details

property	value
status	complete
benchmark	9.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n148.star.cs.uiowa.edu
space	Beerendonk_07

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	295.551 seconds
cpu usage	1129.9
user time	1116.27
system time	13.626
max virtual memory	3.811782E7
max residence set size	1.5091924E7

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^1), O(n^2))

output

WORST_CASE(Omega(n^1), O(n^2)) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). (0) CpxTRS (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxWeightedTrs (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CpxTypedWeightedTrs (5) CompletionProof [UPPER BOUND(ID), 0 ms] (6) CpxTypedWeightedCompleteTrs (7) NarrowingProof [BOTH BOUNDS(ID, ID), 4 ms] (8) CpxTypedWeightedCompleteTrs (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (10) CpxRNTS (11) InliningProof [UPPER BOUND(ID), 482 ms] (12) CpxRNTS (13) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (14) CpxRNTS (15) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] (16) CpxRNTS (17) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (18) CpxRNTS (19) IntTrsBoundProof [UPPER BOUND(ID), 210 ms] (20) CpxRNTS (21) IntTrsBoundProof [UPPER BOUND(ID), 25 ms] (22) CpxRNTS (23) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (24) CpxRNTS (25) IntTrsBoundProof [UPPER BOUND(ID), 133 ms] (26) CpxRNTS (27) IntTrsBoundProof [UPPER BOUND(ID), 53 ms] (28) CpxRNTS (29) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (30) CpxRNTS (31) IntTrsBoundProof [UPPER BOUND(ID), 203 ms] (32) CpxRNTS (33) IntTrsBoundProof [UPPER BOUND(ID), 120 ms] (34) CpxRNTS (35) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (36) CpxRNTS (37) IntTrsBoundProof [UPPER BOUND(ID), 1562 ms] (38) CpxRNTS (39) IntTrsBoundProof [UPPER BOUND(ID), 852 ms] (40) CpxRNTS (41) FinalProof [FINISHED, 0 ms] (42) BOUNDS(1, n^2) (43) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (44) TRS for Loop Detection (45) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (46) BEST (47) proven lower bound (48) LowerBoundPropagationProof [FINISHED, 0 ms] (49) BOUNDS(n^1, INF) (50) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). The TRS R consists of the following rules: cond(true, x, y, z) -> cond(and(gr(x, z), gr(y, z)), p(x), p(y), z) and(true, true) -> true and(x, false) -> false and(false, x) -> false gr(0, 0) -> false gr(0, x) -> false gr(s(x), 0) -> true gr(s(x), s(y)) -> gr(x, y) p(0) -> 0 p(s(x)) -> x S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). The TRS R consists of the following rules: cond(true, x, y, z) -> cond(and(gr(x, z), gr(y, z)), p(x), p(y), z) [1] and(true, true) -> true [1] and(x, false) -> false [1] and(false, x) -> false [1] gr(0, 0) -> false [1] popout

output may be truncated. 'popout' for the full output.

job log

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actions

all output return to Runtime Complexity: TRS Innermost