5.27/2.19	YES
5.27/2.23	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
5.27/2.23	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
5.27/2.23	
5.27/2.23	
5.27/2.23	Termination of the given RelTRS could be proven:
5.27/2.23	
5.27/2.23	(0) RelTRS
5.27/2.23	(1) RelTRS Reverse [EQUIVALENT, 0 ms]
5.27/2.23	(2) RelTRS
5.27/2.23	(3) RelTRSRRRProof [EQUIVALENT, 10 ms]
5.27/2.23	(4) RelTRS
5.27/2.23	(5) RIsEmptyProof [EQUIVALENT, 1 ms]
5.27/2.23	(6) YES
5.27/2.23	
5.27/2.23	
5.27/2.23	----------------------------------------
5.27/2.23	
5.27/2.23	(0)
5.27/2.23	Obligation:
5.27/2.23	Relative term rewrite system:
5.27/2.23	The relative TRS consists of the following R rules:
5.27/2.23	
5.27/2.23	   a(b(b(x1))) -> c(a(c(x1)))
5.27/2.23	   b(a(c(x1))) -> b(b(a(x1)))
5.27/2.23	   a(a(b(x1))) -> c(a(c(x1)))
5.27/2.23	
5.27/2.23	The relative TRS consists of the following S rules:
5.27/2.23	
5.27/2.23	   b(c(b(x1))) -> c(b(a(x1)))
5.27/2.23	   b(c(b(x1))) -> b(a(b(x1)))
5.27/2.23	   c(b(b(x1))) -> a(c(b(x1)))
5.27/2.23	
5.27/2.23	
5.27/2.23	----------------------------------------
5.27/2.23	
5.27/2.23	(1) RelTRS Reverse (EQUIVALENT)
5.27/2.23	We have reversed the following relative TRS [REVERSE]:
5.27/2.23	The set of rules R is 
5.27/2.23	   a(b(b(x1))) -> c(a(c(x1)))
5.27/2.23	   b(a(c(x1))) -> b(b(a(x1)))
5.27/2.23	   a(a(b(x1))) -> c(a(c(x1)))
5.27/2.23	
5.27/2.23	The set of rules S is 
5.27/2.23	   b(c(b(x1))) -> c(b(a(x1)))
5.27/2.23	   b(c(b(x1))) -> b(a(b(x1)))
5.27/2.23	   c(b(b(x1))) -> a(c(b(x1)))
5.27/2.23	
5.27/2.23	We have obtained the following relative TRS:
5.27/2.23	The set of rules R is 
5.27/2.23	   b(b(a(x1))) -> c(a(c(x1)))
5.27/2.23	   c(a(b(x1))) -> a(b(b(x1)))
5.27/2.23	   b(a(a(x1))) -> c(a(c(x1)))
5.27/2.23	
5.27/2.23	The set of rules S is 
5.27/2.23	   b(c(b(x1))) -> a(b(c(x1)))
5.27/2.23	   b(c(b(x1))) -> b(a(b(x1)))
5.27/2.23	   b(b(c(x1))) -> b(c(a(x1)))
5.27/2.23	
5.27/2.23	
5.27/2.23	----------------------------------------
5.27/2.23	
5.27/2.23	(2)
5.27/2.23	Obligation:
5.27/2.23	Relative term rewrite system:
5.27/2.23	The relative TRS consists of the following R rules:
5.27/2.23	
5.27/2.23	   b(b(a(x1))) -> c(a(c(x1)))
5.27/2.23	   c(a(b(x1))) -> a(b(b(x1)))
5.27/2.23	   b(a(a(x1))) -> c(a(c(x1)))
5.27/2.23	
5.27/2.23	The relative TRS consists of the following S rules:
5.27/2.23	
5.27/2.23	   b(c(b(x1))) -> a(b(c(x1)))
5.27/2.23	   b(c(b(x1))) -> b(a(b(x1)))
5.27/2.23	   b(b(c(x1))) -> b(c(a(x1)))
5.27/2.23	
5.27/2.23	
5.27/2.23	----------------------------------------
5.27/2.23	
5.27/2.23	(3) RelTRSRRRProof (EQUIVALENT)
5.27/2.23	We used the following monotonic ordering for rule removal:
5.27/2.23	Knuth-Bendix order [KBO] with precedence:b_1 > c_1 > a_1
5.27/2.23	
5.27/2.23	and weight map:
5.27/2.23	
5.27/2.23	   b_1=1
5.27/2.23	   a_1=1
5.27/2.23	   c_1=1
5.27/2.23	
5.27/2.23	The variable weight is 1With this ordering the following rules can be removed [MATRO] because they are oriented strictly:
5.27/2.23	Rules from R:
5.27/2.23	
5.27/2.23	   b(b(a(x1))) -> c(a(c(x1)))
5.27/2.23	   c(a(b(x1))) -> a(b(b(x1)))
5.27/2.23	   b(a(a(x1))) -> c(a(c(x1)))
5.27/2.23	Rules from S:
5.27/2.23	
5.27/2.23	   b(c(b(x1))) -> a(b(c(x1)))
5.27/2.23	   b(c(b(x1))) -> b(a(b(x1)))
5.27/2.23	   b(b(c(x1))) -> b(c(a(x1)))
5.27/2.23	
5.27/2.23	
5.27/2.23	
5.27/2.23	
5.27/2.23	----------------------------------------
5.27/2.23	
5.27/2.23	(4)
5.27/2.23	Obligation:
5.27/2.23	Relative term rewrite system:
5.27/2.23	R is empty.
5.27/2.23	S is empty.
5.27/2.23	
5.27/2.23	----------------------------------------
5.27/2.23	
5.27/2.23	(5) RIsEmptyProof (EQUIVALENT)
5.27/2.23	The TRS R is empty. Hence, termination is trivially proven.
5.27/2.23	----------------------------------------
5.27/2.23	
5.27/2.23	(6)
5.27/2.23	YES
5.69/2.30	EOF