3.77/1.72	YES
3.77/1.76	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.77/1.76	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.77/1.76	
3.77/1.76	
3.77/1.76	Termination w.r.t. Q of the given QTRS could be proven:
3.77/1.76	
3.77/1.76	(0) QTRS
3.77/1.76	(1) QTRS Reverse [EQUIVALENT, 0 ms]
3.77/1.76	(2) QTRS
3.77/1.76	(3) Strip Symbols Proof [SOUND, 0 ms]
3.77/1.76	(4) QTRS
3.77/1.76	(5) RFCMatchBoundsTRSProof [EQUIVALENT, 13 ms]
3.77/1.76	(6) YES
3.77/1.76	
3.77/1.76	
3.77/1.76	----------------------------------------
3.77/1.76	
3.77/1.76	(0)
3.77/1.76	Obligation:
3.77/1.76	Q restricted rewrite system:
3.77/1.76	The TRS R consists of the following rules:
3.77/1.76	
3.77/1.76	   a(b(b(c(a(c(a(b(c(a(x1)))))))))) -> a(b(c(a(c(a(b(b(c(a(c(a(b(x1)))))))))))))
3.77/1.76	
3.77/1.76	Q is empty.
3.77/1.76	
3.77/1.76	----------------------------------------
3.77/1.76	
3.77/1.76	(1) QTRS Reverse (EQUIVALENT)
3.77/1.76	We applied the QTRS Reverse Processor [REVERSE].
3.77/1.76	----------------------------------------
3.77/1.76	
3.77/1.76	(2)
3.77/1.76	Obligation:
3.77/1.76	Q restricted rewrite system:
3.77/1.76	The TRS R consists of the following rules:
3.77/1.76	
3.77/1.76	   a(c(b(a(c(a(c(b(b(a(x1)))))))))) -> b(a(c(a(c(b(b(a(c(a(c(b(a(x1)))))))))))))
3.77/1.76	
3.77/1.76	Q is empty.
3.77/1.76	
3.77/1.76	----------------------------------------
3.77/1.76	
3.77/1.76	(3) Strip Symbols Proof (SOUND)
3.77/1.76	We were given the following TRS:
3.77/1.76	
3.77/1.76	   a(c(b(a(c(a(c(b(b(a(x1)))))))))) -> b(a(c(a(c(b(b(a(c(a(c(b(a(x1)))))))))))))
3.77/1.76	
3.77/1.76	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
3.77/1.76	
3.77/1.76	   a(c(b(a(c(a(c(b(b(x))))))))) -> b(a(c(a(c(b(b(a(c(a(c(b(x))))))))))))
3.77/1.76	
3.77/1.76	----------------------------------------
3.77/1.76	
3.77/1.76	(4)
3.77/1.76	Obligation:
3.77/1.76	Q restricted rewrite system:
3.77/1.76	The TRS R consists of the following rules:
3.77/1.76	
3.77/1.76	   a(c(b(a(c(a(c(b(b(x))))))))) -> b(a(c(a(c(b(b(a(c(a(c(b(x))))))))))))
3.77/1.76	
3.77/1.76	Q is empty.
3.77/1.76	
3.77/1.76	----------------------------------------
3.77/1.76	
3.77/1.76	(5) RFCMatchBoundsTRSProof (EQUIVALENT)
3.77/1.76	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 2. This implies Q-termination of R.
3.77/1.76	The following rules were used to construct the certificate:
3.77/1.76	
3.77/1.76	   a(c(b(a(c(a(c(b(b(x))))))))) -> b(a(c(a(c(b(b(a(c(a(c(b(x))))))))))))
3.77/1.76	
3.77/1.76	The certificate found is represented by the following graph.
3.77/1.76	The certificate consists of the following enumerated nodes:
3.77/1.76	7, 8, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 172, 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, 199, 200, 201, 202, 203, 204
3.77/1.76	
3.77/1.76	Node 7 is start node and node 8 is final node.
3.77/1.76	
3.77/1.76	Those nodes are connected through the following edges:
3.77/1.76	
3.77/1.76	* 7 to 149 labelled b_1(0)* 8 to 8 labelled #_1(0)* 149 to 150 labelled a_1(0)* 150 to 151 labelled c_1(0)* 151 to 152 labelled a_1(0)* 152 to 153 labelled c_1(0)* 153 to 154 labelled b_1(0)* 154 to 155 labelled b_1(0)* 155 to 156 labelled a_1(0)* 155 to 183 labelled b_1(1)* 156 to 157 labelled c_1(0)* 157 to 158 labelled a_1(0)* 157 to 172 labelled b_1(1)* 158 to 159 labelled c_1(0)* 159 to 8 labelled b_1(0)* 172 to 173 labelled a_1(1)* 173 to 174 labelled c_1(1)* 174 to 175 labelled a_1(1)* 175 to 176 labelled c_1(1)* 176 to 177 labelled b_1(1)* 177 to 178 labelled b_1(1)* 178 to 179 labelled a_1(1)* 178 to 194 labelled b_1(2)* 179 to 180 labelled c_1(1)* 180 to 181 labelled a_1(1)* 180 to 172 labelled b_1(1)* 181 to 182 labelled c_1(1)* 182 to 8 labelled b_1(1)* 183 to 184 labelled a_1(1)* 184 to 185 labelled c_1(1)* 185 to 186 labelled a_1(1)* 186 to 187 labelled c_1(1)* 187 to 188 labelled b_1(1)* 188 to 189 labelled b_1(1)* 189 to 190 labelled a_1(1)* 189 to 194 labelled b_1(2)* 190 to 191 labelled c_1(1)* 191 to 192 labelled a_1(1)* 191 to 172 labelled b_1(1)* 192 to 193 labelled c_1(1)* 193 to 178 labelled b_1(1)* 194 to 195 labelled a_1(2)* 195 to 196 labelled c_1(2)* 196 to 197 labelled a_1(2)* 197 to 198 labelled c_1(2)* 198 to 199 labelled b_1(2)* 199 to 200 labelled b_1(2)* 200 to 201 labelled a_1(2)* 200 to 194 labelled b_1(2)* 201 to 202 labelled c_1(2)* 202 to 203 labelled a_1(2)* 202 to 172 labelled b_1(1)* 203 to 204 labelled c_1(2)* 204 to 178 labelled b_1(2)
3.77/1.76	
3.77/1.76	
3.77/1.76	----------------------------------------
3.77/1.76	
3.77/1.76	(6)
3.77/1.76	YES
3.98/1.79	EOF