2.33/1.29	NO
2.33/1.30	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
2.33/1.30	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.33/1.30	
2.33/1.30	
2.33/1.30	Outermost Termination of the given OTRS could be disproven:
2.33/1.30	
2.33/1.30	(0) OTRS
2.33/1.30	(1) OutermostNonTerminationProof [COMPLETE, 0 ms]
2.33/1.30	(2) NO
2.33/1.30	
2.33/1.30	
2.33/1.30	----------------------------------------
2.33/1.30	
2.33/1.30	(0)
2.33/1.30	Obligation:
2.33/1.30	Term rewrite system R:
2.33/1.30	The TRS R consists of the following rules:
2.33/1.30	
2.33/1.30	   terms(N) -> cons(recip(sqr(N)), terms(s(N)))
2.33/1.30	   sqr(0) -> 0
2.33/1.30	   sqr(s(X)) -> s(add(sqr(X), dbl(X)))
2.33/1.30	   dbl(0) -> 0
2.33/1.30	   dbl(s(X)) -> s(s(dbl(X)))
2.33/1.30	   add(0, X) -> X
2.33/1.30	   add(s(X), Y) -> s(add(X, Y))
2.33/1.30	   first(0, X) -> nil
2.33/1.30	   first(s(X), cons(Y, Z)) -> cons(Y, first(X, Z))
2.33/1.30	
2.33/1.30	
2.33/1.30	
2.33/1.30	Outermost Strategy.
2.33/1.30	
2.33/1.30	----------------------------------------
2.33/1.30	
2.33/1.30	(1) OutermostNonTerminationProof (COMPLETE)
2.33/1.30	Term rewrite system R:
2.33/1.30	The TRS R consists of the following rules:
2.33/1.30	
2.33/1.30	   terms(N) -> cons(recip(sqr(N)), terms(s(N)))
2.33/1.30	   sqr(0) -> 0
2.33/1.30	   sqr(s(X)) -> s(add(sqr(X), dbl(X)))
2.33/1.30	   dbl(0) -> 0
2.33/1.30	   dbl(s(X)) -> s(s(dbl(X)))
2.33/1.30	   add(0, X) -> X
2.33/1.30	   add(s(X), Y) -> s(add(X, Y))
2.33/1.30	   first(0, X) -> nil
2.33/1.30	   first(s(X), cons(Y, Z)) -> cons(Y, first(X, Z))
2.33/1.30	
2.33/1.30	
2.33/1.30	
2.33/1.30	Outermost Strategy.
2.33/1.30	
2.33/1.30	---------- Loop: ----------
2.33/1.30	
2.33/1.30	terms(N) -> cons(recip(sqr(N)), terms(s(N))) with rule terms(N') -> cons(recip(sqr(N')), terms(s(N'))) at position [] and matcher [N' / N]
2.33/1.30	
2.33/1.30	Now an instance of the first term with Matcher [N / s(N)] occurs in the last term at position [1].
2.33/1.30	
2.33/1.30	Context: cons(recip(sqr(N)), [])
2.33/1.30	
2.33/1.30	We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop.
2.33/1.30	----------------------------------------
2.33/1.30	
2.33/1.30	(2)
2.33/1.30	NO
2.66/1.35	EOF