3.19/1.67	YES
3.19/2.19	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.19/2.19	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.19/2.19	
3.19/2.19	
3.19/2.19	Termination w.r.t. Q of the given QTRS could be proven:
3.19/2.19	
3.19/2.19	(0) QTRS
3.19/2.19	(1) RFCMatchBoundsTRSProof [EQUIVALENT, 29 ms]
3.19/2.19	(2) YES
3.19/2.19	
3.19/2.19	
3.19/2.19	----------------------------------------
3.19/2.19	
3.19/2.19	(0)
3.19/2.19	Obligation:
3.19/2.19	Q restricted rewrite system:
3.19/2.19	The TRS R consists of the following rules:
3.19/2.19	
3.19/2.19	   a(l(x1)) -> l(a(x1))
3.19/2.19	   a(c(x1)) -> c(a(x1))
3.19/2.19	   c(a(r(x1))) -> r(a(x1))
3.19/2.19	   l(r(a(x1))) -> a(l(c(c(r(x1)))))
3.19/2.19	
3.19/2.19	Q is empty.
3.19/2.19	
3.19/2.19	----------------------------------------
3.19/2.19	
3.19/2.19	(1) RFCMatchBoundsTRSProof (EQUIVALENT)
3.19/2.19	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 3. This implies Q-termination of R.
3.19/2.19	The following rules were used to construct the certificate:
3.19/2.19	
3.19/2.19	   a(l(x1)) -> l(a(x1))
3.19/2.19	   a(c(x1)) -> c(a(x1))
3.19/2.19	   c(a(r(x1))) -> r(a(x1))
3.19/2.19	   l(r(a(x1))) -> a(l(c(c(r(x1)))))
3.19/2.19	
3.19/2.19	The certificate found is represented by the following graph.
3.19/2.19	The certificate consists of the following enumerated nodes:
3.19/2.19	1, 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 33, 34, 39, 41, 55, 56, 57
3.19/2.19	
3.19/2.19	Node 1 is start node and node 3 is final node.
3.19/2.19	
3.19/2.19	Those nodes are connected through the following edges:
3.19/2.19	
3.19/2.19	* 1 to 5 labelled l_1(0), c_1(0), r_1(0)* 1 to 6 labelled a_1(0)* 1 to 10 labelled l_1(1)* 1 to 11 labelled r_1(1)* 1 to 14 labelled a_1(1)* 1 to 19 labelled l_1(2)* 3 to 3 labelled #_1(0)* 5 to 3 labelled a_1(0)* 5 to 11 labelled l_1(1), c_1(1), r_1(1)* 5 to 20 labelled a_1(2)* 5 to 33 labelled l_1(3)* 6 to 7 labelled l_1(0)* 7 to 8 labelled c_1(0)* 8 to 9 labelled c_1(0)* 9 to 3 labelled r_1(0)* 10 to 7 labelled a_1(1)* 10 to 12 labelled c_1(1)* 11 to 3 labelled a_1(1)* 11 to 11 labelled l_1(1), c_1(1), r_1(1)* 11 to 20 labelled a_1(2)* 11 to 33 labelled l_1(3)* 12 to 8 labelled a_1(1)* 12 to 13 labelled c_1(1)* 12 to 11 labelled r_1(1)* 13 to 9 labelled a_1(1)* 14 to 15 labelled l_1(1)* 15 to 16 labelled c_1(1)* 16 to 17 labelled c_1(1)* 17 to 3 labelled r_1(1)* 17 to 20 labelled r_1(1)* 19 to 15 labelled a_1(2)* 19 to 34 labelled c_1(2)* 20 to 21 labelled l_1(2)* 21 to 22 labelled c_1(2)* 22 to 23 labelled c_1(2)* 23 to 3 labelled r_1(2)* 23 to 20 labelled r_1(2)* 33 to 21 labelled a_1(3)* 33 to 39 labelled c_1(3)* 34 to 16 labelled a_1(2)* 34 to 41 labelled c_1(2)* 34 to 56 labelled r_1(2)* 34 to 5 labelled r_1(2)* 39 to 22 labelled a_1(3)* 39 to 55 labelled c_1(3)* 39 to 57 labelled r_1(3)* 41 to 17 labelled a_1(2)* 55 to 23 labelled a_1(3)* 56 to 3 labelled a_1(2)* 56 to 11 labelled l_1(1), c_1(1), r_1(1)* 56 to 20 labelled a_1(2)* 56 to 33 labelled l_1(3)* 57 to 3 labelled a_1(3)* 57 to 20 labelled a_1(3), a_1(2)* 57 to 11 labelled l_1(1), c_1(1), r_1(1)* 57 to 33 labelled l_1(3)
3.19/2.19	
3.19/2.19	
3.19/2.19	----------------------------------------
3.19/2.19	
3.19/2.19	(2)
3.19/2.19	YES
3.90/2.21	EOF