3.26/1.75	YES
3.42/1.76	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.42/1.76	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.42/1.76	
3.42/1.76	
3.42/1.76	Quasi decreasingness of the given CTRS could be proven:
3.42/1.76	
3.42/1.76	(0) CTRS
3.42/1.76	(1) CTRSToQTRSProof [SOUND, 0 ms]
3.42/1.76	(2) QTRS
3.42/1.76	(3) QTRSRRRProof [EQUIVALENT, 0 ms]
3.42/1.76	(4) QTRS
3.42/1.76	(5) RisEmptyProof [EQUIVALENT, 0 ms]
3.42/1.76	(6) YES
3.42/1.76	
3.42/1.76	
3.42/1.76	----------------------------------------
3.42/1.76	
3.42/1.76	(0)
3.42/1.76	Obligation:
3.42/1.76	Conditional term rewrite system:
3.42/1.76	The TRS R consists of the following rules:
3.42/1.76	
3.42/1.76	   a -> b
3.42/1.76	   g(x, x) -> h(x)
3.42/1.76	   h(x) -> i(x)
3.42/1.76	
3.42/1.76	The conditional TRS C consists of the following conditional rules:
3.42/1.76	
3.42/1.76	   f(x) -> A <= x -> b
3.42/1.76	
3.42/1.76	
3.42/1.76	----------------------------------------
3.42/1.76	
3.42/1.76	(1) CTRSToQTRSProof (SOUND)
3.42/1.76	The conditional rules have been transormed into unconditional rules according to [CTRS,AAECCNOC].
3.42/1.76	----------------------------------------
3.42/1.76	
3.42/1.76	(2)
3.42/1.76	Obligation:
3.42/1.76	Q restricted rewrite system:
3.42/1.76	The TRS R consists of the following rules:
3.42/1.76	
3.42/1.76	   f(x) -> U1(x)
3.42/1.76	   U1(b) -> A
3.42/1.76	   a -> b
3.42/1.76	   g(x, x) -> h(x)
3.42/1.76	   h(x) -> i(x)
3.42/1.76	
3.42/1.76	Q is empty.
3.42/1.76	
3.42/1.76	----------------------------------------
3.42/1.76	
3.42/1.76	(3) QTRSRRRProof (EQUIVALENT)
3.42/1.76	Used ordering:
3.42/1.76	Knuth-Bendix order [KBO] with precedence:f_1 > U1_1 > A > g_2 > h_1 > i_1 > a > b
3.42/1.76	
3.42/1.76	and weight map:
3.42/1.76	
3.42/1.76	   b=1
3.42/1.76	   A=2
3.42/1.76	   a=1
3.42/1.76	   f_1=1
3.42/1.76	   U1_1=1
3.42/1.76	   h_1=1
3.42/1.76	   i_1=1
3.42/1.76	   g_2=0
3.42/1.76	
3.42/1.76	The variable weight is 1With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
3.42/1.76	
3.42/1.76	   f(x) -> U1(x)
3.42/1.76	   U1(b) -> A
3.42/1.76	   a -> b
3.42/1.76	   g(x, x) -> h(x)
3.42/1.76	   h(x) -> i(x)
3.42/1.76	
3.42/1.76	
3.42/1.76	
3.42/1.76	
3.42/1.76	----------------------------------------
3.42/1.76	
3.42/1.76	(4)
3.42/1.76	Obligation:
3.42/1.76	Q restricted rewrite system:
3.42/1.76	R is empty.
3.42/1.76	Q is empty.
3.42/1.76	
3.42/1.76	----------------------------------------
3.42/1.76	
3.42/1.76	(5) RisEmptyProof (EQUIVALENT)
3.42/1.76	The TRS R is empty. Hence, termination is trivially proven.
3.42/1.76	----------------------------------------
3.42/1.76	
3.42/1.76	(6)
3.42/1.76	YES
3.42/1.80	EOF