3.19/1.69	YES
3.46/1.73	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.46/1.73	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.46/1.73	
3.46/1.73	
3.46/1.73	Termination w.r.t. Q of the given QTRS could be proven:
3.46/1.73	
3.46/1.73	(0) QTRS
3.46/1.73	(1) QTRS Reverse [EQUIVALENT, 0 ms]
3.46/1.73	(2) QTRS
3.46/1.73	(3) Strip Symbols Proof [SOUND, 0 ms]
3.46/1.73	(4) QTRS
3.46/1.73	(5) RFCMatchBoundsTRSProof [EQUIVALENT, 2 ms]
3.46/1.73	(6) YES
3.46/1.73	
3.46/1.73	
3.46/1.73	----------------------------------------
3.46/1.73	
3.46/1.73	(0)
3.46/1.73	Obligation:
3.46/1.73	Q restricted rewrite system:
3.46/1.73	The TRS R consists of the following rules:
3.46/1.73	
3.46/1.73	   a(a(b(b(a(b(a(b(a(x1))))))))) -> a(b(a(b(a(b(a(a(b(b(a(a(b(x1)))))))))))))
3.46/1.73	
3.46/1.73	Q is empty.
3.46/1.73	
3.46/1.73	----------------------------------------
3.46/1.73	
3.46/1.73	(1) QTRS Reverse (EQUIVALENT)
3.46/1.73	We applied the QTRS Reverse Processor [REVERSE].
3.46/1.73	----------------------------------------
3.46/1.73	
3.46/1.73	(2)
3.46/1.73	Obligation:
3.46/1.73	Q restricted rewrite system:
3.46/1.73	The TRS R consists of the following rules:
3.46/1.73	
3.46/1.73	   a(b(a(b(a(b(b(a(a(x1))))))))) -> b(a(a(b(b(a(a(b(a(b(a(b(a(x1)))))))))))))
3.46/1.73	
3.46/1.73	Q is empty.
3.46/1.73	
3.46/1.73	----------------------------------------
3.46/1.73	
3.46/1.73	(3) Strip Symbols Proof (SOUND)
3.46/1.73	We were given the following TRS:
3.46/1.73	
3.46/1.73	   a(b(a(b(a(b(b(a(a(x1))))))))) -> b(a(a(b(b(a(a(b(a(b(a(b(a(x1)))))))))))))
3.46/1.73	
3.46/1.73	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
3.46/1.73	
3.46/1.73	   a(b(a(b(a(b(b(a(x)))))))) -> b(a(a(b(b(a(a(b(a(b(a(b(x))))))))))))
3.46/1.73	
3.46/1.73	----------------------------------------
3.46/1.73	
3.46/1.73	(4)
3.46/1.73	Obligation:
3.46/1.73	Q restricted rewrite system:
3.46/1.73	The TRS R consists of the following rules:
3.46/1.73	
3.46/1.73	   a(b(a(b(a(b(b(a(x)))))))) -> b(a(a(b(b(a(a(b(a(b(a(b(x))))))))))))
3.46/1.73	
3.46/1.73	Q is empty.
3.46/1.73	
3.46/1.73	----------------------------------------
3.46/1.73	
3.46/1.73	(5) RFCMatchBoundsTRSProof (EQUIVALENT)
3.46/1.73	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
3.46/1.73	The following rules were used to construct the certificate:
3.46/1.73	
3.46/1.73	   a(b(a(b(a(b(b(a(x)))))))) -> b(a(a(b(b(a(a(b(a(b(a(b(x))))))))))))
3.46/1.73	
3.46/1.73	The certificate found is represented by the following graph.
3.46/1.73	The certificate consists of the following enumerated nodes:
3.46/1.73	4, 7, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100
3.46/1.73	
3.46/1.73	Node 4 is start node and node 7 is final node.
3.46/1.73	
3.46/1.73	Those nodes are connected through the following edges:
3.46/1.73	
3.46/1.73	* 4 to 79 labelled b_1(0)* 7 to 7 labelled #_1(0)* 79 to 80 labelled a_1(0)* 80 to 81 labelled a_1(0)* 81 to 82 labelled b_1(0)* 82 to 83 labelled b_1(0)* 83 to 84 labelled a_1(0)* 84 to 85 labelled a_1(0)* 84 to 90 labelled b_1(1)* 85 to 86 labelled b_1(0)* 86 to 87 labelled a_1(0)* 86 to 90 labelled b_1(1)* 87 to 88 labelled b_1(0)* 88 to 89 labelled a_1(0)* 88 to 90 labelled b_1(1)* 89 to 7 labelled b_1(0)* 90 to 91 labelled a_1(1)* 91 to 92 labelled a_1(1)* 92 to 93 labelled b_1(1)* 93 to 94 labelled b_1(1)* 94 to 95 labelled a_1(1)* 95 to 96 labelled a_1(1)* 95 to 90 labelled b_1(1)* 96 to 97 labelled b_1(1)* 97 to 98 labelled a_1(1)* 97 to 90 labelled b_1(1)* 98 to 99 labelled b_1(1)* 99 to 100 labelled a_1(1)* 99 to 90 labelled b_1(1)* 100 to 7 labelled b_1(1)
3.46/1.73	
3.46/1.73	
3.46/1.73	----------------------------------------
3.46/1.73	
3.46/1.73	(6)
3.46/1.73	YES
3.46/1.77	EOF