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Runti Compl Inner Rewri 22807 pair #381904317
details
property
value
status
complete
benchmark
div_notCeTermin.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n074.star.cs.uiowa.edu
space
AProVE_06
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
292.022639036 seconds
cpu usage
1151.77470611
max memory
6.082052096E9
stage attributes
key
value
output-size
46795
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2).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) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CpxTypedWeightedTrs (5) CompletionProof [UPPER BOUND(ID), 0 ms] (6) CpxTypedWeightedCompleteTrs (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (8) CpxRNTS (9) CompleteCoflocoProof [FINISHED, 1840 ms] (10) BOUNDS(1, n^2) (11) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CpxTRS (13) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (14) typed CpxTrs (15) OrderProof [LOWER BOUND(ID), 0 ms] (16) typed CpxTrs (17) RewriteLemmaProof [LOWER BOUND(ID), 463 ms] (18) BEST (19) proven lower bound (20) LowerBoundPropagationProof [FINISHED, 0 ms] (21) BOUNDS(n^1, INF) (22) typed CpxTrs (23) RewriteLemmaProof [LOWER BOUND(ID), 209 ms] (24) typed CpxTrs (25) RewriteLemmaProof [LOWER BOUND(ID), 131 ms] (26) 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: ge(0, 0) -> true ge(s(x), 0) -> ge(x, 0) ge(0, s(0)) -> false ge(0, s(s(x))) -> ge(0, s(x)) ge(s(x), s(y)) -> ge(x, y) minus(0, 0) -> 0 minus(0, s(x)) -> minus(0, x) minus(s(x), 0) -> s(minus(x, 0)) minus(s(x), s(y)) -> minus(x, y) plus(0, 0) -> 0 plus(0, s(x)) -> s(plus(0, x)) plus(s(x), y) -> s(plus(x, y)) div(x, y) -> ify(ge(y, s(0)), x, y) ify(false, x, y) -> divByZeroError ify(true, x, y) -> if(ge(x, y), x, y) if(false, x, y) -> 0 if(true, x, y) -> s(div(minus(x, y), 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: ge(0, 0) -> true [1] ge(s(x), 0) -> ge(x, 0) [1] ge(0, s(0)) -> false [1] ge(0, s(s(x))) -> ge(0, s(x)) [1] ge(s(x), s(y)) -> ge(x, y) [1] minus(0, 0) -> 0 [1] minus(0, s(x)) -> minus(0, x) [1] minus(s(x), 0) -> s(minus(x, 0)) [1] minus(s(x), s(y)) -> minus(x, y) [1] plus(0, 0) -> 0 [1] plus(0, s(x)) -> s(plus(0, x)) [1] plus(s(x), y) -> s(plus(x, y)) [1] div(x, y) -> ify(ge(y, s(0)), x, y) [1] ify(false, x, y) -> divByZeroError [1] ify(true, x, y) -> if(ge(x, y), x, y) [1] if(false, x, y) -> 0 [1]
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