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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313320
details
property
value
status
complete
benchmark
tpa06.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n080.star.cs.uiowa.edu
space
Secret_06_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.988 seconds
cpu usage
1131.97
user time
1115.72
system time
16.2474
max virtual memory
3.8337792E7
max residence set size
1.4917208E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
1130.62/291.59 WORST_CASE(Omega(n^1), O(n^2)) 1130.95/291.68 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1130.95/291.68 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1130.95/291.68 1130.95/291.68 1130.95/291.68 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1130.95/291.68 1130.95/291.68 (0) CpxTRS 1130.95/291.68 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 1130.95/291.68 (2) CpxWeightedTrs 1130.95/291.68 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1130.95/291.68 (4) CpxTypedWeightedTrs 1130.95/291.68 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 1130.95/291.68 (6) CpxTypedWeightedCompleteTrs 1130.95/291.68 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 1130.95/291.68 (8) CpxRNTS 1130.95/291.68 (9) CompleteCoflocoProof [FINISHED, 30.9 s] 1130.95/291.68 (10) BOUNDS(1, n^2) 1130.95/291.68 (11) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1130.95/291.68 (12) CpxTRS 1130.95/291.68 (13) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1130.95/291.68 (14) typed CpxTrs 1130.95/291.68 (15) OrderProof [LOWER BOUND(ID), 0 ms] 1130.95/291.68 (16) typed CpxTrs 1130.95/291.68 (17) RewriteLemmaProof [LOWER BOUND(ID), 291 ms] 1130.95/291.68 (18) BEST 1130.95/291.68 (19) proven lower bound 1130.95/291.68 (20) LowerBoundPropagationProof [FINISHED, 0 ms] 1130.95/291.68 (21) BOUNDS(n^1, INF) 1130.95/291.68 (22) typed CpxTrs 1130.95/291.68 (23) RewriteLemmaProof [LOWER BOUND(ID), 61 ms] 1130.95/291.68 (24) typed CpxTrs 1130.95/291.68 1130.95/291.68 1130.95/291.68 ---------------------------------------- 1130.95/291.68 1130.95/291.68 (0) 1130.95/291.68 Obligation: 1130.95/291.68 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1130.95/291.68 1130.95/291.68 1130.95/291.68 The TRS R consists of the following rules: 1130.95/291.68 1130.95/291.68 min(0, y) -> 0 1130.95/291.68 min(x, 0) -> 0 1130.95/291.68 min(s(x), s(y)) -> s(min(x, y)) 1130.95/291.68 max(0, y) -> y 1130.95/291.68 max(x, 0) -> x 1130.95/291.68 max(s(x), s(y)) -> s(max(x, y)) 1130.95/291.68 p(s(x)) -> x 1130.95/291.68 f(s(x), s(y), s(z)) -> f(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z)))) 1130.95/291.68 f(0, y, z) -> max(y, z) 1130.95/291.68 f(x, 0, z) -> max(x, z) 1130.95/291.68 f(x, y, 0) -> max(x, y) 1130.95/291.68 1130.95/291.68 S is empty. 1130.95/291.68 Rewrite Strategy: INNERMOST 1130.95/291.68 ---------------------------------------- 1130.95/291.68 1130.95/291.68 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 1130.95/291.68 Transformed relative TRS to weighted TRS 1130.95/291.68 ---------------------------------------- 1130.95/291.68 1130.95/291.68 (2) 1130.95/291.68 Obligation: 1130.95/291.68 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). 1130.95/291.68 1130.95/291.68 1130.95/291.68 The TRS R consists of the following rules: 1130.95/291.68 1130.95/291.68 min(0, y) -> 0 [1] 1130.95/291.68 min(x, 0) -> 0 [1] 1130.95/291.68 min(s(x), s(y)) -> s(min(x, y)) [1] 1130.95/291.68 max(0, y) -> y [1] 1130.95/291.68 max(x, 0) -> x [1] 1130.95/291.68 max(s(x), s(y)) -> s(max(x, y)) [1] 1130.95/291.68 p(s(x)) -> x [1] 1130.95/291.68 f(s(x), s(y), s(z)) -> f(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z)))) [1] 1130.95/291.68 f(0, y, z) -> max(y, z) [1] 1130.95/291.68 f(x, 0, z) -> max(x, z) [1] 1130.95/291.68 f(x, y, 0) -> max(x, y) [1] 1130.95/291.68 1130.95/291.68 Rewrite Strategy: INNERMOST 1130.95/291.68 ---------------------------------------- 1130.95/291.68 1130.95/291.68 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 1130.95/291.68 Infered types. 1130.95/291.68 ---------------------------------------- 1130.95/291.68 1130.95/291.68 (4) 1130.95/291.68 Obligation: 1130.95/291.68 Runtime Complexity Weighted TRS with Types. 1130.95/291.68 The TRS R consists of the following rules: 1130.95/291.68 1130.95/291.68 min(0, y) -> 0 [1] 1130.95/291.68 min(x, 0) -> 0 [1] 1130.95/291.68 min(s(x), s(y)) -> s(min(x, y)) [1] 1130.95/291.68 max(0, y) -> y [1] 1130.95/291.68 max(x, 0) -> x [1] 1130.95/291.68 max(s(x), s(y)) -> s(max(x, y)) [1]
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