2.96/1.69	YES
3.22/1.71	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.22/1.71	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.22/1.71	
3.22/1.71	
3.22/1.71	Termination w.r.t. Q of the given QTRS could be proven:
3.22/1.71	
3.22/1.71	(0) QTRS
3.22/1.71	(1) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
3.22/1.71	(2) YES
3.22/1.71	
3.22/1.71	
3.22/1.71	----------------------------------------
3.22/1.71	
3.22/1.71	(0)
3.22/1.71	Obligation:
3.22/1.71	Q restricted rewrite system:
3.22/1.71	The TRS R consists of the following rules:
3.22/1.71	
3.22/1.71	   a(a(b(x1))) -> b(b(a(a(x1))))
3.22/1.71	   b(a(x1)) -> a(c(b(x1)))
3.22/1.71	
3.22/1.71	Q is empty.
3.22/1.71	
3.22/1.71	----------------------------------------
3.22/1.71	
3.22/1.71	(1) RFCMatchBoundsTRSProof (EQUIVALENT)
3.22/1.71	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 3. This implies Q-termination of R.
3.22/1.71	The following rules were used to construct the certificate:
3.22/1.71	
3.22/1.71	   a(a(b(x1))) -> b(b(a(a(x1))))
3.22/1.71	   b(a(x1)) -> a(c(b(x1)))
3.22/1.71	
3.22/1.71	The certificate found is represented by the following graph.
3.22/1.71	The certificate consists of the following enumerated nodes:
3.22/1.71	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
3.22/1.71	
3.22/1.71	Node 1 is start node and node 2 is final node.
3.22/1.71	
3.22/1.71	Those nodes are connected through the following edges:
3.22/1.71	
3.22/1.71	* 1 to 3 labelled b_1(0)* 1 to 6 labelled a_1(0)* 1 to 15 labelled a_1(1)* 2 to 2 labelled #_1(0)* 3 to 4 labelled b_1(0)* 3 to 8 labelled a_1(1)* 4 to 5 labelled a_1(0)* 4 to 10 labelled b_1(1)* 4 to 19 labelled a_1(2)* 5 to 2 labelled a_1(0)* 5 to 10 labelled b_1(1)* 5 to 19 labelled a_1(2)* 6 to 7 labelled c_1(0)* 7 to 2 labelled b_1(0)* 7 to 13 labelled a_1(1)* 8 to 9 labelled c_1(1)* 9 to 5 labelled b_1(1)* 9 to 13 labelled a_1(1)* 9 to 19 labelled b_1(1)* 9 to 23 labelled a_1(2)* 10 to 11 labelled b_1(1)* 10 to 17 labelled a_1(2)* 10 to 23 labelled a_1(2)* 11 to 12 labelled a_1(1)* 11 to 10 labelled b_1(1)* 11 to 19 labelled a_1(2)* 12 to 2 labelled a_1(1)* 12 to 10 labelled b_1(1)* 12 to 19 labelled a_1(2)* 13 to 14 labelled c_1(1)* 14 to 2 labelled b_1(1)* 14 to 13 labelled a_1(1)* 15 to 16 labelled c_1(1)* 16 to 8 labelled b_1(1)* 17 to 18 labelled c_1(2)* 18 to 12 labelled b_1(2)* 18 to 21 labelled a_1(2)* 18 to 25 labelled a_1(3)* 19 to 20 labelled c_1(2)* 20 to 17 labelled b_1(2)* 20 to 23 labelled b_1(2)* 21 to 22 labelled c_1(2)* 22 to 2 labelled b_1(2)* 22 to 13 labelled a_1(1)* 23 to 24 labelled c_1(2)* 24 to 19 labelled b_1(2)* 25 to 26 labelled c_1(3)* 26 to 19 labelled b_1(3)
3.22/1.71	
3.22/1.71	
3.22/1.71	----------------------------------------
3.22/1.71	
3.22/1.71	(2)
3.22/1.71	YES
3.22/1.74	EOF