3.03/1.60	YES
3.33/1.62	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.33/1.62	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.33/1.62	
3.33/1.62	
3.33/1.62	Termination w.r.t. Q of the given QTRS could be proven:
3.33/1.62	
3.33/1.62	(0) QTRS
3.33/1.62	(1) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
3.33/1.62	(2) YES
3.33/1.62	
3.33/1.62	
3.33/1.62	----------------------------------------
3.33/1.62	
3.33/1.62	(0)
3.33/1.62	Obligation:
3.33/1.62	Q restricted rewrite system:
3.33/1.62	The TRS R consists of the following rules:
3.33/1.62	
3.33/1.62	   a__g(X) -> a__h(X)
3.33/1.62	   a__c -> d
3.33/1.62	   a__h(d) -> a__g(c)
3.33/1.62	   mark(g(X)) -> a__g(X)
3.33/1.62	   mark(h(X)) -> a__h(X)
3.33/1.62	   mark(c) -> a__c
3.33/1.62	   mark(d) -> d
3.33/1.62	   a__g(X) -> g(X)
3.33/1.62	   a__h(X) -> h(X)
3.33/1.62	   a__c -> c
3.33/1.62	
3.33/1.62	The set Q consists of the following terms:
3.33/1.62	
3.33/1.62	   a__g(x0)
3.33/1.62	   a__c
3.33/1.62	   mark(g(x0))
3.33/1.62	   mark(h(x0))
3.33/1.62	   mark(c)
3.33/1.62	   mark(d)
3.33/1.62	   a__h(x0)
3.33/1.62	
3.33/1.62	
3.33/1.62	----------------------------------------
3.33/1.62	
3.33/1.62	(1) RFCMatchBoundsTRSProof (EQUIVALENT)
3.33/1.62	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 4. This implies Q-termination of R.
3.33/1.62	The following rules were used to construct the certificate:
3.33/1.62	
3.33/1.62	   a__g(X) -> a__h(X)
3.33/1.62	   a__c -> d
3.33/1.62	   a__h(d) -> a__g(c)
3.33/1.62	   mark(g(X)) -> a__g(X)
3.33/1.62	   mark(h(X)) -> a__h(X)
3.33/1.62	   mark(c) -> a__c
3.33/1.62	   mark(d) -> d
3.33/1.62	   a__g(X) -> g(X)
3.33/1.62	   a__h(X) -> h(X)
3.33/1.62	   a__c -> c
3.33/1.62	
3.33/1.62	The certificate found is represented by the following graph.
3.33/1.62	The certificate consists of the following enumerated nodes:
3.33/1.62	1, 2, 3, 4
3.33/1.62	
3.33/1.62	Node 1 is start node and node 2 is final node.
3.33/1.62	
3.33/1.62	Those nodes are connected through the following edges:
3.33/1.62	
3.33/1.62	* 1 to 2 labelled a__h_1(0), d(0), a__g_1(0), a__c(0), g_1(0), h_1(0), c(0), h_1(1), a__h_1(1), g_1(1), d(1), c(1), h_1(2)* 1 to 3 labelled a__g_1(0), a__h_1(1), g_1(1), h_1(2)* 1 to 1 labelled a__g_1(1), a__h_1(2), g_1(2), h_1(3)* 1 to 4 labelled a__g_1(2), a__h_1(3), g_1(3), h_1(4)* 2 to 2 labelled #_1(0)* 3 to 2 labelled c(0)* 4 to 2 labelled c(2)
3.33/1.62	
3.33/1.62	
3.33/1.62	----------------------------------------
3.33/1.62	
3.33/1.62	(2)
3.33/1.62	YES
3.33/1.66	EOF