3.85/1.72	YES
4.11/1.79	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
4.11/1.79	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.11/1.79	
4.11/1.79	
4.11/1.79	Termination w.r.t. Q of the given QTRS could be proven:
4.11/1.79	
4.11/1.79	(0) QTRS
4.11/1.79	(1) QTRS Reverse [EQUIVALENT, 0 ms]
4.11/1.79	(2) QTRS
4.11/1.79	(3) Strip Symbols Proof [SOUND, 0 ms]
4.11/1.79	(4) QTRS
4.11/1.79	(5) RFCMatchBoundsTRSProof [EQUIVALENT, 4 ms]
4.11/1.79	(6) YES
4.11/1.79	
4.11/1.79	
4.11/1.79	----------------------------------------
4.11/1.79	
4.11/1.79	(0)
4.11/1.79	Obligation:
4.11/1.79	Q restricted rewrite system:
4.11/1.79	The TRS R consists of the following rules:
4.11/1.79	
4.11/1.79	   a(a(b(b(a(a(b(a(b(a(b(a(x1)))))))))))) -> a(a(b(a(b(a(b(a(a(b(b(a(a(b(x1))))))))))))))
4.11/1.79	
4.11/1.79	Q is empty.
4.11/1.79	
4.11/1.79	----------------------------------------
4.11/1.79	
4.11/1.79	(1) QTRS Reverse (EQUIVALENT)
4.11/1.79	We applied the QTRS Reverse Processor [REVERSE].
4.11/1.79	----------------------------------------
4.11/1.79	
4.11/1.79	(2)
4.11/1.79	Obligation:
4.11/1.79	Q restricted rewrite system:
4.11/1.79	The TRS R consists of the following rules:
4.11/1.79	
4.11/1.79	   a(b(a(b(a(b(a(a(b(b(a(a(x1)))))))))))) -> b(a(a(b(b(a(a(b(a(b(a(b(a(a(x1))))))))))))))
4.11/1.79	
4.11/1.79	Q is empty.
4.11/1.79	
4.11/1.79	----------------------------------------
4.11/1.79	
4.11/1.79	(3) Strip Symbols Proof (SOUND)
4.11/1.79	We were given the following TRS:
4.11/1.79	
4.11/1.79	   a(b(a(b(a(b(a(a(b(b(a(a(x1)))))))))))) -> b(a(a(b(b(a(a(b(a(b(a(b(a(a(x1))))))))))))))
4.11/1.79	
4.11/1.79	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
4.11/1.79	
4.11/1.79	   a(b(a(b(a(b(a(a(b(b(a(x))))))))))) -> b(a(a(b(b(a(a(b(a(b(a(b(a(x)))))))))))))
4.11/1.79	
4.11/1.79	----------------------------------------
4.11/1.79	
4.11/1.79	(4)
4.11/1.79	Obligation:
4.11/1.79	Q restricted rewrite system:
4.11/1.79	The TRS R consists of the following rules:
4.11/1.79	
4.11/1.79	   a(b(a(b(a(b(a(a(b(b(a(x))))))))))) -> b(a(a(b(b(a(a(b(a(b(a(b(a(x)))))))))))))
4.11/1.79	
4.11/1.79	Q is empty.
4.11/1.79	
4.11/1.79	----------------------------------------
4.11/1.79	
4.11/1.79	(5) RFCMatchBoundsTRSProof (EQUIVALENT)
4.11/1.79	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
4.11/1.79	The following rules were used to construct the certificate:
4.11/1.79	
4.11/1.79	   a(b(a(b(a(b(a(a(b(b(a(x))))))))))) -> b(a(a(b(b(a(a(b(a(b(a(b(a(x)))))))))))))
4.11/1.79	
4.11/1.79	The certificate found is represented by the following graph.
4.11/1.79	The certificate consists of the following enumerated nodes:
4.11/1.79	173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198
4.11/1.79	
4.11/1.79	Node 173 is start node and node 174 is final node.
4.11/1.79	
4.11/1.79	Those nodes are connected through the following edges:
4.11/1.79	
4.11/1.79	* 173 to 175 labelled b_1(0)* 174 to 174 labelled #_1(0)* 175 to 176 labelled a_1(0)* 176 to 177 labelled a_1(0)* 177 to 178 labelled b_1(0)* 178 to 179 labelled b_1(0)* 179 to 180 labelled a_1(0)* 180 to 181 labelled a_1(0)* 180 to 187 labelled b_1(1)* 181 to 182 labelled b_1(0)* 182 to 183 labelled a_1(0)* 182 to 187 labelled b_1(1)* 183 to 184 labelled b_1(0)* 184 to 185 labelled a_1(0)* 184 to 187 labelled b_1(1)* 185 to 186 labelled b_1(0)* 186 to 174 labelled a_1(0)* 186 to 187 labelled b_1(1)* 187 to 188 labelled a_1(1)* 188 to 189 labelled a_1(1)* 189 to 190 labelled b_1(1)* 190 to 191 labelled b_1(1)* 191 to 192 labelled a_1(1)* 192 to 193 labelled a_1(1)* 192 to 187 labelled b_1(1)* 193 to 194 labelled b_1(1)* 194 to 195 labelled a_1(1)* 194 to 187 labelled b_1(1)* 195 to 196 labelled b_1(1)* 196 to 197 labelled a_1(1)* 196 to 187 labelled b_1(1)* 197 to 198 labelled b_1(1)* 198 to 174 labelled a_1(1)* 198 to 187 labelled b_1(1)
4.11/1.79	
4.11/1.79	
4.11/1.79	----------------------------------------
4.11/1.79	
4.11/1.79	(6)
4.11/1.79	YES
4.11/1.81	EOF