2.88/1.29	NO
2.88/1.31	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
2.88/1.31	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.88/1.31	
2.88/1.31	
2.88/1.31	Outermost Termination of the given OTRS could be disproven:
2.88/1.31	
2.88/1.31	(0) OTRS
2.88/1.31	(1) OutermostNonTerminationProof [COMPLETE, 53 ms]
2.88/1.31	(2) NO
2.88/1.31	
2.88/1.31	
2.88/1.31	----------------------------------------
2.88/1.31	
2.88/1.31	(0)
2.88/1.31	Obligation:
2.88/1.31	Term rewrite system R:
2.88/1.31	The TRS R consists of the following rules:
2.88/1.31	
2.88/1.31	   ap(f, x) -> x
2.88/1.31	   ap(ap(ap(g, x), y), ap(s, z)) -> ap(ap(ap(g, x), y), ap(ap(x, y), 0))
2.88/1.31	
2.88/1.31	
2.88/1.31	
2.88/1.31	Outermost Strategy.
2.88/1.31	
2.88/1.31	----------------------------------------
2.88/1.31	
2.88/1.31	(1) OutermostNonTerminationProof (COMPLETE)
2.88/1.31	Term rewrite system R:
2.88/1.31	The TRS R consists of the following rules:
2.88/1.31	
2.88/1.31	   ap(f, x) -> x
2.88/1.31	   ap(ap(ap(g, x), y), ap(s, z)) -> ap(ap(ap(g, x), y), ap(ap(x, y), 0))
2.88/1.31	
2.88/1.31	
2.88/1.31	
2.88/1.31	Outermost Strategy.
2.88/1.31	
2.88/1.31	---------- Loop: ----------
2.88/1.31	
2.88/1.31	ap(ap(ap(g, f), s), ap(ap(f, s), 0)) -> ap(ap(ap(g, f), s), ap(s, 0)) with rule ap(f, x') -> x' at position [1,0] and matcher [x' / s]
2.88/1.31	
2.88/1.31	ap(ap(ap(g, f), s), ap(s, 0)) -> ap(ap(ap(g, f), s), ap(ap(f, s), 0)) with rule ap(ap(ap(g, x), y), ap(s, z)) -> ap(ap(ap(g, x), y), ap(ap(x, y), 0)) at position [] and matcher [x / f, y / s, z / 0]
2.88/1.31	
2.88/1.31	Now an instance of the first term with Matcher [ ] occurs in the last term at position [].
2.88/1.31	
2.88/1.31	Context: []
2.88/1.31	
2.88/1.31	We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop.
2.88/1.31	----------------------------------------
2.88/1.31	
2.88/1.31	(2)
2.88/1.31	NO
3.10/1.34	EOF