3.40/1.64	YES
3.40/1.65	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.40/1.65	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.40/1.65	
3.40/1.65	
3.40/1.65	Quasi decreasingness of the given CTRS could be proven:
3.40/1.65	
3.40/1.65	(0) CTRS
3.40/1.65	(1) CTRSToQTRSProof [SOUND, 0 ms]
3.40/1.65	(2) QTRS
3.40/1.65	(3) QTRSRRRProof [EQUIVALENT, 31 ms]
3.40/1.65	(4) QTRS
3.40/1.65	(5) RisEmptyProof [EQUIVALENT, 0 ms]
3.40/1.65	(6) YES
3.40/1.65	
3.40/1.65	
3.40/1.65	----------------------------------------
3.40/1.65	
3.40/1.65	(0)
3.40/1.65	Obligation:
3.40/1.65	Conditional term rewrite system:
3.40/1.65	The TRS R consists of the following rules:
3.40/1.65	
3.40/1.65	   pin(a) -> pout(b)
3.40/1.65	   pin(b) -> pout(c)
3.40/1.65	   tc(x) -> x
3.40/1.65	
3.40/1.65	The conditional TRS C consists of the following conditional rules:
3.40/1.65	
3.40/1.65	   tc(x) -> y <= pin(x) -> pout(z), tc(z) -> y
3.40/1.65	
3.40/1.65	
3.40/1.65	----------------------------------------
3.40/1.65	
3.40/1.65	(1) CTRSToQTRSProof (SOUND)
3.40/1.65	The conditional rules have been transormed into unconditional rules according to [CTRS,AAECCNOC].
3.40/1.65	----------------------------------------
3.40/1.65	
3.40/1.65	(2)
3.40/1.65	Obligation:
3.40/1.65	Q restricted rewrite system:
3.40/1.65	The TRS R consists of the following rules:
3.40/1.65	
3.40/1.65	   tc(x) -> U1(pin(x))
3.40/1.65	   U1(pout(z)) -> U2(tc(z))
3.40/1.65	   U2(y) -> y
3.40/1.65	   pin(a) -> pout(b)
3.40/1.65	   pin(b) -> pout(c)
3.40/1.65	   tc(x) -> x
3.40/1.65	
3.40/1.65	Q is empty.
3.40/1.65	
3.40/1.65	----------------------------------------
3.40/1.65	
3.40/1.65	(3) QTRSRRRProof (EQUIVALENT)
3.40/1.65	Used ordering:
3.40/1.65	Knuth-Bendix order [KBO] with precedence:c > b > pin_1 > pout_1 > a > U2_1 > tc_1 > U1_1 > z
3.40/1.65	
3.40/1.65	and weight map:
3.40/1.65	
3.40/1.65	   z=1
3.40/1.65	   a=6
3.40/1.65	   b=4
3.40/1.65	   c=1
3.40/1.65	   tc_1=4
3.40/1.65	   U1_1=3
3.40/1.65	   pin_1=1
3.40/1.65	   pout_1=3
3.40/1.65	   U2_1=1
3.40/1.65	
3.40/1.65	The variable weight is 1With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
3.40/1.65	
3.40/1.65	   tc(x) -> U1(pin(x))
3.40/1.65	   U1(pout(z)) -> U2(tc(z))
3.40/1.65	   U2(y) -> y
3.40/1.65	   pin(a) -> pout(b)
3.40/1.65	   pin(b) -> pout(c)
3.40/1.65	   tc(x) -> x
3.40/1.65	
3.40/1.65	
3.40/1.65	
3.40/1.65	
3.40/1.65	----------------------------------------
3.40/1.65	
3.40/1.65	(4)
3.40/1.65	Obligation:
3.40/1.65	Q restricted rewrite system:
3.40/1.65	R is empty.
3.40/1.65	Q is empty.
3.40/1.65	
3.40/1.65	----------------------------------------
3.40/1.65	
3.40/1.65	(5) RisEmptyProof (EQUIVALENT)
3.40/1.65	The TRS R is empty. Hence, termination is trivially proven.
3.40/1.65	----------------------------------------
3.40/1.65	
3.40/1.65	(6)
3.40/1.65	YES
3.40/1.66	EOF