2.53/1.20	NO
2.53/1.21	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
2.53/1.21	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.53/1.21	
2.53/1.21	
2.53/1.21	Outermost Termination of the given OTRS could be disproven:
2.53/1.21	
2.53/1.21	(0) OTRS
2.53/1.21	(1) OutermostNonTerminationProof [COMPLETE, 0 ms]
2.53/1.21	(2) NO
2.53/1.21	
2.53/1.21	
2.53/1.21	----------------------------------------
2.53/1.21	
2.53/1.21	(0)
2.53/1.21	Obligation:
2.53/1.21	Term rewrite system R:
2.53/1.21	The TRS R consists of the following rules:
2.53/1.21	
2.53/1.21	   if(true) -> X
2.53/1.21	   if(false) -> Y
2.53/1.21	   fact(X) -> if(zero(X))
2.53/1.21	   add(0, X) -> X
2.53/1.21	   add(s(X), Y) -> s(add(X, Y))
2.53/1.21	   prod(0, X) -> 0
2.53/1.21	   prod(s(X), Y) -> add(Y, prod(X, Y))
2.53/1.21	   zero(0) -> true
2.53/1.21	   zero(s(X)) -> false
2.53/1.21	   p(s(X)) -> X
2.53/1.21	
2.53/1.21	
2.53/1.21	
2.53/1.21	Outermost Strategy.
2.53/1.21	
2.53/1.21	----------------------------------------
2.53/1.21	
2.53/1.21	(1) OutermostNonTerminationProof (COMPLETE)
2.53/1.21	Term rewrite system R:
2.53/1.21	The TRS R consists of the following rules:
2.53/1.21	
2.53/1.21	   if(true) -> X
2.53/1.21	   if(false) -> Y
2.53/1.21	   fact(X) -> if(zero(X))
2.53/1.21	   add(0, X) -> X
2.53/1.21	   add(s(X), Y) -> s(add(X, Y))
2.53/1.21	   prod(0, X) -> 0
2.53/1.21	   prod(s(X), Y) -> add(Y, prod(X, Y))
2.53/1.21	   zero(0) -> true
2.53/1.21	   zero(s(X)) -> false
2.53/1.21	   p(s(X)) -> X
2.53/1.21	
2.53/1.21	
2.53/1.21	
2.53/1.21	Outermost Strategy.
2.53/1.21	
2.53/1.21	---------- Loop: ----------
2.53/1.21	
2.53/1.21	if(true) -> if(true) with rule if(true) -> X at position [] and matcher [X / if(true)]
2.53/1.21	
2.53/1.21	Now an instance of the first term with Matcher [ ] occurs in the last term at position [].
2.53/1.21	
2.53/1.21	Context: []
2.53/1.21	
2.53/1.21	We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop.
2.53/1.21	----------------------------------------
2.53/1.21	
2.53/1.21	(2)
2.53/1.21	NO
2.57/1.24	EOF