3.12/1.65	YES
3.12/1.67	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.12/1.67	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.12/1.67	
3.12/1.67	
3.12/1.67	Termination w.r.t. Q of the given QTRS could be proven:
3.12/1.67	
3.12/1.67	(0) QTRS
3.12/1.67	(1) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
3.12/1.67	(2) YES
3.12/1.67	
3.12/1.67	
3.12/1.67	----------------------------------------
3.12/1.67	
3.12/1.67	(0)
3.12/1.67	Obligation:
3.12/1.67	Q restricted rewrite system:
3.12/1.67	The TRS R consists of the following rules:
3.12/1.67	
3.12/1.67	   a(a(x1)) -> c(b(x1))
3.12/1.67	   b(b(x1)) -> a(c(x1))
3.12/1.67	   c(c(x1)) -> b(a(x1))
3.12/1.67	
3.12/1.67	Q is empty.
3.12/1.67	
3.12/1.67	----------------------------------------
3.12/1.67	
3.12/1.67	(1) RFCMatchBoundsTRSProof (EQUIVALENT)
3.12/1.67	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
3.12/1.67	The following rules were used to construct the certificate:
3.12/1.67	
3.12/1.67	   a(a(x1)) -> c(b(x1))
3.12/1.67	   b(b(x1)) -> a(c(x1))
3.12/1.67	   c(c(x1)) -> b(a(x1))
3.12/1.67	
3.12/1.67	The certificate found is represented by the following graph.
3.12/1.67	The certificate consists of the following enumerated nodes:
3.12/1.67	1, 2, 3, 4, 5, 6, 7, 8
3.12/1.67	
3.12/1.67	Node 1 is start node and node 2 is final node.
3.12/1.67	
3.12/1.67	Those nodes are connected through the following edges:
3.12/1.67	
3.12/1.67	* 1 to 3 labelled c_1(0)* 1 to 4 labelled a_1(0)* 1 to 5 labelled b_1(0)* 2 to 2 labelled #_1(0)* 3 to 2 labelled b_1(0)* 3 to 6 labelled a_1(1)* 4 to 2 labelled c_1(0)* 4 to 7 labelled b_1(1)* 5 to 2 labelled a_1(0)* 5 to 8 labelled c_1(1)* 6 to 2 labelled c_1(1)* 6 to 7 labelled b_1(1)* 7 to 2 labelled a_1(1)* 7 to 8 labelled c_1(1)* 8 to 2 labelled b_1(1)* 8 to 6 labelled a_1(1)
3.12/1.67	
3.12/1.67	
3.12/1.67	----------------------------------------
3.12/1.67	
3.12/1.67	(2)
3.12/1.67	YES
3.25/1.69	EOF