3.09/1.55	YES
3.20/1.59	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.20/1.59	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.20/1.59	
3.20/1.59	
3.20/1.59	Termination w.r.t. Q of the given QTRS could be proven:
3.20/1.59	
3.20/1.59	(0) QTRS
3.20/1.59	(1) QTRS Reverse [EQUIVALENT, 0 ms]
3.20/1.59	(2) QTRS
3.20/1.59	(3) Strip Symbols Proof [SOUND, 0 ms]
3.20/1.59	(4) QTRS
3.20/1.59	(5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
3.20/1.59	(6) YES
3.20/1.59	
3.20/1.59	
3.20/1.59	----------------------------------------
3.20/1.59	
3.20/1.59	(0)
3.20/1.59	Obligation:
3.20/1.59	Q restricted rewrite system:
3.20/1.59	The TRS R consists of the following rules:
3.20/1.59	
3.20/1.59	   a(b(a(a(b(a(x1)))))) -> a(a(b(a(b(a(b(a(b(a(b(a(a(b(x1))))))))))))))
3.20/1.59	
3.20/1.59	Q is empty.
3.20/1.59	
3.20/1.59	----------------------------------------
3.20/1.59	
3.20/1.59	(1) QTRS Reverse (EQUIVALENT)
3.20/1.59	We applied the QTRS Reverse Processor [REVERSE].
3.20/1.59	----------------------------------------
3.20/1.59	
3.20/1.59	(2)
3.20/1.59	Obligation:
3.20/1.59	Q restricted rewrite system:
3.20/1.59	The TRS R consists of the following rules:
3.20/1.59	
3.20/1.59	   a(b(a(a(b(a(x1)))))) -> b(a(a(b(a(b(a(b(a(b(a(b(a(a(x1))))))))))))))
3.20/1.59	
3.20/1.59	Q is empty.
3.20/1.59	
3.20/1.59	----------------------------------------
3.20/1.59	
3.20/1.59	(3) Strip Symbols Proof (SOUND)
3.20/1.59	We were given the following TRS:
3.20/1.59	
3.20/1.59	   a(b(a(a(b(a(x1)))))) -> b(a(a(b(a(b(a(b(a(b(a(b(a(a(x1))))))))))))))
3.20/1.59	
3.20/1.59	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
3.20/1.59	
3.20/1.59	   a(b(a(a(b(x))))) -> b(a(a(b(a(b(a(b(a(b(a(b(a(x)))))))))))))
3.20/1.59	
3.20/1.59	----------------------------------------
3.20/1.59	
3.20/1.59	(4)
3.20/1.59	Obligation:
3.20/1.59	Q restricted rewrite system:
3.20/1.59	The TRS R consists of the following rules:
3.20/1.59	
3.20/1.59	   a(b(a(a(b(x))))) -> b(a(a(b(a(b(a(b(a(b(a(b(a(x)))))))))))))
3.20/1.59	
3.20/1.59	Q is empty.
3.20/1.59	
3.20/1.59	----------------------------------------
3.20/1.59	
3.20/1.59	(5) RFCMatchBoundsTRSProof (EQUIVALENT)
3.20/1.59	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
3.20/1.59	The following rules were used to construct the certificate:
3.20/1.59	
3.20/1.59	   a(b(a(a(b(x))))) -> b(a(a(b(a(b(a(b(a(b(a(b(a(x)))))))))))))
3.20/1.59	
3.20/1.59	The certificate found is represented by the following graph.
3.20/1.59	The certificate consists of the following enumerated nodes:
3.20/1.59	24, 27, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69
3.20/1.59	
3.20/1.59	Node 24 is start node and node 27 is final node.
3.20/1.59	
3.20/1.59	Those nodes are connected through the following edges:
3.20/1.59	
3.20/1.59	* 24 to 34 labelled b_1(0)* 27 to 27 labelled #_1(0)* 34 to 35 labelled a_1(0)* 35 to 36 labelled a_1(0)* 36 to 37 labelled b_1(0)* 37 to 38 labelled a_1(0)* 38 to 39 labelled b_1(0)* 39 to 40 labelled a_1(0)* 40 to 41 labelled b_1(0)* 41 to 42 labelled a_1(0)* 42 to 43 labelled b_1(0)* 43 to 44 labelled a_1(0)* 43 to 58 labelled b_1(1)* 44 to 45 labelled b_1(0)* 45 to 27 labelled a_1(0)* 45 to 58 labelled b_1(1)* 58 to 59 labelled a_1(1)* 59 to 60 labelled a_1(1)* 60 to 61 labelled b_1(1)* 61 to 62 labelled a_1(1)* 62 to 63 labelled b_1(1)* 63 to 64 labelled a_1(1)* 64 to 65 labelled b_1(1)* 65 to 66 labelled a_1(1)* 66 to 67 labelled b_1(1)* 67 to 68 labelled a_1(1)* 67 to 58 labelled b_1(1)* 68 to 69 labelled b_1(1)* 69 to 27 labelled a_1(1)* 69 to 58 labelled b_1(1)
3.20/1.59	
3.20/1.59	
3.20/1.59	----------------------------------------
3.20/1.59	
3.20/1.59	(6)
3.20/1.59	YES
3.20/1.62	EOF