4.15/1.79	NO
4.25/1.83	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
4.25/1.83	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.25/1.83	
4.25/1.83	
4.25/1.83	Termination of the given RelTRS could be disproven:
4.25/1.83	
4.25/1.83	(0) RelTRS
4.25/1.83	(1) RelTRSLoopFinderProof [COMPLETE, 44 ms]
4.25/1.83	(2) NO
4.25/1.83	
4.25/1.83	
4.25/1.83	----------------------------------------
4.25/1.83	
4.25/1.83	(0)
4.25/1.83	Obligation:
4.25/1.83	Relative term rewrite system:
4.25/1.83	The relative TRS consists of the following R rules:
4.25/1.83	
4.25/1.83	   f(a, x) -> f(x, f(b, x))
4.25/1.83	
4.25/1.83	The relative TRS consists of the following S rules:
4.25/1.83	
4.25/1.83	   f(f(x, y), z) -> f(x, f(y, z))
4.25/1.83	   f(x, f(y, z)) -> f(f(x, y), z)
4.25/1.83	
4.25/1.83	
4.25/1.83	----------------------------------------
4.25/1.83	
4.25/1.83	(1) RelTRSLoopFinderProof (COMPLETE)
4.25/1.83	The following loop was found:
4.25/1.83	
4.25/1.83	---------- Loop: ----------
4.25/1.83	
4.25/1.83	f(a, f(x', f(y', a))) -> f(a, f(f(x', y'), a)) with rule f(x'', f(y'', z)) -> f(f(x'', y''), z) at position [1] and matcher [x'' / x', y'' / y', z / a]
4.25/1.83	
4.25/1.83	f(a, f(f(x', y'), a)) -> f(f(f(x', y'), a), f(b, f(f(x', y'), a))) with rule f(a, x) -> f(x, f(b, x)) at position [] and matcher [x / f(f(x', y'), a)]
4.25/1.83	
4.25/1.83	f(f(f(x', y'), a), f(b, f(f(x', y'), a))) -> f(f(x', y'), f(a, f(b, f(f(x', y'), a)))) with rule f(f(x, y), z) -> f(x, f(y, z)) at position [] and matcher [x / f(x', y'), y / a, z / f(b, f(f(x', y'), a))]
4.25/1.83	
4.25/1.83	Now an instance of the first term with Matcher [x' / b, y' / f(x', y')] occurs in the last term at position [1].
4.25/1.83	
4.25/1.83	Context: f(f(x', y'), [])
4.25/1.83	
4.25/1.83	Therefore, the relative TRS problem does not terminate.
4.25/1.83	----------------------------------------
4.25/1.83	
4.25/1.83	(2)
4.25/1.83	NO
4.28/1.86	EOF