3.49/1.63	YES
3.49/1.67	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.49/1.67	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.49/1.67	
3.49/1.67	
3.49/1.67	Termination w.r.t. Q of the given QTRS could be proven:
3.49/1.67	
3.49/1.67	(0) QTRS
3.49/1.67	(1) QTRS Reverse [EQUIVALENT, 0 ms]
3.49/1.67	(2) QTRS
3.49/1.67	(3) Strip Symbols Proof [SOUND, 0 ms]
3.49/1.67	(4) QTRS
3.49/1.67	(5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
3.49/1.67	(6) YES
3.49/1.67	
3.49/1.67	
3.49/1.67	----------------------------------------
3.49/1.67	
3.49/1.67	(0)
3.49/1.67	Obligation:
3.49/1.67	Q restricted rewrite system:
3.49/1.67	The TRS R consists of the following rules:
3.49/1.67	
3.49/1.67	   a(b(a(a(b(a(a(a(a(a(x1)))))))))) -> a(a(a(a(a(a(b(a(a(b(a(a(b(x1)))))))))))))
3.49/1.67	
3.49/1.67	Q is empty.
3.49/1.67	
3.49/1.67	----------------------------------------
3.49/1.67	
3.49/1.67	(1) QTRS Reverse (EQUIVALENT)
3.49/1.67	We applied the QTRS Reverse Processor [REVERSE].
3.49/1.67	----------------------------------------
3.49/1.67	
3.49/1.67	(2)
3.49/1.67	Obligation:
3.49/1.67	Q restricted rewrite system:
3.49/1.67	The TRS R consists of the following rules:
3.49/1.67	
3.49/1.67	   a(a(a(a(a(b(a(a(b(a(x1)))))))))) -> b(a(a(b(a(a(b(a(a(a(a(a(a(x1)))))))))))))
3.49/1.67	
3.49/1.67	Q is empty.
3.49/1.67	
3.49/1.67	----------------------------------------
3.49/1.67	
3.49/1.67	(3) Strip Symbols Proof (SOUND)
3.49/1.67	We were given the following TRS:
3.49/1.67	
3.49/1.67	   a(a(a(a(a(b(a(a(b(a(x1)))))))))) -> b(a(a(b(a(a(b(a(a(a(a(a(a(x1)))))))))))))
3.49/1.67	
3.49/1.67	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
3.49/1.67	
3.49/1.67	   a(a(a(a(a(b(a(a(b(x))))))))) -> b(a(a(b(a(a(b(a(a(a(a(a(x))))))))))))
3.49/1.67	
3.49/1.67	----------------------------------------
3.49/1.67	
3.49/1.67	(4)
3.49/1.67	Obligation:
3.49/1.67	Q restricted rewrite system:
3.49/1.67	The TRS R consists of the following rules:
3.49/1.67	
3.49/1.67	   a(a(a(a(a(b(a(a(b(x))))))))) -> b(a(a(b(a(a(b(a(a(a(a(a(x))))))))))))
3.49/1.67	
3.49/1.67	Q is empty.
3.49/1.67	
3.49/1.67	----------------------------------------
3.49/1.67	
3.49/1.67	(5) RFCMatchBoundsTRSProof (EQUIVALENT)
3.49/1.67	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
3.49/1.67	The following rules were used to construct the certificate:
3.49/1.67	
3.49/1.67	   a(a(a(a(a(b(a(a(b(x))))))))) -> b(a(a(b(a(a(b(a(a(a(a(a(x))))))))))))
3.49/1.67	
3.49/1.67	The certificate found is represented by the following graph.
3.49/1.67	The certificate consists of the following enumerated nodes:
3.49/1.67	134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157
3.49/1.67	
3.49/1.67	Node 134 is start node and node 135 is final node.
3.49/1.67	
3.49/1.67	Those nodes are connected through the following edges:
3.49/1.67	
3.49/1.67	* 134 to 136 labelled b_1(0)* 135 to 135 labelled #_1(0)* 136 to 137 labelled a_1(0)* 137 to 138 labelled a_1(0)* 138 to 139 labelled b_1(0)* 139 to 140 labelled a_1(0)* 140 to 141 labelled a_1(0)* 141 to 142 labelled b_1(0)* 142 to 143 labelled a_1(0)* 142 to 147 labelled b_1(1)* 143 to 144 labelled a_1(0)* 143 to 147 labelled b_1(1)* 144 to 145 labelled a_1(0)* 144 to 147 labelled b_1(1)* 145 to 146 labelled a_1(0)* 145 to 147 labelled b_1(1)* 146 to 135 labelled a_1(0)* 146 to 147 labelled b_1(1)* 147 to 148 labelled a_1(1)* 148 to 149 labelled a_1(1)* 149 to 150 labelled b_1(1)* 150 to 151 labelled a_1(1)* 151 to 152 labelled a_1(1)* 152 to 153 labelled b_1(1)* 153 to 154 labelled a_1(1)* 153 to 147 labelled b_1(1)* 154 to 155 labelled a_1(1)* 154 to 147 labelled b_1(1)* 155 to 156 labelled a_1(1)* 155 to 147 labelled b_1(1)* 156 to 157 labelled a_1(1)* 156 to 147 labelled b_1(1)* 157 to 135 labelled a_1(1)* 157 to 147 labelled b_1(1)
3.49/1.67	
3.49/1.67	
3.49/1.67	----------------------------------------
3.49/1.67	
3.49/1.67	(6)
3.49/1.67	YES
3.87/1.69	EOF