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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308405
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
n099.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
9.65671 seconds
cpu usage
62.8138
user time
59.1547
system time
3.65911
max virtual memory
1.9547432E7
max residence set size
4002992.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^3), O(n^3))
output
31.19/9.61 WORST_CASE(Omega(n^3), O(n^3)) 31.19/9.62 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 31.19/9.62 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 31.19/9.62 31.19/9.62 31.19/9.62 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^3, n^3). 31.19/9.62 31.19/9.62 (0) CpxTRS 31.19/9.62 (1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] 31.19/9.62 (2) CpxTRS 31.19/9.62 (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 31.19/9.62 (4) CpxWeightedTrs 31.19/9.62 (5) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 31.19/9.62 (6) CpxWeightedTrs 31.19/9.62 (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 31.19/9.62 (8) CpxTypedWeightedTrs 31.19/9.62 (9) CompletionProof [UPPER BOUND(ID), 0 ms] 31.19/9.62 (10) CpxTypedWeightedCompleteTrs 31.19/9.62 (11) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] 31.19/9.62 (12) CpxTypedWeightedCompleteTrs 31.19/9.62 (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 31.19/9.62 (14) CpxRNTS 31.19/9.62 (15) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] 31.19/9.62 (16) CpxRNTS 31.19/9.62 (17) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] 31.19/9.62 (18) CpxRNTS 31.19/9.62 (19) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 31.19/9.62 (20) CpxRNTS 31.19/9.62 (21) IntTrsBoundProof [UPPER BOUND(ID), 271 ms] 31.19/9.62 (22) CpxRNTS 31.19/9.62 (23) IntTrsBoundProof [UPPER BOUND(ID), 46 ms] 31.19/9.62 (24) CpxRNTS 31.19/9.62 (25) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 31.19/9.62 (26) CpxRNTS 31.19/9.62 (27) IntTrsBoundProof [UPPER BOUND(ID), 310 ms] 31.19/9.62 (28) CpxRNTS 31.19/9.62 (29) IntTrsBoundProof [UPPER BOUND(ID), 84 ms] 31.19/9.62 (30) CpxRNTS 31.19/9.62 (31) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 31.19/9.62 (32) CpxRNTS 31.19/9.62 (33) IntTrsBoundProof [UPPER BOUND(ID), 1723 ms] 31.19/9.62 (34) CpxRNTS 31.19/9.62 (35) IntTrsBoundProof [UPPER BOUND(ID), 254 ms] 31.19/9.62 (36) CpxRNTS 31.19/9.62 (37) FinalProof [FINISHED, 0 ms] 31.19/9.62 (38) BOUNDS(1, n^3) 31.19/9.62 (39) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 31.19/9.62 (40) CpxTRS 31.19/9.62 (41) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 31.19/9.62 (42) typed CpxTrs 31.19/9.62 (43) OrderProof [LOWER BOUND(ID), 0 ms] 31.19/9.62 (44) typed CpxTrs 31.19/9.62 (45) RewriteLemmaProof [LOWER BOUND(ID), 312 ms] 31.19/9.62 (46) BEST 31.19/9.62 (47) proven lower bound 31.19/9.62 (48) LowerBoundPropagationProof [FINISHED, 0 ms] 31.19/9.62 (49) BOUNDS(n^1, INF) 31.19/9.62 (50) typed CpxTrs 31.19/9.62 (51) RewriteLemmaProof [LOWER BOUND(ID), 1508 ms] 31.19/9.62 (52) typed CpxTrs 31.19/9.62 (53) RewriteLemmaProof [LOWER BOUND(ID), 54 ms] 31.19/9.62 (54) proven lower bound 31.19/9.62 (55) LowerBoundPropagationProof [FINISHED, 0 ms] 31.19/9.62 (56) BOUNDS(n^3, INF) 31.19/9.62 31.19/9.62 31.19/9.62 ---------------------------------------- 31.19/9.62 31.19/9.62 (0) 31.19/9.62 Obligation: 31.19/9.62 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^3, n^3). 31.19/9.62 31.19/9.62 31.19/9.62 The TRS R consists of the following rules: 31.19/9.62 31.19/9.62 +(0, y) -> y 31.19/9.62 +(s(x), y) -> s(+(x, y)) 31.19/9.62 +(p(x), y) -> p(+(x, y)) 31.19/9.62 minus(0) -> 0 31.19/9.62 minus(s(x)) -> p(minus(x)) 31.19/9.62 minus(p(x)) -> s(minus(x)) 31.19/9.62 *(0, y) -> 0 31.19/9.62 *(s(x), y) -> +(*(x, y), y) 31.19/9.62 *(p(x), y) -> +(*(x, y), minus(y)) 31.19/9.62 31.19/9.62 S is empty. 31.19/9.62 Rewrite Strategy: FULL 31.19/9.62 ---------------------------------------- 31.19/9.62 31.19/9.62 (1) RcToIrcProof (BOTH BOUNDS(ID, ID)) 31.19/9.62 Converted rc-obligation to irc-obligation. 31.19/9.62 31.19/9.62 The duplicating contexts are: 31.19/9.62 *(s(x), []) 31.19/9.62 *(p(x), []) 31.19/9.62 31.19/9.62 31.19/9.62 The defined contexts are: 31.19/9.62 +([], x1) 31.19/9.62 +(x0, [])
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