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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308077
details
property
value
status
complete
benchmark
Ex2_Luc02a_L.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n088.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.588 seconds
cpu usage
1035.17
user time
1022.53
system time
12.6398
max virtual memory
3.76408E7
max residence set size
1.36067E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^3), O(n^3))
output
1034.51/291.45 WORST_CASE(Omega(n^3), O(n^3)) 1034.83/291.48 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1034.83/291.48 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1034.83/291.48 1034.83/291.48 1034.83/291.48 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^3, n^3). 1034.83/291.48 1034.83/291.48 (0) CpxTRS 1034.83/291.48 (1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] 1034.83/291.48 (2) CpxTRS 1034.83/291.48 (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 1034.83/291.48 (4) CpxWeightedTrs 1034.83/291.48 (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1034.83/291.48 (6) CpxTypedWeightedTrs 1034.83/291.48 (7) CompletionProof [UPPER BOUND(ID), 0 ms] 1034.83/291.48 (8) CpxTypedWeightedCompleteTrs 1034.83/291.48 (9) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] 1034.83/291.48 (10) CpxTypedWeightedCompleteTrs 1034.83/291.48 (11) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 1034.83/291.48 (12) CpxRNTS 1034.83/291.48 (13) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] 1034.83/291.48 (14) CpxRNTS 1034.83/291.48 (15) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] 1034.83/291.48 (16) CpxRNTS 1034.83/291.48 (17) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 1034.83/291.48 (18) CpxRNTS 1034.83/291.48 (19) IntTrsBoundProof [UPPER BOUND(ID), 182 ms] 1034.83/291.48 (20) CpxRNTS 1034.83/291.48 (21) IntTrsBoundProof [UPPER BOUND(ID), 67 ms] 1034.83/291.48 (22) CpxRNTS 1034.83/291.48 (23) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 1034.83/291.48 (24) CpxRNTS 1034.83/291.48 (25) IntTrsBoundProof [UPPER BOUND(ID), 215 ms] 1034.83/291.48 (26) CpxRNTS 1034.83/291.48 (27) IntTrsBoundProof [UPPER BOUND(ID), 105 ms] 1034.83/291.48 (28) CpxRNTS 1034.83/291.48 (29) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 1034.83/291.48 (30) CpxRNTS 1034.83/291.48 (31) IntTrsBoundProof [UPPER BOUND(ID), 342 ms] 1034.83/291.48 (32) CpxRNTS 1034.83/291.48 (33) IntTrsBoundProof [UPPER BOUND(ID), 125 ms] 1034.83/291.48 (34) CpxRNTS 1034.83/291.48 (35) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 1034.83/291.48 (36) CpxRNTS 1034.83/291.48 (37) IntTrsBoundProof [UPPER BOUND(ID), 564 ms] 1034.83/291.48 (38) CpxRNTS 1034.83/291.48 (39) IntTrsBoundProof [UPPER BOUND(ID), 84 ms] 1034.83/291.48 (40) CpxRNTS 1034.83/291.48 (41) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 1034.83/291.48 (42) CpxRNTS 1034.83/291.48 (43) IntTrsBoundProof [UPPER BOUND(ID), 587 ms] 1034.83/291.48 (44) CpxRNTS 1034.83/291.48 (45) IntTrsBoundProof [UPPER BOUND(ID), 0 ms] 1034.83/291.48 (46) CpxRNTS 1034.83/291.48 (47) FinalProof [FINISHED, 0 ms] 1034.83/291.48 (48) BOUNDS(1, n^3) 1034.83/291.48 (49) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1034.83/291.48 (50) CpxTRS 1034.83/291.48 (51) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1034.83/291.48 (52) typed CpxTrs 1034.83/291.48 (53) OrderProof [LOWER BOUND(ID), 0 ms] 1034.83/291.48 (54) typed CpxTrs 1034.83/291.48 (55) RewriteLemmaProof [LOWER BOUND(ID), 256 ms] 1034.83/291.48 (56) BEST 1034.83/291.48 (57) proven lower bound 1034.83/291.48 (58) LowerBoundPropagationProof [FINISHED, 0 ms] 1034.83/291.48 (59) BOUNDS(n^1, INF) 1034.83/291.48 (60) typed CpxTrs 1034.83/291.48 (61) RewriteLemmaProof [LOWER BOUND(ID), 123 ms] 1034.83/291.48 (62) typed CpxTrs 1034.83/291.48 (63) RewriteLemmaProof [LOWER BOUND(ID), 153 ms] 1034.83/291.48 (64) proven lower bound 1034.83/291.48 (65) LowerBoundPropagationProof [FINISHED, 0 ms] 1034.83/291.48 (66) BOUNDS(n^3, INF) 1034.83/291.48 1034.83/291.48 1034.83/291.48 ---------------------------------------- 1034.83/291.48 1034.83/291.48 (0) 1034.83/291.48 Obligation: 1034.83/291.48 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^3, n^3). 1034.83/291.48 1034.83/291.48 1034.83/291.48 The TRS R consists of the following rules: 1034.83/291.48 1034.83/291.48 terms(N) -> cons(recip(sqr(N))) 1034.83/291.48 sqr(0) -> 0 1034.83/291.48 sqr(s(X)) -> s(add(sqr(X), dbl(X))) 1034.83/291.48 dbl(0) -> 0 1034.83/291.48 dbl(s(X)) -> s(s(dbl(X))) 1034.83/291.48 add(0, X) -> X 1034.83/291.48 add(s(X), Y) -> s(add(X, Y)) 1034.83/291.48 first(0, X) -> nil 1034.83/291.48 first(s(X), cons(Y)) -> cons(Y) 1034.83/291.48 1034.83/291.48 S is empty. 1034.83/291.48 Rewrite Strategy: FULL 1034.83/291.48 ---------------------------------------- 1034.83/291.48 1034.83/291.48 (1) RcToIrcProof (BOTH BOUNDS(ID, ID))
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