3.52/1.68	NO
3.52/1.69	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.52/1.69	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.52/1.69	
3.52/1.69	
3.52/1.69	Termination of the given RelTRS could be disproven:
3.52/1.69	
3.52/1.69	(0) RelTRS
3.52/1.69	(1) RelTRSLoopFinderProof [COMPLETE, 40 ms]
3.52/1.69	(2) NO
3.52/1.69	
3.52/1.69	
3.52/1.69	----------------------------------------
3.52/1.69	
3.52/1.69	(0)
3.52/1.69	Obligation:
3.52/1.69	Relative term rewrite system:
3.52/1.69	The relative TRS consists of the following R rules:
3.52/1.69	
3.52/1.69	   f(s(x), y) -> f(-(s(x), y), y)
3.52/1.69	
3.52/1.69	The relative TRS consists of the following S rules:
3.52/1.69	
3.52/1.69	   +(0, y) -> y
3.52/1.69	   +(s(x), y) -> s(+(x, y))
3.52/1.69	   -(x, 0) -> x
3.52/1.69	   -(0, y) -> 0
3.52/1.69	   -(s(x), s(y)) -> -(x, y)
3.52/1.69	   f(x, y) -> f(x, +(x, y))
3.52/1.69	
3.52/1.69	
3.52/1.69	----------------------------------------
3.52/1.69	
3.52/1.69	(1) RelTRSLoopFinderProof (COMPLETE)
3.52/1.69	The following loop was found:
3.52/1.69	
3.52/1.69	---------- Loop: ----------
3.52/1.69	
3.52/1.69	f(-(s(x), 0), 0) -> f(s(x), 0) with rule -(x', 0) -> x' at position [0] and matcher [x' / s(x)]
3.52/1.69	
3.52/1.69	f(s(x), 0) -> f(-(s(x), 0), 0) with rule f(s(x'), y) -> f(-(s(x'), y), y) at position [] and matcher [x' / x, y / 0]
3.52/1.69	
3.52/1.69	Now an instance of the first term with Matcher [ ] occurs in the last term at position [].
3.52/1.69	
3.52/1.69	Context: []
3.52/1.69	
3.52/1.69	Therefore, the relative TRS problem does not terminate.
3.52/1.69	----------------------------------------
3.52/1.69	
3.52/1.69	(2)
3.52/1.69	NO
3.52/1.71	EOF