5.12/2.14	YES
5.12/2.17	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
5.12/2.17	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
5.12/2.17	
5.12/2.17	
5.12/2.17	Termination of the given RelTRS could be proven:
5.12/2.17	
5.12/2.17	(0) RelTRS
5.12/2.17	(1) RelTRSRRRProof [EQUIVALENT, 35 ms]
5.12/2.17	(2) RelTRS
5.12/2.17	(3) RIsEmptyProof [EQUIVALENT, 3 ms]
5.12/2.17	(4) YES
5.12/2.17	
5.12/2.17	
5.12/2.17	----------------------------------------
5.12/2.17	
5.12/2.17	(0)
5.12/2.17	Obligation:
5.12/2.17	Relative term rewrite system:
5.12/2.17	The relative TRS consists of the following R rules:
5.12/2.17	
5.12/2.17	   c(b(a(x1))) -> c(c(c(x1)))
5.12/2.17	   b(c(c(x1))) -> a(c(c(x1)))
5.12/2.17	
5.12/2.17	The relative TRS consists of the following S rules:
5.12/2.17	
5.12/2.17	   b(a(c(x1))) -> b(c(b(x1)))
5.12/2.17	   a(a(c(x1))) -> c(c(c(x1)))
5.12/2.17	   c(a(c(x1))) -> c(c(b(x1)))
5.12/2.17	   b(c(a(x1))) -> a(a(b(x1)))
5.12/2.17	
5.12/2.17	
5.12/2.17	----------------------------------------
5.12/2.17	
5.12/2.17	(1) RelTRSRRRProof (EQUIVALENT)
5.12/2.17	We used the following monotonic ordering for rule removal:
5.12/2.17	Knuth-Bendix order [KBO] with precedence:b_1 > a_1 > c_1
5.12/2.17	
5.12/2.17	and weight map:
5.12/2.17	
5.12/2.17	   c_1=1
5.12/2.17	   b_1=1
5.12/2.17	   a_1=1
5.12/2.17	
5.12/2.17	The variable weight is 1With this ordering the following rules can be removed [MATRO] because they are oriented strictly:
5.12/2.17	Rules from R:
5.12/2.17	
5.12/2.17	   c(b(a(x1))) -> c(c(c(x1)))
5.12/2.17	   b(c(c(x1))) -> a(c(c(x1)))
5.12/2.17	Rules from S:
5.12/2.17	
5.12/2.17	   b(a(c(x1))) -> b(c(b(x1)))
5.12/2.17	   a(a(c(x1))) -> c(c(c(x1)))
5.12/2.17	   c(a(c(x1))) -> c(c(b(x1)))
5.12/2.17	   b(c(a(x1))) -> a(a(b(x1)))
5.12/2.17	
5.12/2.17	
5.12/2.17	
5.12/2.17	
5.12/2.17	----------------------------------------
5.12/2.17	
5.12/2.17	(2)
5.12/2.17	Obligation:
5.12/2.17	Relative term rewrite system:
5.12/2.17	R is empty.
5.12/2.17	S is empty.
5.12/2.17	
5.12/2.17	----------------------------------------
5.12/2.17	
5.12/2.17	(3) RIsEmptyProof (EQUIVALENT)
5.12/2.17	The TRS R is empty. Hence, termination is trivially proven.
5.12/2.17	----------------------------------------
5.12/2.17	
5.12/2.17	(4)
5.12/2.17	YES
5.39/2.26	EOF