6.23/2.36	YES
6.23/2.39	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
6.23/2.39	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
6.23/2.39	
6.23/2.39	
6.23/2.39	Termination of the given RelTRS could be proven:
6.23/2.39	
6.23/2.39	(0) RelTRS
6.23/2.39	(1) RelTRSRRRProof [EQUIVALENT, 111 ms]
6.23/2.39	(2) RelTRS
6.23/2.39	(3) RelTRSRRRProof [EQUIVALENT, 31 ms]
6.23/2.39	(4) RelTRS
6.23/2.39	(5) RIsEmptyProof [EQUIVALENT, 0 ms]
6.23/2.39	(6) YES
6.23/2.39	
6.23/2.39	
6.23/2.39	----------------------------------------
6.23/2.39	
6.23/2.39	(0)
6.23/2.39	Obligation:
6.23/2.39	Relative term rewrite system:
6.23/2.39	The relative TRS consists of the following R rules:
6.23/2.39	
6.23/2.39	   a(a(b(x1))) -> b(a(x1))
6.23/2.39	   c(b(x1)) -> b(c(a(x1)))
6.23/2.39	
6.23/2.39	The relative TRS consists of the following S rules:
6.23/2.39	
6.23/2.39	   a(x1) -> a(c(a(x1)))
6.23/2.39	
6.23/2.39	
6.23/2.39	----------------------------------------
6.23/2.39	
6.23/2.39	(1) RelTRSRRRProof (EQUIVALENT)
6.23/2.39	We used the following monotonic ordering for rule removal:
6.23/2.39	Matrix interpretation [MATRO] to (N^2, +, *, >=, >) :
6.23/2.39	
6.23/2.39	   <<<
6.23/2.39	 POL(a(x_1)) =  	[[0], [0]] 	 +  	[[1, 1], [2, 2]] 	* 	x_1
6.23/2.39	>>>
6.23/2.39	
6.23/2.39	   <<<
6.23/2.39	 POL(b(x_1)) =  	[[1], [0]] 	 +  	[[2, 2], [0, 0]] 	* 	x_1
6.23/2.39	>>>
6.23/2.39	
6.23/2.39	   <<<
6.23/2.39	 POL(c(x_1)) =  	[[0], [0]] 	 +  	[[1, 0], [0, 0]] 	* 	x_1
6.23/2.39	>>>
6.23/2.39	
6.23/2.39	With this ordering the following rules can be removed [MATRO] because they are oriented strictly:
6.23/2.39	Rules from R:
6.23/2.39	
6.23/2.39	   a(a(b(x1))) -> b(a(x1))
6.23/2.39	Rules from S:
6.23/2.39	none
6.23/2.39	
6.23/2.39	
6.23/2.39	
6.23/2.39	
6.23/2.39	----------------------------------------
6.23/2.39	
6.23/2.39	(2)
6.23/2.39	Obligation:
6.23/2.39	Relative term rewrite system:
6.23/2.39	The relative TRS consists of the following R rules:
6.23/2.39	
6.23/2.39	   c(b(x1)) -> b(c(a(x1)))
6.23/2.39	
6.23/2.39	The relative TRS consists of the following S rules:
6.23/2.39	
6.23/2.39	   a(x1) -> a(c(a(x1)))
6.23/2.39	
6.23/2.39	
6.23/2.39	----------------------------------------
6.23/2.39	
6.23/2.39	(3) RelTRSRRRProof (EQUIVALENT)
6.23/2.39	We used the following monotonic ordering for rule removal:
6.23/2.39	Matrix interpretation [MATRO] to (N^2, +, *, >=, >) :
6.23/2.39	
6.23/2.39	   <<<
6.23/2.39	 POL(c(x_1)) =  	[[0], [2]] 	 +  	[[1, 2], [2, 0]] 	* 	x_1
6.23/2.39	>>>
6.23/2.39	
6.23/2.39	   <<<
6.23/2.39	 POL(b(x_1)) =  	[[0], [2]] 	 +  	[[1, 0], [2, 0]] 	* 	x_1
6.23/2.39	>>>
6.23/2.39	
6.23/2.39	   <<<
6.23/2.39	 POL(a(x_1)) =  	[[0], [0]] 	 +  	[[1, 0], [0, 0]] 	* 	x_1
6.23/2.39	>>>
6.23/2.39	
6.23/2.39	With this ordering the following rules can be removed [MATRO] because they are oriented strictly:
6.23/2.39	Rules from R:
6.23/2.39	
6.23/2.39	   c(b(x1)) -> b(c(a(x1)))
6.23/2.39	Rules from S:
6.23/2.39	none
6.23/2.39	
6.23/2.39	
6.23/2.39	
6.23/2.39	
6.23/2.39	----------------------------------------
6.23/2.39	
6.23/2.39	(4)
6.23/2.39	Obligation:
6.23/2.39	Relative term rewrite system:
6.23/2.39	R is empty.
6.23/2.39	The relative TRS consists of the following S rules:
6.23/2.39	
6.23/2.39	   a(x1) -> a(c(a(x1)))
6.23/2.39	
6.23/2.39	
6.23/2.39	----------------------------------------
6.23/2.39	
6.23/2.39	(5) RIsEmptyProof (EQUIVALENT)
6.23/2.39	The TRS R is empty. Hence, termination is trivially proven.
6.23/2.39	----------------------------------------
6.23/2.39	
6.23/2.39	(6)
6.23/2.39	YES
6.54/2.42	EOF