TRS_Conditional 2019-03-28 22.59 pair #432272523

details

property	value
status	complete
benchmark	311.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n140.star.cs.uiowa.edu
space	COPS

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	3.71293 seconds
cpu usage	10.2928
user time	9.87258
system time	0.420245
max virtual memory	1.855162E7
max residence set size	880428.0

stage attributes

key	value
starexec-result	MAYBE

output

10.01/3.62	MAYBE
10.01/3.62	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
10.01/3.62	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
10.01/3.62	
10.01/3.62	
10.01/3.62	Quasi decreasingness of the given CTRS could not be shown:
10.01/3.62	
10.01/3.62	(0) CTRS
10.01/3.62	(1) CTRSToQTRSProof [SOUND, 0 ms]
10.01/3.62	(2) QTRS
10.01/3.62	(3) QTRSRRRProof [EQUIVALENT, 52 ms]
10.01/3.62	(4) QTRS
10.01/3.62	(5) DependencyPairsProof [EQUIVALENT, 0 ms]
10.01/3.62	(6) QDP
10.01/3.62	(7) DependencyGraphProof [EQUIVALENT, 0 ms]
10.01/3.62	(8) AND
10.01/3.62	    (9) QDP
10.01/3.62	        (10) UsableRulesProof [EQUIVALENT, 0 ms]
10.01/3.62	        (11) QDP
10.01/3.62	        (12) QDPSizeChangeProof [EQUIVALENT, 0 ms]
10.01/3.62	        (13) YES
10.01/3.62	    (14) QDP
10.01/3.62	        (15) UsableRulesProof [EQUIVALENT, 0 ms]
10.01/3.62	        (16) QDP
10.01/3.62	        (17) TransformationProof [EQUIVALENT, 0 ms]
10.01/3.62	        (18) QDP
10.01/3.62	        (19) TransformationProof [EQUIVALENT, 0 ms]
10.01/3.62	        (20) QDP
10.01/3.62	        (21) MRRProof [EQUIVALENT, 0 ms]
10.01/3.62	        (22) QDP
10.01/3.62	        (23) TransformationProof [EQUIVALENT, 0 ms]
10.01/3.62	        (24) QDP
10.01/3.62	        (25) NonTerminationLoopProof [COMPLETE, 0 ms]
10.01/3.62	        (26) NO
10.01/3.62	
10.01/3.62	
10.01/3.62	----------------------------------------
10.01/3.62	
10.01/3.62	(0)
10.01/3.62	Obligation:
10.01/3.62	Conditional term rewrite system:
10.01/3.62	The TRS R consists of the following rules:
10.01/3.62	
10.01/3.62	   gcd(x, 0) -> x
10.01/3.62	   gcd(0, x) -> x
10.01/3.62	   iadd(y) -> tp2(0, y)
10.01/3.62	   iadd(add(x, y)) -> tp2(x, y)
10.01/3.62	
10.01/3.62	The conditional TRS C consists of the following conditional rules:
10.01/3.62	
10.01/3.62	   gcd(z, y) -> gcd(x, y) <= iadd(z) -> tp2(x, y)
10.01/3.62	   gcd(y, z) -> gcd(x, y) <= iadd(z) -> tp2(x, y)
10.01/3.62	   iadd(s(z)) -> tp2(s(x), y) <= iadd(z) -> tp2(x, y)
10.01/3.62	
10.01/3.62	
10.01/3.62	----------------------------------------
10.01/3.62	
10.01/3.62	(1) CTRSToQTRSProof (SOUND)
10.01/3.62	The conditional rules have been transormed into unconditional rules according to [CTRS,AAECCNOC].
10.01/3.62	----------------------------------------
10.01/3.62	
10.01/3.62	(2)
10.01/3.62	Obligation:
10.01/3.62	Q restricted rewrite system:
10.01/3.62	The TRS R consists of the following rules:
10.01/3.62	
10.01/3.62	   gcd(z, y) -> U1(iadd(z), y)
10.01/3.62	   U1(tp2(x, y), y) -> gcd(x, y)
10.01/3.62	   gcd(y, z) -> U2(iadd(z), y)
10.01/3.62	   U2(tp2(x, y), y) -> gcd(x, y)
10.01/3.62	   iadd(s(z)) -> U3(iadd(z))
10.01/3.62	   U3(tp2(x, y)) -> tp2(s(x), y)
10.01/3.62	   gcd(x, 0) -> x
10.01/3.62	   gcd(0, x) -> x
10.01/3.62	   iadd(y) -> tp2(0, y)
10.01/3.62	   iadd(add(x, y)) -> tp2(x, y)
10.01/3.62	
10.01/3.62	Q is empty.
10.01/3.62	
10.01/3.62	----------------------------------------
10.01/3.63	
10.01/3.63	(3) QTRSRRRProof (EQUIVALENT)
10.01/3.63	Used ordering:
10.01/3.63	Polynomial interpretation [POLO]:
10.01/3.63	
10.01/3.63	   POL(0) = 0
10.01/3.63	   POL(U1(x_1, x_2)) = x_1 + 2*x_2
10.01/3.63	   POL(U2(x_1, x_2)) = x_1 + 2*x_2
10.01/3.63	   POL(U3(x_1)) = x_1
10.01/3.63	   POL(add(x_1, x_2)) = 1 + 2*x_1 + 2*x_2
10.01/3.63	   POL(gcd(x_1, x_2)) = 1 + 2*x_1 + 2*x_2
10.01/3.63	   POL(iadd(x_1)) = 1 + x_1
10.01/3.63	   POL(s(x_1)) = x_1
10.01/3.63	   POL(tp2(x_1, x_2)) = 1 + 2*x_1 + x_2
10.01/3.63	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
10.01/3.63	
10.01/3.63	   gcd(x, 0) -> x
10.01/3.63	   gcd(0, x) -> x
10.01/3.63	   iadd(add(x, y)) -> tp2(x, y)
10.01/3.63

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actions all output return to TRS_Conditional 2019-03-28 22.59