TRS_Conditional 2019-03-28 22.59 pair #432272689

details

property	value
status	complete
benchmark	gcd.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n077.star.cs.uiowa.edu
space	Mixed_CTRS

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.05323 seconds
cpu usage	4.62547
user time	4.41022
system time	0.215251
max virtual memory	1.84775E7
max residence set size	326396.0

stage attributes

key	value
starexec-result	YES

output

4.25/1.94	YES
4.25/1.95	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
4.25/1.95	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.25/1.95	
4.25/1.95	
4.25/1.95	Quasi decreasingness of the given CTRS could be proven:
4.25/1.95	
4.25/1.95	(0) CTRS
4.25/1.95	(1) CTRSToQTRSProof [SOUND, 0 ms]
4.25/1.95	(2) QTRS
4.25/1.95	(3) DependencyPairsProof [EQUIVALENT, 0 ms]
4.25/1.95	(4) QDP
4.25/1.95	(5) DependencyGraphProof [EQUIVALENT, 0 ms]
4.25/1.95	(6) AND
4.25/1.95	    (7) QDP
4.25/1.95	        (8) UsableRulesProof [EQUIVALENT, 0 ms]
4.25/1.95	        (9) QDP
4.25/1.95	        (10) QDPSizeChangeProof [EQUIVALENT, 0 ms]
4.25/1.95	        (11) YES
4.25/1.95	    (12) QDP
4.25/1.95	        (13) UsableRulesProof [EQUIVALENT, 0 ms]
4.25/1.95	        (14) QDP
4.25/1.95	        (15) QDPSizeChangeProof [EQUIVALENT, 0 ms]
4.25/1.95	        (16) YES
4.25/1.95	    (17) QDP
4.25/1.95	        (18) QDPOrderProof [EQUIVALENT, 36 ms]
4.25/1.95	        (19) QDP
4.25/1.95	        (20) DependencyGraphProof [EQUIVALENT, 0 ms]
4.25/1.95	        (21) TRUE
4.25/1.95	
4.25/1.95	
4.25/1.95	----------------------------------------
4.25/1.95	
4.25/1.95	(0)
4.25/1.95	Obligation:
4.25/1.95	Conditional term rewrite system:
4.25/1.95	The TRS R consists of the following rules:
4.25/1.95	
4.25/1.95	   less(x, 0) -> false
4.25/1.95	   less(0, s(x)) -> true
4.25/1.95	   less(s(x), s(y)) -> less(x, y)
4.25/1.95	   minus(0, s(y)) -> 0
4.25/1.95	   minus(x, 0) -> x
4.25/1.95	   minus(s(x), s(y)) -> minus(x, y)
4.25/1.95	   gcd(x, x) -> x
4.25/1.95	   gcd(s(x), 0) -> s(x)
4.25/1.95	   gcd(0, s(y)) -> s(y)
4.25/1.95	
4.25/1.95	The conditional TRS C consists of the following conditional rules:
4.25/1.95	
4.25/1.95	   gcd(s(x), s(y)) -> gcd(minus(x, y), s(y)) <= less(y, x) -> true
4.25/1.95	   gcd(s(x), s(y)) -> gcd(s(x), minus(y, x)) <= less(x, y) -> true
4.25/1.95	
4.25/1.95	
4.25/1.95	----------------------------------------
4.25/1.95	
4.25/1.95	(1) CTRSToQTRSProof (SOUND)
4.25/1.95	The conditional rules have been transormed into unconditional rules according to [CTRS,AAECCNOC].
4.25/1.95	----------------------------------------
4.25/1.95	
4.25/1.95	(2)
4.25/1.95	Obligation:
4.25/1.95	Q restricted rewrite system:
4.25/1.95	The TRS R consists of the following rules:
4.25/1.95	
4.25/1.95	   gcd(s(x), s(y)) -> U1(less(y, x), x, y)
4.25/1.95	   U1(true, x, y) -> gcd(minus(x, y), s(y))
4.25/1.95	   gcd(s(x), s(y)) -> U2(less(x, y), x, y)
4.25/1.95	   U2(true, x, y) -> gcd(s(x), minus(y, x))
4.25/1.95	   less(x, 0) -> false
4.25/1.95	   less(0, s(x)) -> true
4.25/1.95	   less(s(x), s(y)) -> less(x, y)
4.25/1.95	   minus(0, s(y)) -> 0
4.25/1.95	   minus(x, 0) -> x
4.25/1.95	   minus(s(x), s(y)) -> minus(x, y)
4.25/1.95	   gcd(x, x) -> x
4.25/1.95	   gcd(s(x), 0) -> s(x)
4.25/1.95	   gcd(0, s(y)) -> s(y)
4.25/1.95	
4.25/1.95	Q is empty.
4.25/1.95	
4.25/1.95	----------------------------------------
4.25/1.95	
4.25/1.95	(3) DependencyPairsProof (EQUIVALENT)
4.25/1.95	Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
4.25/1.95	----------------------------------------
4.25/1.95	
4.25/1.95	(4)
4.25/1.95	Obligation:
4.25/1.95	Q DP problem:
4.25/1.95	The TRS P consists of the following rules:
4.25/1.95	
4.25/1.95	   GCD(s(x), s(y)) -> U1^1(less(y, x), x, y)
4.25/1.95	   GCD(s(x), s(y)) -> LESS(y, x)
4.25/1.95	   U1^1(true, x, y) -> GCD(minus(x, y), s(y))
4.25/1.95	   U1^1(true, x, y) -> MINUS(x, y)
4.25/1.95	   GCD(s(x), s(y)) -> U2^1(less(x, y), x, y)
4.25/1.95	   GCD(s(x), s(y)) -> LESS(x, y)
4.25/1.95	   U2^1(true, x, y) -> GCD(s(x), minus(y, x))
4.25/1.95	   U2^1(true, x, y) -> MINUS(y, x)

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