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Runti Compl Full Rewri 10127 pair #381903175
details
property
value
status
complete
benchmark
wiehe12.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n028.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.482450008 seconds
cpu usage
307.910503799
max memory
5.29577984E9
stage attributes
key
value
output-size
34832
starexec-result
WORST_CASE(Omega(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^2), ?) 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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). (0) CpxTRS (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (4) typed CpxTrs (5) OrderProof [LOWER BOUND(ID), 0 ms] (6) typed CpxTrs (7) RewriteLemmaProof [LOWER BOUND(ID), 242 ms] (8) BEST (9) proven lower bound (10) LowerBoundPropagationProof [FINISHED, 0 ms] (11) BOUNDS(n^1, INF) (12) typed CpxTrs (13) RewriteLemmaProof [LOWER BOUND(ID), 100 ms] (14) typed CpxTrs (15) RewriteLemmaProof [LOWER BOUND(ID), 78 ms] (16) typed CpxTrs (17) RewriteLemmaProof [LOWER BOUND(ID), 67 ms] (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 587 ms] (20) BEST (21) proven lower bound (22) LowerBoundPropagationProof [FINISHED, 0 ms] (23) BOUNDS(n^2, INF) (24) typed CpxTrs (25) RewriteLemmaProof [LOWER BOUND(ID), 0 ms] (26) typed CpxTrs ---------------------------------------- (0) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). The TRS R consists of the following rules: g(s(x), s(y)) -> if(and(f(s(x)), f(s(y))), t(g(k(minus(m(x, y), n(x, y)), s(s(0))), k(n(s(x), s(y)), s(s(0))))), g(minus(m(x, y), n(x, y)), n(s(x), s(y)))) n(0, y) -> 0 n(x, 0) -> 0 n(s(x), s(y)) -> s(n(x, y)) m(0, y) -> y m(x, 0) -> x m(s(x), s(y)) -> s(m(x, y)) k(0, s(y)) -> 0 k(s(x), s(y)) -> s(k(minus(x, y), s(y))) t(x) -> p(x, x) p(s(x), s(y)) -> s(s(p(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y))))) p(s(x), x) -> p(if(gt(x, x), id(x), id(x)), s(x)) p(0, y) -> y p(id(x), s(y)) -> s(p(x, if(gt(s(y), y), y, s(y)))) minus(x, 0) -> x minus(s(x), s(y)) -> minus(x, y) id(x) -> x if(true, x, y) -> x if(false, x, y) -> y not(x) -> if(x, false, true) and(x, false) -> false and(true, true) -> true f(0) -> true f(s(x)) -> h(x) h(0) -> false h(s(x)) -> f(x) gt(s(x), 0) -> true gt(0, y) -> false gt(s(x), s(y)) -> gt(x, y) S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (2) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). The TRS R consists of the following rules: g(s(x), s(y)) -> if(and(f(s(x)), f(s(y))), t(g(k(minus(m(x, y), n(x, y)), s(s(0'))), k(n(s(x), s(y)), s(s(0'))))), g(minus(m(x, y), n(x, y)), n(s(x), s(y)))) n(0', y) -> 0' n(x, 0') -> 0' n(s(x), s(y)) -> s(n(x, y))
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