3.12/1.54	YES
3.12/1.55	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.12/1.55	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.12/1.55	
3.12/1.55	
3.12/1.55	Termination w.r.t. Q of the given QTRS could be proven:
3.12/1.55	
3.12/1.55	(0) QTRS
3.12/1.55	(1) QTRS Reverse [EQUIVALENT, 0 ms]
3.12/1.55	(2) QTRS
3.12/1.55	(3) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
3.12/1.55	(4) YES
3.12/1.55	
3.12/1.55	
3.12/1.55	----------------------------------------
3.12/1.55	
3.12/1.55	(0)
3.12/1.55	Obligation:
3.12/1.55	Q restricted rewrite system:
3.12/1.55	The TRS R consists of the following rules:
3.12/1.55	
3.12/1.55	   b(c(a(x1))) -> a(b(a(b(c(x1)))))
3.12/1.55	   b(x1) -> c(c(x1))
3.12/1.55	   c(d(x1)) -> a(b(c(a(x1))))
3.12/1.55	   a(a(x1)) -> a(c(b(a(x1))))
3.12/1.55	
3.12/1.55	Q is empty.
3.12/1.55	
3.12/1.55	----------------------------------------
3.12/1.55	
3.12/1.55	(1) QTRS Reverse (EQUIVALENT)
3.12/1.55	We applied the QTRS Reverse Processor [REVERSE].
3.12/1.55	----------------------------------------
3.12/1.55	
3.12/1.55	(2)
3.12/1.55	Obligation:
3.12/1.55	Q restricted rewrite system:
3.12/1.55	The TRS R consists of the following rules:
3.12/1.55	
3.12/1.55	   a(c(b(x1))) -> c(b(a(b(a(x1)))))
3.12/1.55	   b(x1) -> c(c(x1))
3.12/1.55	   d(c(x1)) -> a(c(b(a(x1))))
3.12/1.55	   a(a(x1)) -> a(b(c(a(x1))))
3.12/1.55	
3.12/1.55	Q is empty.
3.12/1.55	
3.12/1.55	----------------------------------------
3.12/1.55	
3.12/1.55	(3) RFCMatchBoundsTRSProof (EQUIVALENT)
3.12/1.55	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 3. This implies Q-termination of R.
3.12/1.55	The following rules were used to construct the certificate:
3.12/1.55	
3.12/1.55	   a(c(b(x1))) -> c(b(a(b(a(x1)))))
3.12/1.55	   b(x1) -> c(c(x1))
3.12/1.55	   d(c(x1)) -> a(c(b(a(x1))))
3.12/1.55	   a(a(x1)) -> a(b(c(a(x1))))
3.12/1.55	
3.12/1.55	The certificate found is represented by the following graph.
3.12/1.55	The certificate consists of the following enumerated nodes:
3.12/1.55	3, 4, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 57, 58, 59, 60, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 86, 87, 88, 89, 90, 91, 92
3.12/1.55	
3.12/1.55	Node 3 is start node and node 4 is final node.
3.12/1.55	
3.12/1.55	Those nodes are connected through the following edges:
3.12/1.55	
3.12/1.55	* 3 to 29 labelled c_1(0)* 3 to 33 labelled a_1(0)* 3 to 36 labelled a_1(0)* 3 to 57 labelled c_1(1)* 4 to 4 labelled #_1(0)* 29 to 30 labelled b_1(0)* 29 to 4 labelled c_1(0)* 29 to 39 labelled c_1(1)* 30 to 31 labelled a_1(0)* 31 to 32 labelled b_1(0)* 31 to 40 labelled c_1(1)* 32 to 4 labelled a_1(0)* 32 to 43 labelled c_1(1)* 32 to 47 labelled a_1(1)* 33 to 34 labelled c_1(0)* 34 to 35 labelled b_1(0)* 34 to 41 labelled c_1(1)* 35 to 4 labelled a_1(0)* 35 to 43 labelled c_1(1)* 35 to 47 labelled a_1(1)* 36 to 37 labelled b_1(0)* 36 to 42 labelled c_1(1)* 37 to 38 labelled c_1(0)* 38 to 4 labelled a_1(0)* 38 to 43 labelled c_1(1)* 38 to 47 labelled a_1(1)* 39 to 30 labelled c_1(1)* 40 to 32 labelled c_1(1)* 41 to 35 labelled c_1(1)* 42 to 37 labelled c_1(1)* 43 to 44 labelled b_1(1)* 43 to 65 labelled c_1(2)* 44 to 45 labelled a_1(1)* 45 to 46 labelled b_1(1)* 45 to 66 labelled c_1(2)* 46 to 4 labelled a_1(1)* 46 to 43 labelled c_1(1)* 46 to 47 labelled a_1(1)* 47 to 48 labelled b_1(1)* 47 to 67 labelled c_1(2)* 48 to 49 labelled c_1(1)* 49 to 4 labelled a_1(1)* 49 to 43 labelled c_1(1)* 49 to 47 labelled a_1(1)* 57 to 58 labelled b_1(1)* 57 to 68 labelled c_1(2)* 58 to 59 labelled a_1(1)* 59 to 60 labelled b_1(1)* 59 to 69 labelled c_1(2)* 60 to 35 labelled a_1(1)* 60 to 47 labelled a_1(1)* 60 to 70 labelled a_1(2)* 60 to 73 labelled c_1(2)* 65 to 44 labelled c_1(2)* 66 to 46 labelled c_1(2)* 67 to 48 labelled c_1(2)* 68 to 58 labelled c_1(2)* 69 to 60 labelled c_1(2)* 70 to 71 labelled b_1(2)* 70 to 86 labelled c_1(3)* 71 to 72 labelled c_1(2)* 72 to 47 labelled a_1(2)* 73 to 74 labelled b_1(2)* 73 to 87 labelled c_1(3)* 74 to 75 labelled a_1(2)* 75 to 76 labelled b_1(2)* 75 to 88 labelled c_1(3)* 76 to 44 labelled a_1(2)* 76 to 89 labelled a_1(2)* 86 to 71 labelled c_1(3)* 87 to 74 labelled c_1(3)* 88 to 76 labelled c_1(3)* 89 to 90 labelled b_1(2)* 89 to 92 labelled c_1(3)* 90 to 91 labelled c_1(2)* 91 to 45 labelled a_1(2)* 92 to 90 labelled c_1(3)
3.12/1.55	
3.12/1.55	
3.12/1.55	----------------------------------------
3.12/1.55	
3.12/1.55	(4)
3.12/1.55	YES
3.29/1.59	EOF