3.19/1.57	YES
3.19/1.58	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.19/1.58	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.19/1.58	
3.19/1.58	
3.19/1.58	Termination w.r.t. Q of the given QTRS could be proven:
3.19/1.58	
3.19/1.58	(0) QTRS
3.19/1.58	(1) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
3.19/1.58	(2) YES
3.19/1.58	
3.19/1.58	
3.19/1.58	----------------------------------------
3.19/1.58	
3.19/1.58	(0)
3.19/1.58	Obligation:
3.19/1.58	Q restricted rewrite system:
3.19/1.58	The TRS R consists of the following rules:
3.19/1.58	
3.19/1.58	   f(0) -> cons(0)
3.19/1.58	   f(s(0)) -> f(p(s(0)))
3.19/1.58	   p(s(X)) -> X
3.19/1.58	
3.19/1.58	The set Q consists of the following terms:
3.19/1.58	
3.19/1.58	   f(0)
3.19/1.58	   f(s(0))
3.19/1.58	   p(s(x0))
3.19/1.58	
3.19/1.58	
3.19/1.58	----------------------------------------
3.19/1.58	
3.19/1.58	(1) RFCMatchBoundsTRSProof (EQUIVALENT)
3.19/1.58	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 2. This implies Q-termination of R.
3.19/1.58	The following rules were used to construct the certificate:
3.19/1.58	
3.19/1.58	   f(0) -> cons(0)
3.19/1.58	   f(s(0)) -> f(p(s(0)))
3.19/1.58	   p(s(X)) -> X
3.19/1.58	
3.19/1.58	The certificate found is represented by the following graph.
3.19/1.58	The certificate consists of the following enumerated nodes:
3.19/1.58	1, 2, 3, 4, 5, 6, 7, 8, 9, 10
3.19/1.58	
3.19/1.58	Node 1 is start node and node 2 is final node.
3.19/1.58	
3.19/1.58	Those nodes are connected through the following edges:
3.19/1.58	
3.19/1.58	* 1 to 3 labelled cons_1(0)* 1 to 4 labelled f_1(0)* 1 to 2 labelled f_1(0), 0(0), cons_1(0), s_1(0), p_1(0), f_1(1), 0(1), cons_1(1), s_1(1), p_1(1)* 1 to 7 labelled cons_1(1)* 1 to 8 labelled f_1(1), cons_1(2)* 1 to 1 labelled cons_1(1)* 2 to 2 labelled #_1(0)* 3 to 2 labelled 0(0)* 4 to 5 labelled p_1(0)* 4 to 2 labelled 0(1)* 5 to 6 labelled s_1(0)* 6 to 2 labelled 0(0)* 7 to 2 labelled 0(1)* 8 to 9 labelled p_1(1)* 8 to 2 labelled 0(2)* 9 to 10 labelled s_1(1)* 10 to 2 labelled 0(1)
3.19/1.58	
3.19/1.58	
3.19/1.58	----------------------------------------
3.19/1.58	
3.19/1.58	(2)
3.19/1.58	YES
3.19/1.61	EOF