3.35/1.59	YES
3.35/1.64	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.35/1.64	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.35/1.64	
3.35/1.64	
3.35/1.64	Termination w.r.t. Q of the given QTRS could be proven:
3.35/1.64	
3.35/1.64	(0) QTRS
3.35/1.64	(1) QTRS Reverse [EQUIVALENT, 0 ms]
3.35/1.64	(2) QTRS
3.35/1.64	(3) Strip Symbols Proof [SOUND, 0 ms]
3.35/1.64	(4) QTRS
3.35/1.64	(5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
3.35/1.64	(6) YES
3.35/1.64	
3.35/1.64	
3.35/1.64	----------------------------------------
3.35/1.64	
3.35/1.64	(0)
3.35/1.64	Obligation:
3.35/1.64	Q restricted rewrite system:
3.35/1.64	The TRS R consists of the following rules:
3.35/1.64	
3.35/1.64	   a(b(b(a(a(a(a(x1))))))) -> a(a(a(a(a(b(b(a(a(b(b(x1)))))))))))
3.35/1.64	
3.35/1.64	Q is empty.
3.35/1.64	
3.35/1.64	----------------------------------------
3.35/1.64	
3.35/1.64	(1) QTRS Reverse (EQUIVALENT)
3.35/1.64	We applied the QTRS Reverse Processor [REVERSE].
3.35/1.64	----------------------------------------
3.35/1.64	
3.35/1.64	(2)
3.35/1.64	Obligation:
3.35/1.64	Q restricted rewrite system:
3.35/1.64	The TRS R consists of the following rules:
3.35/1.64	
3.35/1.64	   a(a(a(a(b(b(a(x1))))))) -> b(b(a(a(b(b(a(a(a(a(a(x1)))))))))))
3.35/1.64	
3.35/1.64	Q is empty.
3.35/1.64	
3.35/1.64	----------------------------------------
3.35/1.64	
3.35/1.64	(3) Strip Symbols Proof (SOUND)
3.35/1.64	We were given the following TRS:
3.35/1.64	
3.35/1.64	   a(a(a(a(b(b(a(x1))))))) -> b(b(a(a(b(b(a(a(a(a(a(x1)))))))))))
3.35/1.64	
3.35/1.64	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
3.35/1.64	
3.35/1.64	   a(a(a(a(b(b(x)))))) -> b(b(a(a(b(b(a(a(a(a(x))))))))))
3.35/1.64	
3.35/1.64	----------------------------------------
3.35/1.64	
3.35/1.64	(4)
3.35/1.64	Obligation:
3.35/1.64	Q restricted rewrite system:
3.35/1.64	The TRS R consists of the following rules:
3.35/1.64	
3.35/1.64	   a(a(a(a(b(b(x)))))) -> b(b(a(a(b(b(a(a(a(a(x))))))))))
3.35/1.64	
3.35/1.64	Q is empty.
3.35/1.64	
3.35/1.64	----------------------------------------
3.35/1.64	
3.35/1.64	(5) RFCMatchBoundsTRSProof (EQUIVALENT)
3.35/1.64	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
3.35/1.64	The following rules were used to construct the certificate:
3.35/1.64	
3.35/1.64	   a(a(a(a(b(b(x)))))) -> b(b(a(a(b(b(a(a(a(a(x))))))))))
3.35/1.64	
3.35/1.64	The certificate found is represented by the following graph.
3.35/1.64	The certificate consists of the following enumerated nodes:
3.35/1.64	133, 134, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161
3.35/1.64	
3.35/1.64	Node 133 is start node and node 134 is final node.
3.35/1.64	
3.35/1.64	Those nodes are connected through the following edges:
3.35/1.64	
3.35/1.64	* 133 to 144 labelled b_1(0)* 134 to 134 labelled #_1(0)* 144 to 145 labelled b_1(0)* 145 to 146 labelled a_1(0)* 146 to 147 labelled a_1(0)* 147 to 148 labelled b_1(0)* 148 to 149 labelled b_1(0)* 149 to 150 labelled a_1(0)* 149 to 153 labelled b_1(1)* 150 to 151 labelled a_1(0)* 150 to 153 labelled b_1(1)* 151 to 152 labelled a_1(0)* 151 to 153 labelled b_1(1)* 152 to 134 labelled a_1(0)* 152 to 153 labelled b_1(1)* 153 to 154 labelled b_1(1)* 154 to 155 labelled a_1(1)* 155 to 156 labelled a_1(1)* 156 to 157 labelled b_1(1)* 157 to 158 labelled b_1(1)* 158 to 159 labelled a_1(1)* 158 to 153 labelled b_1(1)* 159 to 160 labelled a_1(1)* 159 to 153 labelled b_1(1)* 160 to 161 labelled a_1(1)* 160 to 153 labelled b_1(1)* 161 to 134 labelled a_1(1)* 161 to 153 labelled b_1(1)
3.35/1.64	
3.35/1.64	
3.35/1.64	----------------------------------------
3.35/1.64	
3.35/1.64	(6)
3.35/1.64	YES
3.63/1.66	EOF