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Runti Compl Inner Rewri 22807 pair #381904289
details
property
value
status
complete
benchmark
2.22.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n030.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.907877922 seconds
cpu usage
314.029013962
max memory
5.203320832E9
stage attributes
key
value
output-size
22706
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2).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) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (14) CpxRNTS (15) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 5 ms] (16) CpxRNTS (17) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (18) CpxRNTS (19) IntTrsBoundProof [UPPER BOUND(ID), 312 ms] (20) CpxRNTS (21) IntTrsBoundProof [UPPER BOUND(ID), 117 ms] (22) CpxRNTS (23) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (24) CpxRNTS (25) IntTrsBoundProof [UPPER BOUND(ID), 383 ms] (26) CpxRNTS (27) IntTrsBoundProof [UPPER BOUND(ID), 165 ms] (28) CpxRNTS (29) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (30) CpxRNTS (31) IntTrsBoundProof [UPPER BOUND(ID), 1463 ms] (32) CpxRNTS (33) IntTrsBoundProof [UPPER BOUND(ID), 175 ms] (34) CpxRNTS (35) FinalProof [FINISHED, 0 ms] (36) BOUNDS(1, n^2) (37) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (38) TRS for Loop Detection (39) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (40) BEST (41) proven lower bound (42) LowerBoundPropagationProof [FINISHED, 0 ms] (43) BOUNDS(n^1, INF) (44) TRS for Loop Detection ---------------------------------------- (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: exp(x, 0) -> s(0) exp(x, s(y)) -> *(x, exp(x, y)) *(0, y) -> 0 *(s(x), y) -> +(y, *(x, y)) -(0, y) -> 0 -(x, 0) -> x -(s(x), s(y)) -> -(x, y) 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: exp(x, 0) -> s(0) [1] exp(x, s(y)) -> *(x, exp(x, y)) [1] *(0, y) -> 0 [1] *(s(x), y) -> +(y, *(x, y)) [1] -(0, y) -> 0 [1] -(x, 0) -> x [1] -(s(x), s(y)) -> -(x, y) [1]
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