0.00/0.48	YES
0.00/0.48	
0.00/0.48	Problem 1: 
0.00/0.48	
0.00/0.48	(VAR v_NonEmpty:S L:S X:S X1:S X2:S XS:S Y:S YS:S)
0.00/0.48	(RULES
0.00/0.48	active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S)))
0.00/0.48	active(app(nil,YS:S)) -> mark(YS:S)
0.00/0.48	active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.00/0.48	active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S))))
0.00/0.48	active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.00/0.48	active(zWadr(nil,YS:S)) -> mark(nil)
0.00/0.48	active(zWadr(XS:S,nil)) -> mark(nil)
0.00/0.48	app(active(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.48	app(mark(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.48	app(X1:S,active(X2:S)) -> app(X1:S,X2:S)
0.00/0.48	app(X1:S,mark(X2:S)) -> app(X1:S,X2:S)
0.00/0.48	cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.48	cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.48	cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.00/0.48	cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.00/0.48	from(active(X:S)) -> from(X:S)
0.00/0.48	from(mark(X:S)) -> from(X:S)
0.00/0.48	mark(app(X1:S,X2:S)) -> active(app(mark(X1:S),mark(X2:S)))
0.00/0.48	mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.00/0.48	mark(from(X:S)) -> active(from(mark(X:S)))
0.00/0.48	mark(prefix(X:S)) -> active(prefix(mark(X:S)))
0.00/0.48	mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.48	mark(zWadr(X1:S,X2:S)) -> active(zWadr(mark(X1:S),mark(X2:S)))
0.00/0.48	mark(nil) -> active(nil)
0.00/0.48	prefix(active(X:S)) -> prefix(X:S)
0.00/0.48	prefix(mark(X:S)) -> prefix(X:S)
0.00/0.48	s(active(X:S)) -> s(X:S)
0.00/0.48	s(mark(X:S)) -> s(X:S)
0.00/0.48	zWadr(active(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.48	zWadr(mark(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.48	zWadr(X1:S,active(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.48	zWadr(X1:S,mark(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.48	) 
0.00/0.48	(STRATEGY INNERMOST)
0.00/0.48	
0.00/0.48	Problem 1: 
0.00/0.48	
0.00/0.48	Dependency Pairs Processor:
0.00/0.48	-> Pairs:
0.00/0.48	 ACTIVE(app(cons(X:S,XS:S),YS:S)) -> APP(XS:S,YS:S)
0.00/0.48	 ACTIVE(app(cons(X:S,XS:S),YS:S)) -> CONS(X:S,app(XS:S,YS:S))
0.00/0.48	 ACTIVE(app(cons(X:S,XS:S),YS:S)) -> MARK(cons(X:S,app(XS:S,YS:S)))
0.00/0.48	 ACTIVE(app(nil,YS:S)) -> MARK(YS:S)
0.00/0.48	 ACTIVE(from(X:S)) -> CONS(X:S,from(s(X:S)))
0.00/0.48	 ACTIVE(from(X:S)) -> FROM(s(X:S))
0.00/0.48	 ACTIVE(from(X:S)) -> MARK(cons(X:S,from(s(X:S))))
0.00/0.48	 ACTIVE(from(X:S)) -> S(X:S)
0.00/0.48	 ACTIVE(prefix(L:S)) -> CONS(nil,zWadr(L:S,prefix(L:S)))
0.00/0.48	 ACTIVE(prefix(L:S)) -> MARK(cons(nil,zWadr(L:S,prefix(L:S))))
0.00/0.48	 ACTIVE(prefix(L:S)) -> ZWADR(L:S,prefix(L:S))
0.00/0.48	 ACTIVE(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> APP(Y:S,cons(X:S,nil))
0.00/0.48	 ACTIVE(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> CONS(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S))
0.00/0.48	 ACTIVE(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> CONS(X:S,nil)
0.00/0.48	 ACTIVE(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> MARK(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.00/0.48	 ACTIVE(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> ZWADR(XS:S,YS:S)
0.00/0.48	 ACTIVE(zWadr(nil,YS:S)) -> MARK(nil)
0.00/0.48	 ACTIVE(zWadr(XS:S,nil)) -> MARK(nil)
0.00/0.48	 APP(active(X1:S),X2:S) -> APP(X1:S,X2:S)
0.00/0.48	 APP(mark(X1:S),X2:S) -> APP(X1:S,X2:S)
0.00/0.48	 APP(X1:S,active(X2:S)) -> APP(X1:S,X2:S)
0.00/0.48	 APP(X1:S,mark(X2:S)) -> APP(X1:S,X2:S)
0.00/0.48	 CONS(active(X1:S),X2:S) -> CONS(X1:S,X2:S)
0.00/0.48	 CONS(mark(X1:S),X2:S) -> CONS(X1:S,X2:S)
0.00/0.48	 CONS(X1:S,active(X2:S)) -> CONS(X1:S,X2:S)
0.00/0.48	 CONS(X1:S,mark(X2:S)) -> CONS(X1:S,X2:S)
0.00/0.48	 FROM(active(X:S)) -> FROM(X:S)
0.00/0.48	 FROM(mark(X:S)) -> FROM(X:S)
0.00/0.48	 MARK(app(X1:S,X2:S)) -> ACTIVE(app(mark(X1:S),mark(X2:S)))
0.00/0.48	 MARK(app(X1:S,X2:S)) -> APP(mark(X1:S),mark(X2:S))
0.00/0.48	 MARK(app(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.48	 MARK(app(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.48	 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S))
0.00/0.48	 MARK(cons(X1:S,X2:S)) -> CONS(mark(X1:S),X2:S)
0.00/0.48	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.48	 MARK(from(X:S)) -> ACTIVE(from(mark(X:S)))
0.00/0.48	 MARK(from(X:S)) -> FROM(mark(X:S))
0.00/0.48	 MARK(from(X:S)) -> MARK(X:S)
0.00/0.48	 MARK(prefix(X:S)) -> ACTIVE(prefix(mark(X:S)))
0.00/0.48	 MARK(prefix(X:S)) -> MARK(X:S)
0.00/0.48	 MARK(prefix(X:S)) -> PREFIX(mark(X:S))
0.00/0.48	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.00/0.48	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.48	 MARK(s(X:S)) -> S(mark(X:S))
0.00/0.48	 MARK(zWadr(X1:S,X2:S)) -> ACTIVE(zWadr(mark(X1:S),mark(X2:S)))
0.00/0.48	 MARK(zWadr(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.48	 MARK(zWadr(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.48	 MARK(zWadr(X1:S,X2:S)) -> ZWADR(mark(X1:S),mark(X2:S))
0.00/0.48	 PREFIX(active(X:S)) -> PREFIX(X:S)
0.00/0.48	 PREFIX(mark(X:S)) -> PREFIX(X:S)
0.00/0.48	 S(active(X:S)) -> S(X:S)
0.00/0.48	 S(mark(X:S)) -> S(X:S)
0.00/0.48	 ZWADR(active(X1:S),X2:S) -> ZWADR(X1:S,X2:S)
0.00/0.48	 ZWADR(mark(X1:S),X2:S) -> ZWADR(X1:S,X2:S)
0.00/0.48	 ZWADR(X1:S,active(X2:S)) -> ZWADR(X1:S,X2:S)
0.00/0.48	 ZWADR(X1:S,mark(X2:S)) -> ZWADR(X1:S,X2:S)
0.00/0.48	-> Rules:
0.00/0.48	 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S)))
0.00/0.48	 active(app(nil,YS:S)) -> mark(YS:S)
0.00/0.48	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.00/0.48	 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S))))
0.00/0.48	 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.00/0.48	 active(zWadr(nil,YS:S)) -> mark(nil)
0.00/0.48	 active(zWadr(XS:S,nil)) -> mark(nil)
0.00/0.48	 app(active(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.48	 app(mark(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.48	 app(X1:S,active(X2:S)) -> app(X1:S,X2:S)
0.00/0.48	 app(X1:S,mark(X2:S)) -> app(X1:S,X2:S)
0.00/0.48	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.48	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.48	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.00/0.48	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.00/0.48	 from(active(X:S)) -> from(X:S)
0.00/0.48	 from(mark(X:S)) -> from(X:S)
0.00/0.48	 mark(app(X1:S,X2:S)) -> active(app(mark(X1:S),mark(X2:S)))
0.00/0.48	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.00/0.48	 mark(from(X:S)) -> active(from(mark(X:S)))
0.00/0.48	 mark(prefix(X:S)) -> active(prefix(mark(X:S)))
0.00/0.48	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.48	 mark(zWadr(X1:S,X2:S)) -> active(zWadr(mark(X1:S),mark(X2:S)))
0.00/0.48	 mark(nil) -> active(nil)
0.00/0.48	 prefix(active(X:S)) -> prefix(X:S)
0.00/0.48	 prefix(mark(X:S)) -> prefix(X:S)
0.00/0.48	 s(active(X:S)) -> s(X:S)
0.00/0.48	 s(mark(X:S)) -> s(X:S)
0.00/0.48	 zWadr(active(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.48	 zWadr(mark(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.48	 zWadr(X1:S,active(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.48	 zWadr(X1:S,mark(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.48	
0.00/0.48	Problem 1: 
0.00/0.48	
0.00/0.48	SCC Processor:
0.00/0.48	-> Pairs:
0.00/0.48	 ACTIVE(app(cons(X:S,XS:S),YS:S)) -> APP(XS:S,YS:S)
0.00/0.48	 ACTIVE(app(cons(X:S,XS:S),YS:S)) -> CONS(X:S,app(XS:S,YS:S))
0.00/0.48	 ACTIVE(app(cons(X:S,XS:S),YS:S)) -> MARK(cons(X:S,app(XS:S,YS:S)))
0.00/0.48	 ACTIVE(app(nil,YS:S)) -> MARK(YS:S)
0.00/0.48	 ACTIVE(from(X:S)) -> CONS(X:S,from(s(X:S)))
0.00/0.48	 ACTIVE(from(X:S)) -> FROM(s(X:S))
0.00/0.48	 ACTIVE(from(X:S)) -> MARK(cons(X:S,from(s(X:S))))
0.00/0.48	 ACTIVE(from(X:S)) -> S(X:S)
0.00/0.48	 ACTIVE(prefix(L:S)) -> CONS(nil,zWadr(L:S,prefix(L:S)))
0.00/0.48	 ACTIVE(prefix(L:S)) -> MARK(cons(nil,zWadr(L:S,prefix(L:S))))
0.00/0.48	 ACTIVE(prefix(L:S)) -> ZWADR(L:S,prefix(L:S))
0.00/0.48	 ACTIVE(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> APP(Y:S,cons(X:S,nil))
0.00/0.48	 ACTIVE(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> CONS(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S))
0.00/0.48	 ACTIVE(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> CONS(X:S,nil)
0.00/0.48	 ACTIVE(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> MARK(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.00/0.48	 ACTIVE(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> ZWADR(XS:S,YS:S)
0.00/0.48	 ACTIVE(zWadr(nil,YS:S)) -> MARK(nil)
0.00/0.48	 ACTIVE(zWadr(XS:S,nil)) -> MARK(nil)
0.00/0.48	 APP(active(X1:S),X2:S) -> APP(X1:S,X2:S)
0.00/0.48	 APP(mark(X1:S),X2:S) -> APP(X1:S,X2:S)
0.00/0.48	 APP(X1:S,active(X2:S)) -> APP(X1:S,X2:S)
0.00/0.48	 APP(X1:S,mark(X2:S)) -> APP(X1:S,X2:S)
0.00/0.48	 CONS(active(X1:S),X2:S) -> CONS(X1:S,X2:S)
0.00/0.48	 CONS(mark(X1:S),X2:S) -> CONS(X1:S,X2:S)
0.00/0.48	 CONS(X1:S,active(X2:S)) -> CONS(X1:S,X2:S)
0.00/0.48	 CONS(X1:S,mark(X2:S)) -> CONS(X1:S,X2:S)
0.00/0.48	 FROM(active(X:S)) -> FROM(X:S)
0.00/0.48	 FROM(mark(X:S)) -> FROM(X:S)
0.00/0.48	 MARK(app(X1:S,X2:S)) -> ACTIVE(app(mark(X1:S),mark(X2:S)))
0.00/0.48	 MARK(app(X1:S,X2:S)) -> APP(mark(X1:S),mark(X2:S))
0.00/0.48	 MARK(app(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.48	 MARK(app(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.48	 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S))
0.00/0.48	 MARK(cons(X1:S,X2:S)) -> CONS(mark(X1:S),X2:S)
0.00/0.48	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.48	 MARK(from(X:S)) -> ACTIVE(from(mark(X:S)))
0.00/0.48	 MARK(from(X:S)) -> FROM(mark(X:S))
0.00/0.48	 MARK(from(X:S)) -> MARK(X:S)
0.00/0.48	 MARK(prefix(X:S)) -> ACTIVE(prefix(mark(X:S)))
0.00/0.48	 MARK(prefix(X:S)) -> MARK(X:S)
0.00/0.48	 MARK(prefix(X:S)) -> PREFIX(mark(X:S))
0.00/0.48	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.00/0.48	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.48	 MARK(s(X:S)) -> S(mark(X:S))
0.00/0.48	 MARK(zWadr(X1:S,X2:S)) -> ACTIVE(zWadr(mark(X1:S),mark(X2:S)))
0.00/0.48	 MARK(zWadr(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.48	 MARK(zWadr(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.48	 MARK(zWadr(X1:S,X2:S)) -> ZWADR(mark(X1:S),mark(X2:S))
0.00/0.48	 PREFIX(active(X:S)) -> PREFIX(X:S)
0.00/0.48	 PREFIX(mark(X:S)) -> PREFIX(X:S)
0.00/0.48	 S(active(X:S)) -> S(X:S)
0.00/0.48	 S(mark(X:S)) -> S(X:S)
0.00/0.48	 ZWADR(active(X1:S),X2:S) -> ZWADR(X1:S,X2:S)
0.00/0.48	 ZWADR(mark(X1:S),X2:S) -> ZWADR(X1:S,X2:S)
0.00/0.48	 ZWADR(X1:S,active(X2:S)) -> ZWADR(X1:S,X2:S)
0.00/0.48	 ZWADR(X1:S,mark(X2:S)) -> ZWADR(X1:S,X2:S)
0.00/0.48	-> Rules:
0.00/0.48	 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S)))
0.00/0.48	 active(app(nil,YS:S)) -> mark(YS:S)
0.00/0.48	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.00/0.48	 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S))))
0.00/0.48	 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.00/0.48	 active(zWadr(nil,YS:S)) -> mark(nil)
0.00/0.48	 active(zWadr(XS:S,nil)) -> mark(nil)
0.00/0.48	 app(active(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.48	 app(mark(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.48	 app(X1:S,active(X2:S)) -> app(X1:S,X2:S)
0.00/0.48	 app(X1:S,mark(X2:S)) -> app(X1:S,X2:S)
0.00/0.48	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.48	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.48	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.00/0.48	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.00/0.48	 from(active(X:S)) -> from(X:S)
0.00/0.48	 from(mark(X:S)) -> from(X:S)
0.00/0.48	 mark(app(X1:S,X2:S)) -> active(app(mark(X1:S),mark(X2:S)))
0.00/0.48	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.00/0.48	 mark(from(X:S)) -> active(from(mark(X:S)))
0.00/0.48	 mark(prefix(X:S)) -> active(prefix(mark(X:S)))
0.00/0.48	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.48	 mark(zWadr(X1:S,X2:S)) -> active(zWadr(mark(X1:S),mark(X2:S)))
0.00/0.48	 mark(nil) -> active(nil)
0.00/0.48	 prefix(active(X:S)) -> prefix(X:S)
0.00/0.48	 prefix(mark(X:S)) -> prefix(X:S)
0.00/0.48	 s(active(X:S)) -> s(X:S)
0.00/0.48	 s(mark(X:S)) -> s(X:S)
0.00/0.48	 zWadr(active(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.48	 zWadr(mark(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.48	 zWadr(X1:S,active(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.48	 zWadr(X1:S,mark(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.48	->Strongly Connected Components:
0.00/0.48	->->Cycle:
0.00/0.48	->->-> Pairs:
0.00/0.48	 ZWADR(active(X1:S),X2:S) -> ZWADR(X1:S,X2:S)
0.00/0.48	 ZWADR(mark(X1:S),X2:S) -> ZWADR(X1:S,X2:S)
0.00/0.48	 ZWADR(X1:S,active(X2:S)) -> ZWADR(X1:S,X2:S)
0.00/0.48	 ZWADR(X1:S,mark(X2:S)) -> ZWADR(X1:S,X2:S)
0.00/0.48	->->-> Rules:
0.00/0.48	 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S)))
0.00/0.48	 active(app(nil,YS:S)) -> mark(YS:S)
0.00/0.48	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.00/0.48	 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S))))
0.00/0.48	 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.00/0.48	 active(zWadr(nil,YS:S)) -> mark(nil)
0.00/0.48	 active(zWadr(XS:S,nil)) -> mark(nil)
0.00/0.48	 app(active(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.48	 app(mark(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.48	 app(X1:S,active(X2:S)) -> app(X1:S,X2:S)
0.00/0.48	 app(X1:S,mark(X2:S)) -> app(X1:S,X2:S)
0.00/0.48	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.48	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.48	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.00/0.48	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.00/0.48	 from(active(X:S)) -> from(X:S)
0.00/0.48	 from(mark(X:S)) -> from(X:S)
0.00/0.48	 mark(app(X1:S,X2:S)) -> active(app(mark(X1:S),mark(X2:S)))
0.00/0.48	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.00/0.48	 mark(from(X:S)) -> active(from(mark(X:S)))
0.00/0.48	 mark(prefix(X:S)) -> active(prefix(mark(X:S)))
0.00/0.48	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.48	 mark(zWadr(X1:S,X2:S)) -> active(zWadr(mark(X1:S),mark(X2:S)))
0.00/0.48	 mark(nil) -> active(nil)
0.00/0.48	 prefix(active(X:S)) -> prefix(X:S)
0.00/0.48	 prefix(mark(X:S)) -> prefix(X:S)
0.00/0.48	 s(active(X:S)) -> s(X:S)
0.00/0.48	 s(mark(X:S)) -> s(X:S)
0.00/0.48	 zWadr(active(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.48	 zWadr(mark(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.48	 zWadr(X1:S,active(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.48	 zWadr(X1:S,mark(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.48	->->Cycle:
0.00/0.48	->->-> Pairs:
0.00/0.48	 S(active(X:S)) -> S(X:S)
0.00/0.48	 S(mark(X:S)) -> S(X:S)
0.00/0.48	->->-> Rules:
0.00/0.48	 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S)))
0.00/0.48	 active(app(nil,YS:S)) -> mark(YS:S)
0.00/0.48	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.00/0.48	 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S))))
0.00/0.48	 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.00/0.48	 active(zWadr(nil,YS:S)) -> mark(nil)
0.00/0.48	 active(zWadr(XS:S,nil)) -> mark(nil)
0.00/0.48	 app(active(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.48	 app(mark(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.48	 app(X1:S,active(X2:S)) -> app(X1:S,X2:S)
0.00/0.48	 app(X1:S,mark(X2:S)) -> app(X1:S,X2:S)
0.00/0.48	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.48	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.48	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.00/0.48	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.00/0.48	 from(active(X:S)) -> from(X:S)
0.00/0.48	 from(mark(X:S)) -> from(X:S)
0.00/0.48	 mark(app(X1:S,X2:S)) -> active(app(mark(X1:S),mark(X2:S)))
0.00/0.48	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.00/0.48	 mark(from(X:S)) -> active(from(mark(X:S)))
0.00/0.48	 mark(prefix(X:S)) -> active(prefix(mark(X:S)))
0.00/0.48	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.48	 mark(zWadr(X1:S,X2:S)) -> active(zWadr(mark(X1:S),mark(X2:S)))
0.00/0.48	 mark(nil) -> active(nil)
0.00/0.48	 prefix(active(X:S)) -> prefix(X:S)
0.00/0.48	 prefix(mark(X:S)) -> prefix(X:S)
0.00/0.48	 s(active(X:S)) -> s(X:S)
0.00/0.48	 s(mark(X:S)) -> s(X:S)
0.00/0.48	 zWadr(active(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.48	 zWadr(mark(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.48	 zWadr(X1:S,active(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.48	 zWadr(X1:S,mark(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.48	->->Cycle:
0.00/0.48	->->-> Pairs:
0.00/0.48	 PREFIX(active(X:S)) -> PREFIX(X:S)
0.00/0.48	 PREFIX(mark(X:S)) -> PREFIX(X:S)
0.00/0.48	->->-> Rules:
0.00/0.48	 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S)))
0.00/0.48	 active(app(nil,YS:S)) -> mark(YS:S)
0.00/0.48	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.00/0.48	 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S))))
0.00/0.48	 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.00/0.48	 active(zWadr(nil,YS:S)) -> mark(nil)
0.00/0.48	 active(zWadr(XS:S,nil)) -> mark(nil)
0.00/0.48	 app(active(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.48	 app(mark(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.48	 app(X1:S,active(X2:S)) -> app(X1:S,X2:S)
0.00/0.48	 app(X1:S,mark(X2:S)) -> app(X1:S,X2:S)
0.00/0.48	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.48	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.48	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.00/0.48	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.00/0.48	 from(active(X:S)) -> from(X:S)
0.00/0.48	 from(mark(X:S)) -> from(X:S)
0.00/0.48	 mark(app(X1:S,X2:S)) -> active(app(mark(X1:S),mark(X2:S)))
0.00/0.48	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.00/0.48	 mark(from(X:S)) -> active(from(mark(X:S)))
0.00/0.48	 mark(prefix(X:S)) -> active(prefix(mark(X:S)))
0.00/0.48	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.48	 mark(zWadr(X1:S,X2:S)) -> active(zWadr(mark(X1:S),mark(X2:S)))
0.00/0.48	 mark(nil) -> active(nil)
0.00/0.48	 prefix(active(X:S)) -> prefix(X:S)
0.00/0.48	 prefix(mark(X:S)) -> prefix(X:S)
0.00/0.48	 s(active(X:S)) -> s(X:S)
0.00/0.48	 s(mark(X:S)) -> s(X:S)
0.00/0.48	 zWadr(active(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.48	 zWadr(mark(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.48	 zWadr(X1:S,active(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.48	 zWadr(X1:S,mark(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.48	->->Cycle:
0.00/0.48	->->-> Pairs:
0.00/0.48	 FROM(active(X:S)) -> FROM(X:S)
0.00/0.48	 FROM(mark(X:S)) -> FROM(X:S)
0.00/0.48	->->-> Rules:
0.00/0.48	 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S)))
0.00/0.48	 active(app(nil,YS:S)) -> mark(YS:S)
0.00/0.48	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.00/0.48	 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S))))
0.00/0.48	 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.00/0.48	 active(zWadr(nil,YS:S)) -> mark(nil)
0.00/0.48	 active(zWadr(XS:S,nil)) -> mark(nil)
0.00/0.48	 app(active(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.48	 app(mark(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.48	 app(X1:S,active(X2:S)) -> app(X1:S,X2:S)
0.00/0.48	 app(X1:S,mark(X2:S)) -> app(X1:S,X2:S)
0.00/0.48	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.48	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.48	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.00/0.48	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.00/0.48	 from(active(X:S)) -> from(X:S)
0.00/0.48	 from(mark(X:S)) -> from(X:S)
0.00/0.48	 mark(app(X1:S,X2:S)) -> active(app(mark(X1:S),mark(X2:S)))
0.00/0.48	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.00/0.48	 mark(from(X:S)) -> active(from(mark(X:S)))
0.00/0.48	 mark(prefix(X:S)) -> active(prefix(mark(X:S)))
0.00/0.48	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.48	 mark(zWadr(X1:S,X2:S)) -> active(zWadr(mark(X1:S),mark(X2:S)))
0.00/0.48	 mark(nil) -> active(nil)
0.00/0.48	 prefix(active(X:S)) -> prefix(X:S)
0.00/0.48	 prefix(mark(X:S)) -> prefix(X:S)
0.00/0.48	 s(active(X:S)) -> s(X:S)
0.00/0.48	 s(mark(X:S)) -> s(X:S)
0.00/0.48	 zWadr(active(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.48	 zWadr(mark(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.48	 zWadr(X1:S,active(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.48	 zWadr(X1:S,mark(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.48	->->Cycle:
0.00/0.48	->->-> Pairs:
0.00/0.48	 CONS(active(X1:S),X2:S) -> CONS(X1:S,X2:S)
0.00/0.48	 CONS(mark(X1:S),X2:S) -> CONS(X1:S,X2:S)
0.00/0.48	 CONS(X1:S,active(X2:S)) -> CONS(X1:S,X2:S)
0.00/0.48	 CONS(X1:S,mark(X2:S)) -> CONS(X1:S,X2:S)
0.00/0.48	->->-> Rules:
0.00/0.48	 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S)))
0.00/0.48	 active(app(nil,YS:S)) -> mark(YS:S)
0.00/0.48	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.00/0.48	 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S))))
0.00/0.48	 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.00/0.48	 active(zWadr(nil,YS:S)) -> mark(nil)
0.00/0.48	 active(zWadr(XS:S,nil)) -> mark(nil)
0.00/0.48	 app(active(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.48	 app(mark(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.48	 app(X1:S,active(X2:S)) -> app(X1:S,X2:S)
0.00/0.48	 app(X1:S,mark(X2:S)) -> app(X1:S,X2:S)
0.00/0.48	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.48	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.48	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.00/0.48	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.00/0.48	 from(active(X:S)) -> from(X:S)
0.00/0.48	 from(mark(X:S)) -> from(X:S)
0.00/0.48	 mark(app(X1:S,X2:S)) -> active(app(mark(X1:S),mark(X2:S)))
0.00/0.48	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.00/0.48	 mark(from(X:S)) -> active(from(mark(X:S)))
0.00/0.48	 mark(prefix(X:S)) -> active(prefix(mark(X:S)))
0.00/0.48	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.48	 mark(zWadr(X1:S,X2:S)) -> active(zWadr(mark(X1:S),mark(X2:S)))
0.00/0.48	 mark(nil) -> active(nil)
0.00/0.48	 prefix(active(X:S)) -> prefix(X:S)
0.00/0.48	 prefix(mark(X:S)) -> prefix(X:S)
0.00/0.48	 s(active(X:S)) -> s(X:S)
0.00/0.48	 s(mark(X:S)) -> s(X:S)
0.00/0.48	 zWadr(active(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.48	 zWadr(mark(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.48	 zWadr(X1:S,active(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.48	 zWadr(X1:S,mark(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.48	->->Cycle:
0.00/0.48	->->-> Pairs:
0.00/0.48	 APP(active(X1:S),X2:S) -> APP(X1:S,X2:S)
0.00/0.48	 APP(mark(X1:S),X2:S) -> APP(X1:S,X2:S)
0.00/0.48	 APP(X1:S,active(X2:S)) -> APP(X1:S,X2:S)
0.00/0.48	 APP(X1:S,mark(X2:S)) -> APP(X1:S,X2:S)
0.00/0.48	->->-> Rules:
0.00/0.48	 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S)))
0.00/0.48	 active(app(nil,YS:S)) -> mark(YS:S)
0.00/0.48	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.00/0.48	 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S))))
0.00/0.48	 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.00/0.48	 active(zWadr(nil,YS:S)) -> mark(nil)
0.00/0.48	 active(zWadr(XS:S,nil)) -> mark(nil)
0.00/0.48	 app(active(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.48	 app(mark(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.48	 app(X1:S,active(X2:S)) -> app(X1:S,X2:S)
0.00/0.48	 app(X1:S,mark(X2:S)) -> app(X1:S,X2:S)
0.00/0.48	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.48	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.48	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.00/0.48	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.00/0.48	 from(active(X:S)) -> from(X:S)
0.00/0.48	 from(mark(X:S)) -> from(X:S)
0.00/0.48	 mark(app(X1:S,X2:S)) -> active(app(mark(X1:S),mark(X2:S)))
0.00/0.48	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.00/0.48	 mark(from(X:S)) -> active(from(mark(X:S)))
0.00/0.48	 mark(prefix(X:S)) -> active(prefix(mark(X:S)))
0.00/0.48	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.48	 mark(zWadr(X1:S,X2:S)) -> active(zWadr(mark(X1:S),mark(X2:S)))
0.00/0.48	 mark(nil) -> active(nil)
0.00/0.48	 prefix(active(X:S)) -> prefix(X:S)
0.00/0.48	 prefix(mark(X:S)) -> prefix(X:S)
0.00/0.48	 s(active(X:S)) -> s(X:S)
0.00/0.48	 s(mark(X:S)) -> s(X:S)
0.00/0.48	 zWadr(active(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.48	 zWadr(mark(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.48	 zWadr(X1:S,active(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.48	 zWadr(X1:S,mark(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.48	->->Cycle:
0.00/0.48	->->-> Pairs:
0.00/0.48	 ACTIVE(app(cons(X:S,XS:S),YS:S)) -> MARK(cons(X:S,app(XS:S,YS:S)))
0.00/0.48	 ACTIVE(app(nil,YS:S)) -> MARK(YS:S)
0.00/0.48	 ACTIVE(from(X:S)) -> MARK(cons(X:S,from(s(X:S))))
0.00/0.48	 ACTIVE(prefix(L:S)) -> MARK(cons(nil,zWadr(L:S,prefix(L:S))))
0.00/0.48	 ACTIVE(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> MARK(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.00/0.48	 MARK(app(X1:S,X2:S)) -> ACTIVE(app(mark(X1:S),mark(X2:S)))
0.00/0.48	 MARK(app(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.48	 MARK(app(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.48	 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S))
0.00/0.48	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.48	 MARK(from(X:S)) -> ACTIVE(from(mark(X:S)))
0.00/0.48	 MARK(from(X:S)) -> MARK(X:S)
0.00/0.48	 MARK(prefix(X:S)) -> ACTIVE(prefix(mark(X:S)))
0.00/0.48	 MARK(prefix(X:S)) -> MARK(X:S)
0.00/0.48	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.00/0.48	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.48	 MARK(zWadr(X1:S,X2:S)) -> ACTIVE(zWadr(mark(X1:S),mark(X2:S)))
0.00/0.48	 MARK(zWadr(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.48	 MARK(zWadr(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.48	->->-> Rules:
0.00/0.48	 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S)))
0.00/0.48	 active(app(nil,YS:S)) -> mark(YS:S)
0.00/0.48	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.00/0.48	 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S))))
0.00/0.48	 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.00/0.48	 active(zWadr(nil,YS:S)) -> mark(nil)
0.00/0.48	 active(zWadr(XS:S,nil)) -> mark(nil)
0.00/0.48	 app(active(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.48	 app(mark(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.48	 app(X1:S,active(X2:S)) -> app(X1:S,X2:S)
0.00/0.48	 app(X1:S,mark(X2:S)) -> app(X1:S,X2:S)
0.00/0.48	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.48	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.48	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.00/0.48	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.00/0.48	 from(active(X:S)) -> from(X:S)
0.00/0.48	 from(mark(X:S)) -> from(X:S)
0.00/0.48	 mark(app(X1:S,X2:S)) -> active(app(mark(X1:S),mark(X2:S)))
0.00/0.48	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.00/0.48	 mark(from(X:S)) -> active(from(mark(X:S)))
0.00/0.48	 mark(prefix(X:S)) -> active(prefix(mark(X:S)))
0.00/0.48	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.48	 mark(zWadr(X1:S,X2:S)) -> active(zWadr(mark(X1:S),mark(X2:S)))
0.00/0.48	 mark(nil) -> active(nil)
0.00/0.48	 prefix(active(X:S)) -> prefix(X:S)
0.00/0.48	 prefix(mark(X:S)) -> prefix(X:S)
0.00/0.48	 s(active(X:S)) -> s(X:S)
0.00/0.48	 s(mark(X:S)) -> s(X:S)
0.00/0.48	 zWadr(active(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.48	 zWadr(mark(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.48	 zWadr(X1:S,active(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.48	 zWadr(X1:S,mark(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.48	
0.00/0.48	
0.00/0.48	The problem is decomposed in 7 subproblems.
0.00/0.48	
0.00/0.48	Problem 1.1: 
0.00/0.48	
0.00/0.48	Subterm Processor:
0.00/0.48	-> Pairs:
0.00/0.48	 ZWADR(active(X1:S),X2:S) -> ZWADR(X1:S,X2:S)
0.00/0.48	 ZWADR(mark(X1:S),X2:S) -> ZWADR(X1:S,X2:S)
0.00/0.48	 ZWADR(X1:S,active(X2:S)) -> ZWADR(X1:S,X2:S)
0.00/0.48	 ZWADR(X1:S,mark(X2:S)) -> ZWADR(X1:S,X2:S)
0.00/0.48	-> Rules:
0.00/0.48	 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S)))
0.00/0.48	 active(app(nil,YS:S)) -> mark(YS:S)
0.00/0.48	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.00/0.48	 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S))))
0.00/0.48	 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.00/0.48	 active(zWadr(nil,YS:S)) -> mark(nil)
0.00/0.48	 active(zWadr(XS:S,nil)) -> mark(nil)
0.00/0.48	 app(active(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.48	 app(mark(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.48	 app(X1:S,active(X2:S)) -> app(X1:S,X2:S)
0.00/0.48	 app(X1:S,mark(X2:S)) -> app(X1:S,X2:S)
0.00/0.48	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.48	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.48	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.00/0.48	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.00/0.48	 from(active(X:S)) -> from(X:S)
0.00/0.48	 from(mark(X:S)) -> from(X:S)
0.00/0.48	 mark(app(X1:S,X2:S)) -> active(app(mark(X1:S),mark(X2:S)))
0.00/0.48	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.00/0.48	 mark(from(X:S)) -> active(from(mark(X:S)))
0.00/0.48	 mark(prefix(X:S)) -> active(prefix(mark(X:S)))
0.00/0.48	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.48	 mark(zWadr(X1:S,X2:S)) -> active(zWadr(mark(X1:S),mark(X2:S)))
0.00/0.48	 mark(nil) -> active(nil)
0.00/0.48	 prefix(active(X:S)) -> prefix(X:S)
0.00/0.48	 prefix(mark(X:S)) -> prefix(X:S)
0.00/0.48	 s(active(X:S)) -> s(X:S)
0.00/0.48	 s(mark(X:S)) -> s(X:S)
0.00/0.48	 zWadr(active(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.48	 zWadr(mark(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.48	 zWadr(X1:S,active(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.48	 zWadr(X1:S,mark(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.48	->Projection:
0.00/0.48	 pi(ZWADR) = 1
0.00/0.48	
0.00/0.48	Problem 1.1: 
0.00/0.48	
0.00/0.48	SCC Processor:
0.00/0.48	-> Pairs:
0.00/0.48	 ZWADR(X1:S,active(X2:S)) -> ZWADR(X1:S,X2:S)
0.00/0.48	 ZWADR(X1:S,mark(X2:S)) -> ZWADR(X1:S,X2:S)
0.00/0.48	-> Rules:
0.00/0.48	 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S)))
0.00/0.48	 active(app(nil,YS:S)) -> mark(YS:S)
0.00/0.48	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.00/0.48	 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S))))
0.00/0.48	 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.00/0.48	 active(zWadr(nil,YS:S)) -> mark(nil)
0.00/0.48	 active(zWadr(XS:S,nil)) -> mark(nil)
0.00/0.48	 app(active(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.48	 app(mark(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.48	 app(X1:S,active(X2:S)) -> app(X1:S,X2:S)
0.00/0.48	 app(X1:S,mark(X2:S)) -> app(X1:S,X2:S)
0.00/0.48	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.48	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.48	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.00/0.48	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.00/0.48	 from(active(X:S)) -> from(X:S)
0.00/0.48	 from(mark(X:S)) -> from(X:S)
0.00/0.48	 mark(app(X1:S,X2:S)) -> active(app(mark(X1:S),mark(X2:S)))
0.00/0.48	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.00/0.48	 mark(from(X:S)) -> active(from(mark(X:S)))
0.00/0.48	 mark(prefix(X:S)) -> active(prefix(mark(X:S)))
0.00/0.48	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.48	 mark(zWadr(X1:S,X2:S)) -> active(zWadr(mark(X1:S),mark(X2:S)))
0.00/0.48	 mark(nil) -> active(nil)
0.00/0.48	 prefix(active(X:S)) -> prefix(X:S)
0.00/0.48	 prefix(mark(X:S)) -> prefix(X:S)
0.00/0.48	 s(active(X:S)) -> s(X:S)
0.00/0.48	 s(mark(X:S)) -> s(X:S)
0.00/0.48	 zWadr(active(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.48	 zWadr(mark(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.48	 zWadr(X1:S,active(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.48	 zWadr(X1:S,mark(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.48	->Strongly Connected Components:
0.00/0.48	->->Cycle:
0.00/0.48	->->-> Pairs:
0.00/0.48	 ZWADR(X1:S,active(X2:S)) -> ZWADR(X1:S,X2:S)
0.00/0.48	 ZWADR(X1:S,mark(X2:S)) -> ZWADR(X1:S,X2:S)
0.00/0.48	->->-> Rules:
0.00/0.48	 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S)))
0.00/0.48	 active(app(nil,YS:S)) -> mark(YS:S)
0.00/0.48	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.00/0.48	 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S))))
0.00/0.48	 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.00/0.48	 active(zWadr(nil,YS:S)) -> mark(nil)
0.00/0.48	 active(zWadr(XS:S,nil)) -> mark(nil)
0.00/0.48	 app(active(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.48	 app(mark(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.48	 app(X1:S,active(X2:S)) -> app(X1:S,X2:S)
0.00/0.48	 app(X1:S,mark(X2:S)) -> app(X1:S,X2:S)
0.00/0.48	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.48	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.48	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.00/0.48	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.00/0.48	 from(active(X:S)) -> from(X:S)
0.00/0.48	 from(mark(X:S)) -> from(X:S)
0.00/0.48	 mark(app(X1:S,X2:S)) -> active(app(mark(X1:S),mark(X2:S)))
0.00/0.48	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.00/0.48	 mark(from(X:S)) -> active(from(mark(X:S)))
0.00/0.48	 mark(prefix(X:S)) -> active(prefix(mark(X:S)))
0.00/0.48	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.48	 mark(zWadr(X1:S,X2:S)) -> active(zWadr(mark(X1:S),mark(X2:S)))
0.00/0.48	 mark(nil) -> active(nil)
0.00/0.48	 prefix(active(X:S)) -> prefix(X:S)
0.00/0.48	 prefix(mark(X:S)) -> prefix(X:S)
0.00/0.48	 s(active(X:S)) -> s(X:S)
0.00/0.48	 s(mark(X:S)) -> s(X:S)
0.00/0.48	 zWadr(active(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.48	 zWadr(mark(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.48	 zWadr(X1:S,active(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.48	 zWadr(X1:S,mark(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.48	
0.00/0.48	Problem 1.1: 
0.00/0.48	
0.00/0.48	Subterm Processor:
0.00/0.48	-> Pairs:
0.00/0.48	 ZWADR(X1:S,active(X2:S)) -> ZWADR(X1:S,X2:S)
0.00/0.48	 ZWADR(X1:S,mark(X2:S)) -> ZWADR(X1:S,X2:S)
0.00/0.48	-> Rules:
0.00/0.48	 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S)))
0.00/0.48	 active(app(nil,YS:S)) -> mark(YS:S)
0.00/0.48	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.00/0.48	 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S))))
0.00/0.48	 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.00/0.48	 active(zWadr(nil,YS:S)) -> mark(nil)
0.00/0.48	 active(zWadr(XS:S,nil)) -> mark(nil)
0.00/0.48	 app(active(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.48	 app(mark(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.48	 app(X1:S,active(X2:S)) -> app(X1:S,X2:S)
0.00/0.48	 app(X1:S,mark(X2:S)) -> app(X1:S,X2:S)
0.00/0.48	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.48	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.48	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.00/0.48	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.00/0.48	 from(active(X:S)) -> from(X:S)
0.00/0.48	 from(mark(X:S)) -> from(X:S)
0.00/0.48	 mark(app(X1:S,X2:S)) -> active(app(mark(X1:S),mark(X2:S)))
0.00/0.48	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.00/0.48	 mark(from(X:S)) -> active(from(mark(X:S)))
0.00/0.48	 mark(prefix(X:S)) -> active(prefix(mark(X:S)))
0.00/0.48	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.48	 mark(zWadr(X1:S,X2:S)) -> active(zWadr(mark(X1:S),mark(X2:S)))
0.00/0.48	 mark(nil) -> active(nil)
0.00/0.48	 prefix(active(X:S)) -> prefix(X:S)
0.00/0.48	 prefix(mark(X:S)) -> prefix(X:S)
0.00/0.48	 s(active(X:S)) -> s(X:S)
0.00/0.48	 s(mark(X:S)) -> s(X:S)
0.00/0.48	 zWadr(active(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.48	 zWadr(mark(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.48	 zWadr(X1:S,active(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.48	 zWadr(X1:S,mark(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.48	->Projection:
0.00/0.48	 pi(ZWADR) = 2
0.00/0.48	
0.00/0.48	Problem 1.1: 
0.00/0.48	
0.00/0.48	SCC Processor:
0.00/0.48	-> Pairs:
0.00/0.48	 Empty
0.00/0.48	-> Rules:
0.00/0.48	 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S)))
0.00/0.48	 active(app(nil,YS:S)) -> mark(YS:S)
0.00/0.48	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.00/0.48	 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S))))
0.00/0.48	 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.00/0.48	 active(zWadr(nil,YS:S)) -> mark(nil)
0.00/0.48	 active(zWadr(XS:S,nil)) -> mark(nil)
0.00/0.48	 app(active(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.48	 app(mark(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.48	 app(X1:S,active(X2:S)) -> app(X1:S,X2:S)
0.00/0.48	 app(X1:S,mark(X2:S)) -> app(X1:S,X2:S)
0.00/0.48	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.48	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.48	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.00/0.48	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.00/0.48	 from(active(X:S)) -> from(X:S)
0.00/0.48	 from(mark(X:S)) -> from(X:S)
0.00/0.48	 mark(app(X1:S,X2:S)) -> active(app(mark(X1:S),mark(X2:S)))
0.00/0.48	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.00/0.48	 mark(from(X:S)) -> active(from(mark(X:S)))
0.00/0.48	 mark(prefix(X:S)) -> active(prefix(mark(X:S)))
0.00/0.48	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.48	 mark(zWadr(X1:S,X2:S)) -> active(zWadr(mark(X1:S),mark(X2:S)))
0.00/0.48	 mark(nil) -> active(nil)
0.00/0.48	 prefix(active(X:S)) -> prefix(X:S)
0.00/0.48	 prefix(mark(X:S)) -> prefix(X:S)
0.00/0.48	 s(active(X:S)) -> s(X:S)
0.00/0.48	 s(mark(X:S)) -> s(X:S)
0.00/0.48	 zWadr(active(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.48	 zWadr(mark(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.48	 zWadr(X1:S,active(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.48	 zWadr(X1:S,mark(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.48	->Strongly Connected Components:
0.00/0.48	 There is no strongly connected component
0.00/0.48	
0.00/0.48	The problem is finite.
0.00/0.48	
0.00/0.48	Problem 1.2: 
0.00/0.48	
0.00/0.48	Subterm Processor:
0.00/0.48	-> Pairs:
0.00/0.48	 S(active(X:S)) -> S(X:S)
0.00/0.48	 S(mark(X:S)) -> S(X:S)
0.00/0.48	-> Rules:
0.00/0.48	 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S)))
0.00/0.48	 active(app(nil,YS:S)) -> mark(YS:S)
0.00/0.48	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.00/0.48	 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S))))
0.00/0.48	 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.00/0.48	 active(zWadr(nil,YS:S)) -> mark(nil)
0.00/0.48	 active(zWadr(XS:S,nil)) -> mark(nil)
0.00/0.48	 app(active(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.48	 app(mark(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.48	 app(X1:S,active(X2:S)) -> app(X1:S,X2:S)
0.00/0.48	 app(X1:S,mark(X2:S)) -> app(X1:S,X2:S)
0.00/0.48	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.48	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.48	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.00/0.48	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.00/0.48	 from(active(X:S)) -> from(X:S)
0.00/0.48	 from(mark(X:S)) -> from(X:S)
0.00/0.48	 mark(app(X1:S,X2:S)) -> active(app(mark(X1:S),mark(X2:S)))
0.00/0.48	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.00/0.48	 mark(from(X:S)) -> active(from(mark(X:S)))
0.00/0.48	 mark(prefix(X:S)) -> active(prefix(mark(X:S)))
0.00/0.48	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.48	 mark(zWadr(X1:S,X2:S)) -> active(zWadr(mark(X1:S),mark(X2:S)))
0.00/0.48	 mark(nil) -> active(nil)
0.00/0.48	 prefix(active(X:S)) -> prefix(X:S)
0.00/0.48	 prefix(mark(X:S)) -> prefix(X:S)
0.00/0.48	 s(active(X:S)) -> s(X:S)
0.00/0.48	 s(mark(X:S)) -> s(X:S)
0.00/0.48	 zWadr(active(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.48	 zWadr(mark(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.48	 zWadr(X1:S,active(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.48	 zWadr(X1:S,mark(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.48	->Projection:
0.00/0.48	 pi(S) = 1
0.00/0.48	
0.00/0.48	Problem 1.2: 
0.00/0.48	
0.00/0.48	SCC Processor:
0.00/0.48	-> Pairs:
0.00/0.48	 Empty
0.00/0.48	-> Rules:
0.00/0.48	 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S)))
0.00/0.48	 active(app(nil,YS:S)) -> mark(YS:S)
0.00/0.48	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.00/0.48	 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S))))
0.00/0.48	 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.00/0.48	 active(zWadr(nil,YS:S)) -> mark(nil)
0.00/0.48	 active(zWadr(XS:S,nil)) -> mark(nil)
0.00/0.48	 app(active(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.48	 app(mark(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.48	 app(X1:S,active(X2:S)) -> app(X1:S,X2:S)
0.00/0.48	 app(X1:S,mark(X2:S)) -> app(X1:S,X2:S)
0.00/0.48	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.48	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.48	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.00/0.48	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.00/0.48	 from(active(X:S)) -> from(X:S)
0.00/0.48	 from(mark(X:S)) -> from(X:S)
0.00/0.48	 mark(app(X1:S,X2:S)) -> active(app(mark(X1:S),mark(X2:S)))
0.00/0.48	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.00/0.48	 mark(from(X:S)) -> active(from(mark(X:S)))
0.00/0.48	 mark(prefix(X:S)) -> active(prefix(mark(X:S)))
0.00/0.48	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.48	 mark(zWadr(X1:S,X2:S)) -> active(zWadr(mark(X1:S),mark(X2:S)))
0.00/0.48	 mark(nil) -> active(nil)
0.00/0.48	 prefix(active(X:S)) -> prefix(X:S)
0.00/0.48	 prefix(mark(X:S)) -> prefix(X:S)
0.00/0.48	 s(active(X:S)) -> s(X:S)
0.00/0.48	 s(mark(X:S)) -> s(X:S)
0.00/0.48	 zWadr(active(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.48	 zWadr(mark(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.48	 zWadr(X1:S,active(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.48	 zWadr(X1:S,mark(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.48	->Strongly Connected Components:
0.00/0.48	 There is no strongly connected component
0.00/0.48	
0.00/0.48	The problem is finite.
0.00/0.48	
0.00/0.48	Problem 1.3: 
0.00/0.48	
0.00/0.48	Subterm Processor:
0.00/0.48	-> Pairs:
0.00/0.48	 PREFIX(active(X:S)) -> PREFIX(X:S)
0.00/0.48	 PREFIX(mark(X:S)) -> PREFIX(X:S)
0.00/0.48	-> Rules:
0.00/0.48	 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S)))
0.00/0.48	 active(app(nil,YS:S)) -> mark(YS:S)
0.00/0.48	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.00/0.48	 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S))))
0.00/0.48	 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.00/0.48	 active(zWadr(nil,YS:S)) -> mark(nil)
0.00/0.48	 active(zWadr(XS:S,nil)) -> mark(nil)
0.00/0.48	 app(active(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.48	 app(mark(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.48	 app(X1:S,active(X2:S)) -> app(X1:S,X2:S)
0.00/0.48	 app(X1:S,mark(X2:S)) -> app(X1:S,X2:S)
0.00/0.48	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.48	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.48	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.00/0.48	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.00/0.48	 from(active(X:S)) -> from(X:S)
0.00/0.48	 from(mark(X:S)) -> from(X:S)
0.00/0.48	 mark(app(X1:S,X2:S)) -> active(app(mark(X1:S),mark(X2:S)))
0.00/0.48	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.00/0.48	 mark(from(X:S)) -> active(from(mark(X:S)))
0.00/0.48	 mark(prefix(X:S)) -> active(prefix(mark(X:S)))
0.00/0.48	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.48	 mark(zWadr(X1:S,X2:S)) -> active(zWadr(mark(X1:S),mark(X2:S)))
0.00/0.48	 mark(nil) -> active(nil)
0.00/0.48	 prefix(active(X:S)) -> prefix(X:S)
0.00/0.48	 prefix(mark(X:S)) -> prefix(X:S)
0.00/0.48	 s(active(X:S)) -> s(X:S)
0.00/0.48	 s(mark(X:S)) -> s(X:S)
0.00/0.48	 zWadr(active(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.48	 zWadr(mark(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.48	 zWadr(X1:S,active(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.48	 zWadr(X1:S,mark(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.48	->Projection:
0.00/0.48	 pi(PREFIX) = 1
0.00/0.48	
0.00/0.48	Problem 1.3: 
0.00/0.48	
0.00/0.48	SCC Processor:
0.00/0.48	-> Pairs:
0.00/0.48	 Empty
0.00/0.48	-> Rules:
0.00/0.48	 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S)))
0.00/0.48	 active(app(nil,YS:S)) -> mark(YS:S)
0.00/0.48	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.00/0.48	 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S))))
0.00/0.48	 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.00/0.48	 active(zWadr(nil,YS:S)) -> mark(nil)
0.00/0.48	 active(zWadr(XS:S,nil)) -> mark(nil)
0.00/0.48	 app(active(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.48	 app(mark(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.48	 app(X1:S,active(X2:S)) -> app(X1:S,X2:S)
0.00/0.48	 app(X1:S,mark(X2:S)) -> app(X1:S,X2:S)
0.00/0.48	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.48	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.48	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.00/0.48	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.00/0.48	 from(active(X:S)) -> from(X:S)
0.00/0.48	 from(mark(X:S)) -> from(X:S)
0.00/0.48	 mark(app(X1:S,X2:S)) -> active(app(mark(X1:S),mark(X2:S)))
0.00/0.48	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.00/0.48	 mark(from(X:S)) -> active(from(mark(X:S)))
0.00/0.48	 mark(prefix(X:S)) -> active(prefix(mark(X:S)))
0.00/0.48	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.48	 mark(zWadr(X1:S,X2:S)) -> active(zWadr(mark(X1:S),mark(X2:S)))
0.00/0.48	 mark(nil) -> active(nil)
0.00/0.48	 prefix(active(X:S)) -> prefix(X:S)
0.00/0.48	 prefix(mark(X:S)) -> prefix(X:S)
0.00/0.48	 s(active(X:S)) -> s(X:S)
0.00/0.48	 s(mark(X:S)) -> s(X:S)
0.00/0.48	 zWadr(active(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.48	 zWadr(mark(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.48	 zWadr(X1:S,active(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.48	 zWadr(X1:S,mark(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.48	->Strongly Connected Components:
0.00/0.49	 There is no strongly connected component
0.00/0.49	
0.00/0.49	The problem is finite.
0.00/0.49	
0.00/0.49	Problem 1.4: 
0.00/0.49	
0.00/0.49	Subterm Processor:
0.00/0.49	-> Pairs:
0.00/0.49	 FROM(active(X:S)) -> FROM(X:S)
0.00/0.49	 FROM(mark(X:S)) -> FROM(X:S)
0.00/0.49	-> Rules:
0.00/0.49	 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S)))
0.00/0.49	 active(app(nil,YS:S)) -> mark(YS:S)
0.00/0.49	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.00/0.49	 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S))))
0.00/0.49	 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.00/0.49	 active(zWadr(nil,YS:S)) -> mark(nil)
0.00/0.49	 active(zWadr(XS:S,nil)) -> mark(nil)
0.00/0.49	 app(active(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.49	 app(mark(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.49	 app(X1:S,active(X2:S)) -> app(X1:S,X2:S)
0.00/0.49	 app(X1:S,mark(X2:S)) -> app(X1:S,X2:S)
0.00/0.49	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.49	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.49	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.00/0.49	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.00/0.49	 from(active(X:S)) -> from(X:S)
0.00/0.49	 from(mark(X:S)) -> from(X:S)
0.00/0.49	 mark(app(X1:S,X2:S)) -> active(app(mark(X1:S),mark(X2:S)))
0.00/0.49	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.00/0.49	 mark(from(X:S)) -> active(from(mark(X:S)))
0.00/0.49	 mark(prefix(X:S)) -> active(prefix(mark(X:S)))
0.00/0.49	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.49	 mark(zWadr(X1:S,X2:S)) -> active(zWadr(mark(X1:S),mark(X2:S)))
0.00/0.49	 mark(nil) -> active(nil)
0.00/0.49	 prefix(active(X:S)) -> prefix(X:S)
0.00/0.49	 prefix(mark(X:S)) -> prefix(X:S)
0.00/0.49	 s(active(X:S)) -> s(X:S)
0.00/0.49	 s(mark(X:S)) -> s(X:S)
0.00/0.49	 zWadr(active(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.49	 zWadr(mark(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.49	 zWadr(X1:S,active(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.49	 zWadr(X1:S,mark(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.49	->Projection:
0.00/0.49	 pi(FROM) = 1
0.00/0.49	
0.00/0.49	Problem 1.4: 
0.00/0.49	
0.00/0.49	SCC Processor:
0.00/0.49	-> Pairs:
0.00/0.49	 Empty
0.00/0.49	-> Rules:
0.00/0.49	 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S)))
0.00/0.49	 active(app(nil,YS:S)) -> mark(YS:S)
0.00/0.49	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.00/0.49	 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S))))
0.00/0.49	 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.00/0.49	 active(zWadr(nil,YS:S)) -> mark(nil)
0.00/0.49	 active(zWadr(XS:S,nil)) -> mark(nil)
0.00/0.49	 app(active(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.49	 app(mark(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.49	 app(X1:S,active(X2:S)) -> app(X1:S,X2:S)
0.00/0.49	 app(X1:S,mark(X2:S)) -> app(X1:S,X2:S)
0.00/0.49	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.49	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.49	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.00/0.49	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.00/0.49	 from(active(X:S)) -> from(X:S)
0.00/0.49	 from(mark(X:S)) -> from(X:S)
0.00/0.49	 mark(app(X1:S,X2:S)) -> active(app(mark(X1:S),mark(X2:S)))
0.00/0.49	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.00/0.49	 mark(from(X:S)) -> active(from(mark(X:S)))
0.00/0.49	 mark(prefix(X:S)) -> active(prefix(mark(X:S)))
0.00/0.49	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.49	 mark(zWadr(X1:S,X2:S)) -> active(zWadr(mark(X1:S),mark(X2:S)))
0.00/0.49	 mark(nil) -> active(nil)
0.00/0.49	 prefix(active(X:S)) -> prefix(X:S)
0.00/0.49	 prefix(mark(X:S)) -> prefix(X:S)
0.00/0.49	 s(active(X:S)) -> s(X:S)
0.00/0.49	 s(mark(X:S)) -> s(X:S)
0.00/0.49	 zWadr(active(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.49	 zWadr(mark(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.49	 zWadr(X1:S,active(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.49	 zWadr(X1:S,mark(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.49	->Strongly Connected Components:
0.00/0.49	 There is no strongly connected component
0.00/0.49	
0.00/0.49	The problem is finite.
0.00/0.49	
0.00/0.49	Problem 1.5: 
0.00/0.49	
0.00/0.49	Subterm Processor:
0.00/0.49	-> Pairs:
0.00/0.49	 CONS(active(X1:S),X2:S) -> CONS(X1:S,X2:S)
0.00/0.49	 CONS(mark(X1:S),X2:S) -> CONS(X1:S,X2:S)
0.00/0.49	 CONS(X1:S,active(X2:S)) -> CONS(X1:S,X2:S)
0.00/0.49	 CONS(X1:S,mark(X2:S)) -> CONS(X1:S,X2:S)
0.00/0.49	-> Rules:
0.00/0.49	 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S)))
0.00/0.49	 active(app(nil,YS:S)) -> mark(YS:S)
0.00/0.49	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.00/0.49	 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S))))
0.00/0.49	 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.00/0.49	 active(zWadr(nil,YS:S)) -> mark(nil)
0.00/0.49	 active(zWadr(XS:S,nil)) -> mark(nil)
0.00/0.49	 app(active(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.49	 app(mark(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.49	 app(X1:S,active(X2:S)) -> app(X1:S,X2:S)
0.00/0.49	 app(X1:S,mark(X2:S)) -> app(X1:S,X2:S)
0.00/0.49	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.49	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.49	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.00/0.49	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.00/0.49	 from(active(X:S)) -> from(X:S)
0.00/0.49	 from(mark(X:S)) -> from(X:S)
0.00/0.49	 mark(app(X1:S,X2:S)) -> active(app(mark(X1:S),mark(X2:S)))
0.00/0.49	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.00/0.49	 mark(from(X:S)) -> active(from(mark(X:S)))
0.00/0.49	 mark(prefix(X:S)) -> active(prefix(mark(X:S)))
0.00/0.49	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.49	 mark(zWadr(X1:S,X2:S)) -> active(zWadr(mark(X1:S),mark(X2:S)))
0.00/0.49	 mark(nil) -> active(nil)
0.00/0.49	 prefix(active(X:S)) -> prefix(X:S)
0.00/0.49	 prefix(mark(X:S)) -> prefix(X:S)
0.00/0.49	 s(active(X:S)) -> s(X:S)
0.00/0.49	 s(mark(X:S)) -> s(X:S)
0.00/0.49	 zWadr(active(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.49	 zWadr(mark(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.49	 zWadr(X1:S,active(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.49	 zWadr(X1:S,mark(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.49	->Projection:
0.00/0.49	 pi(CONS) = 1
0.00/0.49	
0.00/0.49	Problem 1.5: 
0.00/0.49	
0.00/0.49	SCC Processor:
0.00/0.49	-> Pairs:
0.00/0.49	 CONS(X1:S,active(X2:S)) -> CONS(X1:S,X2:S)
0.00/0.49	 CONS(X1:S,mark(X2:S)) -> CONS(X1:S,X2:S)
0.00/0.49	-> Rules:
0.00/0.49	 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S)))
0.00/0.49	 active(app(nil,YS:S)) -> mark(YS:S)
0.00/0.49	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.00/0.49	 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S))))
0.00/0.49	 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.00/0.49	 active(zWadr(nil,YS:S)) -> mark(nil)
0.00/0.49	 active(zWadr(XS:S,nil)) -> mark(nil)
0.00/0.49	 app(active(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.49	 app(mark(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.49	 app(X1:S,active(X2:S)) -> app(X1:S,X2:S)
0.00/0.49	 app(X1:S,mark(X2:S)) -> app(X1:S,X2:S)
0.00/0.49	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.49	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.49	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.00/0.49	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.00/0.49	 from(active(X:S)) -> from(X:S)
0.00/0.49	 from(mark(X:S)) -> from(X:S)
0.00/0.49	 mark(app(X1:S,X2:S)) -> active(app(mark(X1:S),mark(X2:S)))
0.00/0.49	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.00/0.49	 mark(from(X:S)) -> active(from(mark(X:S)))
0.00/0.49	 mark(prefix(X:S)) -> active(prefix(mark(X:S)))
0.00/0.49	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.49	 mark(zWadr(X1:S,X2:S)) -> active(zWadr(mark(X1:S),mark(X2:S)))
0.00/0.49	 mark(nil) -> active(nil)
0.00/0.49	 prefix(active(X:S)) -> prefix(X:S)
0.00/0.49	 prefix(mark(X:S)) -> prefix(X:S)
0.00/0.49	 s(active(X:S)) -> s(X:S)
0.00/0.49	 s(mark(X:S)) -> s(X:S)
0.00/0.49	 zWadr(active(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.49	 zWadr(mark(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.49	 zWadr(X1:S,active(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.49	 zWadr(X1:S,mark(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.49	->Strongly Connected Components:
0.00/0.49	->->Cycle:
0.00/0.49	->->-> Pairs:
0.00/0.49	 CONS(X1:S,active(X2:S)) -> CONS(X1:S,X2:S)
0.00/0.49	 CONS(X1:S,mark(X2:S)) -> CONS(X1:S,X2:S)
0.00/0.49	->->-> Rules:
0.00/0.49	 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S)))
0.00/0.49	 active(app(nil,YS:S)) -> mark(YS:S)
0.00/0.49	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.00/0.49	 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S))))
0.00/0.49	 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.00/0.49	 active(zWadr(nil,YS:S)) -> mark(nil)
0.00/0.49	 active(zWadr(XS:S,nil)) -> mark(nil)
0.00/0.49	 app(active(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.49	 app(mark(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.49	 app(X1:S,active(X2:S)) -> app(X1:S,X2:S)
0.00/0.49	 app(X1:S,mark(X2:S)) -> app(X1:S,X2:S)
0.00/0.49	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.49	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.49	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.00/0.49	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.00/0.49	 from(active(X:S)) -> from(X:S)
0.00/0.49	 from(mark(X:S)) -> from(X:S)
0.00/0.49	 mark(app(X1:S,X2:S)) -> active(app(mark(X1:S),mark(X2:S)))
0.00/0.49	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.00/0.49	 mark(from(X:S)) -> active(from(mark(X:S)))
0.00/0.49	 mark(prefix(X:S)) -> active(prefix(mark(X:S)))
0.00/0.49	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.49	 mark(zWadr(X1:S,X2:S)) -> active(zWadr(mark(X1:S),mark(X2:S)))
0.00/0.49	 mark(nil) -> active(nil)
0.00/0.49	 prefix(active(X:S)) -> prefix(X:S)
0.00/0.49	 prefix(mark(X:S)) -> prefix(X:S)
0.00/0.49	 s(active(X:S)) -> s(X:S)
0.00/0.49	 s(mark(X:S)) -> s(X:S)
0.00/0.49	 zWadr(active(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.49	 zWadr(mark(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.49	 zWadr(X1:S,active(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.49	 zWadr(X1:S,mark(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.49	
0.00/0.49	Problem 1.5: 
0.00/0.49	
0.00/0.49	Subterm Processor:
0.00/0.49	-> Pairs:
0.00/0.49	 CONS(X1:S,active(X2:S)) -> CONS(X1:S,X2:S)
0.00/0.49	 CONS(X1:S,mark(X2:S)) -> CONS(X1:S,X2:S)
0.00/0.49	-> Rules:
0.00/0.49	 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S)))
0.00/0.49	 active(app(nil,YS:S)) -> mark(YS:S)
0.00/0.49	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.00/0.49	 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S))))
0.00/0.49	 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.00/0.49	 active(zWadr(nil,YS:S)) -> mark(nil)
0.00/0.49	 active(zWadr(XS:S,nil)) -> mark(nil)
0.00/0.49	 app(active(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.49	 app(mark(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.49	 app(X1:S,active(X2:S)) -> app(X1:S,X2:S)
0.00/0.49	 app(X1:S,mark(X2:S)) -> app(X1:S,X2:S)
0.00/0.49	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.49	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.49	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.00/0.49	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.00/0.49	 from(active(X:S)) -> from(X:S)
0.00/0.49	 from(mark(X:S)) -> from(X:S)
0.00/0.49	 mark(app(X1:S,X2:S)) -> active(app(mark(X1:S),mark(X2:S)))
0.00/0.49	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.00/0.49	 mark(from(X:S)) -> active(from(mark(X:S)))
0.00/0.49	 mark(prefix(X:S)) -> active(prefix(mark(X:S)))
0.00/0.49	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.49	 mark(zWadr(X1:S,X2:S)) -> active(zWadr(mark(X1:S),mark(X2:S)))
0.00/0.49	 mark(nil) -> active(nil)
0.00/0.49	 prefix(active(X:S)) -> prefix(X:S)
0.00/0.49	 prefix(mark(X:S)) -> prefix(X:S)
0.00/0.49	 s(active(X:S)) -> s(X:S)
0.00/0.49	 s(mark(X:S)) -> s(X:S)
0.00/0.49	 zWadr(active(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.49	 zWadr(mark(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.49	 zWadr(X1:S,active(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.49	 zWadr(X1:S,mark(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.49	->Projection:
0.00/0.49	 pi(CONS) = 2
0.00/0.49	
0.00/0.49	Problem 1.5: 
0.00/0.49	
0.00/0.49	SCC Processor:
0.00/0.49	-> Pairs:
0.00/0.49	 Empty
0.00/0.49	-> Rules:
0.00/0.49	 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S)))
0.00/0.49	 active(app(nil,YS:S)) -> mark(YS:S)
0.00/0.49	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.00/0.49	 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S))))
0.00/0.49	 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.00/0.49	 active(zWadr(nil,YS:S)) -> mark(nil)
0.00/0.49	 active(zWadr(XS:S,nil)) -> mark(nil)
0.00/0.49	 app(active(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.49	 app(mark(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.49	 app(X1:S,active(X2:S)) -> app(X1:S,X2:S)
0.00/0.49	 app(X1:S,mark(X2:S)) -> app(X1:S,X2:S)
0.00/0.49	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.49	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.49	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.00/0.49	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.00/0.49	 from(active(X:S)) -> from(X:S)
0.00/0.49	 from(mark(X:S)) -> from(X:S)
0.00/0.49	 mark(app(X1:S,X2:S)) -> active(app(mark(X1:S),mark(X2:S)))
0.00/0.49	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.00/0.49	 mark(from(X:S)) -> active(from(mark(X:S)))
0.00/0.49	 mark(prefix(X:S)) -> active(prefix(mark(X:S)))
0.00/0.49	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.49	 mark(zWadr(X1:S,X2:S)) -> active(zWadr(mark(X1:S),mark(X2:S)))
0.00/0.49	 mark(nil) -> active(nil)
0.00/0.49	 prefix(active(X:S)) -> prefix(X:S)
0.00/0.49	 prefix(mark(X:S)) -> prefix(X:S)
0.00/0.49	 s(active(X:S)) -> s(X:S)
0.00/0.49	 s(mark(X:S)) -> s(X:S)
0.00/0.49	 zWadr(active(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.49	 zWadr(mark(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.49	 zWadr(X1:S,active(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.49	 zWadr(X1:S,mark(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.49	->Strongly Connected Components:
0.00/0.49	 There is no strongly connected component
0.00/0.49	
0.00/0.49	The problem is finite.
0.00/0.49	
0.00/0.49	Problem 1.6: 
0.00/0.49	
0.00/0.49	Subterm Processor:
0.00/0.49	-> Pairs:
0.00/0.49	 APP(active(X1:S),X2:S) -> APP(X1:S,X2:S)
0.00/0.49	 APP(mark(X1:S),X2:S) -> APP(X1:S,X2:S)
0.00/0.49	 APP(X1:S,active(X2:S)) -> APP(X1:S,X2:S)
0.00/0.49	 APP(X1:S,mark(X2:S)) -> APP(X1:S,X2:S)
0.00/0.49	-> Rules:
0.00/0.49	 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S)))
0.00/0.49	 active(app(nil,YS:S)) -> mark(YS:S)
0.00/0.49	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.00/0.49	 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S))))
0.00/0.49	 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.00/0.49	 active(zWadr(nil,YS:S)) -> mark(nil)
0.00/0.49	 active(zWadr(XS:S,nil)) -> mark(nil)
0.00/0.49	 app(active(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.49	 app(mark(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.49	 app(X1:S,active(X2:S)) -> app(X1:S,X2:S)
0.00/0.49	 app(X1:S,mark(X2:S)) -> app(X1:S,X2:S)
0.00/0.49	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.49	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.49	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.00/0.49	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.00/0.49	 from(active(X:S)) -> from(X:S)
0.00/0.49	 from(mark(X:S)) -> from(X:S)
0.00/0.49	 mark(app(X1:S,X2:S)) -> active(app(mark(X1:S),mark(X2:S)))
0.00/0.49	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.00/0.49	 mark(from(X:S)) -> active(from(mark(X:S)))
0.00/0.49	 mark(prefix(X:S)) -> active(prefix(mark(X:S)))
0.00/0.49	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.49	 mark(zWadr(X1:S,X2:S)) -> active(zWadr(mark(X1:S),mark(X2:S)))
0.00/0.49	 mark(nil) -> active(nil)
0.00/0.49	 prefix(active(X:S)) -> prefix(X:S)
0.00/0.49	 prefix(mark(X:S)) -> prefix(X:S)
0.00/0.49	 s(active(X:S)) -> s(X:S)
0.00/0.49	 s(mark(X:S)) -> s(X:S)
0.00/0.49	 zWadr(active(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.49	 zWadr(mark(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.49	 zWadr(X1:S,active(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.49	 zWadr(X1:S,mark(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.49	->Projection:
0.00/0.49	 pi(APP) = 1
0.00/0.49	
0.00/0.49	Problem 1.6: 
0.00/0.49	
0.00/0.49	SCC Processor:
0.00/0.49	-> Pairs:
0.00/0.49	 APP(X1:S,active(X2:S)) -> APP(X1:S,X2:S)
0.00/0.49	 APP(X1:S,mark(X2:S)) -> APP(X1:S,X2:S)
0.00/0.49	-> Rules:
0.00/0.49	 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S)))
0.00/0.49	 active(app(nil,YS:S)) -> mark(YS:S)
0.00/0.49	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.00/0.49	 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S))))
0.00/0.49	 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.00/0.49	 active(zWadr(nil,YS:S)) -> mark(nil)
0.00/0.49	 active(zWadr(XS:S,nil)) -> mark(nil)
0.00/0.49	 app(active(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.49	 app(mark(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.49	 app(X1:S,active(X2:S)) -> app(X1:S,X2:S)
0.00/0.49	 app(X1:S,mark(X2:S)) -> app(X1:S,X2:S)
0.00/0.49	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.49	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.49	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.00/0.49	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.00/0.49	 from(active(X:S)) -> from(X:S)
0.00/0.49	 from(mark(X:S)) -> from(X:S)
0.00/0.49	 mark(app(X1:S,X2:S)) -> active(app(mark(X1:S),mark(X2:S)))
0.00/0.49	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.00/0.49	 mark(from(X:S)) -> active(from(mark(X:S)))
0.00/0.49	 mark(prefix(X:S)) -> active(prefix(mark(X:S)))
0.00/0.49	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.49	 mark(zWadr(X1:S,X2:S)) -> active(zWadr(mark(X1:S),mark(X2:S)))
0.00/0.49	 mark(nil) -> active(nil)
0.00/0.49	 prefix(active(X:S)) -> prefix(X:S)
0.00/0.49	 prefix(mark(X:S)) -> prefix(X:S)
0.00/0.49	 s(active(X:S)) -> s(X:S)
0.00/0.49	 s(mark(X:S)) -> s(X:S)
0.00/0.49	 zWadr(active(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.49	 zWadr(mark(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.49	 zWadr(X1:S,active(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.49	 zWadr(X1:S,mark(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.49	->Strongly Connected Components:
0.00/0.49	->->Cycle:
0.00/0.49	->->-> Pairs:
0.00/0.49	 APP(X1:S,active(X2:S)) -> APP(X1:S,X2:S)
0.00/0.49	 APP(X1:S,mark(X2:S)) -> APP(X1:S,X2:S)
0.00/0.49	->->-> Rules:
0.00/0.49	 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S)))
0.00/0.49	 active(app(nil,YS:S)) -> mark(YS:S)
0.00/0.49	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.00/0.49	 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S))))
0.00/0.49	 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.00/0.49	 active(zWadr(nil,YS:S)) -> mark(nil)
0.00/0.49	 active(zWadr(XS:S,nil)) -> mark(nil)
0.00/0.49	 app(active(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.49	 app(mark(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.49	 app(X1:S,active(X2:S)) -> app(X1:S,X2:S)
0.00/0.49	 app(X1:S,mark(X2:S)) -> app(X1:S,X2:S)
0.00/0.49	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.49	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.49	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.00/0.49	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.00/0.49	 from(active(X:S)) -> from(X:S)
0.00/0.49	 from(mark(X:S)) -> from(X:S)
0.00/0.49	 mark(app(X1:S,X2:S)) -> active(app(mark(X1:S),mark(X2:S)))
0.00/0.49	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.00/0.49	 mark(from(X:S)) -> active(from(mark(X:S)))
0.00/0.49	 mark(prefix(X:S)) -> active(prefix(mark(X:S)))
0.00/0.49	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.49	 mark(zWadr(X1:S,X2:S)) -> active(zWadr(mark(X1:S),mark(X2:S)))
0.00/0.49	 mark(nil) -> active(nil)
0.00/0.49	 prefix(active(X:S)) -> prefix(X:S)
0.00/0.49	 prefix(mark(X:S)) -> prefix(X:S)
0.00/0.49	 s(active(X:S)) -> s(X:S)
0.00/0.49	 s(mark(X:S)) -> s(X:S)
0.00/0.49	 zWadr(active(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.49	 zWadr(mark(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.49	 zWadr(X1:S,active(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.49	 zWadr(X1:S,mark(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.49	
0.00/0.49	Problem 1.6: 
0.00/0.49	
0.00/0.49	Subterm Processor:
0.00/0.49	-> Pairs:
0.00/0.49	 APP(X1:S,active(X2:S)) -> APP(X1:S,X2:S)
0.00/0.49	 APP(X1:S,mark(X2:S)) -> APP(X1:S,X2:S)
0.00/0.49	-> Rules:
0.00/0.49	 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S)))
0.00/0.49	 active(app(nil,YS:S)) -> mark(YS:S)
0.00/0.49	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.00/0.49	 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S))))
0.00/0.49	 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.00/0.49	 active(zWadr(nil,YS:S)) -> mark(nil)
0.00/0.49	 active(zWadr(XS:S,nil)) -> mark(nil)
0.00/0.49	 app(active(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.49	 app(mark(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.49	 app(X1:S,active(X2:S)) -> app(X1:S,X2:S)
0.00/0.49	 app(X1:S,mark(X2:S)) -> app(X1:S,X2:S)
0.00/0.49	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.49	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.49	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.00/0.49	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.00/0.49	 from(active(X:S)) -> from(X:S)
0.00/0.49	 from(mark(X:S)) -> from(X:S)
0.00/0.49	 mark(app(X1:S,X2:S)) -> active(app(mark(X1:S),mark(X2:S)))
0.00/0.49	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.00/0.49	 mark(from(X:S)) -> active(from(mark(X:S)))
0.00/0.49	 mark(prefix(X:S)) -> active(prefix(mark(X:S)))
0.00/0.49	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.49	 mark(zWadr(X1:S,X2:S)) -> active(zWadr(mark(X1:S),mark(X2:S)))
0.00/0.49	 mark(nil) -> active(nil)
0.00/0.49	 prefix(active(X:S)) -> prefix(X:S)
0.00/0.49	 prefix(mark(X:S)) -> prefix(X:S)
0.00/0.49	 s(active(X:S)) -> s(X:S)
0.00/0.49	 s(mark(X:S)) -> s(X:S)
0.00/0.49	 zWadr(active(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.49	 zWadr(mark(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.49	 zWadr(X1:S,active(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.49	 zWadr(X1:S,mark(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.49	->Projection:
0.00/0.49	 pi(APP) = 2
0.00/0.49	
0.00/0.49	Problem 1.6: 
0.00/0.49	
0.00/0.49	SCC Processor:
0.00/0.49	-> Pairs:
0.00/0.49	 Empty
0.00/0.49	-> Rules:
0.00/0.49	 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S)))
0.00/0.49	 active(app(nil,YS:S)) -> mark(YS:S)
0.00/0.49	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.00/0.49	 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S))))
0.00/0.49	 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.00/0.49	 active(zWadr(nil,YS:S)) -> mark(nil)
0.00/0.49	 active(zWadr(XS:S,nil)) -> mark(nil)
0.00/0.49	 app(active(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.49	 app(mark(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.49	 app(X1:S,active(X2:S)) -> app(X1:S,X2:S)
0.00/0.49	 app(X1:S,mark(X2:S)) -> app(X1:S,X2:S)
0.00/0.49	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.49	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.49	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.00/0.49	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.00/0.49	 from(active(X:S)) -> from(X:S)
0.00/0.49	 from(mark(X:S)) -> from(X:S)
0.00/0.49	 mark(app(X1:S,X2:S)) -> active(app(mark(X1:S),mark(X2:S)))
0.00/0.49	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.00/0.49	 mark(from(X:S)) -> active(from(mark(X:S)))
0.00/0.49	 mark(prefix(X:S)) -> active(prefix(mark(X:S)))
0.00/0.49	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.49	 mark(zWadr(X1:S,X2:S)) -> active(zWadr(mark(X1:S),mark(X2:S)))
0.00/0.49	 mark(nil) -> active(nil)
0.00/0.49	 prefix(active(X:S)) -> prefix(X:S)
0.00/0.49	 prefix(mark(X:S)) -> prefix(X:S)
0.00/0.49	 s(active(X:S)) -> s(X:S)
0.00/0.49	 s(mark(X:S)) -> s(X:S)
0.00/0.49	 zWadr(active(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.49	 zWadr(mark(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.49	 zWadr(X1:S,active(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.49	 zWadr(X1:S,mark(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.49	->Strongly Connected Components:
0.00/0.49	 There is no strongly connected component
0.00/0.49	
0.00/0.49	The problem is finite.
0.00/0.49	
0.00/0.49	Problem 1.7: 
0.00/0.49	
0.00/0.49	Reduction Pairs Processor:
0.00/0.49	-> Pairs:
0.00/0.49	 ACTIVE(app(cons(X:S,XS:S),YS:S)) -> MARK(cons(X:S,app(XS:S,YS:S)))
0.00/0.49	 ACTIVE(app(nil,YS:S)) -> MARK(YS:S)
0.00/0.49	 ACTIVE(from(X:S)) -> MARK(cons(X:S,from(s(X:S))))
0.00/0.49	 ACTIVE(prefix(L:S)) -> MARK(cons(nil,zWadr(L:S,prefix(L:S))))
0.00/0.49	 ACTIVE(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> MARK(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.00/0.49	 MARK(app(X1:S,X2:S)) -> ACTIVE(app(mark(X1:S),mark(X2:S)))
0.00/0.49	 MARK(app(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.49	 MARK(app(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.49	 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S))
0.00/0.49	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.49	 MARK(from(X:S)) -> ACTIVE(from(mark(X:S)))
0.00/0.49	 MARK(from(X:S)) -> MARK(X:S)
0.00/0.49	 MARK(prefix(X:S)) -> ACTIVE(prefix(mark(X:S)))
0.00/0.49	 MARK(prefix(X:S)) -> MARK(X:S)
0.00/0.49	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.00/0.49	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.49	 MARK(zWadr(X1:S,X2:S)) -> ACTIVE(zWadr(mark(X1:S),mark(X2:S)))
0.00/0.49	 MARK(zWadr(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.49	 MARK(zWadr(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.49	-> Rules:
0.00/0.49	 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S)))
0.00/0.49	 active(app(nil,YS:S)) -> mark(YS:S)
0.00/0.49	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.00/0.49	 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S))))
0.00/0.49	 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.00/0.49	 active(zWadr(nil,YS:S)) -> mark(nil)
0.00/0.49	 active(zWadr(XS:S,nil)) -> mark(nil)
0.00/0.49	 app(active(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.49	 app(mark(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.49	 app(X1:S,active(X2:S)) -> app(X1:S,X2:S)
0.00/0.49	 app(X1:S,mark(X2:S)) -> app(X1:S,X2:S)
0.00/0.49	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.49	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.49	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.00/0.49	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.00/0.49	 from(active(X:S)) -> from(X:S)
0.00/0.49	 from(mark(X:S)) -> from(X:S)
0.00/0.49	 mark(app(X1:S,X2:S)) -> active(app(mark(X1:S),mark(X2:S)))
0.00/0.49	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.00/0.49	 mark(from(X:S)) -> active(from(mark(X:S)))
0.00/0.49	 mark(prefix(X:S)) -> active(prefix(mark(X:S)))
0.00/0.49	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.49	 mark(zWadr(X1:S,X2:S)) -> active(zWadr(mark(X1:S),mark(X2:S)))
0.00/0.49	 mark(nil) -> active(nil)
0.00/0.49	 prefix(active(X:S)) -> prefix(X:S)
0.00/0.49	 prefix(mark(X:S)) -> prefix(X:S)
0.00/0.49	 s(active(X:S)) -> s(X:S)
0.00/0.49	 s(mark(X:S)) -> s(X:S)
0.00/0.49	 zWadr(active(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.49	 zWadr(mark(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.49	 zWadr(X1:S,active(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.49	 zWadr(X1:S,mark(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.49	-> Usable rules:
0.00/0.49	 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S)))
0.00/0.49	 active(app(nil,YS:S)) -> mark(YS:S)
0.00/0.49	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.00/0.49	 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S))))
0.00/0.49	 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.00/0.49	 active(zWadr(nil,YS:S)) -> mark(nil)
0.00/0.49	 active(zWadr(XS:S,nil)) -> mark(nil)
0.00/0.49	 app(active(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.49	 app(mark(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.49	 app(X1:S,active(X2:S)) -> app(X1:S,X2:S)
0.00/0.49	 app(X1:S,mark(X2:S)) -> app(X1:S,X2:S)
0.00/0.49	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.49	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.49	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.00/0.49	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.00/0.49	 from(active(X:S)) -> from(X:S)
0.00/0.49	 from(mark(X:S)) -> from(X:S)
0.00/0.49	 mark(app(X1:S,X2:S)) -> active(app(mark(X1:S),mark(X2:S)))
0.00/0.49	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.00/0.49	 mark(from(X:S)) -> active(from(mark(X:S)))
0.00/0.49	 mark(prefix(X:S)) -> active(prefix(mark(X:S)))
0.00/0.49	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.49	 mark(zWadr(X1:S,X2:S)) -> active(zWadr(mark(X1:S),mark(X2:S)))
0.00/0.49	 mark(nil) -> active(nil)
0.00/0.49	 prefix(active(X:S)) -> prefix(X:S)
0.00/0.49	 prefix(mark(X:S)) -> prefix(X:S)
0.00/0.49	 s(active(X:S)) -> s(X:S)
0.00/0.49	 s(mark(X:S)) -> s(X:S)
0.00/0.49	 zWadr(active(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.49	 zWadr(mark(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.49	 zWadr(X1:S,active(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.49	 zWadr(X1:S,mark(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.49	->Interpretation type:
0.00/0.49	 Linear
0.00/0.49	->Coefficients:
0.00/0.49	 Natural Numbers
0.00/0.49	->Dimension:
0.00/0.49	 1
0.00/0.49	->Bound:
0.00/0.49	 2
0.00/0.49	->Interpretation:
0.00/0.49	 
0.00/0.49	[active](X) = X
0.00/0.49	[app](X1,X2) = 2.X1 + 2.X2 + 2
0.00/0.49	[cons](X1,X2) = X1 + 2
0.00/0.49	[from](X) = 2.X + 2
0.00/0.49	[mark](X) = X
0.00/0.49	[prefix](X) = 2.X + 2
0.00/0.49	[s](X) = 2.X
0.00/0.49	[zWadr](X1,X2) = 2.X1 + 2.X2 + 2
0.00/0.49	[fSNonEmpty] = 0
0.00/0.49	[nil] = 0
0.00/0.49	[ACTIVE](X) = 2.X + 2
0.00/0.49	[APP](X1,X2) = 0
0.00/0.49	[CONS](X1,X2) = 0
0.00/0.49	[FROM](X) = 0
0.00/0.49	[MARK](X) = 2.X + 2
0.00/0.49	[PREFIX](X) = 0
0.00/0.49	[S](X) = 0
0.00/0.49	[ZWADR](X1,X2) = 0
0.00/0.49	
0.00/0.49	Problem 1.7: 
0.00/0.49	
0.00/0.49	SCC Processor:
0.00/0.49	-> Pairs:
0.00/0.49	 ACTIVE(app(nil,YS:S)) -> MARK(YS:S)
0.00/0.49	 ACTIVE(from(X:S)) -> MARK(cons(X:S,from(s(X:S))))
0.00/0.49	 ACTIVE(prefix(L:S)) -> MARK(cons(nil,zWadr(L:S,prefix(L:S))))
0.00/0.49	 ACTIVE(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> MARK(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.00/0.49	 MARK(app(X1:S,X2:S)) -> ACTIVE(app(mark(X1:S),mark(X2:S)))
0.00/0.49	 MARK(app(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.49	 MARK(app(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.49	 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S))
0.00/0.49	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.49	 MARK(from(X:S)) -> ACTIVE(from(mark(X:S)))
0.00/0.49	 MARK(from(X:S)) -> MARK(X:S)
0.00/0.49	 MARK(prefix(X:S)) -> ACTIVE(prefix(mark(X:S)))
0.00/0.49	 MARK(prefix(X:S)) -> MARK(X:S)
0.00/0.49	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.00/0.49	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.49	 MARK(zWadr(X1:S,X2:S)) -> ACTIVE(zWadr(mark(X1:S),mark(X2:S)))
0.00/0.49	 MARK(zWadr(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.49	 MARK(zWadr(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.49	-> Rules:
0.00/0.49	 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S)))
0.00/0.49	 active(app(nil,YS:S)) -> mark(YS:S)
0.00/0.49	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.00/0.49	 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S))))
0.00/0.49	 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.00/0.49	 active(zWadr(nil,YS:S)) -> mark(nil)
0.00/0.49	 active(zWadr(XS:S,nil)) -> mark(nil)
0.00/0.49	 app(active(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.49	 app(mark(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.49	 app(X1:S,active(X2:S)) -> app(X1:S,X2:S)
0.00/0.49	 app(X1:S,mark(X2:S)) -> app(X1:S,X2:S)
0.00/0.49	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.49	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.49	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.00/0.49	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.00/0.49	 from(active(X:S)) -> from(X:S)
0.00/0.49	 from(mark(X:S)) -> from(X:S)
0.00/0.49	 mark(app(X1:S,X2:S)) -> active(app(mark(X1:S),mark(X2:S)))
0.00/0.49	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.00/0.49	 mark(from(X:S)) -> active(from(mark(X:S)))
0.00/0.49	 mark(prefix(X:S)) -> active(prefix(mark(X:S)))
0.00/0.49	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.49	 mark(zWadr(X1:S,X2:S)) -> active(zWadr(mark(X1:S),mark(X2:S)))
0.00/0.49	 mark(nil) -> active(nil)
0.00/0.49	 prefix(active(X:S)) -> prefix(X:S)
0.00/0.49	 prefix(mark(X:S)) -> prefix(X:S)
0.00/0.49	 s(active(X:S)) -> s(X:S)
0.00/0.49	 s(mark(X:S)) -> s(X:S)
0.00/0.49	 zWadr(active(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.49	 zWadr(mark(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.49	 zWadr(X1:S,active(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.49	 zWadr(X1:S,mark(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.49	->Strongly Connected Components:
0.00/0.49	->->Cycle:
0.00/0.49	->->-> Pairs:
0.00/0.49	 ACTIVE(app(nil,YS:S)) -> MARK(YS:S)
0.00/0.49	 ACTIVE(from(X:S)) -> MARK(cons(X:S,from(s(X:S))))
0.00/0.49	 ACTIVE(prefix(L:S)) -> MARK(cons(nil,zWadr(L:S,prefix(L:S))))
0.00/0.49	 ACTIVE(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> MARK(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.00/0.49	 MARK(app(X1:S,X2:S)) -> ACTIVE(app(mark(X1:S),mark(X2:S)))
0.00/0.49	 MARK(app(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.49	 MARK(app(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.49	 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S))
0.00/0.49	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.49	 MARK(from(X:S)) -> ACTIVE(from(mark(X:S)))
0.00/0.49	 MARK(from(X:S)) -> MARK(X:S)
0.00/0.49	 MARK(prefix(X:S)) -> ACTIVE(prefix(mark(X:S)))
0.00/0.49	 MARK(prefix(X:S)) -> MARK(X:S)
0.00/0.49	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.00/0.49	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.49	 MARK(zWadr(X1:S,X2:S)) -> ACTIVE(zWadr(mark(X1:S),mark(X2:S)))
0.00/0.49	 MARK(zWadr(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.49	 MARK(zWadr(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.49	->->-> Rules:
0.00/0.49	 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S)))
0.00/0.49	 active(app(nil,YS:S)) -> mark(YS:S)
0.00/0.49	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.00/0.49	 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S))))
0.00/0.49	 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.00/0.49	 active(zWadr(nil,YS:S)) -> mark(nil)
0.00/0.49	 active(zWadr(XS:S,nil)) -> mark(nil)
0.00/0.49	 app(active(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.49	 app(mark(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.49	 app(X1:S,active(X2:S)) -> app(X1:S,X2:S)
0.00/0.49	 app(X1:S,mark(X2:S)) -> app(X1:S,X2:S)
0.00/0.49	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.49	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.49	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.00/0.49	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.00/0.49	 from(active(X:S)) -> from(X:S)
0.00/0.49	 from(mark(X:S)) -> from(X:S)
0.00/0.49	 mark(app(X1:S,X2:S)) -> active(app(mark(X1:S),mark(X2:S)))
0.00/0.49	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.00/0.49	 mark(from(X:S)) -> active(from(mark(X:S)))
0.00/0.49	 mark(prefix(X:S)) -> active(prefix(mark(X:S)))
0.00/0.49	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.49	 mark(zWadr(X1:S,X2:S)) -> active(zWadr(mark(X1:S),mark(X2:S)))
0.00/0.49	 mark(nil) -> active(nil)
0.00/0.49	 prefix(active(X:S)) -> prefix(X:S)
0.00/0.49	 prefix(mark(X:S)) -> prefix(X:S)
0.00/0.49	 s(active(X:S)) -> s(X:S)
0.00/0.49	 s(mark(X:S)) -> s(X:S)
0.00/0.49	 zWadr(active(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.49	 zWadr(mark(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.49	 zWadr(X1:S,active(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.49	 zWadr(X1:S,mark(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.49	
0.00/0.49	Problem 1.7: 
0.00/0.49	
0.00/0.49	Reduction Pairs Processor:
0.00/0.49	-> Pairs:
0.00/0.49	 ACTIVE(app(nil,YS:S)) -> MARK(YS:S)
0.00/0.49	 ACTIVE(from(X:S)) -> MARK(cons(X:S,from(s(X:S))))
0.00/0.49	 ACTIVE(prefix(L:S)) -> MARK(cons(nil,zWadr(L:S,prefix(L:S))))
0.00/0.49	 ACTIVE(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> MARK(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.00/0.49	 MARK(app(X1:S,X2:S)) -> ACTIVE(app(mark(X1:S),mark(X2:S)))
0.00/0.49	 MARK(app(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.49	 MARK(app(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.49	 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S))
0.00/0.49	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.49	 MARK(from(X:S)) -> ACTIVE(from(mark(X:S)))
0.00/0.49	 MARK(from(X:S)) -> MARK(X:S)
0.00/0.49	 MARK(prefix(X:S)) -> ACTIVE(prefix(mark(X:S)))
0.00/0.49	 MARK(prefix(X:S)) -> MARK(X:S)
0.00/0.49	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.00/0.49	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.49	 MARK(zWadr(X1:S,X2:S)) -> ACTIVE(zWadr(mark(X1:S),mark(X2:S)))
0.00/0.49	 MARK(zWadr(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.49	 MARK(zWadr(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.49	-> Rules:
0.00/0.49	 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S)))
0.00/0.49	 active(app(nil,YS:S)) -> mark(YS:S)
0.00/0.49	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.00/0.49	 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S))))
0.00/0.49	 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.00/0.49	 active(zWadr(nil,YS:S)) -> mark(nil)
0.00/0.49	 active(zWadr(XS:S,nil)) -> mark(nil)
0.00/0.49	 app(active(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.49	 app(mark(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.49	 app(X1:S,active(X2:S)) -> app(X1:S,X2:S)
0.00/0.49	 app(X1:S,mark(X2:S)) -> app(X1:S,X2:S)
0.00/0.49	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.49	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.49	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.00/0.49	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.00/0.49	 from(active(X:S)) -> from(X:S)
0.00/0.49	 from(mark(X:S)) -> from(X:S)
0.00/0.49	 mark(app(X1:S,X2:S)) -> active(app(mark(X1:S),mark(X2:S)))
0.00/0.49	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.00/0.49	 mark(from(X:S)) -> active(from(mark(X:S)))
0.00/0.49	 mark(prefix(X:S)) -> active(prefix(mark(X:S)))
0.00/0.49	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.49	 mark(zWadr(X1:S,X2:S)) -> active(zWadr(mark(X1:S),mark(X2:S)))
0.00/0.49	 mark(nil) -> active(nil)
0.00/0.49	 prefix(active(X:S)) -> prefix(X:S)
0.00/0.49	 prefix(mark(X:S)) -> prefix(X:S)
0.00/0.49	 s(active(X:S)) -> s(X:S)
0.00/0.49	 s(mark(X:S)) -> s(X:S)
0.00/0.49	 zWadr(active(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.49	 zWadr(mark(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.49	 zWadr(X1:S,active(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.49	 zWadr(X1:S,mark(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.49	-> Usable rules:
0.00/0.49	 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S)))
0.00/0.49	 active(app(nil,YS:S)) -> mark(YS:S)
0.00/0.49	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.00/0.49	 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S))))
0.00/0.49	 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.00/0.49	 active(zWadr(nil,YS:S)) -> mark(nil)
0.00/0.49	 active(zWadr(XS:S,nil)) -> mark(nil)
0.00/0.49	 app(active(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.49	 app(mark(X1:S),X2:S) -> app(X1:S,X2:S)
0.00/0.49	 app(X1:S,active(X2:S)) -> app(X1:S,X2:S)
0.00/0.49	 app(X1:S,mark(X2:S)) -> app(X1:S,X2:S)
0.00/0.49	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.49	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.00/0.49	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.00/0.49	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.00/0.49	 from(active(X:S)) -> from(X:S)
0.00/0.49	 from(mark(X:S)) -> from(X:S)
0.00/0.49	 mark(app(X1:S,X2:S)) -> active(app(mark(X1:S),mark(X2:S)))
0.00/0.49	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.00/0.49	 mark(from(X:S)) -> active(from(mark(X:S)))
0.00/0.49	 mark(prefix(X:S)) -> active(prefix(mark(X:S)))
0.00/0.49	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.49	 mark(zWadr(X1:S,X2:S)) -> active(zWadr(mark(X1:S),mark(X2:S)))
0.00/0.49	 mark(nil) -> active(nil)
0.00/0.49	 prefix(active(X:S)) -> prefix(X:S)
0.00/0.49	 prefix(mark(X:S)) -> prefix(X:S)
0.00/0.49	 s(active(X:S)) -> s(X:S)
0.00/0.49	 s(mark(X:S)) -> s(X:S)
0.00/0.49	 zWadr(active(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.49	 zWadr(mark(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.00/0.49	 zWadr(X1:S,active(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.49	 zWadr(X1:S,mark(X2:S)) -> zWadr(X1:S,X2:S)
0.00/0.49	->Interpretation type:
0.00/0.49	 Linear
0.00/0.49	->Coefficients:
0.00/0.49	 Natural Numbers
0.00/0.49	->Dimension:
0.00/0.49	 1
0.00/0.49	->Bound:
0.00/0.49	 2
0.00/0.49	->Interpretation:
0.00/0.49	 
0.00/0.49	[active](X) = X
0.00/0.49	[app](X1,X2) = 2.X1 + 2.X2 + 2
0.00/0.49	[cons](X1,X2) = X1 + 2
0.00/0.49	[from](X) = 2.X + 2
0.00/0.49	[mark](X) = X
0.00/0.49	[prefix](X) = 2.X + 2
0.00/0.49	[s](X) = 2.X + 1
0.00/0.49	[zWadr](X1,X2) = 2.X1 + 2.X2 + 1
0.00/0.49	[fSNonEmpty] = 0
0.00/0.49	[nil] = 0
0.00/0.49	[ACTIVE](X) = 2.X + 2
0.00/0.49	[APP](X1,X2) = 0
0.00/0.49	[CONS](X1,X2) = 0
0.00/0.49	[FROM](X) = 0
0.00/0.49	[MARK](X) = 2.X + 2
0.00/0.49	[PREFIX](X) = 0
0.00/0.49	[S](X) = 0
0.00/0.49	[ZWADR](X1,X2) = 0
0.00/0.49	
0.00/0.49	Problem 1.7: 
0.00/0.49	
0.00/0.49	SCC Processor:
0.00/0.49	-> Pairs:
0.00/0.49	 ACTIVE(from(X:S)) -> MARK(cons(X:S,from(s(X:S))))
0.00/0.49	 ACTIVE(prefix(L:S)) -> MARK(cons(nil,zWadr(L:S,prefix(L:S))))
0.00/0.49	 ACTIVE(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> MARK(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.00/0.49	 MARK(app(X1:S,X2:S)) -> ACTIVE(app(mark(X1:S),mark(X2:S)))
0.47/0.49	 MARK(app(X1:S,X2:S)) -> MARK(X1:S)
0.47/0.49	 MARK(app(X1:S,X2:S)) -> MARK(X2:S)
0.47/0.49	 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S))
0.47/0.49	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.47/0.49	 MARK(from(X:S)) -> ACTIVE(from(mark(X:S)))
0.47/0.49	 MARK(from(X:S)) -> MARK(X:S)
0.47/0.49	 MARK(prefix(X:S)) -> ACTIVE(prefix(mark(X:S)))
0.47/0.49	 MARK(prefix(X:S)) -> MARK(X:S)
0.47/0.49	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.47/0.49	 MARK(s(X:S)) -> MARK(X:S)
0.47/0.49	 MARK(zWadr(X1:S,X2:S)) -> ACTIVE(zWadr(mark(X1:S),mark(X2:S)))
0.47/0.49	 MARK(zWadr(X1:S,X2:S)) -> MARK(X1:S)
0.47/0.49	 MARK(zWadr(X1:S,X2:S)) -> MARK(X2:S)
0.47/0.49	-> Rules:
0.47/0.49	 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S)))
0.47/0.49	 active(app(nil,YS:S)) -> mark(YS:S)
0.47/0.49	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.47/0.49	 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S))))
0.47/0.49	 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.47/0.49	 active(zWadr(nil,YS:S)) -> mark(nil)
0.47/0.49	 active(zWadr(XS:S,nil)) -> mark(nil)
0.47/0.49	 app(active(X1:S),X2:S) -> app(X1:S,X2:S)
0.47/0.49	 app(mark(X1:S),X2:S) -> app(X1:S,X2:S)
0.47/0.49	 app(X1:S,active(X2:S)) -> app(X1:S,X2:S)
0.47/0.49	 app(X1:S,mark(X2:S)) -> app(X1:S,X2:S)
0.47/0.49	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.47/0.49	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.47/0.49	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.47/0.49	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.47/0.49	 from(active(X:S)) -> from(X:S)
0.47/0.49	 from(mark(X:S)) -> from(X:S)
0.47/0.49	 mark(app(X1:S,X2:S)) -> active(app(mark(X1:S),mark(X2:S)))
0.47/0.49	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.47/0.49	 mark(from(X:S)) -> active(from(mark(X:S)))
0.47/0.49	 mark(prefix(X:S)) -> active(prefix(mark(X:S)))
0.47/0.49	 mark(s(X:S)) -> active(s(mark(X:S)))
0.47/0.49	 mark(zWadr(X1:S,X2:S)) -> active(zWadr(mark(X1:S),mark(X2:S)))
0.47/0.49	 mark(nil) -> active(nil)
0.47/0.49	 prefix(active(X:S)) -> prefix(X:S)
0.47/0.49	 prefix(mark(X:S)) -> prefix(X:S)
0.47/0.49	 s(active(X:S)) -> s(X:S)
0.47/0.49	 s(mark(X:S)) -> s(X:S)
0.47/0.49	 zWadr(active(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.47/0.49	 zWadr(mark(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.47/0.49	 zWadr(X1:S,active(X2:S)) -> zWadr(X1:S,X2:S)
0.47/0.49	 zWadr(X1:S,mark(X2:S)) -> zWadr(X1:S,X2:S)
0.47/0.49	->Strongly Connected Components:
0.47/0.49	->->Cycle:
0.47/0.49	->->-> Pairs:
0.47/0.49	 ACTIVE(from(X:S)) -> MARK(cons(X:S,from(s(X:S))))
0.47/0.49	 ACTIVE(prefix(L:S)) -> MARK(cons(nil,zWadr(L:S,prefix(L:S))))
0.47/0.49	 ACTIVE(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> MARK(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.47/0.49	 MARK(app(X1:S,X2:S)) -> ACTIVE(app(mark(X1:S),mark(X2:S)))
0.47/0.49	 MARK(app(X1:S,X2:S)) -> MARK(X1:S)
0.47/0.49	 MARK(app(X1:S,X2:S)) -> MARK(X2:S)
0.47/0.49	 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S))
0.47/0.49	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.47/0.49	 MARK(from(X:S)) -> ACTIVE(from(mark(X:S)))
0.47/0.49	 MARK(from(X:S)) -> MARK(X:S)
0.47/0.49	 MARK(prefix(X:S)) -> ACTIVE(prefix(mark(X:S)))
0.47/0.49	 MARK(prefix(X:S)) -> MARK(X:S)
0.47/0.49	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.47/0.49	 MARK(s(X:S)) -> MARK(X:S)
0.47/0.49	 MARK(zWadr(X1:S,X2:S)) -> ACTIVE(zWadr(mark(X1:S),mark(X2:S)))
0.47/0.49	 MARK(zWadr(X1:S,X2:S)) -> MARK(X1:S)
0.47/0.49	 MARK(zWadr(X1:S,X2:S)) -> MARK(X2:S)
0.47/0.49	->->-> Rules:
0.47/0.49	 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S)))
0.47/0.49	 active(app(nil,YS:S)) -> mark(YS:S)
0.47/0.49	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.47/0.49	 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S))))
0.47/0.49	 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.47/0.49	 active(zWadr(nil,YS:S)) -> mark(nil)
0.47/0.49	 active(zWadr(XS:S,nil)) -> mark(nil)
0.47/0.49	 app(active(X1:S),X2:S) -> app(X1:S,X2:S)
0.47/0.49	 app(mark(X1:S),X2:S) -> app(X1:S,X2:S)
0.47/0.49	 app(X1:S,active(X2:S)) -> app(X1:S,X2:S)
0.47/0.49	 app(X1:S,mark(X2:S)) -> app(X1:S,X2:S)
0.47/0.49	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.47/0.49	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.47/0.49	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.47/0.49	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.47/0.49	 from(active(X:S)) -> from(X:S)
0.47/0.49	 from(mark(X:S)) -> from(X:S)
0.47/0.49	 mark(app(X1:S,X2:S)) -> active(app(mark(X1:S),mark(X2:S)))
0.47/0.49	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.47/0.49	 mark(from(X:S)) -> active(from(mark(X:S)))
0.47/0.49	 mark(prefix(X:S)) -> active(prefix(mark(X:S)))
0.47/0.49	 mark(s(X:S)) -> active(s(mark(X:S)))
0.47/0.49	 mark(zWadr(X1:S,X2:S)) -> active(zWadr(mark(X1:S),mark(X2:S)))
0.47/0.49	 mark(nil) -> active(nil)
0.47/0.49	 prefix(active(X:S)) -> prefix(X:S)
0.47/0.49	 prefix(mark(X:S)) -> prefix(X:S)
0.47/0.49	 s(active(X:S)) -> s(X:S)
0.47/0.49	 s(mark(X:S)) -> s(X:S)
0.47/0.49	 zWadr(active(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.47/0.49	 zWadr(mark(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.47/0.49	 zWadr(X1:S,active(X2:S)) -> zWadr(X1:S,X2:S)
0.47/0.49	 zWadr(X1:S,mark(X2:S)) -> zWadr(X1:S,X2:S)
0.47/0.49	
0.47/0.49	Problem 1.7: 
0.47/0.49	
0.47/0.49	Reduction Pairs Processor:
0.47/0.49	-> Pairs:
0.47/0.49	 ACTIVE(from(X:S)) -> MARK(cons(X:S,from(s(X:S))))
0.47/0.49	 ACTIVE(prefix(L:S)) -> MARK(cons(nil,zWadr(L:S,prefix(L:S))))
0.47/0.49	 ACTIVE(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> MARK(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.47/0.49	 MARK(app(X1:S,X2:S)) -> ACTIVE(app(mark(X1:S),mark(X2:S)))
0.47/0.49	 MARK(app(X1:S,X2:S)) -> MARK(X1:S)
0.47/0.49	 MARK(app(X1:S,X2:S)) -> MARK(X2:S)
0.47/0.49	 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S))
0.47/0.49	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.47/0.49	 MARK(from(X:S)) -> ACTIVE(from(mark(X:S)))
0.47/0.49	 MARK(from(X:S)) -> MARK(X:S)
0.47/0.49	 MARK(prefix(X:S)) -> ACTIVE(prefix(mark(X:S)))
0.47/0.49	 MARK(prefix(X:S)) -> MARK(X:S)
0.47/0.49	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.47/0.49	 MARK(s(X:S)) -> MARK(X:S)
0.47/0.49	 MARK(zWadr(X1:S,X2:S)) -> ACTIVE(zWadr(mark(X1:S),mark(X2:S)))
0.47/0.49	 MARK(zWadr(X1:S,X2:S)) -> MARK(X1:S)
0.47/0.49	 MARK(zWadr(X1:S,X2:S)) -> MARK(X2:S)
0.47/0.49	-> Rules:
0.47/0.49	 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S)))
0.47/0.49	 active(app(nil,YS:S)) -> mark(YS:S)
0.47/0.49	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.47/0.49	 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S))))
0.47/0.49	 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.47/0.49	 active(zWadr(nil,YS:S)) -> mark(nil)
0.47/0.49	 active(zWadr(XS:S,nil)) -> mark(nil)
0.47/0.49	 app(active(X1:S),X2:S) -> app(X1:S,X2:S)
0.47/0.49	 app(mark(X1:S),X2:S) -> app(X1:S,X2:S)
0.47/0.49	 app(X1:S,active(X2:S)) -> app(X1:S,X2:S)
0.47/0.49	 app(X1:S,mark(X2:S)) -> app(X1:S,X2:S)
0.47/0.49	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.47/0.49	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.47/0.49	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.47/0.49	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.47/0.49	 from(active(X:S)) -> from(X:S)
0.47/0.49	 from(mark(X:S)) -> from(X:S)
0.47/0.49	 mark(app(X1:S,X2:S)) -> active(app(mark(X1:S),mark(X2:S)))
0.47/0.49	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.47/0.49	 mark(from(X:S)) -> active(from(mark(X:S)))
0.47/0.49	 mark(prefix(X:S)) -> active(prefix(mark(X:S)))
0.47/0.49	 mark(s(X:S)) -> active(s(mark(X:S)))
0.47/0.49	 mark(zWadr(X1:S,X2:S)) -> active(zWadr(mark(X1:S),mark(X2:S)))
0.47/0.49	 mark(nil) -> active(nil)
0.47/0.49	 prefix(active(X:S)) -> prefix(X:S)
0.47/0.49	 prefix(mark(X:S)) -> prefix(X:S)
0.47/0.49	 s(active(X:S)) -> s(X:S)
0.47/0.49	 s(mark(X:S)) -> s(X:S)
0.47/0.49	 zWadr(active(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.47/0.49	 zWadr(mark(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.47/0.49	 zWadr(X1:S,active(X2:S)) -> zWadr(X1:S,X2:S)
0.47/0.49	 zWadr(X1:S,mark(X2:S)) -> zWadr(X1:S,X2:S)
0.47/0.49	-> Usable rules:
0.47/0.49	 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S)))
0.47/0.49	 active(app(nil,YS:S)) -> mark(YS:S)
0.47/0.49	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.47/0.49	 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S))))
0.47/0.49	 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.47/0.49	 active(zWadr(nil,YS:S)) -> mark(nil)
0.47/0.49	 active(zWadr(XS:S,nil)) -> mark(nil)
0.47/0.49	 app(active(X1:S),X2:S) -> app(X1:S,X2:S)
0.47/0.49	 app(mark(X1:S),X2:S) -> app(X1:S,X2:S)
0.47/0.49	 app(X1:S,active(X2:S)) -> app(X1:S,X2:S)
0.47/0.49	 app(X1:S,mark(X2:S)) -> app(X1:S,X2:S)
0.47/0.49	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.47/0.49	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.47/0.49	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.47/0.49	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.47/0.49	 from(active(X:S)) -> from(X:S)
0.47/0.49	 from(mark(X:S)) -> from(X:S)
0.47/0.49	 mark(app(X1:S,X2:S)) -> active(app(mark(X1:S),mark(X2:S)))
0.47/0.49	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.47/0.49	 mark(from(X:S)) -> active(from(mark(X:S)))
0.47/0.49	 mark(prefix(X:S)) -> active(prefix(mark(X:S)))
0.47/0.49	 mark(s(X:S)) -> active(s(mark(X:S)))
0.47/0.49	 mark(zWadr(X1:S,X2:S)) -> active(zWadr(mark(X1:S),mark(X2:S)))
0.47/0.49	 mark(nil) -> active(nil)
0.47/0.49	 prefix(active(X:S)) -> prefix(X:S)
0.47/0.49	 prefix(mark(X:S)) -> prefix(X:S)
0.47/0.49	 s(active(X:S)) -> s(X:S)
0.47/0.49	 s(mark(X:S)) -> s(X:S)
0.47/0.49	 zWadr(active(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.47/0.49	 zWadr(mark(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.47/0.49	 zWadr(X1:S,active(X2:S)) -> zWadr(X1:S,X2:S)
0.47/0.49	 zWadr(X1:S,mark(X2:S)) -> zWadr(X1:S,X2:S)
0.47/0.49	->Interpretation type:
0.47/0.49	 Linear
0.47/0.49	->Coefficients:
0.47/0.49	 Natural Numbers
0.47/0.49	->Dimension:
0.47/0.49	 1
0.47/0.49	->Bound:
0.47/0.49	 2
0.47/0.49	->Interpretation:
0.47/0.49	 
0.47/0.49	[active](X) = X
0.47/0.49	[app](X1,X2) = 2.X1 + X2
0.47/0.49	[cons](X1,X2) = 2.X1 + 1
0.47/0.49	[from](X) = 2.X + 2
0.47/0.49	[mark](X) = X
0.47/0.49	[prefix](X) = 2.X + 2
0.47/0.49	[s](X) = 2.X + 2
0.47/0.49	[zWadr](X1,X2) = 2.X1 + 2.X2 + 1
0.47/0.49	[fSNonEmpty] = 0
0.47/0.49	[nil] = 0
0.47/0.49	[ACTIVE](X) = 2.X + 2
0.47/0.49	[APP](X1,X2) = 0
0.47/0.49	[CONS](X1,X2) = 0
0.47/0.49	[FROM](X) = 0
0.47/0.49	[MARK](X) = 2.X + 2
0.47/0.49	[PREFIX](X) = 0
0.47/0.49	[S](X) = 0
0.47/0.49	[ZWADR](X1,X2) = 0
0.47/0.49	
0.47/0.49	Problem 1.7: 
0.47/0.49	
0.47/0.49	SCC Processor:
0.47/0.49	-> Pairs:
0.47/0.49	 ACTIVE(prefix(L:S)) -> MARK(cons(nil,zWadr(L:S,prefix(L:S))))
0.47/0.49	 ACTIVE(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> MARK(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.47/0.49	 MARK(app(X1:S,X2:S)) -> ACTIVE(app(mark(X1:S),mark(X2:S)))
0.47/0.49	 MARK(app(X1:S,X2:S)) -> MARK(X1:S)
0.47/0.49	 MARK(app(X1:S,X2:S)) -> MARK(X2:S)
0.47/0.49	 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S))
0.47/0.49	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.47/0.49	 MARK(from(X:S)) -> ACTIVE(from(mark(X:S)))
0.47/0.49	 MARK(from(X:S)) -> MARK(X:S)
0.47/0.49	 MARK(prefix(X:S)) -> ACTIVE(prefix(mark(X:S)))
0.47/0.49	 MARK(prefix(X:S)) -> MARK(X:S)
0.47/0.49	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.47/0.49	 MARK(s(X:S)) -> MARK(X:S)
0.47/0.49	 MARK(zWadr(X1:S,X2:S)) -> ACTIVE(zWadr(mark(X1:S),mark(X2:S)))
0.47/0.49	 MARK(zWadr(X1:S,X2:S)) -> MARK(X1:S)
0.47/0.49	 MARK(zWadr(X1:S,X2:S)) -> MARK(X2:S)
0.47/0.49	-> Rules:
0.47/0.49	 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S)))
0.47/0.49	 active(app(nil,YS:S)) -> mark(YS:S)
0.47/0.49	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.47/0.49	 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S))))
0.47/0.49	 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.47/0.49	 active(zWadr(nil,YS:S)) -> mark(nil)
0.47/0.49	 active(zWadr(XS:S,nil)) -> mark(nil)
0.47/0.49	 app(active(X1:S),X2:S) -> app(X1:S,X2:S)
0.47/0.49	 app(mark(X1:S),X2:S) -> app(X1:S,X2:S)
0.47/0.49	 app(X1:S,active(X2:S)) -> app(X1:S,X2:S)
0.47/0.49	 app(X1:S,mark(X2:S)) -> app(X1:S,X2:S)
0.47/0.49	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.47/0.49	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.47/0.49	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.47/0.49	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.47/0.49	 from(active(X:S)) -> from(X:S)
0.47/0.49	 from(mark(X:S)) -> from(X:S)
0.47/0.49	 mark(app(X1:S,X2:S)) -> active(app(mark(X1:S),mark(X2:S)))
0.47/0.49	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.47/0.49	 mark(from(X:S)) -> active(from(mark(X:S)))
0.47/0.49	 mark(prefix(X:S)) -> active(prefix(mark(X:S)))
0.47/0.49	 mark(s(X:S)) -> active(s(mark(X:S)))
0.47/0.49	 mark(zWadr(X1:S,X2:S)) -> active(zWadr(mark(X1:S),mark(X2:S)))
0.47/0.49	 mark(nil) -> active(nil)
0.47/0.49	 prefix(active(X:S)) -> prefix(X:S)
0.47/0.49	 prefix(mark(X:S)) -> prefix(X:S)
0.47/0.49	 s(active(X:S)) -> s(X:S)
0.47/0.49	 s(mark(X:S)) -> s(X:S)
0.47/0.49	 zWadr(active(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.47/0.49	 zWadr(mark(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.47/0.49	 zWadr(X1:S,active(X2:S)) -> zWadr(X1:S,X2:S)
0.47/0.49	 zWadr(X1:S,mark(X2:S)) -> zWadr(X1:S,X2:S)
0.47/0.49	->Strongly Connected Components:
0.47/0.49	->->Cycle:
0.47/0.49	->->-> Pairs:
0.47/0.49	 ACTIVE(prefix(L:S)) -> MARK(cons(nil,zWadr(L:S,prefix(L:S))))
0.47/0.49	 ACTIVE(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> MARK(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.47/0.49	 MARK(app(X1:S,X2:S)) -> ACTIVE(app(mark(X1:S),mark(X2:S)))
0.47/0.49	 MARK(app(X1:S,X2:S)) -> MARK(X1:S)
0.47/0.49	 MARK(app(X1:S,X2:S)) -> MARK(X2:S)
0.47/0.49	 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S))
0.47/0.49	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.47/0.49	 MARK(from(X:S)) -> ACTIVE(from(mark(X:S)))
0.47/0.49	 MARK(from(X:S)) -> MARK(X:S)
0.47/0.49	 MARK(prefix(X:S)) -> ACTIVE(prefix(mark(X:S)))
0.47/0.49	 MARK(prefix(X:S)) -> MARK(X:S)
0.47/0.49	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.47/0.49	 MARK(s(X:S)) -> MARK(X:S)
0.47/0.49	 MARK(zWadr(X1:S,X2:S)) -> ACTIVE(zWadr(mark(X1:S),mark(X2:S)))
0.47/0.49	 MARK(zWadr(X1:S,X2:S)) -> MARK(X1:S)
0.47/0.49	 MARK(zWadr(X1:S,X2:S)) -> MARK(X2:S)
0.47/0.49	->->-> Rules:
0.47/0.49	 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S)))
0.47/0.49	 active(app(nil,YS:S)) -> mark(YS:S)
0.47/0.49	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.47/0.49	 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S))))
0.47/0.49	 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.47/0.49	 active(zWadr(nil,YS:S)) -> mark(nil)
0.47/0.49	 active(zWadr(XS:S,nil)) -> mark(nil)
0.47/0.49	 app(active(X1:S),X2:S) -> app(X1:S,X2:S)
0.47/0.49	 app(mark(X1:S),X2:S) -> app(X1:S,X2:S)
0.47/0.49	 app(X1:S,active(X2:S)) -> app(X1:S,X2:S)
0.47/0.49	 app(X1:S,mark(X2:S)) -> app(X1:S,X2:S)
0.47/0.49	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.47/0.49	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.47/0.49	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.47/0.49	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.47/0.49	 from(active(X:S)) -> from(X:S)
0.47/0.49	 from(mark(X:S)) -> from(X:S)
0.47/0.49	 mark(app(X1:S,X2:S)) -> active(app(mark(X1:S),mark(X2:S)))
0.47/0.49	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.47/0.49	 mark(from(X:S)) -> active(from(mark(X:S)))
0.47/0.49	 mark(prefix(X:S)) -> active(prefix(mark(X:S)))
0.47/0.49	 mark(s(X:S)) -> active(s(mark(X:S)))
0.47/0.49	 mark(zWadr(X1:S,X2:S)) -> active(zWadr(mark(X1:S),mark(X2:S)))
0.47/0.49	 mark(nil) -> active(nil)
0.47/0.49	 prefix(active(X:S)) -> prefix(X:S)
0.47/0.49	 prefix(mark(X:S)) -> prefix(X:S)
0.47/0.49	 s(active(X:S)) -> s(X:S)
0.47/0.49	 s(mark(X:S)) -> s(X:S)
0.47/0.49	 zWadr(active(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.47/0.49	 zWadr(mark(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.47/0.49	 zWadr(X1:S,active(X2:S)) -> zWadr(X1:S,X2:S)
0.47/0.49	 zWadr(X1:S,mark(X2:S)) -> zWadr(X1:S,X2:S)
0.47/0.49	
0.47/0.49	Problem 1.7: 
0.47/0.49	
0.47/0.49	Reduction Pairs Processor:
0.47/0.49	-> Pairs:
0.47/0.49	 ACTIVE(prefix(L:S)) -> MARK(cons(nil,zWadr(L:S,prefix(L:S))))
0.47/0.49	 ACTIVE(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> MARK(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.47/0.49	 MARK(app(X1:S,X2:S)) -> ACTIVE(app(mark(X1:S),mark(X2:S)))
0.47/0.49	 MARK(app(X1:S,X2:S)) -> MARK(X1:S)
0.47/0.49	 MARK(app(X1:S,X2:S)) -> MARK(X2:S)
0.47/0.49	 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S))
0.47/0.49	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.47/0.49	 MARK(from(X:S)) -> ACTIVE(from(mark(X:S)))
0.47/0.49	 MARK(from(X:S)) -> MARK(X:S)
0.47/0.49	 MARK(prefix(X:S)) -> ACTIVE(prefix(mark(X:S)))
0.47/0.49	 MARK(prefix(X:S)) -> MARK(X:S)
0.47/0.49	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.47/0.49	 MARK(s(X:S)) -> MARK(X:S)
0.47/0.49	 MARK(zWadr(X1:S,X2:S)) -> ACTIVE(zWadr(mark(X1:S),mark(X2:S)))
0.47/0.49	 MARK(zWadr(X1:S,X2:S)) -> MARK(X1:S)
0.47/0.49	 MARK(zWadr(X1:S,X2:S)) -> MARK(X2:S)
0.47/0.49	-> Rules:
0.47/0.49	 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S)))
0.47/0.49	 active(app(nil,YS:S)) -> mark(YS:S)
0.47/0.49	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.47/0.49	 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S))))
0.47/0.49	 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.47/0.49	 active(zWadr(nil,YS:S)) -> mark(nil)
0.47/0.49	 active(zWadr(XS:S,nil)) -> mark(nil)
0.47/0.49	 app(active(X1:S),X2:S) -> app(X1:S,X2:S)
0.47/0.49	 app(mark(X1:S),X2:S) -> app(X1:S,X2:S)
0.47/0.49	 app(X1:S,active(X2:S)) -> app(X1:S,X2:S)
0.47/0.49	 app(X1:S,mark(X2:S)) -> app(X1:S,X2:S)
0.47/0.49	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.47/0.49	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.47/0.49	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.47/0.49	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.47/0.49	 from(active(X:S)) -> from(X:S)
0.47/0.49	 from(mark(X:S)) -> from(X:S)
0.47/0.49	 mark(app(X1:S,X2:S)) -> active(app(mark(X1:S),mark(X2:S)))
0.47/0.49	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.47/0.49	 mark(from(X:S)) -> active(from(mark(X:S)))
0.47/0.49	 mark(prefix(X:S)) -> active(prefix(mark(X:S)))
0.47/0.49	 mark(s(X:S)) -> active(s(mark(X:S)))
0.47/0.49	 mark(zWadr(X1:S,X2:S)) -> active(zWadr(mark(X1:S),mark(X2:S)))
0.47/0.49	 mark(nil) -> active(nil)
0.47/0.49	 prefix(active(X:S)) -> prefix(X:S)
0.47/0.49	 prefix(mark(X:S)) -> prefix(X:S)
0.47/0.49	 s(active(X:S)) -> s(X:S)
0.47/0.49	 s(mark(X:S)) -> s(X:S)
0.47/0.49	 zWadr(active(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.47/0.49	 zWadr(mark(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.47/0.49	 zWadr(X1:S,active(X2:S)) -> zWadr(X1:S,X2:S)
0.47/0.49	 zWadr(X1:S,mark(X2:S)) -> zWadr(X1:S,X2:S)
0.47/0.49	-> Usable rules:
0.47/0.49	 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S)))
0.47/0.49	 active(app(nil,YS:S)) -> mark(YS:S)
0.47/0.49	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.47/0.49	 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S))))
0.47/0.49	 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.47/0.49	 active(zWadr(nil,YS:S)) -> mark(nil)
0.47/0.49	 active(zWadr(XS:S,nil)) -> mark(nil)
0.47/0.49	 app(active(X1:S),X2:S) -> app(X1:S,X2:S)
0.47/0.49	 app(mark(X1:S),X2:S) -> app(X1:S,X2:S)
0.47/0.49	 app(X1:S,active(X2:S)) -> app(X1:S,X2:S)
0.47/0.49	 app(X1:S,mark(X2:S)) -> app(X1:S,X2:S)
0.47/0.49	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.47/0.49	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.47/0.49	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.47/0.49	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.47/0.49	 from(active(X:S)) -> from(X:S)
0.47/0.49	 from(mark(X:S)) -> from(X:S)
0.47/0.49	 mark(app(X1:S,X2:S)) -> active(app(mark(X1:S),mark(X2:S)))
0.47/0.49	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.47/0.49	 mark(from(X:S)) -> active(from(mark(X:S)))
0.47/0.49	 mark(prefix(X:S)) -> active(prefix(mark(X:S)))
0.47/0.49	 mark(s(X:S)) -> active(s(mark(X:S)))
0.47/0.49	 mark(zWadr(X1:S,X2:S)) -> active(zWadr(mark(X1:S),mark(X2:S)))
0.47/0.49	 mark(nil) -> active(nil)
0.47/0.49	 prefix(active(X:S)) -> prefix(X:S)
0.47/0.49	 prefix(mark(X:S)) -> prefix(X:S)
0.47/0.49	 s(active(X:S)) -> s(X:S)
0.47/0.49	 s(mark(X:S)) -> s(X:S)
0.47/0.49	 zWadr(active(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.47/0.49	 zWadr(mark(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.47/0.49	 zWadr(X1:S,active(X2:S)) -> zWadr(X1:S,X2:S)
0.47/0.49	 zWadr(X1:S,mark(X2:S)) -> zWadr(X1:S,X2:S)
0.47/0.49	->Interpretation type:
0.47/0.49	 Linear
0.47/0.49	->Coefficients:
0.47/0.49	 Natural Numbers
0.47/0.49	->Dimension:
0.47/0.49	 1
0.47/0.49	->Bound:
0.47/0.49	 2
0.47/0.49	->Interpretation:
0.47/0.49	 
0.47/0.49	[active](X) = X
0.47/0.49	[app](X1,X2) = 2.X1 + 2.X2
0.47/0.49	[cons](X1,X2) = X1 + 1
0.47/0.49	[from](X) = X + 1
0.47/0.49	[mark](X) = X
0.47/0.49	[prefix](X) = 2.X + 2
0.47/0.49	[s](X) = 2.X + 1
0.47/0.49	[zWadr](X1,X2) = 2.X1 + 2.X2 + 2
0.47/0.49	[fSNonEmpty] = 0
0.47/0.49	[nil] = 0
0.47/0.49	[ACTIVE](X) = 2.X + 2
0.47/0.49	[APP](X1,X2) = 0
0.47/0.49	[CONS](X1,X2) = 0
0.47/0.49	[FROM](X) = 0
0.47/0.49	[MARK](X) = 2.X + 2
0.47/0.49	[PREFIX](X) = 0
0.47/0.49	[S](X) = 0
0.47/0.49	[ZWADR](X1,X2) = 0
0.47/0.49	
0.47/0.49	Problem 1.7: 
0.47/0.49	
0.47/0.49	SCC Processor:
0.47/0.49	-> Pairs:
0.47/0.49	 ACTIVE(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> MARK(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.47/0.49	 MARK(app(X1:S,X2:S)) -> ACTIVE(app(mark(X1:S),mark(X2:S)))
0.47/0.49	 MARK(app(X1:S,X2:S)) -> MARK(X1:S)
0.47/0.49	 MARK(app(X1:S,X2:S)) -> MARK(X2:S)
0.47/0.49	 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S))
0.47/0.49	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.47/0.49	 MARK(from(X:S)) -> ACTIVE(from(mark(X:S)))
0.47/0.49	 MARK(from(X:S)) -> MARK(X:S)
0.47/0.49	 MARK(prefix(X:S)) -> ACTIVE(prefix(mark(X:S)))
0.47/0.49	 MARK(prefix(X:S)) -> MARK(X:S)
0.47/0.49	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.47/0.49	 MARK(s(X:S)) -> MARK(X:S)
0.47/0.49	 MARK(zWadr(X1:S,X2:S)) -> ACTIVE(zWadr(mark(X1:S),mark(X2:S)))
0.47/0.49	 MARK(zWadr(X1:S,X2:S)) -> MARK(X1:S)
0.47/0.49	 MARK(zWadr(X1:S,X2:S)) -> MARK(X2:S)
0.47/0.49	-> Rules:
0.47/0.49	 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S)))
0.47/0.49	 active(app(nil,YS:S)) -> mark(YS:S)
0.47/0.49	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.47/0.49	 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S))))
0.47/0.49	 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.47/0.49	 active(zWadr(nil,YS:S)) -> mark(nil)
0.47/0.49	 active(zWadr(XS:S,nil)) -> mark(nil)
0.47/0.49	 app(active(X1:S),X2:S) -> app(X1:S,X2:S)
0.47/0.49	 app(mark(X1:S),X2:S) -> app(X1:S,X2:S)
0.47/0.49	 app(X1:S,active(X2:S)) -> app(X1:S,X2:S)
0.47/0.49	 app(X1:S,mark(X2:S)) -> app(X1:S,X2:S)
0.47/0.49	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.47/0.49	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.47/0.49	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.47/0.49	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.47/0.49	 from(active(X:S)) -> from(X:S)
0.47/0.49	 from(mark(X:S)) -> from(X:S)
0.47/0.49	 mark(app(X1:S,X2:S)) -> active(app(mark(X1:S),mark(X2:S)))
0.47/0.49	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.47/0.49	 mark(from(X:S)) -> active(from(mark(X:S)))
0.47/0.49	 mark(prefix(X:S)) -> active(prefix(mark(X:S)))
0.47/0.49	 mark(s(X:S)) -> active(s(mark(X:S)))
0.47/0.49	 mark(zWadr(X1:S,X2:S)) -> active(zWadr(mark(X1:S),mark(X2:S)))
0.47/0.49	 mark(nil) -> active(nil)
0.47/0.49	 prefix(active(X:S)) -> prefix(X:S)
0.47/0.49	 prefix(mark(X:S)) -> prefix(X:S)
0.47/0.49	 s(active(X:S)) -> s(X:S)
0.47/0.49	 s(mark(X:S)) -> s(X:S)
0.47/0.49	 zWadr(active(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.47/0.49	 zWadr(mark(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.47/0.49	 zWadr(X1:S,active(X2:S)) -> zWadr(X1:S,X2:S)
0.47/0.49	 zWadr(X1:S,mark(X2:S)) -> zWadr(X1:S,X2:S)
0.47/0.49	->Strongly Connected Components:
0.47/0.49	->->Cycle:
0.47/0.49	->->-> Pairs:
0.47/0.49	 ACTIVE(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> MARK(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.47/0.49	 MARK(app(X1:S,X2:S)) -> ACTIVE(app(mark(X1:S),mark(X2:S)))
0.47/0.49	 MARK(app(X1:S,X2:S)) -> MARK(X1:S)
0.47/0.49	 MARK(app(X1:S,X2:S)) -> MARK(X2:S)
0.47/0.49	 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S))
0.47/0.49	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.47/0.49	 MARK(from(X:S)) -> ACTIVE(from(mark(X:S)))
0.47/0.49	 MARK(from(X:S)) -> MARK(X:S)
0.47/0.49	 MARK(prefix(X:S)) -> ACTIVE(prefix(mark(X:S)))
0.47/0.49	 MARK(prefix(X:S)) -> MARK(X:S)
0.47/0.49	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.47/0.49	 MARK(s(X:S)) -> MARK(X:S)
0.47/0.49	 MARK(zWadr(X1:S,X2:S)) -> ACTIVE(zWadr(mark(X1:S),mark(X2:S)))
0.47/0.49	 MARK(zWadr(X1:S,X2:S)) -> MARK(X1:S)
0.47/0.49	 MARK(zWadr(X1:S,X2:S)) -> MARK(X2:S)
0.47/0.49	->->-> Rules:
0.47/0.49	 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S)))
0.47/0.49	 active(app(nil,YS:S)) -> mark(YS:S)
0.47/0.49	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.47/0.49	 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S))))
0.47/0.49	 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.47/0.49	 active(zWadr(nil,YS:S)) -> mark(nil)
0.47/0.49	 active(zWadr(XS:S,nil)) -> mark(nil)
0.47/0.49	 app(active(X1:S),X2:S) -> app(X1:S,X2:S)
0.47/0.49	 app(mark(X1:S),X2:S) -> app(X1:S,X2:S)
0.47/0.49	 app(X1:S,active(X2:S)) -> app(X1:S,X2:S)
0.47/0.49	 app(X1:S,mark(X2:S)) -> app(X1:S,X2:S)
0.47/0.49	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.47/0.49	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.47/0.49	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.47/0.49	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.47/0.49	 from(active(X:S)) -> from(X:S)
0.47/0.49	 from(mark(X:S)) -> from(X:S)
0.47/0.49	 mark(app(X1:S,X2:S)) -> active(app(mark(X1:S),mark(X2:S)))
0.47/0.49	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.47/0.49	 mark(from(X:S)) -> active(from(mark(X:S)))
0.47/0.49	 mark(prefix(X:S)) -> active(prefix(mark(X:S)))
0.47/0.49	 mark(s(X:S)) -> active(s(mark(X:S)))
0.47/0.49	 mark(zWadr(X1:S,X2:S)) -> active(zWadr(mark(X1:S),mark(X2:S)))
0.47/0.49	 mark(nil) -> active(nil)
0.47/0.49	 prefix(active(X:S)) -> prefix(X:S)
0.47/0.49	 prefix(mark(X:S)) -> prefix(X:S)
0.47/0.49	 s(active(X:S)) -> s(X:S)
0.47/0.49	 s(mark(X:S)) -> s(X:S)
0.47/0.49	 zWadr(active(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.47/0.49	 zWadr(mark(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.47/0.49	 zWadr(X1:S,active(X2:S)) -> zWadr(X1:S,X2:S)
0.47/0.49	 zWadr(X1:S,mark(X2:S)) -> zWadr(X1:S,X2:S)
0.47/0.49	
0.47/0.49	Problem 1.7: 
0.47/0.49	
0.47/0.49	Reduction Pairs Processor:
0.47/0.49	-> Pairs:
0.47/0.49	 ACTIVE(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> MARK(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.47/0.49	 MARK(app(X1:S,X2:S)) -> ACTIVE(app(mark(X1:S),mark(X2:S)))
0.47/0.49	 MARK(app(X1:S,X2:S)) -> MARK(X1:S)
0.47/0.49	 MARK(app(X1:S,X2:S)) -> MARK(X2:S)
0.47/0.49	 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S))
0.47/0.49	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.47/0.49	 MARK(from(X:S)) -> ACTIVE(from(mark(X:S)))
0.47/0.49	 MARK(from(X:S)) -> MARK(X:S)
0.47/0.49	 MARK(prefix(X:S)) -> ACTIVE(prefix(mark(X:S)))
0.47/0.49	 MARK(prefix(X:S)) -> MARK(X:S)
0.47/0.49	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.47/0.49	 MARK(s(X:S)) -> MARK(X:S)
0.47/0.49	 MARK(zWadr(X1:S,X2:S)) -> ACTIVE(zWadr(mark(X1:S),mark(X2:S)))
0.47/0.49	 MARK(zWadr(X1:S,X2:S)) -> MARK(X1:S)
0.47/0.49	 MARK(zWadr(X1:S,X2:S)) -> MARK(X2:S)
0.47/0.49	-> Rules:
0.47/0.49	 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S)))
0.47/0.49	 active(app(nil,YS:S)) -> mark(YS:S)
0.47/0.49	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.47/0.49	 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S))))
0.47/0.49	 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.47/0.49	 active(zWadr(nil,YS:S)) -> mark(nil)
0.47/0.49	 active(zWadr(XS:S,nil)) -> mark(nil)
0.47/0.49	 app(active(X1:S),X2:S) -> app(X1:S,X2:S)
0.47/0.49	 app(mark(X1:S),X2:S) -> app(X1:S,X2:S)
0.47/0.49	 app(X1:S,active(X2:S)) -> app(X1:S,X2:S)
0.47/0.49	 app(X1:S,mark(X2:S)) -> app(X1:S,X2:S)
0.47/0.49	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.47/0.49	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.47/0.49	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.47/0.49	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.47/0.49	 from(active(X:S)) -> from(X:S)
0.47/0.49	 from(mark(X:S)) -> from(X:S)
0.47/0.49	 mark(app(X1:S,X2:S)) -> active(app(mark(X1:S),mark(X2:S)))
0.47/0.49	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.47/0.49	 mark(from(X:S)) -> active(from(mark(X:S)))
0.47/0.49	 mark(prefix(X:S)) -> active(prefix(mark(X:S)))
0.47/0.49	 mark(s(X:S)) -> active(s(mark(X:S)))
0.47/0.49	 mark(zWadr(X1:S,X2:S)) -> active(zWadr(mark(X1:S),mark(X2:S)))
0.47/0.49	 mark(nil) -> active(nil)
0.47/0.49	 prefix(active(X:S)) -> prefix(X:S)
0.47/0.49	 prefix(mark(X:S)) -> prefix(X:S)
0.47/0.49	 s(active(X:S)) -> s(X:S)
0.47/0.49	 s(mark(X:S)) -> s(X:S)
0.47/0.49	 zWadr(active(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.47/0.49	 zWadr(mark(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.47/0.49	 zWadr(X1:S,active(X2:S)) -> zWadr(X1:S,X2:S)
0.47/0.49	 zWadr(X1:S,mark(X2:S)) -> zWadr(X1:S,X2:S)
0.47/0.49	-> Usable rules:
0.47/0.49	 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S)))
0.47/0.49	 active(app(nil,YS:S)) -> mark(YS:S)
0.47/0.49	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.47/0.49	 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S))))
0.47/0.49	 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.47/0.49	 active(zWadr(nil,YS:S)) -> mark(nil)
0.47/0.49	 active(zWadr(XS:S,nil)) -> mark(nil)
0.47/0.49	 app(active(X1:S),X2:S) -> app(X1:S,X2:S)
0.47/0.49	 app(mark(X1:S),X2:S) -> app(X1:S,X2:S)
0.47/0.49	 app(X1:S,active(X2:S)) -> app(X1:S,X2:S)
0.47/0.49	 app(X1:S,mark(X2:S)) -> app(X1:S,X2:S)
0.47/0.49	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.47/0.49	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.47/0.49	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.47/0.49	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.47/0.49	 from(active(X:S)) -> from(X:S)
0.47/0.49	 from(mark(X:S)) -> from(X:S)
0.47/0.49	 mark(app(X1:S,X2:S)) -> active(app(mark(X1:S),mark(X2:S)))
0.47/0.49	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.47/0.49	 mark(from(X:S)) -> active(from(mark(X:S)))
0.47/0.49	 mark(prefix(X:S)) -> active(prefix(mark(X:S)))
0.47/0.49	 mark(s(X:S)) -> active(s(mark(X:S)))
0.47/0.49	 mark(zWadr(X1:S,X2:S)) -> active(zWadr(mark(X1:S),mark(X2:S)))
0.47/0.49	 mark(nil) -> active(nil)
0.47/0.49	 prefix(active(X:S)) -> prefix(X:S)
0.47/0.49	 prefix(mark(X:S)) -> prefix(X:S)
0.47/0.49	 s(active(X:S)) -> s(X:S)
0.47/0.49	 s(mark(X:S)) -> s(X:S)
0.47/0.49	 zWadr(active(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.47/0.49	 zWadr(mark(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.47/0.49	 zWadr(X1:S,active(X2:S)) -> zWadr(X1:S,X2:S)
0.47/0.49	 zWadr(X1:S,mark(X2:S)) -> zWadr(X1:S,X2:S)
0.47/0.49	->Interpretation type:
0.47/0.49	 Linear
0.47/0.49	->Coefficients:
0.47/0.49	 Natural Numbers
0.47/0.49	->Dimension:
0.47/0.49	 1
0.47/0.49	->Bound:
0.47/0.49	 2
0.47/0.49	->Interpretation:
0.47/0.49	 
0.47/0.49	[active](X) = X
0.47/0.49	[app](X1,X2) = 2.X1 + X2
0.47/0.49	[cons](X1,X2) = 2.X1
0.47/0.49	[from](X) = 2.X + 2
0.47/0.49	[mark](X) = X
0.47/0.49	[prefix](X) = 2.X + 1
0.47/0.49	[s](X) = 2.X + 2
0.47/0.49	[zWadr](X1,X2) = 2.X1 + 2.X2 + 2
0.47/0.49	[fSNonEmpty] = 0
0.47/0.49	[nil] = 0
0.47/0.49	[ACTIVE](X) = 2.X
0.47/0.49	[APP](X1,X2) = 0
0.47/0.49	[CONS](X1,X2) = 0
0.47/0.49	[FROM](X) = 0
0.47/0.49	[MARK](X) = 2.X
0.47/0.49	[PREFIX](X) = 0
0.47/0.49	[S](X) = 0
0.47/0.49	[ZWADR](X1,X2) = 0
0.47/0.49	
0.47/0.49	Problem 1.7: 
0.47/0.49	
0.47/0.49	SCC Processor:
0.47/0.49	-> Pairs:
0.47/0.49	 MARK(app(X1:S,X2:S)) -> ACTIVE(app(mark(X1:S),mark(X2:S)))
0.47/0.49	 MARK(app(X1:S,X2:S)) -> MARK(X1:S)
0.47/0.49	 MARK(app(X1:S,X2:S)) -> MARK(X2:S)
0.47/0.49	 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S))
0.47/0.49	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.47/0.49	 MARK(from(X:S)) -> ACTIVE(from(mark(X:S)))
0.47/0.49	 MARK(from(X:S)) -> MARK(X:S)
0.47/0.49	 MARK(prefix(X:S)) -> ACTIVE(prefix(mark(X:S)))
0.47/0.49	 MARK(prefix(X:S)) -> MARK(X:S)
0.47/0.49	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.47/0.49	 MARK(s(X:S)) -> MARK(X:S)
0.47/0.49	 MARK(zWadr(X1:S,X2:S)) -> ACTIVE(zWadr(mark(X1:S),mark(X2:S)))
0.47/0.49	 MARK(zWadr(X1:S,X2:S)) -> MARK(X1:S)
0.47/0.49	 MARK(zWadr(X1:S,X2:S)) -> MARK(X2:S)
0.47/0.49	-> Rules:
0.47/0.49	 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S)))
0.47/0.49	 active(app(nil,YS:S)) -> mark(YS:S)
0.47/0.49	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.47/0.49	 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S))))
0.47/0.49	 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.47/0.49	 active(zWadr(nil,YS:S)) -> mark(nil)
0.47/0.49	 active(zWadr(XS:S,nil)) -> mark(nil)
0.47/0.49	 app(active(X1:S),X2:S) -> app(X1:S,X2:S)
0.47/0.49	 app(mark(X1:S),X2:S) -> app(X1:S,X2:S)
0.47/0.49	 app(X1:S,active(X2:S)) -> app(X1:S,X2:S)
0.47/0.49	 app(X1:S,mark(X2:S)) -> app(X1:S,X2:S)
0.47/0.49	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.47/0.49	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.47/0.49	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.47/0.49	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.47/0.49	 from(active(X:S)) -> from(X:S)
0.47/0.49	 from(mark(X:S)) -> from(X:S)
0.47/0.49	 mark(app(X1:S,X2:S)) -> active(app(mark(X1:S),mark(X2:S)))
0.47/0.49	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.47/0.49	 mark(from(X:S)) -> active(from(mark(X:S)))
0.47/0.49	 mark(prefix(X:S)) -> active(prefix(mark(X:S)))
0.47/0.49	 mark(s(X:S)) -> active(s(mark(X:S)))
0.47/0.49	 mark(zWadr(X1:S,X2:S)) -> active(zWadr(mark(X1:S),mark(X2:S)))
0.47/0.49	 mark(nil) -> active(nil)
0.47/0.49	 prefix(active(X:S)) -> prefix(X:S)
0.47/0.49	 prefix(mark(X:S)) -> prefix(X:S)
0.47/0.49	 s(active(X:S)) -> s(X:S)
0.47/0.49	 s(mark(X:S)) -> s(X:S)
0.47/0.49	 zWadr(active(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.47/0.49	 zWadr(mark(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.47/0.49	 zWadr(X1:S,active(X2:S)) -> zWadr(X1:S,X2:S)
0.47/0.49	 zWadr(X1:S,mark(X2:S)) -> zWadr(X1:S,X2:S)
0.47/0.49	->Strongly Connected Components:
0.47/0.49	->->Cycle:
0.47/0.49	->->-> Pairs:
0.47/0.49	 MARK(app(X1:S,X2:S)) -> MARK(X1:S)
0.47/0.49	 MARK(app(X1:S,X2:S)) -> MARK(X2:S)
0.47/0.49	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.47/0.49	 MARK(from(X:S)) -> MARK(X:S)
0.47/0.49	 MARK(prefix(X:S)) -> MARK(X:S)
0.47/0.49	 MARK(s(X:S)) -> MARK(X:S)
0.47/0.49	 MARK(zWadr(X1:S,X2:S)) -> MARK(X1:S)
0.47/0.49	 MARK(zWadr(X1:S,X2:S)) -> MARK(X2:S)
0.47/0.49	->->-> Rules:
0.47/0.49	 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S)))
0.47/0.49	 active(app(nil,YS:S)) -> mark(YS:S)
0.47/0.49	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.47/0.49	 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S))))
0.47/0.49	 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.47/0.49	 active(zWadr(nil,YS:S)) -> mark(nil)
0.47/0.49	 active(zWadr(XS:S,nil)) -> mark(nil)
0.47/0.49	 app(active(X1:S),X2:S) -> app(X1:S,X2:S)
0.47/0.49	 app(mark(X1:S),X2:S) -> app(X1:S,X2:S)
0.47/0.49	 app(X1:S,active(X2:S)) -> app(X1:S,X2:S)
0.47/0.49	 app(X1:S,mark(X2:S)) -> app(X1:S,X2:S)
0.47/0.49	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.47/0.49	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.47/0.49	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.47/0.49	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.47/0.49	 from(active(X:S)) -> from(X:S)
0.47/0.49	 from(mark(X:S)) -> from(X:S)
0.47/0.49	 mark(app(X1:S,X2:S)) -> active(app(mark(X1:S),mark(X2:S)))
0.47/0.49	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.47/0.49	 mark(from(X:S)) -> active(from(mark(X:S)))
0.47/0.49	 mark(prefix(X:S)) -> active(prefix(mark(X:S)))
0.47/0.49	 mark(s(X:S)) -> active(s(mark(X:S)))
0.47/0.49	 mark(zWadr(X1:S,X2:S)) -> active(zWadr(mark(X1:S),mark(X2:S)))
0.47/0.49	 mark(nil) -> active(nil)
0.47/0.49	 prefix(active(X:S)) -> prefix(X:S)
0.47/0.49	 prefix(mark(X:S)) -> prefix(X:S)
0.47/0.49	 s(active(X:S)) -> s(X:S)
0.47/0.49	 s(mark(X:S)) -> s(X:S)
0.47/0.49	 zWadr(active(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.47/0.49	 zWadr(mark(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.47/0.49	 zWadr(X1:S,active(X2:S)) -> zWadr(X1:S,X2:S)
0.47/0.49	 zWadr(X1:S,mark(X2:S)) -> zWadr(X1:S,X2:S)
0.47/0.49	
0.47/0.49	Problem 1.7: 
0.47/0.49	
0.47/0.49	Subterm Processor:
0.47/0.49	-> Pairs:
0.47/0.49	 MARK(app(X1:S,X2:S)) -> MARK(X1:S)
0.47/0.49	 MARK(app(X1:S,X2:S)) -> MARK(X2:S)
0.47/0.49	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.47/0.49	 MARK(from(X:S)) -> MARK(X:S)
0.47/0.49	 MARK(prefix(X:S)) -> MARK(X:S)
0.47/0.49	 MARK(s(X:S)) -> MARK(X:S)
0.47/0.49	 MARK(zWadr(X1:S,X2:S)) -> MARK(X1:S)
0.47/0.49	 MARK(zWadr(X1:S,X2:S)) -> MARK(X2:S)
0.47/0.49	-> Rules:
0.47/0.49	 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S)))
0.47/0.49	 active(app(nil,YS:S)) -> mark(YS:S)
0.47/0.49	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.47/0.49	 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S))))
0.47/0.49	 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.47/0.49	 active(zWadr(nil,YS:S)) -> mark(nil)
0.47/0.49	 active(zWadr(XS:S,nil)) -> mark(nil)
0.47/0.49	 app(active(X1:S),X2:S) -> app(X1:S,X2:S)
0.47/0.49	 app(mark(X1:S),X2:S) -> app(X1:S,X2:S)
0.47/0.49	 app(X1:S,active(X2:S)) -> app(X1:S,X2:S)
0.47/0.49	 app(X1:S,mark(X2:S)) -> app(X1:S,X2:S)
0.47/0.49	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.47/0.49	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.47/0.49	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.47/0.49	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.47/0.49	 from(active(X:S)) -> from(X:S)
0.47/0.49	 from(mark(X:S)) -> from(X:S)
0.47/0.49	 mark(app(X1:S,X2:S)) -> active(app(mark(X1:S),mark(X2:S)))
0.47/0.49	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.47/0.49	 mark(from(X:S)) -> active(from(mark(X:S)))
0.47/0.49	 mark(prefix(X:S)) -> active(prefix(mark(X:S)))
0.47/0.49	 mark(s(X:S)) -> active(s(mark(X:S)))
0.47/0.49	 mark(zWadr(X1:S,X2:S)) -> active(zWadr(mark(X1:S),mark(X2:S)))
0.47/0.49	 mark(nil) -> active(nil)
0.47/0.49	 prefix(active(X:S)) -> prefix(X:S)
0.47/0.49	 prefix(mark(X:S)) -> prefix(X:S)
0.47/0.49	 s(active(X:S)) -> s(X:S)
0.47/0.49	 s(mark(X:S)) -> s(X:S)
0.47/0.49	 zWadr(active(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.47/0.49	 zWadr(mark(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.47/0.49	 zWadr(X1:S,active(X2:S)) -> zWadr(X1:S,X2:S)
0.47/0.49	 zWadr(X1:S,mark(X2:S)) -> zWadr(X1:S,X2:S)
0.47/0.49	->Projection:
0.47/0.49	 pi(MARK) = 1
0.47/0.49	
0.47/0.49	Problem 1.7: 
0.47/0.49	
0.47/0.49	SCC Processor:
0.47/0.49	-> Pairs:
0.47/0.49	 Empty
0.47/0.49	-> Rules:
0.47/0.49	 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S)))
0.47/0.49	 active(app(nil,YS:S)) -> mark(YS:S)
0.47/0.49	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.47/0.49	 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S))))
0.47/0.49	 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)))
0.47/0.49	 active(zWadr(nil,YS:S)) -> mark(nil)
0.47/0.49	 active(zWadr(XS:S,nil)) -> mark(nil)
0.47/0.49	 app(active(X1:S),X2:S) -> app(X1:S,X2:S)
0.47/0.49	 app(mark(X1:S),X2:S) -> app(X1:S,X2:S)
0.47/0.49	 app(X1:S,active(X2:S)) -> app(X1:S,X2:S)
0.47/0.49	 app(X1:S,mark(X2:S)) -> app(X1:S,X2:S)
0.47/0.49	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.47/0.49	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.47/0.49	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.47/0.49	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.47/0.49	 from(active(X:S)) -> from(X:S)
0.47/0.49	 from(mark(X:S)) -> from(X:S)
0.47/0.49	 mark(app(X1:S,X2:S)) -> active(app(mark(X1:S),mark(X2:S)))
0.47/0.49	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.47/0.49	 mark(from(X:S)) -> active(from(mark(X:S)))
0.47/0.49	 mark(prefix(X:S)) -> active(prefix(mark(X:S)))
0.47/0.49	 mark(s(X:S)) -> active(s(mark(X:S)))
0.47/0.49	 mark(zWadr(X1:S,X2:S)) -> active(zWadr(mark(X1:S),mark(X2:S)))
0.47/0.49	 mark(nil) -> active(nil)
0.47/0.49	 prefix(active(X:S)) -> prefix(X:S)
0.47/0.49	 prefix(mark(X:S)) -> prefix(X:S)
0.47/0.49	 s(active(X:S)) -> s(X:S)
0.47/0.49	 s(mark(X:S)) -> s(X:S)
0.47/0.49	 zWadr(active(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.47/0.49	 zWadr(mark(X1:S),X2:S) -> zWadr(X1:S,X2:S)
0.47/0.49	 zWadr(X1:S,active(X2:S)) -> zWadr(X1:S,X2:S)
0.47/0.49	 zWadr(X1:S,mark(X2:S)) -> zWadr(X1:S,X2:S)
0.47/0.49	->Strongly Connected Components:
0.47/0.49	 There is no strongly connected component
0.47/0.49	
0.47/0.49	The problem is finite.
0.47/0.49	EOF