Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308496

details

property	value
status	complete
benchmark	Ex49_GM04.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n040.star.cs.uiowa.edu
space	Strategy_removed_CSR_05

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	8.98591 seconds
cpu usage	23.1845
user time	21.1902
system time	1.99435
max virtual memory	1.9079456E7
max residence set size	4144332.0

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^1), O(n^1))

output

22.95/8.94	WORST_CASE(Omega(n^1), O(n^1))
22.95/8.95	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
22.95/8.95	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
22.95/8.95	
22.95/8.95	
22.95/8.95	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
22.95/8.95	
22.95/8.95	(0) CpxTRS
22.95/8.95	(1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms]
22.95/8.95	(2) CpxTRS
22.95/8.95	    (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
22.95/8.95	    (4) CpxWeightedTrs
22.95/8.95	    (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
22.95/8.95	    (6) CpxTypedWeightedTrs
22.95/8.95	    (7) CompletionProof [UPPER BOUND(ID), 0 ms]
22.95/8.95	    (8) CpxTypedWeightedCompleteTrs
22.95/8.95	    (9) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
22.95/8.95	    (10) CpxTypedWeightedCompleteTrs
22.95/8.95	    (11) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
22.95/8.95	    (12) CpxRNTS
22.95/8.95	    (13) InliningProof [UPPER BOUND(ID), 2 ms]
22.95/8.95	    (14) CpxRNTS
22.95/8.95	    (15) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
22.95/8.95	    (16) CpxRNTS
22.95/8.95	    (17) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms]
22.95/8.95	    (18) CpxRNTS
22.95/8.95	    (19) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
22.95/8.95	    (20) CpxRNTS
22.95/8.95	    (21) IntTrsBoundProof [UPPER BOUND(ID), 263 ms]
22.95/8.95	    (22) CpxRNTS
22.95/8.95	    (23) IntTrsBoundProof [UPPER BOUND(ID), 128 ms]
22.95/8.95	    (24) CpxRNTS
22.95/8.95	    (25) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
22.95/8.95	    (26) CpxRNTS
22.95/8.95	    (27) IntTrsBoundProof [UPPER BOUND(ID), 341 ms]
22.95/8.95	    (28) CpxRNTS
22.95/8.95	    (29) IntTrsBoundProof [UPPER BOUND(ID), 73 ms]
22.95/8.95	    (30) CpxRNTS
22.95/8.95	    (31) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
22.95/8.95	    (32) CpxRNTS
22.95/8.95	    (33) IntTrsBoundProof [UPPER BOUND(ID), 291 ms]
22.95/8.95	    (34) CpxRNTS
22.95/8.95	    (35) IntTrsBoundProof [UPPER BOUND(ID), 115 ms]
22.95/8.95	    (36) CpxRNTS
22.95/8.95	    (37) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
22.95/8.95	    (38) CpxRNTS
22.95/8.95	    (39) IntTrsBoundProof [UPPER BOUND(ID), 467 ms]
22.95/8.95	    (40) CpxRNTS
22.95/8.95	    (41) IntTrsBoundProof [UPPER BOUND(ID), 249 ms]
22.95/8.95	    (42) CpxRNTS
22.95/8.95	    (43) FinalProof [FINISHED, 0 ms]
22.95/8.95	    (44) BOUNDS(1, n^1)
22.95/8.95	(45) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
22.95/8.95	(46) TRS for Loop Detection
22.95/8.95	    (47) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
22.95/8.95	    (48) BEST
22.95/8.95	        (49) proven lower bound
22.95/8.95	            (50) LowerBoundPropagationProof [FINISHED, 0 ms]
22.95/8.95	            (51) BOUNDS(n^1, INF)
22.95/8.95	        (52) TRS for Loop Detection
22.95/8.95	
22.95/8.95	
22.95/8.95	----------------------------------------
22.95/8.95	
22.95/8.95	(0)
22.95/8.95	Obligation:
22.95/8.95	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
22.95/8.95	
22.95/8.95	
22.95/8.95	The TRS R consists of the following rules:
22.95/8.95	
22.95/8.95	   minus(0, Y) -> 0
22.95/8.95	   minus(s(X), s(Y)) -> minus(X, Y)
22.95/8.95	   geq(X, 0) -> true
22.95/8.95	   geq(0, s(Y)) -> false
22.95/8.95	   geq(s(X), s(Y)) -> geq(X, Y)
22.95/8.95	   div(0, s(Y)) -> 0
22.95/8.95	   div(s(X), s(Y)) -> if(geq(X, Y), s(div(minus(X, Y), s(Y))), 0)
22.95/8.95	   if(true, X, Y) -> X
22.95/8.95	   if(false, X, Y) -> Y
22.95/8.95	
22.95/8.95	S is empty.
22.95/8.95	Rewrite Strategy: FULL
22.95/8.95	----------------------------------------
22.95/8.95	
22.95/8.95	(1) RcToIrcProof (BOTH BOUNDS(ID, ID))
22.95/8.95	Converted rc-obligation to irc-obligation.
22.95/8.95	
22.95/8.95	The duplicating contexts are:
22.95/8.95	div(s([]), s(Y))
22.95/8.95	div(s(X), s([]))
22.95/8.95	
22.95/8.95	
22.95/8.95	The defined contexts are:
22.95/8.95	if([], s(x1), 0)
22.95/8.95	if(x0, s([]), 0)
22.95/8.95	div([], s(x1))
22.95/8.95	geq([], x1)
22.95/8.95	minus([], x1)
22.95/8.95

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