3.10/1.56	YES
3.10/1.57	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.10/1.57	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.10/1.57	
3.10/1.57	
3.10/1.57	Termination w.r.t. Q of the given QTRS could be proven:
3.10/1.57	
3.10/1.57	(0) QTRS
3.10/1.57	(1) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
3.10/1.57	(2) YES
3.10/1.57	
3.10/1.57	
3.10/1.57	----------------------------------------
3.10/1.57	
3.10/1.57	(0)
3.10/1.57	Obligation:
3.10/1.57	Q restricted rewrite system:
3.10/1.57	The TRS R consists of the following rules:
3.10/1.57	
3.10/1.57	   b(b(c(a(b(c(x1)))))) -> a(b(b(c(b(c(a(x1)))))))
3.10/1.57	
3.10/1.57	Q is empty.
3.10/1.57	
3.10/1.57	----------------------------------------
3.10/1.57	
3.10/1.57	(1) RFCMatchBoundsTRSProof (EQUIVALENT)
3.10/1.57	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 0. This implies Q-termination of R.
3.10/1.57	The following rules were used to construct the certificate:
3.10/1.57	
3.10/1.57	   b(b(c(a(b(c(x1)))))) -> a(b(b(c(b(c(a(x1)))))))
3.10/1.57	
3.10/1.57	The certificate found is represented by the following graph.
3.10/1.57	The certificate consists of the following enumerated nodes:
3.10/1.57	1, 2, 3, 4, 5, 6, 7, 8
3.10/1.57	
3.10/1.57	Node 1 is start node and node 2 is final node.
3.10/1.57	
3.10/1.57	Those nodes are connected through the following edges:
3.10/1.57	
3.10/1.57	* 1 to 3 labelled a_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 c_1(0)* 6 to 7 labelled b_1(0)* 7 to 8 labelled c_1(0)* 8 to 2 labelled a_1(0)
3.10/1.57	
3.10/1.57	
3.10/1.57	----------------------------------------
3.10/1.57	
3.10/1.57	(2)
3.10/1.57	YES
3.10/1.59	EOF