2.98/1.66	YES
3.28/1.69	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.28/1.69	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.28/1.69	
3.28/1.69	
3.28/1.69	Termination w.r.t. Q of the given QTRS could be proven:
3.28/1.69	
3.28/1.69	(0) QTRS
3.28/1.69	(1) QTRS Reverse [EQUIVALENT, 0 ms]
3.28/1.69	(2) QTRS
3.28/1.69	(3) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
3.28/1.69	(4) YES
3.28/1.69	
3.28/1.69	
3.28/1.69	----------------------------------------
3.28/1.69	
3.28/1.69	(0)
3.28/1.69	Obligation:
3.28/1.69	Q restricted rewrite system:
3.28/1.69	The TRS R consists of the following rules:
3.28/1.69	
3.28/1.69	   b(a(b(a(c(b(a(x1))))))) -> a(b(a(c(b(b(a(b(a(c(x1))))))))))
3.28/1.69	
3.28/1.69	Q is empty.
3.28/1.69	
3.28/1.69	----------------------------------------
3.28/1.69	
3.28/1.69	(1) QTRS Reverse (EQUIVALENT)
3.28/1.69	We applied the QTRS Reverse Processor [REVERSE].
3.28/1.69	----------------------------------------
3.28/1.69	
3.28/1.69	(2)
3.28/1.69	Obligation:
3.28/1.69	Q restricted rewrite system:
3.28/1.69	The TRS R consists of the following rules:
3.28/1.69	
3.28/1.69	   a(b(c(a(b(a(b(x1))))))) -> c(a(b(a(b(b(c(a(b(a(x1))))))))))
3.28/1.69	
3.28/1.69	Q is empty.
3.28/1.69	
3.28/1.69	----------------------------------------
3.28/1.69	
3.28/1.69	(3) RFCMatchBoundsTRSProof (EQUIVALENT)
3.28/1.69	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 2. This implies Q-termination of R.
3.28/1.69	The following rules were used to construct the certificate:
3.28/1.69	
3.28/1.69	   a(b(c(a(b(a(b(x1))))))) -> c(a(b(a(b(b(c(a(b(a(x1))))))))))
3.28/1.69	
3.28/1.69	The certificate found is represented by the following graph.
3.28/1.69	The certificate consists of the following enumerated nodes:
3.28/1.69	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, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58
3.28/1.69	
3.28/1.69	Node 21 is start node and node 22 is final node.
3.28/1.69	
3.28/1.69	Those nodes are connected through the following edges:
3.28/1.69	
3.28/1.69	* 21 to 23 labelled c_1(0)* 22 to 22 labelled #_1(0)* 23 to 24 labelled a_1(0)* 24 to 25 labelled b_1(0)* 25 to 26 labelled a_1(0)* 26 to 27 labelled b_1(0)* 27 to 28 labelled b_1(0)* 28 to 29 labelled c_1(0)* 29 to 30 labelled a_1(0)* 29 to 41 labelled c_1(1)* 30 to 31 labelled b_1(0)* 31 to 22 labelled a_1(0)* 31 to 32 labelled c_1(1)* 32 to 33 labelled a_1(1)* 33 to 34 labelled b_1(1)* 34 to 35 labelled a_1(1)* 35 to 36 labelled b_1(1)* 36 to 37 labelled b_1(1)* 37 to 38 labelled c_1(1)* 38 to 39 labelled a_1(1)* 38 to 50 labelled c_1(2)* 39 to 40 labelled b_1(1)* 40 to 22 labelled a_1(1)* 40 to 32 labelled c_1(1)* 41 to 42 labelled a_1(1)* 42 to 43 labelled b_1(1)* 43 to 44 labelled a_1(1)* 44 to 45 labelled b_1(1)* 45 to 46 labelled b_1(1)* 46 to 47 labelled c_1(1)* 47 to 48 labelled a_1(1)* 47 to 50 labelled c_1(2)* 48 to 49 labelled b_1(1)* 49 to 36 labelled a_1(1)* 49 to 32 labelled c_1(1)* 50 to 51 labelled a_1(2)* 51 to 52 labelled b_1(2)* 52 to 53 labelled a_1(2)* 53 to 54 labelled b_1(2)* 54 to 55 labelled b_1(2)* 55 to 56 labelled c_1(2)* 56 to 57 labelled a_1(2)* 56 to 50 labelled c_1(2)* 57 to 58 labelled b_1(2)* 58 to 36 labelled a_1(2)* 58 to 32 labelled c_1(1)
3.28/1.69	
3.28/1.69	
3.28/1.69	----------------------------------------
3.28/1.69	
3.28/1.69	(4)
3.28/1.69	YES
3.39/1.73	EOF