details

property	value
status	complete
benchmark	Ex2_Luc02a_L.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n138.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	8.1046 seconds
cpu usage	27.797
user time	26.1804
system time	1.61659
max virtual memory	1.9010752E7
max residence set size	3991740.0

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/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^3, n^3).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), 2 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), 2 ms] (14) CpxRNTS (15) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (16) CpxRNTS (17) IntTrsBoundProof [UPPER BOUND(ID), 199 ms] (18) CpxRNTS (19) IntTrsBoundProof [UPPER BOUND(ID), 65 ms] (20) CpxRNTS (21) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (22) CpxRNTS (23) IntTrsBoundProof [UPPER BOUND(ID), 170 ms] (24) CpxRNTS (25) IntTrsBoundProof [UPPER BOUND(ID), 63 ms] (26) CpxRNTS (27) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (28) CpxRNTS (29) IntTrsBoundProof [UPPER BOUND(ID), 248 ms] (30) CpxRNTS (31) IntTrsBoundProof [UPPER BOUND(ID), 4 ms] (32) CpxRNTS (33) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (34) CpxRNTS (35) IntTrsBoundProof [UPPER BOUND(ID), 414 ms] (36) CpxRNTS (37) IntTrsBoundProof [UPPER BOUND(ID), 44 ms] (38) CpxRNTS (39) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (40) CpxRNTS (41) IntTrsBoundProof [UPPER BOUND(ID), 447 ms] (42) CpxRNTS (43) IntTrsBoundProof [UPPER BOUND(ID), 3 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), 274 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), 57 ms] (60) typed CpxTrs (61) RewriteLemmaProof [LOWER BOUND(ID), 99 ms] (62) proven lower bound (63) LowerBoundPropagationProof [FINISHED, 0 ms] (64) BOUNDS(n^3, INF) ---------------------------------------- (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))) 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)) -> cons(Y) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- 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