3.47/1.76	YES
3.71/1.81	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.71/1.81	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.71/1.81	
3.71/1.81	
3.71/1.81	Termination w.r.t. Q of the given QTRS could be proven:
3.71/1.81	
3.71/1.81	(0) QTRS
3.71/1.81	(1) RFCMatchBoundsTRSProof [EQUIVALENT, 38 ms]
3.71/1.81	(2) YES
3.71/1.81	
3.71/1.81	
3.71/1.81	----------------------------------------
3.71/1.81	
3.71/1.81	(0)
3.71/1.81	Obligation:
3.71/1.81	Q restricted rewrite system:
3.71/1.81	The TRS R consists of the following rules:
3.71/1.81	
3.71/1.81	   a(a(x1)) -> a(b(b(b(x1))))
3.71/1.81	   b(a(x1)) -> b(b(c(x1)))
3.71/1.81	   a(b(b(c(x1)))) -> a(a(a(b(x1))))
3.71/1.81	
3.71/1.81	Q is empty.
3.71/1.81	
3.71/1.81	----------------------------------------
3.71/1.81	
3.71/1.81	(1) RFCMatchBoundsTRSProof (EQUIVALENT)
3.71/1.81	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 4. This implies Q-termination of R.
3.71/1.81	The following rules were used to construct the certificate:
3.71/1.81	
3.71/1.81	   a(a(x1)) -> a(b(b(b(x1))))
3.71/1.81	   b(a(x1)) -> b(b(c(x1)))
3.71/1.81	   a(b(b(c(x1)))) -> a(a(a(b(x1))))
3.71/1.81	
3.71/1.81	The certificate found is represented by the following graph.
3.71/1.81	The certificate consists of the following enumerated nodes:
3.71/1.81	1, 3, 4, 5, 6, 7, 8, 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, 87, 88, 89, 90
3.71/1.81	
3.71/1.81	Node 1 is start node and node 3 is final node.
3.71/1.81	
3.71/1.81	Those nodes are connected through the following edges:
3.71/1.81	
3.71/1.81	* 1 to 4 labelled a_1(0)* 1 to 7 labelled b_1(0)* 1 to 37 labelled a_1(0)* 1 to 40 labelled a_1(1)* 3 to 3 labelled #_1(0)* 4 to 5 labelled b_1(0)* 5 to 6 labelled b_1(0)* 6 to 3 labelled b_1(0)* 6 to 43 labelled b_1(1)* 7 to 8 labelled b_1(0)* 8 to 3 labelled c_1(0)* 37 to 38 labelled a_1(0)* 37 to 45 labelled a_1(1)* 38 to 39 labelled a_1(0)* 38 to 48 labelled a_1(1)* 38 to 53 labelled a_1(2)* 39 to 3 labelled b_1(0)* 39 to 43 labelled b_1(1)* 40 to 41 labelled b_1(1)* 41 to 42 labelled b_1(1)* 42 to 38 labelled b_1(1)* 42 to 45 labelled b_1(1)* 42 to 51 labelled b_1(2)* 43 to 44 labelled b_1(1)* 44 to 3 labelled c_1(1)* 45 to 46 labelled b_1(1)* 46 to 47 labelled b_1(1)* 46 to 39 labelled c_1(1)* 47 to 39 labelled b_1(1)* 47 to 48 labelled b_1(1)* 47 to 53 labelled b_1(1)* 47 to 59 labelled b_1(2)* 48 to 49 labelled a_1(1)* 48 to 56 labelled a_1(2)* 49 to 50 labelled a_1(1)* 49 to 48 labelled a_1(1)* 49 to 53 labelled a_1(2)* 49 to 61 labelled a_1(2)* 49 to 68 labelled a_1(3)* 50 to 3 labelled b_1(1)* 50 to 43 labelled b_1(1)* 51 to 52 labelled b_1(2)* 52 to 48 labelled c_1(2)* 52 to 53 labelled c_1(2)* 53 to 54 labelled b_1(2)* 54 to 55 labelled b_1(2)* 55 to 49 labelled b_1(2)* 55 to 56 labelled b_1(2)* 55 to 51 labelled b_1(2)* 55 to 66 labelled b_1(3)* 56 to 57 labelled b_1(2)* 57 to 58 labelled b_1(2)* 57 to 50 labelled c_1(2)* 58 to 50 labelled b_1(2)* 58 to 48 labelled b_1(2)* 58 to 59 labelled b_1(2)* 58 to 64 labelled b_1(3)* 58 to 53 labelled b_1(2)* 58 to 61 labelled b_1(2)* 58 to 68 labelled b_1(2)* 59 to 60 labelled b_1(2)* 60 to 49 labelled c_1(2)* 60 to 56 labelled c_1(2)* 61 to 62 labelled a_1(2)* 61 to 71 labelled a_1(3)* 61 to 56 labelled a_1(2)* 62 to 63 labelled a_1(2)* 62 to 48 labelled a_1(1)* 62 to 53 labelled a_1(2)* 62 to 61 labelled a_1(2)* 62 to 68 labelled a_1(3)* 63 to 3 labelled b_1(2)* 63 to 43 labelled b_1(1)* 64 to 65 labelled b_1(3)* 65 to 56 labelled c_1(3)* 65 to 62 labelled c_1(3)* 65 to 71 labelled c_1(3)* 66 to 67 labelled b_1(3)* 67 to 53 labelled c_1(3)* 67 to 61 labelled c_1(3)* 67 to 68 labelled c_1(3)* 68 to 69 labelled b_1(3)* 69 to 70 labelled b_1(3)* 70 to 62 labelled b_1(3)* 70 to 71 labelled b_1(3)* 70 to 51 labelled b_1(2)* 70 to 56 labelled b_1(3)* 70 to 66 labelled b_1(3)* 70 to 89 labelled b_1(4)* 71 to 72 labelled b_1(3)* 72 to 73 labelled b_1(3)* 72 to 63 labelled c_1(3)* 73 to 63 labelled b_1(3)* 73 to 53 labelled b_1(3)* 73 to 61 labelled b_1(3)* 73 to 64 labelled b_1(3)* 73 to 87 labelled b_1(4)* 73 to 68 labelled b_1(3)* 87 to 88 labelled b_1(4)* 88 to 71 labelled c_1(4)* 89 to 90 labelled b_1(4)* 90 to 68 labelled c_1(4)
3.71/1.81	
3.71/1.81	
3.71/1.81	----------------------------------------
3.71/1.81	
3.71/1.81	(2)
3.71/1.81	YES
3.71/1.84	EOF