3.35/1.68	YES
3.56/1.69	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.56/1.69	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.56/1.69	
3.56/1.69	
3.56/1.69	Termination w.r.t. Q of the given QTRS could be proven:
3.56/1.69	
3.56/1.69	(0) QTRS
3.56/1.69	(1) QTRS Reverse [EQUIVALENT, 0 ms]
3.56/1.69	(2) QTRS
3.56/1.69	(3) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
3.56/1.69	(4) YES
3.56/1.69	
3.56/1.69	
3.56/1.69	----------------------------------------
3.56/1.69	
3.56/1.69	(0)
3.56/1.69	Obligation:
3.56/1.69	Q restricted rewrite system:
3.56/1.69	The TRS R consists of the following rules:
3.56/1.69	
3.56/1.69	   b(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1)))))))
3.56/1.69	
3.56/1.69	Q is empty.
3.56/1.69	
3.56/1.69	----------------------------------------
3.56/1.69	
3.56/1.69	(1) QTRS Reverse (EQUIVALENT)
3.56/1.69	We applied the QTRS Reverse Processor [REVERSE].
3.56/1.69	----------------------------------------
3.56/1.69	
3.56/1.69	(2)
3.56/1.69	Obligation:
3.56/1.69	Q restricted rewrite system:
3.56/1.69	The TRS R consists of the following rules:
3.56/1.69	
3.56/1.69	   a(b(a(a(b(x1))))) -> b(a(a(b(b(a(a(x1)))))))
3.56/1.69	
3.56/1.69	Q is empty.
3.56/1.69	
3.56/1.69	----------------------------------------
3.56/1.69	
3.56/1.69	(3) RFCMatchBoundsTRSProof (EQUIVALENT)
3.56/1.69	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 2. This implies Q-termination of R.
3.56/1.69	The following rules were used to construct the certificate:
3.56/1.69	
3.56/1.69	   a(b(a(a(b(x1))))) -> b(a(a(b(b(a(a(x1)))))))
3.56/1.69	
3.56/1.69	The certificate found is represented by the following graph.
3.56/1.69	The certificate consists of the following enumerated nodes:
3.56/1.69	15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40
3.56/1.69	
3.56/1.69	Node 15 is start node and node 16 is final node.
3.56/1.69	
3.56/1.69	Those nodes are connected through the following edges:
3.56/1.69	
3.56/1.69	* 15 to 17 labelled b_1(0)* 16 to 16 labelled #_1(0)* 17 to 18 labelled a_1(0)* 18 to 19 labelled a_1(0)* 19 to 20 labelled b_1(0)* 20 to 21 labelled b_1(0)* 21 to 22 labelled a_1(0)* 21 to 29 labelled b_1(1)* 22 to 16 labelled a_1(0)* 22 to 23 labelled b_1(1)* 23 to 24 labelled a_1(1)* 24 to 25 labelled a_1(1)* 25 to 26 labelled b_1(1)* 26 to 27 labelled b_1(1)* 27 to 28 labelled a_1(1)* 27 to 35 labelled b_1(2)* 28 to 16 labelled a_1(1)* 28 to 23 labelled b_1(1)* 29 to 30 labelled a_1(1)* 30 to 31 labelled a_1(1)* 31 to 32 labelled b_1(1)* 32 to 33 labelled b_1(1)* 33 to 34 labelled a_1(1)* 33 to 35 labelled b_1(2)* 34 to 26 labelled a_1(1)* 34 to 23 labelled b_1(1)* 35 to 36 labelled a_1(2)* 36 to 37 labelled a_1(2)* 37 to 38 labelled b_1(2)* 38 to 39 labelled b_1(2)* 39 to 40 labelled a_1(2)* 39 to 35 labelled b_1(2)* 40 to 26 labelled a_1(2)* 40 to 23 labelled b_1(1)
3.56/1.69	
3.56/1.69	
3.56/1.69	----------------------------------------
3.56/1.69	
3.56/1.69	(4)
3.56/1.69	YES
3.58/1.78	EOF