5.39/2.21	YES
5.39/2.24	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
5.39/2.24	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
5.39/2.24	
5.39/2.24	
5.39/2.24	Termination of the given RelTRS could be proven:
5.39/2.24	
5.39/2.24	(0) RelTRS
5.39/2.24	(1) FlatCCProof [EQUIVALENT, 0 ms]
5.39/2.24	(2) RelTRS
5.39/2.24	(3) RootLabelingProof [EQUIVALENT, 18 ms]
5.39/2.24	(4) RelTRS
5.39/2.24	(5) RelTRSRRRProof [EQUIVALENT, 17 ms]
5.39/2.24	(6) RelTRS
5.39/2.24	(7) RIsEmptyProof [EQUIVALENT, 0 ms]
5.39/2.24	(8) YES
5.39/2.24	
5.39/2.24	
5.39/2.24	----------------------------------------
5.39/2.24	
5.39/2.24	(0)
5.39/2.24	Obligation:
5.39/2.24	Relative term rewrite system:
5.39/2.24	The relative TRS consists of the following R rules:
5.39/2.24	
5.39/2.24	   a(a(b(x1))) -> c(b(c(x1)))
5.39/2.24	   b(c(b(x1))) -> a(b(c(x1)))
5.39/2.24	   a(a(b(x1))) -> c(a(b(x1)))
5.39/2.24	
5.39/2.24	The relative TRS consists of the following S rules:
5.39/2.24	
5.39/2.24	   a(c(b(x1))) -> c(c(c(x1)))
5.39/2.24	   c(a(c(x1))) -> c(b(b(x1)))
5.39/2.24	   b(a(b(x1))) -> c(c(b(x1)))
5.39/2.24	   c(b(c(x1))) -> c(c(b(x1)))
5.39/2.24	
5.39/2.24	
5.39/2.24	----------------------------------------
5.39/2.24	
5.39/2.24	(1) FlatCCProof (EQUIVALENT)
5.39/2.24	We used flat context closure [ROOTLAB]
5.39/2.24	
5.39/2.24	----------------------------------------
5.39/2.24	
5.39/2.24	(2)
5.39/2.24	Obligation:
5.39/2.24	Relative term rewrite system:
5.39/2.24	The relative TRS consists of the following R rules:
5.39/2.24	
5.39/2.24	   a(a(a(b(x1)))) -> a(c(b(c(x1))))
5.39/2.24	   b(a(a(b(x1)))) -> b(c(b(c(x1))))
5.39/2.24	   c(a(a(b(x1)))) -> c(c(b(c(x1))))
5.39/2.24	   a(b(c(b(x1)))) -> a(a(b(c(x1))))
5.39/2.24	   b(b(c(b(x1)))) -> b(a(b(c(x1))))
5.39/2.24	   c(b(c(b(x1)))) -> c(a(b(c(x1))))
5.39/2.24	   a(a(a(b(x1)))) -> a(c(a(b(x1))))
5.39/2.24	   b(a(a(b(x1)))) -> b(c(a(b(x1))))
5.39/2.24	   c(a(a(b(x1)))) -> c(c(a(b(x1))))
5.39/2.24	
5.39/2.24	The relative TRS consists of the following S rules:
5.39/2.24	
5.39/2.24	   c(a(c(x1))) -> c(b(b(x1)))
5.39/2.24	   c(b(c(x1))) -> c(c(b(x1)))
5.39/2.24	   a(a(c(b(x1)))) -> a(c(c(c(x1))))
5.39/2.24	   b(a(c(b(x1)))) -> b(c(c(c(x1))))
5.39/2.24	   c(a(c(b(x1)))) -> c(c(c(c(x1))))
5.39/2.24	   a(b(a(b(x1)))) -> a(c(c(b(x1))))
5.39/2.24	   b(b(a(b(x1)))) -> b(c(c(b(x1))))
5.39/2.24	   c(b(a(b(x1)))) -> c(c(c(b(x1))))
5.39/2.24	
5.39/2.24	
5.39/2.24	----------------------------------------
5.39/2.24	
5.39/2.24	(3) RootLabelingProof (EQUIVALENT)
5.39/2.24	We used plain root labeling [ROOTLAB] with the following heuristic:
5.39/2.24	LabelAll: All function symbols get labeled
5.39/2.24	
5.39/2.24	
5.39/2.24	----------------------------------------
5.39/2.24	
5.39/2.24	(4)
5.39/2.24	Obligation:
5.39/2.24	Relative term rewrite system:
5.39/2.24	The relative TRS consists of the following R rules:
5.39/2.24	
5.39/2.24	   a_{a_1}(a_{a_1}(a_{b_1}(b_{a_1}(x1)))) -> a_{c_1}(c_{b_1}(b_{c_1}(c_{a_1}(x1))))
5.39/2.24	   a_{a_1}(a_{a_1}(a_{b_1}(b_{b_1}(x1)))) -> a_{c_1}(c_{b_1}(b_{c_1}(c_{b_1}(x1))))
5.39/2.24	   a_{a_1}(a_{a_1}(a_{b_1}(b_{c_1}(x1)))) -> a_{c_1}(c_{b_1}(b_{c_1}(c_{c_1}(x1))))
5.39/2.24	   b_{a_1}(a_{a_1}(a_{b_1}(b_{a_1}(x1)))) -> b_{c_1}(c_{b_1}(b_{c_1}(c_{a_1}(x1))))
5.39/2.24	   b_{a_1}(a_{a_1}(a_{b_1}(b_{b_1}(x1)))) -> b_{c_1}(c_{b_1}(b_{c_1}(c_{b_1}(x1))))
5.39/2.24	   b_{a_1}(a_{a_1}(a_{b_1}(b_{c_1}(x1)))) -> b_{c_1}(c_{b_1}(b_{c_1}(c_{c_1}(x1))))
5.39/2.24	   c_{a_1}(a_{a_1}(a_{b_1}(b_{a_1}(x1)))) -> c_{c_1}(c_{b_1}(b_{c_1}(c_{a_1}(x1))))
5.39/2.24	   c_{a_1}(a_{a_1}(a_{b_1}(b_{b_1}(x1)))) -> c_{c_1}(c_{b_1}(b_{c_1}(c_{b_1}(x1))))
5.39/2.24	   c_{a_1}(a_{a_1}(a_{b_1}(b_{c_1}(x1)))) -> c_{c_1}(c_{b_1}(b_{c_1}(c_{c_1}(x1))))
5.39/2.24	   a_{b_1}(b_{c_1}(c_{b_1}(b_{a_1}(x1)))) -> a_{a_1}(a_{b_1}(b_{c_1}(c_{a_1}(x1))))
5.39/2.24	   a_{b_1}(b_{c_1}(c_{b_1}(b_{b_1}(x1)))) -> a_{a_1}(a_{b_1}(b_{c_1}(c_{b_1}(x1))))
5.39/2.24	   a_{b_1}(b_{c_1}(c_{b_1}(b_{c_1}(x1)))) -> a_{a_1}(a_{b_1}(b_{c_1}(c_{c_1}(x1))))
5.39/2.24	   b_{b_1}(b_{c_1}(c_{b_1}(b_{a_1}(x1)))) -> b_{a_1}(a_{b_1}(b_{c_1}(c_{a_1}(x1))))
5.39/2.24	   b_{b_1}(b_{c_1}(c_{b_1}(b_{b_1}(x1)))) -> b_{a_1}(a_{b_1}(b_{c_1}(c_{b_1}(x1))))
5.39/2.24	   b_{b_1}(b_{c_1}(c_{b_1}(b_{c_1}(x1)))) -> b_{a_1}(a_{b_1}(b_{c_1}(c_{c_1}(x1))))
5.39/2.24	   c_{b_1}(b_{c_1}(c_{b_1}(b_{a_1}(x1)))) -> c_{a_1}(a_{b_1}(b_{c_1}(c_{a_1}(x1))))
5.39/2.24	   c_{b_1}(b_{c_1}(c_{b_1}(b_{b_1}(x1)))) -> c_{a_1}(a_{b_1}(b_{c_1}(c_{b_1}(x1))))
5.39/2.24	   c_{b_1}(b_{c_1}(c_{b_1}(b_{c_1}(x1)))) -> c_{a_1}(a_{b_1}(b_{c_1}(c_{c_1}(x1))))
5.39/2.24	   a_{a_1}(a_{a_1}(a_{b_1}(b_{a_1}(x1)))) -> a_{c_1}(c_{a_1}(a_{b_1}(b_{a_1}(x1))))
5.39/2.24	   a_{a_1}(a_{a_1}(a_{b_1}(b_{b_1}(x1)))) -> a_{c_1}(c_{a_1}(a_{b_1}(b_{b_1}(x1))))
5.39/2.24	   a_{a_1}(a_{a_1}(a_{b_1}(b_{c_1}(x1)))) -> a_{c_1}(c_{a_1}(a_{b_1}(b_{c_1}(x1))))
5.39/2.24	   b_{a_1}(a_{a_1}(a_{b_1}(b_{a_1}(x1)))) -> b_{c_1}(c_{a_1}(a_{b_1}(b_{a_1}(x1))))
5.39/2.24	   b_{a_1}(a_{a_1}(a_{b_1}(b_{b_1}(x1)))) -> b_{c_1}(c_{a_1}(a_{b_1}(b_{b_1}(x1))))
5.39/2.24	   b_{a_1}(a_{a_1}(a_{b_1}(b_{c_1}(x1)))) -> b_{c_1}(c_{a_1}(a_{b_1}(b_{c_1}(x1))))
5.39/2.24	   c_{a_1}(a_{a_1}(a_{b_1}(b_{a_1}(x1)))) -> c_{c_1}(c_{a_1}(a_{b_1}(b_{a_1}(x1))))
5.39/2.24	   c_{a_1}(a_{a_1}(a_{b_1}(b_{b_1}(x1)))) -> c_{c_1}(c_{a_1}(a_{b_1}(b_{b_1}(x1))))
5.39/2.24	   c_{a_1}(a_{a_1}(a_{b_1}(b_{c_1}(x1)))) -> c_{c_1}(c_{a_1}(a_{b_1}(b_{c_1}(x1))))
5.39/2.24	
5.39/2.24	The relative TRS consists of the following S rules:
5.39/2.24	
5.39/2.24	   c_{a_1}(a_{c_1}(c_{a_1}(x1))) -> c_{b_1}(b_{b_1}(b_{a_1}(x1)))
5.39/2.24	   c_{a_1}(a_{c_1}(c_{b_1}(x1))) -> c_{b_1}(b_{b_1}(b_{b_1}(x1)))
5.39/2.24	   c_{a_1}(a_{c_1}(c_{c_1}(x1))) -> c_{b_1}(b_{b_1}(b_{c_1}(x1)))
5.39/2.24	   c_{b_1}(b_{c_1}(c_{a_1}(x1))) -> c_{c_1}(c_{b_1}(b_{a_1}(x1)))
5.39/2.24	   c_{b_1}(b_{c_1}(c_{b_1}(x1))) -> c_{c_1}(c_{b_1}(b_{b_1}(x1)))
5.39/2.24	   c_{b_1}(b_{c_1}(c_{c_1}(x1))) -> c_{c_1}(c_{b_1}(b_{c_1}(x1)))
5.39/2.24	   a_{a_1}(a_{c_1}(c_{b_1}(b_{a_1}(x1)))) -> a_{c_1}(c_{c_1}(c_{c_1}(c_{a_1}(x1))))
5.39/2.24	   a_{a_1}(a_{c_1}(c_{b_1}(b_{b_1}(x1)))) -> a_{c_1}(c_{c_1}(c_{c_1}(c_{b_1}(x1))))
5.39/2.24	   a_{a_1}(a_{c_1}(c_{b_1}(b_{c_1}(x1)))) -> a_{c_1}(c_{c_1}(c_{c_1}(c_{c_1}(x1))))
5.39/2.24	   b_{a_1}(a_{c_1}(c_{b_1}(b_{a_1}(x1)))) -> b_{c_1}(c_{c_1}(c_{c_1}(c_{a_1}(x1))))
5.39/2.24	   b_{a_1}(a_{c_1}(c_{b_1}(b_{b_1}(x1)))) -> b_{c_1}(c_{c_1}(c_{c_1}(c_{b_1}(x1))))
5.39/2.24	   b_{a_1}(a_{c_1}(c_{b_1}(b_{c_1}(x1)))) -> b_{c_1}(c_{c_1}(c_{c_1}(c_{c_1}(x1))))
5.39/2.24	   c_{a_1}(a_{c_1}(c_{b_1}(b_{a_1}(x1)))) -> c_{c_1}(c_{c_1}(c_{c_1}(c_{a_1}(x1))))
5.39/2.24	   c_{a_1}(a_{c_1}(c_{b_1}(b_{b_1}(x1)))) -> c_{c_1}(c_{c_1}(c_{c_1}(c_{b_1}(x1))))
5.39/2.24	   c_{a_1}(a_{c_1}(c_{b_1}(b_{c_1}(x1)))) -> c_{c_1}(c_{c_1}(c_{c_1}(c_{c_1}(x1))))
5.39/2.24	   a_{b_1}(b_{a_1}(a_{b_1}(b_{a_1}(x1)))) -> a_{c_1}(c_{c_1}(c_{b_1}(b_{a_1}(x1))))
5.39/2.24	   a_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(x1)))) -> a_{c_1}(c_{c_1}(c_{b_1}(b_{b_1}(x1))))
5.39/2.24	   a_{b_1}(b_{a_1}(a_{b_1}(b_{c_1}(x1)))) -> a_{c_1}(c_{c_1}(c_{b_1}(b_{c_1}(x1))))
5.39/2.24	   b_{b_1}(b_{a_1}(a_{b_1}(b_{a_1}(x1)))) -> b_{c_1}(c_{c_1}(c_{b_1}(b_{a_1}(x1))))
5.39/2.24	   b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(x1)))) -> b_{c_1}(c_{c_1}(c_{b_1}(b_{b_1}(x1))))
5.39/2.24	   b_{b_1}(b_{a_1}(a_{b_1}(b_{c_1}(x1)))) -> b_{c_1}(c_{c_1}(c_{b_1}(b_{c_1}(x1))))
5.39/2.24	   c_{b_1}(b_{a_1}(a_{b_1}(b_{a_1}(x1)))) -> c_{c_1}(c_{c_1}(c_{b_1}(b_{a_1}(x1))))
5.39/2.24	   c_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(x1)))) -> c_{c_1}(c_{c_1}(c_{b_1}(b_{b_1}(x1))))
5.39/2.24	   c_{b_1}(b_{a_1}(a_{b_1}(b_{c_1}(x1)))) -> c_{c_1}(c_{c_1}(c_{b_1}(b_{c_1}(x1))))
5.39/2.24	
5.39/2.24	
5.39/2.24	----------------------------------------
5.39/2.24	
5.39/2.24	(5) RelTRSRRRProof (EQUIVALENT)
5.39/2.24	We used the following monotonic ordering for rule removal:
5.39/2.24	Knuth-Bendix order [KBO] with precedence:c_{a_1}_1 > c_{b_1}_1 > b_{b_1}_1 > c_{c_1}_1 > b_{c_1}_1 > a_{b_1}_1 > a_{a_1}_1 > a_{c_1}_1 > b_{a_1}_1
5.39/2.24	
5.39/2.24	and weight map:
5.39/2.24	
5.39/2.24	   a_{a_1}_1=24
5.39/2.24	   a_{b_1}_1=23
5.39/2.24	   b_{a_1}_1=17
5.39/2.24	   a_{c_1}_1=25
5.39/2.24	   c_{b_1}_1=30
5.39/2.24	   b_{c_1}_1=1
5.39/2.24	   c_{a_1}_1=23
5.39/2.24	   b_{b_1}_1=24
5.39/2.24	   c_{c_1}_1=7
5.39/2.24	
5.39/2.24	The variable weight is 1With this ordering the following rules can be removed [MATRO] because they are oriented strictly:
5.39/2.24	Rules from R:
5.39/2.24	
5.39/2.24	   a_{a_1}(a_{a_1}(a_{b_1}(b_{a_1}(x1)))) -> a_{c_1}(c_{b_1}(b_{c_1}(c_{a_1}(x1))))
5.39/2.24	   a_{a_1}(a_{a_1}(a_{b_1}(b_{b_1}(x1)))) -> a_{c_1}(c_{b_1}(b_{c_1}(c_{b_1}(x1))))
5.39/2.24	   a_{a_1}(a_{a_1}(a_{b_1}(b_{c_1}(x1)))) -> a_{c_1}(c_{b_1}(b_{c_1}(c_{c_1}(x1))))
5.39/2.24	   b_{a_1}(a_{a_1}(a_{b_1}(b_{a_1}(x1)))) -> b_{c_1}(c_{b_1}(b_{c_1}(c_{a_1}(x1))))
5.39/2.24	   b_{a_1}(a_{a_1}(a_{b_1}(b_{b_1}(x1)))) -> b_{c_1}(c_{b_1}(b_{c_1}(c_{b_1}(x1))))
5.39/2.24	   b_{a_1}(a_{a_1}(a_{b_1}(b_{c_1}(x1)))) -> b_{c_1}(c_{b_1}(b_{c_1}(c_{c_1}(x1))))
5.39/2.24	   c_{a_1}(a_{a_1}(a_{b_1}(b_{a_1}(x1)))) -> c_{c_1}(c_{b_1}(b_{c_1}(c_{a_1}(x1))))
5.39/2.24	   c_{a_1}(a_{a_1}(a_{b_1}(b_{b_1}(x1)))) -> c_{c_1}(c_{b_1}(b_{c_1}(c_{b_1}(x1))))
5.39/2.24	   c_{a_1}(a_{a_1}(a_{b_1}(b_{c_1}(x1)))) -> c_{c_1}(c_{b_1}(b_{c_1}(c_{c_1}(x1))))
5.39/2.24	   a_{b_1}(b_{c_1}(c_{b_1}(b_{a_1}(x1)))) -> a_{a_1}(a_{b_1}(b_{c_1}(c_{a_1}(x1))))
5.39/2.24	   a_{b_1}(b_{c_1}(c_{b_1}(b_{b_1}(x1)))) -> a_{a_1}(a_{b_1}(b_{c_1}(c_{b_1}(x1))))
5.39/2.24	   a_{b_1}(b_{c_1}(c_{b_1}(b_{c_1}(x1)))) -> a_{a_1}(a_{b_1}(b_{c_1}(c_{c_1}(x1))))
5.39/2.24	   b_{b_1}(b_{c_1}(c_{b_1}(b_{a_1}(x1)))) -> b_{a_1}(a_{b_1}(b_{c_1}(c_{a_1}(x1))))
5.39/2.24	   b_{b_1}(b_{c_1}(c_{b_1}(b_{b_1}(x1)))) -> b_{a_1}(a_{b_1}(b_{c_1}(c_{b_1}(x1))))
5.39/2.24	   b_{b_1}(b_{c_1}(c_{b_1}(b_{c_1}(x1)))) -> b_{a_1}(a_{b_1}(b_{c_1}(c_{c_1}(x1))))
5.39/2.24	   c_{b_1}(b_{c_1}(c_{b_1}(b_{a_1}(x1)))) -> c_{a_1}(a_{b_1}(b_{c_1}(c_{a_1}(x1))))
5.39/2.24	   c_{b_1}(b_{c_1}(c_{b_1}(b_{b_1}(x1)))) -> c_{a_1}(a_{b_1}(b_{c_1}(c_{b_1}(x1))))
5.39/2.24	   c_{b_1}(b_{c_1}(c_{b_1}(b_{c_1}(x1)))) -> c_{a_1}(a_{b_1}(b_{c_1}(c_{c_1}(x1))))
5.39/2.24	   a_{a_1}(a_{a_1}(a_{b_1}(b_{a_1}(x1)))) -> a_{c_1}(c_{a_1}(a_{b_1}(b_{a_1}(x1))))
5.39/2.24	   a_{a_1}(a_{a_1}(a_{b_1}(b_{b_1}(x1)))) -> a_{c_1}(c_{a_1}(a_{b_1}(b_{b_1}(x1))))
5.39/2.24	   a_{a_1}(a_{a_1}(a_{b_1}(b_{c_1}(x1)))) -> a_{c_1}(c_{a_1}(a_{b_1}(b_{c_1}(x1))))
5.39/2.24	   b_{a_1}(a_{a_1}(a_{b_1}(b_{a_1}(x1)))) -> b_{c_1}(c_{a_1}(a_{b_1}(b_{a_1}(x1))))
5.39/2.24	   b_{a_1}(a_{a_1}(a_{b_1}(b_{b_1}(x1)))) -> b_{c_1}(c_{a_1}(a_{b_1}(b_{b_1}(x1))))
5.39/2.24	   b_{a_1}(a_{a_1}(a_{b_1}(b_{c_1}(x1)))) -> b_{c_1}(c_{a_1}(a_{b_1}(b_{c_1}(x1))))
5.39/2.24	   c_{a_1}(a_{a_1}(a_{b_1}(b_{a_1}(x1)))) -> c_{c_1}(c_{a_1}(a_{b_1}(b_{a_1}(x1))))
5.39/2.24	   c_{a_1}(a_{a_1}(a_{b_1}(b_{b_1}(x1)))) -> c_{c_1}(c_{a_1}(a_{b_1}(b_{b_1}(x1))))
5.39/2.24	   c_{a_1}(a_{a_1}(a_{b_1}(b_{c_1}(x1)))) -> c_{c_1}(c_{a_1}(a_{b_1}(b_{c_1}(x1))))
5.39/2.24	Rules from S:
5.39/2.24	
5.39/2.24	   c_{a_1}(a_{c_1}(c_{a_1}(x1))) -> c_{b_1}(b_{b_1}(b_{a_1}(x1)))
5.39/2.24	   c_{a_1}(a_{c_1}(c_{b_1}(x1))) -> c_{b_1}(b_{b_1}(b_{b_1}(x1)))
5.39/2.24	   c_{a_1}(a_{c_1}(c_{c_1}(x1))) -> c_{b_1}(b_{b_1}(b_{c_1}(x1)))
5.39/2.24	   c_{b_1}(b_{c_1}(c_{a_1}(x1))) -> c_{c_1}(c_{b_1}(b_{a_1}(x1)))
5.39/2.24	   c_{b_1}(b_{c_1}(c_{b_1}(x1))) -> c_{c_1}(c_{b_1}(b_{b_1}(x1)))
5.39/2.24	   c_{b_1}(b_{c_1}(c_{c_1}(x1))) -> c_{c_1}(c_{b_1}(b_{c_1}(x1)))
5.39/2.24	   a_{a_1}(a_{c_1}(c_{b_1}(b_{a_1}(x1)))) -> a_{c_1}(c_{c_1}(c_{c_1}(c_{a_1}(x1))))
5.39/2.24	   a_{a_1}(a_{c_1}(c_{b_1}(b_{b_1}(x1)))) -> a_{c_1}(c_{c_1}(c_{c_1}(c_{b_1}(x1))))
5.39/2.24	   a_{a_1}(a_{c_1}(c_{b_1}(b_{c_1}(x1)))) -> a_{c_1}(c_{c_1}(c_{c_1}(c_{c_1}(x1))))
5.39/2.24	   b_{a_1}(a_{c_1}(c_{b_1}(b_{a_1}(x1)))) -> b_{c_1}(c_{c_1}(c_{c_1}(c_{a_1}(x1))))
5.39/2.24	   b_{a_1}(a_{c_1}(c_{b_1}(b_{b_1}(x1)))) -> b_{c_1}(c_{c_1}(c_{c_1}(c_{b_1}(x1))))
5.39/2.24	   b_{a_1}(a_{c_1}(c_{b_1}(b_{c_1}(x1)))) -> b_{c_1}(c_{c_1}(c_{c_1}(c_{c_1}(x1))))
5.39/2.24	   c_{a_1}(a_{c_1}(c_{b_1}(b_{a_1}(x1)))) -> c_{c_1}(c_{c_1}(c_{c_1}(c_{a_1}(x1))))
5.39/2.24	   c_{a_1}(a_{c_1}(c_{b_1}(b_{b_1}(x1)))) -> c_{c_1}(c_{c_1}(c_{c_1}(c_{b_1}(x1))))
5.39/2.24	   c_{a_1}(a_{c_1}(c_{b_1}(b_{c_1}(x1)))) -> c_{c_1}(c_{c_1}(c_{c_1}(c_{c_1}(x1))))
5.39/2.24	   a_{b_1}(b_{a_1}(a_{b_1}(b_{a_1}(x1)))) -> a_{c_1}(c_{c_1}(c_{b_1}(b_{a_1}(x1))))
5.39/2.24	   a_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(x1)))) -> a_{c_1}(c_{c_1}(c_{b_1}(b_{b_1}(x1))))
5.39/2.24	   a_{b_1}(b_{a_1}(a_{b_1}(b_{c_1}(x1)))) -> a_{c_1}(c_{c_1}(c_{b_1}(b_{c_1}(x1))))
5.39/2.24	   b_{b_1}(b_{a_1}(a_{b_1}(b_{a_1}(x1)))) -> b_{c_1}(c_{c_1}(c_{b_1}(b_{a_1}(x1))))
5.39/2.24	   b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(x1)))) -> b_{c_1}(c_{c_1}(c_{b_1}(b_{b_1}(x1))))
5.39/2.24	   b_{b_1}(b_{a_1}(a_{b_1}(b_{c_1}(x1)))) -> b_{c_1}(c_{c_1}(c_{b_1}(b_{c_1}(x1))))
5.39/2.24	   c_{b_1}(b_{a_1}(a_{b_1}(b_{a_1}(x1)))) -> c_{c_1}(c_{c_1}(c_{b_1}(b_{a_1}(x1))))
5.39/2.24	   c_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(x1)))) -> c_{c_1}(c_{c_1}(c_{b_1}(b_{b_1}(x1))))
5.39/2.24	   c_{b_1}(b_{a_1}(a_{b_1}(b_{c_1}(x1)))) -> c_{c_1}(c_{c_1}(c_{b_1}(b_{c_1}(x1))))
5.39/2.24	
5.39/2.24	
5.39/2.24	
5.39/2.24	
5.39/2.24	----------------------------------------
5.39/2.24	
5.39/2.24	(6)
5.39/2.24	Obligation:
5.39/2.24	Relative term rewrite system:
5.39/2.24	R is empty.
5.39/2.24	S is empty.
5.39/2.24	
5.39/2.24	----------------------------------------
5.39/2.24	
5.39/2.24	(7) RIsEmptyProof (EQUIVALENT)
5.39/2.24	The TRS R is empty. Hence, termination is trivially proven.
5.39/2.24	----------------------------------------
5.39/2.24	
5.39/2.24	(8)
5.39/2.24	YES
5.75/2.31	EOF