3.23/1.60	YES
3.23/1.61	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.23/1.61	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.23/1.61	
3.23/1.61	
3.23/1.61	Termination w.r.t. Q of the given QTRS could be proven:
3.23/1.61	
3.23/1.61	(0) QTRS
3.23/1.61	(1) QTRS Reverse [EQUIVALENT, 0 ms]
3.23/1.61	(2) QTRS
3.23/1.61	(3) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
3.23/1.61	(4) YES
3.23/1.61	
3.23/1.61	
3.23/1.61	----------------------------------------
3.23/1.61	
3.23/1.61	(0)
3.23/1.61	Obligation:
3.23/1.61	Q restricted rewrite system:
3.23/1.61	The TRS R consists of the following rules:
3.23/1.61	
3.23/1.61	   a(b(x1)) -> b(a(a(x1)))
3.23/1.61	   b(c(x1)) -> c(b(x1))
3.23/1.61	   a(a(x1)) -> a(c(a(x1)))
3.23/1.61	
3.23/1.61	Q is empty.
3.23/1.61	
3.23/1.61	----------------------------------------
3.23/1.61	
3.23/1.61	(1) QTRS Reverse (EQUIVALENT)
3.23/1.61	We applied the QTRS Reverse Processor [REVERSE].
3.23/1.61	----------------------------------------
3.23/1.61	
3.23/1.61	(2)
3.23/1.61	Obligation:
3.23/1.61	Q restricted rewrite system:
3.23/1.61	The TRS R consists of the following rules:
3.23/1.61	
3.23/1.61	   b(a(x1)) -> a(a(b(x1)))
3.23/1.61	   c(b(x1)) -> b(c(x1))
3.23/1.61	   a(a(x1)) -> a(c(a(x1)))
3.23/1.61	
3.23/1.61	Q is empty.
3.23/1.61	
3.23/1.61	----------------------------------------
3.23/1.61	
3.23/1.61	(3) RFCMatchBoundsTRSProof (EQUIVALENT)
3.23/1.61	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 3. This implies Q-termination of R.
3.23/1.61	The following rules were used to construct the certificate:
3.23/1.61	
3.23/1.61	   b(a(x1)) -> a(a(b(x1)))
3.23/1.61	   c(b(x1)) -> b(c(x1))
3.23/1.61	   a(a(x1)) -> a(c(a(x1)))
3.23/1.61	
3.23/1.61	The certificate found is represented by the following graph.
3.23/1.61	The certificate consists of the following enumerated nodes:
3.23/1.61	3, 4, 5, 6, 7, 8, 9, 15, 16, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36
3.23/1.61	
3.23/1.61	Node 3 is start node and node 4 is final node.
3.23/1.61	
3.23/1.61	Those nodes are connected through the following edges:
3.23/1.61	
3.23/1.61	* 3 to 5 labelled a_1(0)* 3 to 7 labelled b_1(0)* 3 to 8 labelled a_1(0)* 3 to 15 labelled a_1(1)* 4 to 4 labelled #_1(0)* 5 to 6 labelled a_1(0)* 5 to 27 labelled a_1(1)* 6 to 4 labelled b_1(0)* 6 to 22 labelled a_1(1)* 6 to 31 labelled a_1(2)* 7 to 4 labelled c_1(0)* 7 to 24 labelled b_1(1)* 8 to 9 labelled c_1(0)* 9 to 4 labelled a_1(0)* 9 to 25 labelled a_1(1)* 15 to 16 labelled c_1(1)* 16 to 6 labelled a_1(1)* 16 to 29 labelled a_1(2)* 16 to 27 labelled a_1(1)* 22 to 23 labelled a_1(1)* 22 to 29 labelled a_1(2)* 23 to 4 labelled b_1(1)* 23 to 22 labelled a_1(1)* 23 to 31 labelled a_1(2)* 24 to 4 labelled c_1(1)* 24 to 24 labelled b_1(1)* 25 to 26 labelled c_1(1)* 26 to 4 labelled a_1(1)* 26 to 25 labelled a_1(1)* 27 to 28 labelled c_1(1)* 28 to 22 labelled a_1(1)* 28 to 31 labelled a_1(1), a_1(2)* 29 to 30 labelled c_1(2)* 30 to 22 labelled a_1(2)* 30 to 31 labelled a_1(2)* 30 to 33 labelled a_1(3)* 31 to 32 labelled c_1(2)* 32 to 23 labelled a_1(2)* 32 to 29 labelled a_1(2)* 32 to 35 labelled a_1(3)* 33 to 34 labelled c_1(3)* 34 to 29 labelled a_1(3)* 35 to 36 labelled c_1(3)* 36 to 31 labelled a_1(3)
3.23/1.61	
3.23/1.61	
3.23/1.61	----------------------------------------
3.23/1.61	
3.23/1.61	(4)
3.23/1.61	YES
3.54/1.67	EOF