3.18/1.65	YES
3.55/1.67	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.55/1.67	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.55/1.67	
3.55/1.67	
3.55/1.67	Termination w.r.t. Q of the given QTRS could be proven:
3.55/1.67	
3.55/1.67	(0) QTRS
3.55/1.67	(1) RFCMatchBoundsTRSProof [EQUIVALENT, 16 ms]
3.55/1.67	(2) YES
3.55/1.67	
3.55/1.67	
3.55/1.67	----------------------------------------
3.55/1.67	
3.55/1.67	(0)
3.55/1.67	Obligation:
3.55/1.67	Q restricted rewrite system:
3.55/1.67	The TRS R consists of the following rules:
3.55/1.67	
3.55/1.67	   a(b(a(a(x1)))) -> c(b(a(b(a(x1)))))
3.55/1.67	   a(c(b(x1))) -> a(a(b(c(b(a(x1))))))
3.55/1.67	
3.55/1.67	Q is empty.
3.55/1.67	
3.55/1.67	----------------------------------------
3.55/1.67	
3.55/1.67	(1) RFCMatchBoundsTRSProof (EQUIVALENT)
3.55/1.67	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 2. This implies Q-termination of R.
3.55/1.67	The following rules were used to construct the certificate:
3.55/1.67	
3.55/1.67	   a(b(a(a(x1)))) -> c(b(a(b(a(x1)))))
3.55/1.67	   a(c(b(x1))) -> a(a(b(c(b(a(x1))))))
3.55/1.67	
3.55/1.67	The certificate found is represented by the following graph.
3.55/1.67	The certificate consists of the following enumerated nodes:
3.55/1.67	1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24
3.55/1.67	
3.55/1.67	Node 1 is start node and node 2 is final node.
3.55/1.67	
3.55/1.67	Those nodes are connected through the following edges:
3.55/1.67	
3.55/1.67	* 1 to 3 labelled c_1(0)* 1 to 7 labelled a_1(0)* 2 to 2 labelled #_1(0)* 3 to 4 labelled b_1(0)* 4 to 5 labelled a_1(0)* 4 to 12 labelled c_1(1)* 5 to 6 labelled b_1(0)* 6 to 2 labelled a_1(0)* 6 to 12 labelled c_1(1)* 6 to 16 labelled a_1(1)* 7 to 8 labelled a_1(0)* 8 to 9 labelled b_1(0)* 9 to 10 labelled c_1(0)* 10 to 11 labelled b_1(0)* 11 to 2 labelled a_1(0)* 11 to 12 labelled c_1(1)* 11 to 16 labelled a_1(1)* 12 to 13 labelled b_1(1)* 13 to 14 labelled a_1(1)* 13 to 12 labelled c_1(1)* 13 to 21 labelled c_1(2)* 14 to 15 labelled b_1(1)* 15 to 2 labelled a_1(1)* 15 to 12 labelled c_1(1)* 15 to 16 labelled a_1(1)* 15 to 17 labelled a_1(1)* 16 to 17 labelled a_1(1)* 17 to 18 labelled b_1(1)* 18 to 19 labelled c_1(1)* 19 to 20 labelled b_1(1)* 20 to 2 labelled a_1(1)* 20 to 12 labelled c_1(1)* 20 to 16 labelled a_1(1)* 21 to 22 labelled b_1(2)* 22 to 23 labelled a_1(2)* 23 to 24 labelled b_1(2)* 24 to 17 labelled a_1(2)
3.55/1.67	
3.55/1.67	
3.55/1.67	----------------------------------------
3.55/1.67	
3.55/1.67	(2)
3.55/1.67	YES
3.55/1.70	EOF