4.64/2.01	YES
4.64/2.04	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
4.64/2.04	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.64/2.04	
4.64/2.04	
4.64/2.04	Termination of the given RelTRS could be proven:
4.64/2.04	
4.64/2.04	(0) RelTRS
4.64/2.04	(1) RelTRS Reverse [EQUIVALENT, 0 ms]
4.64/2.04	(2) RelTRS
4.64/2.04	(3) FlatCCProof [EQUIVALENT, 0 ms]
4.64/2.04	(4) RelTRS
4.64/2.04	(5) RootLabelingProof [EQUIVALENT, 0 ms]
4.64/2.04	(6) RelTRS
4.64/2.04	(7) RelTRSRRRProof [EQUIVALENT, 37 ms]
4.64/2.04	(8) RelTRS
4.64/2.04	(9) RIsEmptyProof [EQUIVALENT, 2 ms]
4.64/2.04	(10) YES
4.64/2.04	
4.64/2.04	
4.64/2.04	----------------------------------------
4.64/2.04	
4.64/2.04	(0)
4.64/2.04	Obligation:
4.64/2.04	Relative term rewrite system:
4.64/2.04	The relative TRS consists of the following R rules:
4.64/2.04	
4.64/2.04	   b(b(b(x1))) -> x1
4.64/2.04	   c(c(c(x1))) -> a(a(x1))
4.64/2.04	
4.64/2.04	The relative TRS consists of the following S rules:
4.64/2.04	
4.64/2.04	   a(x1) -> a(c(b(x1)))
4.64/2.04	
4.64/2.04	
4.64/2.04	----------------------------------------
4.64/2.04	
4.64/2.04	(1) RelTRS Reverse (EQUIVALENT)
4.64/2.04	We have reversed the following relative TRS [REVERSE]:
4.64/2.04	The set of rules R is 
4.64/2.04	   b(b(b(x1))) -> x1
4.64/2.04	   c(c(c(x1))) -> a(a(x1))
4.64/2.04	
4.64/2.04	The set of rules S is 
4.64/2.04	   a(x1) -> a(c(b(x1)))
4.64/2.04	
4.64/2.04	We have obtained the following relative TRS:
4.64/2.04	The set of rules R is 
4.64/2.04	   b(b(b(x1))) -> x1
4.64/2.04	   c(c(c(x1))) -> a(a(x1))
4.64/2.04	
4.64/2.04	The set of rules S is 
4.64/2.04	   a(x1) -> b(c(a(x1)))
4.64/2.04	
4.64/2.04	
4.64/2.04	----------------------------------------
4.64/2.04	
4.64/2.04	(2)
4.64/2.04	Obligation:
4.64/2.04	Relative term rewrite system:
4.64/2.04	The relative TRS consists of the following R rules:
4.64/2.04	
4.64/2.04	   b(b(b(x1))) -> x1
4.64/2.04	   c(c(c(x1))) -> a(a(x1))
4.64/2.04	
4.64/2.04	The relative TRS consists of the following S rules:
4.64/2.04	
4.64/2.04	   a(x1) -> b(c(a(x1)))
4.64/2.04	
4.64/2.04	
4.64/2.04	----------------------------------------
4.64/2.04	
4.64/2.04	(3) FlatCCProof (EQUIVALENT)
4.64/2.04	We used flat context closure [ROOTLAB]
4.64/2.04	
4.64/2.04	----------------------------------------
4.64/2.04	
4.64/2.04	(4)
4.64/2.04	Obligation:
4.64/2.04	Relative term rewrite system:
4.64/2.04	The relative TRS consists of the following R rules:
4.64/2.04	
4.64/2.04	   b(b(b(b(x1)))) -> b(x1)
4.64/2.04	   c(b(b(b(x1)))) -> c(x1)
4.64/2.04	   a(b(b(b(x1)))) -> a(x1)
4.64/2.04	   b(c(c(c(x1)))) -> b(a(a(x1)))
4.64/2.04	   c(c(c(c(x1)))) -> c(a(a(x1)))
4.64/2.04	   a(c(c(c(x1)))) -> a(a(a(x1)))
4.64/2.04	
4.64/2.04	The relative TRS consists of the following S rules:
4.64/2.04	
4.64/2.04	   b(a(x1)) -> b(b(c(a(x1))))
4.64/2.04	   c(a(x1)) -> c(b(c(a(x1))))
4.64/2.04	   a(a(x1)) -> a(b(c(a(x1))))
4.64/2.04	
4.64/2.04	
4.64/2.04	----------------------------------------
4.64/2.04	
4.64/2.04	(5) RootLabelingProof (EQUIVALENT)
4.64/2.04	We used plain root labeling [ROOTLAB] with the following heuristic:
4.64/2.04	LabelAll: All function symbols get labeled
4.64/2.04	
4.64/2.04	
4.64/2.04	----------------------------------------
4.64/2.04	
4.64/2.04	(6)
4.64/2.04	Obligation:
4.64/2.04	Relative term rewrite system:
4.64/2.04	The relative TRS consists of the following R rules:
4.64/2.04	
4.64/2.04	   b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1)))) -> b_{b_1}(x1)
4.64/2.04	   b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1)))) -> b_{c_1}(x1)
4.64/2.04	   b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x1)))) -> b_{a_1}(x1)
4.64/2.04	   c_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1)))) -> c_{b_1}(x1)
4.64/2.04	   c_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1)))) -> c_{c_1}(x1)
4.64/2.04	   c_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x1)))) -> c_{a_1}(x1)
4.64/2.04	   a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1)))) -> a_{b_1}(x1)
4.64/2.04	   a_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1)))) -> a_{c_1}(x1)
4.64/2.04	   a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x1)))) -> a_{a_1}(x1)
4.64/2.04	   b_{c_1}(c_{c_1}(c_{c_1}(c_{b_1}(x1)))) -> b_{a_1}(a_{a_1}(a_{b_1}(x1)))
4.64/2.04	   b_{c_1}(c_{c_1}(c_{c_1}(c_{c_1}(x1)))) -> b_{a_1}(a_{a_1}(a_{c_1}(x1)))
4.64/2.04	   b_{c_1}(c_{c_1}(c_{c_1}(c_{a_1}(x1)))) -> b_{a_1}(a_{a_1}(a_{a_1}(x1)))
4.64/2.04	   c_{c_1}(c_{c_1}(c_{c_1}(c_{b_1}(x1)))) -> c_{a_1}(a_{a_1}(a_{b_1}(x1)))
4.64/2.04	   c_{c_1}(c_{c_1}(c_{c_1}(c_{c_1}(x1)))) -> c_{a_1}(a_{a_1}(a_{c_1}(x1)))
4.64/2.04	   c_{c_1}(c_{c_1}(c_{c_1}(c_{a_1}(x1)))) -> c_{a_1}(a_{a_1}(a_{a_1}(x1)))
4.64/2.04	   a_{c_1}(c_{c_1}(c_{c_1}(c_{b_1}(x1)))) -> a_{a_1}(a_{a_1}(a_{b_1}(x1)))
4.64/2.04	   a_{c_1}(c_{c_1}(c_{c_1}(c_{c_1}(x1)))) -> a_{a_1}(a_{a_1}(a_{c_1}(x1)))
4.64/2.04	   a_{c_1}(c_{c_1}(c_{c_1}(c_{a_1}(x1)))) -> a_{a_1}(a_{a_1}(a_{a_1}(x1)))
4.64/2.04	
4.64/2.04	The relative TRS consists of the following S rules:
4.64/2.04	
4.64/2.04	   b_{a_1}(a_{b_1}(x1)) -> b_{b_1}(b_{c_1}(c_{a_1}(a_{b_1}(x1))))
4.64/2.04	   b_{a_1}(a_{c_1}(x1)) -> b_{b_1}(b_{c_1}(c_{a_1}(a_{c_1}(x1))))
4.64/2.04	   b_{a_1}(a_{a_1}(x1)) -> b_{b_1}(b_{c_1}(c_{a_1}(a_{a_1}(x1))))
4.64/2.04	   c_{a_1}(a_{b_1}(x1)) -> c_{b_1}(b_{c_1}(c_{a_1}(a_{b_1}(x1))))
4.64/2.04	   c_{a_1}(a_{c_1}(x1)) -> c_{b_1}(b_{c_1}(c_{a_1}(a_{c_1}(x1))))
4.64/2.04	   c_{a_1}(a_{a_1}(x1)) -> c_{b_1}(b_{c_1}(c_{a_1}(a_{a_1}(x1))))
4.64/2.04	   a_{a_1}(a_{b_1}(x1)) -> a_{b_1}(b_{c_1}(c_{a_1}(a_{b_1}(x1))))
4.64/2.04	   a_{a_1}(a_{c_1}(x1)) -> a_{b_1}(b_{c_1}(c_{a_1}(a_{c_1}(x1))))
4.64/2.04	   a_{a_1}(a_{a_1}(x1)) -> a_{b_1}(b_{c_1}(c_{a_1}(a_{a_1}(x1))))
4.64/2.04	
4.64/2.04	
4.64/2.04	----------------------------------------
4.64/2.04	
4.64/2.04	(7) RelTRSRRRProof (EQUIVALENT)
4.64/2.04	We used the following monotonic ordering for rule removal:
4.64/2.04	Polynomial interpretation [POLO]:
4.64/2.04	
4.64/2.04	   POL(a_{a_1}(x_1)) = x_1
4.64/2.04	   POL(a_{b_1}(x_1)) = x_1
4.64/2.04	   POL(a_{c_1}(x_1)) = 1 + x_1
4.64/2.04	   POL(b_{a_1}(x_1)) = 1 + x_1
4.64/2.04	   POL(b_{b_1}(x_1)) = 1 + x_1
4.64/2.04	   POL(b_{c_1}(x_1)) = x_1
4.64/2.04	   POL(c_{a_1}(x_1)) = x_1
4.64/2.04	   POL(c_{b_1}(x_1)) = x_1
4.64/2.04	   POL(c_{c_1}(x_1)) = 1 + x_1
4.64/2.04	With this ordering the following rules can be removed [MATRO] because they are oriented strictly:
4.64/2.04	Rules from R:
4.64/2.04	
4.64/2.04	   b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1)))) -> b_{b_1}(x1)
4.64/2.04	   b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1)))) -> b_{c_1}(x1)
4.64/2.04	   b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x1)))) -> b_{a_1}(x1)
4.64/2.04	   c_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1)))) -> c_{b_1}(x1)
4.64/2.04	   c_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1)))) -> c_{c_1}(x1)
4.64/2.04	   c_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x1)))) -> c_{a_1}(x1)
4.64/2.04	   a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1)))) -> a_{b_1}(x1)
4.64/2.04	   a_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1)))) -> a_{c_1}(x1)
4.64/2.04	   a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x1)))) -> a_{a_1}(x1)
4.64/2.04	   b_{c_1}(c_{c_1}(c_{c_1}(c_{b_1}(x1)))) -> b_{a_1}(a_{a_1}(a_{b_1}(x1)))
4.64/2.04	   b_{c_1}(c_{c_1}(c_{c_1}(c_{c_1}(x1)))) -> b_{a_1}(a_{a_1}(a_{c_1}(x1)))
4.64/2.04	   b_{c_1}(c_{c_1}(c_{c_1}(c_{a_1}(x1)))) -> b_{a_1}(a_{a_1}(a_{a_1}(x1)))
4.64/2.04	   c_{c_1}(c_{c_1}(c_{c_1}(c_{b_1}(x1)))) -> c_{a_1}(a_{a_1}(a_{b_1}(x1)))
4.64/2.04	   c_{c_1}(c_{c_1}(c_{c_1}(c_{c_1}(x1)))) -> c_{a_1}(a_{a_1}(a_{c_1}(x1)))
4.64/2.04	   c_{c_1}(c_{c_1}(c_{c_1}(c_{a_1}(x1)))) -> c_{a_1}(a_{a_1}(a_{a_1}(x1)))
4.64/2.04	   a_{c_1}(c_{c_1}(c_{c_1}(c_{b_1}(x1)))) -> a_{a_1}(a_{a_1}(a_{b_1}(x1)))
4.64/2.04	   a_{c_1}(c_{c_1}(c_{c_1}(c_{c_1}(x1)))) -> a_{a_1}(a_{a_1}(a_{c_1}(x1)))
4.64/2.04	   a_{c_1}(c_{c_1}(c_{c_1}(c_{a_1}(x1)))) -> a_{a_1}(a_{a_1}(a_{a_1}(x1)))
4.64/2.04	Rules from S:
4.64/2.04	none
4.64/2.04	
4.64/2.04	
4.64/2.04	
4.64/2.04	
4.64/2.04	----------------------------------------
4.64/2.04	
4.64/2.04	(8)
4.64/2.04	Obligation:
4.64/2.04	Relative term rewrite system:
4.64/2.04	R is empty.
4.64/2.04	The relative TRS consists of the following S rules:
4.64/2.04	
4.64/2.04	   b_{a_1}(a_{b_1}(x1)) -> b_{b_1}(b_{c_1}(c_{a_1}(a_{b_1}(x1))))
4.64/2.04	   b_{a_1}(a_{c_1}(x1)) -> b_{b_1}(b_{c_1}(c_{a_1}(a_{c_1}(x1))))
4.64/2.04	   b_{a_1}(a_{a_1}(x1)) -> b_{b_1}(b_{c_1}(c_{a_1}(a_{a_1}(x1))))
4.64/2.04	   c_{a_1}(a_{b_1}(x1)) -> c_{b_1}(b_{c_1}(c_{a_1}(a_{b_1}(x1))))
4.64/2.04	   c_{a_1}(a_{c_1}(x1)) -> c_{b_1}(b_{c_1}(c_{a_1}(a_{c_1}(x1))))
4.64/2.04	   c_{a_1}(a_{a_1}(x1)) -> c_{b_1}(b_{c_1}(c_{a_1}(a_{a_1}(x1))))
4.64/2.04	   a_{a_1}(a_{b_1}(x1)) -> a_{b_1}(b_{c_1}(c_{a_1}(a_{b_1}(x1))))
4.64/2.04	   a_{a_1}(a_{c_1}(x1)) -> a_{b_1}(b_{c_1}(c_{a_1}(a_{c_1}(x1))))
4.64/2.04	   a_{a_1}(a_{a_1}(x1)) -> a_{b_1}(b_{c_1}(c_{a_1}(a_{a_1}(x1))))
4.64/2.04	
4.64/2.04	
4.64/2.04	----------------------------------------
4.64/2.04	
4.64/2.04	(9) RIsEmptyProof (EQUIVALENT)
4.64/2.04	The TRS R is empty. Hence, termination is trivially proven.
4.64/2.04	----------------------------------------
4.64/2.04	
4.64/2.04	(10)
4.64/2.04	YES
4.98/2.07	EOF