2.64/1.34	NO
2.64/1.35	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
2.64/1.35	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.64/1.35	
2.64/1.35	
2.64/1.35	Outermost Termination of the given OTRS could be disproven:
2.64/1.35	
2.64/1.35	(0) OTRS
2.64/1.35	(1) OutermostNonTerminationProof [COMPLETE, 0 ms]
2.64/1.35	(2) NO
2.64/1.35	
2.64/1.35	
2.64/1.35	----------------------------------------
2.64/1.35	
2.64/1.35	(0)
2.64/1.35	Obligation:
2.64/1.35	Term rewrite system R:
2.64/1.35	The TRS R consists of the following rules:
2.64/1.35	
2.64/1.35	   and(true, X) -> X
2.64/1.35	   and(false, Y) -> false
2.64/1.35	   if(true, X, Y) -> X
2.64/1.35	   if(false, X, Y) -> Y
2.64/1.35	   add(0, X) -> X
2.64/1.35	   add(s(X), Y) -> s(add(X, Y))
2.64/1.35	   first(0, X) -> nil
2.64/1.35	   first(s(X), cons(Y, Z)) -> cons(Y, first(X, Z))
2.64/1.35	   from(X) -> cons(X, from(s(X)))
2.64/1.35	
2.64/1.35	
2.64/1.35	
2.64/1.35	Outermost Strategy.
2.64/1.35	
2.64/1.35	----------------------------------------
2.64/1.35	
2.64/1.35	(1) OutermostNonTerminationProof (COMPLETE)
2.64/1.35	Term rewrite system R:
2.64/1.35	The TRS R consists of the following rules:
2.64/1.35	
2.64/1.35	   and(true, X) -> X
2.64/1.35	   and(false, Y) -> false
2.64/1.35	   if(true, X, Y) -> X
2.64/1.35	   if(false, X, Y) -> Y
2.64/1.35	   add(0, X) -> X
2.64/1.35	   add(s(X), Y) -> s(add(X, Y))
2.64/1.35	   first(0, X) -> nil
2.64/1.35	   first(s(X), cons(Y, Z)) -> cons(Y, first(X, Z))
2.64/1.35	   from(X) -> cons(X, from(s(X)))
2.64/1.35	
2.64/1.35	
2.64/1.35	
2.64/1.35	Outermost Strategy.
2.64/1.35	
2.64/1.35	---------- Loop: ----------
2.64/1.35	
2.64/1.35	from(X) -> cons(X, from(s(X))) with rule from(X') -> cons(X', from(s(X'))) at position [] and matcher [X' / X]
2.64/1.35	
2.64/1.35	Now an instance of the first term with Matcher [X / s(X)] occurs in the last term at position [1].
2.64/1.35	
2.64/1.35	Context: cons(X, [])
2.64/1.35	
2.64/1.35	We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop.
2.64/1.35	----------------------------------------
2.64/1.35	
2.64/1.35	(2)
2.64/1.35	NO
2.84/2.03	EOF