53.22/14.30	YES
53.50/14.31	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
53.50/14.31	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
53.50/14.31	
53.50/14.31	
53.50/14.31	Termination of the given RelTRS could be proven:
53.50/14.31	
53.50/14.31	(0) RelTRS
53.50/14.31	(1) RelTRS S Cleaner [EQUIVALENT, 0 ms]
53.50/14.31	(2) RelTRS
53.50/14.31	(3) RelTRS Reverse [EQUIVALENT, 0 ms]
53.50/14.31	(4) RelTRS
53.50/14.31	(5) RelTRSRRRProof [EQUIVALENT, 2910 ms]
53.50/14.31	(6) RelTRS
53.50/14.31	(7) RelTRSRRRProof [EQUIVALENT, 3 ms]
53.50/14.31	(8) RelTRS
53.50/14.31	(9) RIsEmptyProof [EQUIVALENT, 0 ms]
53.50/14.31	(10) YES
53.50/14.31	
53.50/14.31	
53.50/14.31	----------------------------------------
53.50/14.31	
53.50/14.31	(0)
53.50/14.31	Obligation:
53.50/14.31	Relative term rewrite system:
53.50/14.31	The relative TRS consists of the following R rules:
53.50/14.31	
53.50/14.31	   b(b(b(x1))) -> c(a(a(x1)))
53.50/14.31	   b(b(c(x1))) -> b(b(b(x1)))
53.50/14.31	
53.50/14.31	The relative TRS consists of the following S rules:
53.50/14.31	
53.50/14.31	   a(b(a(x1))) -> a(b(a(x1)))
53.50/14.31	   c(c(a(x1))) -> c(c(c(x1)))
53.50/14.31	   c(a(a(x1))) -> b(a(b(x1)))
53.50/14.31	   c(a(c(x1))) -> b(a(c(x1)))
53.50/14.31	
53.50/14.31	
53.50/14.31	----------------------------------------
53.50/14.31	
53.50/14.31	(1) RelTRS S Cleaner (EQUIVALENT)
53.50/14.31	We have deleted all rules from S that have the shape t -> t:
53.50/14.31	
53.50/14.31	   a(b(a(x1))) -> a(b(a(x1)))
53.50/14.31	
53.50/14.31	
53.50/14.31	----------------------------------------
53.50/14.31	
53.50/14.31	(2)
53.50/14.31	Obligation:
53.50/14.31	Relative term rewrite system:
53.50/14.31	The relative TRS consists of the following R rules:
53.50/14.31	
53.50/14.31	   b(b(b(x1))) -> c(a(a(x1)))
53.50/14.31	   b(b(c(x1))) -> b(b(b(x1)))
53.50/14.31	
53.50/14.31	The relative TRS consists of the following S rules:
53.50/14.31	
53.50/14.31	   c(c(a(x1))) -> c(c(c(x1)))
53.50/14.31	   c(a(a(x1))) -> b(a(b(x1)))
53.50/14.31	   c(a(c(x1))) -> b(a(c(x1)))
53.50/14.31	
53.50/14.31	
53.50/14.31	----------------------------------------
53.50/14.31	
53.50/14.31	(3) RelTRS Reverse (EQUIVALENT)
53.50/14.31	We have reversed the following relative TRS [REVERSE]:
53.50/14.31	The set of rules R is 
53.50/14.31	   b(b(b(x1))) -> c(a(a(x1)))
53.50/14.31	   b(b(c(x1))) -> b(b(b(x1)))
53.50/14.31	
53.50/14.31	The set of rules S is 
53.50/14.31	   c(c(a(x1))) -> c(c(c(x1)))
53.50/14.31	   c(a(a(x1))) -> b(a(b(x1)))
53.50/14.31	   c(a(c(x1))) -> b(a(c(x1)))
53.50/14.31	
53.50/14.31	We have obtained the following relative TRS:
53.50/14.31	The set of rules R is 
53.50/14.31	   b(b(b(x1))) -> a(a(c(x1)))
53.50/14.31	   c(b(b(x1))) -> b(b(b(x1)))
53.50/14.31	
53.50/14.31	The set of rules S is 
53.50/14.31	   a(c(c(x1))) -> c(c(c(x1)))
53.50/14.31	   a(a(c(x1))) -> b(a(b(x1)))
53.50/14.31	   c(a(c(x1))) -> c(a(b(x1)))
53.50/14.31	
53.50/14.31	
53.50/14.31	----------------------------------------
53.50/14.31	
53.50/14.31	(4)
53.50/14.31	Obligation:
53.50/14.31	Relative term rewrite system:
53.50/14.31	The relative TRS consists of the following R rules:
53.50/14.31	
53.50/14.31	   b(b(b(x1))) -> a(a(c(x1)))
53.50/14.31	   c(b(b(x1))) -> b(b(b(x1)))
53.50/14.31	
53.50/14.31	The relative TRS consists of the following S rules:
53.50/14.31	
53.50/14.31	   a(c(c(x1))) -> c(c(c(x1)))
53.50/14.31	   a(a(c(x1))) -> b(a(b(x1)))
53.50/14.31	   c(a(c(x1))) -> c(a(b(x1)))
53.50/14.31	
53.50/14.31	
53.50/14.31	----------------------------------------
53.50/14.31	
53.50/14.31	(5) RelTRSRRRProof (EQUIVALENT)
53.50/14.31	We used the following monotonic ordering for rule removal:
53.50/14.31	Matrix interpretation [MATRO] to (N^6, +, *, >=, >) :
53.50/14.31	
53.50/14.31	   <<<
53.50/14.31	 POL(b(x_1)) =  	[[0], [0], [0], [0], [0], [0]] 	 +  	[[1, 0, 1, 0, 0, 0], [1, 0, 0, 1, 0, 0], [0, 0, 0, 1, 0, 1], [0, 0, 0, 1, 0, 1], [0, 0, 1, 0, 0, 1], [1, 0, 1, 0, 0, 0]] 	* 	x_1
53.50/14.31	>>>
53.50/14.31	
53.50/14.31	   <<<
53.50/14.31	 POL(a(x_1)) =  	[[0], [0], [0], [0], [0], [0]] 	 +  	[[1, 1, 0, 0, 0, 0], [1, 0, 0, 0, 1, 0], [0, 0, 0, 1, 1, 0], [0, 0, 0, 1, 1, 0], [0, 1, 0, 1, 0, 0], [1, 1, 0, 0, 0, 0]] 	* 	x_1
53.50/14.31	>>>
53.50/14.31	
53.50/14.31	   <<<
53.50/14.31	 POL(c(x_1)) =  	[[0], [0], [1], [0], [0], [1]] 	 +  	[[1, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 1], [1, 0, 0, 1, 0, 0], [1, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 1], [1, 0, 0, 1, 0, 0]] 	* 	x_1
53.50/14.31	>>>
53.50/14.31	
53.50/14.31	With this ordering the following rules can be removed [MATRO] because they are oriented strictly:
53.50/14.31	Rules from R:
53.50/14.31	none
53.50/14.31	Rules from S:
53.50/14.31	
53.50/14.31	   a(c(c(x1))) -> c(c(c(x1)))
53.50/14.31	
53.50/14.31	
53.50/14.31	
53.50/14.31	
53.50/14.31	----------------------------------------
53.50/14.31	
53.50/14.31	(6)
53.50/14.31	Obligation:
53.50/14.31	Relative term rewrite system:
53.50/14.31	The relative TRS consists of the following R rules:
53.50/14.31	
53.50/14.31	   b(b(b(x1))) -> a(a(c(x1)))
53.50/14.31	   c(b(b(x1))) -> b(b(b(x1)))
53.50/14.31	
53.50/14.31	The relative TRS consists of the following S rules:
53.50/14.31	
53.50/14.31	   a(a(c(x1))) -> b(a(b(x1)))
53.50/14.31	   c(a(c(x1))) -> c(a(b(x1)))
53.50/14.31	
53.50/14.31	
53.50/14.31	----------------------------------------
53.50/14.31	
53.50/14.31	(7) RelTRSRRRProof (EQUIVALENT)
53.50/14.31	We used the following monotonic ordering for rule removal:
53.50/14.31	Knuth-Bendix order [KBO] with precedence:c_1 > b_1 > a_1
53.50/14.31	
53.50/14.31	and weight map:
53.50/14.31	
53.50/14.31	   b_1=2
53.50/14.31	   a_1=1
53.50/14.31	   c_1=4
53.50/14.31	
53.50/14.31	The variable weight is 1With this ordering the following rules can be removed [MATRO] because they are oriented strictly:
53.50/14.31	Rules from R:
53.50/14.31	
53.50/14.31	   b(b(b(x1))) -> a(a(c(x1)))
53.50/14.31	   c(b(b(x1))) -> b(b(b(x1)))
53.50/14.31	Rules from S:
53.50/14.31	
53.50/14.31	   a(a(c(x1))) -> b(a(b(x1)))
53.50/14.31	   c(a(c(x1))) -> c(a(b(x1)))
53.50/14.31	
53.50/14.31	
53.50/14.31	
53.50/14.31	
53.50/14.31	----------------------------------------
53.50/14.31	
53.50/14.31	(8)
53.50/14.31	Obligation:
53.50/14.31	Relative term rewrite system:
53.50/14.31	R is empty.
53.50/14.31	S is empty.
53.50/14.31	
53.50/14.31	----------------------------------------
53.50/14.31	
53.50/14.31	(9) RIsEmptyProof (EQUIVALENT)
53.50/14.31	The TRS R is empty. Hence, termination is trivially proven.
53.50/14.31	----------------------------------------
53.50/14.31	
53.50/14.31	(10)
53.50/14.31	YES
53.60/14.40	EOF