark(X:S)) -> isQid(X:S)
1.17/1.19	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.17/1.19	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.17/1.19	 mark(isList(X:S)) -> active(isList(X:S))
1.17/1.19	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.17/1.19	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.17/1.19	 mark(isPal(X:S)) -> active(isPal(X:S))
1.17/1.19	 mark(isQid(X:S)) -> active(isQid(X:S))
1.17/1.19	 mark(a) -> active(a)
1.17/1.19	 mark(e) -> active(e)
1.17/1.19	 mark(i) -> active(i)
1.17/1.19	 mark(nil) -> active(nil)
1.17/1.19	 mark(o) -> active(o)
1.17/1.19	 mark(tt) -> active(tt)
1.17/1.19	 mark(u) -> active(u)
1.17/1.19	-> Usable rules:
1.17/1.19	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.19	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.19	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.17/1.19	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.17/1.19	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.17/1.19	 active(__(nil,X:S)) -> mark(X:S)
1.17/1.19	 active(__(X:S,nil)) -> mark(X:S)
1.17/1.19	 active(and(tt,X:S)) -> mark(X:S)
1.17/1.19	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.17/1.19	 active(isList(nil)) -> mark(tt)
1.17/1.19	 active(isList(V:S)) -> mark(isNeList(V:S))
1.17/1.19	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.17/1.19	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.17/1.19	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.17/1.19	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.17/1.19	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.17/1.19	 active(isPal(nil)) -> mark(tt)
1.17/1.19	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.17/1.19	 active(isQid(a)) -> mark(tt)
1.17/1.19	 active(isQid(e)) -> mark(tt)
1.17/1.19	 active(isQid(i)) -> mark(tt)
1.17/1.19	 active(isQid(o)) -> mark(tt)
1.17/1.19	 active(isQid(u)) -> mark(tt)
1.17/1.19	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.19	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.19	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.17/1.19	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.17/1.19	 isList(active(X:S)) -> isList(X:S)
1.17/1.19	 isList(mark(X:S)) -> isList(X:S)
1.17/1.19	 isNeList(active(X:S)) -> isNeList(X:S)
1.17/1.19	 isNeList(mark(X:S)) -> isNeList(X:S)
1.17/1.19	 isNePal(active(X:S)) -> isNePal(X:S)
1.17/1.19	 isNePal(mark(X:S)) -> isNePal(X:S)
1.17/1.19	 isPal(active(X:S)) -> isPal(X:S)
1.17/1.19	 isPal(mark(X:S)) -> isPal(X:S)
1.17/1.19	 isQid(active(X:S)) -> isQid(X:S)
1.17/1.19	 isQid(mark(X:S)) -> isQid(X:S)
1.17/1.19	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.17/1.19	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.17/1.19	 mark(isList(X:S)) -> active(isList(X:S))
1.17/1.19	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.17/1.19	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.17/1.19	 mark(isPal(X:S)) -> active(isPal(X:S))
1.17/1.19	 mark(isQid(X:S)) -> active(isQid(X:S))
1.17/1.19	 mark(a) -> active(a)
1.17/1.19	 mark(e) -> active(e)
1.17/1.19	 mark(i) -> active(i)
1.17/1.19	 mark(nil) -> active(nil)
1.17/1.19	 mark(o) -> active(o)
1.17/1.19	 mark(tt) -> active(tt)
1.17/1.19	 mark(u) -> active(u)
1.17/1.19	->Interpretation type:
1.17/1.19	 Linear
1.17/1.19	->Coefficients:
1.17/1.19	 Natural Numbers
1.17/1.19	->Dimension:
1.17/1.19	 1
1.17/1.19	->Bound:
1.17/1.19	 2
1.17/1.19	->Interpretation:
1.17/1.19	 
1.17/1.19	[__](X1,X2) = 2.X1 + X2 + 2
1.17/1.19	[active](X) = X
1.17/1.19	[and](X1,X2) = X1 + X2 + 1
1.17/1.19	[isList](X) = 2.X + 2
1.17/1.19	[isNeList](X) = 2.X + 2
1.17/1.19	[isNePal](X) = 2.X
1.17/1.19	[isPal](X) = 2.X
1.17/1.19	[isQid](X) = 2.X
1.17/1.19	[mark](X) = X
1.17/1.19	[a] = 1
1.17/1.19	[e] = 2
1.17/1.19	[fSNonEmpty] = 0
1.17/1.19	[i] = 2
1.17/1.19	[nil] = 2
1.17/1.19	[o] = 2
1.17/1.19	[tt] = 2
1.17/1.19	[u] = 1
1.17/1.19	[__#](X1,X2) = 0
1.17/1.19	[ACTIVE](X) = 2.X + 2
1.17/1.19	[AND](X1,X2) = 0
1.17/1.19	[ISLIST](X) = 0
1.17/1.19	[ISNELIST](X) = 0
1.17/1.19	[ISNEPAL](X) = 0
1.17/1.19	[ISPAL](X) = 0
1.17/1.19	[ISQID](X) = 0
1.17/1.19	[MARK](X) = 2.X + 2
1.17/1.19	
1.17/1.19	Problem 1.8: 
1.17/1.19	
1.17/1.19	SCC Processor:
1.17/1.19	-> Pairs:
1.17/1.19	 ACTIVE(isNePal(V:S)) -> MARK(isQid(V:S))
1.17/1.19	 ACTIVE(isPal(V:S)) -> MARK(isNePal(V:S))
1.17/1.19	 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
1.17/1.19	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.19	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.17/1.19	 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S))
1.17/1.19	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.19	 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
1.17/1.19	 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
1.17/1.19	-> Rules:
1.17/1.19	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.19	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.19	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.17/1.19	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.17/1.19	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.17/1.19	 active(__(nil,X:S)) -> mark(X:S)
1.17/1.19	 active(__(X:S,nil)) -> mark(X:S)
1.17/1.19	 active(and(tt,X:S)) -> mark(X:S)
1.17/1.19	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.17/1.19	 active(isList(nil)) -> mark(tt)
1.17/1.19	 active(isList(V:S)) -> mark(isNeList(V:S))
1.17/1.19	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.17/1.19	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.17/1.19	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.17/1.19	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.17/1.19	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.17/1.19	 active(isPal(nil)) -> mark(tt)
1.17/1.19	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.17/1.19	 active(isQid(a)) -> mark(tt)
1.17/1.19	 active(isQid(e)) -> mark(tt)
1.17/1.19	 active(isQid(i)) -> mark(tt)
1.17/1.19	 active(isQid(o)) -> mark(tt)
1.17/1.19	 active(isQid(u)) -> mark(tt)
1.17/1.19	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.19	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.19	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.17/1.19	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.17/1.19	 isList(active(X:S)) -> isList(X:S)
1.17/1.19	 isList(mark(X:S)) -> isList(X:S)
1.17/1.19	 isNeList(active(X:S)) -> isNeList(X:S)
1.17/1.19	 isNeList(mark(X:S)) -> isNeList(X:S)
1.17/1.19	 isNePal(active(X:S)) -> isNePal(X:S)
1.17/1.19	 isNePal(mark(X:S)) -> isNePal(X:S)
1.17/1.19	 isPal(active(X:S)) -> isPal(X:S)
1.17/1.19	 isPal(mark(X:S)) -> isPal(X:S)
1.17/1.19	 isQid(active(X:S)) -> isQid(X:S)
1.17/1.19	 isQid(mark(X:S)) -> isQid(X:S)
1.17/1.19	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.17/1.19	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.17/1.19	 mark(isList(X:S)) -> active(isList(X:S))
1.17/1.19	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.17/1.19	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.17/1.19	 mark(isPal(X:S)) -> active(isPal(X:S))
1.17/1.19	 mark(isQid(X:S)) -> active(isQid(X:S))
1.17/1.19	 mark(a) -> active(a)
1.17/1.19	 mark(e) -> active(e)
1.17/1.19	 mark(i) -> active(i)
1.17/1.19	 mark(nil) -> active(nil)
1.17/1.19	 mark(o) -> active(o)
1.17/1.19	 mark(tt) -> active(tt)
1.17/1.19	 mark(u) -> active(u)
1.17/1.19	->Strongly Connected Components:
1.17/1.19	->->Cycle:
1.17/1.19	->->-> Pairs:
1.17/1.19	 ACTIVE(isNePal(V:S)) -> MARK(isQid(V:S))
1.17/1.19	 ACTIVE(isPal(V:S)) -> MARK(isNePal(V:S))
1.17/1.19	 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
1.17/1.19	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.19	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.17/1.19	 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S))
1.17/1.19	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.19	 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
1.17/1.19	 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
1.17/1.19	->->-> Rules:
1.17/1.19	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.19	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.19	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.17/1.19	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.17/1.19	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.17/1.19	 active(__(nil,X:S)) -> mark(X:S)
1.17/1.19	 active(__(X:S,nil)) -> mark(X:S)
1.17/1.19	 active(and(tt,X:S)) -> mark(X:S)
1.17/1.19	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.17/1.19	 active(isList(nil)) -> mark(tt)
1.17/1.19	 active(isList(V:S)) -> mark(isNeList(V:S))
1.17/1.19	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.17/1.19	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.17/1.19	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.17/1.19	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.17/1.19	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.17/1.19	 active(isPal(nil)) -> mark(tt)
1.17/1.19	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.17/1.19	 active(isQid(a)) -> mark(tt)
1.17/1.19	 active(isQid(e)) -> mark(tt)
1.17/1.19	 active(isQid(i)) -> mark(tt)
1.17/1.19	 active(isQid(o)) -> mark(tt)
1.17/1.19	 active(isQid(u)) -> mark(tt)
1.17/1.19	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.19	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.19	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.17/1.19	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.17/1.19	 isList(active(X:S)) -> isList(X:S)
1.17/1.19	 isList(mark(X:S)) -> isList(X:S)
1.17/1.19	 isNeList(active(X:S)) -> isNeList(X:S)
1.17/1.19	 isNeList(mark(X:S)) -> isNeList(X:S)
1.17/1.19	 isNePal(active(X:S)) -> isNePal(X:S)
1.17/1.19	 isNePal(mark(X:S)) -> isNePal(X:S)
1.17/1.19	 isPal(active(X:S)) -> isPal(X:S)
1.17/1.19	 isPal(mark(X:S)) -> isPal(X:S)
1.17/1.19	 isQid(active(X:S)) -> isQid(X:S)
1.17/1.19	 isQid(mark(X:S)) -> isQid(X:S)
1.17/1.19	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.17/1.19	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.17/1.19	 mark(isList(X:S)) -> active(isList(X:S))
1.17/1.19	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.17/1.19	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.17/1.19	 mark(isPal(X:S)) -> active(isPal(X:S))
1.17/1.19	 mark(isQid(X:S)) -> active(isQid(X:S))
1.17/1.19	 mark(a) -> active(a)
1.17/1.19	 mark(e) -> active(e)
1.17/1.19	 mark(i) -> active(i)
1.17/1.19	 mark(nil) -> active(nil)
1.17/1.19	 mark(o) -> active(o)
1.17/1.19	 mark(tt) -> active(tt)
1.17/1.19	 mark(u) -> active(u)
1.17/1.19	
1.17/1.19	Problem 1.8: 
1.17/1.19	
1.17/1.19	Reduction Pairs Processor:
1.17/1.19	-> Pairs:
1.17/1.19	 ACTIVE(isNePal(V:S)) -> MARK(isQid(V:S))
1.17/1.19	 ACTIVE(isPal(V:S)) -> MARK(isNePal(V:S))
1.17/1.19	 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
1.17/1.19	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.19	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.17/1.19	 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S))
1.17/1.19	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.19	 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
1.17/1.19	 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
1.17/1.19	-> Rules:
1.17/1.19	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.19	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.19	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.17/1.19	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.17/1.19	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.17/1.19	 active(__(nil,X:S)) -> mark(X:S)
1.17/1.19	 active(__(X:S,nil)) -> mark(X:S)
1.17/1.19	 active(and(tt,X:S)) -> mark(X:S)
1.17/1.19	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.17/1.19	 active(isList(nil)) -> mark(tt)
1.17/1.19	 active(isList(V:S)) -> mark(isNeList(V:S))
1.17/1.19	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.17/1.19	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.17/1.19	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.17/1.19	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.17/1.19	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.17/1.19	 active(isPal(nil)) -> mark(tt)
1.17/1.19	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.17/1.19	 active(isQid(a)) -> mark(tt)
1.17/1.19	 active(isQid(e)) -> mark(tt)
1.17/1.19	 active(isQid(i)) -> mark(tt)
1.17/1.19	 active(isQid(o)) -> mark(tt)
1.17/1.19	 active(isQid(u)) -> mark(tt)
1.17/1.20	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.20	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.20	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.17/1.20	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.17/1.20	 isList(active(X:S)) -> isList(X:S)
1.17/1.20	 isList(mark(X:S)) -> isList(X:S)
1.17/1.20	 isNeList(active(X:S)) -> isNeList(X:S)
1.17/1.20	 isNeList(mark(X:S)) -> isNeList(X:S)
1.17/1.20	 isNePal(active(X:S)) -> isNePal(X:S)
1.17/1.20	 isNePal(mark(X:S)) -> isNePal(X:S)
1.17/1.20	 isPal(active(X:S)) -> isPal(X:S)
1.17/1.20	 isPal(mark(X:S)) -> isPal(X:S)
1.17/1.20	 isQid(active(X:S)) -> isQid(X:S)
1.17/1.20	 isQid(mark(X:S)) -> isQid(X:S)
1.17/1.20	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.17/1.20	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.17/1.20	 mark(isList(X:S)) -> active(isList(X:S))
1.17/1.20	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.17/1.20	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.17/1.20	 mark(isPal(X:S)) -> active(isPal(X:S))
1.17/1.20	 mark(isQid(X:S)) -> active(isQid(X:S))
1.17/1.20	 mark(a) -> active(a)
1.17/1.20	 mark(e) -> active(e)
1.17/1.20	 mark(i) -> active(i)
1.17/1.20	 mark(nil) -> active(nil)
1.17/1.20	 mark(o) -> active(o)
1.17/1.20	 mark(tt) -> active(tt)
1.17/1.20	 mark(u) -> active(u)
1.17/1.20	-> Usable rules:
1.17/1.20	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.20	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.20	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.17/1.20	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.17/1.20	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.17/1.20	 active(__(nil,X:S)) -> mark(X:S)
1.17/1.20	 active(__(X:S,nil)) -> mark(X:S)
1.17/1.20	 active(and(tt,X:S)) -> mark(X:S)
1.17/1.20	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.17/1.20	 active(isList(nil)) -> mark(tt)
1.17/1.20	 active(isList(V:S)) -> mark(isNeList(V:S))
1.17/1.20	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.17/1.20	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.17/1.20	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.17/1.20	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.17/1.20	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.17/1.20	 active(isPal(nil)) -> mark(tt)
1.17/1.20	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.17/1.20	 active(isQid(a)) -> mark(tt)
1.17/1.20	 active(isQid(e)) -> mark(tt)
1.17/1.20	 active(isQid(i)) -> mark(tt)
1.17/1.20	 active(isQid(o)) -> mark(tt)
1.17/1.20	 active(isQid(u)) -> mark(tt)
1.17/1.20	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.20	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.20	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.17/1.20	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.17/1.20	 isList(active(X:S)) -> isList(X:S)
1.17/1.20	 isList(mark(X:S)) -> isList(X:S)
1.17/1.20	 isNeList(active(X:S)) -> isNeList(X:S)
1.17/1.20	 isNeList(mark(X:S)) -> isNeList(X:S)
1.17/1.20	 isNePal(active(X:S)) -> isNePal(X:S)
1.17/1.20	 isNePal(mark(X:S)) -> isNePal(X:S)
1.17/1.20	 isPal(active(X:S)) -> isPal(X:S)
1.17/1.20	 isPal(mark(X:S)) -> isPal(X:S)
1.17/1.20	 isQid(active(X:S)) -> isQid(X:S)
1.17/1.20	 isQid(mark(X:S)) -> isQid(X:S)
1.17/1.20	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.17/1.20	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.17/1.20	 mark(isList(X:S)) -> active(isList(X:S))
1.17/1.20	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.17/1.20	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.17/1.20	 mark(isPal(X:S)) -> active(isPal(X:S))
1.17/1.20	 mark(isQid(X:S)) -> active(isQid(X:S))
1.17/1.20	 mark(a) -> active(a)
1.17/1.20	 mark(e) -> active(e)
1.17/1.20	 mark(i) -> active(i)
1.17/1.20	 mark(nil) -> active(nil)
1.17/1.20	 mark(o) -> active(o)
1.17/1.20	 mark(tt) -> active(tt)
1.17/1.20	 mark(u) -> active(u)
1.17/1.20	->Interpretation type:
1.17/1.20	 Linear
1.17/1.20	->Coefficients:
1.17/1.20	 Natural Numbers
1.17/1.20	->Dimension:
1.17/1.20	 1
1.17/1.20	->Bound:
1.17/1.20	 2
1.17/1.20	->Interpretation:
1.17/1.20	 
1.17/1.20	[__](X1,X2) = 2.X1 + X2 + 2
1.17/1.20	[active](X) = X
1.17/1.20	[and](X1,X2) = 2.X1 + 2.X2
1.17/1.20	[isList](X) = 0
1.17/1.20	[isNeList](X) = 0
1.17/1.20	[isNePal](X) = 2.X + 2
1.17/1.20	[isPal](X) = 2.X + 2
1.17/1.20	[isQid](X) = 0
1.17/1.20	[mark](X) = X
1.17/1.20	[a] = 0
1.17/1.20	[e] = 1
1.17/1.20	[fSNonEmpty] = 0
1.17/1.20	[i] = 0
1.17/1.20	[nil] = 2
1.17/1.20	[o] = 2
1.17/1.20	[tt] = 0
1.17/1.20	[u] = 2
1.17/1.20	[__#](X1,X2) = 0
1.17/1.20	[ACTIVE](X) = 2.X + 2
1.17/1.20	[AND](X1,X2) = 0
1.17/1.20	[ISLIST](X) = 0
1.17/1.20	[ISNELIST](X) = 0
1.17/1.20	[ISNEPAL](X) = 0
1.17/1.20	[ISPAL](X) = 0
1.17/1.20	[ISQID](X) = 0
1.17/1.20	[MARK](X) = 2.X + 2
1.17/1.20	
1.17/1.20	Problem 1.8: 
1.17/1.20	
1.17/1.20	SCC Processor:
1.17/1.20	-> Pairs:
1.17/1.20	 ACTIVE(isPal(V:S)) -> MARK(isNePal(V:S))
1.17/1.20	 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
1.17/1.20	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.20	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.17/1.20	 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S))
1.17/1.20	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.20	 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S))
1.17/1.20	 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
1.17/1.20	-> Rules:
1.17/1.20	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.20	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.20	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.17/1.20	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.17/1.20	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.17/1.20	 active(__(nil,X:S)) -> mark(X:S)
1.17/1.20	 active(__(X:S,nil)) -> mark(X:S)
1.17/1.20	 active(and(tt,X:S)) -> mark(X:S)
1.17/1.20	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.17/1.20	 active(isList(nil)) -> mark(tt)
1.17/1.20	 active(isList(V:S)) -> mark(isNeList(V:S))
1.17/1.20	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.17/1.20	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.17/1.20	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.17/1.20	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.17/1.20	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.17/1.20	 active(isPal(nil)) -> mark(tt)
1.17/1.20	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.17/1.20	 active(isQid(a)) -> mark(tt)
1.17/1.20	 active(isQid(e)) -> mark(tt)
1.17/1.20	 active(isQid(i)) -> mark(tt)
1.17/1.20	 active(isQid(o)) -> mark(tt)
1.17/1.20	 active(isQid(u)) -> mark(tt)
1.17/1.20	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.20	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.20	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.17/1.20	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.17/1.20	 isList(active(X:S)) -> isList(X:S)
1.17/1.20	 isList(mark(X:S)) -> isList(X:S)
1.17/1.20	 isNeList(active(X:S)) -> isNeList(X:S)
1.17/1.20	 isNeList(mark(X:S)) -> isNeList(X:S)
1.17/1.20	 isNePal(active(X:S)) -> isNePal(X:S)
1.17/1.20	 isNePal(mark(X:S)) -> isNePal(X:S)
1.17/1.20	 isPal(active(X:S)) -> isPal(X:S)
1.17/1.20	 isPal(mark(X:S)) -> isPal(X:S)
1.17/1.20	 isQid(active(X:S)) -> isQid(X:S)
1.17/1.20	 isQid(mark(X:S)) -> isQid(X:S)
1.17/1.20	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.17/1.20	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.17/1.20	 mark(isList(X:S)) -> active(isList(X:S))
1.17/1.20	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.17/1.20	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.17/1.20	 mark(isPal(X:S)) -> active(isPal(X:S))
1.17/1.20	 mark(isQid(X:S)) -> active(isQid(X:S))
1.17/1.20	 mark(a) -> active(a)
1.17/1.20	 mark(e) -> active(e)
1.17/1.20	 mark(i) -> active(i)
1.17/1.20	 mark(nil) -> active(nil)
1.17/1.20	 mark(o) -> active(o)
1.17/1.20	 mark(tt) -> active(tt)
1.17/1.20	 mark(u) -> active(u)
1.17/1.20	->Strongly Connected Components:
1.17/1.20	->->Cycle:
1.17/1.20	->->-> Pairs:
1.17/1.20	 ACTIVE(isPal(V:S)) -> MARK(isNePal(V:S))
1.17/1.20	 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
1.17/1.20	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.20	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.17/1.20	 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S))
1.17/1.20	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.20	 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
1.17/1.20	->->-> Rules:
1.17/1.20	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.20	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.20	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.17/1.20	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.17/1.20	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.17/1.20	 active(__(nil,X:S)) -> mark(X:S)
1.17/1.20	 active(__(X:S,nil)) -> mark(X:S)
1.17/1.20	 active(and(tt,X:S)) -> mark(X:S)
1.17/1.20	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.17/1.20	 active(isList(nil)) -> mark(tt)
1.17/1.20	 active(isList(V:S)) -> mark(isNeList(V:S))
1.17/1.20	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.17/1.20	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.17/1.20	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.17/1.20	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.17/1.20	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.17/1.20	 active(isPal(nil)) -> mark(tt)
1.17/1.20	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.17/1.20	 active(isQid(a)) -> mark(tt)
1.17/1.20	 active(isQid(e)) -> mark(tt)
1.17/1.20	 active(isQid(i)) -> mark(tt)
1.17/1.20	 active(isQid(o)) -> mark(tt)
1.17/1.20	 active(isQid(u)) -> mark(tt)
1.17/1.20	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.20	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.20	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.17/1.20	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.17/1.20	 isList(active(X:S)) -> isList(X:S)
1.17/1.20	 isList(mark(X:S)) -> isList(X:S)
1.17/1.20	 isNeList(active(X:S)) -> isNeList(X:S)
1.17/1.20	 isNeList(mark(X:S)) -> isNeList(X:S)
1.17/1.20	 isNePal(active(X:S)) -> isNePal(X:S)
1.17/1.20	 isNePal(mark(X:S)) -> isNePal(X:S)
1.17/1.20	 isPal(active(X:S)) -> isPal(X:S)
1.17/1.20	 isPal(mark(X:S)) -> isPal(X:S)
1.17/1.20	 isQid(active(X:S)) -> isQid(X:S)
1.17/1.20	 isQid(mark(X:S)) -> isQid(X:S)
1.17/1.20	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.17/1.20	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.17/1.20	 mark(isList(X:S)) -> active(isList(X:S))
1.17/1.20	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.17/1.20	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.17/1.20	 mark(isPal(X:S)) -> active(isPal(X:S))
1.17/1.20	 mark(isQid(X:S)) -> active(isQid(X:S))
1.17/1.20	 mark(a) -> active(a)
1.17/1.20	 mark(e) -> active(e)
1.17/1.20	 mark(i) -> active(i)
1.17/1.20	 mark(nil) -> active(nil)
1.17/1.20	 mark(o) -> active(o)
1.17/1.20	 mark(tt) -> active(tt)
1.17/1.20	 mark(u) -> active(u)
1.17/1.20	
1.17/1.20	Problem 1.8: 
1.17/1.20	
1.17/1.20	Reduction Pairs Processor:
1.17/1.20	-> Pairs:
1.17/1.20	 ACTIVE(isPal(V:S)) -> MARK(isNePal(V:S))
1.17/1.20	 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
1.17/1.20	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.20	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.17/1.20	 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S))
1.17/1.20	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.20	 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
1.17/1.20	-> Rules:
1.17/1.20	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.20	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.20	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.17/1.20	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.17/1.20	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.17/1.20	 active(__(nil,X:S)) -> mark(X:S)
1.17/1.20	 active(__(X:S,nil)) -> mark(X:S)
1.17/1.20	 active(and(tt,X:S)) -> mark(X:S)
1.17/1.20	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.17/1.20	 active(isList(nil)) -> mark(tt)
1.17/1.20	 active(isList(V:S)) -> mark(isNeList(V:S))
1.17/1.20	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.17/1.20	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.17/1.20	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.17/1.20	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.17/1.20	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.17/1.20	 active(isPal(nil)) -> mark(tt)
1.17/1.20	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.17/1.20	 active(isQid(a)) -> mark(tt)
1.17/1.20	 active(isQid(e)) -> mark(tt)
1.17/1.20	 active(isQid(i)) -> mark(tt)
1.17/1.20	 active(isQid(o)) -> mark(tt)
1.17/1.20	 active(isQid(u)) -> mark(tt)
1.17/1.20	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.20	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.20	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.17/1.20	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.17/1.20	 isList(active(X:S)) -> isList(X:S)
1.17/1.20	 isList(mark(X:S)) -> isList(X:S)
1.17/1.20	 isNeList(active(X:S)) -> isNeList(X:S)
1.17/1.20	 isNeList(mark(X:S)) -> isNeList(X:S)
1.17/1.20	 isNePal(active(X:S)) -> isNePal(X:S)
1.17/1.20	 isNePal(mark(X:S)) -> isNePal(X:S)
1.17/1.20	 isPal(active(X:S)) -> isPal(X:S)
1.17/1.20	 isPal(mark(X:S)) -> isPal(X:S)
1.17/1.20	 isQid(active(X:S)) -> isQid(X:S)
1.17/1.20	 isQid(mark(X:S)) -> isQid(X:S)
1.17/1.20	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.17/1.20	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.17/1.20	 mark(isList(X:S)) -> active(isList(X:S))
1.17/1.20	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.17/1.20	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.17/1.20	 mark(isPal(X:S)) -> active(isPal(X:S))
1.17/1.20	 mark(isQid(X:S)) -> active(isQid(X:S))
1.17/1.20	 mark(a) -> active(a)
1.17/1.20	 mark(e) -> active(e)
1.17/1.20	 mark(i) -> active(i)
1.17/1.20	 mark(nil) -> active(nil)
1.17/1.20	 mark(o) -> active(o)
1.17/1.20	 mark(tt) -> active(tt)
1.17/1.20	 mark(u) -> active(u)
1.17/1.20	-> Usable rules:
1.17/1.20	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.20	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.20	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.17/1.20	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.17/1.20	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.17/1.20	 active(__(nil,X:S)) -> mark(X:S)
1.17/1.20	 active(__(X:S,nil)) -> mark(X:S)
1.17/1.20	 active(and(tt,X:S)) -> mark(X:S)
1.17/1.20	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.17/1.20	 active(isList(nil)) -> mark(tt)
1.17/1.20	 active(isList(V:S)) -> mark(isNeList(V:S))
1.17/1.20	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.17/1.20	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.17/1.20	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.17/1.20	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.17/1.20	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.17/1.20	 active(isPal(nil)) -> mark(tt)
1.17/1.20	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.17/1.20	 active(isQid(a)) -> mark(tt)
1.17/1.20	 active(isQid(e)) -> mark(tt)
1.17/1.20	 active(isQid(i)) -> mark(tt)
1.17/1.20	 active(isQid(o)) -> mark(tt)
1.17/1.20	 active(isQid(u)) -> mark(tt)
1.17/1.20	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.20	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.20	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.17/1.20	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.17/1.20	 isList(active(X:S)) -> isList(X:S)
1.17/1.20	 isList(mark(X:S)) -> isList(X:S)
1.17/1.20	 isNeList(active(X:S)) -> isNeList(X:S)
1.17/1.20	 isNeList(mark(X:S)) -> isNeList(X:S)
1.17/1.20	 isNePal(active(X:S)) -> isNePal(X:S)
1.17/1.20	 isNePal(mark(X:S)) -> isNePal(X:S)
1.17/1.20	 isPal(active(X:S)) -> isPal(X:S)
1.17/1.20	 isPal(mark(X:S)) -> isPal(X:S)
1.17/1.20	 isQid(active(X:S)) -> isQid(X:S)
1.17/1.20	 isQid(mark(X:S)) -> isQid(X:S)
1.17/1.20	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.17/1.20	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.17/1.20	 mark(isList(X:S)) -> active(isList(X:S))
1.17/1.20	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.17/1.20	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.17/1.20	 mark(isPal(X:S)) -> active(isPal(X:S))
1.17/1.20	 mark(isQid(X:S)) -> active(isQid(X:S))
1.17/1.20	 mark(a) -> active(a)
1.17/1.20	 mark(e) -> active(e)
1.17/1.20	 mark(i) -> active(i)
1.17/1.20	 mark(nil) -> active(nil)
1.17/1.20	 mark(o) -> active(o)
1.17/1.20	 mark(tt) -> active(tt)
1.17/1.20	 mark(u) -> active(u)
1.17/1.20	->Interpretation type:
1.17/1.20	 Linear
1.17/1.20	->Coefficients:
1.17/1.20	 Natural Numbers
1.17/1.20	->Dimension:
1.17/1.20	 1
1.17/1.20	->Bound:
1.17/1.20	 2
1.17/1.20	->Interpretation:
1.17/1.20	 
1.17/1.20	[__](X1,X2) = 2.X1 + X2 + 2
1.17/1.20	[active](X) = X
1.17/1.20	[and](X1,X2) = X1 + X2 + 2
1.17/1.20	[isList](X) = 2.X + 2
1.17/1.20	[isNeList](X) = 2.X + 2
1.17/1.20	[isNePal](X) = 2.X + 1
1.17/1.20	[isPal](X) = 2.X + 2
1.17/1.20	[isQid](X) = 2.X + 1
1.17/1.20	[mark](X) = X
1.17/1.20	[a] = 2
1.17/1.20	[e] = 2
1.17/1.20	[fSNonEmpty] = 0
1.17/1.20	[i] = 2
1.17/1.20	[nil] = 2
1.17/1.20	[o] = 2
1.17/1.20	[tt] = 0
1.17/1.20	[u] = 2
1.17/1.20	[__#](X1,X2) = 0
1.17/1.20	[ACTIVE](X) = 2.X
1.17/1.20	[AND](X1,X2) = 0
1.17/1.20	[ISLIST](X) = 0
1.17/1.20	[ISNELIST](X) = 0
1.17/1.20	[ISNEPAL](X) = 0
1.17/1.20	[ISPAL](X) = 0
1.17/1.20	[ISQID](X) = 0
1.17/1.20	[MARK](X) = 2.X + 1
1.17/1.20	
1.17/1.20	Problem 1.8: 
1.17/1.20	
1.17/1.20	SCC Processor:
1.17/1.20	-> Pairs:
1.17/1.20	 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
1.17/1.20	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.20	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.17/1.20	 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S))
1.17/1.20	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.20	 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S))
1.17/1.20	-> Rules:
1.17/1.20	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.20	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.20	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.17/1.20	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.17/1.20	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.17/1.20	 active(__(nil,X:S)) -> mark(X:S)
1.17/1.20	 active(__(X:S,nil)) -> mark(X:S)
1.17/1.20	 active(and(tt,X:S)) -> mark(X:S)
1.17/1.20	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.17/1.20	 active(isList(nil)) -> mark(tt)
1.17/1.20	 active(isList(V:S)) -> mark(isNeList(V:S))
1.17/1.20	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.17/1.20	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.17/1.20	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.17/1.20	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.17/1.20	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.17/1.20	 active(isPal(nil)) -> mark(tt)
1.17/1.20	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.17/1.20	 active(isQid(a)) -> mark(tt)
1.17/1.20	 active(isQid(e)) -> mark(tt)
1.17/1.20	 active(isQid(i)) -> mark(tt)
1.17/1.20	 active(isQid(o)) -> mark(tt)
1.17/1.20	 active(isQid(u)) -> mark(tt)
1.17/1.20	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.20	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.20	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.17/1.20	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.17/1.20	 isList(active(X:S)) -> isList(X:S)
1.17/1.20	 isList(mark(X:S)) -> isList(X:S)
1.17/1.20	 isNeList(active(X:S)) -> isNeList(X:S)
1.17/1.20	 isNeList(mark(X:S)) -> isNeList(X:S)
1.17/1.20	 isNePal(active(X:S)) -> isNePal(X:S)
1.17/1.20	 isNePal(mark(X:S)) -> isNePal(X:S)
1.17/1.20	 isPal(active(X:S)) -> isPal(X:S)
1.17/1.20	 isPal(mark(X:S)) -> isPal(X:S)
1.17/1.20	 isQid(active(X:S)) -> isQid(X:S)
1.17/1.20	 isQid(mark(X:S)) -> isQid(X:S)
1.17/1.20	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.17/1.20	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.17/1.20	 mark(isList(X:S)) -> active(isList(X:S))
1.17/1.20	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.17/1.20	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.17/1.20	 mark(isPal(X:S)) -> active(isPal(X:S))
1.17/1.20	 mark(isQid(X:S)) -> active(isQid(X:S))
1.17/1.20	 mark(a) -> active(a)
1.17/1.20	 mark(e) -> active(e)
1.17/1.20	 mark(i) -> active(i)
1.17/1.20	 mark(nil) -> active(nil)
1.17/1.20	 mark(o) -> active(o)
1.17/1.20	 mark(tt) -> active(tt)
1.17/1.20	 mark(u) -> active(u)
1.17/1.20	->Strongly Connected Components:
1.17/1.20	->->Cycle:
1.17/1.20	->->-> Pairs:
1.17/1.20	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.20	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.17/1.20	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.20	->->-> Rules:
1.17/1.20	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.20	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.20	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.17/1.20	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.17/1.20	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.17/1.20	 active(__(nil,X:S)) -> mark(X:S)
1.17/1.20	 active(__(X:S,nil)) -> mark(X:S)
1.17/1.20	 active(and(tt,X:S)) -> mark(X:S)
1.17/1.20	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.17/1.20	 active(isList(nil)) -> mark(tt)
1.17/1.20	 active(isList(V:S)) -> mark(isNeList(V:S))
1.17/1.20	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.17/1.20	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.17/1.20	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.17/1.20	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.17/1.20	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.17/1.20	 active(isPal(nil)) -> mark(tt)
1.17/1.20	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.17/1.20	 active(isQid(a)) -> mark(tt)
1.17/1.20	 active(isQid(e)) -> mark(tt)
1.17/1.20	 active(isQid(i)) -> mark(tt)
1.17/1.20	 active(isQid(o)) -> mark(tt)
1.17/1.20	 active(isQid(u)) -> mark(tt)
1.17/1.20	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.20	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.20	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.17/1.20	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.17/1.20	 isList(active(X:S)) -> isList(X:S)
1.17/1.20	 isList(mark(X:S)) -> isList(X:S)
1.17/1.20	 isNeList(active(X:S)) -> isNeList(X:S)
1.17/1.20	 isNeList(mark(X:S)) -> isNeList(X:S)
1.17/1.20	 isNePal(active(X:S)) -> isNePal(X:S)
1.17/1.20	 isNePal(mark(X:S)) -> isNePal(X:S)
1.17/1.20	 isPal(active(X:S)) -> isPal(X:S)
1.17/1.20	 isPal(mark(X:S)) -> isPal(X:S)
1.17/1.20	 isQid(active(X:S)) -> isQid(X:S)
1.17/1.20	 isQid(mark(X:S)) -> isQid(X:S)
1.17/1.20	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.17/1.20	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.17/1.20	 mark(isList(X:S)) -> active(isList(X:S))
1.17/1.20	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.17/1.20	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.17/1.20	 mark(isPal(X:S)) -> active(isPal(X:S))
1.17/1.20	 mark(isQid(X:S)) -> active(isQid(X:S))
1.17/1.20	 mark(a) -> active(a)
1.17/1.20	 mark(e) -> active(e)
1.17/1.20	 mark(i) -> active(i)
1.17/1.20	 mark(nil) -> active(nil)
1.17/1.20	 mark(o) -> active(o)
1.17/1.20	 mark(tt) -> active(tt)
1.17/1.20	 mark(u) -> active(u)
1.17/1.20	
1.17/1.20	Problem 1.8: 
1.17/1.20	
1.17/1.20	Subterm Processor:
1.17/1.20	-> Pairs:
1.17/1.20	 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.20	 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
1.17/1.20	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
1.17/1.20	-> Rules:
1.17/1.20	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.20	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.20	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.17/1.20	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.17/1.20	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.17/1.20	 active(__(nil,X:S)) -> mark(X:S)
1.17/1.20	 active(__(X:S,nil)) -> mark(X:S)
1.17/1.20	 active(and(tt,X:S)) -> mark(X:S)
1.17/1.20	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.17/1.20	 active(isList(nil)) -> mark(tt)
1.17/1.20	 active(isList(V:S)) -> mark(isNeList(V:S))
1.17/1.20	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.17/1.20	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.17/1.20	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.17/1.20	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.17/1.20	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.17/1.20	 active(isPal(nil)) -> mark(tt)
1.17/1.20	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.17/1.20	 active(isQid(a)) -> mark(tt)
1.17/1.20	 active(isQid(e)) -> mark(tt)
1.17/1.20	 active(isQid(i)) -> mark(tt)
1.17/1.20	 active(isQid(o)) -> mark(tt)
1.17/1.20	 active(isQid(u)) -> mark(tt)
1.17/1.20	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.20	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.20	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.17/1.20	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.17/1.20	 isList(active(X:S)) -> isList(X:S)
1.17/1.20	 isList(mark(X:S)) -> isList(X:S)
1.17/1.20	 isNeList(active(X:S)) -> isNeList(X:S)
1.17/1.20	 isNeList(mark(X:S)) -> isNeList(X:S)
1.17/1.20	 isNePal(active(X:S)) -> isNePal(X:S)
1.17/1.20	 isNePal(mark(X:S)) -> isNePal(X:S)
1.17/1.20	 isPal(active(X:S)) -> isPal(X:S)
1.17/1.20	 isPal(mark(X:S)) -> isPal(X:S)
1.17/1.20	 isQid(active(X:S)) -> isQid(X:S)
1.17/1.20	 isQid(mark(X:S)) -> isQid(X:S)
1.17/1.20	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.17/1.20	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.17/1.20	 mark(isList(X:S)) -> active(isList(X:S))
1.17/1.20	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.17/1.20	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.17/1.20	 mark(isPal(X:S)) -> active(isPal(X:S))
1.17/1.20	 mark(isQid(X:S)) -> active(isQid(X:S))
1.17/1.20	 mark(a) -> active(a)
1.17/1.20	 mark(e) -> active(e)
1.17/1.20	 mark(i) -> active(i)
1.17/1.20	 mark(nil) -> active(nil)
1.17/1.20	 mark(o) -> active(o)
1.17/1.20	 mark(tt) -> active(tt)
1.17/1.20	 mark(u) -> active(u)
1.17/1.20	->Projection:
1.17/1.20	 pi(MARK) = 1
1.17/1.20	
1.17/1.20	Problem 1.8: 
1.17/1.20	
1.17/1.20	SCC Processor:
1.17/1.20	-> Pairs:
1.17/1.20	 Empty
1.17/1.20	-> Rules:
1.17/1.20	 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.20	 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
1.17/1.20	 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
1.17/1.20	 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
1.17/1.20	 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
1.17/1.20	 active(__(nil,X:S)) -> mark(X:S)
1.17/1.20	 active(__(X:S,nil)) -> mark(X:S)
1.17/1.20	 active(and(tt,X:S)) -> mark(X:S)
1.17/1.20	 active(isList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isList(V2:S)))
1.17/1.20	 active(isList(nil)) -> mark(tt)
1.17/1.20	 active(isList(V:S)) -> mark(isNeList(V:S))
1.17/1.20	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isList(V1:S),isNeList(V2:S)))
1.17/1.20	 active(isNeList(__(V1:S,V2:S))) -> mark(and(isNeList(V1:S),isList(V2:S)))
1.17/1.20	 active(isNeList(V:S)) -> mark(isQid(V:S))
1.17/1.20	 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(and(isQid(I:S),isPal(P:S)))
1.17/1.20	 active(isNePal(V:S)) -> mark(isQid(V:S))
1.17/1.20	 active(isPal(nil)) -> mark(tt)
1.17/1.20	 active(isPal(V:S)) -> mark(isNePal(V:S))
1.17/1.20	 active(isQid(a)) -> mark(tt)
1.17/1.20	 active(isQid(e)) -> mark(tt)
1.17/1.20	 active(isQid(i)) -> mark(tt)
1.17/1.20	 active(isQid(o)) -> mark(tt)
1.17/1.20	 active(isQid(u)) -> mark(tt)
1.17/1.20	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.20	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
1.17/1.20	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
1.17/1.20	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
1.17/1.20	 isList(active(X:S)) -> isList(X:S)
1.17/1.20	 isList(mark(X:S)) -> isList(X:S)
1.17/1.20	 isNeList(active(X:S)) -> isNeList(X:S)
1.17/1.20	 isNeList(mark(X:S)) -> isNeList(X:S)
1.17/1.20	 isNePal(active(X:S)) -> isNePal(X:S)
1.17/1.20	 isNePal(mark(X:S)) -> isNePal(X:S)
1.17/1.20	 isPal(active(X:S)) -> isPal(X:S)
1.17/1.20	 isPal(mark(X:S)) -> isPal(X:S)
1.17/1.20	 isQid(active(X:S)) -> isQid(X:S)
1.17/1.20	 isQid(mark(X:S)) -> isQid(X:S)
1.17/1.20	 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
1.17/1.20	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
1.17/1.20	 mark(isList(X:S)) -> active(isList(X:S))
1.17/1.20	 mark(isNeList(X:S)) -> active(isNeList(X:S))
1.17/1.20	 mark(isNePal(X:S)) -> active(isNePal(X:S))
1.17/1.20	 mark(isPal(X:S)) -> active(isPal(X:S))
1.17/1.20	 mark(isQid(X:S)) -> active(isQid(X:S))
1.17/1.20	 mark(a) -> active(a)
1.17/1.20	 mark(e) -> active(e)
1.17/1.20	 mark(i) -> active(i)
1.17/1.20	 mark(nil) -> active(nil)
1.17/1.20	 mark(o) -> active(o)
1.17/1.20	 mark(tt) -> active(tt)
1.17/1.20	 mark(u) -> active(u)
1.17/1.20	->Strongly Connected Components:
1.17/1.20	 There is no strongly connected component
1.17/1.20	
1.17/1.20	The problem is finite.
1.17/1.20	EOF