Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313766
details
property
value
status
complete
benchmark
#3.16.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n180.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.549 seconds
cpu usage
316.272
user time
314.087
system time
2.18479
max virtual memory
1.9077852E7
max residence set size
5374424.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), O(n^3))
output
316.14/291.49 WORST_CASE(Omega(n^2), O(n^3)) 316.14/291.50 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 316.14/291.50 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 316.14/291.50 316.14/291.50 316.14/291.50 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, n^3). 316.14/291.50 316.14/291.50 (0) CpxTRS 316.14/291.50 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 316.14/291.50 (2) CpxWeightedTrs 316.14/291.50 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 316.14/291.50 (4) CpxTypedWeightedTrs 316.14/291.50 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 316.14/291.50 (6) CpxTypedWeightedCompleteTrs 316.14/291.50 (7) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] 316.14/291.50 (8) CpxTypedWeightedCompleteTrs 316.14/291.50 (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 5 ms] 316.14/291.50 (10) CpxRNTS 316.14/291.50 (11) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] 316.14/291.50 (12) CpxRNTS 316.14/291.50 (13) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] 316.14/291.50 (14) CpxRNTS 316.14/291.50 (15) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 316.14/291.50 (16) CpxRNTS 316.14/291.50 (17) IntTrsBoundProof [UPPER BOUND(ID), 626 ms] 316.14/291.50 (18) CpxRNTS 316.14/291.50 (19) IntTrsBoundProof [UPPER BOUND(ID), 170 ms] 316.14/291.50 (20) CpxRNTS 316.14/291.50 (21) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 316.14/291.50 (22) CpxRNTS 316.14/291.50 (23) IntTrsBoundProof [UPPER BOUND(ID), 557 ms] 316.14/291.50 (24) CpxRNTS 316.14/291.50 (25) IntTrsBoundProof [UPPER BOUND(ID), 55 ms] 316.14/291.50 (26) CpxRNTS 316.14/291.50 (27) FinalProof [FINISHED, 0 ms] 316.14/291.50 (28) BOUNDS(1, n^3) 316.14/291.50 (29) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 316.14/291.50 (30) CpxTRS 316.14/291.50 (31) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 316.14/291.50 (32) typed CpxTrs 316.14/291.50 (33) OrderProof [LOWER BOUND(ID), 0 ms] 316.14/291.50 (34) typed CpxTrs 316.14/291.50 (35) RewriteLemmaProof [LOWER BOUND(ID), 289 ms] 316.14/291.50 (36) BEST 316.14/291.50 (37) proven lower bound 316.14/291.50 (38) LowerBoundPropagationProof [FINISHED, 0 ms] 316.14/291.50 (39) BOUNDS(n^1, INF) 316.14/291.50 (40) typed CpxTrs 316.14/291.50 (41) RewriteLemmaProof [LOWER BOUND(ID), 60 ms] 316.14/291.50 (42) proven lower bound 316.14/291.50 (43) LowerBoundPropagationProof [FINISHED, 0 ms] 316.14/291.50 (44) BOUNDS(n^2, INF) 316.14/291.50 316.14/291.50 316.14/291.50 ---------------------------------------- 316.14/291.50 316.14/291.50 (0) 316.14/291.50 Obligation: 316.14/291.50 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, n^3). 316.14/291.50 316.14/291.50 316.14/291.50 The TRS R consists of the following rules: 316.14/291.50 316.14/291.50 times(x, 0) -> 0 316.14/291.50 times(x, s(y)) -> plus(times(x, y), x) 316.14/291.50 plus(x, 0) -> x 316.14/291.50 plus(0, x) -> x 316.14/291.50 plus(x, s(y)) -> s(plus(x, y)) 316.14/291.50 plus(s(x), y) -> s(plus(x, y)) 316.14/291.50 316.14/291.50 S is empty. 316.14/291.50 Rewrite Strategy: INNERMOST 316.14/291.50 ---------------------------------------- 316.14/291.50 316.14/291.50 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 316.14/291.50 Transformed relative TRS to weighted TRS 316.14/291.50 ---------------------------------------- 316.14/291.50 316.14/291.50 (2) 316.14/291.50 Obligation: 316.14/291.50 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^3). 316.14/291.50 316.14/291.50 316.14/291.50 The TRS R consists of the following rules: 316.14/291.50 316.14/291.50 times(x, 0) -> 0 [1] 316.14/291.50 times(x, s(y)) -> plus(times(x, y), x) [1] 316.14/291.50 plus(x, 0) -> x [1] 316.14/291.50 plus(0, x) -> x [1] 316.14/291.50 plus(x, s(y)) -> s(plus(x, y)) [1] 316.14/291.50 plus(s(x), y) -> s(plus(x, y)) [1] 316.14/291.50 316.14/291.50 Rewrite Strategy: INNERMOST 316.14/291.50 ---------------------------------------- 316.14/291.50 316.14/291.50 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 316.14/291.50 Infered types. 316.14/291.50 ---------------------------------------- 316.14/291.50 316.14/291.50 (4)
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40