109.71/28.83	YES
110.25/28.90	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
110.25/28.90	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
110.25/28.90	
110.25/28.90	
110.25/28.90	Termination w.r.t. Q of the given QTRS could be proven:
110.25/28.90	
110.25/28.90	(0) QTRS
110.25/28.90	(1) FlatCCProof [EQUIVALENT, 0 ms]
110.25/28.90	(2) QTRS
110.25/28.90	(3) RootLabelingProof [EQUIVALENT, 0 ms]
110.25/28.90	(4) QTRS
110.25/28.90	(5) QTRSRRRProof [EQUIVALENT, 328 ms]
110.25/28.90	(6) QTRS
110.25/28.90	(7) DependencyPairsProof [EQUIVALENT, 165 ms]
110.25/28.90	(8) QDP
110.25/28.90	(9) DependencyGraphProof [EQUIVALENT, 0 ms]
110.25/28.90	(10) QDP
110.25/28.90	(11) QDPOrderProof [EQUIVALENT, 4904 ms]
110.25/28.90	(12) QDP
110.25/28.90	(13) DependencyGraphProof [EQUIVALENT, 0 ms]
110.25/28.90	(14) TRUE
110.25/28.90	
110.25/28.90	
110.25/28.90	----------------------------------------
110.25/28.90	
110.25/28.90	(0)
110.25/28.90	Obligation:
110.25/28.90	Q restricted rewrite system:
110.25/28.90	The TRS R consists of the following rules:
110.25/28.90	
110.25/28.90	   a(b(x1)) -> c(d(x1))
110.25/28.90	   d(d(x1)) -> b(e(x1))
110.25/28.90	   b(x1) -> d(c(x1))
110.25/28.90	   d(x1) -> x1
110.25/28.90	   e(c(x1)) -> d(a(x1))
110.25/28.90	   a(x1) -> e(d(x1))
110.25/28.90	
110.25/28.90	Q is empty.
110.25/28.90	
110.25/28.90	----------------------------------------
110.25/28.90	
110.25/28.90	(1) FlatCCProof (EQUIVALENT)
110.25/28.90	We used flat context closure [ROOTLAB]
110.25/28.90	As Q is empty the flat context closure was sound AND complete.
110.25/28.90	
110.25/28.90	----------------------------------------
110.25/28.90	
110.25/28.90	(2)
110.25/28.90	Obligation:
110.25/28.90	Q restricted rewrite system:
110.25/28.90	The TRS R consists of the following rules:
110.25/28.90	
110.25/28.90	   a(a(b(x1))) -> a(c(d(x1)))
110.25/28.90	   b(a(b(x1))) -> b(c(d(x1)))
110.25/28.90	   c(a(b(x1))) -> c(c(d(x1)))
110.25/28.90	   d(a(b(x1))) -> d(c(d(x1)))
110.25/28.90	   e(a(b(x1))) -> e(c(d(x1)))
110.25/28.90	   a(d(d(x1))) -> a(b(e(x1)))
110.25/28.90	   b(d(d(x1))) -> b(b(e(x1)))
110.25/28.90	   c(d(d(x1))) -> c(b(e(x1)))
110.25/28.90	   d(d(d(x1))) -> d(b(e(x1)))
110.25/28.90	   e(d(d(x1))) -> e(b(e(x1)))
110.25/28.90	   a(b(x1)) -> a(d(c(x1)))
110.25/28.90	   b(b(x1)) -> b(d(c(x1)))
110.25/28.90	   c(b(x1)) -> c(d(c(x1)))
110.25/28.90	   d(b(x1)) -> d(d(c(x1)))
110.25/28.90	   e(b(x1)) -> e(d(c(x1)))
110.25/28.90	   a(d(x1)) -> a(x1)
110.25/28.90	   b(d(x1)) -> b(x1)
110.25/28.90	   c(d(x1)) -> c(x1)
110.25/28.90	   d(d(x1)) -> d(x1)
110.25/28.90	   e(d(x1)) -> e(x1)
110.25/28.90	   a(e(c(x1))) -> a(d(a(x1)))
110.25/28.90	   b(e(c(x1))) -> b(d(a(x1)))
110.25/28.90	   c(e(c(x1))) -> c(d(a(x1)))
110.25/28.90	   d(e(c(x1))) -> d(d(a(x1)))
110.25/28.90	   e(e(c(x1))) -> e(d(a(x1)))
110.25/28.90	   a(a(x1)) -> a(e(d(x1)))
110.25/28.90	   b(a(x1)) -> b(e(d(x1)))
110.25/28.90	   c(a(x1)) -> c(e(d(x1)))
110.25/28.90	   d(a(x1)) -> d(e(d(x1)))
110.25/28.90	   e(a(x1)) -> e(e(d(x1)))
110.25/28.90	
110.25/28.90	Q is empty.
110.25/28.90	
110.25/28.90	----------------------------------------
110.25/28.90	
110.25/28.90	(3) RootLabelingProof (EQUIVALENT)
110.25/28.90	We used plain root labeling [ROOTLAB] with the following heuristic:
110.25/28.90	LabelAll: All function symbols get labeled
110.25/28.90	
110.25/28.90	As Q is empty the root labeling was sound AND complete.
110.25/28.90	
110.25/28.90	----------------------------------------
110.25/28.90	
110.25/28.90	(4)
110.25/28.90	Obligation:
110.25/28.90	Q restricted rewrite system:
110.25/28.90	The TRS R consists of the following rules:
110.25/28.90	
110.25/28.90	   a_{a_1}(a_{b_1}(b_{a_1}(x1))) -> a_{c_1}(c_{d_1}(d_{a_1}(x1)))
110.25/28.90	   a_{a_1}(a_{b_1}(b_{b_1}(x1))) -> a_{c_1}(c_{d_1}(d_{b_1}(x1)))
110.25/28.90	   a_{a_1}(a_{b_1}(b_{c_1}(x1))) -> a_{c_1}(c_{d_1}(d_{c_1}(x1)))
110.25/28.90	   a_{a_1}(a_{b_1}(b_{d_1}(x1))) -> a_{c_1}(c_{d_1}(d_{d_1}(x1)))
110.25/28.90	   a_{a_1}(a_{b_1}(b_{e_1}(x1))) -> a_{c_1}(c_{d_1}(d_{e_1}(x1)))
110.25/28.90	   b_{a_1}(a_{b_1}(b_{a_1}(x1))) -> b_{c_1}(c_{d_1}(d_{a_1}(x1)))
110.25/28.90	   b_{a_1}(a_{b_1}(b_{b_1}(x1))) -> b_{c_1}(c_{d_1}(d_{b_1}(x1)))
110.25/28.90	   b_{a_1}(a_{b_1}(b_{c_1}(x1))) -> b_{c_1}(c_{d_1}(d_{c_1}(x1)))
110.25/28.90	   b_{a_1}(a_{b_1}(b_{d_1}(x1))) -> b_{c_1}(c_{d_1}(d_{d_1}(x1)))
110.25/28.90	   b_{a_1}(a_{b_1}(b_{e_1}(x1))) -> b_{c_1}(c_{d_1}(d_{e_1}(x1)))
110.25/28.90	   c_{a_1}(a_{b_1}(b_{a_1}(x1))) -> c_{c_1}(c_{d_1}(d_{a_1}(x1)))
110.25/28.90	   c_{a_1}(a_{b_1}(b_{b_1}(x1))) -> c_{c_1}(c_{d_1}(d_{b_1}(x1)))
110.25/28.90	   c_{a_1}(a_{b_1}(b_{c_1}(x1))) -> c_{c_1}(c_{d_1}(d_{c_1}(x1)))
110.25/28.90	   c_{a_1}(a_{b_1}(b_{d_1}(x1))) -> c_{c_1}(c_{d_1}(d_{d_1}(x1)))
110.25/28.90	   c_{a_1}(a_{b_1}(b_{e_1}(x1))) -> c_{c_1}(c_{d_1}(d_{e_1}(x1)))
110.25/28.90	   d_{a_1}(a_{b_1}(b_{a_1}(x1))) -> d_{c_1}(c_{d_1}(d_{a_1}(x1)))
110.25/28.90	   d_{a_1}(a_{b_1}(b_{b_1}(x1))) -> d_{c_1}(c_{d_1}(d_{b_1}(x1)))
110.25/28.90	   d_{a_1}(a_{b_1}(b_{c_1}(x1))) -> d_{c_1}(c_{d_1}(d_{c_1}(x1)))
110.25/28.90	   d_{a_1}(a_{b_1}(b_{d_1}(x1))) -> d_{c_1}(c_{d_1}(d_{d_1}(x1)))
110.25/28.90	   d_{a_1}(a_{b_1}(b_{e_1}(x1))) -> d_{c_1}(c_{d_1}(d_{e_1}(x1)))
110.25/28.90	   e_{a_1}(a_{b_1}(b_{a_1}(x1))) -> e_{c_1}(c_{d_1}(d_{a_1}(x1)))
110.25/28.90	   e_{a_1}(a_{b_1}(b_{b_1}(x1))) -> e_{c_1}(c_{d_1}(d_{b_1}(x1)))
110.25/28.90	   e_{a_1}(a_{b_1}(b_{c_1}(x1))) -> e_{c_1}(c_{d_1}(d_{c_1}(x1)))
110.25/28.90	   e_{a_1}(a_{b_1}(b_{d_1}(x1))) -> e_{c_1}(c_{d_1}(d_{d_1}(x1)))
110.25/28.90	   e_{a_1}(a_{b_1}(b_{e_1}(x1))) -> e_{c_1}(c_{d_1}(d_{e_1}(x1)))
110.25/28.90	   a_{d_1}(d_{d_1}(d_{a_1}(x1))) -> a_{b_1}(b_{e_1}(e_{a_1}(x1)))
110.25/28.90	   a_{d_1}(d_{d_1}(d_{b_1}(x1))) -> a_{b_1}(b_{e_1}(e_{b_1}(x1)))
110.25/28.90	   a_{d_1}(d_{d_1}(d_{c_1}(x1))) -> a_{b_1}(b_{e_1}(e_{c_1}(x1)))
110.25/28.90	   a_{d_1}(d_{d_1}(d_{d_1}(x1))) -> a_{b_1}(b_{e_1}(e_{d_1}(x1)))
110.25/28.90	   a_{d_1}(d_{d_1}(d_{e_1}(x1))) -> a_{b_1}(b_{e_1}(e_{e_1}(x1)))
110.25/28.90	   b_{d_1}(d_{d_1}(d_{a_1}(x1))) -> b_{b_1}(b_{e_1}(e_{a_1}(x1)))
110.25/28.90	   b_{d_1}(d_{d_1}(d_{b_1}(x1))) -> b_{b_1}(b_{e_1}(e_{b_1}(x1)))
110.25/28.90	   b_{d_1}(d_{d_1}(d_{c_1}(x1))) -> b_{b_1}(b_{e_1}(e_{c_1}(x1)))
110.25/28.90	   b_{d_1}(d_{d_1}(d_{d_1}(x1))) -> b_{b_1}(b_{e_1}(e_{d_1}(x1)))
110.25/28.90	   b_{d_1}(d_{d_1}(d_{e_1}(x1))) -> b_{b_1}(b_{e_1}(e_{e_1}(x1)))
110.25/28.90	   c_{d_1}(d_{d_1}(d_{a_1}(x1))) -> c_{b_1}(b_{e_1}(e_{a_1}(x1)))
110.25/28.90	   c_{d_1}(d_{d_1}(d_{b_1}(x1))) -> c_{b_1}(b_{e_1}(e_{b_1}(x1)))
110.25/28.90	   c_{d_1}(d_{d_1}(d_{c_1}(x1))) -> c_{b_1}(b_{e_1}(e_{c_1}(x1)))
110.25/28.90	   c_{d_1}(d_{d_1}(d_{d_1}(x1))) -> c_{b_1}(b_{e_1}(e_{d_1}(x1)))
110.25/28.90	   c_{d_1}(d_{d_1}(d_{e_1}(x1))) -> c_{b_1}(b_{e_1}(e_{e_1}(x1)))
110.25/28.90	   d_{d_1}(d_{d_1}(d_{a_1}(x1))) -> d_{b_1}(b_{e_1}(e_{a_1}(x1)))
110.25/28.90	   d_{d_1}(d_{d_1}(d_{b_1}(x1))) -> d_{b_1}(b_{e_1}(e_{b_1}(x1)))
110.25/28.90	   d_{d_1}(d_{d_1}(d_{c_1}(x1))) -> d_{b_1}(b_{e_1}(e_{c_1}(x1)))
110.25/28.90	   d_{d_1}(d_{d_1}(d_{d_1}(x1))) -> d_{b_1}(b_{e_1}(e_{d_1}(x1)))
110.25/28.90	   d_{d_1}(d_{d_1}(d_{e_1}(x1))) -> d_{b_1}(b_{e_1}(e_{e_1}(x1)))
110.25/28.90	   e_{d_1}(d_{d_1}(d_{a_1}(x1))) -> e_{b_1}(b_{e_1}(e_{a_1}(x1)))
110.25/28.90	   e_{d_1}(d_{d_1}(d_{b_1}(x1))) -> e_{b_1}(b_{e_1}(e_{b_1}(x1)))
110.25/28.90	   e_{d_1}(d_{d_1}(d_{c_1}(x1))) -> e_{b_1}(b_{e_1}(e_{c_1}(x1)))
110.25/28.90	   e_{d_1}(d_{d_1}(d_{d_1}(x1))) -> e_{b_1}(b_{e_1}(e_{d_1}(x1)))
110.25/28.90	   e_{d_1}(d_{d_1}(d_{e_1}(x1))) -> e_{b_1}(b_{e_1}(e_{e_1}(x1)))
110.25/28.90	   a_{b_1}(b_{a_1}(x1)) -> a_{d_1}(d_{c_1}(c_{a_1}(x1)))
110.25/28.90	   a_{b_1}(b_{b_1}(x1)) -> a_{d_1}(d_{c_1}(c_{b_1}(x1)))
110.25/28.90	   a_{b_1}(b_{c_1}(x1)) -> a_{d_1}(d_{c_1}(c_{c_1}(x1)))
110.25/28.90	   a_{b_1}(b_{d_1}(x1)) -> a_{d_1}(d_{c_1}(c_{d_1}(x1)))
110.25/28.90	   a_{b_1}(b_{e_1}(x1)) -> a_{d_1}(d_{c_1}(c_{e_1}(x1)))
110.25/28.90	   b_{b_1}(b_{a_1}(x1)) -> b_{d_1}(d_{c_1}(c_{a_1}(x1)))
110.25/28.90	   b_{b_1}(b_{b_1}(x1)) -> b_{d_1}(d_{c_1}(c_{b_1}(x1)))
110.25/28.90	   b_{b_1}(b_{c_1}(x1)) -> b_{d_1}(d_{c_1}(c_{c_1}(x1)))
110.25/28.90	   b_{b_1}(b_{d_1}(x1)) -> b_{d_1}(d_{c_1}(c_{d_1}(x1)))
110.25/28.90	   b_{b_1}(b_{e_1}(x1)) -> b_{d_1}(d_{c_1}(c_{e_1}(x1)))
110.25/28.90	   c_{b_1}(b_{a_1}(x1)) -> c_{d_1}(d_{c_1}(c_{a_1}(x1)))
110.25/28.90	   c_{b_1}(b_{b_1}(x1)) -> c_{d_1}(d_{c_1}(c_{b_1}(x1)))
110.25/28.90	   c_{b_1}(b_{c_1}(x1)) -> c_{d_1}(d_{c_1}(c_{c_1}(x1)))
110.25/28.90	   c_{b_1}(b_{d_1}(x1)) -> c_{d_1}(d_{c_1}(c_{d_1}(x1)))
110.25/28.90	   c_{b_1}(b_{e_1}(x1)) -> c_{d_1}(d_{c_1}(c_{e_1}(x1)))
110.25/28.90	   d_{b_1}(b_{a_1}(x1)) -> d_{d_1}(d_{c_1}(c_{a_1}(x1)))
110.25/28.90	   d_{b_1}(b_{b_1}(x1)) -> d_{d_1}(d_{c_1}(c_{b_1}(x1)))
110.25/28.90	   d_{b_1}(b_{c_1}(x1)) -> d_{d_1}(d_{c_1}(c_{c_1}(x1)))
110.25/28.90	   d_{b_1}(b_{d_1}(x1)) -> d_{d_1}(d_{c_1}(c_{d_1}(x1)))
110.25/28.90	   d_{b_1}(b_{e_1}(x1)) -> d_{d_1}(d_{c_1}(c_{e_1}(x1)))
110.25/28.90	   e_{b_1}(b_{a_1}(x1)) -> e_{d_1}(d_{c_1}(c_{a_1}(x1)))
110.25/28.90	   e_{b_1}(b_{b_1}(x1)) -> e_{d_1}(d_{c_1}(c_{b_1}(x1)))
110.25/28.90	   e_{b_1}(b_{c_1}(x1)) -> e_{d_1}(d_{c_1}(c_{c_1}(x1)))
110.25/28.90	   e_{b_1}(b_{d_1}(x1)) -> e_{d_1}(d_{c_1}(c_{d_1}(x1)))
110.25/28.90	   e_{b_1}(b_{e_1}(x1)) -> e_{d_1}(d_{c_1}(c_{e_1}(x1)))
110.25/28.90	   a_{d_1}(d_{a_1}(x1)) -> a_{a_1}(x1)
110.25/28.90	   a_{d_1}(d_{b_1}(x1)) -> a_{b_1}(x1)
110.25/28.90	   a_{d_1}(d_{c_1}(x1)) -> a_{c_1}(x1)
110.25/28.90	   a_{d_1}(d_{d_1}(x1)) -> a_{d_1}(x1)
110.25/28.90	   a_{d_1}(d_{e_1}(x1)) -> a_{e_1}(x1)
110.25/28.90	   b_{d_1}(d_{a_1}(x1)) -> b_{a_1}(x1)
110.25/28.90	   b_{d_1}(d_{b_1}(x1)) -> b_{b_1}(x1)
110.25/28.90	   b_{d_1}(d_{c_1}(x1)) -> b_{c_1}(x1)
110.25/28.90	   b_{d_1}(d_{d_1}(x1)) -> b_{d_1}(x1)
110.25/28.90	   b_{d_1}(d_{e_1}(x1)) -> b_{e_1}(x1)
110.25/28.90	   c_{d_1}(d_{a_1}(x1)) -> c_{a_1}(x1)
110.25/28.90	   c_{d_1}(d_{b_1}(x1)) -> c_{b_1}(x1)
110.25/28.90	   c_{d_1}(d_{c_1}(x1)) -> c_{c_1}(x1)
110.25/28.90	   c_{d_1}(d_{d_1}(x1)) -> c_{d_1}(x1)
110.25/28.90	   c_{d_1}(d_{e_1}(x1)) -> c_{e_1}(x1)
110.25/28.90	   d_{d_1}(d_{a_1}(x1)) -> d_{a_1}(x1)
110.25/28.90	   d_{d_1}(d_{b_1}(x1)) -> d_{b_1}(x1)
110.25/28.90	   d_{d_1}(d_{c_1}(x1)) -> d_{c_1}(x1)
110.25/28.90	   d_{d_1}(d_{d_1}(x1)) -> d_{d_1}(x1)
110.25/28.90	   d_{d_1}(d_{e_1}(x1)) -> d_{e_1}(x1)
110.25/28.90	   e_{d_1}(d_{a_1}(x1)) -> e_{a_1}(x1)
110.25/28.90	   e_{d_1}(d_{b_1}(x1)) -> e_{b_1}(x1)
110.25/28.90	   e_{d_1}(d_{c_1}(x1)) -> e_{c_1}(x1)
110.25/28.90	   e_{d_1}(d_{d_1}(x1)) -> e_{d_1}(x1)
110.25/28.90	   e_{d_1}(d_{e_1}(x1)) -> e_{e_1}(x1)
110.25/28.90	   a_{e_1}(e_{c_1}(c_{a_1}(x1))) -> a_{d_1}(d_{a_1}(a_{a_1}(x1)))
110.25/28.90	   a_{e_1}(e_{c_1}(c_{b_1}(x1))) -> a_{d_1}(d_{a_1}(a_{b_1}(x1)))
110.25/28.90	   a_{e_1}(e_{c_1}(c_{c_1}(x1))) -> a_{d_1}(d_{a_1}(a_{c_1}(x1)))
110.25/28.90	   a_{e_1}(e_{c_1}(c_{d_1}(x1))) -> a_{d_1}(d_{a_1}(a_{d_1}(x1)))
110.25/28.90	   a_{e_1}(e_{c_1}(c_{e_1}(x1))) -> a_{d_1}(d_{a_1}(a_{e_1}(x1)))
110.25/28.90	   b_{e_1}(e_{c_1}(c_{a_1}(x1))) -> b_{d_1}(d_{a_1}(a_{a_1}(x1)))
110.25/28.90	   b_{e_1}(e_{c_1}(c_{b_1}(x1))) -> b_{d_1}(d_{a_1}(a_{b_1}(x1)))
110.25/28.90	   b_{e_1}(e_{c_1}(c_{c_1}(x1))) -> b_{d_1}(d_{a_1}(a_{c_1}(x1)))
110.25/28.90	   b_{e_1}(e_{c_1}(c_{d_1}(x1))) -> b_{d_1}(d_{a_1}(a_{d_1}(x1)))
110.25/28.90	   b_{e_1}(e_{c_1}(c_{e_1}(x1))) -> b_{d_1}(d_{a_1}(a_{e_1}(x1)))
110.25/28.90	   c_{e_1}(e_{c_1}(c_{a_1}(x1))) -> c_{d_1}(d_{a_1}(a_{a_1}(x1)))
110.25/28.90	   c_{e_1}(e_{c_1}(c_{b_1}(x1))) -> c_{d_1}(d_{a_1}(a_{b_1}(x1)))
110.25/28.90	   c_{e_1}(e_{c_1}(c_{c_1}(x1))) -> c_{d_1}(d_{a_1}(a_{c_1}(x1)))
110.25/28.90	   c_{e_1}(e_{c_1}(c_{d_1}(x1))) -> c_{d_1}(d_{a_1}(a_{d_1}(x1)))
110.25/28.90	   c_{e_1}(e_{c_1}(c_{e_1}(x1))) -> c_{d_1}(d_{a_1}(a_{e_1}(x1)))
110.25/28.90	   d_{e_1}(e_{c_1}(c_{a_1}(x1))) -> d_{d_1}(d_{a_1}(a_{a_1}(x1)))
110.25/28.90	   d_{e_1}(e_{c_1}(c_{b_1}(x1))) -> d_{d_1}(d_{a_1}(a_{b_1}(x1)))
110.25/28.90	   d_{e_1}(e_{c_1}(c_{c_1}(x1))) -> d_{d_1}(d_{a_1}(a_{c_1}(x1)))
110.25/28.90	   d_{e_1}(e_{c_1}(c_{d_1}(x1))) -> d_{d_1}(d_{a_1}(a_{d_1}(x1)))
110.25/28.90	   d_{e_1}(e_{c_1}(c_{e_1}(x1))) -> d_{d_1}(d_{a_1}(a_{e_1}(x1)))
110.25/28.90	   e_{e_1}(e_{c_1}(c_{a_1}(x1))) -> e_{d_1}(d_{a_1}(a_{a_1}(x1)))
110.25/28.90	   e_{e_1}(e_{c_1}(c_{b_1}(x1))) -> e_{d_1}(d_{a_1}(a_{b_1}(x1)))
110.25/28.90	   e_{e_1}(e_{c_1}(c_{c_1}(x1))) -> e_{d_1}(d_{a_1}(a_{c_1}(x1)))
110.25/28.90	   e_{e_1}(e_{c_1}(c_{d_1}(x1))) -> e_{d_1}(d_{a_1}(a_{d_1}(x1)))
110.25/28.90	   e_{e_1}(e_{c_1}(c_{e_1}(x1))) -> e_{d_1}(d_{a_1}(a_{e_1}(x1)))
110.25/28.90	   a_{a_1}(a_{a_1}(x1)) -> a_{e_1}(e_{d_1}(d_{a_1}(x1)))
110.25/28.90	   a_{a_1}(a_{b_1}(x1)) -> a_{e_1}(e_{d_1}(d_{b_1}(x1)))
110.25/28.90	   a_{a_1}(a_{c_1}(x1)) -> a_{e_1}(e_{d_1}(d_{c_1}(x1)))
110.25/28.90	   a_{a_1}(a_{d_1}(x1)) -> a_{e_1}(e_{d_1}(d_{d_1}(x1)))
110.25/28.90	   a_{a_1}(a_{e_1}(x1)) -> a_{e_1}(e_{d_1}(d_{e_1}(x1)))
110.25/28.90	   b_{a_1}(a_{a_1}(x1)) -> b_{e_1}(e_{d_1}(d_{a_1}(x1)))
110.25/28.90	   b_{a_1}(a_{b_1}(x1)) -> b_{e_1}(e_{d_1}(d_{b_1}(x1)))
110.25/28.90	   b_{a_1}(a_{c_1}(x1)) -> b_{e_1}(e_{d_1}(d_{c_1}(x1)))
110.25/28.90	   b_{a_1}(a_{d_1}(x1)) -> b_{e_1}(e_{d_1}(d_{d_1}(x1)))
110.25/28.90	   b_{a_1}(a_{e_1}(x1)) -> b_{e_1}(e_{d_1}(d_{e_1}(x1)))
110.25/28.90	   c_{a_1}(a_{a_1}(x1)) -> c_{e_1}(e_{d_1}(d_{a_1}(x1)))
110.25/28.90	   c_{a_1}(a_{b_1}(x1)) -> c_{e_1}(e_{d_1}(d_{b_1}(x1)))
110.25/28.90	   c_{a_1}(a_{c_1}(x1)) -> c_{e_1}(e_{d_1}(d_{c_1}(x1)))
110.25/28.90	   c_{a_1}(a_{d_1}(x1)) -> c_{e_1}(e_{d_1}(d_{d_1}(x1)))
110.25/28.90	   c_{a_1}(a_{e_1}(x1)) -> c_{e_1}(e_{d_1}(d_{e_1}(x1)))
110.25/28.90	   d_{a_1}(a_{a_1}(x1)) -> d_{e_1}(e_{d_1}(d_{a_1}(x1)))
110.25/28.90	   d_{a_1}(a_{b_1}(x1)) -> d_{e_1}(e_{d_1}(d_{b_1}(x1)))
110.25/28.90	   d_{a_1}(a_{c_1}(x1)) -> d_{e_1}(e_{d_1}(d_{c_1}(x1)))
110.25/28.90	   d_{a_1}(a_{d_1}(x1)) -> d_{e_1}(e_{d_1}(d_{d_1}(x1)))
110.25/28.90	   d_{a_1}(a_{e_1}(x1)) -> d_{e_1}(e_{d_1}(d_{e_1}(x1)))
110.25/28.90	   e_{a_1}(a_{a_1}(x1)) -> e_{e_1}(e_{d_1}(d_{a_1}(x1)))
110.25/28.90	   e_{a_1}(a_{b_1}(x1)) -> e_{e_1}(e_{d_1}(d_{b_1}(x1)))
110.25/28.90	   e_{a_1}(a_{c_1}(x1)) -> e_{e_1}(e_{d_1}(d_{c_1}(x1)))
110.25/28.90	   e_{a_1}(a_{d_1}(x1)) -> e_{e_1}(e_{d_1}(d_{d_1}(x1)))
110.25/28.90	   e_{a_1}(a_{e_1}(x1)) -> e_{e_1}(e_{d_1}(d_{e_1}(x1)))
110.25/28.90	
110.25/28.90	Q is empty.
110.25/28.90	
110.25/28.90	----------------------------------------
110.25/28.90	
110.25/28.90	(5) QTRSRRRProof (EQUIVALENT)
110.25/28.90	Used ordering:
110.25/28.90	Polynomial interpretation [POLO]:
110.25/28.90	
110.25/28.90	   POL(a_{a_1}(x_1)) = 2 + x_1
110.25/28.90	   POL(a_{b_1}(x_1)) = 10 + x_1
110.25/28.90	   POL(a_{c_1}(x_1)) = 6 + x_1
110.25/28.90	   POL(a_{d_1}(x_1)) = 5 + x_1
110.25/28.90	   POL(a_{e_1}(x_1)) = x_1
110.25/28.90	   POL(b_{a_1}(x_1)) = 4 + x_1
110.25/28.90	   POL(b_{b_1}(x_1)) = 10 + x_1
110.25/28.90	   POL(b_{c_1}(x_1)) = 8 + x_1
110.25/28.90	   POL(b_{d_1}(x_1)) = 5 + x_1
110.25/28.90	   POL(b_{e_1}(x_1)) = x_1
110.25/28.90	   POL(c_{a_1}(x_1)) = 3 + x_1
110.25/28.90	   POL(c_{b_1}(x_1)) = 10 + x_1
110.25/28.90	   POL(c_{c_1}(x_1)) = 7 + x_1
110.25/28.90	   POL(c_{d_1}(x_1)) = 5 + x_1
110.25/28.90	   POL(c_{e_1}(x_1)) = x_1
110.25/28.90	   POL(d_{a_1}(x_1)) = x_1
110.25/28.90	   POL(d_{b_1}(x_1)) = 10 + x_1
110.25/28.90	   POL(d_{c_1}(x_1)) = 5 + x_1
110.25/28.90	   POL(d_{d_1}(x_1)) = 5 + x_1
110.25/28.90	   POL(d_{e_1}(x_1)) = x_1
110.25/28.90	   POL(e_{a_1}(x_1)) = x_1
110.25/28.90	   POL(e_{b_1}(x_1)) = 5 + x_1
110.25/28.90	   POL(e_{c_1}(x_1)) = 5 + x_1
110.25/28.90	   POL(e_{d_1}(x_1)) = x_1
110.25/28.90	   POL(e_{e_1}(x_1)) = x_1
110.25/28.90	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
110.25/28.90	
110.25/28.90	   a_{a_1}(a_{b_1}(b_{a_1}(x1))) -> a_{c_1}(c_{d_1}(d_{a_1}(x1)))
110.25/28.90	   a_{a_1}(a_{b_1}(b_{b_1}(x1))) -> a_{c_1}(c_{d_1}(d_{b_1}(x1)))
110.25/28.90	   a_{a_1}(a_{b_1}(b_{c_1}(x1))) -> a_{c_1}(c_{d_1}(d_{c_1}(x1)))
110.25/28.90	   a_{a_1}(a_{b_1}(b_{d_1}(x1))) -> a_{c_1}(c_{d_1}(d_{d_1}(x1)))
110.25/28.90	   a_{a_1}(a_{b_1}(b_{e_1}(x1))) -> a_{c_1}(c_{d_1}(d_{e_1}(x1)))
110.25/28.90	   b_{a_1}(a_{b_1}(b_{a_1}(x1))) -> b_{c_1}(c_{d_1}(d_{a_1}(x1)))
110.25/28.90	   b_{a_1}(a_{b_1}(b_{b_1}(x1))) -> b_{c_1}(c_{d_1}(d_{b_1}(x1)))
110.25/28.90	   b_{a_1}(a_{b_1}(b_{c_1}(x1))) -> b_{c_1}(c_{d_1}(d_{c_1}(x1)))
110.25/28.90	   b_{a_1}(a_{b_1}(b_{d_1}(x1))) -> b_{c_1}(c_{d_1}(d_{d_1}(x1)))
110.25/28.90	   b_{a_1}(a_{b_1}(b_{e_1}(x1))) -> b_{c_1}(c_{d_1}(d_{e_1}(x1)))
110.25/28.90	   c_{a_1}(a_{b_1}(b_{a_1}(x1))) -> c_{c_1}(c_{d_1}(d_{a_1}(x1)))
110.25/28.90	   c_{a_1}(a_{b_1}(b_{b_1}(x1))) -> c_{c_1}(c_{d_1}(d_{b_1}(x1)))
110.25/28.90	   c_{a_1}(a_{b_1}(b_{c_1}(x1))) -> c_{c_1}(c_{d_1}(d_{c_1}(x1)))
110.25/28.90	   c_{a_1}(a_{b_1}(b_{d_1}(x1))) -> c_{c_1}(c_{d_1}(d_{d_1}(x1)))
110.25/28.90	   c_{a_1}(a_{b_1}(b_{e_1}(x1))) -> c_{c_1}(c_{d_1}(d_{e_1}(x1)))
110.25/28.90	   d_{a_1}(a_{b_1}(b_{a_1}(x1))) -> d_{c_1}(c_{d_1}(d_{a_1}(x1)))
110.25/28.90	   d_{a_1}(a_{b_1}(b_{c_1}(x1))) -> d_{c_1}(c_{d_1}(d_{c_1}(x1)))
110.25/28.90	   e_{a_1}(a_{b_1}(b_{a_1}(x1))) -> e_{c_1}(c_{d_1}(d_{a_1}(x1)))
110.25/28.90	   e_{a_1}(a_{b_1}(b_{c_1}(x1))) -> e_{c_1}(c_{d_1}(d_{c_1}(x1)))
110.25/28.90	   a_{d_1}(d_{d_1}(d_{b_1}(x1))) -> a_{b_1}(b_{e_1}(e_{b_1}(x1)))
110.25/28.90	   a_{d_1}(d_{d_1}(d_{d_1}(x1))) -> a_{b_1}(b_{e_1}(e_{d_1}(x1)))
110.25/28.90	   b_{d_1}(d_{d_1}(d_{b_1}(x1))) -> b_{b_1}(b_{e_1}(e_{b_1}(x1)))
110.25/28.90	   b_{d_1}(d_{d_1}(d_{d_1}(x1))) -> b_{b_1}(b_{e_1}(e_{d_1}(x1)))
110.25/28.90	   c_{d_1}(d_{d_1}(d_{b_1}(x1))) -> c_{b_1}(b_{e_1}(e_{b_1}(x1)))
110.25/28.90	   c_{d_1}(d_{d_1}(d_{d_1}(x1))) -> c_{b_1}(b_{e_1}(e_{d_1}(x1)))
110.25/28.90	   d_{d_1}(d_{d_1}(d_{b_1}(x1))) -> d_{b_1}(b_{e_1}(e_{b_1}(x1)))
110.25/28.90	   d_{d_1}(d_{d_1}(d_{d_1}(x1))) -> d_{b_1}(b_{e_1}(e_{d_1}(x1)))
110.25/28.90	   e_{d_1}(d_{d_1}(d_{b_1}(x1))) -> e_{b_1}(b_{e_1}(e_{b_1}(x1)))
110.25/28.90	   e_{d_1}(d_{d_1}(d_{d_1}(x1))) -> e_{b_1}(b_{e_1}(e_{d_1}(x1)))
110.25/28.90	   a_{b_1}(b_{a_1}(x1)) -> a_{d_1}(d_{c_1}(c_{a_1}(x1)))
110.25/28.90	   a_{b_1}(b_{c_1}(x1)) -> a_{d_1}(d_{c_1}(c_{c_1}(x1)))
110.25/28.90	   b_{b_1}(b_{a_1}(x1)) -> b_{d_1}(d_{c_1}(c_{a_1}(x1)))
110.25/28.90	   b_{b_1}(b_{c_1}(x1)) -> b_{d_1}(d_{c_1}(c_{c_1}(x1)))
110.25/28.90	   c_{b_1}(b_{a_1}(x1)) -> c_{d_1}(d_{c_1}(c_{a_1}(x1)))
110.25/28.90	   c_{b_1}(b_{c_1}(x1)) -> c_{d_1}(d_{c_1}(c_{c_1}(x1)))
110.25/28.90	   d_{b_1}(b_{a_1}(x1)) -> d_{d_1}(d_{c_1}(c_{a_1}(x1)))
110.25/28.90	   d_{b_1}(b_{c_1}(x1)) -> d_{d_1}(d_{c_1}(c_{c_1}(x1)))
110.25/28.90	   e_{b_1}(b_{a_1}(x1)) -> e_{d_1}(d_{c_1}(c_{a_1}(x1)))
110.25/28.90	   e_{b_1}(b_{c_1}(x1)) -> e_{d_1}(d_{c_1}(c_{c_1}(x1)))
110.25/28.90	   a_{d_1}(d_{a_1}(x1)) -> a_{a_1}(x1)
110.25/28.90	   a_{d_1}(d_{b_1}(x1)) -> a_{b_1}(x1)
110.25/28.90	   a_{d_1}(d_{c_1}(x1)) -> a_{c_1}(x1)
110.25/28.90	   a_{d_1}(d_{d_1}(x1)) -> a_{d_1}(x1)
110.25/28.90	   a_{d_1}(d_{e_1}(x1)) -> a_{e_1}(x1)
110.25/28.90	   b_{d_1}(d_{a_1}(x1)) -> b_{a_1}(x1)
110.25/28.90	   b_{d_1}(d_{b_1}(x1)) -> b_{b_1}(x1)
110.25/28.90	   b_{d_1}(d_{c_1}(x1)) -> b_{c_1}(x1)
110.25/28.90	   b_{d_1}(d_{d_1}(x1)) -> b_{d_1}(x1)
110.25/28.90	   b_{d_1}(d_{e_1}(x1)) -> b_{e_1}(x1)
110.25/28.90	   c_{d_1}(d_{a_1}(x1)) -> c_{a_1}(x1)
110.25/28.90	   c_{d_1}(d_{b_1}(x1)) -> c_{b_1}(x1)
110.25/28.90	   c_{d_1}(d_{c_1}(x1)) -> c_{c_1}(x1)
110.25/28.90	   c_{d_1}(d_{d_1}(x1)) -> c_{d_1}(x1)
110.25/28.90	   c_{d_1}(d_{e_1}(x1)) -> c_{e_1}(x1)
110.25/28.90	   d_{d_1}(d_{a_1}(x1)) -> d_{a_1}(x1)
110.25/28.90	   d_{d_1}(d_{b_1}(x1)) -> d_{b_1}(x1)
110.25/28.90	   d_{d_1}(d_{c_1}(x1)) -> d_{c_1}(x1)
110.25/28.90	   d_{d_1}(d_{d_1}(x1)) -> d_{d_1}(x1)
110.25/28.90	   d_{d_1}(d_{e_1}(x1)) -> d_{e_1}(x1)
110.25/28.90	   e_{d_1}(d_{b_1}(x1)) -> e_{b_1}(x1)
110.25/28.90	   e_{d_1}(d_{d_1}(x1)) -> e_{d_1}(x1)
110.25/28.90	   a_{e_1}(e_{c_1}(c_{a_1}(x1))) -> a_{d_1}(d_{a_1}(a_{a_1}(x1)))
110.25/28.90	   a_{e_1}(e_{c_1}(c_{c_1}(x1))) -> a_{d_1}(d_{a_1}(a_{c_1}(x1)))
110.25/28.90	   b_{e_1}(e_{c_1}(c_{a_1}(x1))) -> b_{d_1}(d_{a_1}(a_{a_1}(x1)))
110.25/28.90	   b_{e_1}(e_{c_1}(c_{c_1}(x1))) -> b_{d_1}(d_{a_1}(a_{c_1}(x1)))
110.25/28.90	   c_{e_1}(e_{c_1}(c_{a_1}(x1))) -> c_{d_1}(d_{a_1}(a_{a_1}(x1)))
110.25/28.90	   c_{e_1}(e_{c_1}(c_{c_1}(x1))) -> c_{d_1}(d_{a_1}(a_{c_1}(x1)))
110.25/28.90	   d_{e_1}(e_{c_1}(c_{a_1}(x1))) -> d_{d_1}(d_{a_1}(a_{a_1}(x1)))
110.25/28.90	   d_{e_1}(e_{c_1}(c_{c_1}(x1))) -> d_{d_1}(d_{a_1}(a_{c_1}(x1)))
110.25/28.90	   e_{e_1}(e_{c_1}(c_{a_1}(x1))) -> e_{d_1}(d_{a_1}(a_{a_1}(x1)))
110.25/28.90	   e_{e_1}(e_{c_1}(c_{b_1}(x1))) -> e_{d_1}(d_{a_1}(a_{b_1}(x1)))
110.25/28.90	   e_{e_1}(e_{c_1}(c_{c_1}(x1))) -> e_{d_1}(d_{a_1}(a_{c_1}(x1)))
110.25/28.90	   e_{e_1}(e_{c_1}(c_{d_1}(x1))) -> e_{d_1}(d_{a_1}(a_{d_1}(x1)))
110.25/28.90	   e_{e_1}(e_{c_1}(c_{e_1}(x1))) -> e_{d_1}(d_{a_1}(a_{e_1}(x1)))
110.25/28.90	   a_{a_1}(a_{a_1}(x1)) -> a_{e_1}(e_{d_1}(d_{a_1}(x1)))
110.25/28.91	   a_{a_1}(a_{b_1}(x1)) -> a_{e_1}(e_{d_1}(d_{b_1}(x1)))
110.25/28.91	   a_{a_1}(a_{c_1}(x1)) -> a_{e_1}(e_{d_1}(d_{c_1}(x1)))
110.25/28.91	   a_{a_1}(a_{d_1}(x1)) -> a_{e_1}(e_{d_1}(d_{d_1}(x1)))
110.25/28.91	   a_{a_1}(a_{e_1}(x1)) -> a_{e_1}(e_{d_1}(d_{e_1}(x1)))
110.25/28.91	   b_{a_1}(a_{a_1}(x1)) -> b_{e_1}(e_{d_1}(d_{a_1}(x1)))
110.25/28.91	   b_{a_1}(a_{b_1}(x1)) -> b_{e_1}(e_{d_1}(d_{b_1}(x1)))
110.25/28.91	   b_{a_1}(a_{c_1}(x1)) -> b_{e_1}(e_{d_1}(d_{c_1}(x1)))
110.25/28.91	   b_{a_1}(a_{d_1}(x1)) -> b_{e_1}(e_{d_1}(d_{d_1}(x1)))
110.25/28.91	   b_{a_1}(a_{e_1}(x1)) -> b_{e_1}(e_{d_1}(d_{e_1}(x1)))
110.25/28.91	   c_{a_1}(a_{a_1}(x1)) -> c_{e_1}(e_{d_1}(d_{a_1}(x1)))
110.25/28.91	   c_{a_1}(a_{b_1}(x1)) -> c_{e_1}(e_{d_1}(d_{b_1}(x1)))
110.25/28.91	   c_{a_1}(a_{c_1}(x1)) -> c_{e_1}(e_{d_1}(d_{c_1}(x1)))
110.25/28.91	   c_{a_1}(a_{d_1}(x1)) -> c_{e_1}(e_{d_1}(d_{d_1}(x1)))
110.25/28.91	   c_{a_1}(a_{e_1}(x1)) -> c_{e_1}(e_{d_1}(d_{e_1}(x1)))
110.25/28.91	   d_{a_1}(a_{a_1}(x1)) -> d_{e_1}(e_{d_1}(d_{a_1}(x1)))
110.25/28.91	   d_{a_1}(a_{c_1}(x1)) -> d_{e_1}(e_{d_1}(d_{c_1}(x1)))
110.25/28.91	   e_{a_1}(a_{a_1}(x1)) -> e_{e_1}(e_{d_1}(d_{a_1}(x1)))
110.25/28.91	   e_{a_1}(a_{c_1}(x1)) -> e_{e_1}(e_{d_1}(d_{c_1}(x1)))
110.25/28.91	
110.25/28.91	
110.25/28.91	
110.25/28.91	
110.25/28.91	----------------------------------------
110.25/28.91	
110.25/28.91	(6)
110.25/28.91	Obligation:
110.25/28.91	Q restricted rewrite system:
110.25/28.91	The TRS R consists of the following rules:
110.25/28.91	
110.25/28.91	   d_{a_1}(a_{b_1}(b_{b_1}(x1))) -> d_{c_1}(c_{d_1}(d_{b_1}(x1)))
110.25/28.91	   d_{a_1}(a_{b_1}(b_{d_1}(x1))) -> d_{c_1}(c_{d_1}(d_{d_1}(x1)))
110.25/28.91	   d_{a_1}(a_{b_1}(b_{e_1}(x1))) -> d_{c_1}(c_{d_1}(d_{e_1}(x1)))
110.25/28.91	   e_{a_1}(a_{b_1}(b_{b_1}(x1))) -> e_{c_1}(c_{d_1}(d_{b_1}(x1)))
110.25/28.91	   e_{a_1}(a_{b_1}(b_{d_1}(x1))) -> e_{c_1}(c_{d_1}(d_{d_1}(x1)))
110.25/28.91	   e_{a_1}(a_{b_1}(b_{e_1}(x1))) -> e_{c_1}(c_{d_1}(d_{e_1}(x1)))
110.25/28.91	   a_{d_1}(d_{d_1}(d_{a_1}(x1))) -> a_{b_1}(b_{e_1}(e_{a_1}(x1)))
110.25/28.91	   a_{d_1}(d_{d_1}(d_{c_1}(x1))) -> a_{b_1}(b_{e_1}(e_{c_1}(x1)))
110.25/28.91	   a_{d_1}(d_{d_1}(d_{e_1}(x1))) -> a_{b_1}(b_{e_1}(e_{e_1}(x1)))
110.25/28.91	   b_{d_1}(d_{d_1}(d_{a_1}(x1))) -> b_{b_1}(b_{e_1}(e_{a_1}(x1)))
110.25/28.91	   b_{d_1}(d_{d_1}(d_{c_1}(x1))) -> b_{b_1}(b_{e_1}(e_{c_1}(x1)))
110.25/28.91	   b_{d_1}(d_{d_1}(d_{e_1}(x1))) -> b_{b_1}(b_{e_1}(e_{e_1}(x1)))
110.25/28.91	   c_{d_1}(d_{d_1}(d_{a_1}(x1))) -> c_{b_1}(b_{e_1}(e_{a_1}(x1)))
110.25/28.91	   c_{d_1}(d_{d_1}(d_{c_1}(x1))) -> c_{b_1}(b_{e_1}(e_{c_1}(x1)))
110.25/28.91	   c_{d_1}(d_{d_1}(d_{e_1}(x1))) -> c_{b_1}(b_{e_1}(e_{e_1}(x1)))
110.25/28.91	   d_{d_1}(d_{d_1}(d_{a_1}(x1))) -> d_{b_1}(b_{e_1}(e_{a_1}(x1)))
110.25/28.91	   d_{d_1}(d_{d_1}(d_{c_1}(x1))) -> d_{b_1}(b_{e_1}(e_{c_1}(x1)))
110.25/28.91	   d_{d_1}(d_{d_1}(d_{e_1}(x1))) -> d_{b_1}(b_{e_1}(e_{e_1}(x1)))
110.25/28.91	   e_{d_1}(d_{d_1}(d_{a_1}(x1))) -> e_{b_1}(b_{e_1}(e_{a_1}(x1)))
110.25/28.91	   e_{d_1}(d_{d_1}(d_{c_1}(x1))) -> e_{b_1}(b_{e_1}(e_{c_1}(x1)))
110.25/28.91	   e_{d_1}(d_{d_1}(d_{e_1}(x1))) -> e_{b_1}(b_{e_1}(e_{e_1}(x1)))
110.25/28.91	   a_{b_1}(b_{b_1}(x1)) -> a_{d_1}(d_{c_1}(c_{b_1}(x1)))
110.25/28.91	   a_{b_1}(b_{d_1}(x1)) -> a_{d_1}(d_{c_1}(c_{d_1}(x1)))
110.25/28.91	   a_{b_1}(b_{e_1}(x1)) -> a_{d_1}(d_{c_1}(c_{e_1}(x1)))
110.25/28.91	   b_{b_1}(b_{b_1}(x1)) -> b_{d_1}(d_{c_1}(c_{b_1}(x1)))
110.25/28.91	   b_{b_1}(b_{d_1}(x1)) -> b_{d_1}(d_{c_1}(c_{d_1}(x1)))
110.25/28.91	   b_{b_1}(b_{e_1}(x1)) -> b_{d_1}(d_{c_1}(c_{e_1}(x1)))
110.25/28.91	   c_{b_1}(b_{b_1}(x1)) -> c_{d_1}(d_{c_1}(c_{b_1}(x1)))
110.25/28.91	   c_{b_1}(b_{d_1}(x1)) -> c_{d_1}(d_{c_1}(c_{d_1}(x1)))
110.25/28.91	   c_{b_1}(b_{e_1}(x1)) -> c_{d_1}(d_{c_1}(c_{e_1}(x1)))
110.25/28.91	   d_{b_1}(b_{b_1}(x1)) -> d_{d_1}(d_{c_1}(c_{b_1}(x1)))
110.25/28.91	   d_{b_1}(b_{d_1}(x1)) -> d_{d_1}(d_{c_1}(c_{d_1}(x1)))
110.25/28.91	   d_{b_1}(b_{e_1}(x1)) -> d_{d_1}(d_{c_1}(c_{e_1}(x1)))
110.25/28.91	   e_{b_1}(b_{b_1}(x1)) -> e_{d_1}(d_{c_1}(c_{b_1}(x1)))
110.25/28.91	   e_{b_1}(b_{d_1}(x1)) -> e_{d_1}(d_{c_1}(c_{d_1}(x1)))
110.25/28.91	   e_{b_1}(b_{e_1}(x1)) -> e_{d_1}(d_{c_1}(c_{e_1}(x1)))
110.25/28.91	   e_{d_1}(d_{a_1}(x1)) -> e_{a_1}(x1)
110.25/28.91	   e_{d_1}(d_{c_1}(x1)) -> e_{c_1}(x1)
110.25/28.91	   e_{d_1}(d_{e_1}(x1)) -> e_{e_1}(x1)
110.25/28.91	   a_{e_1}(e_{c_1}(c_{b_1}(x1))) -> a_{d_1}(d_{a_1}(a_{b_1}(x1)))
110.25/28.91	   a_{e_1}(e_{c_1}(c_{d_1}(x1))) -> a_{d_1}(d_{a_1}(a_{d_1}(x1)))
110.25/28.91	   a_{e_1}(e_{c_1}(c_{e_1}(x1))) -> a_{d_1}(d_{a_1}(a_{e_1}(x1)))
110.25/28.91	   b_{e_1}(e_{c_1}(c_{b_1}(x1))) -> b_{d_1}(d_{a_1}(a_{b_1}(x1)))
110.25/28.91	   b_{e_1}(e_{c_1}(c_{d_1}(x1))) -> b_{d_1}(d_{a_1}(a_{d_1}(x1)))
110.25/28.91	   b_{e_1}(e_{c_1}(c_{e_1}(x1))) -> b_{d_1}(d_{a_1}(a_{e_1}(x1)))
110.25/28.91	   c_{e_1}(e_{c_1}(c_{b_1}(x1))) -> c_{d_1}(d_{a_1}(a_{b_1}(x1)))
110.25/28.91	   c_{e_1}(e_{c_1}(c_{d_1}(x1))) -> c_{d_1}(d_{a_1}(a_{d_1}(x1)))
110.25/28.91	   c_{e_1}(e_{c_1}(c_{e_1}(x1))) -> c_{d_1}(d_{a_1}(a_{e_1}(x1)))
110.25/28.91	   d_{e_1}(e_{c_1}(c_{b_1}(x1))) -> d_{d_1}(d_{a_1}(a_{b_1}(x1)))
110.25/28.91	   d_{e_1}(e_{c_1}(c_{d_1}(x1))) -> d_{d_1}(d_{a_1}(a_{d_1}(x1)))
110.25/28.91	   d_{e_1}(e_{c_1}(c_{e_1}(x1))) -> d_{d_1}(d_{a_1}(a_{e_1}(x1)))
110.25/28.91	   d_{a_1}(a_{b_1}(x1)) -> d_{e_1}(e_{d_1}(d_{b_1}(x1)))
110.25/28.91	   d_{a_1}(a_{d_1}(x1)) -> d_{e_1}(e_{d_1}(d_{d_1}(x1)))
110.25/28.91	   d_{a_1}(a_{e_1}(x1)) -> d_{e_1}(e_{d_1}(d_{e_1}(x1)))
110.25/28.91	   e_{a_1}(a_{b_1}(x1)) -> e_{e_1}(e_{d_1}(d_{b_1}(x1)))
110.25/28.91	   e_{a_1}(a_{d_1}(x1)) -> e_{e_1}(e_{d_1}(d_{d_1}(x1)))
110.25/28.91	   e_{a_1}(a_{e_1}(x1)) -> e_{e_1}(e_{d_1}(d_{e_1}(x1)))
110.25/28.91	
110.25/28.91	Q is empty.
110.25/28.91	
110.25/28.91	----------------------------------------
110.25/28.91	
110.25/28.91	(7) DependencyPairsProof (EQUIVALENT)
110.25/28.91	Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
110.25/28.91	----------------------------------------
110.25/28.91	
110.25/28.91	(8)
110.25/28.91	Obligation:
110.25/28.91	Q DP problem:
110.25/28.91	The TRS P consists of the following rules:
110.25/28.91	
110.25/28.91	   D_{A_1}(a_{b_1}(b_{b_1}(x1))) -> C_{D_1}(d_{b_1}(x1))
110.25/28.91	   D_{A_1}(a_{b_1}(b_{b_1}(x1))) -> D_{B_1}(x1)
110.25/28.91	   D_{A_1}(a_{b_1}(b_{d_1}(x1))) -> C_{D_1}(d_{d_1}(x1))
110.25/28.91	   D_{A_1}(a_{b_1}(b_{d_1}(x1))) -> D_{D_1}(x1)
110.25/28.91	   D_{A_1}(a_{b_1}(b_{e_1}(x1))) -> C_{D_1}(d_{e_1}(x1))
110.25/28.91	   D_{A_1}(a_{b_1}(b_{e_1}(x1))) -> D_{E_1}(x1)
110.25/28.91	   E_{A_1}(a_{b_1}(b_{b_1}(x1))) -> C_{D_1}(d_{b_1}(x1))
110.25/28.91	   E_{A_1}(a_{b_1}(b_{b_1}(x1))) -> D_{B_1}(x1)
110.25/28.91	   E_{A_1}(a_{b_1}(b_{d_1}(x1))) -> C_{D_1}(d_{d_1}(x1))
110.25/28.91	   E_{A_1}(a_{b_1}(b_{d_1}(x1))) -> D_{D_1}(x1)
110.25/28.91	   E_{A_1}(a_{b_1}(b_{e_1}(x1))) -> C_{D_1}(d_{e_1}(x1))
110.25/28.91	   E_{A_1}(a_{b_1}(b_{e_1}(x1))) -> D_{E_1}(x1)
110.25/28.91	   A_{D_1}(d_{d_1}(d_{a_1}(x1))) -> A_{B_1}(b_{e_1}(e_{a_1}(x1)))
110.25/28.91	   A_{D_1}(d_{d_1}(d_{a_1}(x1))) -> B_{E_1}(e_{a_1}(x1))
110.25/28.91	   A_{D_1}(d_{d_1}(d_{a_1}(x1))) -> E_{A_1}(x1)
110.25/28.91	   A_{D_1}(d_{d_1}(d_{c_1}(x1))) -> A_{B_1}(b_{e_1}(e_{c_1}(x1)))
110.25/28.91	   A_{D_1}(d_{d_1}(d_{c_1}(x1))) -> B_{E_1}(e_{c_1}(x1))
110.25/28.91	   A_{D_1}(d_{d_1}(d_{e_1}(x1))) -> A_{B_1}(b_{e_1}(e_{e_1}(x1)))
110.25/28.91	   A_{D_1}(d_{d_1}(d_{e_1}(x1))) -> B_{E_1}(e_{e_1}(x1))
110.25/28.91	   B_{D_1}(d_{d_1}(d_{a_1}(x1))) -> B_{B_1}(b_{e_1}(e_{a_1}(x1)))
110.25/28.91	   B_{D_1}(d_{d_1}(d_{a_1}(x1))) -> B_{E_1}(e_{a_1}(x1))
110.25/28.91	   B_{D_1}(d_{d_1}(d_{a_1}(x1))) -> E_{A_1}(x1)
110.25/28.91	   B_{D_1}(d_{d_1}(d_{c_1}(x1))) -> B_{B_1}(b_{e_1}(e_{c_1}(x1)))
110.25/28.91	   B_{D_1}(d_{d_1}(d_{c_1}(x1))) -> B_{E_1}(e_{c_1}(x1))
110.25/28.91	   B_{D_1}(d_{d_1}(d_{e_1}(x1))) -> B_{B_1}(b_{e_1}(e_{e_1}(x1)))
110.25/28.91	   B_{D_1}(d_{d_1}(d_{e_1}(x1))) -> B_{E_1}(e_{e_1}(x1))
110.25/28.91	   C_{D_1}(d_{d_1}(d_{a_1}(x1))) -> C_{B_1}(b_{e_1}(e_{a_1}(x1)))
110.25/28.91	   C_{D_1}(d_{d_1}(d_{a_1}(x1))) -> B_{E_1}(e_{a_1}(x1))
110.25/28.91	   C_{D_1}(d_{d_1}(d_{a_1}(x1))) -> E_{A_1}(x1)
110.25/28.91	   C_{D_1}(d_{d_1}(d_{c_1}(x1))) -> C_{B_1}(b_{e_1}(e_{c_1}(x1)))
110.25/28.91	   C_{D_1}(d_{d_1}(d_{c_1}(x1))) -> B_{E_1}(e_{c_1}(x1))
110.25/28.91	   C_{D_1}(d_{d_1}(d_{e_1}(x1))) -> C_{B_1}(b_{e_1}(e_{e_1}(x1)))
110.25/28.91	   C_{D_1}(d_{d_1}(d_{e_1}(x1))) -> B_{E_1}(e_{e_1}(x1))
110.25/28.91	   D_{D_1}(d_{d_1}(d_{a_1}(x1))) -> D_{B_1}(b_{e_1}(e_{a_1}(x1)))
110.25/28.91	   D_{D_1}(d_{d_1}(d_{a_1}(x1))) -> B_{E_1}(e_{a_1}(x1))
110.25/28.91	   D_{D_1}(d_{d_1}(d_{a_1}(x1))) -> E_{A_1}(x1)
110.25/28.91	   D_{D_1}(d_{d_1}(d_{c_1}(x1))) -> D_{B_1}(b_{e_1}(e_{c_1}(x1)))
110.25/28.91	   D_{D_1}(d_{d_1}(d_{c_1}(x1))) -> B_{E_1}(e_{c_1}(x1))
110.25/28.91	   D_{D_1}(d_{d_1}(d_{e_1}(x1))) -> D_{B_1}(b_{e_1}(e_{e_1}(x1)))
110.25/28.91	   D_{D_1}(d_{d_1}(d_{e_1}(x1))) -> B_{E_1}(e_{e_1}(x1))
110.25/28.91	   E_{D_1}(d_{d_1}(d_{a_1}(x1))) -> E_{B_1}(b_{e_1}(e_{a_1}(x1)))
110.25/28.91	   E_{D_1}(d_{d_1}(d_{a_1}(x1))) -> B_{E_1}(e_{a_1}(x1))
110.25/28.91	   E_{D_1}(d_{d_1}(d_{a_1}(x1))) -> E_{A_1}(x1)
110.25/28.91	   E_{D_1}(d_{d_1}(d_{c_1}(x1))) -> E_{B_1}(b_{e_1}(e_{c_1}(x1)))
110.25/28.91	   E_{D_1}(d_{d_1}(d_{c_1}(x1))) -> B_{E_1}(e_{c_1}(x1))
110.25/28.91	   E_{D_1}(d_{d_1}(d_{e_1}(x1))) -> E_{B_1}(b_{e_1}(e_{e_1}(x1)))
110.25/28.91	   E_{D_1}(d_{d_1}(d_{e_1}(x1))) -> B_{E_1}(e_{e_1}(x1))
110.25/28.91	   A_{B_1}(b_{b_1}(x1)) -> A_{D_1}(d_{c_1}(c_{b_1}(x1)))
110.25/28.91	   A_{B_1}(b_{b_1}(x1)) -> C_{B_1}(x1)
110.25/28.91	   A_{B_1}(b_{d_1}(x1)) -> A_{D_1}(d_{c_1}(c_{d_1}(x1)))
110.25/28.91	   A_{B_1}(b_{d_1}(x1)) -> C_{D_1}(x1)
110.25/28.91	   A_{B_1}(b_{e_1}(x1)) -> A_{D_1}(d_{c_1}(c_{e_1}(x1)))
110.25/28.91	   A_{B_1}(b_{e_1}(x1)) -> C_{E_1}(x1)
110.25/28.91	   B_{B_1}(b_{b_1}(x1)) -> B_{D_1}(d_{c_1}(c_{b_1}(x1)))
110.25/28.91	   B_{B_1}(b_{b_1}(x1)) -> C_{B_1}(x1)
110.25/28.91	   B_{B_1}(b_{d_1}(x1)) -> B_{D_1}(d_{c_1}(c_{d_1}(x1)))
110.25/28.91	   B_{B_1}(b_{d_1}(x1)) -> C_{D_1}(x1)
110.25/28.91	   B_{B_1}(b_{e_1}(x1)) -> B_{D_1}(d_{c_1}(c_{e_1}(x1)))
110.25/28.91	   B_{B_1}(b_{e_1}(x1)) -> C_{E_1}(x1)
110.25/28.91	   C_{B_1}(b_{b_1}(x1)) -> C_{D_1}(d_{c_1}(c_{b_1}(x1)))
110.25/28.91	   C_{B_1}(b_{b_1}(x1)) -> C_{B_1}(x1)
110.25/28.91	   C_{B_1}(b_{d_1}(x1)) -> C_{D_1}(d_{c_1}(c_{d_1}(x1)))
110.25/28.91	   C_{B_1}(b_{d_1}(x1)) -> C_{D_1}(x1)
110.25/28.91	   C_{B_1}(b_{e_1}(x1)) -> C_{D_1}(d_{c_1}(c_{e_1}(x1)))
110.25/28.91	   C_{B_1}(b_{e_1}(x1)) -> C_{E_1}(x1)
110.25/28.91	   D_{B_1}(b_{b_1}(x1)) -> D_{D_1}(d_{c_1}(c_{b_1}(x1)))
110.25/28.91	   D_{B_1}(b_{b_1}(x1)) -> C_{B_1}(x1)
110.25/28.91	   D_{B_1}(b_{d_1}(x1)) -> D_{D_1}(d_{c_1}(c_{d_1}(x1)))
110.25/28.91	   D_{B_1}(b_{d_1}(x1)) -> C_{D_1}(x1)
110.25/28.91	   D_{B_1}(b_{e_1}(x1)) -> D_{D_1}(d_{c_1}(c_{e_1}(x1)))
110.25/28.91	   D_{B_1}(b_{e_1}(x1)) -> C_{E_1}(x1)
110.25/28.91	   E_{B_1}(b_{b_1}(x1)) -> E_{D_1}(d_{c_1}(c_{b_1}(x1)))
110.25/28.91	   E_{B_1}(b_{b_1}(x1)) -> C_{B_1}(x1)
110.25/28.91	   E_{B_1}(b_{d_1}(x1)) -> E_{D_1}(d_{c_1}(c_{d_1}(x1)))
110.25/28.91	   E_{B_1}(b_{d_1}(x1)) -> C_{D_1}(x1)
110.25/28.91	   E_{B_1}(b_{e_1}(x1)) -> E_{D_1}(d_{c_1}(c_{e_1}(x1)))
110.25/28.91	   E_{B_1}(b_{e_1}(x1)) -> C_{E_1}(x1)
110.25/28.91	   E_{D_1}(d_{a_1}(x1)) -> E_{A_1}(x1)
110.25/28.91	   A_{E_1}(e_{c_1}(c_{b_1}(x1))) -> A_{D_1}(d_{a_1}(a_{b_1}(x1)))
110.25/28.91	   A_{E_1}(e_{c_1}(c_{b_1}(x1))) -> D_{A_1}(a_{b_1}(x1))
110.25/28.91	   A_{E_1}(e_{c_1}(c_{b_1}(x1))) -> A_{B_1}(x1)
110.25/28.91	   A_{E_1}(e_{c_1}(c_{d_1}(x1))) -> A_{D_1}(d_{a_1}(a_{d_1}(x1)))
110.25/28.91	   A_{E_1}(e_{c_1}(c_{d_1}(x1))) -> D_{A_1}(a_{d_1}(x1))
110.25/28.91	   A_{E_1}(e_{c_1}(c_{d_1}(x1))) -> A_{D_1}(x1)
110.25/28.91	   A_{E_1}(e_{c_1}(c_{e_1}(x1))) -> A_{D_1}(d_{a_1}(a_{e_1}(x1)))
110.25/28.91	   A_{E_1}(e_{c_1}(c_{e_1}(x1))) -> D_{A_1}(a_{e_1}(x1))
110.25/28.91	   A_{E_1}(e_{c_1}(c_{e_1}(x1))) -> A_{E_1}(x1)
110.25/28.91	   B_{E_1}(e_{c_1}(c_{b_1}(x1))) -> B_{D_1}(d_{a_1}(a_{b_1}(x1)))
110.25/28.91	   B_{E_1}(e_{c_1}(c_{b_1}(x1))) -> D_{A_1}(a_{b_1}(x1))
110.25/28.91	   B_{E_1}(e_{c_1}(c_{b_1}(x1))) -> A_{B_1}(x1)
110.25/28.91	   B_{E_1}(e_{c_1}(c_{d_1}(x1))) -> B_{D_1}(d_{a_1}(a_{d_1}(x1)))
110.25/28.91	   B_{E_1}(e_{c_1}(c_{d_1}(x1))) -> D_{A_1}(a_{d_1}(x1))
110.25/28.91	   B_{E_1}(e_{c_1}(c_{d_1}(x1))) -> A_{D_1}(x1)
110.25/28.91	   B_{E_1}(e_{c_1}(c_{e_1}(x1))) -> B_{D_1}(d_{a_1}(a_{e_1}(x1)))
110.25/28.91	   B_{E_1}(e_{c_1}(c_{e_1}(x1))) -> D_{A_1}(a_{e_1}(x1))
110.25/28.91	   B_{E_1}(e_{c_1}(c_{e_1}(x1))) -> A_{E_1}(x1)
110.25/28.91	   C_{E_1}(e_{c_1}(c_{b_1}(x1))) -> C_{D_1}(d_{a_1}(a_{b_1}(x1)))
110.25/28.91	   C_{E_1}(e_{c_1}(c_{b_1}(x1))) -> D_{A_1}(a_{b_1}(x1))
110.25/28.91	   C_{E_1}(e_{c_1}(c_{b_1}(x1))) -> A_{B_1}(x1)
110.25/28.91	   C_{E_1}(e_{c_1}(c_{d_1}(x1))) -> C_{D_1}(d_{a_1}(a_{d_1}(x1)))
110.25/28.91	   C_{E_1}(e_{c_1}(c_{d_1}(x1))) -> D_{A_1}(a_{d_1}(x1))
110.25/28.91	   C_{E_1}(e_{c_1}(c_{d_1}(x1))) -> A_{D_1}(x1)
110.25/28.91	   C_{E_1}(e_{c_1}(c_{e_1}(x1))) -> C_{D_1}(d_{a_1}(a_{e_1}(x1)))
110.25/28.91	   C_{E_1}(e_{c_1}(c_{e_1}(x1))) -> D_{A_1}(a_{e_1}(x1))
110.25/28.91	   C_{E_1}(e_{c_1}(c_{e_1}(x1))) -> A_{E_1}(x1)
110.25/28.91	   D_{E_1}(e_{c_1}(c_{b_1}(x1))) -> D_{D_1}(d_{a_1}(a_{b_1}(x1)))
110.25/28.91	   D_{E_1}(e_{c_1}(c_{b_1}(x1))) -> D_{A_1}(a_{b_1}(x1))
110.25/28.91	   D_{E_1}(e_{c_1}(c_{b_1}(x1))) -> A_{B_1}(x1)
110.25/28.91	   D_{E_1}(e_{c_1}(c_{d_1}(x1))) -> D_{D_1}(d_{a_1}(a_{d_1}(x1)))
110.25/28.91	   D_{E_1}(e_{c_1}(c_{d_1}(x1))) -> D_{A_1}(a_{d_1}(x1))
110.25/28.91	   D_{E_1}(e_{c_1}(c_{d_1}(x1))) -> A_{D_1}(x1)
110.25/28.91	   D_{E_1}(e_{c_1}(c_{e_1}(x1))) -> D_{D_1}(d_{a_1}(a_{e_1}(x1)))
110.25/28.91	   D_{E_1}(e_{c_1}(c_{e_1}(x1))) -> D_{A_1}(a_{e_1}(x1))
110.25/28.91	   D_{E_1}(e_{c_1}(c_{e_1}(x1))) -> A_{E_1}(x1)
110.25/28.91	   D_{A_1}(a_{b_1}(x1)) -> D_{E_1}(e_{d_1}(d_{b_1}(x1)))
110.25/28.91	   D_{A_1}(a_{b_1}(x1)) -> E_{D_1}(d_{b_1}(x1))
110.25/28.91	   D_{A_1}(a_{b_1}(x1)) -> D_{B_1}(x1)
110.25/28.91	   D_{A_1}(a_{d_1}(x1)) -> D_{E_1}(e_{d_1}(d_{d_1}(x1)))
110.25/28.91	   D_{A_1}(a_{d_1}(x1)) -> E_{D_1}(d_{d_1}(x1))
110.25/28.91	   D_{A_1}(a_{d_1}(x1)) -> D_{D_1}(x1)
110.25/28.91	   D_{A_1}(a_{e_1}(x1)) -> D_{E_1}(e_{d_1}(d_{e_1}(x1)))
110.25/28.91	   D_{A_1}(a_{e_1}(x1)) -> E_{D_1}(d_{e_1}(x1))
110.25/28.91	   D_{A_1}(a_{e_1}(x1)) -> D_{E_1}(x1)
110.25/28.91	   E_{A_1}(a_{b_1}(x1)) -> E_{D_1}(d_{b_1}(x1))
110.25/28.91	   E_{A_1}(a_{b_1}(x1)) -> D_{B_1}(x1)
110.25/28.91	   E_{A_1}(a_{d_1}(x1)) -> E_{D_1}(d_{d_1}(x1))
110.25/28.91	   E_{A_1}(a_{d_1}(x1)) -> D_{D_1}(x1)
110.25/28.91	   E_{A_1}(a_{e_1}(x1)) -> E_{D_1}(d_{e_1}(x1))
110.25/28.91	   E_{A_1}(a_{e_1}(x1)) -> D_{E_1}(x1)
110.25/28.91	
110.25/28.91	The TRS R consists of the following rules:
110.25/28.91	
110.25/28.91	   d_{a_1}(a_{b_1}(b_{b_1}(x1))) -> d_{c_1}(c_{d_1}(d_{b_1}(x1)))
110.25/28.91	   d_{a_1}(a_{b_1}(b_{d_1}(x1))) -> d_{c_1}(c_{d_1}(d_{d_1}(x1)))
110.25/28.91	   d_{a_1}(a_{b_1}(b_{e_1}(x1))) -> d_{c_1}(c_{d_1}(d_{e_1}(x1)))
110.25/28.91	   e_{a_1}(a_{b_1}(b_{b_1}(x1))) -> e_{c_1}(c_{d_1}(d_{b_1}(x1)))
110.25/28.91	   e_{a_1}(a_{b_1}(b_{d_1}(x1))) -> e_{c_1}(c_{d_1}(d_{d_1}(x1)))
110.25/28.91	   e_{a_1}(a_{b_1}(b_{e_1}(x1))) -> e_{c_1}(c_{d_1}(d_{e_1}(x1)))
110.25/28.91	   a_{d_1}(d_{d_1}(d_{a_1}(x1))) -> a_{b_1}(b_{e_1}(e_{a_1}(x1)))
110.25/28.91	   a_{d_1}(d_{d_1}(d_{c_1}(x1))) -> a_{b_1}(b_{e_1}(e_{c_1}(x1)))
110.25/28.91	   a_{d_1}(d_{d_1}(d_{e_1}(x1))) -> a_{b_1}(b_{e_1}(e_{e_1}(x1)))
110.25/28.91	   b_{d_1}(d_{d_1}(d_{a_1}(x1))) -> b_{b_1}(b_{e_1}(e_{a_1}(x1)))
110.25/28.91	   b_{d_1}(d_{d_1}(d_{c_1}(x1))) -> b_{b_1}(b_{e_1}(e_{c_1}(x1)))
110.25/28.91	   b_{d_1}(d_{d_1}(d_{e_1}(x1))) -> b_{b_1}(b_{e_1}(e_{e_1}(x1)))
110.25/28.91	   c_{d_1}(d_{d_1}(d_{a_1}(x1))) -> c_{b_1}(b_{e_1}(e_{a_1}(x1)))
110.25/28.91	   c_{d_1}(d_{d_1}(d_{c_1}(x1))) -> c_{b_1}(b_{e_1}(e_{c_1}(x1)))
110.25/28.91	   c_{d_1}(d_{d_1}(d_{e_1}(x1))) -> c_{b_1}(b_{e_1}(e_{e_1}(x1)))
110.25/28.91	   d_{d_1}(d_{d_1}(d_{a_1}(x1))) -> d_{b_1}(b_{e_1}(e_{a_1}(x1)))
110.25/28.91	   d_{d_1}(d_{d_1}(d_{c_1}(x1))) -> d_{b_1}(b_{e_1}(e_{c_1}(x1)))
110.25/28.91	   d_{d_1}(d_{d_1}(d_{e_1}(x1))) -> d_{b_1}(b_{e_1}(e_{e_1}(x1)))
110.25/28.91	   e_{d_1}(d_{d_1}(d_{a_1}(x1))) -> e_{b_1}(b_{e_1}(e_{a_1}(x1)))
110.25/28.91	   e_{d_1}(d_{d_1}(d_{c_1}(x1))) -> e_{b_1}(b_{e_1}(e_{c_1}(x1)))
110.25/28.91	   e_{d_1}(d_{d_1}(d_{e_1}(x1))) -> e_{b_1}(b_{e_1}(e_{e_1}(x1)))
110.25/28.91	   a_{b_1}(b_{b_1}(x1)) -> a_{d_1}(d_{c_1}(c_{b_1}(x1)))
110.25/28.91	   a_{b_1}(b_{d_1}(x1)) -> a_{d_1}(d_{c_1}(c_{d_1}(x1)))
110.25/28.91	   a_{b_1}(b_{e_1}(x1)) -> a_{d_1}(d_{c_1}(c_{e_1}(x1)))
110.25/28.91	   b_{b_1}(b_{b_1}(x1)) -> b_{d_1}(d_{c_1}(c_{b_1}(x1)))
110.25/28.91	   b_{b_1}(b_{d_1}(x1)) -> b_{d_1}(d_{c_1}(c_{d_1}(x1)))
110.25/28.91	   b_{b_1}(b_{e_1}(x1)) -> b_{d_1}(d_{c_1}(c_{e_1}(x1)))
110.25/28.91	   c_{b_1}(b_{b_1}(x1)) -> c_{d_1}(d_{c_1}(c_{b_1}(x1)))
110.25/28.91	   c_{b_1}(b_{d_1}(x1)) -> c_{d_1}(d_{c_1}(c_{d_1}(x1)))
110.25/28.91	   c_{b_1}(b_{e_1}(x1)) -> c_{d_1}(d_{c_1}(c_{e_1}(x1)))
110.25/28.91	   d_{b_1}(b_{b_1}(x1)) -> d_{d_1}(d_{c_1}(c_{b_1}(x1)))
110.25/28.91	   d_{b_1}(b_{d_1}(x1)) -> d_{d_1}(d_{c_1}(c_{d_1}(x1)))
110.25/28.91	   d_{b_1}(b_{e_1}(x1)) -> d_{d_1}(d_{c_1}(c_{e_1}(x1)))
110.25/28.91	   e_{b_1}(b_{b_1}(x1)) -> e_{d_1}(d_{c_1}(c_{b_1}(x1)))
110.25/28.91	   e_{b_1}(b_{d_1}(x1)) -> e_{d_1}(d_{c_1}(c_{d_1}(x1)))
110.25/28.91	   e_{b_1}(b_{e_1}(x1)) -> e_{d_1}(d_{c_1}(c_{e_1}(x1)))
110.25/28.91	   e_{d_1}(d_{a_1}(x1)) -> e_{a_1}(x1)
110.25/28.91	   e_{d_1}(d_{c_1}(x1)) -> e_{c_1}(x1)
110.25/28.91	   e_{d_1}(d_{e_1}(x1)) -> e_{e_1}(x1)
110.25/28.91	   a_{e_1}(e_{c_1}(c_{b_1}(x1))) -> a_{d_1}(d_{a_1}(a_{b_1}(x1)))
110.25/28.91	   a_{e_1}(e_{c_1}(c_{d_1}(x1))) -> a_{d_1}(d_{a_1}(a_{d_1}(x1)))
110.25/28.91	   a_{e_1}(e_{c_1}(c_{e_1}(x1))) -> a_{d_1}(d_{a_1}(a_{e_1}(x1)))
110.25/28.91	   b_{e_1}(e_{c_1}(c_{b_1}(x1))) -> b_{d_1}(d_{a_1}(a_{b_1}(x1)))
110.25/28.91	   b_{e_1}(e_{c_1}(c_{d_1}(x1))) -> b_{d_1}(d_{a_1}(a_{d_1}(x1)))
110.25/28.91	   b_{e_1}(e_{c_1}(c_{e_1}(x1))) -> b_{d_1}(d_{a_1}(a_{e_1}(x1)))
110.25/28.91	   c_{e_1}(e_{c_1}(c_{b_1}(x1))) -> c_{d_1}(d_{a_1}(a_{b_1}(x1)))
110.25/28.91	   c_{e_1}(e_{c_1}(c_{d_1}(x1))) -> c_{d_1}(d_{a_1}(a_{d_1}(x1)))
110.25/28.91	   c_{e_1}(e_{c_1}(c_{e_1}(x1))) -> c_{d_1}(d_{a_1}(a_{e_1}(x1)))
110.25/28.91	   d_{e_1}(e_{c_1}(c_{b_1}(x1))) -> d_{d_1}(d_{a_1}(a_{b_1}(x1)))
110.25/28.91	   d_{e_1}(e_{c_1}(c_{d_1}(x1))) -> d_{d_1}(d_{a_1}(a_{d_1}(x1)))
110.25/28.91	   d_{e_1}(e_{c_1}(c_{e_1}(x1))) -> d_{d_1}(d_{a_1}(a_{e_1}(x1)))
110.25/28.91	   d_{a_1}(a_{b_1}(x1)) -> d_{e_1}(e_{d_1}(d_{b_1}(x1)))
110.25/28.91	   d_{a_1}(a_{d_1}(x1)) -> d_{e_1}(e_{d_1}(d_{d_1}(x1)))
110.25/28.91	   d_{a_1}(a_{e_1}(x1)) -> d_{e_1}(e_{d_1}(d_{e_1}(x1)))
110.25/28.91	   e_{a_1}(a_{b_1}(x1)) -> e_{e_1}(e_{d_1}(d_{b_1}(x1)))
110.25/28.91	   e_{a_1}(a_{d_1}(x1)) -> e_{e_1}(e_{d_1}(d_{d_1}(x1)))
110.25/28.91	   e_{a_1}(a_{e_1}(x1)) -> e_{e_1}(e_{d_1}(d_{e_1}(x1)))
110.25/28.91	
110.25/28.91	Q is empty.
110.25/28.91	We have to consider all minimal (P,Q,R)-chains.
110.25/28.91	----------------------------------------
110.25/28.91	
110.25/28.91	(9) DependencyGraphProof (EQUIVALENT)
110.25/28.91	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 21 less nodes.
110.25/28.91	----------------------------------------
110.25/28.91	
110.25/28.91	(10)
110.25/28.91	Obligation:
110.25/28.91	Q DP problem:
110.25/28.91	The TRS P consists of the following rules:
110.25/28.91	
110.25/28.91	   C_{D_1}(d_{d_1}(d_{a_1}(x1))) -> C_{B_1}(b_{e_1}(e_{a_1}(x1)))
110.25/28.91	   C_{B_1}(b_{b_1}(x1)) -> C_{B_1}(x1)
110.25/28.91	   C_{B_1}(b_{d_1}(x1)) -> C_{D_1}(x1)
110.25/28.91	   C_{D_1}(d_{d_1}(d_{a_1}(x1))) -> B_{E_1}(e_{a_1}(x1))
110.25/28.91	   B_{E_1}(e_{c_1}(c_{b_1}(x1))) -> B_{D_1}(d_{a_1}(a_{b_1}(x1)))
110.25/28.91	   B_{D_1}(d_{d_1}(d_{a_1}(x1))) -> B_{B_1}(b_{e_1}(e_{a_1}(x1)))
110.25/28.91	   B_{B_1}(b_{b_1}(x1)) -> C_{B_1}(x1)
110.25/28.91	   C_{B_1}(b_{e_1}(x1)) -> C_{E_1}(x1)
110.25/28.91	   C_{E_1}(e_{c_1}(c_{b_1}(x1))) -> C_{D_1}(d_{a_1}(a_{b_1}(x1)))
110.25/28.91	   C_{D_1}(d_{d_1}(d_{a_1}(x1))) -> E_{A_1}(x1)
110.25/28.91	   E_{A_1}(a_{b_1}(b_{b_1}(x1))) -> C_{D_1}(d_{b_1}(x1))
110.25/28.91	   C_{D_1}(d_{d_1}(d_{c_1}(x1))) -> C_{B_1}(b_{e_1}(e_{c_1}(x1)))
110.25/28.91	   C_{D_1}(d_{d_1}(d_{c_1}(x1))) -> B_{E_1}(e_{c_1}(x1))
110.25/28.91	   B_{E_1}(e_{c_1}(c_{b_1}(x1))) -> D_{A_1}(a_{b_1}(x1))
110.25/28.91	   D_{A_1}(a_{b_1}(b_{b_1}(x1))) -> C_{D_1}(d_{b_1}(x1))
110.25/28.91	   C_{D_1}(d_{d_1}(d_{e_1}(x1))) -> C_{B_1}(b_{e_1}(e_{e_1}(x1)))
110.25/28.91	   D_{A_1}(a_{b_1}(b_{b_1}(x1))) -> D_{B_1}(x1)
110.25/28.91	   D_{B_1}(b_{b_1}(x1)) -> C_{B_1}(x1)
110.25/28.91	   D_{B_1}(b_{d_1}(x1)) -> C_{D_1}(x1)
110.25/28.91	   D_{B_1}(b_{e_1}(x1)) -> C_{E_1}(x1)
110.25/28.91	   C_{E_1}(e_{c_1}(c_{b_1}(x1))) -> D_{A_1}(a_{b_1}(x1))
110.25/28.91	   D_{A_1}(a_{b_1}(b_{d_1}(x1))) -> C_{D_1}(d_{d_1}(x1))
110.25/28.91	   D_{A_1}(a_{b_1}(b_{d_1}(x1))) -> D_{D_1}(x1)
110.25/28.91	   D_{D_1}(d_{d_1}(d_{a_1}(x1))) -> D_{B_1}(b_{e_1}(e_{a_1}(x1)))
110.25/28.91	   D_{D_1}(d_{d_1}(d_{a_1}(x1))) -> B_{E_1}(e_{a_1}(x1))
110.25/28.91	   B_{E_1}(e_{c_1}(c_{b_1}(x1))) -> A_{B_1}(x1)
110.25/28.91	   A_{B_1}(b_{b_1}(x1)) -> C_{B_1}(x1)
110.25/28.91	   A_{B_1}(b_{d_1}(x1)) -> C_{D_1}(x1)
110.25/28.91	   A_{B_1}(b_{e_1}(x1)) -> C_{E_1}(x1)
110.25/28.91	   C_{E_1}(e_{c_1}(c_{b_1}(x1))) -> A_{B_1}(x1)
110.25/28.91	   C_{E_1}(e_{c_1}(c_{d_1}(x1))) -> C_{D_1}(d_{a_1}(a_{d_1}(x1)))
110.25/28.91	   C_{E_1}(e_{c_1}(c_{d_1}(x1))) -> D_{A_1}(a_{d_1}(x1))
110.25/28.91	   D_{A_1}(a_{b_1}(b_{e_1}(x1))) -> C_{D_1}(d_{e_1}(x1))
110.25/28.91	   D_{A_1}(a_{b_1}(b_{e_1}(x1))) -> D_{E_1}(x1)
110.25/28.91	   D_{E_1}(e_{c_1}(c_{b_1}(x1))) -> D_{D_1}(d_{a_1}(a_{b_1}(x1)))
110.25/28.91	   D_{D_1}(d_{d_1}(d_{a_1}(x1))) -> E_{A_1}(x1)
110.25/28.91	   E_{A_1}(a_{b_1}(b_{b_1}(x1))) -> D_{B_1}(x1)
110.25/28.91	   E_{A_1}(a_{b_1}(b_{d_1}(x1))) -> C_{D_1}(d_{d_1}(x1))
110.25/28.91	   E_{A_1}(a_{b_1}(b_{d_1}(x1))) -> D_{D_1}(x1)
110.25/28.91	   D_{D_1}(d_{d_1}(d_{c_1}(x1))) -> D_{B_1}(b_{e_1}(e_{c_1}(x1)))
110.25/28.91	   D_{D_1}(d_{d_1}(d_{c_1}(x1))) -> B_{E_1}(e_{c_1}(x1))
110.25/28.91	   B_{E_1}(e_{c_1}(c_{d_1}(x1))) -> B_{D_1}(d_{a_1}(a_{d_1}(x1)))
110.25/28.91	   B_{D_1}(d_{d_1}(d_{a_1}(x1))) -> B_{E_1}(e_{a_1}(x1))
110.25/28.91	   B_{E_1}(e_{c_1}(c_{d_1}(x1))) -> D_{A_1}(a_{d_1}(x1))
110.25/28.91	   D_{A_1}(a_{b_1}(x1)) -> D_{E_1}(e_{d_1}(d_{b_1}(x1)))
110.25/28.91	   D_{E_1}(e_{c_1}(c_{b_1}(x1))) -> D_{A_1}(a_{b_1}(x1))
110.25/28.91	   D_{A_1}(a_{b_1}(x1)) -> E_{D_1}(d_{b_1}(x1))
110.25/28.91	   E_{D_1}(d_{d_1}(d_{a_1}(x1))) -> E_{B_1}(b_{e_1}(e_{a_1}(x1)))
110.25/28.91	   E_{B_1}(b_{b_1}(x1)) -> C_{B_1}(x1)
110.25/28.91	   E_{B_1}(b_{d_1}(x1)) -> C_{D_1}(x1)
110.25/28.91	   E_{B_1}(b_{e_1}(x1)) -> C_{E_1}(x1)
110.25/28.91	   C_{E_1}(e_{c_1}(c_{d_1}(x1))) -> A_{D_1}(x1)
110.25/28.91	   A_{D_1}(d_{d_1}(d_{a_1}(x1))) -> A_{B_1}(b_{e_1}(e_{a_1}(x1)))
110.25/28.91	   A_{D_1}(d_{d_1}(d_{a_1}(x1))) -> B_{E_1}(e_{a_1}(x1))
110.25/28.91	   B_{E_1}(e_{c_1}(c_{d_1}(x1))) -> A_{D_1}(x1)
110.25/28.91	   A_{D_1}(d_{d_1}(d_{a_1}(x1))) -> E_{A_1}(x1)
110.25/28.91	   E_{A_1}(a_{b_1}(b_{e_1}(x1))) -> C_{D_1}(d_{e_1}(x1))
110.25/28.91	   E_{A_1}(a_{b_1}(b_{e_1}(x1))) -> D_{E_1}(x1)
110.25/28.91	   D_{E_1}(e_{c_1}(c_{b_1}(x1))) -> A_{B_1}(x1)
110.25/28.91	   D_{E_1}(e_{c_1}(c_{d_1}(x1))) -> D_{D_1}(d_{a_1}(a_{d_1}(x1)))
110.25/28.91	   D_{D_1}(d_{d_1}(d_{e_1}(x1))) -> D_{B_1}(b_{e_1}(e_{e_1}(x1)))
110.25/28.91	   D_{E_1}(e_{c_1}(c_{d_1}(x1))) -> D_{A_1}(a_{d_1}(x1))
110.25/28.91	   D_{A_1}(a_{b_1}(x1)) -> D_{B_1}(x1)
110.25/28.91	   D_{A_1}(a_{d_1}(x1)) -> D_{E_1}(e_{d_1}(d_{d_1}(x1)))
110.25/28.91	   D_{E_1}(e_{c_1}(c_{d_1}(x1))) -> A_{D_1}(x1)
110.25/28.91	   A_{D_1}(d_{d_1}(d_{c_1}(x1))) -> A_{B_1}(b_{e_1}(e_{c_1}(x1)))
110.25/28.91	   A_{D_1}(d_{d_1}(d_{c_1}(x1))) -> B_{E_1}(e_{c_1}(x1))
110.25/28.91	   B_{E_1}(e_{c_1}(c_{e_1}(x1))) -> B_{D_1}(d_{a_1}(a_{e_1}(x1)))
110.25/28.91	   B_{D_1}(d_{d_1}(d_{a_1}(x1))) -> E_{A_1}(x1)
110.25/28.91	   E_{A_1}(a_{b_1}(x1)) -> E_{D_1}(d_{b_1}(x1))
110.25/28.91	   E_{D_1}(d_{d_1}(d_{a_1}(x1))) -> B_{E_1}(e_{a_1}(x1))
110.25/28.91	   B_{E_1}(e_{c_1}(c_{e_1}(x1))) -> D_{A_1}(a_{e_1}(x1))
110.25/28.91	   D_{A_1}(a_{d_1}(x1)) -> E_{D_1}(d_{d_1}(x1))
110.25/28.91	   E_{D_1}(d_{d_1}(d_{a_1}(x1))) -> E_{A_1}(x1)
110.25/28.91	   E_{A_1}(a_{b_1}(x1)) -> D_{B_1}(x1)
110.25/28.91	   E_{A_1}(a_{d_1}(x1)) -> E_{D_1}(d_{d_1}(x1))
110.25/28.91	   E_{D_1}(d_{d_1}(d_{c_1}(x1))) -> E_{B_1}(b_{e_1}(e_{c_1}(x1)))
110.25/28.91	   E_{D_1}(d_{d_1}(d_{c_1}(x1))) -> B_{E_1}(e_{c_1}(x1))
110.25/28.91	   B_{E_1}(e_{c_1}(c_{e_1}(x1))) -> A_{E_1}(x1)
110.25/28.91	   A_{E_1}(e_{c_1}(c_{b_1}(x1))) -> A_{D_1}(d_{a_1}(a_{b_1}(x1)))
110.25/28.91	   A_{D_1}(d_{d_1}(d_{e_1}(x1))) -> A_{B_1}(b_{e_1}(e_{e_1}(x1)))
110.25/28.91	   A_{E_1}(e_{c_1}(c_{b_1}(x1))) -> D_{A_1}(a_{b_1}(x1))
110.25/28.91	   D_{A_1}(a_{d_1}(x1)) -> D_{D_1}(x1)
110.25/28.91	   A_{E_1}(e_{c_1}(c_{b_1}(x1))) -> A_{B_1}(x1)
110.25/28.91	   A_{E_1}(e_{c_1}(c_{d_1}(x1))) -> A_{D_1}(d_{a_1}(a_{d_1}(x1)))
110.25/28.91	   A_{E_1}(e_{c_1}(c_{d_1}(x1))) -> D_{A_1}(a_{d_1}(x1))
110.25/28.91	   A_{E_1}(e_{c_1}(c_{d_1}(x1))) -> A_{D_1}(x1)
110.25/28.91	   A_{E_1}(e_{c_1}(c_{e_1}(x1))) -> A_{D_1}(d_{a_1}(a_{e_1}(x1)))
110.25/28.91	   A_{E_1}(e_{c_1}(c_{e_1}(x1))) -> D_{A_1}(a_{e_1}(x1))
110.25/28.91	   D_{A_1}(a_{e_1}(x1)) -> D_{E_1}(e_{d_1}(d_{e_1}(x1)))
110.25/28.91	   D_{E_1}(e_{c_1}(c_{e_1}(x1))) -> D_{D_1}(d_{a_1}(a_{e_1}(x1)))
110.25/28.91	   D_{E_1}(e_{c_1}(c_{e_1}(x1))) -> D_{A_1}(a_{e_1}(x1))
110.25/28.91	   D_{A_1}(a_{e_1}(x1)) -> E_{D_1}(d_{e_1}(x1))
110.25/28.91	   E_{D_1}(d_{d_1}(d_{e_1}(x1))) -> E_{B_1}(b_{e_1}(e_{e_1}(x1)))
110.25/28.91	   D_{A_1}(a_{e_1}(x1)) -> D_{E_1}(x1)
110.25/28.91	   D_{E_1}(e_{c_1}(c_{e_1}(x1))) -> A_{E_1}(x1)
110.25/28.91	   A_{E_1}(e_{c_1}(c_{e_1}(x1))) -> A_{E_1}(x1)
110.25/28.91	   E_{A_1}(a_{d_1}(x1)) -> D_{D_1}(x1)
110.25/28.91	   E_{A_1}(a_{e_1}(x1)) -> E_{D_1}(d_{e_1}(x1))
110.25/28.91	   E_{A_1}(a_{e_1}(x1)) -> D_{E_1}(x1)
110.25/28.91	   B_{D_1}(d_{d_1}(d_{c_1}(x1))) -> B_{B_1}(b_{e_1}(e_{c_1}(x1)))
110.25/28.91	   B_{B_1}(b_{d_1}(x1)) -> C_{D_1}(x1)
110.25/28.91	   B_{B_1}(b_{e_1}(x1)) -> C_{E_1}(x1)
110.25/28.91	   C_{E_1}(e_{c_1}(c_{e_1}(x1))) -> C_{D_1}(d_{a_1}(a_{e_1}(x1)))
110.25/28.91	   C_{E_1}(e_{c_1}(c_{e_1}(x1))) -> D_{A_1}(a_{e_1}(x1))
110.25/28.91	   C_{E_1}(e_{c_1}(c_{e_1}(x1))) -> A_{E_1}(x1)
110.25/28.91	   B_{D_1}(d_{d_1}(d_{c_1}(x1))) -> B_{E_1}(e_{c_1}(x1))
110.25/28.91	   B_{D_1}(d_{d_1}(d_{e_1}(x1))) -> B_{B_1}(b_{e_1}(e_{e_1}(x1)))
110.25/28.91	
110.25/28.91	The TRS R consists of the following rules:
110.25/28.91	
110.25/28.91	   d_{a_1}(a_{b_1}(b_{b_1}(x1))) -> d_{c_1}(c_{d_1}(d_{b_1}(x1)))
110.25/28.91	   d_{a_1}(a_{b_1}(b_{d_1}(x1))) -> d_{c_1}(c_{d_1}(d_{d_1}(x1)))
110.25/28.91	   d_{a_1}(a_{b_1}(b_{e_1}(x1))) -> d_{c_1}(c_{d_1}(d_{e_1}(x1)))
110.25/28.91	   e_{a_1}(a_{b_1}(b_{b_1}(x1))) -> e_{c_1}(c_{d_1}(d_{b_1}(x1)))
110.25/28.91	   e_{a_1}(a_{b_1}(b_{d_1}(x1))) -> e_{c_1}(c_{d_1}(d_{d_1}(x1)))
110.25/28.91	   e_{a_1}(a_{b_1}(b_{e_1}(x1))) -> e_{c_1}(c_{d_1}(d_{e_1}(x1)))
110.25/28.91	   a_{d_1}(d_{d_1}(d_{a_1}(x1))) -> a_{b_1}(b_{e_1}(e_{a_1}(x1)))
110.25/28.91	   a_{d_1}(d_{d_1}(d_{c_1}(x1))) -> a_{b_1}(b_{e_1}(e_{c_1}(x1)))
110.25/28.91	   a_{d_1}(d_{d_1}(d_{e_1}(x1))) -> a_{b_1}(b_{e_1}(e_{e_1}(x1)))
110.25/28.91	   b_{d_1}(d_{d_1}(d_{a_1}(x1))) -> b_{b_1}(b_{e_1}(e_{a_1}(x1)))
110.25/28.91	   b_{d_1}(d_{d_1}(d_{c_1}(x1))) -> b_{b_1}(b_{e_1}(e_{c_1}(x1)))
110.25/28.91	   b_{d_1}(d_{d_1}(d_{e_1}(x1))) -> b_{b_1}(b_{e_1}(e_{e_1}(x1)))
110.25/28.91	   c_{d_1}(d_{d_1}(d_{a_1}(x1))) -> c_{b_1}(b_{e_1}(e_{a_1}(x1)))
110.25/28.91	   c_{d_1}(d_{d_1}(d_{c_1}(x1))) -> c_{b_1}(b_{e_1}(e_{c_1}(x1)))
110.25/28.91	   c_{d_1}(d_{d_1}(d_{e_1}(x1))) -> c_{b_1}(b_{e_1}(e_{e_1}(x1)))
110.25/28.91	   d_{d_1}(d_{d_1}(d_{a_1}(x1))) -> d_{b_1}(b_{e_1}(e_{a_1}(x1)))
110.25/28.91	   d_{d_1}(d_{d_1}(d_{c_1}(x1))) -> d_{b_1}(b_{e_1}(e_{c_1}(x1)))
110.25/28.91	   d_{d_1}(d_{d_1}(d_{e_1}(x1))) -> d_{b_1}(b_{e_1}(e_{e_1}(x1)))
110.25/28.91	   e_{d_1}(d_{d_1}(d_{a_1}(x1))) -> e_{b_1}(b_{e_1}(e_{a_1}(x1)))
110.25/28.91	   e_{d_1}(d_{d_1}(d_{c_1}(x1))) -> e_{b_1}(b_{e_1}(e_{c_1}(x1)))
110.25/28.91	   e_{d_1}(d_{d_1}(d_{e_1}(x1))) -> e_{b_1}(b_{e_1}(e_{e_1}(x1)))
110.25/28.91	   a_{b_1}(b_{b_1}(x1)) -> a_{d_1}(d_{c_1}(c_{b_1}(x1)))
110.25/28.91	   a_{b_1}(b_{d_1}(x1)) -> a_{d_1}(d_{c_1}(c_{d_1}(x1)))
110.25/28.91	   a_{b_1}(b_{e_1}(x1)) -> a_{d_1}(d_{c_1}(c_{e_1}(x1)))
110.25/28.91	   b_{b_1}(b_{b_1}(x1)) -> b_{d_1}(d_{c_1}(c_{b_1}(x1)))
110.25/28.91	   b_{b_1}(b_{d_1}(x1)) -> b_{d_1}(d_{c_1}(c_{d_1}(x1)))
110.25/28.91	   b_{b_1}(b_{e_1}(x1)) -> b_{d_1}(d_{c_1}(c_{e_1}(x1)))
110.25/28.91	   c_{b_1}(b_{b_1}(x1)) -> c_{d_1}(d_{c_1}(c_{b_1}(x1)))
110.25/28.91	   c_{b_1}(b_{d_1}(x1)) -> c_{d_1}(d_{c_1}(c_{d_1}(x1)))
110.25/28.91	   c_{b_1}(b_{e_1}(x1)) -> c_{d_1}(d_{c_1}(c_{e_1}(x1)))
110.25/28.91	   d_{b_1}(b_{b_1}(x1)) -> d_{d_1}(d_{c_1}(c_{b_1}(x1)))
110.25/28.91	   d_{b_1}(b_{d_1}(x1)) -> d_{d_1}(d_{c_1}(c_{d_1}(x1)))
110.25/28.91	   d_{b_1}(b_{e_1}(x1)) -> d_{d_1}(d_{c_1}(c_{e_1}(x1)))
110.25/28.91	   e_{b_1}(b_{b_1}(x1)) -> e_{d_1}(d_{c_1}(c_{b_1}(x1)))
110.25/28.91	   e_{b_1}(b_{d_1}(x1)) -> e_{d_1}(d_{c_1}(c_{d_1}(x1)))
110.25/28.91	   e_{b_1}(b_{e_1}(x1)) -> e_{d_1}(d_{c_1}(c_{e_1}(x1)))
110.25/28.91	   e_{d_1}(d_{a_1}(x1)) -> e_{a_1}(x1)
110.25/28.91	   e_{d_1}(d_{c_1}(x1)) -> e_{c_1}(x1)
110.25/28.91	   e_{d_1}(d_{e_1}(x1)) -> e_{e_1}(x1)
110.25/28.91	   a_{e_1}(e_{c_1}(c_{b_1}(x1))) -> a_{d_1}(d_{a_1}(a_{b_1}(x1)))
110.25/28.91	   a_{e_1}(e_{c_1}(c_{d_1}(x1))) -> a_{d_1}(d_{a_1}(a_{d_1}(x1)))
110.25/28.91	   a_{e_1}(e_{c_1}(c_{e_1}(x1))) -> a_{d_1}(d_{a_1}(a_{e_1}(x1)))
110.25/28.91	   b_{e_1}(e_{c_1}(c_{b_1}(x1))) -> b_{d_1}(d_{a_1}(a_{b_1}(x1)))
110.25/28.91	   b_{e_1}(e_{c_1}(c_{d_1}(x1))) -> b_{d_1}(d_{a_1}(a_{d_1}(x1)))
110.25/28.91	   b_{e_1}(e_{c_1}(c_{e_1}(x1))) -> b_{d_1}(d_{a_1}(a_{e_1}(x1)))
110.25/28.91	   c_{e_1}(e_{c_1}(c_{b_1}(x1))) -> c_{d_1}(d_{a_1}(a_{b_1}(x1)))
110.25/28.91	   c_{e_1}(e_{c_1}(c_{d_1}(x1))) -> c_{d_1}(d_{a_1}(a_{d_1}(x1)))
110.25/28.91	   c_{e_1}(e_{c_1}(c_{e_1}(x1))) -> c_{d_1}(d_{a_1}(a_{e_1}(x1)))
110.25/28.91	   d_{e_1}(e_{c_1}(c_{b_1}(x1))) -> d_{d_1}(d_{a_1}(a_{b_1}(x1)))
110.25/28.91	   d_{e_1}(e_{c_1}(c_{d_1}(x1))) -> d_{d_1}(d_{a_1}(a_{d_1}(x1)))
110.25/28.91	   d_{e_1}(e_{c_1}(c_{e_1}(x1))) -> d_{d_1}(d_{a_1}(a_{e_1}(x1)))
110.25/28.91	   d_{a_1}(a_{b_1}(x1)) -> d_{e_1}(e_{d_1}(d_{b_1}(x1)))
110.25/28.91	   d_{a_1}(a_{d_1}(x1)) -> d_{e_1}(e_{d_1}(d_{d_1}(x1)))
110.25/28.91	   d_{a_1}(a_{e_1}(x1)) -> d_{e_1}(e_{d_1}(d_{e_1}(x1)))
110.25/28.91	   e_{a_1}(a_{b_1}(x1)) -> e_{e_1}(e_{d_1}(d_{b_1}(x1)))
110.25/28.91	   e_{a_1}(a_{d_1}(x1)) -> e_{e_1}(e_{d_1}(d_{d_1}(x1)))
110.25/28.91	   e_{a_1}(a_{e_1}(x1)) -> e_{e_1}(e_{d_1}(d_{e_1}(x1)))
110.25/28.91	
110.25/28.91	Q is empty.
110.25/28.91	We have to consider all minimal (P,Q,R)-chains.
110.25/28.91	----------------------------------------
110.25/28.91	
110.25/28.91	(11) QDPOrderProof (EQUIVALENT)
110.25/28.91	We use the reduction pair processor [LPAR04,JAR06].
110.25/28.91	
110.25/28.91	
110.25/28.91	The following pairs can be oriented strictly and are deleted.
110.25/28.91	
110.25/28.91	   C_{B_1}(b_{b_1}(x1)) -> C_{B_1}(x1)
110.25/28.91	   C_{B_1}(b_{d_1}(x1)) -> C_{D_1}(x1)
110.25/28.91	   C_{D_1}(d_{d_1}(d_{a_1}(x1))) -> B_{E_1}(e_{a_1}(x1))
110.25/28.91	   B_{D_1}(d_{d_1}(d_{a_1}(x1))) -> B_{B_1}(b_{e_1}(e_{a_1}(x1)))
110.25/28.91	   B_{B_1}(b_{b_1}(x1)) -> C_{B_1}(x1)
110.25/28.91	   C_{B_1}(b_{e_1}(x1)) -> C_{E_1}(x1)
110.25/28.91	   C_{E_1}(e_{c_1}(c_{b_1}(x1))) -> C_{D_1}(d_{a_1}(a_{b_1}(x1)))
110.25/28.91	   C_{D_1}(d_{d_1}(d_{a_1}(x1))) -> E_{A_1}(x1)
110.25/28.91	   E_{A_1}(a_{b_1}(b_{b_1}(x1))) -> C_{D_1}(d_{b_1}(x1))
110.25/28.91	   C_{D_1}(d_{d_1}(d_{c_1}(x1))) -> B_{E_1}(e_{c_1}(x1))
110.25/28.91	   D_{A_1}(a_{b_1}(b_{b_1}(x1))) -> C_{D_1}(d_{b_1}(x1))
110.25/28.91	   D_{A_1}(a_{b_1}(b_{b_1}(x1))) -> D_{B_1}(x1)
110.25/28.91	   D_{B_1}(b_{b_1}(x1)) -> C_{B_1}(x1)
110.25/28.91	   D_{B_1}(b_{d_1}(x1)) -> C_{D_1}(x1)
110.25/28.91	   D_{B_1}(b_{e_1}(x1)) -> C_{E_1}(x1)
110.25/28.91	   C_{E_1}(e_{c_1}(c_{b_1}(x1))) -> D_{A_1}(a_{b_1}(x1))
110.25/28.91	   D_{A_1}(a_{b_1}(b_{d_1}(x1))) -> C_{D_1}(d_{d_1}(x1))
110.25/28.91	   D_{A_1}(a_{b_1}(b_{d_1}(x1))) -> D_{D_1}(x1)
110.25/28.91	   D_{D_1}(d_{d_1}(d_{a_1}(x1))) -> D_{B_1}(b_{e_1}(e_{a_1}(x1)))
110.25/28.91	   D_{D_1}(d_{d_1}(d_{a_1}(x1))) -> B_{E_1}(e_{a_1}(x1))
110.25/28.91	   B_{E_1}(e_{c_1}(c_{b_1}(x1))) -> A_{B_1}(x1)
110.25/28.91	   A_{B_1}(b_{b_1}(x1)) -> C_{B_1}(x1)
110.25/28.91	   A_{B_1}(b_{d_1}(x1)) -> C_{D_1}(x1)
110.25/28.91	   C_{E_1}(e_{c_1}(c_{b_1}(x1))) -> A_{B_1}(x1)
110.25/28.91	   C_{E_1}(e_{c_1}(c_{d_1}(x1))) -> C_{D_1}(d_{a_1}(a_{d_1}(x1)))
110.25/28.91	   C_{E_1}(e_{c_1}(c_{d_1}(x1))) -> D_{A_1}(a_{d_1}(x1))
110.25/28.91	   D_{A_1}(a_{b_1}(b_{e_1}(x1))) -> C_{D_1}(d_{e_1}(x1))
110.25/28.91	   D_{A_1}(a_{b_1}(b_{e_1}(x1))) -> D_{E_1}(x1)
110.25/28.91	   D_{D_1}(d_{d_1}(d_{a_1}(x1))) -> E_{A_1}(x1)
110.25/28.91	   E_{A_1}(a_{b_1}(b_{b_1}(x1))) -> D_{B_1}(x1)
110.25/28.91	   E_{A_1}(a_{b_1}(b_{d_1}(x1))) -> C_{D_1}(d_{d_1}(x1))
110.25/28.91	   E_{A_1}(a_{b_1}(b_{d_1}(x1))) -> D_{D_1}(x1)
110.25/28.91	   D_{D_1}(d_{d_1}(d_{c_1}(x1))) -> D_{B_1}(b_{e_1}(e_{c_1}(x1)))
110.25/28.91	   D_{D_1}(d_{d_1}(d_{c_1}(x1))) -> B_{E_1}(e_{c_1}(x1))
110.25/28.91	   B_{D_1}(d_{d_1}(d_{a_1}(x1))) -> B_{E_1}(e_{a_1}(x1))
110.25/28.91	   D_{E_1}(e_{c_1}(c_{b_1}(x1))) -> D_{A_1}(a_{b_1}(x1))
110.25/28.91	   E_{B_1}(b_{b_1}(x1)) -> C_{B_1}(x1)
110.25/28.91	   E_{B_1}(b_{d_1}(x1)) -> C_{D_1}(x1)
110.25/28.91	   E_{B_1}(b_{e_1}(x1)) -> C_{E_1}(x1)
110.25/28.91	   C_{E_1}(e_{c_1}(c_{d_1}(x1))) -> A_{D_1}(x1)
110.25/28.91	   A_{D_1}(d_{d_1}(d_{a_1}(x1))) -> A_{B_1}(b_{e_1}(e_{a_1}(x1)))
110.25/28.91	   A_{D_1}(d_{d_1}(d_{a_1}(x1))) -> B_{E_1}(e_{a_1}(x1))
110.25/28.91	   B_{E_1}(e_{c_1}(c_{d_1}(x1))) -> A_{D_1}(x1)
110.25/28.91	   E_{A_1}(a_{b_1}(b_{e_1}(x1))) -> C_{D_1}(d_{e_1}(x1))
110.25/28.91	   E_{A_1}(a_{b_1}(b_{e_1}(x1))) -> D_{E_1}(x1)
110.25/28.91	   D_{E_1}(e_{c_1}(c_{b_1}(x1))) -> A_{B_1}(x1)
110.25/28.91	   D_{D_1}(d_{d_1}(d_{e_1}(x1))) -> D_{B_1}(b_{e_1}(e_{e_1}(x1)))
110.25/28.91	   D_{E_1}(e_{c_1}(c_{d_1}(x1))) -> D_{A_1}(a_{d_1}(x1))
110.25/28.91	   D_{A_1}(a_{b_1}(x1)) -> D_{B_1}(x1)
110.25/28.91	   D_{E_1}(e_{c_1}(c_{d_1}(x1))) -> A_{D_1}(x1)
110.25/28.91	   A_{D_1}(d_{d_1}(d_{c_1}(x1))) -> A_{B_1}(b_{e_1}(e_{c_1}(x1)))
110.25/28.91	   A_{D_1}(d_{d_1}(d_{c_1}(x1))) -> B_{E_1}(e_{c_1}(x1))
110.25/28.91	   B_{D_1}(d_{d_1}(d_{a_1}(x1))) -> E_{A_1}(x1)
110.25/28.91	   E_{A_1}(a_{b_1}(x1)) -> E_{D_1}(d_{b_1}(x1))
110.25/28.91	   E_{D_1}(d_{d_1}(d_{a_1}(x1))) -> B_{E_1}(e_{a_1}(x1))
110.25/28.91	   E_{D_1}(d_{d_1}(d_{a_1}(x1))) -> E_{A_1}(x1)
110.25/28.91	   E_{A_1}(a_{b_1}(x1)) -> D_{B_1}(x1)
110.25/28.91	   E_{A_1}(a_{d_1}(x1)) -> E_{D_1}(d_{d_1}(x1))
110.25/28.91	   E_{D_1}(d_{d_1}(d_{c_1}(x1))) -> B_{E_1}(e_{c_1}(x1))
110.25/28.91	   A_{E_1}(e_{c_1}(c_{b_1}(x1))) -> A_{D_1}(d_{a_1}(a_{b_1}(x1)))
110.25/28.91	   A_{D_1}(d_{d_1}(d_{e_1}(x1))) -> A_{B_1}(b_{e_1}(e_{e_1}(x1)))
110.25/28.91	   A_{E_1}(e_{c_1}(c_{b_1}(x1))) -> D_{A_1}(a_{b_1}(x1))
110.25/28.91	   A_{E_1}(e_{c_1}(c_{b_1}(x1))) -> A_{B_1}(x1)
110.25/28.91	   A_{E_1}(e_{c_1}(c_{d_1}(x1))) -> A_{D_1}(d_{a_1}(a_{d_1}(x1)))
110.25/28.91	   A_{E_1}(e_{c_1}(c_{d_1}(x1))) -> D_{A_1}(a_{d_1}(x1))
110.25/28.91	   A_{E_1}(e_{c_1}(c_{d_1}(x1))) -> A_{D_1}(x1)
110.25/28.91	   A_{E_1}(e_{c_1}(c_{e_1}(x1))) -> A_{D_1}(d_{a_1}(a_{e_1}(x1)))
110.25/28.91	   A_{E_1}(e_{c_1}(c_{e_1}(x1))) -> D_{A_1}(a_{e_1}(x1))
110.25/28.91	   D_{E_1}(e_{c_1}(c_{e_1}(x1))) -> D_{A_1}(a_{e_1}(x1))
110.25/28.91	   D_{E_1}(e_{c_1}(c_{e_1}(x1))) -> A_{E_1}(x1)
110.25/28.91	   A_{E_1}(e_{c_1}(c_{e_1}(x1))) -> A_{E_1}(x1)
110.25/28.91	   E_{A_1}(a_{d_1}(x1)) -> D_{D_1}(x1)
110.25/28.91	   E_{A_1}(a_{e_1}(x1)) -> E_{D_1}(d_{e_1}(x1))
110.25/28.91	   E_{A_1}(a_{e_1}(x1)) -> D_{E_1}(x1)
110.25/28.91	   B_{D_1}(d_{d_1}(d_{c_1}(x1))) -> B_{B_1}(b_{e_1}(e_{c_1}(x1)))
110.25/28.91	   B_{B_1}(b_{d_1}(x1)) -> C_{D_1}(x1)
110.25/28.91	   C_{E_1}(e_{c_1}(c_{e_1}(x1))) -> C_{D_1}(d_{a_1}(a_{e_1}(x1)))
110.25/28.91	   C_{E_1}(e_{c_1}(c_{e_1}(x1))) -> D_{A_1}(a_{e_1}(x1))
110.25/28.91	   C_{E_1}(e_{c_1}(c_{e_1}(x1))) -> A_{E_1}(x1)
110.25/28.91	   B_{D_1}(d_{d_1}(d_{c_1}(x1))) -> B_{E_1}(e_{c_1}(x1))
110.25/28.91	   B_{D_1}(d_{d_1}(d_{e_1}(x1))) -> B_{B_1}(b_{e_1}(e_{e_1}(x1)))
110.25/28.91	The remaining pairs can at least be oriented weakly.
110.25/28.91	Used ordering:  Polynomial Order [NEGPOLO,POLO] with Interpretation:
110.25/28.91	
110.25/28.91	POL( B_{E_1}_1(x_1) ) = max{0, 2x_1 - 2}
110.25/28.91	POL( D_{E_1}_1(x_1) ) = 2x_1
110.25/28.91	POL( A_{B_1}_1(x_1) ) = 2x_1
110.25/28.91	POL( b_{e_1}_1(x_1) ) = x_1
110.25/28.91	POL( A_{D_1}_1(x_1) ) = max{0, 2x_1 - 1}
110.25/28.91	POL( d_{e_1}_1(x_1) ) = x_1
110.25/28.91	POL( B_{B_1}_1(x_1) ) = 2x_1
110.25/28.91	POL( B_{D_1}_1(x_1) ) = 2x_1
110.25/28.91	POL( C_{B_1}_1(x_1) ) = 2x_1 + 2
110.25/28.91	POL( C_{D_1}_1(x_1) ) = 2x_1
110.25/28.91	POL( D_{B_1}_1(x_1) ) = 2x_1 + 2
110.25/28.91	POL( D_{D_1}_1(x_1) ) = 2x_1 + 2
110.25/28.91	POL( E_{B_1}_1(x_1) ) = 2x_1 + 2
110.25/28.91	POL( b_{d_1}_1(x_1) ) = x_1 + 1
110.25/28.91	POL( d_{b_1}_1(x_1) ) = x_1 + 2
110.25/28.91	POL( D_{A_1}_1(x_1) ) = 2x_1
110.25/28.91	POL( a_{b_1}_1(x_1) ) = x_1 + 2
110.25/28.91	POL( a_{d_1}_1(x_1) ) = x_1 + 1
110.25/28.91	POL( E_{D_1}_1(x_1) ) = 2x_1
110.25/28.91	POL( d_{d_1}_1(x_1) ) = x_1 + 1
110.25/28.91	POL( d_{a_1}_1(x_1) ) = x_1
110.25/28.91	POL( c_{b_1}_1(x_1) ) = x_1 + 2
110.25/28.91	POL( d_{c_1}_1(x_1) ) = x_1 + 1
110.25/28.91	POL( e_{a_1}_1(x_1) ) = x_1
110.25/28.91	POL( b_{b_1}_1(x_1) ) = x_1 + 2
110.25/28.91	POL( e_{c_1}_1(x_1) ) = x_1 + 1
110.25/28.91	POL( c_{d_1}_1(x_1) ) = x_1 + 1
110.25/28.91	POL( e_{e_1}_1(x_1) ) = max{0, -2}
110.25/28.91	POL( e_{d_1}_1(x_1) ) = x_1
110.25/28.91	POL( a_{e_1}_1(x_1) ) = x_1
110.25/28.91	POL( e_{b_1}_1(x_1) ) = x_1 + 1
110.25/28.91	POL( c_{e_1}_1(x_1) ) = x_1
110.25/28.91	POL( C_{E_1}_1(x_1) ) = 2x_1
110.25/28.91	POL( E_{A_1}_1(x_1) ) = 2x_1 + 1
110.25/28.91	POL( A_{E_1}_1(x_1) ) = 2x_1
110.25/28.91	
110.25/28.91	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
110.25/28.91	
110.25/28.91	   e_{a_1}(a_{b_1}(b_{b_1}(x1))) -> e_{c_1}(c_{d_1}(d_{b_1}(x1)))
110.25/28.91	   e_{a_1}(a_{b_1}(b_{d_1}(x1))) -> e_{c_1}(c_{d_1}(d_{d_1}(x1)))
110.25/28.91	   e_{a_1}(a_{b_1}(b_{e_1}(x1))) -> e_{c_1}(c_{d_1}(d_{e_1}(x1)))
110.25/28.91	   e_{a_1}(a_{b_1}(x1)) -> e_{e_1}(e_{d_1}(d_{b_1}(x1)))
110.25/28.91	   e_{a_1}(a_{d_1}(x1)) -> e_{e_1}(e_{d_1}(d_{d_1}(x1)))
110.25/28.91	   e_{a_1}(a_{e_1}(x1)) -> e_{e_1}(e_{d_1}(d_{e_1}(x1)))
110.25/28.91	   b_{e_1}(e_{c_1}(c_{b_1}(x1))) -> b_{d_1}(d_{a_1}(a_{b_1}(x1)))
110.25/28.91	   b_{e_1}(e_{c_1}(c_{d_1}(x1))) -> b_{d_1}(d_{a_1}(a_{d_1}(x1)))
110.25/28.91	   b_{e_1}(e_{c_1}(c_{e_1}(x1))) -> b_{d_1}(d_{a_1}(a_{e_1}(x1)))
110.25/28.91	   a_{b_1}(b_{b_1}(x1)) -> a_{d_1}(d_{c_1}(c_{b_1}(x1)))
110.25/28.91	   a_{b_1}(b_{d_1}(x1)) -> a_{d_1}(d_{c_1}(c_{d_1}(x1)))
110.25/28.91	   a_{b_1}(b_{e_1}(x1)) -> a_{d_1}(d_{c_1}(c_{e_1}(x1)))
110.25/28.91	   d_{a_1}(a_{b_1}(b_{b_1}(x1))) -> d_{c_1}(c_{d_1}(d_{b_1}(x1)))
110.25/28.91	   d_{a_1}(a_{b_1}(b_{d_1}(x1))) -> d_{c_1}(c_{d_1}(d_{d_1}(x1)))
110.25/28.91	   d_{a_1}(a_{b_1}(b_{e_1}(x1))) -> d_{c_1}(c_{d_1}(d_{e_1}(x1)))
110.25/28.91	   d_{a_1}(a_{b_1}(x1)) -> d_{e_1}(e_{d_1}(d_{b_1}(x1)))
110.25/28.91	   d_{a_1}(a_{d_1}(x1)) -> d_{e_1}(e_{d_1}(d_{d_1}(x1)))
110.25/28.91	   d_{a_1}(a_{e_1}(x1)) -> d_{e_1}(e_{d_1}(d_{e_1}(x1)))
110.25/28.91	   d_{b_1}(b_{b_1}(x1)) -> d_{d_1}(d_{c_1}(c_{b_1}(x1)))
110.25/28.91	   d_{b_1}(b_{d_1}(x1)) -> d_{d_1}(d_{c_1}(c_{d_1}(x1)))
110.25/28.91	   d_{b_1}(b_{e_1}(x1)) -> d_{d_1}(d_{c_1}(c_{e_1}(x1)))
110.25/28.91	   d_{d_1}(d_{d_1}(d_{a_1}(x1))) -> d_{b_1}(b_{e_1}(e_{a_1}(x1)))
110.25/28.91	   d_{d_1}(d_{d_1}(d_{c_1}(x1))) -> d_{b_1}(b_{e_1}(e_{c_1}(x1)))
110.25/28.91	   d_{d_1}(d_{d_1}(d_{e_1}(x1))) -> d_{b_1}(b_{e_1}(e_{e_1}(x1)))
110.25/28.91	   a_{d_1}(d_{d_1}(d_{a_1}(x1))) -> a_{b_1}(b_{e_1}(e_{a_1}(x1)))
110.25/28.91	   a_{d_1}(d_{d_1}(d_{c_1}(x1))) -> a_{b_1}(b_{e_1}(e_{c_1}(x1)))
110.25/28.91	   a_{d_1}(d_{d_1}(d_{e_1}(x1))) -> a_{b_1}(b_{e_1}(e_{e_1}(x1)))
110.25/28.91	   d_{e_1}(e_{c_1}(c_{b_1}(x1))) -> d_{d_1}(d_{a_1}(a_{b_1}(x1)))
110.25/28.91	   d_{e_1}(e_{c_1}(c_{d_1}(x1))) -> d_{d_1}(d_{a_1}(a_{d_1}(x1)))
110.25/28.91	   d_{e_1}(e_{c_1}(c_{e_1}(x1))) -> d_{d_1}(d_{a_1}(a_{e_1}(x1)))
110.25/28.91	   e_{d_1}(d_{d_1}(d_{a_1}(x1))) -> e_{b_1}(b_{e_1}(e_{a_1}(x1)))
110.25/28.91	   e_{d_1}(d_{d_1}(d_{c_1}(x1))) -> e_{b_1}(b_{e_1}(e_{c_1}(x1)))
110.25/28.91	   e_{d_1}(d_{d_1}(d_{e_1}(x1))) -> e_{b_1}(b_{e_1}(e_{e_1}(x1)))
110.25/28.91	   e_{d_1}(d_{a_1}(x1)) -> e_{a_1}(x1)
110.25/28.91	   e_{d_1}(d_{c_1}(x1)) -> e_{c_1}(x1)
110.25/28.91	   e_{d_1}(d_{e_1}(x1)) -> e_{e_1}(x1)
110.25/28.91	   a_{e_1}(e_{c_1}(c_{b_1}(x1))) -> a_{d_1}(d_{a_1}(a_{b_1}(x1)))
110.25/28.91	   a_{e_1}(e_{c_1}(c_{d_1}(x1))) -> a_{d_1}(d_{a_1}(a_{d_1}(x1)))
110.25/28.91	   a_{e_1}(e_{c_1}(c_{e_1}(x1))) -> a_{d_1}(d_{a_1}(a_{e_1}(x1)))
110.25/28.91	   c_{b_1}(b_{b_1}(x1)) -> c_{d_1}(d_{c_1}(c_{b_1}(x1)))
110.25/28.91	   c_{b_1}(b_{d_1}(x1)) -> c_{d_1}(d_{c_1}(c_{d_1}(x1)))
110.25/28.91	   c_{b_1}(b_{e_1}(x1)) -> c_{d_1}(d_{c_1}(c_{e_1}(x1)))
110.25/28.91	   c_{d_1}(d_{d_1}(d_{a_1}(x1))) -> c_{b_1}(b_{e_1}(e_{a_1}(x1)))
110.25/28.91	   c_{d_1}(d_{d_1}(d_{c_1}(x1))) -> c_{b_1}(b_{e_1}(e_{c_1}(x1)))
110.25/28.91	   c_{d_1}(d_{d_1}(d_{e_1}(x1))) -> c_{b_1}(b_{e_1}(e_{e_1}(x1)))
110.25/28.91	   b_{d_1}(d_{d_1}(d_{a_1}(x1))) -> b_{b_1}(b_{e_1}(e_{a_1}(x1)))
110.25/28.91	   b_{d_1}(d_{d_1}(d_{c_1}(x1))) -> b_{b_1}(b_{e_1}(e_{c_1}(x1)))
110.25/28.91	   b_{d_1}(d_{d_1}(d_{e_1}(x1))) -> b_{b_1}(b_{e_1}(e_{e_1}(x1)))
110.25/28.91	   c_{e_1}(e_{c_1}(c_{b_1}(x1))) -> c_{d_1}(d_{a_1}(a_{b_1}(x1)))
110.25/28.91	   c_{e_1}(e_{c_1}(c_{d_1}(x1))) -> c_{d_1}(d_{a_1}(a_{d_1}(x1)))
110.25/28.91	   c_{e_1}(e_{c_1}(c_{e_1}(x1))) -> c_{d_1}(d_{a_1}(a_{e_1}(x1)))
110.25/28.91	   e_{b_1}(b_{b_1}(x1)) -> e_{d_1}(d_{c_1}(c_{b_1}(x1)))
110.25/28.91	   e_{b_1}(b_{d_1}(x1)) -> e_{d_1}(d_{c_1}(c_{d_1}(x1)))
110.25/28.91	   e_{b_1}(b_{e_1}(x1)) -> e_{d_1}(d_{c_1}(c_{e_1}(x1)))
110.25/28.91	   b_{b_1}(b_{b_1}(x1)) -> b_{d_1}(d_{c_1}(c_{b_1}(x1)))
110.25/28.91	   b_{b_1}(b_{d_1}(x1)) -> b_{d_1}(d_{c_1}(c_{d_1}(x1)))
110.25/28.91	   b_{b_1}(b_{e_1}(x1)) -> b_{d_1}(d_{c_1}(c_{e_1}(x1)))
110.25/28.91	
110.25/28.91	
110.25/28.91	----------------------------------------
110.25/28.91	
110.25/28.91	(12)
110.25/28.91	Obligation:
110.25/28.91	Q DP problem:
110.25/28.91	The TRS P consists of the following rules:
110.25/28.91	
110.25/28.91	   C_{D_1}(d_{d_1}(d_{a_1}(x1))) -> C_{B_1}(b_{e_1}(e_{a_1}(x1)))
110.25/28.91	   B_{E_1}(e_{c_1}(c_{b_1}(x1))) -> B_{D_1}(d_{a_1}(a_{b_1}(x1)))
110.25/28.91	   C_{D_1}(d_{d_1}(d_{c_1}(x1))) -> C_{B_1}(b_{e_1}(e_{c_1}(x1)))
110.25/28.91	   B_{E_1}(e_{c_1}(c_{b_1}(x1))) -> D_{A_1}(a_{b_1}(x1))
110.25/28.91	   C_{D_1}(d_{d_1}(d_{e_1}(x1))) -> C_{B_1}(b_{e_1}(e_{e_1}(x1)))
110.25/28.91	   A_{B_1}(b_{e_1}(x1)) -> C_{E_1}(x1)
110.25/28.91	   D_{E_1}(e_{c_1}(c_{b_1}(x1))) -> D_{D_1}(d_{a_1}(a_{b_1}(x1)))
110.25/28.91	   B_{E_1}(e_{c_1}(c_{d_1}(x1))) -> B_{D_1}(d_{a_1}(a_{d_1}(x1)))
110.25/28.91	   B_{E_1}(e_{c_1}(c_{d_1}(x1))) -> D_{A_1}(a_{d_1}(x1))
110.25/28.91	   D_{A_1}(a_{b_1}(x1)) -> D_{E_1}(e_{d_1}(d_{b_1}(x1)))
110.25/28.91	   D_{A_1}(a_{b_1}(x1)) -> E_{D_1}(d_{b_1}(x1))
110.25/28.91	   E_{D_1}(d_{d_1}(d_{a_1}(x1))) -> E_{B_1}(b_{e_1}(e_{a_1}(x1)))
110.25/28.91	   A_{D_1}(d_{d_1}(d_{a_1}(x1))) -> E_{A_1}(x1)
110.25/28.91	   D_{E_1}(e_{c_1}(c_{d_1}(x1))) -> D_{D_1}(d_{a_1}(a_{d_1}(x1)))
110.25/28.91	   D_{A_1}(a_{d_1}(x1)) -> D_{E_1}(e_{d_1}(d_{d_1}(x1)))
110.25/28.91	   B_{E_1}(e_{c_1}(c_{e_1}(x1))) -> B_{D_1}(d_{a_1}(a_{e_1}(x1)))
110.25/28.91	   B_{E_1}(e_{c_1}(c_{e_1}(x1))) -> D_{A_1}(a_{e_1}(x1))
110.25/28.91	   D_{A_1}(a_{d_1}(x1)) -> E_{D_1}(d_{d_1}(x1))
110.25/28.91	   E_{D_1}(d_{d_1}(d_{c_1}(x1))) -> E_{B_1}(b_{e_1}(e_{c_1}(x1)))
110.25/28.91	   B_{E_1}(e_{c_1}(c_{e_1}(x1))) -> A_{E_1}(x1)
110.25/28.91	   D_{A_1}(a_{d_1}(x1)) -> D_{D_1}(x1)
110.25/28.91	   D_{A_1}(a_{e_1}(x1)) -> D_{E_1}(e_{d_1}(d_{e_1}(x1)))
110.25/28.91	   D_{E_1}(e_{c_1}(c_{e_1}(x1))) -> D_{D_1}(d_{a_1}(a_{e_1}(x1)))
110.25/28.91	   D_{A_1}(a_{e_1}(x1)) -> E_{D_1}(d_{e_1}(x1))
110.25/28.91	   E_{D_1}(d_{d_1}(d_{e_1}(x1))) -> E_{B_1}(b_{e_1}(e_{e_1}(x1)))
110.25/28.91	   D_{A_1}(a_{e_1}(x1)) -> D_{E_1}(x1)
110.25/28.91	   B_{B_1}(b_{e_1}(x1)) -> C_{E_1}(x1)
110.25/28.91	
110.25/28.91	The TRS R consists of the following rules:
110.25/28.91	
110.25/28.91	   d_{a_1}(a_{b_1}(b_{b_1}(x1))) -> d_{c_1}(c_{d_1}(d_{b_1}(x1)))
110.25/28.91	   d_{a_1}(a_{b_1}(b_{d_1}(x1))) -> d_{c_1}(c_{d_1}(d_{d_1}(x1)))
110.25/28.91	   d_{a_1}(a_{b_1}(b_{e_1}(x1))) -> d_{c_1}(c_{d_1}(d_{e_1}(x1)))
110.25/28.91	   e_{a_1}(a_{b_1}(b_{b_1}(x1))) -> e_{c_1}(c_{d_1}(d_{b_1}(x1)))
110.25/28.91	   e_{a_1}(a_{b_1}(b_{d_1}(x1))) -> e_{c_1}(c_{d_1}(d_{d_1}(x1)))
110.25/28.91	   e_{a_1}(a_{b_1}(b_{e_1}(x1))) -> e_{c_1}(c_{d_1}(d_{e_1}(x1)))
110.25/28.91	   a_{d_1}(d_{d_1}(d_{a_1}(x1))) -> a_{b_1}(b_{e_1}(e_{a_1}(x1)))
110.25/28.91	   a_{d_1}(d_{d_1}(d_{c_1}(x1))) -> a_{b_1}(b_{e_1}(e_{c_1}(x1)))
110.25/28.91	   a_{d_1}(d_{d_1}(d_{e_1}(x1))) -> a_{b_1}(b_{e_1}(e_{e_1}(x1)))
110.25/28.91	   b_{d_1}(d_{d_1}(d_{a_1}(x1))) -> b_{b_1}(b_{e_1}(e_{a_1}(x1)))
110.25/28.91	   b_{d_1}(d_{d_1}(d_{c_1}(x1))) -> b_{b_1}(b_{e_1}(e_{c_1}(x1)))
110.25/28.91	   b_{d_1}(d_{d_1}(d_{e_1}(x1))) -> b_{b_1}(b_{e_1}(e_{e_1}(x1)))
110.25/28.91	   c_{d_1}(d_{d_1}(d_{a_1}(x1))) -> c_{b_1}(b_{e_1}(e_{a_1}(x1)))
110.25/28.91	   c_{d_1}(d_{d_1}(d_{c_1}(x1))) -> c_{b_1}(b_{e_1}(e_{c_1}(x1)))
110.25/28.91	   c_{d_1}(d_{d_1}(d_{e_1}(x1))) -> c_{b_1}(b_{e_1}(e_{e_1}(x1)))
110.25/28.91	   d_{d_1}(d_{d_1}(d_{a_1}(x1))) -> d_{b_1}(b_{e_1}(e_{a_1}(x1)))
110.25/28.91	   d_{d_1}(d_{d_1}(d_{c_1}(x1))) -> d_{b_1}(b_{e_1}(e_{c_1}(x1)))
110.25/28.91	   d_{d_1}(d_{d_1}(d_{e_1}(x1))) -> d_{b_1}(b_{e_1}(e_{e_1}(x1)))
110.25/28.91	   e_{d_1}(d_{d_1}(d_{a_1}(x1))) -> e_{b_1}(b_{e_1}(e_{a_1}(x1)))
110.25/28.91	   e_{d_1}(d_{d_1}(d_{c_1}(x1))) -> e_{b_1}(b_{e_1}(e_{c_1}(x1)))
110.25/28.91	   e_{d_1}(d_{d_1}(d_{e_1}(x1))) -> e_{b_1}(b_{e_1}(e_{e_1}(x1)))
110.25/28.91	   a_{b_1}(b_{b_1}(x1)) -> a_{d_1}(d_{c_1}(c_{b_1}(x1)))
110.25/28.91	   a_{b_1}(b_{d_1}(x1)) -> a_{d_1}(d_{c_1}(c_{d_1}(x1)))
110.25/28.91	   a_{b_1}(b_{e_1}(x1)) -> a_{d_1}(d_{c_1}(c_{e_1}(x1)))
110.25/28.91	   b_{b_1}(b_{b_1}(x1)) -> b_{d_1}(d_{c_1}(c_{b_1}(x1)))
110.25/28.91	   b_{b_1}(b_{d_1}(x1)) -> b_{d_1}(d_{c_1}(c_{d_1}(x1)))
110.25/28.91	   b_{b_1}(b_{e_1}(x1)) -> b_{d_1}(d_{c_1}(c_{e_1}(x1)))
110.25/28.91	   c_{b_1}(b_{b_1}(x1)) -> c_{d_1}(d_{c_1}(c_{b_1}(x1)))
110.25/28.91	   c_{b_1}(b_{d_1}(x1)) -> c_{d_1}(d_{c_1}(c_{d_1}(x1)))
110.25/28.91	   c_{b_1}(b_{e_1}(x1)) -> c_{d_1}(d_{c_1}(c_{e_1}(x1)))
110.25/28.91	   d_{b_1}(b_{b_1}(x1)) -> d_{d_1}(d_{c_1}(c_{b_1}(x1)))
110.25/28.91	   d_{b_1}(b_{d_1}(x1)) -> d_{d_1}(d_{c_1}(c_{d_1}(x1)))
110.25/28.91	   d_{b_1}(b_{e_1}(x1)) -> d_{d_1}(d_{c_1}(c_{e_1}(x1)))
110.25/28.91	   e_{b_1}(b_{b_1}(x1)) -> e_{d_1}(d_{c_1}(c_{b_1}(x1)))
110.25/28.91	   e_{b_1}(b_{d_1}(x1)) -> e_{d_1}(d_{c_1}(c_{d_1}(x1)))
110.25/28.91	   e_{b_1}(b_{e_1}(x1)) -> e_{d_1}(d_{c_1}(c_{e_1}(x1)))
110.25/28.91	   e_{d_1}(d_{a_1}(x1)) -> e_{a_1}(x1)
110.25/28.91	   e_{d_1}(d_{c_1}(x1)) -> e_{c_1}(x1)
110.25/28.91	   e_{d_1}(d_{e_1}(x1)) -> e_{e_1}(x1)
110.25/28.91	   a_{e_1}(e_{c_1}(c_{b_1}(x1))) -> a_{d_1}(d_{a_1}(a_{b_1}(x1)))
110.25/28.91	   a_{e_1}(e_{c_1}(c_{d_1}(x1))) -> a_{d_1}(d_{a_1}(a_{d_1}(x1)))
110.25/28.91	   a_{e_1}(e_{c_1}(c_{e_1}(x1))) -> a_{d_1}(d_{a_1}(a_{e_1}(x1)))
110.25/28.91	   b_{e_1}(e_{c_1}(c_{b_1}(x1))) -> b_{d_1}(d_{a_1}(a_{b_1}(x1)))
110.25/28.91	   b_{e_1}(e_{c_1}(c_{d_1}(x1))) -> b_{d_1}(d_{a_1}(a_{d_1}(x1)))
110.25/28.91	   b_{e_1}(e_{c_1}(c_{e_1}(x1))) -> b_{d_1}(d_{a_1}(a_{e_1}(x1)))
110.25/28.91	   c_{e_1}(e_{c_1}(c_{b_1}(x1))) -> c_{d_1}(d_{a_1}(a_{b_1}(x1)))
110.25/28.91	   c_{e_1}(e_{c_1}(c_{d_1}(x1))) -> c_{d_1}(d_{a_1}(a_{d_1}(x1)))
110.25/28.91	   c_{e_1}(e_{c_1}(c_{e_1}(x1))) -> c_{d_1}(d_{a_1}(a_{e_1}(x1)))
110.25/28.91	   d_{e_1}(e_{c_1}(c_{b_1}(x1))) -> d_{d_1}(d_{a_1}(a_{b_1}(x1)))
110.25/28.91	   d_{e_1}(e_{c_1}(c_{d_1}(x1))) -> d_{d_1}(d_{a_1}(a_{d_1}(x1)))
110.25/28.91	   d_{e_1}(e_{c_1}(c_{e_1}(x1))) -> d_{d_1}(d_{a_1}(a_{e_1}(x1)))
110.25/28.91	   d_{a_1}(a_{b_1}(x1)) -> d_{e_1}(e_{d_1}(d_{b_1}(x1)))
110.25/28.91	   d_{a_1}(a_{d_1}(x1)) -> d_{e_1}(e_{d_1}(d_{d_1}(x1)))
110.25/28.91	   d_{a_1}(a_{e_1}(x1)) -> d_{e_1}(e_{d_1}(d_{e_1}(x1)))
110.25/28.91	   e_{a_1}(a_{b_1}(x1)) -> e_{e_1}(e_{d_1}(d_{b_1}(x1)))
110.25/28.91	   e_{a_1}(a_{d_1}(x1)) -> e_{e_1}(e_{d_1}(d_{d_1}(x1)))
110.25/28.91	   e_{a_1}(a_{e_1}(x1)) -> e_{e_1}(e_{d_1}(d_{e_1}(x1)))
110.25/28.91	
110.25/28.91	Q is empty.
110.25/28.91	We have to consider all minimal (P,Q,R)-chains.
110.25/28.91	----------------------------------------
110.25/28.91	
110.25/28.91	(13) DependencyGraphProof (EQUIVALENT)
110.25/28.91	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 27 less nodes.
110.25/28.91	----------------------------------------
110.25/28.91	
110.25/28.91	(14)
110.25/28.91	TRUE
110.52/29.04	EOF