3.77/1.73	YES
3.94/1.79	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.94/1.79	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.94/1.79	
3.94/1.79	
3.94/1.79	Termination w.r.t. Q of the given QTRS could be proven:
3.94/1.79	
3.94/1.79	(0) QTRS
3.94/1.79	(1) RFCMatchBoundsTRSProof [EQUIVALENT, 20 ms]
3.94/1.79	(2) YES
3.94/1.79	
3.94/1.79	
3.94/1.79	----------------------------------------
3.94/1.79	
3.94/1.79	(0)
3.94/1.79	Obligation:
3.94/1.79	Q restricted rewrite system:
3.94/1.79	The TRS R consists of the following rules:
3.94/1.79	
3.94/1.79	   a(l(x1)) -> l(a(x1))
3.94/1.79	   r(a(a(x1))) -> a(a(r(x1)))
3.94/1.79	   b(l(x1)) -> b(a(r(x1)))
3.94/1.79	   r(b(x1)) -> l(b(x1))
3.94/1.79	
3.94/1.79	Q is empty.
3.94/1.79	
3.94/1.79	----------------------------------------
3.94/1.79	
3.94/1.79	(1) RFCMatchBoundsTRSProof (EQUIVALENT)
3.94/1.79	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 3. This implies Q-termination of R.
3.94/1.79	The following rules were used to construct the certificate:
3.94/1.79	
3.94/1.79	   a(l(x1)) -> l(a(x1))
3.94/1.79	   r(a(a(x1))) -> a(a(r(x1)))
3.94/1.79	   b(l(x1)) -> b(a(r(x1)))
3.94/1.79	   r(b(x1)) -> l(b(x1))
3.94/1.79	
3.94/1.79	The certificate found is represented by the following graph.
3.94/1.79	The certificate consists of the following enumerated nodes:
3.94/1.79	1, 3, 14, 15, 16, 23, 24, 25, 26, 27, 28, 29, 30, 31, 36, 37, 38, 41, 42
3.94/1.79	
3.94/1.79	Node 1 is start node and node 3 is final node.
3.94/1.79	
3.94/1.79	Those nodes are connected through the following edges:
3.94/1.79	
3.94/1.79	* 1 to 14 labelled l_1(0)* 1 to 15 labelled a_1(0), b_1(0)* 1 to 28 labelled l_1(1)* 1 to 29 labelled b_1(1)* 3 to 3 labelled #_1(0)* 14 to 3 labelled a_1(0), b_1(0)* 14 to 23 labelled l_1(1)* 14 to 24 labelled b_1(1)* 14 to 36 labelled b_1(2)* 15 to 16 labelled a_1(0)* 15 to 27 labelled l_1(1)* 16 to 3 labelled r_1(0)* 16 to 24 labelled a_1(1)* 16 to 26 labelled l_1(1)* 16 to 38 labelled l_1(2)* 23 to 3 labelled a_1(1)* 23 to 23 labelled l_1(1)* 24 to 25 labelled a_1(1)* 24 to 31 labelled l_1(2)* 25 to 3 labelled r_1(1)* 25 to 24 labelled a_1(1)* 25 to 26 labelled l_1(1)* 25 to 38 labelled l_1(2)* 26 to 3 labelled b_1(1)* 26 to 24 labelled b_1(1)* 26 to 36 labelled b_1(2)* 27 to 26 labelled a_1(1)* 27 to 38 labelled a_1(1)* 28 to 27 labelled a_1(1)* 29 to 30 labelled a_1(1)* 30 to 27 labelled r_1(1)* 30 to 36 labelled a_1(2)* 31 to 26 labelled a_1(2)* 31 to 38 labelled a_1(2)* 36 to 37 labelled a_1(2)* 37 to 31 labelled r_1(2)* 37 to 41 labelled a_1(3)* 38 to 31 labelled a_1(2)* 41 to 42 labelled a_1(3)* 42 to 31 labelled r_1(3)* 42 to 41 labelled a_1(3)
3.94/1.79	
3.94/1.79	
3.94/1.79	----------------------------------------
3.94/1.79	
3.94/1.79	(2)
3.94/1.79	YES
3.94/1.83	EOF