4.02/1.82	YES
4.09/1.85	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
4.09/1.85	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.09/1.85	
4.09/1.85	
4.09/1.85	Termination w.r.t. Q of the given QTRS could be proven:
4.09/1.85	
4.09/1.85	(0) QTRS
4.09/1.85	(1) QTRS Reverse [EQUIVALENT, 0 ms]
4.09/1.85	(2) QTRS
4.09/1.85	(3) Strip Symbols Proof [SOUND, 0 ms]
4.09/1.85	(4) QTRS
4.09/1.85	(5) RFCMatchBoundsTRSProof [EQUIVALENT, 2 ms]
4.09/1.85	(6) YES
4.09/1.85	
4.09/1.85	
4.09/1.85	----------------------------------------
4.09/1.85	
4.09/1.85	(0)
4.09/1.85	Obligation:
4.09/1.85	Q restricted rewrite system:
4.09/1.85	The TRS R consists of the following rules:
4.09/1.85	
4.09/1.85	   a(c(b(a(b(a(c(b(a(x1))))))))) -> a(b(a(c(b(a(c(b(a(b(a(c(x1))))))))))))
4.09/1.85	
4.09/1.85	Q is empty.
4.09/1.85	
4.09/1.85	----------------------------------------
4.09/1.85	
4.09/1.85	(1) QTRS Reverse (EQUIVALENT)
4.09/1.85	We applied the QTRS Reverse Processor [REVERSE].
4.09/1.85	----------------------------------------
4.09/1.85	
4.09/1.85	(2)
4.09/1.85	Obligation:
4.09/1.85	Q restricted rewrite system:
4.09/1.85	The TRS R consists of the following rules:
4.09/1.85	
4.09/1.85	   a(b(c(a(b(a(b(c(a(x1))))))))) -> c(a(b(a(b(c(a(b(c(a(b(a(x1))))))))))))
4.09/1.85	
4.09/1.85	Q is empty.
4.09/1.85	
4.09/1.85	----------------------------------------
4.09/1.85	
4.09/1.85	(3) Strip Symbols Proof (SOUND)
4.09/1.85	We were given the following TRS:
4.09/1.85	
4.09/1.85	   a(b(c(a(b(a(b(c(a(x1))))))))) -> c(a(b(a(b(c(a(b(c(a(b(a(x1))))))))))))
4.09/1.85	
4.09/1.85	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
4.09/1.85	
4.09/1.85	   a(b(c(a(b(a(b(c(x)))))))) -> c(a(b(a(b(c(a(b(c(a(b(x)))))))))))
4.09/1.85	
4.09/1.85	----------------------------------------
4.09/1.85	
4.09/1.85	(4)
4.09/1.85	Obligation:
4.09/1.85	Q restricted rewrite system:
4.09/1.85	The TRS R consists of the following rules:
4.09/1.85	
4.09/1.85	   a(b(c(a(b(a(b(c(x)))))))) -> c(a(b(a(b(c(a(b(c(a(b(x)))))))))))
4.09/1.85	
4.09/1.85	Q is empty.
4.09/1.85	
4.09/1.85	----------------------------------------
4.09/1.85	
4.09/1.85	(5) RFCMatchBoundsTRSProof (EQUIVALENT)
4.09/1.85	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
4.09/1.85	The following rules were used to construct the certificate:
4.09/1.85	
4.09/1.85	   a(b(c(a(b(a(b(c(x)))))))) -> c(a(b(a(b(c(a(b(c(a(b(x)))))))))))
4.09/1.85	
4.09/1.85	The certificate found is represented by the following graph.
4.09/1.85	The certificate consists of the following enumerated nodes:
4.09/1.85	303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324
4.09/1.85	
4.09/1.85	Node 303 is start node and node 304 is final node.
4.09/1.85	
4.09/1.85	Those nodes are connected through the following edges:
4.09/1.85	
4.09/1.85	* 303 to 305 labelled c_1(0)* 304 to 304 labelled #_1(0)* 305 to 306 labelled a_1(0)* 306 to 307 labelled b_1(0)* 307 to 308 labelled a_1(0)* 308 to 309 labelled b_1(0)* 309 to 310 labelled c_1(0)* 310 to 311 labelled a_1(0)* 310 to 315 labelled c_1(1)* 311 to 312 labelled b_1(0)* 312 to 313 labelled c_1(0)* 313 to 314 labelled a_1(0)* 313 to 315 labelled c_1(1)* 314 to 304 labelled b_1(0)* 315 to 316 labelled a_1(1)* 316 to 317 labelled b_1(1)* 317 to 318 labelled a_1(1)* 318 to 319 labelled b_1(1)* 319 to 320 labelled c_1(1)* 320 to 321 labelled a_1(1)* 320 to 315 labelled c_1(1)* 321 to 322 labelled b_1(1)* 322 to 323 labelled c_1(1)* 323 to 324 labelled a_1(1)* 323 to 315 labelled c_1(1)* 324 to 304 labelled b_1(1)
4.09/1.85	
4.09/1.85	
4.09/1.85	----------------------------------------
4.09/1.85	
4.09/1.85	(6)
4.09/1.85	YES
4.09/1.88	EOF