3.25/1.72	YES
3.25/1.74	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.25/1.74	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.25/1.74	
3.25/1.74	
3.25/1.74	Termination w.r.t. Q of the given QTRS could be proven:
3.25/1.74	
3.25/1.74	(0) QTRS
3.25/1.74	(1) RFCMatchBoundsTRSProof [EQUIVALENT, 13 ms]
3.25/1.74	(2) YES
3.25/1.74	
3.25/1.74	
3.25/1.74	----------------------------------------
3.25/1.74	
3.25/1.74	(0)
3.25/1.74	Obligation:
3.25/1.74	Q restricted rewrite system:
3.25/1.74	The TRS R consists of the following rules:
3.25/1.74	
3.25/1.74	   a(b(x1)) -> b(a(x1))
3.25/1.74	   b(a(x1)) -> a(a(c(b(x1))))
3.25/1.74	
3.25/1.74	Q is empty.
3.25/1.74	
3.25/1.74	----------------------------------------
3.25/1.74	
3.25/1.74	(1) RFCMatchBoundsTRSProof (EQUIVALENT)
3.25/1.74	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 3. This implies Q-termination of R.
3.25/1.74	The following rules were used to construct the certificate:
3.25/1.74	
3.25/1.74	   a(b(x1)) -> b(a(x1))
3.25/1.74	   b(a(x1)) -> a(a(c(b(x1))))
3.25/1.74	
3.25/1.74	The certificate found is represented by the following graph.
3.25/1.74	The certificate consists of the following enumerated nodes:
3.25/1.74	1, 3, 5, 7, 9, 11, 14, 16, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29
3.25/1.74	
3.25/1.74	Node 1 is start node and node 3 is final node.
3.25/1.74	
3.25/1.74	Those nodes are connected through the following edges:
3.25/1.74	
3.25/1.74	* 1 to 5 labelled b_1(0)* 1 to 7 labelled a_1(0)* 1 to 14 labelled a_1(1)* 3 to 3 labelled #_1(0)* 5 to 3 labelled a_1(0)* 5 to 20 labelled b_1(1)* 5 to 21 labelled a_1(2)* 7 to 9 labelled a_1(0)* 9 to 11 labelled c_1(0)* 11 to 3 labelled b_1(0)* 11 to 14 labelled a_1(1)* 14 to 16 labelled a_1(1)* 16 to 18 labelled c_1(1)* 18 to 3 labelled b_1(1)* 18 to 14 labelled a_1(1)* 18 to 21 labelled b_1(1)* 18 to 24 labelled a_1(2)* 20 to 3 labelled a_1(1)* 20 to 20 labelled b_1(1)* 20 to 21 labelled a_1(2)* 21 to 22 labelled a_1(2)* 22 to 23 labelled c_1(2)* 23 to 3 labelled b_1(2)* 23 to 14 labelled a_1(1)* 23 to 21 labelled b_1(2)* 23 to 27 labelled a_1(3)* 24 to 25 labelled a_1(2)* 25 to 26 labelled c_1(2)* 26 to 22 labelled b_1(2)* 27 to 28 labelled a_1(3)* 28 to 29 labelled c_1(3)* 29 to 22 labelled b_1(3)
3.25/1.74	
3.25/1.74	
3.25/1.74	----------------------------------------
3.25/1.74	
3.25/1.74	(2)
3.25/1.74	YES
3.55/1.79	EOF