2.66/1.37	NO
2.66/1.37	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
2.66/1.37	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.66/1.37	
2.66/1.37	
2.66/1.37	Outermost Termination of the given OTRS could be disproven:
2.66/1.37	
2.66/1.37	(0) OTRS
2.66/1.37	(1) OutermostNonTerminationProof [COMPLETE, 42 ms]
2.66/1.37	(2) NO
2.66/1.37	
2.66/1.37	
2.66/1.37	----------------------------------------
2.66/1.37	
2.66/1.37	(0)
2.66/1.37	Obligation:
2.66/1.37	Term rewrite system R:
2.66/1.37	The TRS R consists of the following rules:
2.66/1.37	
2.66/1.37	   p(0) -> 0
2.66/1.37	   p(s(X)) -> X
2.66/1.37	   leq(0, Y) -> true
2.66/1.37	   leq(s(X), 0) -> false
2.66/1.37	   leq(s(X), s(Y)) -> leq(X, Y)
2.66/1.37	   if(true, X, Y) -> activate(X)
2.66/1.37	   if(false, X, Y) -> activate(Y)
2.66/1.37	   diff(X, Y) -> if(leq(X, Y), n__0, n__s(diff(p(X), Y)))
2.66/1.37	   0 -> n__0
2.66/1.37	   s(X) -> n__s(X)
2.66/1.37	   activate(n__0) -> 0
2.66/1.37	   activate(n__s(X)) -> s(X)
2.66/1.37	   activate(X) -> X
2.66/1.37	
2.66/1.37	
2.66/1.37	
2.66/1.37	Outermost Strategy.
2.66/1.37	
2.66/1.37	----------------------------------------
2.66/1.37	
2.66/1.37	(1) OutermostNonTerminationProof (COMPLETE)
2.66/1.37	Term rewrite system R:
2.66/1.37	The TRS R consists of the following rules:
2.66/1.37	
2.66/1.37	   p(0) -> 0
2.66/1.37	   p(s(X)) -> X
2.66/1.37	   leq(0, Y) -> true
2.66/1.37	   leq(s(X), 0) -> false
2.66/1.37	   leq(s(X), s(Y)) -> leq(X, Y)
2.66/1.37	   if(true, X, Y) -> activate(X)
2.66/1.37	   if(false, X, Y) -> activate(Y)
2.66/1.37	   diff(X, Y) -> if(leq(X, Y), n__0, n__s(diff(p(X), Y)))
2.66/1.37	   0 -> n__0
2.66/1.37	   s(X) -> n__s(X)
2.66/1.37	   activate(n__0) -> 0
2.66/1.37	   activate(n__s(X)) -> s(X)
2.66/1.37	   activate(X) -> X
2.66/1.37	
2.66/1.37	
2.66/1.37	
2.66/1.37	Outermost Strategy.
2.66/1.37	
2.66/1.37	---------- Loop: ----------
2.66/1.37	
2.66/1.37	diff(X, Y) -> if(leq(X, Y), n__0, n__s(diff(p(X), Y))) with rule diff(X', Y') -> if(leq(X', Y'), n__0, n__s(diff(p(X'), Y'))) at position [] and matcher [X' / X, Y' / Y]
2.66/1.37	
2.66/1.37	Now an instance of the first term with Matcher [X / p(X)] occurs in the last term at position [2,0].
2.66/1.37	
2.66/1.37	Context: if(leq(X, Y), n__0, n__s([]))
2.66/1.37	
2.66/1.37	We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop.
2.66/1.37	----------------------------------------
2.66/1.37	
2.66/1.37	(2)
2.66/1.37	NO
2.88/1.41	EOF