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Runti Compl Inner Rewri 22807 pair #381904386
details
property
value
status
complete
benchmark
#4.23.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n046.star.cs.uiowa.edu
space
Strategy_removed_AG01
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.478873968 seconds
cpu usage
407.655311041
max memory
6.160904192E9
stage attributes
key
value
output-size
18919
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
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^1), O(n^2)) 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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2).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), 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), 293 ms] (18) CpxRNTS (19) IntTrsBoundProof [UPPER BOUND(ID), 86 ms] (20) CpxRNTS (21) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (22) CpxRNTS (23) IntTrsBoundProof [UPPER BOUND(ID), 566 ms] (24) CpxRNTS (25) IntTrsBoundProof [UPPER BOUND(ID), 329 ms] (26) CpxRNTS (27) FinalProof [FINISHED, 0 ms] (28) BOUNDS(1, n^2) (29) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (30) CpxTRS (31) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (32) typed CpxTrs (33) OrderProof [LOWER BOUND(ID), 0 ms] (34) typed CpxTrs (35) RewriteLemmaProof [LOWER BOUND(ID), 285 ms] (36) BEST (37) proven lower bound (38) LowerBoundPropagationProof [FINISHED, 0 ms] (39) BOUNDS(n^1, INF) (40) typed CpxTrs (41) RewriteLemmaProof [LOWER BOUND(ID), 201 ms] (42) BOUNDS(1, INF) ---------------------------------------- (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: quot(0, s(y), s(z)) -> 0 quot(s(x), s(y), z) -> quot(x, y, z) plus(0, y) -> y plus(s(x), y) -> s(plus(x, y)) quot(x, 0, s(z)) -> s(quot(x, plus(z, s(0)), s(z))) 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: quot(0, s(y), s(z)) -> 0 [1] quot(s(x), s(y), z) -> quot(x, y, z) [1] plus(0, y) -> y [1] plus(s(x), y) -> s(plus(x, y)) [1] quot(x, 0, s(z)) -> s(quot(x, plus(z, s(0)), s(z))) [1] Rewrite Strategy: INNERMOST ---------------------------------------- (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ----------------------------------------
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