482.71/123.14	YES
482.91/123.15	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
482.91/123.15	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
482.91/123.15	
482.91/123.15	
482.91/123.15	Termination of the given RelTRS could be proven:
482.91/123.15	
482.91/123.15	(0) RelTRS
482.91/123.15	(1) RelTRSRRRProof [EQUIVALENT, 68.1 s]
482.91/123.15	(2) RelTRS
482.91/123.15	(3) RIsEmptyProof [EQUIVALENT, 0 ms]
482.91/123.15	(4) YES
482.91/123.15	
482.91/123.15	
482.91/123.15	----------------------------------------
482.91/123.15	
482.91/123.15	(0)
482.91/123.15	Obligation:
482.91/123.15	Relative term rewrite system:
482.91/123.15	The relative TRS consists of the following R rules:
482.91/123.15	
482.91/123.15	   b(a(a(b(x1)))) -> a(a(a(a(x1))))
482.91/123.15	   a(b(b(a(x1)))) -> b(b(b(b(x1))))
482.91/123.15	
482.91/123.15	The relative TRS consists of the following S rules:
482.91/123.15	
482.91/123.15	   b(x1) -> b(b(b(x1)))
482.91/123.15	
482.91/123.15	
482.91/123.15	----------------------------------------
482.91/123.15	
482.91/123.15	(1) RelTRSRRRProof (EQUIVALENT)
482.91/123.15	We used the following monotonic ordering for rule removal:
482.91/123.15	Matrix interpretation [MATRO] to (N^6, +, *, >=, >) :
482.91/123.15	
482.91/123.15	   <<<
482.91/123.15	 POL(b(x_1)) =  	[[0], [0], [1], [0], [0], [0]] 	 +  	[[1, 0, 0, 1, 0, 0], [0, 0, 0, 1, 0, 1], [0, 1, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0]] 	* 	x_1
482.91/123.15	>>>
482.91/123.15	
482.91/123.15	   <<<
482.91/123.15	 POL(a(x_1)) =  	[[0], [0], [0], [0], [1], [0]] 	 +  	[[1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]] 	* 	x_1
482.91/123.15	>>>
482.91/123.15	
482.91/123.15	With this ordering the following rules can be removed [MATRO] because they are oriented strictly:
482.91/123.15	Rules from R:
482.91/123.15	
482.91/123.15	   b(a(a(b(x1)))) -> a(a(a(a(x1))))
482.91/123.15	   a(b(b(a(x1)))) -> b(b(b(b(x1))))
482.91/123.15	Rules from S:
482.91/123.15	none
482.91/123.15	
482.91/123.15	
482.91/123.15	
482.91/123.15	
482.91/123.15	----------------------------------------
482.91/123.15	
482.91/123.15	(2)
482.91/123.15	Obligation:
482.91/123.15	Relative term rewrite system:
482.91/123.15	R is empty.
482.91/123.15	The relative TRS consists of the following S rules:
482.91/123.15	
482.91/123.15	   b(x1) -> b(b(b(x1)))
482.91/123.15	
482.91/123.15	
482.91/123.15	----------------------------------------
482.91/123.15	
482.91/123.15	(3) RIsEmptyProof (EQUIVALENT)
482.91/123.15	The TRS R is empty. Hence, termination is trivially proven.
482.91/123.15	----------------------------------------
482.91/123.15	
482.91/123.15	(4)
482.91/123.15	YES
482.91/123.20	EOF