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Runti Compl Full Rewri 10127 pair #381902911
details
property
value
status
complete
benchmark
kabasci02.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n053.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.475713968 seconds
cpu usage
344.117083606
max memory
6.183370752E9
stage attributes
key
value
output-size
27596
starexec-result
WORST_CASE(Omega(n^3), ?)
output
/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^3), ?) proof of /export/starexec/sandbox2/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^3, INF).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), 209 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), 104 ms] (14) BEST (15) proven lower bound (16) LowerBoundPropagationProof [FINISHED, 0 ms] (17) BOUNDS(n^3, INF) (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 56 ms] (20) typed CpxTrs (21) RewriteLemmaProof [LOWER BOUND(ID), 40 ms] (22) typed CpxTrs ---------------------------------------- (0) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^3, INF). The TRS R consists of the following rules: p(0) -> 0 p(s(x)) -> x plus(x, 0) -> x plus(0, y) -> y plus(s(x), y) -> s(plus(x, y)) plus(s(x), y) -> s(plus(p(s(x)), y)) plus(x, s(y)) -> s(plus(x, p(s(y)))) times(0, y) -> 0 times(s(0), y) -> y times(s(x), y) -> plus(y, times(x, y)) div(0, y) -> 0 div(x, y) -> quot(x, y, y) quot(zero(y), s(y), z) -> 0 quot(s(x), s(y), z) -> quot(x, y, z) quot(x, 0, s(z)) -> s(div(x, s(z))) div(div(x, y), z) -> div(x, times(zero(y), z)) eq(0, 0) -> true eq(s(x), 0) -> false eq(0, s(y)) -> false eq(s(x), s(y)) -> eq(x, y) divides(y, x) -> eq(x, times(div(x, y), y)) prime(s(s(x))) -> pr(s(s(x)), s(x)) pr(x, s(0)) -> true pr(x, s(s(y))) -> if(divides(s(s(y)), x), x, s(y)) if(true, x, y) -> false if(false, x, y) -> pr(x, y) zero(div(x, x)) -> x zero(divides(x, x)) -> x zero(times(x, x)) -> x zero(quot(x, x, x)) -> x zero(s(x)) -> if(eq(x, s(0)), plus(zero(0), 0), s(plus(0, zero(0)))) 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^3, INF). The TRS R consists of the following rules: p(0') -> 0' p(s(x)) -> x plus(x, 0') -> x plus(0', y) -> y plus(s(x), y) -> s(plus(x, y)) plus(s(x), y) -> s(plus(p(s(x)), y))
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