107.78/28.41	YES
107.78/28.45	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
107.78/28.45	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
107.78/28.45	
107.78/28.45	
107.78/28.45	Termination w.r.t. Q of the given QTRS could be proven:
107.78/28.45	
107.78/28.45	(0) QTRS
107.78/28.45	(1) QTRS Reverse [EQUIVALENT, 0 ms]
107.78/28.45	(2) QTRS
107.78/28.45	(3) FlatCCProof [EQUIVALENT, 0 ms]
107.78/28.45	(4) QTRS
107.78/28.45	(5) RootLabelingProof [EQUIVALENT, 1 ms]
107.78/28.45	(6) QTRS
107.78/28.45	(7) QTRSRRRProof [EQUIVALENT, 103 ms]
107.78/28.45	(8) QTRS
107.78/28.45	(9) DependencyPairsProof [EQUIVALENT, 284 ms]
107.78/28.45	(10) QDP
107.78/28.45	(11) DependencyGraphProof [EQUIVALENT, 0 ms]
107.78/28.45	(12) QDP
107.78/28.45	(13) UsableRulesProof [EQUIVALENT, 47 ms]
107.78/28.45	(14) QDP
107.78/28.45	(15) QDPOrderProof [EQUIVALENT, 239 ms]
107.78/28.45	(16) QDP
107.78/28.45	(17) DependencyGraphProof [EQUIVALENT, 0 ms]
107.78/28.45	(18) QDP
107.78/28.45	(19) QDPOrderProof [EQUIVALENT, 107 ms]
107.78/28.45	(20) QDP
107.78/28.45	(21) QDPOrderProof [EQUIVALENT, 94 ms]
107.78/28.45	(22) QDP
107.78/28.45	(23) DependencyGraphProof [EQUIVALENT, 0 ms]
107.78/28.45	(24) QDP
107.78/28.45	(25) QDPOrderProof [EQUIVALENT, 66 ms]
107.78/28.45	(26) QDP
107.78/28.45	(27) DependencyGraphProof [EQUIVALENT, 0 ms]
107.78/28.45	(28) QDP
107.78/28.45	(29) QDPOrderProof [EQUIVALENT, 3740 ms]
107.78/28.45	(30) QDP
107.78/28.45	(31) PisEmptyProof [EQUIVALENT, 0 ms]
107.78/28.45	(32) YES
107.78/28.45	
107.78/28.45	
107.78/28.45	----------------------------------------
107.78/28.45	
107.78/28.45	(0)
107.78/28.45	Obligation:
107.78/28.45	Q restricted rewrite system:
107.78/28.45	The TRS R consists of the following rules:
107.78/28.45	
107.78/28.45	   b(b(d(d(b(b(x1)))))) -> c(c(d(d(b(b(x1))))))
107.78/28.45	   b(b(a(a(c(c(x1)))))) -> b(b(c(c(x1))))
107.78/28.45	   a(a(d(d(x1)))) -> d(d(c(c(x1))))
107.78/28.45	   b(b(b(b(b(b(x1)))))) -> a(a(b(b(c(c(x1))))))
107.78/28.45	   d(d(c(c(x1)))) -> b(b(d(d(x1))))
107.78/28.45	   d(d(c(c(x1)))) -> d(d(b(b(d(d(x1))))))
107.78/28.45	   d(d(a(a(c(c(x1)))))) -> b(b(b(b(x1))))
107.78/28.45	
107.78/28.45	Q is empty.
107.78/28.45	
107.78/28.45	----------------------------------------
107.78/28.45	
107.78/28.45	(1) QTRS Reverse (EQUIVALENT)
107.78/28.45	We applied the QTRS Reverse Processor [REVERSE].
107.78/28.45	----------------------------------------
107.78/28.45	
107.78/28.45	(2)
107.78/28.45	Obligation:
107.78/28.45	Q restricted rewrite system:
107.78/28.45	The TRS R consists of the following rules:
107.78/28.45	
107.78/28.45	   b(b(d(d(b(b(x1)))))) -> b(b(d(d(c(c(x1))))))
107.78/28.45	   c(c(a(a(b(b(x1)))))) -> c(c(b(b(x1))))
107.78/28.45	   d(d(a(a(x1)))) -> c(c(d(d(x1))))
107.78/28.45	   b(b(b(b(b(b(x1)))))) -> c(c(b(b(a(a(x1))))))
107.78/28.45	   c(c(d(d(x1)))) -> d(d(b(b(x1))))
107.78/28.45	   c(c(d(d(x1)))) -> d(d(b(b(d(d(x1))))))
107.78/28.45	   c(c(a(a(d(d(x1)))))) -> b(b(b(b(x1))))
107.78/28.45	
107.78/28.45	Q is empty.
107.78/28.45	
107.78/28.45	----------------------------------------
107.78/28.45	
107.78/28.45	(3) FlatCCProof (EQUIVALENT)
107.78/28.45	We used flat context closure [ROOTLAB]
107.78/28.45	As Q is empty the flat context closure was sound AND complete.
107.78/28.45	
107.78/28.45	----------------------------------------
107.78/28.45	
107.78/28.45	(4)
107.78/28.45	Obligation:
107.78/28.45	Q restricted rewrite system:
107.78/28.45	The TRS R consists of the following rules:
107.78/28.45	
107.78/28.45	   b(b(d(d(b(b(x1)))))) -> b(b(d(d(c(c(x1))))))
107.78/28.45	   c(c(a(a(b(b(x1)))))) -> c(c(b(b(x1))))
107.78/28.45	   b(d(d(a(a(x1))))) -> b(c(c(d(d(x1)))))
107.78/28.45	   d(d(d(a(a(x1))))) -> d(c(c(d(d(x1)))))
107.78/28.45	   c(d(d(a(a(x1))))) -> c(c(c(d(d(x1)))))
107.78/28.45	   a(d(d(a(a(x1))))) -> a(c(c(d(d(x1)))))
107.78/28.45	   b(b(b(b(b(b(b(x1))))))) -> b(c(c(b(b(a(a(x1)))))))
107.78/28.45	   d(b(b(b(b(b(b(x1))))))) -> d(c(c(b(b(a(a(x1)))))))
107.78/28.45	   c(b(b(b(b(b(b(x1))))))) -> c(c(c(b(b(a(a(x1)))))))
107.78/28.45	   a(b(b(b(b(b(b(x1))))))) -> a(c(c(b(b(a(a(x1)))))))
107.78/28.45	   b(c(c(d(d(x1))))) -> b(d(d(b(b(x1)))))
107.78/28.45	   d(c(c(d(d(x1))))) -> d(d(d(b(b(x1)))))
107.78/28.45	   c(c(c(d(d(x1))))) -> c(d(d(b(b(x1)))))
107.78/28.45	   a(c(c(d(d(x1))))) -> a(d(d(b(b(x1)))))
107.78/28.45	   b(c(c(d(d(x1))))) -> b(d(d(b(b(d(d(x1)))))))
107.78/28.45	   d(c(c(d(d(x1))))) -> d(d(d(b(b(d(d(x1)))))))
107.78/28.45	   c(c(c(d(d(x1))))) -> c(d(d(b(b(d(d(x1)))))))
107.78/28.45	   a(c(c(d(d(x1))))) -> a(d(d(b(b(d(d(x1)))))))
107.78/28.45	   b(c(c(a(a(d(d(x1))))))) -> b(b(b(b(b(x1)))))
107.78/28.45	   d(c(c(a(a(d(d(x1))))))) -> d(b(b(b(b(x1)))))
107.78/28.45	   c(c(c(a(a(d(d(x1))))))) -> c(b(b(b(b(x1)))))
107.78/28.45	   a(c(c(a(a(d(d(x1))))))) -> a(b(b(b(b(x1)))))
107.78/28.45	
107.78/28.45	Q is empty.
107.78/28.45	
107.78/28.45	----------------------------------------
107.78/28.45	
107.78/28.45	(5) RootLabelingProof (EQUIVALENT)
107.78/28.45	We used plain root labeling [ROOTLAB] with the following heuristic:
107.78/28.45	LabelAll: All function symbols get labeled
107.78/28.45	
107.78/28.45	As Q is empty the root labeling was sound AND complete.
107.78/28.45	
107.78/28.45	----------------------------------------
107.78/28.45	
107.78/28.45	(6)
107.78/28.45	Obligation:
107.78/28.45	Q restricted rewrite system:
107.78/28.45	The TRS R consists of the following rules:
107.78/28.45	
107.78/28.45	   b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))) -> b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{b_1}(x1))))))
107.78/28.45	   b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))) -> b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{d_1}(x1))))))
107.78/28.45	   b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))) -> b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{c_1}(x1))))))
107.78/28.45	   b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{a_1}(x1)))))) -> b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{a_1}(x1))))))
107.78/28.45	   c_{c_1}(c_{a_1}(a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(x1)))))) -> c_{c_1}(c_{b_1}(b_{b_1}(b_{b_1}(x1))))
107.78/28.45	   c_{c_1}(c_{a_1}(a_{a_1}(a_{b_1}(b_{b_1}(b_{d_1}(x1)))))) -> c_{c_1}(c_{b_1}(b_{b_1}(b_{d_1}(x1))))
107.78/28.45	   c_{c_1}(c_{a_1}(a_{a_1}(a_{b_1}(b_{b_1}(b_{c_1}(x1)))))) -> c_{c_1}(c_{b_1}(b_{b_1}(b_{c_1}(x1))))
107.78/28.45	   c_{c_1}(c_{a_1}(a_{a_1}(a_{b_1}(b_{b_1}(b_{a_1}(x1)))))) -> c_{c_1}(c_{b_1}(b_{b_1}(b_{a_1}(x1))))
107.78/28.45	   b_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{b_1}(x1))))) -> b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1)))))
107.78/28.45	   b_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{d_1}(x1))))) -> b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1)))))
107.78/28.45	   b_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{c_1}(x1))))) -> b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1)))))
107.78/28.45	   b_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
107.78/28.45	   d_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{b_1}(x1))))) -> d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1)))))
107.78/28.45	   d_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{d_1}(x1))))) -> d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1)))))
107.78/28.45	   d_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{c_1}(x1))))) -> d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1)))))
107.78/28.45	   d_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
107.78/28.45	   c_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{b_1}(x1))))) -> c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1)))))
107.78/28.45	   c_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{d_1}(x1))))) -> c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1)))))
107.78/28.45	   c_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{c_1}(x1))))) -> c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1)))))
107.78/28.45	   c_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
107.78/28.45	   a_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{b_1}(x1))))) -> a_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1)))))
107.78/28.45	   a_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{d_1}(x1))))) -> a_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1)))))
107.78/28.45	   a_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{c_1}(x1))))) -> a_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1)))))
107.78/28.45	   a_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> a_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
107.78/28.45	   b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1))))))) -> b_{c_1}(c_{c_1}(c_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{b_1}(x1)))))))
107.78/28.45	   b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1))))))) -> b_{c_1}(c_{c_1}(c_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{d_1}(x1)))))))
107.78/28.45	   b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1))))))) -> b_{c_1}(c_{c_1}(c_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{c_1}(x1)))))))
107.78/28.45	   b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x1))))))) -> b_{c_1}(c_{c_1}(c_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{a_1}(x1)))))))
107.78/28.45	   d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1))))))) -> d_{c_1}(c_{c_1}(c_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{b_1}(x1)))))))
107.78/28.45	   d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1))))))) -> d_{c_1}(c_{c_1}(c_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{d_1}(x1)))))))
107.78/28.45	   d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1))))))) -> d_{c_1}(c_{c_1}(c_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{c_1}(x1)))))))
107.78/28.45	   d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x1))))))) -> d_{c_1}(c_{c_1}(c_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{a_1}(x1)))))))
107.78/28.45	   c_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1))))))) -> c_{c_1}(c_{c_1}(c_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{b_1}(x1)))))))
107.78/28.45	   c_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1))))))) -> c_{c_1}(c_{c_1}(c_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{d_1}(x1)))))))
107.78/28.45	   c_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1))))))) -> c_{c_1}(c_{c_1}(c_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{c_1}(x1)))))))
107.78/28.45	   c_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x1))))))) -> c_{c_1}(c_{c_1}(c_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{a_1}(x1)))))))
107.78/28.45	   a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1))))))) -> a_{c_1}(c_{c_1}(c_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{b_1}(x1)))))))
107.78/28.45	   a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1))))))) -> a_{c_1}(c_{c_1}(c_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{d_1}(x1)))))))
107.78/28.45	   a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1))))))) -> a_{c_1}(c_{c_1}(c_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{c_1}(x1)))))))
107.78/28.45	   a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x1))))))) -> a_{c_1}(c_{c_1}(c_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{a_1}(x1)))))))
107.78/28.45	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))
107.78/28.45	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))
107.78/28.45	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))
107.78/28.45	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{a_1}(x1)))))
107.78/28.45	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))
107.78/28.45	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))
107.78/28.45	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))
107.78/28.45	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{a_1}(x1)))))
107.78/28.45	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))
107.78/28.45	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))
107.78/28.45	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))
107.78/28.45	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{a_1}(x1)))))
107.78/28.45	   a_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> a_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))
107.78/28.45	   a_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> a_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))
107.78/28.45	   a_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> a_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))
107.78/28.45	   a_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> a_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{a_1}(x1)))))
107.78/28.45	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1)))))))
107.78/28.45	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1)))))))
107.78/28.45	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1)))))))
107.78/28.45	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1)))))))
107.78/28.45	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1)))))))
107.78/28.45	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1)))))))
107.78/28.45	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1)))))))
107.78/28.45	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1)))))))
107.78/28.45	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1)))))))
107.78/28.45	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1)))))))
107.78/28.45	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1)))))))
107.78/28.45	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1)))))))
107.78/28.45	   a_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> a_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1)))))))
107.78/28.45	   a_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> a_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1)))))))
107.78/28.45	   a_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> a_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1)))))))
107.78/28.45	   a_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> a_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1)))))))
107.78/28.45	   b_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1)))))
107.78/28.45	   b_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1)))))
107.78/28.45	   b_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1)))))
107.78/28.45	   b_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{a_1}(x1))))))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x1)))))
107.78/28.45	   d_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1)))))
107.78/28.45	   d_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1)))))
107.78/28.45	   d_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1)))))
107.78/28.45	   d_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{a_1}(x1))))))) -> d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x1)))))
107.78/28.45	   c_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> c_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1)))))
107.78/28.45	   c_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> c_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1)))))
107.78/28.45	   c_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> c_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1)))))
107.78/28.45	   c_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{a_1}(x1))))))) -> c_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x1)))))
107.78/28.45	   a_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1)))))
107.78/28.45	   a_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1)))))
107.78/28.45	   a_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1)))))
107.78/28.45	   a_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{a_1}(x1))))))) -> a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x1)))))
107.78/28.45	
107.78/28.45	Q is empty.
107.78/28.45	
107.78/28.45	----------------------------------------
107.78/28.45	
107.78/28.45	(7) QTRSRRRProof (EQUIVALENT)
107.78/28.45	Used ordering:
107.78/28.45	Polynomial interpretation [POLO]:
107.78/28.45	
107.78/28.45	   POL(a_{a_1}(x_1)) = 1 + x_1
107.78/28.45	   POL(a_{b_1}(x_1)) = 1 + x_1
107.78/28.45	   POL(a_{c_1}(x_1)) = 1 + x_1
107.78/28.45	   POL(a_{d_1}(x_1)) = 1 + x_1
107.78/28.45	   POL(b_{a_1}(x_1)) = x_1
107.78/28.45	   POL(b_{b_1}(x_1)) = 1 + x_1
107.78/28.45	   POL(b_{c_1}(x_1)) = x_1
107.78/28.45	   POL(b_{d_1}(x_1)) = x_1
107.78/28.45	   POL(c_{a_1}(x_1)) = 1 + x_1
107.78/28.45	   POL(c_{b_1}(x_1)) = x_1
107.78/28.45	   POL(c_{c_1}(x_1)) = 1 + x_1
107.78/28.45	   POL(c_{d_1}(x_1)) = 1 + x_1
107.78/28.45	   POL(d_{a_1}(x_1)) = 2 + x_1
107.78/28.45	   POL(d_{b_1}(x_1)) = 1 + x_1
107.78/28.45	   POL(d_{c_1}(x_1)) = x_1
107.78/28.45	   POL(d_{d_1}(x_1)) = x_1
107.78/28.45	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
107.78/28.45	
107.78/28.45	   b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))) -> b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{b_1}(x1))))))
107.78/28.45	   c_{c_1}(c_{a_1}(a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(x1)))))) -> c_{c_1}(c_{b_1}(b_{b_1}(b_{b_1}(x1))))
107.78/28.45	   c_{c_1}(c_{a_1}(a_{a_1}(a_{b_1}(b_{b_1}(b_{d_1}(x1)))))) -> c_{c_1}(c_{b_1}(b_{b_1}(b_{d_1}(x1))))
107.78/28.45	   c_{c_1}(c_{a_1}(a_{a_1}(a_{b_1}(b_{b_1}(b_{c_1}(x1)))))) -> c_{c_1}(c_{b_1}(b_{b_1}(b_{c_1}(x1))))
107.78/28.45	   c_{c_1}(c_{a_1}(a_{a_1}(a_{b_1}(b_{b_1}(b_{a_1}(x1)))))) -> c_{c_1}(c_{b_1}(b_{b_1}(b_{a_1}(x1))))
107.78/28.45	   b_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{b_1}(x1))))) -> b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1)))))
107.78/28.45	   b_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{d_1}(x1))))) -> b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1)))))
107.78/28.45	   b_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{c_1}(x1))))) -> b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1)))))
107.78/28.45	   d_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{b_1}(x1))))) -> d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1)))))
107.78/28.45	   d_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{d_1}(x1))))) -> d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1)))))
107.78/28.45	   d_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{c_1}(x1))))) -> d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1)))))
107.78/28.45	   c_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{b_1}(x1))))) -> c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1)))))
107.78/28.45	   c_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{d_1}(x1))))) -> c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1)))))
107.78/28.45	   c_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{c_1}(x1))))) -> c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1)))))
107.78/28.45	   a_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{b_1}(x1))))) -> a_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1)))))
107.78/28.45	   a_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{d_1}(x1))))) -> a_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1)))))
107.78/28.45	   a_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{c_1}(x1))))) -> a_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1)))))
107.78/28.48	   b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1))))))) -> b_{c_1}(c_{c_1}(c_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{b_1}(x1)))))))
107.78/28.48	   b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1))))))) -> b_{c_1}(c_{c_1}(c_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{d_1}(x1)))))))
107.78/28.48	   b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1))))))) -> b_{c_1}(c_{c_1}(c_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{c_1}(x1)))))))
107.78/28.48	   b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x1))))))) -> b_{c_1}(c_{c_1}(c_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{a_1}(x1)))))))
107.78/28.48	   d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1))))))) -> d_{c_1}(c_{c_1}(c_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{b_1}(x1)))))))
107.78/28.48	   d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1))))))) -> d_{c_1}(c_{c_1}(c_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{d_1}(x1)))))))
107.78/28.48	   d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1))))))) -> d_{c_1}(c_{c_1}(c_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{c_1}(x1)))))))
107.78/28.48	   d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x1))))))) -> d_{c_1}(c_{c_1}(c_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{a_1}(x1)))))))
107.78/28.48	   c_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1))))))) -> c_{c_1}(c_{c_1}(c_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{b_1}(x1)))))))
107.78/28.48	   a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1))))))) -> a_{c_1}(c_{c_1}(c_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{b_1}(x1)))))))
107.78/28.48	   a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1))))))) -> a_{c_1}(c_{c_1}(c_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{d_1}(x1)))))))
107.78/28.48	   a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1))))))) -> a_{c_1}(c_{c_1}(c_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{c_1}(x1)))))))
107.78/28.48	   a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x1))))))) -> a_{c_1}(c_{c_1}(c_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{a_1}(x1)))))))
107.78/28.48	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{a_1}(x1)))))
107.78/28.48	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{a_1}(x1)))))
107.78/28.48	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{a_1}(x1)))))
107.78/28.48	   a_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> a_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{a_1}(x1)))))
107.78/28.48	   b_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{a_1}(x1))))))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x1)))))
107.78/28.48	   d_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{a_1}(x1))))))) -> d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x1)))))
107.78/28.48	   c_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> c_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1)))))
107.78/28.48	   c_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> c_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1)))))
107.78/28.48	   c_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> c_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1)))))
107.78/28.48	   c_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{a_1}(x1))))))) -> c_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x1)))))
107.78/28.48	   a_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1)))))
107.78/28.48	   a_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1)))))
107.78/28.48	   a_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1)))))
107.78/28.48	   a_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{a_1}(x1))))))) -> a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x1)))))
107.78/28.48	
107.78/28.48	
107.78/28.48	
107.78/28.48	
107.78/28.48	----------------------------------------
107.78/28.48	
107.78/28.48	(8)
107.78/28.48	Obligation:
107.78/28.48	Q restricted rewrite system:
107.78/28.48	The TRS R consists of the following rules:
107.78/28.48	
107.78/28.48	   b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))) -> b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{d_1}(x1))))))
107.78/28.48	   b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))) -> b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{c_1}(x1))))))
107.78/28.48	   b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{a_1}(x1)))))) -> b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{a_1}(x1))))))
107.78/28.48	   b_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
107.78/28.48	   d_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
107.78/28.48	   c_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
107.78/28.48	   a_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> a_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
107.78/28.48	   c_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1))))))) -> c_{c_1}(c_{c_1}(c_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{d_1}(x1)))))))
107.78/28.48	   c_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1))))))) -> c_{c_1}(c_{c_1}(c_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{c_1}(x1)))))))
107.78/28.48	   c_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x1))))))) -> c_{c_1}(c_{c_1}(c_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{a_1}(x1)))))))
107.78/28.48	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))
107.78/28.48	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))
107.78/28.48	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))
107.78/28.48	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))
107.78/28.48	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))
107.78/28.48	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))
107.78/28.48	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))
107.78/28.48	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))
107.78/28.48	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))
107.78/28.48	   a_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> a_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))
107.78/28.48	   a_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> a_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))
107.78/28.48	   a_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> a_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))
107.78/28.48	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1)))))))
107.78/28.48	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1)))))))
107.78/28.48	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1)))))))
107.78/28.48	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1)))))))
107.78/28.48	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1)))))))
107.78/28.48	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1)))))))
107.78/28.48	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1)))))))
107.78/28.48	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1)))))))
107.78/28.48	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1)))))))
107.78/28.48	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1)))))))
107.78/28.48	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1)))))))
107.78/28.48	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1)))))))
107.78/28.48	   a_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> a_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1)))))))
107.78/28.48	   a_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> a_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1)))))))
107.78/28.48	   a_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> a_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1)))))))
107.78/28.48	   a_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> a_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1)))))))
107.78/28.48	   b_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1)))))
107.78/28.48	   b_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1)))))
107.78/28.48	   b_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1)))))
107.78/28.48	   d_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1)))))
107.78/28.48	   d_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1)))))
107.78/28.48	   d_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1)))))
107.78/28.48	
107.78/28.48	Q is empty.
107.78/28.48	
107.78/28.48	----------------------------------------
107.78/28.48	
107.78/28.48	(9) DependencyPairsProof (EQUIVALENT)
107.78/28.48	Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
107.78/28.48	----------------------------------------
107.78/28.48	
107.78/28.48	(10)
107.78/28.48	Obligation:
107.78/28.48	Q DP problem:
107.78/28.48	The TRS P consists of the following rules:
107.78/28.48	
107.78/28.48	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{d_1}(x1))))))
107.78/28.48	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))) -> B_{D_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{d_1}(x1)))))
107.78/28.48	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))) -> D_{D_1}(d_{c_1}(c_{c_1}(c_{d_1}(x1))))
107.78/28.48	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))) -> D_{C_1}(c_{c_1}(c_{d_1}(x1)))
107.78/28.48	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))) -> C_{C_1}(c_{d_1}(x1))
107.78/28.48	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))) -> C_{D_1}(x1)
107.78/28.48	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{c_1}(x1))))))
107.78/28.48	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))) -> B_{D_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{c_1}(x1)))))
107.78/28.48	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))) -> D_{D_1}(d_{c_1}(c_{c_1}(c_{c_1}(x1))))
107.78/28.48	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))) -> D_{C_1}(c_{c_1}(c_{c_1}(x1)))
107.78/28.48	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))) -> C_{C_1}(c_{c_1}(x1))
107.78/28.48	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))) -> C_{C_1}(x1)
107.78/28.48	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{a_1}(x1)))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{a_1}(x1))))))
107.78/28.48	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{a_1}(x1)))))) -> B_{D_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{a_1}(x1)))))
107.78/28.48	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{a_1}(x1)))))) -> D_{D_1}(d_{c_1}(c_{c_1}(c_{a_1}(x1))))
107.78/28.48	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{a_1}(x1)))))) -> D_{C_1}(c_{c_1}(c_{a_1}(x1)))
107.78/28.48	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{a_1}(x1)))))) -> C_{C_1}(c_{a_1}(x1))
107.78/28.48	   B_{D_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
107.78/28.48	   B_{D_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> C_{C_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))
107.78/28.48	   B_{D_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> C_{D_1}(d_{d_1}(d_{a_1}(x1)))
107.78/28.48	   B_{D_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> D_{D_1}(d_{a_1}(x1))
107.78/28.48	   D_{D_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
107.78/28.48	   D_{D_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> C_{C_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))
107.78/28.48	   D_{D_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> C_{D_1}(d_{d_1}(d_{a_1}(x1)))
107.78/28.48	   D_{D_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> D_{D_1}(d_{a_1}(x1))
107.78/28.48	   C_{D_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
107.78/28.48	   C_{D_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> C_{C_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))
107.78/28.48	   C_{D_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> C_{D_1}(d_{d_1}(d_{a_1}(x1)))
107.78/28.48	   C_{D_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> D_{D_1}(d_{a_1}(x1))
107.78/28.48	   A_{D_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> A_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
107.78/28.48	   A_{D_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> C_{C_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))
107.78/28.48	   A_{D_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> C_{D_1}(d_{d_1}(d_{a_1}(x1)))
107.78/28.48	   A_{D_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> D_{D_1}(d_{a_1}(x1))
107.78/28.48	   C_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1))))))) -> C_{C_1}(c_{c_1}(c_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{d_1}(x1)))))))
107.78/28.48	   C_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1))))))) -> C_{C_1}(c_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{d_1}(x1))))))
107.78/28.48	   C_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1))))))) -> C_{B_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{d_1}(x1)))))
107.78/28.48	   C_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1))))))) -> B_{B_1}(b_{a_1}(a_{a_1}(a_{d_1}(x1))))
107.78/28.48	   C_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1))))))) -> A_{D_1}(x1)
107.78/28.48	   C_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1))))))) -> C_{C_1}(c_{c_1}(c_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{c_1}(x1)))))))
107.78/28.48	   C_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1))))))) -> C_{C_1}(c_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{c_1}(x1))))))
107.78/28.48	   C_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1))))))) -> C_{B_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{c_1}(x1)))))
107.78/28.48	   C_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1))))))) -> B_{B_1}(b_{a_1}(a_{a_1}(a_{c_1}(x1))))
107.78/28.48	   C_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1))))))) -> A_{C_1}(x1)
107.78/28.48	   C_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x1))))))) -> C_{C_1}(c_{c_1}(c_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{a_1}(x1)))))))
107.78/28.48	   C_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x1))))))) -> C_{C_1}(c_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{a_1}(x1))))))
107.78/28.48	   C_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x1))))))) -> C_{B_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{a_1}(x1)))))
107.78/28.48	   C_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x1))))))) -> B_{B_1}(b_{a_1}(a_{a_1}(a_{a_1}(x1))))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{D_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> D_{D_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1))))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(b_{b_1}(x1))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(x1)
107.78/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{D_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> D_{D_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1))))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{B_1}(b_{d_1}(x1))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{D_1}(x1)
107.78/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{D_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> D_{D_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1))))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{B_1}(b_{c_1}(x1))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{C_1}(x1)
107.78/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> D_{D_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> D_{D_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1))))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(b_{b_1}(x1))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(x1)
107.78/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> D_{D_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> D_{D_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1))))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{B_1}(b_{d_1}(x1))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{D_1}(x1)
107.78/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> D_{D_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> D_{D_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1))))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{B_1}(b_{c_1}(x1))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{C_1}(x1)
107.78/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> C_{D_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))
107.78/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> D_{D_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1))))
107.78/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(b_{b_1}(x1))
107.78/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(x1)
107.78/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> C_{D_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))
107.78/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> D_{D_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1))))
107.78/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{B_1}(b_{d_1}(x1))
107.78/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{D_1}(x1)
107.78/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> C_{D_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))
107.78/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> D_{D_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1))))
107.78/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{B_1}(b_{c_1}(x1))
107.78/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{C_1}(x1)
107.78/28.48	   A_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> A_{D_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))
107.78/28.48	   A_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> D_{D_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1))))
107.78/28.48	   A_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(b_{b_1}(x1))
107.78/28.48	   A_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(x1)
107.78/28.48	   A_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> A_{D_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))
107.78/28.48	   A_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> D_{D_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1))))
107.78/28.48	   A_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{B_1}(b_{d_1}(x1))
107.78/28.48	   A_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{D_1}(x1)
107.78/28.48	   A_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> A_{D_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))
107.78/28.48	   A_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> D_{D_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1))))
107.78/28.48	   A_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{B_1}(b_{c_1}(x1))
107.78/28.48	   A_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{C_1}(x1)
107.78/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{D_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1)))))))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> D_{D_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1))))))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1))))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{D_1}(d_{d_1}(d_{b_1}(x1)))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{D_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1)))))))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> D_{D_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1))))))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1))))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{D_1}(d_{d_1}(d_{d_1}(x1)))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{D_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1)))))))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> D_{D_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1))))))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1))))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{D_1}(d_{d_1}(d_{c_1}(x1)))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> B_{D_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1)))))))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> D_{D_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1))))))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1))))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> B_{D_1}(d_{d_1}(d_{a_1}(x1)))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> D_{D_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1)))))))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> D_{D_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1))))))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1))))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{D_1}(d_{d_1}(d_{b_1}(x1)))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> D_{D_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1)))))))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> D_{D_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1))))))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1))))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{D_1}(d_{d_1}(d_{d_1}(x1)))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> D_{D_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1)))))))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> D_{D_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1))))))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1))))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{D_1}(d_{d_1}(d_{c_1}(x1)))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> D_{D_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1)))))))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> D_{D_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1))))))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1))))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> B_{D_1}(d_{d_1}(d_{a_1}(x1)))
107.78/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> C_{D_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1)))))))
107.78/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> D_{D_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1))))))
107.78/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1))))
107.78/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{D_1}(d_{d_1}(d_{b_1}(x1)))
107.78/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> C_{D_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1)))))))
107.78/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> D_{D_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1))))))
107.78/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1))))
107.78/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{D_1}(d_{d_1}(d_{d_1}(x1)))
107.78/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> C_{D_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1)))))))
107.78/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> D_{D_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1))))))
107.78/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1))))
107.78/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{D_1}(d_{d_1}(d_{c_1}(x1)))
107.78/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> C_{D_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1)))))))
107.78/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> D_{D_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1))))))
107.78/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1))))
107.78/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> B_{D_1}(d_{d_1}(d_{a_1}(x1)))
107.78/28.48	   A_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> A_{D_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1)))))))
107.78/28.48	   A_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> D_{D_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1))))))
107.78/28.48	   A_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1))))
107.78/28.48	   A_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{D_1}(d_{d_1}(d_{b_1}(x1)))
107.78/28.48	   A_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> A_{D_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1)))))))
107.78/28.48	   A_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> D_{D_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1))))))
107.78/28.48	   A_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1))))
107.78/28.48	   A_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{D_1}(d_{d_1}(d_{d_1}(x1)))
107.78/28.48	   A_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> A_{D_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1)))))))
107.78/28.48	   A_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> D_{D_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1))))))
107.78/28.48	   A_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1))))
107.78/28.48	   A_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{D_1}(d_{d_1}(d_{c_1}(x1)))
107.78/28.48	   A_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> A_{D_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1)))))))
107.78/28.48	   A_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> D_{D_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1))))))
107.78/28.48	   A_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1))))
107.78/28.48	   A_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> B_{D_1}(d_{d_1}(d_{a_1}(x1)))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1)))))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1))))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> B_{B_1}(b_{b_1}(b_{b_1}(x1)))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> B_{B_1}(b_{b_1}(x1))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> B_{B_1}(x1)
107.78/28.48	   B_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1)))))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> B_{B_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1))))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> B_{B_1}(b_{b_1}(b_{d_1}(x1)))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> B_{B_1}(b_{d_1}(x1))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> B_{D_1}(x1)
107.78/28.48	   B_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1)))))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> B_{B_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1))))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> B_{B_1}(b_{b_1}(b_{c_1}(x1)))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> B_{B_1}(b_{c_1}(x1))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> B_{C_1}(x1)
107.78/28.48	   D_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1))))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> B_{B_1}(b_{b_1}(b_{b_1}(x1)))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> B_{B_1}(b_{b_1}(x1))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> B_{B_1}(x1)
107.78/28.48	   D_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> B_{B_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1))))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> B_{B_1}(b_{b_1}(b_{d_1}(x1)))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> B_{B_1}(b_{d_1}(x1))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> B_{D_1}(x1)
107.78/28.48	   D_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> B_{B_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1))))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> B_{B_1}(b_{b_1}(b_{c_1}(x1)))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> B_{B_1}(b_{c_1}(x1))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> B_{C_1}(x1)
107.78/28.48	
107.78/28.48	The TRS R consists of the following rules:
107.78/28.48	
107.78/28.48	   b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))) -> b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{d_1}(x1))))))
107.78/28.48	   b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))) -> b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{c_1}(x1))))))
107.78/28.48	   b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{a_1}(x1)))))) -> b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{a_1}(x1))))))
107.78/28.48	   b_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
107.78/28.48	   d_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
107.78/28.48	   c_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
107.78/28.48	   a_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> a_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
107.78/28.48	   c_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1))))))) -> c_{c_1}(c_{c_1}(c_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{d_1}(x1)))))))
107.78/28.48	   c_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1))))))) -> c_{c_1}(c_{c_1}(c_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{c_1}(x1)))))))
107.78/28.48	   c_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x1))))))) -> c_{c_1}(c_{c_1}(c_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{a_1}(x1)))))))
107.78/28.48	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))
107.78/28.48	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))
107.78/28.48	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))
107.78/28.48	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))
107.78/28.48	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))
107.78/28.48	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))
107.78/28.48	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))
107.78/28.48	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))
107.78/28.48	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))
107.78/28.48	   a_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> a_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))
107.78/28.48	   a_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> a_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))
107.78/28.48	   a_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> a_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))
107.78/28.48	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1)))))))
107.78/28.48	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1)))))))
107.78/28.48	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1)))))))
107.78/28.48	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1)))))))
107.78/28.48	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1)))))))
107.78/28.48	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1)))))))
107.78/28.48	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1)))))))
107.78/28.48	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1)))))))
107.78/28.48	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1)))))))
107.78/28.48	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1)))))))
107.78/28.48	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1)))))))
107.78/28.48	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1)))))))
107.78/28.48	   a_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> a_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1)))))))
107.78/28.48	   a_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> a_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1)))))))
107.78/28.48	   a_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> a_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1)))))))
107.78/28.48	   a_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> a_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1)))))))
107.78/28.48	   b_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1)))))
107.78/28.48	   b_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1)))))
107.78/28.48	   b_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1)))))
107.78/28.48	   d_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1)))))
107.78/28.48	   d_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1)))))
107.78/28.48	   d_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1)))))
107.78/28.48	
107.78/28.48	Q is empty.
107.78/28.48	We have to consider all minimal (P,Q,R)-chains.
107.78/28.48	----------------------------------------
107.78/28.48	
107.78/28.48	(11) DependencyGraphProof (EQUIVALENT)
107.78/28.48	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 110 less nodes.
107.78/28.48	----------------------------------------
107.78/28.48	
107.78/28.48	(12)
107.78/28.48	Obligation:
107.78/28.48	Q DP problem:
107.78/28.48	The TRS P consists of the following rules:
107.78/28.48	
107.78/28.48	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))) -> D_{C_1}(c_{c_1}(c_{d_1}(x1)))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(b_{b_1}(x1))
107.78/28.48	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{d_1}(x1))))))
107.78/28.48	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))) -> C_{C_1}(c_{d_1}(x1))
107.78/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(b_{b_1}(x1))
107.78/28.48	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))) -> C_{D_1}(x1)
107.78/28.48	   C_{D_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
107.78/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(x1)
107.78/28.48	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{c_1}(x1))))))
107.78/28.48	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))) -> D_{C_1}(c_{c_1}(c_{c_1}(x1)))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(x1)
107.78/28.48	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))) -> C_{C_1}(c_{c_1}(x1))
107.78/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{B_1}(b_{d_1}(x1))
107.78/28.48	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))) -> C_{C_1}(x1)
107.78/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{D_1}(x1)
107.78/28.48	   B_{D_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(b_{b_1}(x1))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(x1)
107.78/28.48	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{a_1}(x1)))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{a_1}(x1))))))
107.78/28.48	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{a_1}(x1)))))) -> D_{C_1}(c_{c_1}(c_{a_1}(x1)))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1))))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> B_{B_1}(b_{b_1}(b_{b_1}(x1)))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> B_{B_1}(b_{b_1}(x1))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> B_{B_1}(x1)
107.78/28.48	   D_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> B_{B_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1))))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> B_{B_1}(b_{b_1}(b_{d_1}(x1)))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> B_{B_1}(b_{d_1}(x1))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> B_{D_1}(x1)
107.78/28.48	   B_{D_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> C_{C_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))
107.78/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{B_1}(b_{c_1}(x1))
107.78/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{C_1}(x1)
107.78/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{B_1}(b_{d_1}(x1))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{D_1}(x1)
107.78/28.48	   B_{D_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> C_{D_1}(d_{d_1}(d_{a_1}(x1)))
107.78/28.48	   C_{D_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> C_{C_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))
107.78/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1))))
107.78/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1))))
107.78/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1))))
107.78/28.48	   C_{D_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> C_{D_1}(d_{d_1}(d_{a_1}(x1)))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{B_1}(b_{c_1}(x1))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{C_1}(x1)
107.78/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1))))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1))))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1))))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1))))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> B_{D_1}(d_{d_1}(d_{a_1}(x1)))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1)))))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1))))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> B_{B_1}(b_{b_1}(b_{b_1}(x1)))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> B_{B_1}(b_{b_1}(x1))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> B_{B_1}(x1)
107.78/28.48	   B_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1)))))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> B_{B_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1))))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> B_{B_1}(b_{b_1}(b_{d_1}(x1)))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> B_{B_1}(b_{d_1}(x1))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> B_{D_1}(x1)
107.78/28.48	   B_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1)))))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> B_{B_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1))))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> B_{B_1}(b_{b_1}(b_{c_1}(x1)))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> B_{B_1}(b_{c_1}(x1))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> B_{C_1}(x1)
107.78/28.48	   D_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> B_{B_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1))))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> B_{B_1}(b_{b_1}(b_{c_1}(x1)))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> B_{B_1}(b_{c_1}(x1))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> B_{C_1}(x1)
107.78/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1))))
107.78/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> B_{D_1}(d_{d_1}(d_{a_1}(x1)))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{B_1}(b_{d_1}(x1))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{D_1}(x1)
107.78/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{B_1}(b_{c_1}(x1))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{C_1}(x1)
107.78/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1))))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1))))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1))))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1))))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> B_{D_1}(d_{d_1}(d_{a_1}(x1)))
107.78/28.48	
107.78/28.48	The TRS R consists of the following rules:
107.78/28.48	
107.78/28.48	   b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))) -> b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{d_1}(x1))))))
107.78/28.48	   b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))) -> b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{c_1}(x1))))))
107.78/28.48	   b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{a_1}(x1)))))) -> b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{a_1}(x1))))))
107.78/28.48	   b_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
107.78/28.48	   d_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
107.78/28.48	   c_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
107.78/28.48	   a_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> a_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
107.78/28.48	   c_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1))))))) -> c_{c_1}(c_{c_1}(c_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{d_1}(x1)))))))
107.78/28.48	   c_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1))))))) -> c_{c_1}(c_{c_1}(c_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{c_1}(x1)))))))
107.78/28.48	   c_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x1))))))) -> c_{c_1}(c_{c_1}(c_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{a_1}(x1)))))))
107.78/28.48	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))
107.78/28.48	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))
107.78/28.48	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))
107.78/28.48	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))
107.78/28.48	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))
107.78/28.48	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))
107.78/28.48	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))
107.78/28.48	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))
107.78/28.48	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))
107.78/28.48	   a_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> a_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))
107.78/28.48	   a_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> a_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))
107.78/28.48	   a_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> a_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))
107.78/28.48	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1)))))))
107.78/28.48	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1)))))))
107.78/28.48	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1)))))))
107.78/28.48	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1)))))))
107.78/28.48	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1)))))))
107.78/28.48	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1)))))))
107.78/28.48	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1)))))))
107.78/28.48	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1)))))))
107.78/28.48	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1)))))))
107.78/28.48	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1)))))))
107.78/28.48	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1)))))))
107.78/28.48	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1)))))))
107.78/28.48	   a_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> a_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1)))))))
107.78/28.48	   a_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> a_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1)))))))
107.78/28.48	   a_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> a_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1)))))))
107.78/28.48	   a_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> a_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1)))))))
107.78/28.48	   b_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1)))))
107.78/28.48	   b_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1)))))
107.78/28.48	   b_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1)))))
107.78/28.48	   d_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1)))))
107.78/28.48	   d_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1)))))
107.78/28.48	   d_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1)))))
107.78/28.48	
107.78/28.48	Q is empty.
107.78/28.48	We have to consider all minimal (P,Q,R)-chains.
107.78/28.48	----------------------------------------
107.78/28.48	
107.78/28.48	(13) UsableRulesProof (EQUIVALENT)
107.78/28.48	We can use the usable rules and reduction pair processor [LPAR04] with the Ce-compatible extension of the polynomial order that maps every function symbol to the sum of its arguments. Then, we can delete all non-usable rules [FROCOS05] from R.
107.78/28.48	----------------------------------------
107.78/28.48	
107.78/28.48	(14)
107.78/28.48	Obligation:
107.78/28.48	Q DP problem:
107.78/28.48	The TRS P consists of the following rules:
107.78/28.48	
107.78/28.48	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))) -> D_{C_1}(c_{c_1}(c_{d_1}(x1)))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(b_{b_1}(x1))
107.78/28.48	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{d_1}(x1))))))
107.78/28.48	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))) -> C_{C_1}(c_{d_1}(x1))
107.78/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(b_{b_1}(x1))
107.78/28.48	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))) -> C_{D_1}(x1)
107.78/28.48	   C_{D_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
107.78/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(x1)
107.78/28.48	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{c_1}(x1))))))
107.78/28.48	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))) -> D_{C_1}(c_{c_1}(c_{c_1}(x1)))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(x1)
107.78/28.48	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))) -> C_{C_1}(c_{c_1}(x1))
107.78/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{B_1}(b_{d_1}(x1))
107.78/28.48	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))) -> C_{C_1}(x1)
107.78/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{D_1}(x1)
107.78/28.48	   B_{D_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(b_{b_1}(x1))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(x1)
107.78/28.48	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{a_1}(x1)))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{a_1}(x1))))))
107.78/28.48	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{a_1}(x1)))))) -> D_{C_1}(c_{c_1}(c_{a_1}(x1)))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1))))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> B_{B_1}(b_{b_1}(b_{b_1}(x1)))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> B_{B_1}(b_{b_1}(x1))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> B_{B_1}(x1)
107.78/28.48	   D_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> B_{B_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1))))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> B_{B_1}(b_{b_1}(b_{d_1}(x1)))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> B_{B_1}(b_{d_1}(x1))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> B_{D_1}(x1)
107.78/28.48	   B_{D_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> C_{C_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))
107.78/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{B_1}(b_{c_1}(x1))
107.78/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{C_1}(x1)
107.78/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{B_1}(b_{d_1}(x1))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{D_1}(x1)
107.78/28.48	   B_{D_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> C_{D_1}(d_{d_1}(d_{a_1}(x1)))
107.78/28.48	   C_{D_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> C_{C_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))
107.78/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1))))
107.78/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1))))
107.78/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1))))
107.78/28.48	   C_{D_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> C_{D_1}(d_{d_1}(d_{a_1}(x1)))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{B_1}(b_{c_1}(x1))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{C_1}(x1)
107.78/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1))))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1))))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1))))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1))))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> B_{D_1}(d_{d_1}(d_{a_1}(x1)))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1)))))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1))))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> B_{B_1}(b_{b_1}(b_{b_1}(x1)))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> B_{B_1}(b_{b_1}(x1))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> B_{B_1}(x1)
107.78/28.48	   B_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1)))))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> B_{B_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1))))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> B_{B_1}(b_{b_1}(b_{d_1}(x1)))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> B_{B_1}(b_{d_1}(x1))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> B_{D_1}(x1)
107.78/28.48	   B_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1)))))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> B_{B_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1))))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> B_{B_1}(b_{b_1}(b_{c_1}(x1)))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> B_{B_1}(b_{c_1}(x1))
107.78/28.48	   B_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> B_{C_1}(x1)
107.78/28.48	   D_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> B_{B_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1))))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> B_{B_1}(b_{b_1}(b_{c_1}(x1)))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> B_{B_1}(b_{c_1}(x1))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> B_{C_1}(x1)
107.78/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1))))
107.78/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> B_{D_1}(d_{d_1}(d_{a_1}(x1)))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{B_1}(b_{d_1}(x1))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{D_1}(x1)
107.78/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{B_1}(b_{c_1}(x1))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{C_1}(x1)
107.78/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1))))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1))))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1))))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1))))
107.78/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> B_{D_1}(d_{d_1}(d_{a_1}(x1)))
107.78/28.48	
107.78/28.48	The TRS R consists of the following rules:
107.78/28.48	
107.78/28.48	   b_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
107.78/28.48	   c_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
107.78/28.48	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))
107.78/28.48	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))
107.78/28.48	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.48	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1)))))))
108.26/28.48	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1)))))))
108.26/28.48	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1)))))))
108.26/28.48	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1)))))))
108.26/28.48	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.48	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.48	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.48	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1)))))))
108.26/28.48	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1)))))))
108.26/28.48	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1)))))))
108.26/28.48	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1)))))))
108.26/28.48	   b_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.48	   b_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.48	   b_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.48	   b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))) -> b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{c_1}(x1))))))
108.26/28.48	   b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))) -> b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{d_1}(x1))))))
108.26/28.48	   b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{a_1}(x1)))))) -> b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{a_1}(x1))))))
108.26/28.48	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.48	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.48	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.48	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1)))))))
108.26/28.48	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1)))))))
108.26/28.48	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1)))))))
108.26/28.48	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1)))))))
108.26/28.48	   d_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.48	   d_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.48	   d_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.48	   d_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
108.26/28.48	
108.26/28.48	Q is empty.
108.26/28.48	We have to consider all minimal (P,Q,R)-chains.
108.26/28.48	----------------------------------------
108.26/28.48	
108.26/28.48	(15) QDPOrderProof (EQUIVALENT)
108.26/28.48	We use the reduction pair processor [LPAR04,JAR06].
108.26/28.48	
108.26/28.48	
108.26/28.48	The following pairs can be oriented strictly and are deleted.
108.26/28.48	
108.26/28.48	   D_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1))))
108.26/28.48	   D_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> B_{B_1}(b_{b_1}(b_{b_1}(x1)))
108.26/28.48	   D_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> B_{B_1}(b_{b_1}(x1))
108.26/28.48	   D_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> B_{B_1}(x1)
108.26/28.48	   D_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> B_{B_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1))))
108.26/28.48	   D_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> B_{B_1}(b_{b_1}(b_{d_1}(x1)))
108.26/28.48	   D_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> B_{B_1}(b_{d_1}(x1))
108.26/28.48	   D_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> B_{D_1}(x1)
108.26/28.48	   B_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.48	   B_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1))))
108.26/28.48	   B_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> B_{B_1}(b_{b_1}(b_{b_1}(x1)))
108.26/28.48	   B_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> B_{B_1}(b_{b_1}(x1))
108.26/28.48	   B_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> B_{B_1}(x1)
108.26/28.48	   B_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.48	   B_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> B_{B_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1))))
108.26/28.48	   B_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> B_{B_1}(b_{b_1}(b_{d_1}(x1)))
108.26/28.48	   B_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> B_{B_1}(b_{d_1}(x1))
108.26/28.48	   B_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> B_{D_1}(x1)
108.26/28.48	   B_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.48	   B_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> B_{B_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1))))
108.26/28.48	   B_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> B_{B_1}(b_{b_1}(b_{c_1}(x1)))
108.26/28.48	   B_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> B_{B_1}(b_{c_1}(x1))
108.26/28.48	   B_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> B_{C_1}(x1)
108.26/28.48	   D_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> B_{B_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1))))
108.26/28.48	   D_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> B_{B_1}(b_{b_1}(b_{c_1}(x1)))
108.26/28.48	   D_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> B_{B_1}(b_{c_1}(x1))
108.26/28.48	   D_{C_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> B_{C_1}(x1)
108.26/28.48	The remaining pairs can at least be oriented weakly.
108.26/28.48	Used ordering:  Polynomial interpretation [POLO]:
108.26/28.48	
108.26/28.48	   POL(B_{B_1}(x_1)) = x_1
108.26/28.48	   POL(B_{C_1}(x_1)) = x_1
108.26/28.48	   POL(B_{D_1}(x_1)) = 0
108.26/28.48	   POL(C_{C_1}(x_1)) = x_1
108.26/28.48	   POL(C_{D_1}(x_1)) = 0
108.26/28.48	   POL(D_{C_1}(x_1)) = x_1
108.26/28.48	   POL(a_{a_1}(x_1)) = x_1
108.26/28.48	   POL(a_{d_1}(x_1)) = x_1
108.26/28.48	   POL(b_{a_1}(x_1)) = 1 + x_1
108.26/28.48	   POL(b_{b_1}(x_1)) = x_1
108.26/28.48	   POL(b_{c_1}(x_1)) = x_1
108.26/28.48	   POL(b_{d_1}(x_1)) = x_1
108.26/28.48	   POL(c_{a_1}(x_1)) = 1 + x_1
108.26/28.48	   POL(c_{c_1}(x_1)) = x_1
108.26/28.48	   POL(c_{d_1}(x_1)) = x_1
108.26/28.48	   POL(d_{a_1}(x_1)) = 0
108.26/28.48	   POL(d_{b_1}(x_1)) = x_1
108.26/28.48	   POL(d_{c_1}(x_1)) = x_1
108.26/28.48	   POL(d_{d_1}(x_1)) = x_1
108.26/28.48	
108.26/28.48	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
108.26/28.48	
108.26/28.48	   c_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
108.26/28.48	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.48	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.48	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.48	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1)))))))
108.26/28.48	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1)))))))
108.26/28.48	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1)))))))
108.26/28.48	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1)))))))
108.26/28.48	   b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))) -> b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{d_1}(x1))))))
108.26/28.48	   b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))) -> b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{c_1}(x1))))))
108.26/28.48	   b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{a_1}(x1)))))) -> b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{a_1}(x1))))))
108.26/28.48	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.48	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.48	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.48	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1)))))))
108.26/28.48	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1)))))))
108.26/28.48	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1)))))))
108.26/28.48	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1)))))))
108.26/28.48	   d_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.48	   d_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.48	   d_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.48	   d_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
108.26/28.48	   b_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
108.26/28.48	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.48	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.48	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.48	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1)))))))
108.26/28.48	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1)))))))
108.26/28.48	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1)))))))
108.26/28.48	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1)))))))
108.26/28.48	   b_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.48	   b_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.48	   b_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.48	
108.26/28.48	
108.26/28.48	----------------------------------------
108.26/28.48	
108.26/28.48	(16)
108.26/28.48	Obligation:
108.26/28.48	Q DP problem:
108.26/28.48	The TRS P consists of the following rules:
108.26/28.48	
108.26/28.48	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))) -> D_{C_1}(c_{c_1}(c_{d_1}(x1)))
108.26/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(b_{b_1}(x1))
108.26/28.48	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{d_1}(x1))))))
108.26/28.48	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))) -> C_{C_1}(c_{d_1}(x1))
108.26/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(b_{b_1}(x1))
108.26/28.48	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))) -> C_{D_1}(x1)
108.26/28.48	   C_{D_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
108.26/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(x1)
108.26/28.48	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{c_1}(x1))))))
108.26/28.48	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))) -> D_{C_1}(c_{c_1}(c_{c_1}(x1)))
108.26/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(x1)
108.26/28.48	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))) -> C_{C_1}(c_{c_1}(x1))
108.26/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{B_1}(b_{d_1}(x1))
108.26/28.48	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))) -> C_{C_1}(x1)
108.26/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{D_1}(x1)
108.26/28.48	   B_{D_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
108.26/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(b_{b_1}(x1))
108.26/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(x1)
108.26/28.48	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{a_1}(x1)))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{a_1}(x1))))))
108.26/28.48	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{a_1}(x1)))))) -> D_{C_1}(c_{c_1}(c_{a_1}(x1)))
108.26/28.48	   B_{D_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> C_{C_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))
108.26/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{B_1}(b_{c_1}(x1))
108.26/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{C_1}(x1)
108.26/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{B_1}(b_{d_1}(x1))
108.26/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{D_1}(x1)
108.26/28.48	   B_{D_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> C_{D_1}(d_{d_1}(d_{a_1}(x1)))
108.26/28.48	   C_{D_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> C_{C_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))
108.26/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1))))
108.26/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1))))
108.26/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1))))
108.26/28.48	   C_{D_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> C_{D_1}(d_{d_1}(d_{a_1}(x1)))
108.26/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{B_1}(b_{c_1}(x1))
108.26/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{C_1}(x1)
108.26/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1))))
108.26/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1))))
108.26/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1))))
108.26/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1))))
108.26/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> B_{D_1}(d_{d_1}(d_{a_1}(x1)))
108.26/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1))))
108.26/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> B_{D_1}(d_{d_1}(d_{a_1}(x1)))
108.26/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{B_1}(b_{d_1}(x1))
108.26/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{D_1}(x1)
108.26/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{B_1}(b_{c_1}(x1))
108.26/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{C_1}(x1)
108.26/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1))))
108.26/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1))))
108.26/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1))))
108.26/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1))))
108.26/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> B_{D_1}(d_{d_1}(d_{a_1}(x1)))
108.26/28.48	
108.26/28.48	The TRS R consists of the following rules:
108.26/28.48	
108.26/28.48	   b_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
108.26/28.48	   c_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
108.26/28.48	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.48	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.48	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.48	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1)))))))
108.26/28.48	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1)))))))
108.26/28.48	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1)))))))
108.26/28.48	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1)))))))
108.26/28.48	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.48	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.48	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.48	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1)))))))
108.26/28.48	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1)))))))
108.26/28.48	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1)))))))
108.26/28.48	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1)))))))
108.26/28.48	   b_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.48	   b_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.48	   b_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.48	   b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))) -> b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{c_1}(x1))))))
108.26/28.48	   b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))) -> b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{d_1}(x1))))))
108.26/28.48	   b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{a_1}(x1)))))) -> b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{a_1}(x1))))))
108.26/28.48	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.48	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.48	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.48	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1)))))))
108.26/28.48	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1)))))))
108.26/28.48	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1)))))))
108.26/28.48	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1)))))))
108.26/28.48	   d_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.48	   d_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.48	   d_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.48	   d_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
108.26/28.48	
108.26/28.48	Q is empty.
108.26/28.48	We have to consider all minimal (P,Q,R)-chains.
108.26/28.48	----------------------------------------
108.26/28.48	
108.26/28.48	(17) DependencyGraphProof (EQUIVALENT)
108.26/28.48	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
108.26/28.48	----------------------------------------
108.26/28.48	
108.26/28.48	(18)
108.26/28.48	Obligation:
108.26/28.48	Q DP problem:
108.26/28.48	The TRS P consists of the following rules:
108.26/28.48	
108.26/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(b_{b_1}(x1))
108.26/28.48	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{d_1}(x1))))))
108.26/28.48	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))) -> D_{C_1}(c_{c_1}(c_{d_1}(x1)))
108.26/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(x1)
108.26/28.48	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))) -> C_{C_1}(c_{d_1}(x1))
108.26/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(b_{b_1}(x1))
108.26/28.48	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))) -> C_{D_1}(x1)
108.26/28.48	   C_{D_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
108.26/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(x1)
108.26/28.48	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{c_1}(x1))))))
108.26/28.48	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))) -> D_{C_1}(c_{c_1}(c_{c_1}(x1)))
108.26/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{B_1}(b_{d_1}(x1))
108.26/28.48	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))) -> C_{C_1}(c_{c_1}(x1))
108.26/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{B_1}(b_{d_1}(x1))
108.26/28.48	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))) -> C_{C_1}(x1)
108.26/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{D_1}(x1)
108.26/28.48	   B_{D_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
108.26/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(b_{b_1}(x1))
108.26/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(x1)
108.26/28.48	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{a_1}(x1)))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{a_1}(x1))))))
108.26/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{B_1}(b_{d_1}(x1))
108.26/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{D_1}(x1)
108.26/28.48	   B_{D_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> C_{C_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))
108.26/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{B_1}(b_{c_1}(x1))
108.26/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{C_1}(x1)
108.26/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{B_1}(b_{c_1}(x1))
108.26/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{C_1}(x1)
108.26/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1))))
108.26/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1))))
108.26/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1))))
108.26/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1))))
108.26/28.48	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> B_{D_1}(d_{d_1}(d_{a_1}(x1)))
108.26/28.48	   B_{D_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> C_{D_1}(d_{d_1}(d_{a_1}(x1)))
108.26/28.48	   C_{D_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> C_{C_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))
108.26/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1))))
108.26/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1))))
108.26/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1))))
108.26/28.48	   C_{D_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> C_{D_1}(d_{d_1}(d_{a_1}(x1)))
108.26/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1))))
108.26/28.48	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> B_{D_1}(d_{d_1}(d_{a_1}(x1)))
108.26/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{D_1}(x1)
108.26/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{B_1}(b_{c_1}(x1))
108.26/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{C_1}(x1)
108.26/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1))))
108.26/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1))))
108.26/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1))))
108.26/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1))))
108.26/28.48	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> B_{D_1}(d_{d_1}(d_{a_1}(x1)))
108.26/28.48	
108.26/28.48	The TRS R consists of the following rules:
108.26/28.48	
108.26/28.48	   b_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
108.26/28.48	   c_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
108.26/28.48	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.48	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.48	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.48	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1)))))))
108.26/28.48	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1)))))))
108.26/28.48	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1)))))))
108.26/28.48	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1)))))))
108.26/28.48	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.48	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.48	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.48	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1)))))))
108.26/28.48	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1)))))))
108.26/28.48	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1)))))))
108.26/28.48	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1)))))))
108.26/28.48	   b_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.48	   b_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.48	   b_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.48	   b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))) -> b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{c_1}(x1))))))
108.26/28.48	   b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))) -> b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{d_1}(x1))))))
108.26/28.48	   b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{a_1}(x1)))))) -> b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{a_1}(x1))))))
108.26/28.48	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.48	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.48	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.48	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1)))))))
108.26/28.48	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1)))))))
108.26/28.48	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1)))))))
108.26/28.48	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1)))))))
108.26/28.48	   d_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.48	   d_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.48	   d_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.48	   d_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
108.26/28.48	
108.26/28.48	Q is empty.
108.26/28.48	We have to consider all minimal (P,Q,R)-chains.
108.26/28.48	----------------------------------------
108.26/28.48	
108.26/28.48	(19) QDPOrderProof (EQUIVALENT)
108.26/28.48	We use the reduction pair processor [LPAR04,JAR06].
108.26/28.48	
108.26/28.48	
108.26/28.48	The following pairs can be oriented strictly and are deleted.
108.26/28.48	
108.26/28.48	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{a_1}(x1)))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{a_1}(x1))))))
108.26/28.48	The remaining pairs can at least be oriented weakly.
108.26/28.48	Used ordering:  Polynomial interpretation [POLO]:
108.26/28.48	
108.26/28.48	   POL(B_{B_1}(x_1)) = x_1
108.26/28.48	   POL(B_{C_1}(x_1)) = x_1
108.26/28.48	   POL(B_{D_1}(x_1)) = x_1
108.26/28.48	   POL(C_{C_1}(x_1)) = x_1
108.26/28.48	   POL(C_{D_1}(x_1)) = 0
108.26/28.48	   POL(D_{C_1}(x_1)) = x_1
108.26/28.48	   POL(a_{a_1}(x_1)) = x_1
108.26/28.48	   POL(a_{d_1}(x_1)) = x_1
108.26/28.48	   POL(b_{a_1}(x_1)) = 1 + x_1
108.26/28.48	   POL(b_{b_1}(x_1)) = x_1
108.26/28.48	   POL(b_{c_1}(x_1)) = x_1
108.26/28.48	   POL(b_{d_1}(x_1)) = x_1
108.26/28.48	   POL(c_{a_1}(x_1)) = x_1
108.26/28.48	   POL(c_{c_1}(x_1)) = x_1
108.26/28.48	   POL(c_{d_1}(x_1)) = x_1
108.26/28.48	   POL(d_{a_1}(x_1)) = 0
108.26/28.48	   POL(d_{b_1}(x_1)) = x_1
108.26/28.48	   POL(d_{c_1}(x_1)) = x_1
108.26/28.48	   POL(d_{d_1}(x_1)) = x_1
108.26/28.48	
108.26/28.48	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
108.26/28.48	
108.26/28.48	   b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))) -> b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{d_1}(x1))))))
108.26/28.48	   b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))) -> b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{c_1}(x1))))))
108.26/28.48	   b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{a_1}(x1)))))) -> b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{a_1}(x1))))))
108.26/28.48	   c_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
108.26/28.48	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.48	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.48	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.48	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1)))))))
108.26/28.48	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1)))))))
108.26/28.48	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1)))))))
108.26/28.48	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1)))))))
108.26/28.48	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.48	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.48	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.48	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1)))))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1)))))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1)))))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1)))))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.50	   d_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
108.26/28.50	   b_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1)))))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1)))))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1)))))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1)))))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.50	
108.26/28.50	
108.26/28.50	----------------------------------------
108.26/28.50	
108.26/28.50	(20)
108.26/28.50	Obligation:
108.26/28.50	Q DP problem:
108.26/28.50	The TRS P consists of the following rules:
108.26/28.50	
108.26/28.50	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(b_{b_1}(x1))
108.26/28.50	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{d_1}(x1))))))
108.26/28.50	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))) -> D_{C_1}(c_{c_1}(c_{d_1}(x1)))
108.26/28.50	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(x1)
108.26/28.50	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))) -> C_{C_1}(c_{d_1}(x1))
108.26/28.50	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(b_{b_1}(x1))
108.26/28.50	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))) -> C_{D_1}(x1)
108.26/28.50	   C_{D_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
108.26/28.50	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(x1)
108.26/28.50	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{c_1}(x1))))))
108.26/28.50	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))) -> D_{C_1}(c_{c_1}(c_{c_1}(x1)))
108.26/28.50	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{B_1}(b_{d_1}(x1))
108.26/28.50	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))) -> C_{C_1}(c_{c_1}(x1))
108.26/28.50	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{B_1}(b_{d_1}(x1))
108.26/28.50	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))) -> C_{C_1}(x1)
108.26/28.50	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{D_1}(x1)
108.26/28.50	   B_{D_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
108.26/28.50	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(b_{b_1}(x1))
108.26/28.50	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(x1)
108.26/28.50	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{B_1}(b_{d_1}(x1))
108.26/28.50	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{D_1}(x1)
108.26/28.50	   B_{D_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> C_{C_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))
108.26/28.50	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{B_1}(b_{c_1}(x1))
108.26/28.50	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{C_1}(x1)
108.26/28.50	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{B_1}(b_{c_1}(x1))
108.26/28.50	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{C_1}(x1)
108.26/28.50	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1))))
108.26/28.50	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1))))
108.26/28.50	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1))))
108.26/28.50	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1))))
108.26/28.50	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> B_{D_1}(d_{d_1}(d_{a_1}(x1)))
108.26/28.50	   B_{D_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> C_{D_1}(d_{d_1}(d_{a_1}(x1)))
108.26/28.50	   C_{D_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> C_{C_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))
108.26/28.50	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1))))
108.26/28.50	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1))))
108.26/28.50	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1))))
108.26/28.50	   C_{D_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> C_{D_1}(d_{d_1}(d_{a_1}(x1)))
108.26/28.50	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1))))
108.26/28.50	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> B_{D_1}(d_{d_1}(d_{a_1}(x1)))
108.26/28.50	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{D_1}(x1)
108.26/28.50	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{B_1}(b_{c_1}(x1))
108.26/28.50	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{C_1}(x1)
108.26/28.50	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1))))
108.26/28.50	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1))))
108.26/28.50	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1))))
108.26/28.50	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1))))
108.26/28.50	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> B_{D_1}(d_{d_1}(d_{a_1}(x1)))
108.26/28.50	
108.26/28.50	The TRS R consists of the following rules:
108.26/28.50	
108.26/28.50	   b_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
108.26/28.50	   c_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
108.26/28.50	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.50	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.50	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.50	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1)))))))
108.26/28.50	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1)))))))
108.26/28.50	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1)))))))
108.26/28.50	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1)))))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1)))))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1)))))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1)))))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1)))))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.50	   b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))) -> b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{c_1}(x1))))))
108.26/28.50	   b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))) -> b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{d_1}(x1))))))
108.26/28.50	   b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{a_1}(x1)))))) -> b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{a_1}(x1))))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1)))))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1)))))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1)))))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1)))))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.50	   d_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
108.26/28.50	
108.26/28.50	Q is empty.
108.26/28.50	We have to consider all minimal (P,Q,R)-chains.
108.26/28.50	----------------------------------------
108.26/28.50	
108.26/28.50	(21) QDPOrderProof (EQUIVALENT)
108.26/28.50	We use the reduction pair processor [LPAR04,JAR06].
108.26/28.50	
108.26/28.50	
108.26/28.50	The following pairs can be oriented strictly and are deleted.
108.26/28.50	
108.26/28.50	   C_{D_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
108.26/28.50	   B_{D_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
108.26/28.50	   B_{D_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> C_{C_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))
108.26/28.50	   B_{D_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> C_{D_1}(d_{d_1}(d_{a_1}(x1)))
108.26/28.50	   C_{D_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> C_{C_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))
108.26/28.50	   C_{D_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> C_{D_1}(d_{d_1}(d_{a_1}(x1)))
108.26/28.50	The remaining pairs can at least be oriented weakly.
108.26/28.50	Used ordering:  Polynomial interpretation [POLO]:
108.26/28.50	
108.26/28.50	   POL(B_{B_1}(x_1)) = x_1
108.26/28.50	   POL(B_{C_1}(x_1)) = x_1
108.26/28.50	   POL(B_{D_1}(x_1)) = x_1
108.26/28.50	   POL(C_{C_1}(x_1)) = x_1
108.26/28.50	   POL(C_{D_1}(x_1)) = x_1
108.26/28.50	   POL(D_{C_1}(x_1)) = x_1
108.26/28.50	   POL(a_{a_1}(x_1)) = 1 + x_1
108.26/28.50	   POL(a_{d_1}(x_1)) = x_1
108.26/28.50	   POL(b_{a_1}(x_1)) = x_1
108.26/28.50	   POL(b_{b_1}(x_1)) = x_1
108.26/28.50	   POL(b_{c_1}(x_1)) = x_1
108.26/28.50	   POL(b_{d_1}(x_1)) = x_1
108.26/28.50	   POL(c_{a_1}(x_1)) = x_1
108.26/28.50	   POL(c_{c_1}(x_1)) = x_1
108.26/28.50	   POL(c_{d_1}(x_1)) = x_1
108.26/28.50	   POL(d_{a_1}(x_1)) = x_1
108.26/28.50	   POL(d_{b_1}(x_1)) = x_1
108.26/28.50	   POL(d_{c_1}(x_1)) = x_1
108.26/28.50	   POL(d_{d_1}(x_1)) = x_1
108.26/28.50	
108.26/28.50	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
108.26/28.50	
108.26/28.50	   b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))) -> b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{d_1}(x1))))))
108.26/28.50	   b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))) -> b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{c_1}(x1))))))
108.26/28.50	   b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{a_1}(x1)))))) -> b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{a_1}(x1))))))
108.26/28.50	   c_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
108.26/28.50	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.50	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.50	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.50	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1)))))))
108.26/28.50	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1)))))))
108.26/28.50	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1)))))))
108.26/28.50	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1)))))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1)))))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1)))))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1)))))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1)))))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.50	   d_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
108.26/28.50	   b_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1)))))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1)))))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1)))))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1)))))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.50	
108.26/28.50	
108.26/28.50	----------------------------------------
108.26/28.50	
108.26/28.50	(22)
108.26/28.50	Obligation:
108.26/28.50	Q DP problem:
108.26/28.50	The TRS P consists of the following rules:
108.26/28.50	
108.26/28.50	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(b_{b_1}(x1))
108.26/28.50	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{d_1}(x1))))))
108.26/28.50	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))) -> D_{C_1}(c_{c_1}(c_{d_1}(x1)))
108.26/28.50	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(x1)
108.26/28.50	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))) -> C_{C_1}(c_{d_1}(x1))
108.26/28.50	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(b_{b_1}(x1))
108.26/28.50	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))) -> C_{D_1}(x1)
108.26/28.50	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(x1)
108.26/28.50	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{c_1}(x1))))))
108.26/28.50	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))) -> D_{C_1}(c_{c_1}(c_{c_1}(x1)))
108.26/28.50	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{B_1}(b_{d_1}(x1))
108.26/28.50	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))) -> C_{C_1}(c_{c_1}(x1))
108.26/28.50	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{B_1}(b_{d_1}(x1))
108.26/28.50	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))) -> C_{C_1}(x1)
108.26/28.50	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{D_1}(x1)
108.26/28.50	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(b_{b_1}(x1))
108.26/28.50	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(x1)
108.26/28.50	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{B_1}(b_{d_1}(x1))
108.26/28.50	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{D_1}(x1)
108.26/28.50	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{B_1}(b_{c_1}(x1))
108.26/28.50	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{C_1}(x1)
108.26/28.50	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{B_1}(b_{c_1}(x1))
108.26/28.50	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{C_1}(x1)
108.26/28.50	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1))))
108.26/28.50	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1))))
108.26/28.50	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1))))
108.26/28.50	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1))))
108.26/28.50	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> B_{D_1}(d_{d_1}(d_{a_1}(x1)))
108.26/28.50	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1))))
108.26/28.50	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1))))
108.26/28.50	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1))))
108.26/28.50	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1))))
108.26/28.50	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> B_{D_1}(d_{d_1}(d_{a_1}(x1)))
108.26/28.50	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{D_1}(x1)
108.26/28.50	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{B_1}(b_{c_1}(x1))
108.26/28.50	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{C_1}(x1)
108.26/28.50	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1))))
108.26/28.50	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1))))
108.26/28.50	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1))))
108.26/28.50	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1))))
108.26/28.50	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> B_{D_1}(d_{d_1}(d_{a_1}(x1)))
108.26/28.50	
108.26/28.50	The TRS R consists of the following rules:
108.26/28.50	
108.26/28.50	   b_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
108.26/28.50	   c_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
108.26/28.50	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.50	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.50	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.50	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1)))))))
108.26/28.50	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1)))))))
108.26/28.50	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1)))))))
108.26/28.50	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1)))))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1)))))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1)))))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1)))))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1)))))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.50	   b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))) -> b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{c_1}(x1))))))
108.26/28.50	   b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))) -> b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{d_1}(x1))))))
108.26/28.50	   b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{a_1}(x1)))))) -> b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{a_1}(x1))))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1)))))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1)))))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1)))))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1)))))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.50	   d_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
108.26/28.50	
108.26/28.50	Q is empty.
108.26/28.50	We have to consider all minimal (P,Q,R)-chains.
108.26/28.50	----------------------------------------
108.26/28.50	
108.26/28.50	(23) DependencyGraphProof (EQUIVALENT)
108.26/28.50	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 7 less nodes.
108.26/28.50	----------------------------------------
108.26/28.50	
108.26/28.50	(24)
108.26/28.50	Obligation:
108.26/28.50	Q DP problem:
108.26/28.50	The TRS P consists of the following rules:
108.26/28.50	
108.26/28.50	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{d_1}(x1))))))
108.26/28.50	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))) -> D_{C_1}(c_{c_1}(c_{d_1}(x1)))
108.26/28.50	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(b_{b_1}(x1))
108.26/28.50	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))) -> C_{C_1}(c_{d_1}(x1))
108.26/28.50	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(b_{b_1}(x1))
108.26/28.50	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{c_1}(x1))))))
108.26/28.50	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))) -> D_{C_1}(c_{c_1}(c_{c_1}(x1)))
108.26/28.50	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(x1)
108.26/28.50	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))) -> C_{C_1}(c_{c_1}(x1))
108.26/28.50	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(x1)
108.26/28.50	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))) -> C_{C_1}(x1)
108.26/28.50	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{B_1}(b_{d_1}(x1))
108.26/28.50	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{B_1}(b_{c_1}(x1))
108.26/28.50	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{C_1}(x1)
108.26/28.50	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(b_{b_1}(x1))
108.26/28.50	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(x1)
108.26/28.50	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{B_1}(b_{d_1}(x1))
108.26/28.50	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{B_1}(b_{c_1}(x1))
108.26/28.50	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{C_1}(x1)
108.26/28.50	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1))))
108.26/28.50	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1))))
108.26/28.50	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1))))
108.26/28.50	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1))))
108.26/28.50	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1))))
108.26/28.50	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1))))
108.26/28.50	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1))))
108.26/28.50	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1))))
108.26/28.50	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{B_1}(b_{d_1}(x1))
108.26/28.50	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{B_1}(b_{c_1}(x1))
108.26/28.50	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{C_1}(x1)
108.26/28.50	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1))))
108.26/28.50	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1))))
108.26/28.50	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1))))
108.26/28.50	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1))))
108.26/28.50	
108.26/28.50	The TRS R consists of the following rules:
108.26/28.50	
108.26/28.50	   b_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
108.26/28.50	   c_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
108.26/28.50	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.50	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.50	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.50	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1)))))))
108.26/28.50	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1)))))))
108.26/28.50	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1)))))))
108.26/28.50	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1)))))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1)))))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1)))))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1)))))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1)))))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.50	   b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))) -> b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{c_1}(x1))))))
108.26/28.50	   b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))) -> b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{d_1}(x1))))))
108.26/28.50	   b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{a_1}(x1)))))) -> b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{a_1}(x1))))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1)))))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1)))))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1)))))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1)))))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.50	   d_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
108.26/28.50	
108.26/28.50	Q is empty.
108.26/28.50	We have to consider all minimal (P,Q,R)-chains.
108.26/28.50	----------------------------------------
108.26/28.50	
108.26/28.50	(25) QDPOrderProof (EQUIVALENT)
108.26/28.50	We use the reduction pair processor [LPAR04,JAR06].
108.26/28.50	
108.26/28.50	
108.26/28.50	The following pairs can be oriented strictly and are deleted.
108.26/28.50	
108.26/28.50	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(b_{b_1}(x1))
108.26/28.50	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))) -> C_{C_1}(c_{d_1}(x1))
108.26/28.50	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(b_{b_1}(x1))
108.26/28.50	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(x1)
108.26/28.50	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))) -> C_{C_1}(c_{c_1}(x1))
108.26/28.50	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(x1)
108.26/28.50	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))) -> C_{C_1}(x1)
108.26/28.50	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{B_1}(b_{d_1}(x1))
108.26/28.50	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{B_1}(b_{c_1}(x1))
108.26/28.50	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{C_1}(x1)
108.26/28.50	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(b_{b_1}(x1))
108.26/28.50	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(x1)
108.26/28.50	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{B_1}(b_{d_1}(x1))
108.26/28.50	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{B_1}(b_{c_1}(x1))
108.26/28.50	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{C_1}(x1)
108.26/28.50	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1))))
108.26/28.50	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1))))
108.26/28.50	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1))))
108.26/28.50	   B_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1))))
108.26/28.50	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1))))
108.26/28.50	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1))))
108.26/28.50	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1))))
108.26/28.50	   C_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1))))
108.26/28.50	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{B_1}(b_{d_1}(x1))
108.26/28.50	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{B_1}(b_{c_1}(x1))
108.26/28.50	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{C_1}(x1)
108.26/28.50	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1))))
108.26/28.50	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1))))
108.26/28.50	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1))))
108.26/28.50	   D_{C_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1))))
108.26/28.50	The remaining pairs can at least be oriented weakly.
108.26/28.50	Used ordering:  Polynomial interpretation [POLO]:
108.26/28.50	
108.26/28.50	   POL(B_{B_1}(x_1)) = x_1
108.26/28.50	   POL(B_{C_1}(x_1)) = x_1
108.26/28.50	   POL(C_{C_1}(x_1)) = x_1
108.26/28.50	   POL(D_{C_1}(x_1)) = x_1
108.26/28.50	   POL(a_{a_1}(x_1)) = 1 + x_1
108.26/28.50	   POL(a_{d_1}(x_1)) = 1 + x_1
108.26/28.50	   POL(b_{a_1}(x_1)) = x_1
108.26/28.50	   POL(b_{b_1}(x_1)) = 1 + x_1
108.26/28.50	   POL(b_{c_1}(x_1)) = x_1
108.26/28.50	   POL(b_{d_1}(x_1)) = x_1
108.26/28.50	   POL(c_{a_1}(x_1)) = 1 + x_1
108.26/28.50	   POL(c_{c_1}(x_1)) = 1 + x_1
108.26/28.50	   POL(c_{d_1}(x_1)) = 1 + x_1
108.26/28.50	   POL(d_{a_1}(x_1)) = x_1
108.26/28.50	   POL(d_{b_1}(x_1)) = 1 + x_1
108.26/28.50	   POL(d_{c_1}(x_1)) = x_1
108.26/28.50	   POL(d_{d_1}(x_1)) = x_1
108.26/28.50	
108.26/28.50	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
108.26/28.50	
108.26/28.50	   c_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
108.26/28.50	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.50	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.50	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.50	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1)))))))
108.26/28.50	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1)))))))
108.26/28.50	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1)))))))
108.26/28.50	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1)))))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1)))))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1)))))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1)))))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1)))))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.50	   d_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
108.26/28.50	   b_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
108.26/28.50	   b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))) -> b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{d_1}(x1))))))
108.26/28.50	   b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))) -> b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{c_1}(x1))))))
108.26/28.50	   b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{a_1}(x1)))))) -> b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{a_1}(x1))))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1)))))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1)))))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1)))))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1)))))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.50	
108.26/28.50	
108.26/28.50	----------------------------------------
108.26/28.50	
108.26/28.50	(26)
108.26/28.50	Obligation:
108.26/28.50	Q DP problem:
108.26/28.50	The TRS P consists of the following rules:
108.26/28.50	
108.26/28.50	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{d_1}(x1))))))
108.26/28.50	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))) -> D_{C_1}(c_{c_1}(c_{d_1}(x1)))
108.26/28.50	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{c_1}(x1))))))
108.26/28.50	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))) -> D_{C_1}(c_{c_1}(c_{c_1}(x1)))
108.26/28.50	
108.26/28.50	The TRS R consists of the following rules:
108.26/28.50	
108.26/28.50	   b_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
108.26/28.50	   c_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
108.26/28.50	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.50	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.50	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.50	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1)))))))
108.26/28.50	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1)))))))
108.26/28.50	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1)))))))
108.26/28.50	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1)))))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1)))))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1)))))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1)))))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1)))))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.50	   b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))) -> b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{c_1}(x1))))))
108.26/28.50	   b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))) -> b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{d_1}(x1))))))
108.26/28.50	   b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{a_1}(x1)))))) -> b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{a_1}(x1))))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1)))))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1)))))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1)))))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1)))))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.50	   d_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
108.26/28.50	
108.26/28.50	Q is empty.
108.26/28.50	We have to consider all minimal (P,Q,R)-chains.
108.26/28.50	----------------------------------------
108.26/28.50	
108.26/28.50	(27) DependencyGraphProof (EQUIVALENT)
108.26/28.50	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes.
108.26/28.50	----------------------------------------
108.26/28.50	
108.26/28.50	(28)
108.26/28.50	Obligation:
108.26/28.50	Q DP problem:
108.26/28.50	The TRS P consists of the following rules:
108.26/28.50	
108.26/28.50	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{c_1}(x1))))))
108.26/28.50	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{d_1}(x1))))))
108.26/28.50	
108.26/28.50	The TRS R consists of the following rules:
108.26/28.50	
108.26/28.50	   b_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
108.26/28.50	   c_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
108.26/28.50	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.50	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.50	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.50	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1)))))))
108.26/28.50	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1)))))))
108.26/28.50	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1)))))))
108.26/28.50	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1)))))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1)))))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1)))))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1)))))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1)))))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.50	   b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))) -> b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{c_1}(x1))))))
108.26/28.50	   b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))) -> b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{d_1}(x1))))))
108.26/28.50	   b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{a_1}(x1)))))) -> b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{a_1}(x1))))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1)))))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1)))))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1)))))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1)))))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.50	   d_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
108.26/28.50	
108.26/28.50	Q is empty.
108.26/28.50	We have to consider all minimal (P,Q,R)-chains.
108.26/28.50	----------------------------------------
108.26/28.50	
108.26/28.50	(29) QDPOrderProof (EQUIVALENT)
108.26/28.50	We use the reduction pair processor [LPAR04,JAR06].
108.26/28.50	
108.26/28.50	
108.26/28.50	The following pairs can be oriented strictly and are deleted.
108.26/28.50	
108.26/28.50	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{c_1}(x1))))))
108.26/28.50	   B_{B_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))) -> B_{B_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{d_1}(x1))))))
108.26/28.50	The remaining pairs can at least be oriented weakly.
108.26/28.50	Used ordering:  Matrix interpretation [MATRO] with arctic natural numbers [ARCTIC]:
108.26/28.50	
108.26/28.50	   <<<
108.26/28.50	 POL(B_{B_1}(x_1)) =  	[[0A]] 	 +  	[[0A, 0A, 0A]] 	* 	x_1
108.26/28.50	>>>
108.26/28.50	
108.26/28.50	   <<<
108.26/28.50	 POL(b_{d_1}(x_1)) =  	[[0A], [0A], [0A]] 	 +  	[[0A, -I, 0A], [0A, -I, -I], [-I, -I, -I]] 	* 	x_1
108.26/28.50	>>>
108.26/28.50	
108.26/28.50	   <<<
108.26/28.50	 POL(d_{d_1}(x_1)) =  	[[0A], [0A], [0A]] 	 +  	[[-I, -I, 0A], [0A, -I, -I], [-I, 0A, -I]] 	* 	x_1
108.26/28.50	>>>
108.26/28.50	
108.26/28.50	   <<<
108.26/28.50	 POL(d_{b_1}(x_1)) =  	[[0A], [0A], [-I]] 	 +  	[[0A, 0A, 0A], [0A, 1A, 0A], [-I, -I, 0A]] 	* 	x_1
108.26/28.50	>>>
108.26/28.50	
108.26/28.50	   <<<
108.26/28.50	 POL(b_{b_1}(x_1)) =  	[[0A], [-I], [-I]] 	 +  	[[-I, -I, 0A], [-I, -I, 0A], [-I, -I, -I]] 	* 	x_1
108.26/28.50	>>>
108.26/28.50	
108.26/28.50	   <<<
108.26/28.50	 POL(b_{c_1}(x_1)) =  	[[1A], [0A], [0A]] 	 +  	[[-I, -I, -I], [-I, -I, -I], [-I, -I, -I]] 	* 	x_1
108.26/28.50	>>>
108.26/28.50	
108.26/28.50	   <<<
108.26/28.50	 POL(d_{c_1}(x_1)) =  	[[1A], [0A], [0A]] 	 +  	[[-I, -I, -I], [-I, -I, -I], [-I, -I, -I]] 	* 	x_1
108.26/28.50	>>>
108.26/28.50	
108.26/28.50	   <<<
108.26/28.50	 POL(c_{c_1}(x_1)) =  	[[0A], [0A], [0A]] 	 +  	[[0A, -I, 0A], [-I, 0A, 0A], [0A, -I, 0A]] 	* 	x_1
108.26/28.50	>>>
108.26/28.50	
108.26/28.50	   <<<
108.26/28.50	 POL(c_{d_1}(x_1)) =  	[[0A], [0A], [0A]] 	 +  	[[-I, -I, -I], [0A, 0A, 0A], [0A, 0A, 0A]] 	* 	x_1
108.26/28.50	>>>
108.26/28.50	
108.26/28.50	   <<<
108.26/28.50	 POL(d_{a_1}(x_1)) =  	[[-I], [1A], [1A]] 	 +  	[[0A, 0A, 0A], [0A, 0A, 0A], [0A, 0A, -I]] 	* 	x_1
108.26/28.50	>>>
108.26/28.50	
108.26/28.50	   <<<
108.26/28.50	 POL(c_{a_1}(x_1)) =  	[[0A], [0A], [0A]] 	 +  	[[0A, 0A, 0A], [-I, -I, -I], [0A, 0A, 0A]] 	* 	x_1
108.26/28.50	>>>
108.26/28.50	
108.26/28.50	   <<<
108.26/28.50	 POL(a_{a_1}(x_1)) =  	[[-I], [-I], [-I]] 	 +  	[[0A, 0A, 0A], [0A, 0A, 0A], [0A, 0A, 0A]] 	* 	x_1
108.26/28.50	>>>
108.26/28.50	
108.26/28.50	   <<<
108.26/28.50	 POL(a_{d_1}(x_1)) =  	[[0A], [0A], [0A]] 	 +  	[[0A, 0A, 0A], [0A, 0A, 0A], [0A, 0A, 0A]] 	* 	x_1
108.26/28.50	>>>
108.26/28.50	
108.26/28.50	   <<<
108.26/28.50	 POL(b_{a_1}(x_1)) =  	[[0A], [0A], [0A]] 	 +  	[[0A, 0A, 0A], [0A, 0A, 0A], [0A, 0A, 0A]] 	* 	x_1
108.26/28.50	>>>
108.26/28.50	
108.26/28.50	
108.26/28.50	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
108.26/28.50	
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1)))))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1)))))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1)))))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1)))))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.50	   d_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
108.26/28.50	   b_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
108.26/28.50	   b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))) -> b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{d_1}(x1))))))
108.26/28.50	   b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))) -> b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{c_1}(x1))))))
108.26/28.50	   b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{a_1}(x1)))))) -> b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{a_1}(x1))))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1)))))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1)))))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1)))))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1)))))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.50	
108.26/28.50	
108.26/28.50	----------------------------------------
108.26/28.50	
108.26/28.50	(30)
108.26/28.50	Obligation:
108.26/28.50	Q DP problem:
108.26/28.50	P is empty.
108.26/28.50	The TRS R consists of the following rules:
108.26/28.50	
108.26/28.50	   b_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
108.26/28.50	   c_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
108.26/28.50	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.50	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.50	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.50	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1)))))))
108.26/28.50	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1)))))))
108.26/28.50	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1)))))))
108.26/28.50	   c_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> c_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1)))))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1)))))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1)))))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1)))))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1)))))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.50	   b_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.50	   b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))) -> b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{c_1}(x1))))))
108.26/28.50	   b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))) -> b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{d_1}(x1))))))
108.26/28.50	   b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{a_1}(x1)))))) -> b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(c_{c_1}(c_{a_1}(x1))))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{b_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{b_1}(x1)))))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{d_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{d_1}(x1)))))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{c_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{c_1}(x1)))))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1))))) -> d_{d_1}(d_{d_1}(d_{b_1}(b_{b_1}(b_{d_1}(d_{d_1}(d_{a_1}(x1)))))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{b_1}(x1))))))) -> d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1)))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{d_1}(x1))))))) -> d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{d_1}(x1)))))
108.26/28.50	   d_{c_1}(c_{c_1}(c_{a_1}(a_{a_1}(a_{d_1}(d_{d_1}(d_{c_1}(x1))))))) -> d_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1)))))
108.26/28.50	   d_{d_1}(d_{d_1}(d_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> d_{c_1}(c_{c_1}(c_{d_1}(d_{d_1}(d_{a_1}(x1)))))
108.26/28.50	
108.26/28.50	Q is empty.
108.26/28.50	We have to consider all minimal (P,Q,R)-chains.
108.26/28.50	----------------------------------------
108.26/28.50	
108.26/28.50	(31) PisEmptyProof (EQUIVALENT)
108.26/28.50	The TRS P is empty. Hence, there is no (P,Q,R) chain.
108.26/28.50	----------------------------------------
108.26/28.50	
108.26/28.50	(32)
108.26/28.50	YES
108.59/28.77	EOF