3.58/1.70	YES
3.92/1.71	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.92/1.71	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.92/1.71	
3.92/1.71	
3.92/1.71	Termination of the given RelTRS could be proven:
3.92/1.71	
3.92/1.71	(0) RelTRS
3.92/1.71	(1) RelTRSRRRProof [EQUIVALENT, 32 ms]
3.92/1.71	(2) RelTRS
3.92/1.71	(3) RIsEmptyProof [EQUIVALENT, 0 ms]
3.92/1.71	(4) YES
3.92/1.71	
3.92/1.71	
3.92/1.71	----------------------------------------
3.92/1.71	
3.92/1.71	(0)
3.92/1.71	Obligation:
3.92/1.71	Relative term rewrite system:
3.92/1.71	The relative TRS consists of the following R rules:
3.92/1.71	
3.92/1.71	   R(x, B2) -> B2
3.92/1.71	
3.92/1.71	The relative TRS consists of the following S rules:
3.92/1.71	
3.92/1.71	   B1 -> R(T, B1)
3.92/1.71	
3.92/1.71	
3.92/1.71	----------------------------------------
3.92/1.71	
3.92/1.71	(1) RelTRSRRRProof (EQUIVALENT)
3.92/1.71	We used the following monotonic ordering for rule removal:
3.92/1.71	Matrix interpretation [MATRO] to (N^2, +, *, >=, >) :
3.92/1.71	
3.92/1.71	   <<<
3.92/1.71	 POL(R(x_1, x_2)) =  	[[0], [0]] 	 +  	[[1, 0], [1, 0]] 	* 	x_1 	 +  	[[1, 1], [1, 0]] 	* 	x_2
3.92/1.71	>>>
3.92/1.71	
3.92/1.71	   <<<
3.92/1.71	 POL(B2) =  	[[1], [1]]
3.92/1.71	>>>
3.92/1.71	
3.92/1.71	   <<<
3.92/1.71	 POL(B1) =  	[[0], [0]]
3.92/1.71	>>>
3.92/1.71	
3.92/1.71	   <<<
3.92/1.71	 POL(T) =  	[[0], [1]]
3.92/1.71	>>>
3.92/1.71	
3.92/1.71	With this ordering the following rules can be removed [MATRO] because they are oriented strictly:
3.92/1.71	Rules from R:
3.92/1.71	
3.92/1.71	   R(x, B2) -> B2
3.92/1.71	Rules from S:
3.92/1.71	none
3.92/1.71	
3.92/1.71	
3.92/1.71	
3.92/1.71	
3.92/1.71	----------------------------------------
3.92/1.71	
3.92/1.71	(2)
3.92/1.71	Obligation:
3.92/1.71	Relative term rewrite system:
3.92/1.71	R is empty.
3.92/1.71	The relative TRS consists of the following S rules:
3.92/1.71	
3.92/1.71	   B1 -> R(T, B1)
3.92/1.71	
3.92/1.71	
3.92/1.71	----------------------------------------
3.92/1.71	
3.92/1.71	(3) RIsEmptyProof (EQUIVALENT)
3.92/1.71	The TRS R is empty. Hence, termination is trivially proven.
3.92/1.71	----------------------------------------
3.92/1.71	
3.92/1.71	(4)
3.92/1.71	YES
3.92/1.76	EOF