Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313916
details
property
value
status
complete
benchmark
div.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n003.star.cs.uiowa.edu
space
AProVE_09_Inductive
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.579 seconds
cpu usage
1125.48
user time
1112.12
system time
13.3574
max virtual memory
5.6602936E7
max residence set size
1.4946776E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^3))
output
1125.17/291.47 WORST_CASE(Omega(n^1), O(n^3)) 1125.17/291.49 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1125.17/291.49 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1125.17/291.49 1125.17/291.49 1125.17/291.49 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^3). 1125.17/291.49 1125.17/291.49 (0) CpxTRS 1125.17/291.49 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 1125.17/291.49 (2) CpxWeightedTrs 1125.17/291.49 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1125.17/291.49 (4) CpxTypedWeightedTrs 1125.17/291.49 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 1125.17/291.49 (6) CpxTypedWeightedCompleteTrs 1125.17/291.49 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 1125.17/291.49 (8) CpxRNTS 1125.17/291.49 (9) CompleteCoflocoProof [FINISHED, 708 ms] 1125.17/291.49 (10) BOUNDS(1, n^3) 1125.17/291.49 (11) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1125.17/291.49 (12) CpxTRS 1125.17/291.49 (13) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1125.17/291.49 (14) typed CpxTrs 1125.17/291.49 (15) OrderProof [LOWER BOUND(ID), 0 ms] 1125.17/291.49 (16) typed CpxTrs 1125.17/291.49 (17) RewriteLemmaProof [LOWER BOUND(ID), 301 ms] 1125.17/291.49 (18) BEST 1125.17/291.49 (19) proven lower bound 1125.17/291.49 (20) LowerBoundPropagationProof [FINISHED, 0 ms] 1125.17/291.49 (21) BOUNDS(n^1, INF) 1125.17/291.49 (22) typed CpxTrs 1125.17/291.49 (23) RewriteLemmaProof [LOWER BOUND(ID), 75 ms] 1125.17/291.49 (24) typed CpxTrs 1125.17/291.49 1125.17/291.49 1125.17/291.49 ---------------------------------------- 1125.17/291.49 1125.17/291.49 (0) 1125.17/291.49 Obligation: 1125.17/291.49 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^3). 1125.17/291.49 1125.17/291.49 1125.17/291.49 The TRS R consists of the following rules: 1125.17/291.49 1125.17/291.49 minus(s(x), y) -> if(gt(s(x), y), x, y) 1125.17/291.49 if(true, x, y) -> s(minus(x, y)) 1125.17/291.49 if(false, x, y) -> 0 1125.17/291.49 ge(x, 0) -> true 1125.17/291.49 ge(0, s(x)) -> false 1125.17/291.49 ge(s(x), s(y)) -> ge(x, y) 1125.17/291.49 gt(0, y) -> false 1125.17/291.49 gt(s(x), 0) -> true 1125.17/291.49 gt(s(x), s(y)) -> gt(x, y) 1125.17/291.49 div(x, y) -> if1(ge(x, y), x, y) 1125.17/291.49 if1(true, x, y) -> if2(gt(y, 0), x, y) 1125.17/291.49 if1(false, x, y) -> 0 1125.17/291.49 if2(true, x, y) -> s(div(minus(x, y), y)) 1125.17/291.49 if2(false, x, y) -> 0 1125.17/291.49 1125.17/291.49 S is empty. 1125.17/291.49 Rewrite Strategy: INNERMOST 1125.17/291.49 ---------------------------------------- 1125.17/291.49 1125.17/291.49 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 1125.17/291.49 Transformed relative TRS to weighted TRS 1125.17/291.49 ---------------------------------------- 1125.17/291.49 1125.17/291.49 (2) 1125.17/291.49 Obligation: 1125.17/291.49 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^3). 1125.17/291.49 1125.17/291.49 1125.17/291.49 The TRS R consists of the following rules: 1125.17/291.49 1125.17/291.49 minus(s(x), y) -> if(gt(s(x), y), x, y) [1] 1125.17/291.49 if(true, x, y) -> s(minus(x, y)) [1] 1125.17/291.49 if(false, x, y) -> 0 [1] 1125.17/291.49 ge(x, 0) -> true [1] 1125.17/291.49 ge(0, s(x)) -> false [1] 1125.17/291.49 ge(s(x), s(y)) -> ge(x, y) [1] 1125.17/291.49 gt(0, y) -> false [1] 1125.17/291.49 gt(s(x), 0) -> true [1] 1125.17/291.49 gt(s(x), s(y)) -> gt(x, y) [1] 1125.17/291.49 div(x, y) -> if1(ge(x, y), x, y) [1] 1125.17/291.49 if1(true, x, y) -> if2(gt(y, 0), x, y) [1] 1125.17/291.49 if1(false, x, y) -> 0 [1] 1125.17/291.49 if2(true, x, y) -> s(div(minus(x, y), y)) [1] 1125.17/291.49 if2(false, x, y) -> 0 [1] 1125.17/291.49 1125.17/291.49 Rewrite Strategy: INNERMOST 1125.17/291.49 ---------------------------------------- 1125.17/291.49 1125.17/291.49 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 1125.17/291.49 Infered types. 1125.17/291.49 ---------------------------------------- 1125.17/291.49 1125.17/291.49 (4) 1125.17/291.49 Obligation: 1125.17/291.49 Runtime Complexity Weighted TRS with Types. 1125.17/291.49 The TRS R consists of the following rules: 1125.17/291.49
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
