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Runti Compl Inner Rewri 22807 pair #381904277
details
property
value
status
complete
benchmark
gcdMinMax.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n038.star.cs.uiowa.edu
space
Mixed_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
292.29553318 seconds
cpu usage
1133.18786489
max memory
9.845743616E9
stage attributes
key
value
output-size
128454
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2).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) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (10) CpxRNTS (11) CompleteCoflocoProof [FINISHED, 13.7 s] (12) BOUNDS(1, n^2) (13) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (14) CpxTRS (15) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (16) typed CpxTrs (17) OrderProof [LOWER BOUND(ID), 0 ms] (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 302 ms] (20) BEST (21) proven lower bound (22) LowerBoundPropagationProof [FINISHED, 0 ms] (23) BOUNDS(n^1, INF) (24) typed CpxTrs (25) RewriteLemmaProof [LOWER BOUND(ID), 93 ms] (26) typed CpxTrs (27) RewriteLemmaProof [LOWER BOUND(ID), 65 ms] (28) 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: min(x, 0) -> 0 min(0, y) -> 0 min(s(x), s(y)) -> s(min(x, y)) max(x, 0) -> x max(0, y) -> y max(s(x), s(y)) -> s(max(x, y)) -(x, 0) -> x -(s(x), s(y)) -> -(x, y) gcd(s(x), s(y)) -> gcd(-(s(max(x, y)), s(min(x, y))), s(min(x, y))) gcd(s(x), 0) -> s(x) gcd(0, s(y)) -> s(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: min(x, 0) -> 0 [1] min(0, y) -> 0 [1] min(s(x), s(y)) -> s(min(x, y)) [1] max(x, 0) -> x [1] max(0, y) -> y [1] max(s(x), s(y)) -> s(max(x, y)) [1] -(x, 0) -> x [1] -(s(x), s(y)) -> -(x, y) [1] gcd(s(x), s(y)) -> gcd(-(s(max(x, y)), s(min(x, y))), s(min(x, y))) [1] gcd(s(x), 0) -> s(x) [1] gcd(0, s(y)) -> s(y) [1] Rewrite Strategy: INNERMOST ---------------------------------------- (3) CpxWeightedTrsRenamingProof (BOTH BOUNDS(ID, ID)) Renamed defined symbols to avoid conflicts with arithmetic symbols: - => minus
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