3.54/1.70	YES
3.74/1.72	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.74/1.72	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.74/1.72	
3.74/1.72	
3.74/1.72	Termination w.r.t. Q of the given QTRS could be proven:
3.74/1.72	
3.74/1.72	(0) QTRS
3.74/1.72	(1) QTRS Reverse [EQUIVALENT, 0 ms]
3.74/1.72	(2) QTRS
3.74/1.72	(3) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
3.74/1.72	(4) YES
3.74/1.72	
3.74/1.72	
3.74/1.72	----------------------------------------
3.74/1.72	
3.74/1.72	(0)
3.74/1.72	Obligation:
3.74/1.72	Q restricted rewrite system:
3.74/1.72	The TRS R consists of the following rules:
3.74/1.72	
3.74/1.72	   a(b(x1)) -> b(a(a(x1)))
3.74/1.72	   b(x1) -> c(a(c(x1)))
3.74/1.72	   a(a(x1)) -> a(c(a(x1)))
3.74/1.72	
3.74/1.72	Q is empty.
3.74/1.72	
3.74/1.72	----------------------------------------
3.74/1.72	
3.74/1.72	(1) QTRS Reverse (EQUIVALENT)
3.74/1.72	We applied the QTRS Reverse Processor [REVERSE].
3.74/1.72	----------------------------------------
3.74/1.72	
3.74/1.72	(2)
3.74/1.72	Obligation:
3.74/1.72	Q restricted rewrite system:
3.74/1.72	The TRS R consists of the following rules:
3.74/1.72	
3.74/1.72	   b(a(x1)) -> a(a(b(x1)))
3.74/1.72	   b(x1) -> c(a(c(x1)))
3.74/1.72	   a(a(x1)) -> a(c(a(x1)))
3.74/1.72	
3.74/1.72	Q is empty.
3.74/1.72	
3.74/1.72	----------------------------------------
3.74/1.72	
3.74/1.72	(3) RFCMatchBoundsTRSProof (EQUIVALENT)
3.74/1.72	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 3. This implies Q-termination of R.
3.74/1.72	The following rules were used to construct the certificate:
3.74/1.72	
3.74/1.72	   b(a(x1)) -> a(a(b(x1)))
3.74/1.72	   b(x1) -> c(a(c(x1)))
3.74/1.72	   a(a(x1)) -> a(c(a(x1)))
3.74/1.72	
3.74/1.72	The certificate found is represented by the following graph.
3.74/1.72	The certificate consists of the following enumerated nodes:
3.74/1.72	46, 48, 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
3.74/1.72	
3.74/1.72	Node 46 is start node and node 48 is final node.
3.74/1.72	
3.74/1.72	Those nodes are connected through the following edges:
3.74/1.72	
3.74/1.72	* 46 to 51 labelled a_1(0)* 46 to 53 labelled c_1(0)* 46 to 55 labelled a_1(0)* 46 to 59 labelled a_1(1)* 48 to 48 labelled #_1(0)* 51 to 52 labelled a_1(0)* 51 to 67 labelled a_1(1)* 52 to 48 labelled b_1(0)* 52 to 57 labelled c_1(1)* 52 to 61 labelled a_1(1)* 52 to 71 labelled a_1(2)* 53 to 54 labelled a_1(0)* 54 to 48 labelled c_1(0)* 55 to 56 labelled c_1(0)* 56 to 48 labelled a_1(0)* 56 to 63 labelled a_1(1)* 57 to 58 labelled a_1(1)* 58 to 48 labelled c_1(1)* 59 to 60 labelled c_1(1)* 60 to 52 labelled a_1(1)* 60 to 69 labelled a_1(2)* 60 to 67 labelled a_1(1)* 61 to 62 labelled a_1(1)* 61 to 69 labelled a_1(2)* 62 to 48 labelled b_1(1)* 62 to 65 labelled c_1(2)* 62 to 61 labelled a_1(1)* 62 to 71 labelled a_1(2)* 63 to 64 labelled c_1(1)* 64 to 48 labelled a_1(1)* 64 to 63 labelled a_1(1)* 65 to 66 labelled a_1(2)* 66 to 48 labelled c_1(2)* 67 to 68 labelled c_1(1)* 68 to 61 labelled a_1(1)* 68 to 71 labelled a_1(1), a_1(2)* 69 to 70 labelled c_1(2)* 70 to 61 labelled a_1(2)* 70 to 71 labelled a_1(2)* 70 to 73 labelled a_1(3)* 71 to 72 labelled c_1(2)* 72 to 62 labelled a_1(2)* 72 to 69 labelled a_1(2)* 72 to 75 labelled a_1(3)* 73 to 74 labelled c_1(3)* 74 to 69 labelled a_1(3)* 75 to 76 labelled c_1(3)* 76 to 71 labelled a_1(3)
3.74/1.72	
3.74/1.72	
3.74/1.72	----------------------------------------
3.74/1.72	
3.74/1.72	(4)
3.74/1.72	YES
3.74/1.75	EOF