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Runti Compl Full Rewri 10127 pair #381902363
details
property
value
status
complete
benchmark
IJCAR_12.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n050.star.cs.uiowa.edu
space
AProVE_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
9.75037312508 seconds
cpu usage
28.927506634
max memory
4.091568128E9
stage attributes
key
value
output-size
26367
starexec-result
WORST_CASE(Omega(n^2), O(n^2))
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^2), O(n^2)) 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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, n^2). (0) CpxTRS (1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms] (2) CpxTRS (3) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CpxTRS (5) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxWeightedTrs (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxTypedWeightedTrs (9) CompletionProof [UPPER BOUND(ID), 0 ms] (10) CpxTypedWeightedCompleteTrs (11) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (12) CpxRNTS (13) CompleteCoflocoProof [FINISHED, 418 ms] (14) BOUNDS(1, n^2) (15) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (16) CpxTRS (17) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (18) typed CpxTrs (19) OrderProof [LOWER BOUND(ID), 0 ms] (20) typed CpxTrs (21) RewriteLemmaProof [LOWER BOUND(ID), 265 ms] (22) BEST (23) proven lower bound (24) LowerBoundPropagationProof [FINISHED, 0 ms] (25) BOUNDS(n^1, INF) (26) typed CpxTrs (27) RewriteLemmaProof [LOWER BOUND(ID), 54 ms] (28) BEST (29) proven lower bound (30) LowerBoundPropagationProof [FINISHED, 0 ms] (31) BOUNDS(n^2, INF) (32) typed CpxTrs (33) RewriteLemmaProof [LOWER BOUND(ID), 61 ms] (34) typed CpxTrs ---------------------------------------- (0) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, n^2). The TRS R consists of the following rules: plus(x, 0) -> x plus(0, y) -> y plus(s(x), y) -> s(plus(x, 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(0, 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(y, z)) S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) NestedDefinedSymbolProof (UPPER BOUND(ID)) The following defined symbols can occur below the 1th argument of plus: plus, times Hence, the left-hand sides of the following rules are not basic-reachable and can be removed: div(div(x, y), z) -> div(x, times(y, z)) ---------------------------------------- (2) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^2). The TRS R consists of the following rules: plus(x, 0) -> x plus(0, y) -> y plus(s(x), y) -> s(plus(x, 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(0, s(y), z) -> 0
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