2.93/1.63	YES
2.93/1.64	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
2.93/1.64	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.93/1.64	
2.93/1.64	
2.93/1.64	Termination w.r.t. Q of the given QTRS could be proven:
2.93/1.64	
2.93/1.64	(0) QTRS
2.93/1.64	(1) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
2.93/1.64	(2) YES
2.93/1.64	
2.93/1.64	
2.93/1.64	----------------------------------------
2.93/1.64	
2.93/1.64	(0)
2.93/1.64	Obligation:
2.93/1.64	Q restricted rewrite system:
2.93/1.64	The TRS R consists of the following rules:
2.93/1.64	
2.93/1.64	   a(b(b(a(a(b(x1)))))) -> a(a(b(b(a(b(a(x1)))))))
2.93/1.64	
2.93/1.64	Q is empty.
2.93/1.64	
2.93/1.64	----------------------------------------
2.93/1.64	
2.93/1.64	(1) RFCMatchBoundsTRSProof (EQUIVALENT)
2.93/1.64	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
2.93/1.64	The following rules were used to construct the certificate:
2.93/1.64	
2.93/1.64	   a(b(b(a(a(b(x1)))))) -> a(a(b(b(a(b(a(x1)))))))
2.93/1.64	
2.93/1.64	The certificate found is represented by the following graph.
2.93/1.64	The certificate consists of the following enumerated nodes:
2.93/1.64	1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14
2.93/1.64	
2.93/1.64	Node 1 is start node and node 2 is final node.
2.93/1.64	
2.93/1.64	Those nodes are connected through the following edges:
2.93/1.64	
2.93/1.64	* 1 to 3 labelled a_1(0)* 2 to 2 labelled #_1(0)* 3 to 4 labelled a_1(0)* 4 to 5 labelled b_1(0)* 5 to 6 labelled b_1(0)* 6 to 7 labelled a_1(0)* 7 to 8 labelled b_1(0)* 8 to 2 labelled a_1(0)* 8 to 9 labelled a_1(1)* 9 to 10 labelled a_1(1)* 10 to 11 labelled b_1(1)* 11 to 12 labelled b_1(1)* 12 to 13 labelled a_1(1)* 13 to 14 labelled b_1(1)* 14 to 2 labelled a_1(1)* 14 to 9 labelled a_1(1)
2.93/1.64	
2.93/1.64	
2.93/1.64	----------------------------------------
2.93/1.64	
2.93/1.64	(2)
2.93/1.64	YES
3.31/1.69	EOF