3.38/1.53	YES
3.38/1.54	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.38/1.54	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.38/1.54	
3.38/1.54	
3.38/1.54	Quasi decreasingness of the given CTRS could be proven:
3.38/1.54	
3.38/1.54	(0) CTRS
3.38/1.54	(1) CTRSToQTRSProof [SOUND, 0 ms]
3.38/1.54	(2) QTRS
3.38/1.54	(3) QTRSRRRProof [EQUIVALENT, 0 ms]
3.38/1.54	(4) QTRS
3.38/1.54	(5) RisEmptyProof [EQUIVALENT, 0 ms]
3.38/1.54	(6) YES
3.38/1.54	
3.38/1.54	
3.38/1.54	----------------------------------------
3.38/1.54	
3.38/1.54	(0)
3.38/1.54	Obligation:
3.38/1.54	Conditional term rewrite system:
3.38/1.54	The TRS R consists of the following rules:
3.38/1.54	
3.38/1.54	   h(c) -> d
3.38/1.54	
3.38/1.54	The conditional TRS C consists of the following conditional rules:
3.38/1.54	
3.38/1.54	   f(x, y) -> z <= x -> z
3.38/1.54	   g(x) -> b <= h(x) -> d
3.38/1.54	
3.38/1.54	
3.38/1.54	----------------------------------------
3.38/1.54	
3.38/1.54	(1) CTRSToQTRSProof (SOUND)
3.38/1.54	The conditional rules have been transormed into unconditional rules according to [CTRS,AAECCNOC].
3.38/1.54	----------------------------------------
3.38/1.54	
3.38/1.54	(2)
3.38/1.54	Obligation:
3.38/1.54	Q restricted rewrite system:
3.38/1.54	The TRS R consists of the following rules:
3.38/1.54	
3.38/1.54	   f(x, y) -> U1(x)
3.38/1.54	   U1(z) -> z
3.38/1.54	   g(x) -> U2(h(x))
3.38/1.54	   U2(d) -> b
3.38/1.54	   h(c) -> d
3.38/1.54	
3.38/1.54	Q is empty.
3.38/1.54	
3.38/1.54	----------------------------------------
3.38/1.54	
3.38/1.54	(3) QTRSRRRProof (EQUIVALENT)
3.38/1.54	Used ordering:
3.38/1.54	Knuth-Bendix order [KBO] with precedence:c > g_1 > U2_1 > b > h_1 > d > f_2 > U1_1
3.38/1.54	
3.38/1.54	and weight map:
3.38/1.54	
3.38/1.54	   d=2
3.38/1.54	   b=3
3.38/1.54	   c=1
3.38/1.54	   U1_1=1
3.38/1.54	   g_1=2
3.38/1.54	   U2_1=1
3.38/1.54	   h_1=1
3.38/1.54	   f_2=0
3.38/1.54	
3.38/1.54	The variable weight is 1With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
3.38/1.54	
3.38/1.54	   f(x, y) -> U1(x)
3.38/1.54	   U1(z) -> z
3.38/1.54	   g(x) -> U2(h(x))
3.38/1.54	   U2(d) -> b
3.38/1.54	   h(c) -> d
3.38/1.54	
3.38/1.54	
3.38/1.54	
3.38/1.54	
3.38/1.54	----------------------------------------
3.38/1.54	
3.38/1.54	(4)
3.38/1.54	Obligation:
3.38/1.54	Q restricted rewrite system:
3.38/1.54	R is empty.
3.38/1.54	Q is empty.
3.38/1.54	
3.38/1.54	----------------------------------------
3.38/1.54	
3.38/1.54	(5) RisEmptyProof (EQUIVALENT)
3.38/1.54	The TRS R is empty. Hence, termination is trivially proven.
3.38/1.54	----------------------------------------
3.38/1.54	
3.38/1.54	(6)
3.38/1.54	YES
3.47/1.63	EOF