2.44/1.20	NO
2.44/1.21	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
2.44/1.21	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.44/1.21	
2.44/1.21	
2.44/1.21	Outermost Termination of the given OTRS could be disproven:
2.44/1.21	
2.44/1.21	(0) OTRS
2.44/1.21	(1) OutermostNonTerminationProof [COMPLETE, 0 ms]
2.44/1.21	(2) NO
2.44/1.21	
2.44/1.21	
2.44/1.21	----------------------------------------
2.44/1.21	
2.44/1.21	(0)
2.44/1.21	Obligation:
2.44/1.21	Term rewrite system R:
2.44/1.21	The TRS R consists of the following rules:
2.44/1.21	
2.44/1.21	   sel(s(N), cons(X)) -> sel(N, XS)
2.44/1.21	   from(X) -> cons(X)
2.44/1.21	   sel(0, cons(X)) -> X
2.44/1.21	   minus(X, 0) -> 0
2.44/1.21	   minus(s(X), s(Y)) -> minus(X, Y)
2.44/1.21	   quot(0, s(Y)) -> 0
2.44/1.21	   quot(s(X), s(Y)) -> s(quot(minus(X, Y), s(Y)))
2.44/1.21	   zWquot(XS, nil) -> nil
2.44/1.21	   zWquot(nil, XS) -> nil
2.44/1.21	   zWquot(cons(X), cons(Y)) -> cons(quot(X, Y))
2.44/1.21	
2.44/1.21	
2.44/1.21	
2.44/1.21	Outermost Strategy.
2.44/1.21	
2.44/1.21	----------------------------------------
2.44/1.21	
2.44/1.21	(1) OutermostNonTerminationProof (COMPLETE)
2.44/1.21	Term rewrite system R:
2.44/1.21	The TRS R consists of the following rules:
2.44/1.21	
2.44/1.21	   sel(s(N), cons(X)) -> sel(N, XS)
2.44/1.21	   from(X) -> cons(X)
2.44/1.21	   sel(0, cons(X)) -> X
2.44/1.21	   minus(X, 0) -> 0
2.44/1.21	   minus(s(X), s(Y)) -> minus(X, Y)
2.44/1.21	   quot(0, s(Y)) -> 0
2.44/1.21	   quot(s(X), s(Y)) -> s(quot(minus(X, Y), s(Y)))
2.44/1.21	   zWquot(XS, nil) -> nil
2.44/1.21	   zWquot(nil, XS) -> nil
2.44/1.21	   zWquot(cons(X), cons(Y)) -> cons(quot(X, Y))
2.44/1.21	
2.44/1.21	
2.44/1.21	
2.44/1.21	Outermost Strategy.
2.44/1.21	
2.44/1.21	---------- Loop: ----------
2.44/1.21	
2.44/1.21	sel(s(N), cons(X)) -> sel(N, sel(s(N), cons(X))) with rule sel(s(N''), cons(X'')) -> sel(N'', XS) at position [] and matcher [N'' / N, X'' / X, XS / sel(s(N), cons(X))]
2.44/1.21	
2.44/1.21	Now an instance of the first term with Matcher [ ] occurs in the last term at position [1].
2.44/1.21	
2.44/1.21	Context: sel(N, [])
2.44/1.21	
2.44/1.21	We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop.
2.44/1.21	----------------------------------------
2.44/1.21	
2.44/1.21	(2)
2.44/1.21	NO
2.46/1.24	EOF