details

property	value
status	complete
benchmark	ExSec11_1_Luc02a_Z.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n139.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.576 seconds
cpu usage	1087.21
user time	1071.81
system time	15.3963
max virtual memory	3.7773052E7
max residence set size	1.5362388E7

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^3), O(n^3))

output

WORST_CASE(Omega(n^3), O(n^3)) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^3, n^3). (0) CpxTRS (1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms] (2) CpxTRS (3) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CpxTRS (5) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxWeightedTrs (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxTypedWeightedTrs (9) CompletionProof [UPPER BOUND(ID), 0 ms] (10) CpxTypedWeightedCompleteTrs (11) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CpxTypedWeightedCompleteTrs (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (14) CpxRNTS (15) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (16) CpxRNTS (17) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] (18) CpxRNTS (19) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (20) CpxRNTS (21) IntTrsBoundProof [UPPER BOUND(ID), 139 ms] (22) CpxRNTS (23) IntTrsBoundProof [UPPER BOUND(ID), 78 ms] (24) CpxRNTS (25) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (26) CpxRNTS (27) IntTrsBoundProof [UPPER BOUND(ID), 240 ms] (28) CpxRNTS (29) IntTrsBoundProof [UPPER BOUND(ID), 82 ms] (30) CpxRNTS (31) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (32) CpxRNTS (33) IntTrsBoundProof [UPPER BOUND(ID), 231 ms] (34) CpxRNTS (35) IntTrsBoundProof [UPPER BOUND(ID), 73 ms] (36) CpxRNTS (37) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (38) CpxRNTS (39) IntTrsBoundProof [UPPER BOUND(ID), 322 ms] (40) CpxRNTS (41) IntTrsBoundProof [UPPER BOUND(ID), 34 ms] (42) CpxRNTS (43) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (44) CpxRNTS (45) IntTrsBoundProof [UPPER BOUND(ID), 527 ms] (46) CpxRNTS (47) IntTrsBoundProof [UPPER BOUND(ID), 0 ms] (48) CpxRNTS (49) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (50) CpxRNTS (51) IntTrsBoundProof [UPPER BOUND(ID), 1926 ms] (52) CpxRNTS (53) IntTrsBoundProof [UPPER BOUND(ID), 9 ms] (54) CpxRNTS (55) FinalProof [FINISHED, 0 ms] (56) BOUNDS(1, n^3) (57) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (58) CpxTRS (59) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (60) typed CpxTrs (61) OrderProof [LOWER BOUND(ID), 0 ms] (62) typed CpxTrs (63) RewriteLemmaProof [LOWER BOUND(ID), 299 ms] (64) BEST (65) proven lower bound (66) LowerBoundPropagationProof [FINISHED, 0 ms] (67) BOUNDS(n^1, INF) (68) typed CpxTrs (69) RewriteLemmaProof [LOWER BOUND(ID), 76 ms] (70) typed CpxTrs (71) RewriteLemmaProof [LOWER BOUND(ID), 107 ms] (72) BEST (73) proven lower bound (74) LowerBoundPropagationProof [FINISHED, 0 ms] (75) BOUNDS(n^3, INF) (76) typed CpxTrs (77) RewriteLemmaProof [LOWER BOUND(ID), 47 ms] (78) BOUNDS(1, INF) ---------------------------------------- (0) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^3, n^3). The TRS R consists of the following rules: terms(N) -> cons(recip(sqr(N)), n__terms(s(N))) sqr(0) -> 0 sqr(s(X)) -> s(add(sqr(X), dbl(X))) popout

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

job log

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actions

all output return to Runtime Complexity: TRS