3.80/1.83	YES
4.18/1.85	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
4.18/1.85	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.18/1.85	
4.18/1.85	
4.18/1.85	Termination w.r.t. Q of the given QTRS could be proven:
4.18/1.85	
4.18/1.85	(0) QTRS
4.18/1.85	(1) QTRS Reverse [EQUIVALENT, 0 ms]
4.18/1.85	(2) QTRS
4.18/1.85	(3) Strip Symbols Proof [SOUND, 0 ms]
4.18/1.85	(4) QTRS
4.18/1.85	(5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
4.18/1.85	(6) YES
4.18/1.85	
4.18/1.85	
4.18/1.85	----------------------------------------
4.18/1.85	
4.18/1.85	(0)
4.18/1.85	Obligation:
4.18/1.85	Q restricted rewrite system:
4.18/1.85	The TRS R consists of the following rules:
4.18/1.85	
4.18/1.85	   a(b(b(a(a(b(b(a(a(b(a(x1))))))))))) -> a(b(a(a(b(b(a(a(b(b(a(a(b(x1)))))))))))))
4.18/1.85	
4.18/1.85	Q is empty.
4.18/1.85	
4.18/1.85	----------------------------------------
4.18/1.85	
4.18/1.85	(1) QTRS Reverse (EQUIVALENT)
4.18/1.85	We applied the QTRS Reverse Processor [REVERSE].
4.18/1.85	----------------------------------------
4.18/1.85	
4.18/1.85	(2)
4.18/1.85	Obligation:
4.18/1.85	Q restricted rewrite system:
4.18/1.85	The TRS R consists of the following rules:
4.18/1.85	
4.18/1.85	   a(b(a(a(b(b(a(a(b(b(a(x1))))))))))) -> b(a(a(b(b(a(a(b(b(a(a(b(a(x1)))))))))))))
4.18/1.85	
4.18/1.85	Q is empty.
4.18/1.85	
4.18/1.85	----------------------------------------
4.18/1.85	
4.18/1.85	(3) Strip Symbols Proof (SOUND)
4.18/1.85	We were given the following TRS:
4.18/1.85	
4.18/1.85	   a(b(a(a(b(b(a(a(b(b(a(x1))))))))))) -> b(a(a(b(b(a(a(b(b(a(a(b(a(x1)))))))))))))
4.18/1.85	
4.18/1.85	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
4.18/1.85	
4.18/1.85	   a(b(a(a(b(b(a(a(b(b(x)))))))))) -> b(a(a(b(b(a(a(b(b(a(a(b(x))))))))))))
4.18/1.85	
4.18/1.85	----------------------------------------
4.18/1.85	
4.18/1.85	(4)
4.18/1.85	Obligation:
4.18/1.85	Q restricted rewrite system:
4.18/1.85	The TRS R consists of the following rules:
4.18/1.85	
4.18/1.85	   a(b(a(a(b(b(a(a(b(b(x)))))))))) -> b(a(a(b(b(a(a(b(b(a(a(b(x))))))))))))
4.18/1.85	
4.18/1.85	Q is empty.
4.18/1.85	
4.18/1.85	----------------------------------------
4.18/1.85	
4.18/1.85	(5) RFCMatchBoundsTRSProof (EQUIVALENT)
4.18/1.85	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 2. This implies Q-termination of R.
4.18/1.85	The following rules were used to construct the certificate:
4.18/1.85	
4.18/1.85	   a(b(a(a(b(b(a(a(b(b(x)))))))))) -> b(a(a(b(b(a(a(b(b(a(a(b(x))))))))))))
4.18/1.85	
4.18/1.85	The certificate found is represented by the following graph.
4.18/1.85	The certificate consists of the following enumerated nodes:
4.18/1.85	29, 30, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86
4.18/1.85	
4.18/1.85	Node 29 is start node and node 30 is final node.
4.18/1.85	
4.18/1.85	Those nodes are connected through the following edges:
4.18/1.85	
4.18/1.85	* 29 to 43 labelled b_1(0)* 30 to 30 labelled #_1(0)* 43 to 44 labelled a_1(0)* 44 to 45 labelled a_1(0)* 45 to 46 labelled b_1(0)* 46 to 47 labelled b_1(0)* 47 to 48 labelled a_1(0)* 48 to 49 labelled a_1(0)* 49 to 50 labelled b_1(0)* 50 to 51 labelled b_1(0)* 51 to 52 labelled a_1(0)* 51 to 65 labelled b_1(1)* 52 to 53 labelled a_1(0)* 52 to 54 labelled b_1(1)* 53 to 30 labelled b_1(0)* 54 to 55 labelled a_1(1)* 55 to 56 labelled a_1(1)* 56 to 57 labelled b_1(1)* 57 to 58 labelled b_1(1)* 58 to 59 labelled a_1(1)* 59 to 60 labelled a_1(1)* 60 to 61 labelled b_1(1)* 61 to 62 labelled b_1(1)* 62 to 63 labelled a_1(1)* 62 to 76 labelled b_1(2)* 63 to 64 labelled a_1(1)* 63 to 54 labelled b_1(1)* 64 to 30 labelled b_1(1)* 65 to 66 labelled a_1(1)* 66 to 67 labelled a_1(1)* 67 to 68 labelled b_1(1)* 68 to 69 labelled b_1(1)* 69 to 70 labelled a_1(1)* 70 to 71 labelled a_1(1)* 71 to 72 labelled b_1(1)* 72 to 73 labelled b_1(1)* 73 to 74 labelled a_1(1)* 73 to 76 labelled b_1(2)* 74 to 75 labelled a_1(1)* 74 to 54 labelled b_1(1)* 75 to 62 labelled b_1(1)* 76 to 77 labelled a_1(2)* 77 to 78 labelled a_1(2)* 78 to 79 labelled b_1(2)* 79 to 80 labelled b_1(2)* 80 to 81 labelled a_1(2)* 81 to 82 labelled a_1(2)* 82 to 83 labelled b_1(2)* 83 to 84 labelled b_1(2)* 84 to 85 labelled a_1(2)* 84 to 76 labelled b_1(2)* 85 to 86 labelled a_1(2)* 85 to 54 labelled b_1(1)* 86 to 62 labelled b_1(2)
4.18/1.85	
4.18/1.85	
4.18/1.85	----------------------------------------
4.18/1.85	
4.18/1.85	(6)
4.18/1.85	YES
4.18/1.87	EOF