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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313578
details
property
value
status
complete
benchmark
2.12.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n066.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
10.7228 seconds
cpu usage
28.8606
user time
26.6368
system time
2.22386
max virtual memory
1.9084456E7
max residence set size
4231584.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^3), O(n^3))
output
28.39/9.59 WORST_CASE(Omega(n^3), O(n^3)) 28.71/10.27 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 28.71/10.27 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 28.71/10.27 28.71/10.27 28.71/10.27 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^3, n^3). 28.71/10.27 28.71/10.27 (0) CpxTRS 28.71/10.27 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 28.71/10.27 (2) CpxWeightedTrs 28.71/10.27 (3) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 28.71/10.27 (4) CpxWeightedTrs 28.71/10.27 (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 28.71/10.27 (6) CpxTypedWeightedTrs 28.71/10.27 (7) CompletionProof [UPPER BOUND(ID), 0 ms] 28.71/10.27 (8) CpxTypedWeightedCompleteTrs 28.71/10.27 (9) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] 28.71/10.27 (10) CpxTypedWeightedCompleteTrs 28.71/10.27 (11) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 28.71/10.27 (12) CpxRNTS 28.71/10.27 (13) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] 28.71/10.27 (14) CpxRNTS 28.71/10.27 (15) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] 28.71/10.27 (16) CpxRNTS 28.71/10.27 (17) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 28.71/10.27 (18) CpxRNTS 28.71/10.27 (19) IntTrsBoundProof [UPPER BOUND(ID), 146 ms] 28.71/10.27 (20) CpxRNTS 28.71/10.27 (21) IntTrsBoundProof [UPPER BOUND(ID), 117 ms] 28.71/10.27 (22) CpxRNTS 28.71/10.27 (23) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 28.71/10.27 (24) CpxRNTS 28.71/10.27 (25) IntTrsBoundProof [UPPER BOUND(ID), 340 ms] 28.71/10.27 (26) CpxRNTS 28.71/10.27 (27) IntTrsBoundProof [UPPER BOUND(ID), 84 ms] 28.71/10.27 (28) CpxRNTS 28.71/10.27 (29) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 28.71/10.27 (30) CpxRNTS 28.71/10.27 (31) IntTrsBoundProof [UPPER BOUND(ID), 1675 ms] 28.71/10.27 (32) CpxRNTS 28.71/10.27 (33) IntTrsBoundProof [UPPER BOUND(ID), 169 ms] 28.71/10.27 (34) CpxRNTS 28.71/10.27 (35) FinalProof [FINISHED, 0 ms] 28.71/10.27 (36) BOUNDS(1, n^3) 28.71/10.27 (37) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 28.71/10.27 (38) CpxTRS 28.71/10.27 (39) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 28.71/10.27 (40) typed CpxTrs 28.71/10.27 (41) OrderProof [LOWER BOUND(ID), 0 ms] 28.71/10.27 (42) typed CpxTrs 28.71/10.27 (43) RewriteLemmaProof [LOWER BOUND(ID), 317 ms] 28.71/10.27 (44) BEST 28.71/10.27 (45) proven lower bound 28.71/10.27 (46) LowerBoundPropagationProof [FINISHED, 0 ms] 28.71/10.27 (47) BOUNDS(n^1, INF) 28.71/10.27 (48) typed CpxTrs 28.71/10.27 (49) RewriteLemmaProof [LOWER BOUND(ID), 1769 ms] 28.71/10.27 (50) typed CpxTrs 28.71/10.27 (51) RewriteLemmaProof [LOWER BOUND(ID), 47 ms] 28.71/10.27 (52) proven lower bound 28.71/10.27 (53) LowerBoundPropagationProof [FINISHED, 0 ms] 28.71/10.27 (54) BOUNDS(n^3, INF) 28.71/10.27 28.71/10.27 28.71/10.27 ---------------------------------------- 28.71/10.27 28.71/10.27 (0) 28.71/10.27 Obligation: 28.71/10.27 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^3, n^3). 28.71/10.27 28.71/10.27 28.71/10.27 The TRS R consists of the following rules: 28.71/10.27 28.71/10.27 +(0, y) -> y 28.71/10.27 +(s(x), y) -> s(+(x, y)) 28.71/10.27 +(p(x), y) -> p(+(x, y)) 28.71/10.27 minus(0) -> 0 28.71/10.27 minus(s(x)) -> p(minus(x)) 28.71/10.27 minus(p(x)) -> s(minus(x)) 28.71/10.27 *(0, y) -> 0 28.71/10.27 *(s(x), y) -> +(*(x, y), y) 28.71/10.27 *(p(x), y) -> +(*(x, y), minus(y)) 28.71/10.27 28.71/10.27 S is empty. 28.71/10.27 Rewrite Strategy: INNERMOST 28.71/10.27 ---------------------------------------- 28.71/10.27 28.71/10.27 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 28.71/10.27 Transformed relative TRS to weighted TRS 28.71/10.27 ---------------------------------------- 28.71/10.27 28.71/10.27 (2) 28.71/10.27 Obligation: 28.71/10.27 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^3). 28.71/10.27 28.71/10.27 28.71/10.27 The TRS R consists of the following rules: 28.71/10.27 28.71/10.27 +(0, y) -> y [1] 28.71/10.27 +(s(x), y) -> s(+(x, y)) [1]
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