details

property	value
status	complete
benchmark	Ex2_Luc02a_Z.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n038.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	13.0010259151 seconds
cpu usage	45.486761354
max memory	4.369297408E9

stage attributes

key	value
output-size	52572
starexec-result	WORST_CASE(Omega(n^3), O(n^3))

output

/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^3), O(n^3)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^3, n^3). (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), 0 ms] (8) CpxTypedWeightedCompleteTrs (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (10) CpxRNTS (11) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CpxRNTS (13) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] (14) CpxRNTS (15) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (16) CpxRNTS (17) IntTrsBoundProof [UPPER BOUND(ID), 192 ms] (18) CpxRNTS (19) IntTrsBoundProof [UPPER BOUND(ID), 4 ms] (20) CpxRNTS (21) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (22) CpxRNTS (23) IntTrsBoundProof [UPPER BOUND(ID), 302 ms] (24) CpxRNTS (25) IntTrsBoundProof [UPPER BOUND(ID), 86 ms] (26) CpxRNTS (27) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (28) CpxRNTS (29) IntTrsBoundProof [UPPER BOUND(ID), 485 ms] (30) CpxRNTS (31) IntTrsBoundProof [UPPER BOUND(ID), 44 ms] (32) CpxRNTS (33) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (34) CpxRNTS (35) IntTrsBoundProof [UPPER BOUND(ID), 668 ms] (36) CpxRNTS (37) IntTrsBoundProof [UPPER BOUND(ID), 3 ms] (38) CpxRNTS (39) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (40) CpxRNTS (41) IntTrsBoundProof [UPPER BOUND(ID), 2624 ms] (42) CpxRNTS (43) IntTrsBoundProof [UPPER BOUND(ID), 5 ms] (44) CpxRNTS (45) FinalProof [FINISHED, 0 ms] (46) BOUNDS(1, n^3) (47) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (48) CpxTRS (49) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (50) typed CpxTrs (51) OrderProof [LOWER BOUND(ID), 0 ms] (52) typed CpxTrs (53) RewriteLemmaProof [LOWER BOUND(ID), 284 ms] (54) BEST (55) proven lower bound (56) LowerBoundPropagationProof [FINISHED, 0 ms] (57) BOUNDS(n^1, INF) (58) typed CpxTrs (59) RewriteLemmaProof [LOWER BOUND(ID), 86 ms] (60) typed CpxTrs (61) RewriteLemmaProof [LOWER BOUND(ID), 101 ms] (62) BEST (63) proven lower bound (64) LowerBoundPropagationProof [FINISHED, 0 ms] (65) BOUNDS(n^3, INF) (66) typed CpxTrs ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) 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))) dbl(0) -> 0 dbl(s(X)) -> s(s(dbl(X))) add(0, X) -> X add(s(X), Y) -> s(add(X, Y)) first(0, X) -> nil first(s(X), cons(Y, Z)) -> cons(Y, n__first(X, activate(Z))) popout

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

job log

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actions

all output return to Runti Compl Inner Rewri 22807