3.44/1.71	YES
3.44/1.73	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.44/1.73	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.44/1.73	
3.44/1.73	
3.44/1.73	Termination w.r.t. Q of the given QTRS could be proven:
3.44/1.73	
3.44/1.73	(0) QTRS
3.44/1.73	(1) QTRS Reverse [EQUIVALENT, 0 ms]
3.44/1.73	(2) QTRS
3.44/1.73	(3) Strip Symbols Proof [SOUND, 0 ms]
3.44/1.73	(4) QTRS
3.44/1.73	(5) RFCMatchBoundsTRSProof [EQUIVALENT, 6 ms]
3.44/1.73	(6) YES
3.44/1.73	
3.44/1.73	
3.44/1.73	----------------------------------------
3.44/1.73	
3.44/1.73	(0)
3.44/1.73	Obligation:
3.44/1.73	Q restricted rewrite system:
3.44/1.73	The TRS R consists of the following rules:
3.44/1.73	
3.44/1.73	   a(b(a(a(b(a(b(a(x1)))))))) -> a(a(b(a(b(a(b(a(a(b(x1))))))))))
3.44/1.73	
3.44/1.73	Q is empty.
3.44/1.73	
3.44/1.73	----------------------------------------
3.44/1.73	
3.44/1.73	(1) QTRS Reverse (EQUIVALENT)
3.44/1.73	We applied the QTRS Reverse Processor [REVERSE].
3.44/1.73	----------------------------------------
3.44/1.73	
3.44/1.73	(2)
3.44/1.73	Obligation:
3.44/1.73	Q restricted rewrite system:
3.44/1.73	The TRS R consists of the following rules:
3.44/1.73	
3.44/1.73	   a(b(a(b(a(a(b(a(x1)))))))) -> b(a(a(b(a(b(a(b(a(a(x1))))))))))
3.44/1.73	
3.44/1.73	Q is empty.
3.44/1.73	
3.44/1.73	----------------------------------------
3.44/1.73	
3.44/1.73	(3) Strip Symbols Proof (SOUND)
3.44/1.73	We were given the following TRS:
3.44/1.73	
3.44/1.73	   a(b(a(b(a(a(b(a(x1)))))))) -> b(a(a(b(a(b(a(b(a(a(x1))))))))))
3.44/1.73	
3.44/1.73	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
3.44/1.73	
3.44/1.73	   a(b(a(b(a(a(b(x))))))) -> b(a(a(b(a(b(a(b(a(x)))))))))
3.44/1.73	
3.44/1.73	----------------------------------------
3.44/1.73	
3.44/1.73	(4)
3.44/1.73	Obligation:
3.44/1.73	Q restricted rewrite system:
3.44/1.73	The TRS R consists of the following rules:
3.44/1.73	
3.44/1.73	   a(b(a(b(a(a(b(x))))))) -> b(a(a(b(a(b(a(b(a(x)))))))))
3.44/1.73	
3.44/1.73	Q is empty.
3.44/1.73	
3.44/1.73	----------------------------------------
3.44/1.73	
3.44/1.73	(5) RFCMatchBoundsTRSProof (EQUIVALENT)
3.44/1.73	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
3.44/1.73	The following rules were used to construct the certificate:
3.44/1.73	
3.44/1.73	   a(b(a(b(a(a(b(x))))))) -> b(a(a(b(a(b(a(b(a(x)))))))))
3.44/1.73	
3.44/1.73	The certificate found is represented by the following graph.
3.44/1.73	The certificate consists of the following enumerated nodes:
3.44/1.73	211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228
3.44/1.73	
3.44/1.73	Node 211 is start node and node 212 is final node.
3.44/1.73	
3.44/1.73	Those nodes are connected through the following edges:
3.44/1.73	
3.44/1.73	* 211 to 213 labelled b_1(0)* 212 to 212 labelled #_1(0)* 213 to 214 labelled a_1(0)* 214 to 215 labelled a_1(0)* 215 to 216 labelled b_1(0)* 216 to 217 labelled a_1(0)* 216 to 221 labelled b_1(1)* 217 to 218 labelled b_1(0)* 218 to 219 labelled a_1(0)* 218 to 221 labelled b_1(1)* 219 to 220 labelled b_1(0)* 220 to 212 labelled a_1(0)* 220 to 221 labelled b_1(1)* 221 to 222 labelled a_1(1)* 222 to 223 labelled a_1(1)* 223 to 224 labelled b_1(1)* 224 to 225 labelled a_1(1)* 224 to 221 labelled b_1(1)* 225 to 226 labelled b_1(1)* 226 to 227 labelled a_1(1)* 226 to 221 labelled b_1(1)* 227 to 228 labelled b_1(1)* 228 to 212 labelled a_1(1)* 228 to 221 labelled b_1(1)
3.44/1.73	
3.44/1.73	
3.44/1.73	----------------------------------------
3.44/1.73	
3.44/1.73	(6)
3.44/1.73	YES
3.44/1.75	EOF