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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308313
details
property
value
status
complete
benchmark
ExSec11_1_Luc02a_Z.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n007.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.698 seconds
cpu usage
1100.52
user time
1085.02
system time
15.4957
max virtual memory
3.8034472E7
max residence set size
1.4878436E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^3), O(n^3))
output
1099.96/291.54 WORST_CASE(Omega(n^3), O(n^3)) 1099.96/291.57 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1099.96/291.57 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1099.96/291.57 1099.96/291.57 1099.96/291.57 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^3, n^3). 1099.96/291.57 1099.96/291.57 (0) CpxTRS 1099.96/291.57 (1) NestedDefinedSymbolProof [UPPER BOUND(ID), 6 ms] 1099.96/291.57 (2) CpxTRS 1099.96/291.57 (3) RcToIrcProof [BOTH BOUNDS(ID, ID), 9 ms] 1099.96/291.57 (4) CpxTRS 1099.96/291.57 (5) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 1099.96/291.57 (6) CpxWeightedTrs 1099.96/291.57 (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1099.96/291.57 (8) CpxTypedWeightedTrs 1099.96/291.57 (9) CompletionProof [UPPER BOUND(ID), 0 ms] 1099.96/291.57 (10) CpxTypedWeightedCompleteTrs 1099.96/291.57 (11) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] 1099.96/291.57 (12) CpxTypedWeightedCompleteTrs 1099.96/291.57 (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 1099.96/291.57 (14) CpxRNTS 1099.96/291.57 (15) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] 1099.96/291.57 (16) CpxRNTS 1099.96/291.57 (17) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 4 ms] 1099.96/291.57 (18) CpxRNTS 1099.96/291.57 (19) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 1099.96/291.57 (20) CpxRNTS 1099.96/291.57 (21) IntTrsBoundProof [UPPER BOUND(ID), 202 ms] 1099.96/291.57 (22) CpxRNTS 1099.96/291.57 (23) IntTrsBoundProof [UPPER BOUND(ID), 87 ms] 1099.96/291.57 (24) CpxRNTS 1099.96/291.57 (25) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 1099.96/291.57 (26) CpxRNTS 1099.96/291.57 (27) IntTrsBoundProof [UPPER BOUND(ID), 269 ms] 1099.96/291.57 (28) CpxRNTS 1099.96/291.57 (29) IntTrsBoundProof [UPPER BOUND(ID), 85 ms] 1099.96/291.57 (30) CpxRNTS 1099.96/291.57 (31) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 1099.96/291.57 (32) CpxRNTS 1099.96/291.57 (33) IntTrsBoundProof [UPPER BOUND(ID), 252 ms] 1099.96/291.57 (34) CpxRNTS 1099.96/291.57 (35) IntTrsBoundProof [UPPER BOUND(ID), 83 ms] 1099.96/291.57 (36) CpxRNTS 1099.96/291.57 (37) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 1099.96/291.57 (38) CpxRNTS 1099.96/291.57 (39) IntTrsBoundProof [UPPER BOUND(ID), 514 ms] 1099.96/291.57 (40) CpxRNTS 1099.96/291.57 (41) IntTrsBoundProof [UPPER BOUND(ID), 34 ms] 1099.96/291.57 (42) CpxRNTS 1099.96/291.57 (43) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 1099.96/291.57 (44) CpxRNTS 1099.96/291.57 (45) IntTrsBoundProof [UPPER BOUND(ID), 679 ms] 1099.96/291.57 (46) CpxRNTS 1099.96/291.57 (47) IntTrsBoundProof [UPPER BOUND(ID), 2 ms] 1099.96/291.57 (48) CpxRNTS 1099.96/291.57 (49) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 1099.96/291.57 (50) CpxRNTS 1099.96/291.57 (51) IntTrsBoundProof [UPPER BOUND(ID), 2788 ms] 1099.96/291.57 (52) CpxRNTS 1099.96/291.57 (53) IntTrsBoundProof [UPPER BOUND(ID), 10 ms] 1099.96/291.57 (54) CpxRNTS 1099.96/291.57 (55) FinalProof [FINISHED, 0 ms] 1099.96/291.57 (56) BOUNDS(1, n^3) 1099.96/291.57 (57) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1099.96/291.57 (58) CpxTRS 1099.96/291.57 (59) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1099.96/291.57 (60) typed CpxTrs 1099.96/291.57 (61) OrderProof [LOWER BOUND(ID), 0 ms] 1099.96/291.57 (62) typed CpxTrs 1099.96/291.57 (63) RewriteLemmaProof [LOWER BOUND(ID), 307 ms] 1099.96/291.57 (64) BEST 1099.96/291.57 (65) proven lower bound 1099.96/291.57 (66) LowerBoundPropagationProof [FINISHED, 0 ms] 1099.96/291.57 (67) BOUNDS(n^1, INF) 1099.96/291.57 (68) typed CpxTrs 1099.96/291.57 (69) RewriteLemmaProof [LOWER BOUND(ID), 78 ms] 1099.96/291.57 (70) typed CpxTrs 1099.96/291.57 (71) RewriteLemmaProof [LOWER BOUND(ID), 66 ms] 1099.96/291.57 (72) BEST 1099.96/291.57 (73) proven lower bound 1099.96/291.57 (74) LowerBoundPropagationProof [FINISHED, 0 ms] 1099.96/291.57 (75) BOUNDS(n^3, INF) 1099.96/291.57 (76) typed CpxTrs 1099.96/291.57 (77) RewriteLemmaProof [LOWER BOUND(ID), 30 ms] 1099.96/291.57 (78) BOUNDS(1, INF) 1099.96/291.57 1099.96/291.57 1099.96/291.57 ---------------------------------------- 1099.96/291.57 1099.96/291.57 (0) 1099.96/291.57 Obligation: 1099.96/291.57 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^3, n^3). 1099.96/291.57 1099.96/291.57 1099.96/291.57 The TRS R consists of the following rules: 1099.96/291.57 1099.96/291.57 terms(N) -> cons(recip(sqr(N)), n__terms(s(N))) 1099.96/291.57 sqr(0) -> 0 1099.96/291.57 sqr(s(X)) -> s(add(sqr(X), dbl(X)))
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