4.85/1.95	YES
4.85/1.96	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
4.85/1.96	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.85/1.96	
4.85/1.96	
4.85/1.96	Termination of the given RelTRS could be proven:
4.85/1.96	
4.85/1.96	(0) RelTRS
4.85/1.96	(1) RelTRSRRRProof [EQUIVALENT, 28 ms]
4.85/1.96	(2) RelTRS
4.85/1.96	(3) RIsEmptyProof [EQUIVALENT, 1 ms]
4.85/1.96	(4) YES
4.85/1.96	
4.85/1.96	
4.85/1.96	----------------------------------------
4.85/1.96	
4.85/1.96	(0)
4.85/1.96	Obligation:
4.85/1.96	Relative term rewrite system:
4.85/1.96	The relative TRS consists of the following R rules:
4.85/1.96	
4.85/1.96	   b(a(b(x1))) -> a(b(a(x1)))
4.85/1.96	   c(c(a(x1))) -> b(a(c(x1)))
4.85/1.96	   c(a(c(x1))) -> b(b(c(x1)))
4.85/1.96	   b(a(c(x1))) -> a(c(c(x1)))
4.85/1.96	
4.85/1.96	The relative TRS consists of the following S rules:
4.85/1.96	
4.85/1.96	   c(a(b(x1))) -> a(b(c(x1)))
4.85/1.96	   b(a(a(x1))) -> a(c(c(x1)))
4.85/1.96	   b(c(b(x1))) -> a(b(a(x1)))
4.85/1.96	
4.85/1.96	
4.85/1.96	----------------------------------------
4.85/1.96	
4.85/1.96	(1) RelTRSRRRProof (EQUIVALENT)
4.85/1.96	We used the following monotonic ordering for rule removal:
4.85/1.96	Knuth-Bendix order [KBO] with precedence:c_1 > b_1 > a_1
4.85/1.96	
4.85/1.96	and weight map:
4.85/1.96	
4.85/1.96	   b_1=1
4.85/1.96	   a_1=1
4.85/1.96	   c_1=1
4.85/1.96	
4.85/1.96	The variable weight is 1With this ordering the following rules can be removed [MATRO] because they are oriented strictly:
4.85/1.96	Rules from R:
4.85/1.96	
4.85/1.96	   b(a(b(x1))) -> a(b(a(x1)))
4.85/1.96	   c(c(a(x1))) -> b(a(c(x1)))
4.85/1.96	   c(a(c(x1))) -> b(b(c(x1)))
4.85/1.96	   b(a(c(x1))) -> a(c(c(x1)))
4.85/1.96	Rules from S:
4.85/1.96	
4.85/1.96	   c(a(b(x1))) -> a(b(c(x1)))
4.85/1.96	   b(a(a(x1))) -> a(c(c(x1)))
4.85/1.96	   b(c(b(x1))) -> a(b(a(x1)))
4.85/1.96	
4.85/1.96	
4.85/1.96	
4.85/1.96	
4.85/1.96	----------------------------------------
4.85/1.96	
4.85/1.96	(2)
4.85/1.96	Obligation:
4.85/1.96	Relative term rewrite system:
4.85/1.96	R is empty.
4.85/1.96	S is empty.
4.85/1.96	
4.85/1.96	----------------------------------------
4.85/1.96	
4.85/1.96	(3) RIsEmptyProof (EQUIVALENT)
4.85/1.96	The TRS R is empty. Hence, termination is trivially proven.
4.85/1.96	----------------------------------------
4.85/1.96	
4.85/1.96	(4)
4.85/1.96	YES
5.14/2.01	EOF