3.79/1.71	YES
3.79/1.72	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.79/1.72	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.79/1.72	
3.79/1.72	
3.79/1.72	Termination w.r.t. Q of the given QTRS could be proven:
3.79/1.72	
3.79/1.72	(0) QTRS
3.79/1.72	(1) QTRS Reverse [EQUIVALENT, 0 ms]
3.79/1.72	(2) QTRS
3.79/1.72	(3) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
3.79/1.72	(4) YES
3.79/1.72	
3.79/1.72	
3.79/1.72	----------------------------------------
3.79/1.72	
3.79/1.72	(0)
3.79/1.72	Obligation:
3.79/1.72	Q restricted rewrite system:
3.79/1.72	The TRS R consists of the following rules:
3.79/1.72	
3.79/1.72	   b(a(a(b(a(x1))))) -> a(b(a(a(b(b(a(a(b(x1)))))))))
3.79/1.72	
3.79/1.72	Q is empty.
3.79/1.72	
3.79/1.72	----------------------------------------
3.79/1.72	
3.79/1.72	(1) QTRS Reverse (EQUIVALENT)
3.79/1.72	We applied the QTRS Reverse Processor [REVERSE].
3.79/1.72	----------------------------------------
3.79/1.72	
3.79/1.72	(2)
3.79/1.72	Obligation:
3.79/1.72	Q restricted rewrite system:
3.79/1.72	The TRS R consists of the following rules:
3.79/1.72	
3.79/1.72	   a(b(a(a(b(x1))))) -> b(a(a(b(b(a(a(b(a(x1)))))))))
3.79/1.72	
3.79/1.72	Q is empty.
3.79/1.72	
3.79/1.72	----------------------------------------
3.79/1.72	
3.79/1.72	(3) RFCMatchBoundsTRSProof (EQUIVALENT)
3.79/1.72	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 2. This implies Q-termination of R.
3.79/1.72	The following rules were used to construct the certificate:
3.79/1.72	
3.79/1.72	   a(b(a(a(b(x1))))) -> b(a(a(b(b(a(a(b(a(x1)))))))))
3.79/1.72	
3.79/1.72	The certificate found is represented by the following graph.
3.79/1.72	The certificate consists of the following enumerated nodes:
3.79/1.72	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, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220
3.79/1.72	
3.79/1.72	Node 179 is start node and node 180 is final node.
3.79/1.72	
3.79/1.72	Those nodes are connected through the following edges:
3.79/1.72	
3.79/1.72	* 179 to 181 labelled b_1(0)* 180 to 180 labelled #_1(0)* 181 to 182 labelled a_1(0)* 182 to 183 labelled a_1(0)* 183 to 184 labelled b_1(0)* 184 to 185 labelled b_1(0)* 185 to 186 labelled a_1(0)* 185 to 197 labelled b_1(1)* 186 to 187 labelled a_1(0)* 186 to 189 labelled b_1(1)* 187 to 188 labelled b_1(0)* 188 to 180 labelled a_1(0)* 188 to 189 labelled b_1(1)* 189 to 190 labelled a_1(1)* 190 to 191 labelled a_1(1)* 191 to 192 labelled b_1(1)* 192 to 193 labelled b_1(1)* 193 to 194 labelled a_1(1)* 193 to 205 labelled b_1(2)* 194 to 195 labelled a_1(1)* 194 to 189 labelled b_1(1)* 195 to 196 labelled b_1(1)* 196 to 180 labelled a_1(1)* 196 to 189 labelled b_1(1)* 197 to 198 labelled a_1(1)* 198 to 199 labelled a_1(1)* 199 to 200 labelled b_1(1)* 200 to 201 labelled b_1(1)* 201 to 202 labelled a_1(1)* 202 to 203 labelled a_1(1)* 203 to 204 labelled b_1(1)* 204 to 192 labelled a_1(1)* 204 to 213 labelled b_1(2)* 205 to 206 labelled a_1(2)* 206 to 207 labelled a_1(2)* 207 to 208 labelled b_1(2)* 208 to 209 labelled b_1(2)* 209 to 210 labelled a_1(2)* 210 to 211 labelled a_1(2)* 211 to 212 labelled b_1(2)* 212 to 192 labelled a_1(2)* 212 to 213 labelled b_1(2)* 213 to 214 labelled a_1(2)* 214 to 215 labelled a_1(2)* 215 to 216 labelled b_1(2)* 216 to 217 labelled b_1(2)* 217 to 218 labelled a_1(2)* 217 to 205 labelled b_1(2)* 218 to 219 labelled a_1(2)* 218 to 189 labelled b_1(1)* 219 to 220 labelled b_1(2)* 220 to 196 labelled a_1(2)* 220 to 205 labelled b_1(2)
3.79/1.72	
3.79/1.72	
3.79/1.72	----------------------------------------
3.79/1.72	
3.79/1.72	(4)
3.79/1.72	YES
3.91/2.68	EOF