3.43/1.66	YES
3.43/1.67	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.43/1.67	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.43/1.67	
3.43/1.67	
3.43/1.67	Termination w.r.t. Q of the given QTRS could be proven:
3.43/1.67	
3.43/1.67	(0) QTRS
3.43/1.67	(1) RFCMatchBoundsTRSProof [EQUIVALENT, 22 ms]
3.43/1.67	(2) YES
3.43/1.67	
3.43/1.67	
3.43/1.67	----------------------------------------
3.43/1.67	
3.43/1.67	(0)
3.43/1.67	Obligation:
3.43/1.67	Q restricted rewrite system:
3.43/1.67	The TRS R consists of the following rules:
3.43/1.67	
3.43/1.67	   g(c(x1)) -> g(f(c(x1)))
3.43/1.67	   g(f(c(x1))) -> g(f(f(c(x1))))
3.43/1.67	   g(g(x1)) -> g(f(g(x1)))
3.43/1.67	   f(f(g(x1))) -> g(f(x1))
3.43/1.67	
3.43/1.67	Q is empty.
3.43/1.67	
3.43/1.67	----------------------------------------
3.43/1.67	
3.43/1.67	(1) RFCMatchBoundsTRSProof (EQUIVALENT)
3.43/1.67	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 3. This implies Q-termination of R.
3.43/1.67	The following rules were used to construct the certificate:
3.43/1.67	
3.43/1.67	   g(c(x1)) -> g(f(c(x1)))
3.43/1.67	   g(f(c(x1))) -> g(f(f(c(x1))))
3.43/1.67	   g(g(x1)) -> g(f(g(x1)))
3.43/1.67	   f(f(g(x1))) -> g(f(x1))
3.43/1.67	
3.43/1.67	The certificate found is represented by the following graph.
3.43/1.67	The certificate consists of the following enumerated nodes:
3.43/1.67	1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20
3.43/1.67	
3.43/1.67	Node 1 is start node and node 2 is final node.
3.43/1.67	
3.43/1.67	Those nodes are connected through the following edges:
3.43/1.67	
3.43/1.67	* 1 to 3 labelled g_1(0)* 1 to 5 labelled g_1(0)* 1 to 11 labelled g_1(1)* 1 to 9 labelled g_1(1)* 1 to 14 labelled g_1(2)* 2 to 2 labelled #_1(0)* 3 to 4 labelled f_1(0)* 3 to 2 labelled f_1(0)* 3 to 8 labelled g_1(1)* 3 to 11 labelled g_1(1)* 3 to 17 labelled g_1(2)* 4 to 2 labelled c_1(0), g_1(0)* 4 to 9 labelled g_1(1)* 4 to 11 labelled g_1(1)* 4 to 14 labelled g_1(2)* 5 to 6 labelled f_1(0)* 6 to 7 labelled f_1(0)* 7 to 2 labelled c_1(0)* 8 to 2 labelled f_1(1)* 8 to 8 labelled g_1(1)* 8 to 17 labelled g_1(2)* 8 to 11 labelled g_1(1)* 9 to 10 labelled f_1(1)* 10 to 2 labelled c_1(1), g_1(1)* 10 to 9 labelled g_1(1)* 10 to 11 labelled g_1(1)* 10 to 14 labelled g_1(2)* 11 to 12 labelled f_1(1)* 12 to 13 labelled f_1(1)* 12 to 8 labelled g_1(1)* 12 to 17 labelled g_1(2), g_1(1)* 12 to 11 labelled g_1(1)* 13 to 2 labelled c_1(1)* 14 to 15 labelled f_1(2)* 15 to 16 labelled f_1(2)* 16 to 2 labelled c_1(2)* 17 to 18 labelled f_1(2)* 18 to 8 labelled g_1(2)* 18 to 17 labelled g_1(2)* 18 to 19 labelled g_1(3)* 18 to 11 labelled g_1(2), g_1(1)* 19 to 20 labelled f_1(3)* 20 to 17 labelled g_1(3)
3.43/1.67	
3.43/1.67	
3.43/1.67	----------------------------------------
3.43/1.67	
3.43/1.67	(2)
3.43/1.67	YES
3.59/1.72	EOF