3.28/1.60	NO
3.28/1.61	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.28/1.61	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.28/1.61	
3.28/1.61	
3.28/1.61	Termination of the given RelTRS could be disproven:
3.28/1.61	
3.28/1.61	(0) RelTRS
3.28/1.61	(1) RelTRSLoopFinderProof [COMPLETE, 0 ms]
3.28/1.61	(2) NO
3.28/1.61	
3.28/1.61	
3.28/1.61	----------------------------------------
3.28/1.61	
3.28/1.61	(0)
3.28/1.61	Obligation:
3.28/1.61	Relative term rewrite system:
3.28/1.61	The relative TRS consists of the following R rules:
3.28/1.61	
3.28/1.61	   min(x, 0) -> 0
3.28/1.61	   min(0, y) -> 0
3.28/1.61	   min(s(x), s(y)) -> s(min(x, y))
3.28/1.61	   max(x, 0) -> x
3.28/1.61	   max(0, y) -> y
3.28/1.61	   max(s(x), s(y)) -> s(max(x, y))
3.28/1.61	   -(x, 0) -> x
3.28/1.61	   -(s(x), s(y)) -> -(x, y)
3.28/1.61	   gcd(nil) -> 0
3.28/1.61	   gcd(cons(x, nil)) -> x
3.28/1.61	   gcd(cons(0, y)) -> gcd(y)
3.28/1.61	   gcd(cons(x, cons(y, z))) -> gcd(cons(-(x, y), cons(y, z)))
3.28/1.61	
3.28/1.61	The relative TRS consists of the following S rules:
3.28/1.61	
3.28/1.61	   gcd(cons(x, cons(y, z))) -> gcd(cons(max(x, y), cons(min(x, y), z)))
3.28/1.61	
3.28/1.61	
3.28/1.61	----------------------------------------
3.28/1.61	
3.28/1.61	(1) RelTRSLoopFinderProof (COMPLETE)
3.28/1.61	The following loop was found:
3.28/1.61	
3.28/1.61	---------- Loop: ----------
3.28/1.61	
3.28/1.61	gcd(cons(x, cons(y, z))) -> gcd(cons(-(x, y), cons(y, z))) with rule gcd(cons(x', cons(y', z'))) -> gcd(cons(-(x', y'), cons(y', z'))) at position [] and matcher [x' / x, y' / y, z' / z]
3.28/1.61	
3.28/1.61	Now an instance of the first term with Matcher [x / -(x, y)] occurs in the last term at position [].
3.28/1.61	
3.28/1.61	Context: []
3.28/1.61	
3.28/1.61	Therefore, the relative TRS problem does not terminate.
3.28/1.61	----------------------------------------
3.28/1.61	
3.28/1.61	(2)
3.28/1.61	NO
3.45/1.63	EOF