2.65/1.28	NO
2.65/1.30	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
2.65/1.30	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.65/1.30	
2.65/1.30	
2.65/1.30	Outermost Termination of the given OTRS could be disproven:
2.65/1.30	
2.65/1.30	(0) OTRS
2.65/1.30	(1) OutermostNonTerminationProof [COMPLETE, 0 ms]
2.65/1.30	(2) NO
2.65/1.30	
2.65/1.30	
2.65/1.30	----------------------------------------
2.65/1.30	
2.65/1.30	(0)
2.65/1.30	Obligation:
2.65/1.30	Term rewrite system R:
2.65/1.30	The TRS R consists of the following rules:
2.65/1.30	
2.65/1.30	   fact(X) -> if(zero(X), n__s(0), n__prod(X, fact(p(X))))
2.65/1.30	   add(0, X) -> X
2.65/1.30	   add(s(X), Y) -> s(add(X, Y))
2.65/1.30	   prod(0, X) -> 0
2.65/1.30	   prod(s(X), Y) -> add(Y, prod(X, Y))
2.65/1.30	   if(true, X, Y) -> activate(X)
2.65/1.30	   if(false, X, Y) -> activate(Y)
2.65/1.30	   zero(0) -> true
2.65/1.30	   zero(s(X)) -> false
2.65/1.30	   p(s(X)) -> X
2.65/1.30	   s(X) -> n__s(X)
2.65/1.30	   prod(X1, X2) -> n__prod(X1, X2)
2.65/1.30	   activate(n__s(X)) -> s(X)
2.65/1.30	   activate(n__prod(X1, X2)) -> prod(X1, X2)
2.65/1.30	   activate(X) -> X
2.65/1.30	
2.65/1.30	
2.65/1.30	
2.65/1.30	Outermost Strategy.
2.65/1.30	
2.65/1.30	----------------------------------------
2.65/1.30	
2.65/1.30	(1) OutermostNonTerminationProof (COMPLETE)
2.65/1.30	Term rewrite system R:
2.65/1.30	The TRS R consists of the following rules:
2.65/1.30	
2.65/1.30	   fact(X) -> if(zero(X), n__s(0), n__prod(X, fact(p(X))))
2.65/1.30	   add(0, X) -> X
2.65/1.30	   add(s(X), Y) -> s(add(X, Y))
2.65/1.30	   prod(0, X) -> 0
2.65/1.30	   prod(s(X), Y) -> add(Y, prod(X, Y))
2.65/1.30	   if(true, X, Y) -> activate(X)
2.65/1.30	   if(false, X, Y) -> activate(Y)
2.65/1.30	   zero(0) -> true
2.65/1.30	   zero(s(X)) -> false
2.65/1.30	   p(s(X)) -> X
2.65/1.30	   s(X) -> n__s(X)
2.65/1.30	   prod(X1, X2) -> n__prod(X1, X2)
2.65/1.30	   activate(n__s(X)) -> s(X)
2.65/1.30	   activate(n__prod(X1, X2)) -> prod(X1, X2)
2.65/1.30	   activate(X) -> X
2.65/1.30	
2.65/1.30	
2.65/1.30	
2.65/1.30	Outermost Strategy.
2.65/1.30	
2.65/1.30	---------- Loop: ----------
2.65/1.30	
2.65/1.30	fact(X) -> if(zero(X), n__s(0), n__prod(X, fact(p(X)))) with rule fact(X') -> if(zero(X'), n__s(0), n__prod(X', fact(p(X')))) at position [] and matcher [X' / X]
2.65/1.30	
2.65/1.30	Now an instance of the first term with Matcher [X / p(X)] occurs in the last term at position [2,1].
2.65/1.30	
2.65/1.30	Context: if(zero(X), n__s(0), n__prod(X, []))
2.65/1.30	
2.65/1.30	We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop.
2.65/1.30	----------------------------------------
2.65/1.30	
2.65/1.30	(2)
2.65/1.30	NO
2.80/1.33	EOF