3.01/1.50	YES
3.01/1.52	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.01/1.52	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.01/1.52	
3.01/1.52	
3.01/1.52	Termination w.r.t. Q of the given QTRS could be proven:
3.01/1.52	
3.01/1.52	(0) QTRS
3.01/1.52	(1) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
3.01/1.52	(2) YES
3.01/1.52	
3.01/1.52	
3.01/1.52	----------------------------------------
3.01/1.52	
3.01/1.52	(0)
3.01/1.52	Obligation:
3.01/1.52	Q restricted rewrite system:
3.01/1.52	The TRS R consists of the following rules:
3.01/1.52	
3.01/1.52	   0(x1) -> 1(x1)
3.01/1.52	   4(5(4(5(x1)))) -> 4(4(5(5(x1))))
3.01/1.52	   5(5(5(5(5(5(4(4(4(4(4(4(x1)))))))))))) -> 2(x1)
3.01/1.52	
3.01/1.52	Q is empty.
3.01/1.52	
3.01/1.52	----------------------------------------
3.01/1.52	
3.01/1.52	(1) RFCMatchBoundsTRSProof (EQUIVALENT)
3.01/1.52	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
3.01/1.52	The following rules were used to construct the certificate:
3.01/1.52	
3.01/1.52	   0(x1) -> 1(x1)
3.01/1.52	   4(5(4(5(x1)))) -> 4(4(5(5(x1))))
3.01/1.52	   5(5(5(5(5(5(4(4(4(4(4(4(x1)))))))))))) -> 2(x1)
3.01/1.52	
3.01/1.52	The certificate found is represented by the following graph.
3.01/1.52	The certificate consists of the following enumerated nodes:
3.01/1.52	1, 2, 3, 4, 5
3.01/1.52	
3.01/1.52	Node 1 is start node and node 2 is final node.
3.01/1.52	
3.01/1.52	Those nodes are connected through the following edges:
3.01/1.52	
3.01/1.52	* 1 to 2 labelled 1_1(0), 2_1(0)* 1 to 3 labelled 4_1(0)* 2 to 2 labelled #_1(0)* 3 to 4 labelled 4_1(0)* 4 to 5 labelled 5_1(0)* 4 to 2 labelled 2_1(1)* 5 to 2 labelled 5_1(0), 2_1(1)
3.01/1.52	
3.01/1.52	
3.01/1.52	----------------------------------------
3.01/1.52	
3.01/1.52	(2)
3.01/1.52	YES
3.01/1.56	EOF