3.23/1.63	YES
3.57/1.67	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.57/1.67	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.57/1.67	
3.57/1.67	
3.57/1.67	Termination w.r.t. Q of the given QTRS could be proven:
3.57/1.67	
3.57/1.67	(0) QTRS
3.57/1.67	(1) QTRS Reverse [EQUIVALENT, 0 ms]
3.57/1.67	(2) QTRS
3.57/1.67	(3) Strip Symbols Proof [SOUND, 0 ms]
3.57/1.67	(4) QTRS
3.57/1.67	(5) RFCMatchBoundsTRSProof [EQUIVALENT, 3 ms]
3.57/1.67	(6) YES
3.57/1.67	
3.57/1.67	
3.57/1.67	----------------------------------------
3.57/1.67	
3.57/1.67	(0)
3.57/1.67	Obligation:
3.57/1.67	Q restricted rewrite system:
3.57/1.67	The TRS R consists of the following rules:
3.57/1.67	
3.57/1.67	   a(b(a(a(a(a(a(a(a(x1))))))))) -> a(a(a(a(a(a(a(a(b(a(a(a(b(x1)))))))))))))
3.57/1.67	
3.57/1.67	Q is empty.
3.57/1.67	
3.57/1.67	----------------------------------------
3.57/1.67	
3.57/1.67	(1) QTRS Reverse (EQUIVALENT)
3.57/1.67	We applied the QTRS Reverse Processor [REVERSE].
3.57/1.67	----------------------------------------
3.57/1.67	
3.57/1.67	(2)
3.57/1.67	Obligation:
3.57/1.67	Q restricted rewrite system:
3.57/1.67	The TRS R consists of the following rules:
3.57/1.67	
3.57/1.67	   a(a(a(a(a(a(a(b(a(x1))))))))) -> b(a(a(a(b(a(a(a(a(a(a(a(a(x1)))))))))))))
3.57/1.67	
3.57/1.67	Q is empty.
3.57/1.67	
3.57/1.67	----------------------------------------
3.57/1.67	
3.57/1.67	(3) Strip Symbols Proof (SOUND)
3.57/1.67	We were given the following TRS:
3.57/1.67	
3.57/1.67	   a(a(a(a(a(a(a(b(a(x1))))))))) -> b(a(a(a(b(a(a(a(a(a(a(a(a(x1)))))))))))))
3.57/1.67	
3.57/1.67	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
3.57/1.67	
3.57/1.67	   a(a(a(a(a(a(a(b(x)))))))) -> b(a(a(a(b(a(a(a(a(a(a(a(x))))))))))))
3.57/1.67	
3.57/1.67	----------------------------------------
3.57/1.67	
3.57/1.67	(4)
3.57/1.67	Obligation:
3.57/1.67	Q restricted rewrite system:
3.57/1.67	The TRS R consists of the following rules:
3.57/1.67	
3.57/1.67	   a(a(a(a(a(a(a(b(x)))))))) -> b(a(a(a(b(a(a(a(a(a(a(a(x))))))))))))
3.57/1.67	
3.57/1.67	Q is empty.
3.57/1.67	
3.57/1.67	----------------------------------------
3.57/1.67	
3.57/1.67	(5) RFCMatchBoundsTRSProof (EQUIVALENT)
3.57/1.67	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
3.57/1.67	The following rules were used to construct the certificate:
3.57/1.67	
3.57/1.67	   a(a(a(a(a(a(a(b(x)))))))) -> b(a(a(a(b(a(a(a(a(a(a(a(x))))))))))))
3.57/1.67	
3.57/1.67	The certificate found is represented by the following graph.
3.57/1.67	The certificate consists of the following enumerated nodes:
3.57/1.67	7, 8, 35, 38, 40, 42, 45, 47, 49, 51, 52, 53, 54, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121
3.57/1.67	
3.57/1.67	Node 7 is start node and node 8 is final node.
3.57/1.67	
3.57/1.67	Those nodes are connected through the following edges:
3.57/1.67	
3.57/1.67	* 7 to 35 labelled b_1(0)* 8 to 8 labelled #_1(0)* 35 to 38 labelled a_1(0)* 38 to 40 labelled a_1(0)* 40 to 42 labelled a_1(0)* 42 to 45 labelled b_1(0)* 45 to 47 labelled a_1(0)* 45 to 111 labelled b_1(1)* 47 to 49 labelled a_1(0)* 47 to 111 labelled b_1(1)* 49 to 51 labelled a_1(0)* 49 to 111 labelled b_1(1)* 51 to 52 labelled a_1(0)* 51 to 111 labelled b_1(1)* 52 to 53 labelled a_1(0)* 52 to 111 labelled b_1(1)* 53 to 54 labelled a_1(0)* 53 to 111 labelled b_1(1)* 54 to 8 labelled a_1(0)* 54 to 111 labelled b_1(1)* 111 to 112 labelled a_1(1)* 112 to 113 labelled a_1(1)* 113 to 114 labelled a_1(1)* 114 to 115 labelled b_1(1)* 115 to 116 labelled a_1(1)* 115 to 111 labelled b_1(1)* 116 to 117 labelled a_1(1)* 116 to 111 labelled b_1(1)* 117 to 118 labelled a_1(1)* 117 to 111 labelled b_1(1)* 118 to 119 labelled a_1(1)* 118 to 111 labelled b_1(1)* 119 to 120 labelled a_1(1)* 119 to 111 labelled b_1(1)* 120 to 121 labelled a_1(1)* 120 to 111 labelled b_1(1)* 121 to 8 labelled a_1(1)* 121 to 111 labelled b_1(1)
3.57/1.67	
3.57/1.67	
3.57/1.67	----------------------------------------
3.57/1.67	
3.57/1.67	(6)
3.57/1.67	YES
3.70/1.70	EOF