3.27/1.67	YES
3.27/1.69	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.27/1.69	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.27/1.69	
3.27/1.69	
3.27/1.69	Termination w.r.t. Q of the given QTRS could be proven:
3.27/1.69	
3.27/1.69	(0) QTRS
3.27/1.69	(1) RFCMatchBoundsTRSProof [EQUIVALENT, 29 ms]
3.27/1.69	(2) YES
3.27/1.69	
3.27/1.69	
3.27/1.69	----------------------------------------
3.27/1.69	
3.27/1.69	(0)
3.27/1.69	Obligation:
3.27/1.69	Q restricted rewrite system:
3.27/1.69	The TRS R consists of the following rules:
3.27/1.69	
3.27/1.69	   b(a(a(a(b(a(a(x1))))))) -> a(a(a(b(b(a(a(a(b(x1)))))))))
3.27/1.69	
3.27/1.69	Q is empty.
3.27/1.69	
3.27/1.69	----------------------------------------
3.27/1.69	
3.27/1.69	(1) RFCMatchBoundsTRSProof (EQUIVALENT)
3.27/1.69	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 4. This implies Q-termination of R.
3.27/1.69	The following rules were used to construct the certificate:
3.27/1.69	
3.27/1.69	   b(a(a(a(b(a(a(x1))))))) -> a(a(a(b(b(a(a(a(b(x1)))))))))
3.27/1.69	
3.27/1.69	The certificate found is represented by the following graph.
3.27/1.69	The certificate consists of the following enumerated nodes:
3.27/1.69	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, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82
3.27/1.69	
3.27/1.69	Node 1 is start node and node 2 is final node.
3.27/1.69	
3.27/1.69	Those nodes are connected through the following edges:
3.27/1.69	
3.27/1.69	* 1 to 3 labelled a_1(0)* 2 to 2 labelled #_1(0)* 3 to 4 labelled a_1(0)* 4 to 5 labelled a_1(0)* 5 to 6 labelled b_1(0)* 5 to 19 labelled a_1(1)* 6 to 7 labelled b_1(0)* 6 to 11 labelled a_1(1)* 7 to 8 labelled a_1(0)* 8 to 9 labelled a_1(0)* 9 to 10 labelled a_1(0)* 10 to 2 labelled b_1(0)* 10 to 11 labelled a_1(1)* 11 to 12 labelled a_1(1)* 12 to 13 labelled a_1(1)* 13 to 14 labelled b_1(1)* 13 to 27 labelled a_1(2)* 14 to 15 labelled b_1(1)* 14 to 11 labelled a_1(1)* 15 to 16 labelled a_1(1)* 16 to 17 labelled a_1(1)* 17 to 18 labelled a_1(1)* 18 to 2 labelled b_1(1)* 18 to 11 labelled a_1(1)* 19 to 20 labelled a_1(1)* 20 to 21 labelled a_1(1)* 21 to 22 labelled b_1(1)* 21 to 51 labelled a_1(2)* 22 to 23 labelled b_1(1)* 22 to 35 labelled a_1(2)* 23 to 24 labelled a_1(1)* 24 to 25 labelled a_1(1)* 25 to 26 labelled a_1(1)* 26 to 12 labelled b_1(1)* 27 to 28 labelled a_1(2)* 28 to 29 labelled a_1(2)* 29 to 30 labelled b_1(2)* 29 to 59 labelled a_1(3)* 30 to 31 labelled b_1(2)* 30 to 35 labelled a_1(2)* 31 to 32 labelled a_1(2)* 32 to 33 labelled a_1(2)* 33 to 34 labelled a_1(2)* 34 to 12 labelled b_1(2)* 35 to 36 labelled a_1(2)* 36 to 37 labelled a_1(2)* 37 to 38 labelled b_1(2)* 37 to 75 labelled a_1(3)* 38 to 39 labelled b_1(2)* 38 to 43 labelled a_1(3)* 39 to 40 labelled a_1(2)* 40 to 41 labelled a_1(2)* 41 to 42 labelled a_1(2)* 42 to 27 labelled b_1(2)* 43 to 44 labelled a_1(3)* 44 to 45 labelled a_1(3)* 45 to 46 labelled b_1(3)* 46 to 47 labelled b_1(3)* 46 to 67 labelled a_1(4)* 47 to 48 labelled a_1(3)* 48 to 49 labelled a_1(3)* 49 to 50 labelled a_1(3)* 50 to 29 labelled b_1(3)* 51 to 52 labelled a_1(2)* 52 to 53 labelled a_1(2)* 53 to 54 labelled b_1(2)* 54 to 55 labelled b_1(2)* 55 to 56 labelled a_1(2)* 56 to 57 labelled a_1(2)* 57 to 58 labelled a_1(2)* 58 to 44 labelled b_1(2)* 59 to 60 labelled a_1(3)* 60 to 61 labelled a_1(3)* 61 to 62 labelled b_1(3)* 62 to 63 labelled b_1(3)* 63 to 64 labelled a_1(3)* 64 to 65 labelled a_1(3)* 65 to 66 labelled a_1(3)* 66 to 44 labelled b_1(3)* 67 to 68 labelled a_1(4)* 68 to 69 labelled a_1(4)* 69 to 70 labelled b_1(4)* 70 to 71 labelled b_1(4)* 71 to 72 labelled a_1(4)* 72 to 73 labelled a_1(4)* 73 to 74 labelled a_1(4)* 74 to 60 labelled b_1(4)* 75 to 76 labelled a_1(3)* 76 to 77 labelled a_1(3)* 77 to 78 labelled b_1(3)* 78 to 79 labelled b_1(3)* 79 to 80 labelled a_1(3)* 80 to 81 labelled a_1(3)* 81 to 82 labelled a_1(3)* 82 to 68 labelled b_1(3)
3.27/1.69	
3.27/1.69	
3.27/1.69	----------------------------------------
3.27/1.69	
3.27/1.69	(2)
3.27/1.69	YES
3.60/1.73	EOF