3.74/1.74	YES
3.74/1.76	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.74/1.76	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.74/1.76	
3.74/1.76	
3.74/1.76	Termination of the given RelTRS could be proven:
3.74/1.76	
3.74/1.76	(0) RelTRS
3.74/1.76	(1) RelTRSRRRProof [EQUIVALENT, 50 ms]
3.74/1.76	(2) RelTRS
3.74/1.76	(3) RIsEmptyProof [EQUIVALENT, 0 ms]
3.74/1.76	(4) YES
3.74/1.76	
3.74/1.76	
3.74/1.76	----------------------------------------
3.74/1.76	
3.74/1.76	(0)
3.74/1.76	Obligation:
3.74/1.76	Relative term rewrite system:
3.74/1.76	The relative TRS consists of the following R rules:
3.74/1.76	
3.74/1.76	   f(x) -> x
3.74/1.76	   g(x) -> x
3.74/1.76	
3.74/1.76	The relative TRS consists of the following S rules:
3.74/1.76	
3.74/1.76	   f(x) -> g(x)
3.74/1.76	   g(x) -> f(x)
3.74/1.76	
3.74/1.76	
3.74/1.76	----------------------------------------
3.74/1.76	
3.74/1.76	(1) RelTRSRRRProof (EQUIVALENT)
3.74/1.76	We used the following monotonic ordering for rule removal:
3.74/1.76	Polynomial interpretation [POLO]:
3.74/1.76	
3.74/1.76	   POL(f(x_1)) = 1 + x_1
3.74/1.76	   POL(g(x_1)) = 1 + x_1
3.74/1.76	With this ordering the following rules can be removed [MATRO] because they are oriented strictly:
3.74/1.76	Rules from R:
3.74/1.76	
3.74/1.76	   f(x) -> x
3.74/1.76	   g(x) -> x
3.74/1.76	Rules from S:
3.74/1.76	none
3.74/1.76	
3.74/1.76	
3.74/1.76	
3.74/1.76	
3.74/1.76	----------------------------------------
3.74/1.76	
3.74/1.76	(2)
3.74/1.76	Obligation:
3.74/1.76	Relative term rewrite system:
3.74/1.76	R is empty.
3.74/1.76	The relative TRS consists of the following S rules:
3.74/1.76	
3.74/1.76	   f(x) -> g(x)
3.74/1.76	   g(x) -> f(x)
3.74/1.76	
3.74/1.76	
3.74/1.76	----------------------------------------
3.74/1.76	
3.74/1.76	(3) RIsEmptyProof (EQUIVALENT)
3.74/1.76	The TRS R is empty. Hence, termination is trivially proven.
3.74/1.76	----------------------------------------
3.74/1.76	
3.74/1.76	(4)
3.74/1.76	YES
3.74/1.78	EOF