3.73/1.68	YES
4.00/2.27	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
4.00/2.27	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.00/2.27	
4.00/2.27	
4.00/2.27	Termination w.r.t. Q of the given QTRS could be proven:
4.00/2.27	
4.00/2.27	(0) QTRS
4.00/2.27	(1) QTRS Reverse [EQUIVALENT, 0 ms]
4.00/2.27	(2) QTRS
4.00/2.27	(3) Strip Symbols Proof [SOUND, 0 ms]
4.00/2.27	(4) QTRS
4.00/2.27	(5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
4.00/2.27	(6) YES
4.00/2.27	
4.00/2.27	
4.00/2.27	----------------------------------------
4.00/2.27	
4.00/2.27	(0)
4.00/2.27	Obligation:
4.00/2.27	Q restricted rewrite system:
4.00/2.27	The TRS R consists of the following rules:
4.00/2.27	
4.00/2.27	   a(b(a(b(a(a(a(a(x1)))))))) -> a(a(a(a(a(b(a(b(a(a(a(b(a(b(x1))))))))))))))
4.00/2.27	
4.00/2.27	Q is empty.
4.00/2.27	
4.00/2.27	----------------------------------------
4.00/2.27	
4.00/2.27	(1) QTRS Reverse (EQUIVALENT)
4.00/2.27	We applied the QTRS Reverse Processor [REVERSE].
4.00/2.27	----------------------------------------
4.00/2.27	
4.00/2.27	(2)
4.00/2.27	Obligation:
4.00/2.27	Q restricted rewrite system:
4.00/2.27	The TRS R consists of the following rules:
4.00/2.27	
4.00/2.27	   a(a(a(a(b(a(b(a(x1)))))))) -> b(a(b(a(a(a(b(a(b(a(a(a(a(a(x1))))))))))))))
4.00/2.27	
4.00/2.27	Q is empty.
4.00/2.27	
4.00/2.27	----------------------------------------
4.00/2.27	
4.00/2.27	(3) Strip Symbols Proof (SOUND)
4.00/2.27	We were given the following TRS:
4.00/2.27	
4.00/2.27	   a(a(a(a(b(a(b(a(x1)))))))) -> b(a(b(a(a(a(b(a(b(a(a(a(a(a(x1))))))))))))))
4.00/2.27	
4.00/2.27	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
4.00/2.27	
4.00/2.27	   a(a(a(a(b(a(b(x))))))) -> b(a(b(a(a(a(b(a(b(a(a(a(a(x)))))))))))))
4.00/2.27	
4.00/2.27	----------------------------------------
4.00/2.27	
4.00/2.27	(4)
4.00/2.27	Obligation:
4.00/2.27	Q restricted rewrite system:
4.00/2.27	The TRS R consists of the following rules:
4.00/2.27	
4.00/2.27	   a(a(a(a(b(a(b(x))))))) -> b(a(b(a(a(a(b(a(b(a(a(a(a(x)))))))))))))
4.00/2.27	
4.00/2.27	Q is empty.
4.00/2.27	
4.00/2.27	----------------------------------------
4.00/2.27	
4.00/2.27	(5) RFCMatchBoundsTRSProof (EQUIVALENT)
4.00/2.27	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
4.00/2.27	The following rules were used to construct the certificate:
4.00/2.27	
4.00/2.27	   a(a(a(a(b(a(b(x))))))) -> b(a(b(a(a(a(b(a(b(a(a(a(a(x)))))))))))))
4.00/2.27	
4.00/2.27	The certificate found is represented by the following graph.
4.00/2.27	The certificate consists of the following enumerated nodes:
4.00/2.27	45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160
4.00/2.27	
4.00/2.27	Node 45 is start node and node 46 is final node.
4.00/2.27	
4.00/2.27	Those nodes are connected through the following edges:
4.00/2.27	
4.00/2.27	* 45 to 47 labelled b_1(0)* 46 to 46 labelled #_1(0)* 47 to 48 labelled a_1(0)* 48 to 49 labelled b_1(0)* 49 to 50 labelled a_1(0)* 50 to 51 labelled a_1(0)* 51 to 52 labelled a_1(0)* 52 to 53 labelled b_1(0)* 53 to 54 labelled a_1(0)* 54 to 55 labelled b_1(0)* 55 to 56 labelled a_1(0)* 55 to 149 labelled b_1(1)* 56 to 57 labelled a_1(0)* 56 to 149 labelled b_1(1)* 57 to 58 labelled a_1(0)* 57 to 149 labelled b_1(1)* 58 to 46 labelled a_1(0)* 58 to 149 labelled b_1(1)* 149 to 150 labelled a_1(1)* 150 to 151 labelled b_1(1)* 151 to 152 labelled a_1(1)* 152 to 153 labelled a_1(1)* 153 to 154 labelled a_1(1)* 154 to 155 labelled b_1(1)* 155 to 156 labelled a_1(1)* 156 to 157 labelled b_1(1)* 157 to 158 labelled a_1(1)* 157 to 149 labelled b_1(1)* 158 to 159 labelled a_1(1)* 158 to 149 labelled b_1(1)* 159 to 160 labelled a_1(1)* 159 to 149 labelled b_1(1)* 160 to 46 labelled a_1(1)* 160 to 149 labelled b_1(1)
4.00/2.27	
4.00/2.27	
4.00/2.27	----------------------------------------
4.00/2.27	
4.00/2.27	(6)
4.00/2.27	YES
4.02/2.43	EOF