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Runti Compl Full Rewri 10127 pair #381902745
details
property
value
status
complete
benchmark
divExp.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n027.star.cs.uiowa.edu
space
Secret_06_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.526233912 seconds
cpu usage
995.590914976
max memory
1.1813687296E10
stage attributes
key
value
output-size
28222
starexec-result
WORST_CASE(Omega(n^1), O(n^3))
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^3)) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^3). (0) CpxTRS (1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) RelTrsToWeightedTrsProof [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), 5 ms] (12) CpxRNTS (13) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (14) CpxRNTS (15) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] (16) CpxRNTS (17) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (18) CpxRNTS (19) IntTrsBoundProof [UPPER BOUND(ID), 488 ms] (20) CpxRNTS (21) IntTrsBoundProof [UPPER BOUND(ID), 219 ms] (22) CpxRNTS (23) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (24) CpxRNTS (25) IntTrsBoundProof [UPPER BOUND(ID), 899 ms] (26) CpxRNTS (27) IntTrsBoundProof [UPPER BOUND(ID), 379 ms] (28) CpxRNTS (29) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (30) CpxRNTS (31) IntTrsBoundProof [UPPER BOUND(ID), 372 ms] (32) CpxRNTS (33) IntTrsBoundProof [UPPER BOUND(ID), 4 ms] (34) CpxRNTS (35) FinalProof [FINISHED, 0 ms] (36) BOUNDS(1, n^3) (37) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (38) CpxTRS (39) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (40) typed CpxTrs (41) OrderProof [LOWER BOUND(ID), 0 ms] (42) typed CpxTrs (43) RewriteLemmaProof [LOWER BOUND(ID), 278 ms] (44) BEST (45) proven lower bound (46) LowerBoundPropagationProof [FINISHED, 0 ms] (47) BOUNDS(n^1, INF) (48) typed CpxTrs ---------------------------------------- (0) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^3). The TRS R consists of the following rules: minus(x, x) -> 0 minus(s(x), s(y)) -> minus(x, y) minus(0, x) -> 0 minus(x, 0) -> x div(s(x), s(y)) -> s(div(minus(x, y), s(y))) div(0, s(y)) -> 0 f(x, 0, b) -> x f(x, s(y), b) -> div(f(x, minus(s(y), s(0)), b), b) S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) RcToIrcProof (BOTH BOUNDS(ID, ID)) Converted rc-obligation to irc-obligation. The duplicating contexts are: div(s(x), s([])) f(x, s(y), []) The defined contexts are: div([], x1) f(x0, [], x2) div([], s(x1)) minus([], x1) minus(s([]), s(0))
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