2.89/1.48	YES
3.15/1.48	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.15/1.48	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.15/1.48	
3.15/1.48	
3.15/1.48	Termination w.r.t. Q of the given QTRS could be proven:
3.15/1.48	
3.15/1.48	(0) QTRS
3.15/1.48	(1) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
3.15/1.48	(2) YES
3.15/1.48	
3.15/1.48	
3.15/1.48	----------------------------------------
3.15/1.48	
3.15/1.48	(0)
3.15/1.48	Obligation:
3.15/1.48	Q restricted rewrite system:
3.15/1.48	The TRS R consists of the following rules:
3.15/1.48	
3.15/1.48	   f(0) -> cons(0)
3.15/1.48	   f(s(0)) -> f(p(s(0)))
3.15/1.48	   p(s(0)) -> 0
3.15/1.48	
3.15/1.48	The set Q consists of the following terms:
3.15/1.48	
3.15/1.48	   f(0)
3.15/1.48	   f(s(0))
3.15/1.48	   p(s(0))
3.15/1.48	
3.15/1.48	
3.15/1.48	----------------------------------------
3.15/1.48	
3.15/1.48	(1) RFCMatchBoundsTRSProof (EQUIVALENT)
3.15/1.48	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
3.15/1.48	The following rules were used to construct the certificate:
3.15/1.48	
3.15/1.48	   f(0) -> cons(0)
3.15/1.48	   f(s(0)) -> f(p(s(0)))
3.15/1.48	   p(s(0)) -> 0
3.15/1.48	
3.15/1.48	The certificate found is represented by the following graph.
3.15/1.48	The certificate consists of the following enumerated nodes:
3.15/1.48	1, 2, 3, 4, 5, 6
3.15/1.48	
3.15/1.48	Node 1 is start node and node 2 is final node.
3.15/1.48	
3.15/1.48	Those nodes are connected through the following edges:
3.15/1.48	
3.15/1.48	* 1 to 3 labelled cons_1(0)* 1 to 4 labelled f_1(0), cons_1(1)* 1 to 2 labelled 0(0)* 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)
3.15/1.48	
3.15/1.48	
3.15/1.48	----------------------------------------
3.15/1.48	
3.15/1.48	(2)
3.15/1.48	YES
3.15/1.52	EOF