2.87/1.31	NO
2.87/1.31	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
2.87/1.31	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.87/1.31	
2.87/1.31	
2.87/1.31	Outermost Termination of the given OTRS could be disproven:
2.87/1.31	
2.87/1.31	(0) OTRS
2.87/1.31	(1) OutermostNonTerminationProof [COMPLETE, 36 ms]
2.87/1.31	(2) NO
2.87/1.31	
2.87/1.31	
2.87/1.31	----------------------------------------
2.87/1.31	
2.87/1.31	(0)
2.87/1.31	Obligation:
2.87/1.31	Term rewrite system R:
2.87/1.31	The TRS R consists of the following rules:
2.87/1.31	
2.87/1.31	   fact(X) -> if(zero(X), s(0), prod(X, fact(p(X))))
2.87/1.31	   add(0, X) -> X
2.87/1.31	   add(s(X), Y) -> s(add(X, Y))
2.87/1.31	   prod(0, X) -> 0
2.87/1.31	   prod(s(X), Y) -> add(Y, prod(X, Y))
2.87/1.31	   if(true, X, Y) -> X
2.87/1.31	   if(false, X, Y) -> Y
2.87/1.31	   zero(0) -> true
2.87/1.31	   zero(s(X)) -> false
2.87/1.31	   p(s(X)) -> X
2.87/1.31	
2.87/1.31	
2.87/1.31	
2.87/1.31	Outermost Strategy.
2.87/1.31	
2.87/1.31	----------------------------------------
2.87/1.31	
2.87/1.31	(1) OutermostNonTerminationProof (COMPLETE)
2.87/1.31	Term rewrite system R:
2.87/1.31	The TRS R consists of the following rules:
2.87/1.31	
2.87/1.31	   fact(X) -> if(zero(X), s(0), prod(X, fact(p(X))))
2.87/1.31	   add(0, X) -> X
2.87/1.31	   add(s(X), Y) -> s(add(X, Y))
2.87/1.31	   prod(0, X) -> 0
2.87/1.31	   prod(s(X), Y) -> add(Y, prod(X, Y))
2.87/1.31	   if(true, X, Y) -> X
2.87/1.31	   if(false, X, Y) -> Y
2.87/1.31	   zero(0) -> true
2.87/1.31	   zero(s(X)) -> false
2.87/1.31	   p(s(X)) -> X
2.87/1.31	
2.87/1.31	
2.87/1.31	
2.87/1.31	Outermost Strategy.
2.87/1.31	
2.87/1.31	---------- Loop: ----------
2.87/1.31	
2.87/1.31	fact(X) -> if(zero(X), s(0), prod(X, fact(p(X)))) with rule fact(X') -> if(zero(X'), s(0), prod(X', fact(p(X')))) at position [] and matcher [X' / X]
2.87/1.31	
2.87/1.31	Now an instance of the first term with Matcher [X / p(X)] occurs in the last term at position [2,1].
2.87/1.31	
2.87/1.31	Context: if(zero(X), s(0), prod(X, []))
2.87/1.31	
2.87/1.31	We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop.
2.87/1.31	----------------------------------------
2.87/1.31	
2.87/1.31	(2)
2.87/1.31	NO
3.03/1.76	EOF