3.39/1.64	YES
3.73/1.69	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.73/1.69	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.73/1.69	
3.73/1.69	
3.73/1.69	Termination w.r.t. Q of the given QTRS could be proven:
3.73/1.69	
3.73/1.69	(0) QTRS
3.73/1.69	(1) QTRS Reverse [EQUIVALENT, 0 ms]
3.73/1.69	(2) QTRS
3.73/1.69	(3) Strip Symbols Proof [SOUND, 0 ms]
3.73/1.69	(4) QTRS
3.73/1.69	(5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
3.73/1.69	(6) YES
3.73/1.69	
3.73/1.69	
3.73/1.69	----------------------------------------
3.73/1.69	
3.73/1.69	(0)
3.73/1.69	Obligation:
3.73/1.69	Q restricted rewrite system:
3.73/1.69	The TRS R consists of the following rules:
3.73/1.69	
3.73/1.69	   a(b(a(a(b(a(b(a(x1)))))))) -> a(a(b(a(b(a(b(a(b(a(a(b(a(b(x1))))))))))))))
3.73/1.69	
3.73/1.69	Q is empty.
3.73/1.69	
3.73/1.69	----------------------------------------
3.73/1.69	
3.73/1.69	(1) QTRS Reverse (EQUIVALENT)
3.73/1.69	We applied the QTRS Reverse Processor [REVERSE].
3.73/1.69	----------------------------------------
3.73/1.69	
3.73/1.69	(2)
3.73/1.69	Obligation:
3.73/1.69	Q restricted rewrite system:
3.73/1.69	The TRS R consists of the following rules:
3.73/1.69	
3.73/1.69	   a(b(a(b(a(a(b(a(x1)))))))) -> b(a(b(a(a(b(a(b(a(b(a(b(a(a(x1))))))))))))))
3.73/1.69	
3.73/1.69	Q is empty.
3.73/1.69	
3.73/1.69	----------------------------------------
3.73/1.69	
3.73/1.69	(3) Strip Symbols Proof (SOUND)
3.73/1.69	We were given the following TRS:
3.73/1.69	
3.73/1.69	   a(b(a(b(a(a(b(a(x1)))))))) -> b(a(b(a(a(b(a(b(a(b(a(b(a(a(x1))))))))))))))
3.73/1.69	
3.73/1.69	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
3.73/1.69	
3.73/1.69	   a(b(a(b(a(a(b(x))))))) -> b(a(b(a(a(b(a(b(a(b(a(b(a(x)))))))))))))
3.73/1.69	
3.73/1.69	----------------------------------------
3.73/1.69	
3.73/1.69	(4)
3.73/1.69	Obligation:
3.73/1.69	Q restricted rewrite system:
3.73/1.69	The TRS R consists of the following rules:
3.73/1.69	
3.73/1.69	   a(b(a(b(a(a(b(x))))))) -> b(a(b(a(a(b(a(b(a(b(a(b(a(x)))))))))))))
3.73/1.69	
3.73/1.69	Q is empty.
3.73/1.69	
3.73/1.69	----------------------------------------
3.73/1.69	
3.73/1.69	(5) RFCMatchBoundsTRSProof (EQUIVALENT)
3.73/1.69	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
3.73/1.69	The following rules were used to construct the certificate:
3.73/1.69	
3.73/1.69	   a(b(a(b(a(a(b(x))))))) -> b(a(b(a(a(b(a(b(a(b(a(b(a(x)))))))))))))
3.73/1.69	
3.73/1.69	The certificate found is represented by the following graph.
3.73/1.69	The certificate consists of the following enumerated nodes:
3.73/1.69	189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214
3.73/1.69	
3.73/1.69	Node 189 is start node and node 190 is final node.
3.73/1.69	
3.73/1.69	Those nodes are connected through the following edges:
3.73/1.69	
3.73/1.69	* 189 to 191 labelled b_1(0)* 190 to 190 labelled #_1(0)* 191 to 192 labelled a_1(0)* 192 to 193 labelled b_1(0)* 193 to 194 labelled a_1(0)* 194 to 195 labelled a_1(0)* 195 to 196 labelled b_1(0)* 196 to 197 labelled a_1(0)* 197 to 198 labelled b_1(0)* 198 to 199 labelled a_1(0)* 198 to 203 labelled b_1(1)* 199 to 200 labelled b_1(0)* 200 to 201 labelled a_1(0)* 200 to 203 labelled b_1(1)* 201 to 202 labelled b_1(0)* 202 to 190 labelled a_1(0)* 202 to 203 labelled b_1(1)* 203 to 204 labelled a_1(1)* 204 to 205 labelled b_1(1)* 205 to 206 labelled a_1(1)* 206 to 207 labelled a_1(1)* 207 to 208 labelled b_1(1)* 208 to 209 labelled a_1(1)* 209 to 210 labelled b_1(1)* 210 to 211 labelled a_1(1)* 210 to 203 labelled b_1(1)* 211 to 212 labelled b_1(1)* 212 to 213 labelled a_1(1)* 212 to 203 labelled b_1(1)* 213 to 214 labelled b_1(1)* 214 to 190 labelled a_1(1)* 214 to 203 labelled b_1(1)
3.73/1.69	
3.73/1.69	
3.73/1.69	----------------------------------------
3.73/1.69	
3.73/1.69	(6)
3.73/1.69	YES
3.85/1.72	EOF