3.57/1.72	YES
3.57/1.73	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.57/1.73	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.57/1.73	
3.57/1.73	
3.57/1.73	Termination w.r.t. Q of the given QTRS could be proven:
3.57/1.73	
3.57/1.73	(0) QTRS
3.57/1.73	(1) RFCMatchBoundsTRSProof [EQUIVALENT, 12 ms]
3.57/1.73	(2) YES
3.57/1.73	
3.57/1.73	
3.57/1.73	----------------------------------------
3.57/1.73	
3.57/1.73	(0)
3.57/1.73	Obligation:
3.57/1.73	Q restricted rewrite system:
3.57/1.73	The TRS R consists of the following rules:
3.57/1.73	
3.57/1.73	   0(1(2(3(4(x1))))) -> 0(2(3(1(4(x1)))))
3.57/1.73	   0(5(1(2(3(4(x1)))))) -> 0(1(2(5(3(4(x1))))))
3.57/1.73	   0(5(1(2(3(4(x1)))))) -> 0(5(2(1(3(4(x1))))))
3.57/1.73	   0(5(1(2(3(4(x1)))))) -> 5(0(2(3(1(4(x1))))))
3.57/1.73	   0(5(2(3(1(4(x1)))))) -> 0(1(5(2(3(4(x1))))))
3.57/1.73	
3.57/1.73	Q is empty.
3.57/1.73	
3.57/1.73	----------------------------------------
3.57/1.73	
3.57/1.73	(1) RFCMatchBoundsTRSProof (EQUIVALENT)
3.57/1.73	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 0. This implies Q-termination of R.
3.57/1.73	The following rules were used to construct the certificate:
3.57/1.73	
3.57/1.73	   0(1(2(3(4(x1))))) -> 0(2(3(1(4(x1)))))
3.57/1.73	   0(5(1(2(3(4(x1)))))) -> 0(1(2(5(3(4(x1))))))
3.57/1.73	   0(5(1(2(3(4(x1)))))) -> 0(5(2(1(3(4(x1))))))
3.57/1.73	   0(5(1(2(3(4(x1)))))) -> 5(0(2(3(1(4(x1))))))
3.57/1.73	   0(5(2(3(1(4(x1)))))) -> 0(1(5(2(3(4(x1))))))
3.57/1.73	
3.57/1.73	The certificate found is represented by the following graph.
3.57/1.73	The certificate consists of the following enumerated nodes:
3.57/1.73	1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21
3.57/1.73	
3.57/1.73	Node 1 is start node and node 2 is final node.
3.57/1.73	
3.57/1.73	Those nodes are connected through the following edges:
3.57/1.73	
3.57/1.73	* 1 to 3 labelled 0_1(0)* 1 to 7 labelled 0_1(0)* 1 to 12 labelled 0_1(0)* 1 to 1 labelled 5_1(0)* 1 to 17 labelled 0_1(0)* 2 to 2 labelled #_1(0)* 3 to 4 labelled 2_1(0)* 4 to 5 labelled 3_1(0)* 5 to 6 labelled 1_1(0)* 6 to 2 labelled 4_1(0)* 7 to 8 labelled 1_1(0)* 8 to 9 labelled 2_1(0)* 9 to 10 labelled 5_1(0)* 10 to 11 labelled 3_1(0)* 11 to 2 labelled 4_1(0)* 12 to 13 labelled 5_1(0)* 13 to 14 labelled 2_1(0)* 14 to 15 labelled 1_1(0)* 15 to 16 labelled 3_1(0)* 16 to 2 labelled 4_1(0)* 17 to 18 labelled 1_1(0)* 18 to 19 labelled 5_1(0)* 19 to 20 labelled 2_1(0)* 20 to 21 labelled 3_1(0)* 21 to 2 labelled 4_1(0)
3.57/1.73	
3.57/1.73	
3.57/1.73	----------------------------------------
3.57/1.73	
3.57/1.73	(2)
3.57/1.73	YES
3.57/1.78	EOF