3.18/1.73	YES
3.18/1.74	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.18/1.74	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.18/1.74	
3.18/1.74	
3.18/1.74	Termination w.r.t. Q of the given QTRS could be proven:
3.18/1.74	
3.18/1.74	(0) QTRS
3.18/1.74	(1) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
3.18/1.74	(2) YES
3.18/1.74	
3.18/1.74	
3.18/1.74	----------------------------------------
3.18/1.74	
3.18/1.74	(0)
3.18/1.74	Obligation:
3.18/1.74	Q restricted rewrite system:
3.18/1.74	The TRS R consists of the following rules:
3.18/1.74	
3.18/1.74	   a(a(b(b(x1)))) -> b(b(b(a(a(a(x1))))))
3.18/1.74	
3.18/1.74	Q is empty.
3.18/1.74	
3.18/1.74	----------------------------------------
3.18/1.74	
3.18/1.74	(1) RFCMatchBoundsTRSProof (EQUIVALENT)
3.18/1.74	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 4. This implies Q-termination of R.
3.18/1.74	The following rules were used to construct the certificate:
3.18/1.74	
3.18/1.74	   a(a(b(b(x1)))) -> b(b(b(a(a(a(x1))))))
3.18/1.74	
3.18/1.74	The certificate found is represented by the following graph.
3.18/1.74	The certificate consists of the following enumerated nodes:
3.18/1.74	1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 20, 21, 22, 23, 24, 30, 31, 32, 33, 34, 45, 46, 47, 48, 49, 55, 56, 57, 58, 59, 65, 66, 67, 68, 69, 75, 76, 77, 78, 79
3.18/1.74	
3.18/1.74	Node 1 is start node and node 2 is final node.
3.18/1.74	
3.18/1.74	Those nodes are connected through the following edges:
3.18/1.74	
3.18/1.74	* 1 to 3 labelled b_1(0)* 2 to 2 labelled #_1(0)* 3 to 4 labelled b_1(0)* 4 to 5 labelled b_1(0)* 5 to 6 labelled a_1(0)* 5 to 20 labelled b_1(1)* 6 to 7 labelled a_1(0)* 6 to 8 labelled b_1(1)* 7 to 2 labelled a_1(0)* 7 to 8 labelled b_1(1)* 8 to 9 labelled b_1(1)* 9 to 10 labelled b_1(1)* 10 to 11 labelled a_1(1)* 10 to 30 labelled b_1(2)* 11 to 12 labelled a_1(1)* 11 to 8 labelled b_1(1)* 12 to 2 labelled a_1(1)* 12 to 8 labelled b_1(1)* 20 to 21 labelled b_1(1)* 21 to 22 labelled b_1(1)* 22 to 23 labelled a_1(1)* 23 to 24 labelled a_1(1)* 23 to 45 labelled b_1(2)* 24 to 9 labelled a_1(1)* 30 to 31 labelled b_1(2)* 31 to 32 labelled b_1(2)* 32 to 33 labelled a_1(2)* 33 to 34 labelled a_1(2)* 33 to 45 labelled b_1(2)* 34 to 9 labelled a_1(2)* 45 to 46 labelled b_1(2)* 46 to 47 labelled b_1(2)* 47 to 48 labelled a_1(2)* 48 to 49 labelled a_1(2)* 48 to 55 labelled b_1(3)* 49 to 30 labelled a_1(2)* 55 to 56 labelled b_1(3)* 56 to 57 labelled b_1(3)* 57 to 58 labelled a_1(3)* 57 to 75 labelled b_1(4)* 58 to 59 labelled a_1(3)* 59 to 32 labelled a_1(3)* 59 to 65 labelled b_1(3)* 65 to 66 labelled b_1(3)* 66 to 67 labelled b_1(3)* 67 to 68 labelled a_1(3)* 68 to 69 labelled a_1(3)* 69 to 46 labelled a_1(3)* 75 to 76 labelled b_1(4)* 76 to 77 labelled b_1(4)* 77 to 78 labelled a_1(4)* 78 to 79 labelled a_1(4)* 79 to 66 labelled a_1(4)
3.18/1.74	
3.18/1.74	
3.18/1.74	----------------------------------------
3.18/1.74	
3.18/1.74	(2)
3.18/1.74	YES
3.43/1.77	EOF