3.40/1.74	YES
3.66/1.80	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.66/1.80	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.66/1.80	
3.66/1.80	
3.66/1.80	Termination w.r.t. Q of the given QTRS could be proven:
3.66/1.80	
3.66/1.80	(0) QTRS
3.66/1.80	(1) Strip Symbols Proof [SOUND, 0 ms]
3.66/1.80	(2) QTRS
3.66/1.80	(3) RFCMatchBoundsTRSProof [EQUIVALENT, 3 ms]
3.66/1.80	(4) YES
3.66/1.80	
3.66/1.80	
3.66/1.80	----------------------------------------
3.66/1.80	
3.66/1.80	(0)
3.66/1.80	Obligation:
3.66/1.80	Q restricted rewrite system:
3.66/1.80	The TRS R consists of the following rules:
3.66/1.80	
3.66/1.80	   b(a(b(a(b(a(a(a(b(x1))))))))) -> a(a(b(a(a(a(b(a(b(a(b(a(b(x1)))))))))))))
3.66/1.80	
3.66/1.80	Q is empty.
3.66/1.80	
3.66/1.80	----------------------------------------
3.66/1.80	
3.66/1.80	(1) Strip Symbols Proof (SOUND)
3.66/1.80	We were given the following TRS:
3.66/1.80	
3.66/1.80	   b(a(b(a(b(a(a(a(b(x1))))))))) -> a(a(b(a(a(a(b(a(b(a(b(a(b(x1)))))))))))))
3.66/1.80	
3.66/1.80	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
3.66/1.80	
3.66/1.80	   b(a(b(a(b(a(a(a(x)))))))) -> a(a(b(a(a(a(b(a(b(a(b(a(x))))))))))))
3.66/1.80	
3.66/1.80	----------------------------------------
3.66/1.80	
3.66/1.80	(2)
3.66/1.80	Obligation:
3.66/1.80	Q restricted rewrite system:
3.66/1.80	The TRS R consists of the following rules:
3.66/1.80	
3.66/1.80	   b(a(b(a(b(a(a(a(x)))))))) -> a(a(b(a(a(a(b(a(b(a(b(a(x))))))))))))
3.66/1.80	
3.66/1.80	Q is empty.
3.66/1.80	
3.66/1.80	----------------------------------------
3.66/1.80	
3.66/1.80	(3) RFCMatchBoundsTRSProof (EQUIVALENT)
3.66/1.80	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
3.66/1.80	The following rules were used to construct the certificate:
3.66/1.80	
3.66/1.80	   b(a(b(a(b(a(a(a(x)))))))) -> a(a(b(a(a(a(b(a(b(a(b(a(x))))))))))))
3.66/1.80	
3.66/1.80	The certificate found is represented by the following graph.
3.66/1.80	The certificate consists of the following enumerated nodes:
3.66/1.80	173, 174, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220
3.66/1.80	
3.66/1.80	Node 173 is start node and node 174 is final node.
3.66/1.80	
3.66/1.80	Those nodes are connected through the following edges:
3.66/1.80	
3.66/1.80	* 173 to 199 labelled a_1(0)* 174 to 174 labelled #_1(0)* 199 to 200 labelled a_1(0)* 200 to 201 labelled b_1(0)* 201 to 202 labelled a_1(0)* 202 to 203 labelled a_1(0)* 203 to 204 labelled a_1(0)* 204 to 205 labelled b_1(0)* 204 to 210 labelled a_1(1)* 205 to 206 labelled a_1(0)* 206 to 207 labelled b_1(0)* 206 to 210 labelled a_1(1)* 207 to 208 labelled a_1(0)* 208 to 209 labelled b_1(0)* 208 to 210 labelled a_1(1)* 209 to 174 labelled a_1(0)* 210 to 211 labelled a_1(1)* 211 to 212 labelled b_1(1)* 212 to 213 labelled a_1(1)* 213 to 214 labelled a_1(1)* 214 to 215 labelled a_1(1)* 215 to 216 labelled b_1(1)* 215 to 210 labelled a_1(1)* 216 to 217 labelled a_1(1)* 217 to 218 labelled b_1(1)* 217 to 210 labelled a_1(1)* 218 to 219 labelled a_1(1)* 219 to 220 labelled b_1(1)* 219 to 210 labelled a_1(1)* 220 to 174 labelled a_1(1)
3.66/1.81	
3.66/1.81	
3.66/1.81	----------------------------------------
3.66/1.81	
3.66/1.81	(4)
3.66/1.81	YES
3.88/1.84	EOF