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Runti Compl Inner Rewri 22807 pair #381904052
details
property
value
status
complete
benchmark
tpa2.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n036.star.cs.uiowa.edu
space
Secret_05_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.959589958 seconds
cpu usage
368.361957929
max memory
5.689593856E9
stage attributes
key
value
output-size
31908
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^2)) proof of /export/starexec/sandbox/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). (0) CpxTRS (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxWeightedTrs (3) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CpxWeightedTrs (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxTypedWeightedTrs (7) CompletionProof [UPPER BOUND(ID), 0 ms] (8) CpxTypedWeightedCompleteTrs (9) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (10) CpxTypedWeightedCompleteTrs (11) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (12) CpxRNTS (13) InliningProof [UPPER BOUND(ID), 519 ms] (14) CpxRNTS (15) SimplificationProof [BOTH BOUNDS(ID, ID), 4 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), 354 ms] (22) CpxRNTS (23) IntTrsBoundProof [UPPER BOUND(ID), 160 ms] (24) CpxRNTS (25) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (26) CpxRNTS (27) IntTrsBoundProof [UPPER BOUND(ID), 140 ms] (28) CpxRNTS (29) IntTrsBoundProof [UPPER BOUND(ID), 5 ms] (30) CpxRNTS (31) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (32) CpxRNTS (33) IntTrsBoundProof [UPPER BOUND(ID), 1052 ms] (34) CpxRNTS (35) IntTrsBoundProof [UPPER BOUND(ID), 1180 ms] (36) CpxRNTS (37) FinalProof [FINISHED, 0 ms] (38) BOUNDS(1, n^2) (39) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (40) CpxTRS (41) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (42) typed CpxTrs (43) OrderProof [LOWER BOUND(ID), 0 ms] (44) typed CpxTrs (45) RewriteLemmaProof [LOWER BOUND(ID), 289 ms] (46) BEST (47) proven lower bound (48) LowerBoundPropagationProof [FINISHED, 0 ms] (49) BOUNDS(n^1, INF) (50) typed CpxTrs ---------------------------------------- (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: -(x, 0) -> x -(s(x), s(y)) -> -(x, y) p(s(x)) -> x f(s(x), y) -> f(p(-(s(x), y)), p(-(y, s(x)))) f(x, s(y)) -> f(p(-(x, s(y))), p(-(s(y), 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: -(x, 0) -> x [1] -(s(x), s(y)) -> -(x, y) [1] p(s(x)) -> x [1] f(s(x), y) -> f(p(-(s(x), y)), p(-(y, s(x)))) [1]
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