TRS_Innermost 2019-03-28 22.12 pair #432270760

details

property	value
status	complete
benchmark	wiehe13.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n065.star.cs.uiowa.edu
space	Mixed_innermost

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.61939 seconds
cpu usage	6.2524
user time	5.98359
system time	0.268811
max virtual memory	1.8611084E7
max residence set size	438192.0

stage attributes

key	value
starexec-result	YES

output

6.01/2.54	YES
6.15/2.55	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
6.15/2.55	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
6.15/2.55	
6.15/2.55	
6.15/2.55	Termination w.r.t. Q of the given QTRS could be proven:
6.15/2.55	
6.15/2.55	(0) QTRS
6.15/2.55	(1) DependencyPairsProof [EQUIVALENT, 0 ms]
6.15/2.55	(2) QDP
6.15/2.55	(3) DependencyGraphProof [EQUIVALENT, 0 ms]
6.15/2.55	(4) AND
6.15/2.55	    (5) QDP
6.15/2.55	        (6) UsableRulesProof [EQUIVALENT, 0 ms]
6.15/2.55	        (7) QDP
6.15/2.55	        (8) QReductionProof [EQUIVALENT, 0 ms]
6.15/2.55	        (9) QDP
6.15/2.55	        (10) QDPSizeChangeProof [EQUIVALENT, 0 ms]
6.15/2.55	        (11) YES
6.15/2.55	    (12) QDP
6.15/2.55	        (13) UsableRulesProof [EQUIVALENT, 0 ms]
6.15/2.55	        (14) QDP
6.15/2.55	        (15) QReductionProof [EQUIVALENT, 0 ms]
6.15/2.55	        (16) QDP
6.15/2.55	        (17) TransformationProof [EQUIVALENT, 0 ms]
6.15/2.55	        (18) QDP
6.15/2.55	        (19) TransformationProof [EQUIVALENT, 0 ms]
6.15/2.55	        (20) QDP
6.15/2.55	        (21) UsableRulesProof [EQUIVALENT, 0 ms]
6.15/2.55	        (22) QDP
6.15/2.55	        (23) QReductionProof [EQUIVALENT, 0 ms]
6.15/2.55	        (24) QDP
6.15/2.55	        (25) TransformationProof [EQUIVALENT, 0 ms]
6.15/2.55	        (26) QDP
6.15/2.55	        (27) TransformationProof [EQUIVALENT, 0 ms]
6.15/2.55	        (28) QDP
6.15/2.55	        (29) TransformationProof [EQUIVALENT, 0 ms]
6.15/2.55	        (30) QDP
6.15/2.55	        (31) UsableRulesProof [EQUIVALENT, 0 ms]
6.15/2.55	        (32) QDP
6.15/2.55	        (33) QReductionProof [EQUIVALENT, 0 ms]
6.15/2.55	        (34) QDP
6.15/2.55	        (35) QDPOrderProof [EQUIVALENT, 41 ms]
6.15/2.55	        (36) QDP
6.15/2.55	        (37) QDPOrderProof [EQUIVALENT, 8 ms]
6.15/2.55	        (38) QDP
6.15/2.55	        (39) PisEmptyProof [EQUIVALENT, 0 ms]
6.15/2.55	        (40) YES
6.15/2.55	    (41) QDP
6.15/2.55	        (42) UsableRulesProof [EQUIVALENT, 0 ms]
6.15/2.55	        (43) QDP
6.15/2.55	        (44) QReductionProof [EQUIVALENT, 0 ms]
6.15/2.55	        (45) QDP
6.15/2.55	        (46) QDPOrderProof [EQUIVALENT, 28 ms]
6.15/2.55	        (47) QDP
6.15/2.55	        (48) QDPOrderProof [EQUIVALENT, 0 ms]
6.15/2.55	        (49) QDP
6.15/2.55	        (50) PisEmptyProof [EQUIVALENT, 0 ms]
6.15/2.55	        (51) YES
6.15/2.55	
6.15/2.55	
6.15/2.55	----------------------------------------
6.15/2.55	
6.15/2.55	(0)
6.15/2.55	Obligation:
6.15/2.55	Q restricted rewrite system:
6.15/2.55	The TRS R consists of the following rules:
6.15/2.55	
6.15/2.55	   quot(0, s(y), s(z)) -> 0
6.15/2.55	   quot(s(x), s(y), z) -> quot(x, y, z)
6.15/2.55	   plus(s(x), s(y)) -> s(s(plus(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))))
6.15/2.55	   plus(s(x), x) -> plus(if(gt(x, x), id(x), id(x)), s(x))
6.15/2.55	   plus(zero, y) -> y
6.15/2.55	   plus(id(x), s(y)) -> s(plus(x, if(gt(s(y), y), y, s(y))))
6.15/2.55	   id(x) -> x
6.15/2.55	   if(true, x, y) -> x
6.15/2.55	   if(false, x, y) -> y
6.15/2.55	   not(x) -> if(x, false, true)
6.15/2.55	   gt(s(x), zero) -> true
6.15/2.55	   gt(zero, y) -> false
6.15/2.55	   gt(s(x), s(y)) -> gt(x, y)
6.15/2.55	   quot(x, 0, s(z)) -> s(quot(x, plus(z, s(0)), s(z)))
6.15/2.55	
6.15/2.55	The set Q consists of the following terms:
6.15/2.55	
6.15/2.55	   quot(0, s(x0), s(x1))
6.15/2.55	   quot(s(x0), s(x1), x2)
6.15/2.55	   plus(s(x0), s(x1))
6.15/2.55	   plus(s(x0), x0)
6.15/2.55	   plus(zero, x0)
6.15/2.55	   id(x0)
6.15/2.55	   if(true, x0, x1)
6.15/2.55	   if(false, x0, x1)
6.15/2.55	   not(x0)
6.15/2.55	   gt(s(x0), zero)
6.15/2.55	   gt(zero, x0)
6.15/2.55	   gt(s(x0), s(x1))
6.15/2.55	   quot(x0, 0, s(x1))
6.15/2.55	
6.15/2.55

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actions all output return to TRS_Innermost 2019-03-28 22.12