6.15/2.60	YES
6.87/2.63	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
6.87/2.63	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
6.87/2.63	
6.87/2.63	
6.87/2.63	Termination of the given RelTRS could be proven:
6.87/2.63	
6.87/2.63	(0) RelTRS
6.87/2.63	(1) RelTRS Reverse [EQUIVALENT, 0 ms]
6.87/2.63	(2) RelTRS
6.87/2.63	(3) RelTRSRRRProof [EQUIVALENT, 333 ms]
6.87/2.63	(4) RelTRS
6.87/2.63	(5) RIsEmptyProof [EQUIVALENT, 0 ms]
6.87/2.63	(6) YES
6.87/2.63	
6.87/2.63	
6.87/2.63	----------------------------------------
6.87/2.63	
6.87/2.63	(0)
6.87/2.63	Obligation:
6.87/2.63	Relative term rewrite system:
6.87/2.63	The relative TRS consists of the following R rules:
6.87/2.63	
6.87/2.63	   a(c(c(x1))) -> b(a(a(x1)))
6.87/2.63	   b(a(b(x1))) -> b(c(a(x1)))
6.87/2.63	
6.87/2.63	The relative TRS consists of the following S rules:
6.87/2.63	
6.87/2.63	   a(a(c(x1))) -> c(a(b(x1)))
6.87/2.63	   c(c(b(x1))) -> a(b(a(x1)))
6.87/2.63	   b(c(b(x1))) -> b(a(c(x1)))
6.87/2.63	   b(c(c(x1))) -> c(b(b(x1)))
6.87/2.63	   a(a(b(x1))) -> a(c(a(x1)))
6.87/2.63	
6.87/2.63	
6.87/2.63	----------------------------------------
6.87/2.63	
6.87/2.63	(1) RelTRS Reverse (EQUIVALENT)
6.87/2.63	We have reversed the following relative TRS [REVERSE]:
6.87/2.63	The set of rules R is 
6.87/2.63	   a(c(c(x1))) -> b(a(a(x1)))
6.87/2.63	   b(a(b(x1))) -> b(c(a(x1)))
6.87/2.63	
6.87/2.63	The set of rules S is 
6.87/2.63	   a(a(c(x1))) -> c(a(b(x1)))
6.87/2.63	   c(c(b(x1))) -> a(b(a(x1)))
6.87/2.63	   b(c(b(x1))) -> b(a(c(x1)))
6.87/2.63	   b(c(c(x1))) -> c(b(b(x1)))
6.87/2.63	   a(a(b(x1))) -> a(c(a(x1)))
6.87/2.63	
6.87/2.63	We have obtained the following relative TRS:
6.87/2.63	The set of rules R is 
6.87/2.63	   c(c(a(x1))) -> a(a(b(x1)))
6.87/2.63	   b(a(b(x1))) -> a(c(b(x1)))
6.87/2.63	
6.87/2.63	The set of rules S is 
6.87/2.63	   c(a(a(x1))) -> b(a(c(x1)))
6.87/2.63	   b(c(c(x1))) -> a(b(a(x1)))
6.87/2.63	   b(c(b(x1))) -> c(a(b(x1)))
6.87/2.63	   c(c(b(x1))) -> b(b(c(x1)))
6.87/2.63	   b(a(a(x1))) -> a(c(a(x1)))
6.87/2.63	
6.87/2.63	
6.87/2.63	----------------------------------------
6.87/2.63	
6.87/2.63	(2)
6.87/2.63	Obligation:
6.87/2.63	Relative term rewrite system:
6.87/2.63	The relative TRS consists of the following R rules:
6.87/2.63	
6.87/2.63	   c(c(a(x1))) -> a(a(b(x1)))
6.87/2.63	   b(a(b(x1))) -> a(c(b(x1)))
6.87/2.63	
6.87/2.63	The relative TRS consists of the following S rules:
6.87/2.63	
6.87/2.63	   c(a(a(x1))) -> b(a(c(x1)))
6.87/2.63	   b(c(c(x1))) -> a(b(a(x1)))
6.87/2.63	   b(c(b(x1))) -> c(a(b(x1)))
6.87/2.63	   c(c(b(x1))) -> b(b(c(x1)))
6.87/2.63	   b(a(a(x1))) -> a(c(a(x1)))
6.87/2.63	
6.87/2.63	
6.87/2.63	----------------------------------------
6.87/2.63	
6.87/2.63	(3) RelTRSRRRProof (EQUIVALENT)
6.87/2.63	We used the following monotonic ordering for rule removal:
6.87/2.63	Matrix interpretation [MATRO] to (N^2, +, *, >=, >) :
6.87/2.63	
6.87/2.63	   <<<
6.87/2.63	 POL(c(x_1)) =  	[[1], [1]] 	 +  	[[1, 2], [0, 2]] 	* 	x_1
6.87/2.63	>>>
6.87/2.63	
6.87/2.63	   <<<
6.87/2.63	 POL(a(x_1)) =  	[[0], [1]] 	 +  	[[1, 0], [0, 2]] 	* 	x_1
6.87/2.63	>>>
6.87/2.63	
6.87/2.63	   <<<
6.87/2.63	 POL(b(x_1)) =  	[[1], [1]] 	 +  	[[1, 1], [0, 2]] 	* 	x_1
6.87/2.63	>>>
6.87/2.63	
6.87/2.63	With this ordering the following rules can be removed [MATRO] because they are oriented strictly:
6.87/2.63	Rules from R:
6.87/2.63	
6.87/2.63	   c(c(a(x1))) -> a(a(b(x1)))
6.87/2.63	   b(a(b(x1))) -> a(c(b(x1)))
6.87/2.63	Rules from S:
6.87/2.63	
6.87/2.63	   c(a(a(x1))) -> b(a(c(x1)))
6.87/2.63	   b(c(c(x1))) -> a(b(a(x1)))
6.87/2.63	   c(c(b(x1))) -> b(b(c(x1)))
6.87/2.63	   b(a(a(x1))) -> a(c(a(x1)))
6.87/2.63	
6.87/2.63	
6.87/2.63	
6.87/2.63	
6.87/2.63	----------------------------------------
6.87/2.63	
6.87/2.63	(4)
6.87/2.63	Obligation:
6.87/2.63	Relative term rewrite system:
6.87/2.63	R is empty.
6.87/2.63	The relative TRS consists of the following S rules:
6.87/2.63	
6.87/2.63	   b(c(b(x1))) -> c(a(b(x1)))
6.87/2.63	
6.87/2.63	
6.87/2.63	----------------------------------------
6.87/2.63	
6.87/2.63	(5) RIsEmptyProof (EQUIVALENT)
6.87/2.63	The TRS R is empty. Hence, termination is trivially proven.
6.87/2.63	----------------------------------------
6.87/2.63	
6.87/2.63	(6)
6.87/2.63	YES
6.87/2.68	EOF