3.45/2.29	YES
3.49/2.30	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.49/2.30	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.49/2.30	
3.49/2.30	
3.49/2.30	Quasi decreasingness of the given CTRS could be proven:
3.49/2.30	
3.49/2.30	(0) CTRS
3.49/2.30	(1) CTRSToQTRSProof [SOUND, 0 ms]
3.49/2.30	(2) QTRS
3.49/2.30	(3) QTRSRRRProof [EQUIVALENT, 50 ms]
3.49/2.30	(4) QTRS
3.49/2.30	(5) RisEmptyProof [EQUIVALENT, 0 ms]
3.49/2.30	(6) YES
3.49/2.30	
3.49/2.30	
3.49/2.30	----------------------------------------
3.49/2.30	
3.49/2.30	(0)
3.49/2.30	Obligation:
3.49/2.30	Conditional term rewrite system:
3.49/2.30	The TRS R consists of the following rules:
3.49/2.30	
3.49/2.30	   a -> t(c)
3.49/2.30	   a -> t(d)
3.49/2.30	   g(x, x) -> h(x, x)
3.49/2.30	
3.49/2.30	The conditional TRS C consists of the following conditional rules:
3.49/2.30	
3.49/2.30	   f(x, y) -> z <= x -> t(z)
3.49/2.30	
3.49/2.30	
3.49/2.30	----------------------------------------
3.49/2.30	
3.49/2.30	(1) CTRSToQTRSProof (SOUND)
3.49/2.30	The conditional rules have been transormed into unconditional rules according to [CTRS,AAECCNOC].
3.49/2.30	----------------------------------------
3.49/2.30	
3.49/2.30	(2)
3.49/2.30	Obligation:
3.49/2.30	Q restricted rewrite system:
3.49/2.30	The TRS R consists of the following rules:
3.49/2.30	
3.49/2.30	   f(x, y) -> U1(x)
3.49/2.30	   U1(t(z)) -> z
3.49/2.30	   a -> t(c)
3.49/2.30	   a -> t(d)
3.49/2.30	   g(x, x) -> h(x, x)
3.49/2.30	
3.49/2.30	Q is empty.
3.49/2.30	
3.49/2.30	----------------------------------------
3.49/2.30	
3.49/2.30	(3) QTRSRRRProof (EQUIVALENT)
3.49/2.30	Used ordering:
3.49/2.30	Quasi precedence:
3.49/2.30	f_2 > U1_1
3.49/2.30	a > t_1
3.49/2.30	a > c
3.49/2.30	a > d
3.49/2.30	g_2 > h_2
3.49/2.30	
3.49/2.30	
3.49/2.30	Status:
3.49/2.30	f_2: multiset status
3.49/2.30	U1_1: multiset status
3.49/2.30	t_1: multiset status
3.49/2.30	a: multiset status
3.49/2.30	c: multiset status
3.49/2.30	d: multiset status
3.49/2.30	g_2: multiset status
3.49/2.30	h_2: multiset status
3.49/2.30	
3.49/2.30	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
3.49/2.30	
3.49/2.30	   f(x, y) -> U1(x)
3.49/2.30	   U1(t(z)) -> z
3.49/2.30	   a -> t(c)
3.49/2.30	   a -> t(d)
3.49/2.30	   g(x, x) -> h(x, x)
3.49/2.30	
3.49/2.30	
3.49/2.30	
3.49/2.30	
3.49/2.30	----------------------------------------
3.49/2.30	
3.49/2.30	(4)
3.49/2.30	Obligation:
3.49/2.30	Q restricted rewrite system:
3.49/2.30	R is empty.
3.49/2.30	Q is empty.
3.49/2.30	
3.49/2.30	----------------------------------------
3.49/2.30	
3.49/2.30	(5) RisEmptyProof (EQUIVALENT)
3.49/2.30	The TRS R is empty. Hence, termination is trivially proven.
3.49/2.30	----------------------------------------
3.49/2.30	
3.49/2.30	(6)
3.49/2.30	YES
3.50/2.37	EOF