3.31/1.71	YES
3.31/1.72	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.31/1.72	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.31/1.72	
3.31/1.72	
3.31/1.72	Termination w.r.t. Q of the given QTRS could be proven:
3.31/1.72	
3.31/1.72	(0) QTRS
3.31/1.72	(1) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
3.31/1.72	(2) YES
3.31/1.72	
3.31/1.72	
3.31/1.72	----------------------------------------
3.31/1.72	
3.31/1.72	(0)
3.31/1.72	Obligation:
3.31/1.72	Q restricted rewrite system:
3.31/1.72	The TRS R consists of the following rules:
3.31/1.72	
3.31/1.72	   b(a(a(b(b(a(x1)))))) -> a(a(b(b(a(a(a(b(b(x1)))))))))
3.31/1.72	
3.31/1.72	Q is empty.
3.31/1.72	
3.31/1.72	----------------------------------------
3.31/1.72	
3.31/1.72	(1) RFCMatchBoundsTRSProof (EQUIVALENT)
3.31/1.72	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 2. This implies Q-termination of R.
3.31/1.72	The following rules were used to construct the certificate:
3.31/1.72	
3.31/1.72	   b(a(a(b(b(a(x1)))))) -> a(a(b(b(a(a(a(b(b(x1)))))))))
3.31/1.72	
3.31/1.72	The certificate found is represented by the following graph.
3.31/1.72	The certificate consists of the following enumerated nodes:
3.31/1.72	1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34
3.31/1.72	
3.31/1.72	Node 1 is start node and node 2 is final node.
3.31/1.72	
3.31/1.72	Those nodes are connected through the following edges:
3.31/1.72	
3.31/1.72	* 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 a_1(0)* 8 to 9 labelled a_1(0)* 9 to 10 labelled b_1(0)* 9 to 19 labelled a_1(1)* 10 to 2 labelled b_1(0)* 10 to 11 labelled a_1(1)* 11 to 12 labelled a_1(1)* 12 to 13 labelled b_1(1)* 13 to 14 labelled b_1(1)* 14 to 15 labelled a_1(1)* 15 to 16 labelled a_1(1)* 16 to 17 labelled a_1(1)* 17 to 18 labelled b_1(1)* 17 to 27 labelled a_1(2)* 18 to 2 labelled b_1(1)* 18 to 11 labelled a_1(1)* 19 to 20 labelled a_1(1)* 20 to 21 labelled b_1(1)* 21 to 22 labelled b_1(1)* 22 to 23 labelled a_1(1)* 23 to 24 labelled a_1(1)* 24 to 25 labelled a_1(1)* 25 to 26 labelled b_1(1)* 25 to 27 labelled a_1(2)* 26 to 15 labelled b_1(1)* 26 to 11 labelled a_1(1)* 27 to 28 labelled a_1(2)* 28 to 29 labelled b_1(2)* 29 to 30 labelled b_1(2)* 30 to 31 labelled a_1(2)* 31 to 32 labelled a_1(2)* 32 to 33 labelled a_1(2)* 33 to 34 labelled b_1(2)* 33 to 27 labelled a_1(2)* 34 to 15 labelled b_1(2)* 34 to 11 labelled a_1(1)
3.31/1.72	
3.31/1.72	
3.31/1.72	----------------------------------------
3.31/1.72	
3.31/1.72	(2)
3.31/1.72	YES
3.46/1.76	EOF