3.31/1.61	YES
3.31/1.63	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.31/1.63	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.31/1.63	
3.31/1.63	
3.31/1.63	Termination w.r.t. Q of the given QTRS could be proven:
3.31/1.63	
3.31/1.63	(0) QTRS
3.31/1.63	(1) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
3.31/1.63	(2) YES
3.31/1.63	
3.31/1.63	
3.31/1.63	----------------------------------------
3.31/1.63	
3.31/1.63	(0)
3.31/1.63	Obligation:
3.31/1.63	Q restricted rewrite system:
3.31/1.63	The TRS R consists of the following rules:
3.31/1.63	
3.31/1.63	   a(b(x1)) -> b(a(x1))
3.31/1.63	   b(a(x1)) -> a(c(b(x1)))
3.31/1.63	
3.31/1.63	Q is empty.
3.31/1.63	
3.31/1.63	----------------------------------------
3.31/1.63	
3.31/1.63	(1) RFCMatchBoundsTRSProof (EQUIVALENT)
3.31/1.63	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 2. This implies Q-termination of R.
3.31/1.63	The following rules were used to construct the certificate:
3.31/1.63	
3.31/1.63	   a(b(x1)) -> b(a(x1))
3.31/1.63	   b(a(x1)) -> a(c(b(x1)))
3.31/1.63	
3.31/1.63	The certificate found is represented by the following graph.
3.31/1.63	The certificate consists of the following enumerated nodes:
3.31/1.63	1, 2, 3, 4, 5, 6, 7, 8, 9, 10
3.31/1.63	
3.31/1.63	Node 1 is start node and node 2 is final node.
3.31/1.63	
3.31/1.63	Those nodes are connected through the following edges:
3.31/1.63	
3.31/1.63	* 1 to 3 labelled b_1(0)* 1 to 4 labelled a_1(0)* 1 to 6 labelled a_1(1)* 2 to 2 labelled #_1(0)* 3 to 2 labelled a_1(0)* 3 to 8 labelled b_1(1)* 3 to 9 labelled a_1(2)* 4 to 5 labelled c_1(0)* 5 to 2 labelled b_1(0)* 5 to 6 labelled a_1(1)* 6 to 7 labelled c_1(1)* 7 to 2 labelled b_1(1)* 7 to 6 labelled a_1(1)* 7 to 9 labelled b_1(1)* 8 to 2 labelled a_1(1)* 8 to 8 labelled b_1(1)* 8 to 9 labelled a_1(2)* 9 to 10 labelled c_1(2)* 10 to 2 labelled b_1(2)* 10 to 6 labelled a_1(1)* 10 to 9 labelled b_1(2)
3.31/1.63	
3.31/1.63	
3.31/1.63	----------------------------------------
3.31/1.63	
3.31/1.63	(2)
3.31/1.63	YES
3.31/1.67	EOF