3.18/1.60	YES
3.50/1.64	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.50/1.64	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.50/1.64	
3.50/1.64	
3.50/1.64	Termination w.r.t. Q of the given QTRS could be proven:
3.50/1.64	
3.50/1.64	(0) QTRS
3.50/1.64	(1) QTRS Reverse [EQUIVALENT, 0 ms]
3.50/1.64	(2) QTRS
3.50/1.64	(3) Strip Symbols Proof [SOUND, 0 ms]
3.50/1.64	(4) QTRS
3.50/1.64	(5) RFCMatchBoundsTRSProof [EQUIVALENT, 3 ms]
3.50/1.64	(6) YES
3.50/1.64	
3.50/1.64	
3.50/1.64	----------------------------------------
3.50/1.64	
3.50/1.64	(0)
3.50/1.64	Obligation:
3.50/1.64	Q restricted rewrite system:
3.50/1.64	The TRS R consists of the following rules:
3.50/1.64	
3.50/1.64	   a(b(c(a(b(c(a(a(a(x1))))))))) -> a(a(a(a(b(c(a(b(c(a(b(c(x1))))))))))))
3.50/1.64	
3.50/1.64	Q is empty.
3.50/1.64	
3.50/1.64	----------------------------------------
3.50/1.64	
3.50/1.64	(1) QTRS Reverse (EQUIVALENT)
3.50/1.64	We applied the QTRS Reverse Processor [REVERSE].
3.50/1.64	----------------------------------------
3.50/1.64	
3.50/1.64	(2)
3.50/1.64	Obligation:
3.50/1.64	Q restricted rewrite system:
3.50/1.64	The TRS R consists of the following rules:
3.50/1.64	
3.50/1.64	   a(a(a(c(b(a(c(b(a(x1))))))))) -> c(b(a(c(b(a(c(b(a(a(a(a(x1))))))))))))
3.50/1.64	
3.50/1.64	Q is empty.
3.50/1.64	
3.50/1.64	----------------------------------------
3.50/1.64	
3.50/1.64	(3) Strip Symbols Proof (SOUND)
3.50/1.64	We were given the following TRS:
3.50/1.64	
3.50/1.64	   a(a(a(c(b(a(c(b(a(x1))))))))) -> c(b(a(c(b(a(c(b(a(a(a(a(x1))))))))))))
3.50/1.64	
3.50/1.64	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
3.50/1.64	
3.50/1.64	   a(a(a(c(b(a(c(b(x)))))))) -> c(b(a(c(b(a(c(b(a(a(a(x)))))))))))
3.50/1.64	
3.50/1.64	----------------------------------------
3.50/1.64	
3.50/1.64	(4)
3.50/1.64	Obligation:
3.50/1.64	Q restricted rewrite system:
3.50/1.64	The TRS R consists of the following rules:
3.50/1.64	
3.50/1.64	   a(a(a(c(b(a(c(b(x)))))))) -> c(b(a(c(b(a(c(b(a(a(a(x)))))))))))
3.50/1.64	
3.50/1.64	Q is empty.
3.50/1.64	
3.50/1.64	----------------------------------------
3.50/1.64	
3.50/1.64	(5) RFCMatchBoundsTRSProof (EQUIVALENT)
3.50/1.64	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
3.50/1.64	The following rules were used to construct the certificate:
3.50/1.64	
3.50/1.64	   a(a(a(c(b(a(c(b(x)))))))) -> c(b(a(c(b(a(c(b(a(a(a(x)))))))))))
3.50/1.64	
3.50/1.64	The certificate found is represented by the following graph.
3.50/1.64	The certificate consists of the following enumerated nodes:
3.50/1.64	155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176
3.50/1.64	
3.50/1.64	Node 155 is start node and node 156 is final node.
3.50/1.64	
3.50/1.64	Those nodes are connected through the following edges:
3.50/1.64	
3.50/1.64	* 155 to 157 labelled c_1(0)* 156 to 156 labelled #_1(0)* 157 to 158 labelled b_1(0)* 158 to 159 labelled a_1(0)* 159 to 160 labelled c_1(0)* 160 to 161 labelled b_1(0)* 161 to 162 labelled a_1(0)* 162 to 163 labelled c_1(0)* 163 to 164 labelled b_1(0)* 164 to 165 labelled a_1(0)* 164 to 167 labelled c_1(1)* 165 to 166 labelled a_1(0)* 165 to 167 labelled c_1(1)* 166 to 156 labelled a_1(0)* 166 to 167 labelled c_1(1)* 167 to 168 labelled b_1(1)* 168 to 169 labelled a_1(1)* 169 to 170 labelled c_1(1)* 170 to 171 labelled b_1(1)* 171 to 172 labelled a_1(1)* 172 to 173 labelled c_1(1)* 173 to 174 labelled b_1(1)* 174 to 175 labelled a_1(1)* 174 to 167 labelled c_1(1)* 175 to 176 labelled a_1(1)* 175 to 167 labelled c_1(1)* 176 to 156 labelled a_1(1)* 176 to 167 labelled c_1(1)
3.50/1.64	
3.50/1.64	
3.50/1.64	----------------------------------------
3.50/1.64	
3.50/1.64	(6)
3.50/1.64	YES
3.50/1.66	EOF