3.20/1.66	YES
3.56/1.67	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.56/1.67	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.56/1.67	
3.56/1.67	
3.56/1.67	Termination w.r.t. Q of the given QTRS could be proven:
3.56/1.67	
3.56/1.67	(0) QTRS
3.56/1.67	(1) RFCMatchBoundsTRSProof [EQUIVALENT, 9 ms]
3.56/1.67	(2) YES
3.56/1.67	
3.56/1.67	
3.56/1.67	----------------------------------------
3.56/1.67	
3.56/1.67	(0)
3.56/1.67	Obligation:
3.56/1.67	Q restricted rewrite system:
3.56/1.67	The TRS R consists of the following rules:
3.56/1.67	
3.56/1.67	   b(a(b(b(a(b(a(x1))))))) -> a(b(a(a(b(b(a(b(b(a(x1))))))))))
3.56/1.67	
3.56/1.67	Q is empty.
3.56/1.67	
3.56/1.67	----------------------------------------
3.56/1.67	
3.56/1.67	(1) RFCMatchBoundsTRSProof (EQUIVALENT)
3.56/1.67	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
3.56/1.67	The following rules were used to construct the certificate:
3.56/1.67	
3.56/1.67	   b(a(b(b(a(b(a(x1))))))) -> a(b(a(a(b(b(a(b(b(a(x1))))))))))
3.56/1.67	
3.56/1.67	The certificate found is represented by the following graph.
3.56/1.67	The certificate consists of the following enumerated nodes:
3.56/1.67	1, 5, 7, 16, 17, 18, 19, 20, 21, 22, 23, 41, 42, 43, 44, 45, 46, 47, 48, 49
3.56/1.67	
3.56/1.67	Node 1 is start node and node 5 is final node.
3.56/1.67	
3.56/1.67	Those nodes are connected through the following edges:
3.56/1.67	
3.56/1.67	* 1 to 7 labelled a_1(0)* 5 to 5 labelled #_1(0)* 7 to 16 labelled b_1(0)* 16 to 17 labelled a_1(0)* 17 to 18 labelled a_1(0)* 18 to 19 labelled b_1(0)* 19 to 20 labelled b_1(0)* 19 to 41 labelled a_1(1)* 20 to 21 labelled a_1(0)* 21 to 22 labelled b_1(0)* 22 to 23 labelled b_1(0)* 22 to 41 labelled a_1(1)* 23 to 5 labelled a_1(0)* 41 to 42 labelled b_1(1)* 42 to 43 labelled a_1(1)* 43 to 44 labelled a_1(1)* 44 to 45 labelled b_1(1)* 45 to 46 labelled b_1(1)* 45 to 41 labelled a_1(1)* 46 to 47 labelled a_1(1)* 47 to 48 labelled b_1(1)* 48 to 49 labelled b_1(1)* 48 to 41 labelled a_1(1)* 49 to 5 labelled a_1(1)
3.56/1.67	
3.56/1.67	
3.56/1.67	----------------------------------------
3.56/1.67	
3.56/1.67	(2)
3.56/1.67	YES
3.63/1.71	EOF