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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307873
details
property
value
status
complete
benchmark
divExp.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n166.star.cs.uiowa.edu
space
Secret_06_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.709 seconds
cpu usage
991.928
user time
979.337
system time
12.5913
max virtual memory
3.724416E7
max residence set size
1.1791584E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^3))
output
991.51/291.57 WORST_CASE(Omega(n^1), O(n^3)) 991.57/291.60 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 991.57/291.60 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 991.57/291.60 991.57/291.60 991.57/291.60 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^3). 991.57/291.60 991.57/291.60 (0) CpxTRS 991.57/291.60 (1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] 991.57/291.60 (2) CpxTRS 991.57/291.60 (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 991.57/291.60 (4) CpxWeightedTrs 991.57/291.60 (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 991.57/291.60 (6) CpxTypedWeightedTrs 991.57/291.60 (7) CompletionProof [UPPER BOUND(ID), 0 ms] 991.57/291.60 (8) CpxTypedWeightedCompleteTrs 991.57/291.60 (9) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] 991.57/291.60 (10) CpxTypedWeightedCompleteTrs 991.57/291.60 (11) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 6 ms] 991.57/291.60 (12) CpxRNTS 991.57/291.60 (13) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] 991.57/291.60 (14) CpxRNTS 991.57/291.60 (15) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] 991.57/291.60 (16) CpxRNTS 991.57/291.60 (17) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 991.57/291.60 (18) CpxRNTS 991.57/291.60 (19) IntTrsBoundProof [UPPER BOUND(ID), 507 ms] 991.57/291.60 (20) CpxRNTS 991.57/291.60 (21) IntTrsBoundProof [UPPER BOUND(ID), 179 ms] 991.57/291.60 (22) CpxRNTS 991.57/291.60 (23) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 991.57/291.60 (24) CpxRNTS 991.57/291.60 (25) IntTrsBoundProof [UPPER BOUND(ID), 841 ms] 991.57/291.60 (26) CpxRNTS 991.57/291.60 (27) IntTrsBoundProof [UPPER BOUND(ID), 342 ms] 991.57/291.60 (28) CpxRNTS 991.57/291.60 (29) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 991.57/291.60 (30) CpxRNTS 991.57/291.60 (31) IntTrsBoundProof [UPPER BOUND(ID), 352 ms] 991.57/291.60 (32) CpxRNTS 991.57/291.60 (33) IntTrsBoundProof [UPPER BOUND(ID), 5 ms] 991.57/291.60 (34) CpxRNTS 991.57/291.60 (35) FinalProof [FINISHED, 0 ms] 991.57/291.60 (36) BOUNDS(1, n^3) 991.57/291.60 (37) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 991.57/291.60 (38) CpxTRS 991.57/291.60 (39) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 991.57/291.60 (40) typed CpxTrs 991.57/291.60 (41) OrderProof [LOWER BOUND(ID), 0 ms] 991.57/291.60 (42) typed CpxTrs 991.57/291.60 (43) RewriteLemmaProof [LOWER BOUND(ID), 240 ms] 991.57/291.60 (44) BEST 991.57/291.60 (45) proven lower bound 991.57/291.60 (46) LowerBoundPropagationProof [FINISHED, 0 ms] 991.57/291.60 (47) BOUNDS(n^1, INF) 991.57/291.60 (48) typed CpxTrs 991.57/291.60 991.57/291.60 991.57/291.60 ---------------------------------------- 991.57/291.60 991.57/291.60 (0) 991.57/291.60 Obligation: 991.57/291.60 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^3). 991.57/291.60 991.57/291.60 991.57/291.60 The TRS R consists of the following rules: 991.57/291.60 991.57/291.60 minus(x, x) -> 0 991.57/291.60 minus(s(x), s(y)) -> minus(x, y) 991.57/291.60 minus(0, x) -> 0 991.57/291.60 minus(x, 0) -> x 991.57/291.60 div(s(x), s(y)) -> s(div(minus(x, y), s(y))) 991.57/291.60 div(0, s(y)) -> 0 991.57/291.60 f(x, 0, b) -> x 991.57/291.60 f(x, s(y), b) -> div(f(x, minus(s(y), s(0)), b), b) 991.57/291.60 991.57/291.60 S is empty. 991.57/291.60 Rewrite Strategy: FULL 991.57/291.60 ---------------------------------------- 991.57/291.60 991.57/291.60 (1) RcToIrcProof (BOTH BOUNDS(ID, ID)) 991.57/291.60 Converted rc-obligation to irc-obligation. 991.57/291.60 991.57/291.60 The duplicating contexts are: 991.57/291.60 div(s(x), s([])) 991.57/291.60 f(x, s(y), []) 991.57/291.60 991.57/291.60 991.57/291.60 The defined contexts are: 991.57/291.60 div([], x1) 991.57/291.60 f(x0, [], x2) 991.57/291.60 div([], s(x1)) 991.57/291.60 minus([], x1) 991.57/291.60 minus(s([]), s(0)) 991.57/291.60 991.57/291.60 991.57/291.60 [] just represents basic- or constructor-terms in the following defined contexts: 991.57/291.60 f(x0, [], x2) 991.57/291.60 div([], s(x1)) 991.57/291.60
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