3.52/1.71	YES
3.52/1.73	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.52/1.73	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.52/1.73	
3.52/1.73	
3.52/1.73	Termination w.r.t. Q of the given QTRS could be proven:
3.52/1.73	
3.52/1.73	(0) QTRS
3.52/1.73	(1) QTRS Reverse [EQUIVALENT, 0 ms]
3.52/1.73	(2) QTRS
3.52/1.73	(3) Strip Symbols Proof [SOUND, 0 ms]
3.52/1.73	(4) QTRS
3.52/1.73	(5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
3.52/1.73	(6) YES
3.52/1.73	
3.52/1.73	
3.52/1.73	----------------------------------------
3.52/1.73	
3.52/1.73	(0)
3.52/1.73	Obligation:
3.52/1.73	Q restricted rewrite system:
3.52/1.73	The TRS R consists of the following rules:
3.52/1.73	
3.52/1.73	   a(b(a(a(b(a(b(a(b(a(b(a(x1)))))))))))) -> a(a(b(a(b(a(b(a(b(a(b(a(a(b(x1))))))))))))))
3.52/1.73	
3.52/1.73	Q is empty.
3.52/1.73	
3.52/1.73	----------------------------------------
3.52/1.73	
3.52/1.73	(1) QTRS Reverse (EQUIVALENT)
3.52/1.73	We applied the QTRS Reverse Processor [REVERSE].
3.52/1.73	----------------------------------------
3.52/1.73	
3.52/1.73	(2)
3.52/1.73	Obligation:
3.52/1.73	Q restricted rewrite system:
3.52/1.73	The TRS R consists of the following rules:
3.52/1.73	
3.52/1.73	   a(b(a(b(a(b(a(b(a(a(b(a(x1)))))))))))) -> b(a(a(b(a(b(a(b(a(b(a(b(a(a(x1))))))))))))))
3.52/1.73	
3.52/1.73	Q is empty.
3.52/1.73	
3.52/1.73	----------------------------------------
3.52/1.73	
3.52/1.73	(3) Strip Symbols Proof (SOUND)
3.52/1.73	We were given the following TRS:
3.52/1.73	
3.52/1.73	   a(b(a(b(a(b(a(b(a(a(b(a(x1)))))))))))) -> b(a(a(b(a(b(a(b(a(b(a(b(a(a(x1))))))))))))))
3.52/1.73	
3.52/1.73	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
3.52/1.73	
3.52/1.73	   a(b(a(b(a(b(a(b(a(a(b(x))))))))))) -> b(a(a(b(a(b(a(b(a(b(a(b(a(x)))))))))))))
3.52/1.73	
3.52/1.73	----------------------------------------
3.52/1.73	
3.52/1.73	(4)
3.52/1.73	Obligation:
3.52/1.73	Q restricted rewrite system:
3.52/1.73	The TRS R consists of the following rules:
3.52/1.73	
3.52/1.73	   a(b(a(b(a(b(a(b(a(a(b(x))))))))))) -> b(a(a(b(a(b(a(b(a(b(a(b(a(x)))))))))))))
3.52/1.73	
3.52/1.73	Q is empty.
3.52/1.73	
3.52/1.73	----------------------------------------
3.52/1.73	
3.52/1.73	(5) RFCMatchBoundsTRSProof (EQUIVALENT)
3.52/1.73	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
3.52/1.73	The following rules were used to construct the certificate:
3.52/1.73	
3.52/1.73	   a(b(a(b(a(b(a(b(a(a(b(x))))))))))) -> b(a(a(b(a(b(a(b(a(b(a(b(a(x)))))))))))))
3.52/1.73	
3.52/1.73	The certificate found is represented by the following graph.
3.52/1.73	The certificate consists of the following enumerated nodes:
3.52/1.73	7, 8, 22, 23, 24, 26, 27, 29, 30, 32, 34, 36, 38, 40, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84
3.52/1.73	
3.52/1.73	Node 7 is start node and node 8 is final node.
3.52/1.73	
3.52/1.73	Those nodes are connected through the following edges:
3.52/1.73	
3.52/1.73	* 7 to 22 labelled b_1(0)* 8 to 8 labelled #_1(0)* 22 to 23 labelled a_1(0)* 23 to 24 labelled a_1(0)* 24 to 26 labelled b_1(0)* 26 to 27 labelled a_1(0)* 26 to 73 labelled b_1(1)* 27 to 29 labelled b_1(0)* 29 to 30 labelled a_1(0)* 29 to 73 labelled b_1(1)* 30 to 32 labelled b_1(0)* 32 to 34 labelled a_1(0)* 32 to 73 labelled b_1(1)* 34 to 36 labelled b_1(0)* 36 to 38 labelled a_1(0)* 36 to 73 labelled b_1(1)* 38 to 40 labelled b_1(0)* 40 to 8 labelled a_1(0)* 40 to 73 labelled b_1(1)* 73 to 74 labelled a_1(1)* 74 to 75 labelled a_1(1)* 75 to 76 labelled b_1(1)* 76 to 77 labelled a_1(1)* 76 to 73 labelled b_1(1)* 77 to 78 labelled b_1(1)* 78 to 79 labelled a_1(1)* 78 to 73 labelled b_1(1)* 79 to 80 labelled b_1(1)* 80 to 81 labelled a_1(1)* 80 to 73 labelled b_1(1)* 81 to 82 labelled b_1(1)* 82 to 83 labelled a_1(1)* 82 to 73 labelled b_1(1)* 83 to 84 labelled b_1(1)* 84 to 8 labelled a_1(1)* 84 to 73 labelled b_1(1)
3.52/1.73	
3.52/1.73	
3.52/1.73	----------------------------------------
3.52/1.73	
3.52/1.73	(6)
3.52/1.73	YES
3.68/1.77	EOF