3.20/1.65	YES
3.62/2.15	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.62/2.15	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.62/2.15	
3.62/2.15	
3.62/2.15	Termination w.r.t. Q of the given QTRS could be proven:
3.62/2.15	
3.62/2.15	(0) QTRS
3.62/2.15	(1) QTRS Reverse [EQUIVALENT, 0 ms]
3.62/2.15	(2) QTRS
3.62/2.15	(3) RFCMatchBoundsTRSProof [EQUIVALENT, 1 ms]
3.62/2.15	(4) YES
3.62/2.15	
3.62/2.15	
3.62/2.15	----------------------------------------
3.62/2.15	
3.62/2.15	(0)
3.62/2.15	Obligation:
3.62/2.15	Q restricted rewrite system:
3.62/2.15	The TRS R consists of the following rules:
3.62/2.15	
3.62/2.15	   b(a(a(b(a(b(x1)))))) -> a(b(a(b(a(b(a(x1)))))))
3.62/2.15	
3.62/2.15	Q is empty.
3.62/2.15	
3.62/2.15	----------------------------------------
3.62/2.15	
3.62/2.15	(1) QTRS Reverse (EQUIVALENT)
3.62/2.15	We applied the QTRS Reverse Processor [REVERSE].
3.62/2.15	----------------------------------------
3.62/2.15	
3.62/2.15	(2)
3.62/2.15	Obligation:
3.62/2.15	Q restricted rewrite system:
3.62/2.15	The TRS R consists of the following rules:
3.62/2.15	
3.62/2.15	   b(a(b(a(a(b(x1)))))) -> a(b(a(b(a(b(a(x1)))))))
3.62/2.15	
3.62/2.15	Q is empty.
3.62/2.15	
3.62/2.15	----------------------------------------
3.62/2.15	
3.62/2.15	(3) RFCMatchBoundsTRSProof (EQUIVALENT)
3.62/2.15	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 2. This implies Q-termination of R.
3.62/2.15	The following rules were used to construct the certificate:
3.62/2.15	
3.62/2.15	   b(a(b(a(a(b(x1)))))) -> a(b(a(b(a(b(a(x1)))))))
3.62/2.15	
3.62/2.15	The certificate found is represented by the following graph.
3.62/2.15	The certificate consists of the following enumerated nodes:
3.62/2.15	1, 3, 5, 6, 7, 8, 9, 10, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46
3.62/2.15	
3.62/2.15	Node 1 is start node and node 3 is final node.
3.62/2.15	
3.62/2.15	Those nodes are connected through the following edges:
3.62/2.15	
3.62/2.15	* 1 to 5 labelled a_1(0)* 3 to 3 labelled #_1(0)* 5 to 6 labelled b_1(0)* 5 to 23 labelled a_1(1)* 6 to 7 labelled a_1(0)* 7 to 8 labelled b_1(0)* 7 to 17 labelled a_1(1)* 8 to 9 labelled a_1(0)* 9 to 10 labelled b_1(0)* 9 to 17 labelled a_1(1)* 10 to 3 labelled a_1(0)* 17 to 18 labelled b_1(1)* 17 to 29 labelled a_1(2)* 18 to 19 labelled a_1(1)* 19 to 20 labelled b_1(1)* 19 to 17 labelled a_1(1)* 20 to 21 labelled a_1(1)* 21 to 22 labelled b_1(1)* 21 to 17 labelled a_1(1)* 22 to 3 labelled a_1(1)* 23 to 24 labelled b_1(1)* 24 to 25 labelled a_1(1)* 25 to 26 labelled b_1(1)* 25 to 35 labelled a_1(2)* 26 to 27 labelled a_1(1)* 27 to 28 labelled b_1(1)* 28 to 18 labelled a_1(1)* 29 to 30 labelled b_1(2)* 30 to 31 labelled a_1(2)* 31 to 32 labelled b_1(2)* 31 to 35 labelled a_1(2)* 32 to 33 labelled a_1(2)* 33 to 34 labelled b_1(2)* 34 to 18 labelled a_1(2)* 35 to 36 labelled b_1(2)* 36 to 37 labelled a_1(2)* 37 to 38 labelled b_1(2)* 37 to 41 labelled a_1(2)* 38 to 39 labelled a_1(2)* 39 to 40 labelled b_1(2)* 40 to 20 labelled a_1(2)* 41 to 42 labelled b_1(2)* 42 to 43 labelled a_1(2)* 43 to 44 labelled b_1(2)* 43 to 17 labelled a_1(1)* 44 to 45 labelled a_1(2)* 45 to 46 labelled b_1(2)* 46 to 22 labelled a_1(2)
3.62/2.15	
3.62/2.15	
3.62/2.15	----------------------------------------
3.62/2.15	
3.62/2.15	(4)
3.62/2.15	YES
3.62/2.20	EOF