2.96/1.51	YES
2.96/1.52	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
2.96/1.52	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.96/1.52	
2.96/1.52	
2.96/1.52	Termination w.r.t. Q of the given QTRS could be proven:
2.96/1.52	
2.96/1.52	(0) QTRS
2.96/1.52	(1) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
2.96/1.52	(2) YES
2.96/1.52	
2.96/1.52	
2.96/1.52	----------------------------------------
2.96/1.52	
2.96/1.52	(0)
2.96/1.52	Obligation:
2.96/1.52	Q restricted rewrite system:
2.96/1.52	The TRS R consists of the following rules:
2.96/1.52	
2.96/1.52	   c(a(b(a(x1)))) -> a(b(a(a(c(a(b(c(a(b(x1))))))))))
2.96/1.52	
2.96/1.52	Q is empty.
2.96/1.52	
2.96/1.52	----------------------------------------
2.96/1.52	
2.96/1.52	(1) RFCMatchBoundsTRSProof (EQUIVALENT)
2.96/1.52	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 2. This implies Q-termination of R.
2.96/1.52	The following rules were used to construct the certificate:
2.96/1.52	
2.96/1.52	   c(a(b(a(x1)))) -> a(b(a(a(c(a(b(c(a(b(x1))))))))))
2.96/1.52	
2.96/1.52	The certificate found is represented by the following graph.
2.96/1.52	The certificate consists of the following enumerated nodes:
2.96/1.52	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
2.96/1.52	
2.96/1.52	Node 1 is start node and node 2 is final node.
2.96/1.52	
2.96/1.52	Those nodes are connected through the following edges:
2.96/1.52	
2.96/1.52	* 1 to 3 labelled a_1(0)* 2 to 2 labelled #_1(0)* 3 to 4 labelled b_1(0)* 4 to 5 labelled a_1(0)* 5 to 6 labelled a_1(0)* 6 to 7 labelled c_1(0)* 6 to 21 labelled a_1(1)* 7 to 8 labelled a_1(0)* 8 to 9 labelled b_1(0)* 9 to 10 labelled c_1(0)* 9 to 12 labelled a_1(1)* 10 to 11 labelled a_1(0)* 11 to 2 labelled b_1(0)* 12 to 13 labelled b_1(1)* 13 to 14 labelled a_1(1)* 14 to 15 labelled a_1(1)* 15 to 16 labelled c_1(1)* 15 to 30 labelled a_1(2)* 16 to 17 labelled a_1(1)* 17 to 18 labelled b_1(1)* 18 to 19 labelled c_1(1)* 18 to 12 labelled a_1(1)* 19 to 20 labelled a_1(1)* 20 to 2 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)* 24 to 25 labelled c_1(1)* 25 to 26 labelled a_1(1)* 26 to 27 labelled b_1(1)* 27 to 28 labelled c_1(1)* 28 to 29 labelled a_1(1)* 29 to 12 labelled b_1(1)* 30 to 31 labelled b_1(2)* 31 to 32 labelled a_1(2)* 32 to 33 labelled a_1(2)* 33 to 34 labelled c_1(2)* 34 to 35 labelled a_1(2)* 35 to 36 labelled b_1(2)* 36 to 37 labelled c_1(2)* 37 to 38 labelled a_1(2)* 38 to 12 labelled b_1(2)
2.96/1.52	
2.96/1.52	
2.96/1.52	----------------------------------------
2.96/1.52	
2.96/1.52	(2)
2.96/1.52	YES
3.17/1.55	EOF