2.41/1.33	NO
2.41/1.34	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
2.41/1.34	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.41/1.34	
2.41/1.34	
2.41/1.34	Outermost Termination of the given OTRS could be disproven:
2.41/1.34	
2.41/1.34	(0) OTRS
2.41/1.34	(1) OutermostNonTerminationProof [COMPLETE, 0 ms]
2.41/1.34	(2) NO
2.41/1.34	
2.41/1.34	
2.41/1.34	----------------------------------------
2.41/1.34	
2.41/1.34	(0)
2.41/1.34	Obligation:
2.41/1.34	Term rewrite system R:
2.41/1.34	The TRS R consists of the following rules:
2.41/1.34	
2.41/1.34	   p(0) -> 0
2.41/1.34	   p(s(X)) -> X
2.41/1.34	   leq(0, Y) -> true
2.41/1.34	   leq(s(X), 0) -> false
2.41/1.34	   leq(s(X), s(Y)) -> leq(X, Y)
2.41/1.34	   if(true, X, Y) -> X
2.41/1.34	   if(false, X, Y) -> Y
2.41/1.34	   diff(X, Y) -> if(leq(X, Y), 0, s(diff(p(X), Y)))
2.41/1.34	
2.41/1.34	
2.41/1.34	
2.41/1.34	Outermost Strategy.
2.41/1.34	
2.41/1.34	----------------------------------------
2.41/1.34	
2.41/1.34	(1) OutermostNonTerminationProof (COMPLETE)
2.41/1.34	Term rewrite system R:
2.41/1.34	The TRS R consists of the following rules:
2.41/1.34	
2.41/1.34	   p(0) -> 0
2.41/1.34	   p(s(X)) -> X
2.41/1.34	   leq(0, Y) -> true
2.41/1.34	   leq(s(X), 0) -> false
2.41/1.34	   leq(s(X), s(Y)) -> leq(X, Y)
2.41/1.34	   if(true, X, Y) -> X
2.41/1.34	   if(false, X, Y) -> Y
2.41/1.34	   diff(X, Y) -> if(leq(X, Y), 0, s(diff(p(X), Y)))
2.41/1.34	
2.41/1.34	
2.41/1.34	
2.41/1.34	Outermost Strategy.
2.41/1.34	
2.41/1.34	---------- Loop: ----------
2.41/1.34	
2.41/1.34	diff(X, Y) -> if(leq(X, Y), 0, s(diff(p(X), Y))) with rule diff(X', Y') -> if(leq(X', Y'), 0, s(diff(p(X'), Y'))) at position [] and matcher [X' / X, Y' / Y]
2.41/1.34	
2.41/1.34	Now an instance of the first term with Matcher [X / p(X)] occurs in the last term at position [2,0].
2.41/1.34	
2.41/1.34	Context: if(leq(X, Y), 0, s([]))
2.41/1.34	
2.41/1.34	We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop.
2.41/1.34	----------------------------------------
2.41/1.34	
2.41/1.34	(2)
2.41/1.34	NO
2.41/1.39	EOF