3.30/2.29	YES
3.32/2.30	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.32/2.30	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.32/2.30	
3.32/2.30	
3.32/2.30	Quasi decreasingness of the given CTRS could be proven:
3.32/2.30	
3.32/2.30	(0) CTRS
3.32/2.30	(1) CTRSToQTRSProof [SOUND, 0 ms]
3.32/2.30	(2) QTRS
3.32/2.30	(3) QTRSRRRProof [EQUIVALENT, 43 ms]
3.32/2.30	(4) QTRS
3.32/2.30	(5) QTRSRRRProof [EQUIVALENT, 6 ms]
3.32/2.30	(6) QTRS
3.32/2.30	(7) RisEmptyProof [EQUIVALENT, 0 ms]
3.32/2.30	(8) YES
3.32/2.30	
3.32/2.30	
3.32/2.30	----------------------------------------
3.32/2.30	
3.32/2.30	(0)
3.32/2.30	Obligation:
3.32/2.30	Conditional term rewrite system:
3.32/2.30	The TRS R consists of the following rules:
3.32/2.30	
3.32/2.30	   a -> b
3.32/2.30	
3.32/2.30	The conditional TRS C consists of the following conditional rules:
3.32/2.30	
3.32/2.30	   f(x) -> x <= x -> b
3.32/2.30	
3.32/2.30	
3.32/2.30	----------------------------------------
3.32/2.30	
3.32/2.30	(1) CTRSToQTRSProof (SOUND)
3.32/2.30	The conditional rules have been transormed into unconditional rules according to [CTRS,AAECCNOC].
3.32/2.30	----------------------------------------
3.32/2.30	
3.32/2.30	(2)
3.32/2.30	Obligation:
3.32/2.30	Q restricted rewrite system:
3.32/2.30	The TRS R consists of the following rules:
3.32/2.30	
3.32/2.30	   f(x) -> U1(x, x)
3.32/2.30	   U1(b, x) -> x
3.32/2.30	   a -> b
3.32/2.30	
3.32/2.30	Q is empty.
3.32/2.30	
3.32/2.30	----------------------------------------
3.32/2.30	
3.32/2.30	(3) QTRSRRRProof (EQUIVALENT)
3.32/2.30	Used ordering:
3.32/2.30	Polynomial interpretation [POLO]:
3.32/2.30	
3.32/2.30	   POL(U1(x_1, x_2)) = 2 + x_1 + x_2
3.32/2.30	   POL(a) = 1
3.32/2.30	   POL(b) = 1
3.32/2.30	   POL(f(x_1)) = 2 + 2*x_1
3.32/2.30	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
3.32/2.30	
3.32/2.30	   U1(b, x) -> x
3.32/2.30	
3.32/2.30	
3.32/2.30	
3.32/2.30	
3.32/2.30	----------------------------------------
3.32/2.30	
3.32/2.30	(4)
3.32/2.30	Obligation:
3.32/2.30	Q restricted rewrite system:
3.32/2.30	The TRS R consists of the following rules:
3.32/2.30	
3.32/2.30	   f(x) -> U1(x, x)
3.32/2.30	   a -> b
3.32/2.30	
3.32/2.30	Q is empty.
3.32/2.30	
3.32/2.30	----------------------------------------
3.32/2.30	
3.32/2.30	(5) QTRSRRRProof (EQUIVALENT)
3.32/2.30	Used ordering:
3.32/2.30	Quasi precedence:
3.32/2.30	f_1 > U1_2
3.32/2.30	a > b
3.32/2.30	
3.32/2.30	
3.32/2.30	Status:
3.32/2.30	f_1: multiset status
3.32/2.30	U1_2: multiset status
3.32/2.30	a: multiset status
3.32/2.30	b: multiset status
3.32/2.30	
3.32/2.30	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
3.32/2.30	
3.32/2.30	   f(x) -> U1(x, x)
3.32/2.30	   a -> b
3.32/2.30	
3.32/2.30	
3.32/2.30	
3.32/2.30	
3.32/2.30	----------------------------------------
3.32/2.30	
3.32/2.30	(6)
3.32/2.30	Obligation:
3.32/2.30	Q restricted rewrite system:
3.32/2.30	R is empty.
3.32/2.30	Q is empty.
3.32/2.30	
3.32/2.30	----------------------------------------
3.32/2.30	
3.32/2.30	(7) RisEmptyProof (EQUIVALENT)
3.32/2.30	The TRS R is empty. Hence, termination is trivially proven.
3.32/2.30	----------------------------------------
3.32/2.30	
3.32/2.30	(8)
3.32/2.30	YES
3.35/2.43	EOF