4.07/1.81	YES
4.07/1.81	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
4.07/1.81	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.07/1.81	
4.07/1.81	
4.07/1.81	Termination of the given RelTRS could be proven:
4.07/1.81	
4.07/1.81	(0) RelTRS
4.07/1.81	(1) RelTRSRRRProof [EQUIVALENT, 35 ms]
4.07/1.81	(2) RelTRS
4.07/1.81	(3) RIsEmptyProof [EQUIVALENT, 0 ms]
4.07/1.81	(4) YES
4.07/1.81	
4.07/1.81	
4.07/1.81	----------------------------------------
4.07/1.81	
4.07/1.81	(0)
4.07/1.81	Obligation:
4.07/1.81	Relative term rewrite system:
4.07/1.81	The relative TRS consists of the following R rules:
4.07/1.81	
4.07/1.81	   c(c(a(x1))) -> c(a(b(x1)))
4.07/1.81	   b(b(b(x1))) -> a(a(a(x1)))
4.07/1.81	   b(b(a(x1))) -> c(c(a(x1)))
4.07/1.81	
4.07/1.81	The relative TRS consists of the following S rules:
4.07/1.81	
4.07/1.81	   c(a(a(x1))) -> a(a(a(x1)))
4.07/1.81	   b(a(a(x1))) -> c(c(c(x1)))
4.07/1.81	   b(c(b(x1))) -> c(b(a(x1)))
4.07/1.81	
4.07/1.81	
4.07/1.81	----------------------------------------
4.07/1.81	
4.07/1.81	(1) RelTRSRRRProof (EQUIVALENT)
4.07/1.81	We used the following monotonic ordering for rule removal:
4.07/1.81	Knuth-Bendix order [KBO] with precedence:b_1 > c_1 > a_1
4.07/1.81	
4.07/1.81	and weight map:
4.07/1.81	
4.07/1.81	   c_1=1
4.07/1.81	   a_1=1
4.07/1.81	   b_1=1
4.07/1.81	
4.07/1.81	The variable weight is 1With this ordering the following rules can be removed [MATRO] because they are oriented strictly:
4.07/1.81	Rules from R:
4.07/1.81	
4.07/1.81	   c(c(a(x1))) -> c(a(b(x1)))
4.07/1.81	   b(b(b(x1))) -> a(a(a(x1)))
4.07/1.81	   b(b(a(x1))) -> c(c(a(x1)))
4.07/1.81	Rules from S:
4.07/1.81	
4.07/1.81	   c(a(a(x1))) -> a(a(a(x1)))
4.07/1.81	   b(a(a(x1))) -> c(c(c(x1)))
4.07/1.81	   b(c(b(x1))) -> c(b(a(x1)))
4.07/1.81	
4.07/1.81	
4.07/1.81	
4.07/1.81	
4.07/1.81	----------------------------------------
4.07/1.81	
4.07/1.81	(2)
4.07/1.81	Obligation:
4.07/1.81	Relative term rewrite system:
4.07/1.81	R is empty.
4.07/1.81	S is empty.
4.07/1.81	
4.07/1.81	----------------------------------------
4.07/1.81	
4.07/1.81	(3) RIsEmptyProof (EQUIVALENT)
4.07/1.81	The TRS R is empty. Hence, termination is trivially proven.
4.07/1.81	----------------------------------------
4.07/1.81	
4.07/1.81	(4)
4.07/1.81	YES
4.15/1.87	EOF