Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313908
details
property
value
status
complete
benchmark
log.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n127.star.cs.uiowa.edu
space
AProVE_09_Inductive
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
14.4703 seconds
cpu usage
49.3042
user time
46.8398
system time
2.46435
max virtual memory
1.8931048E7
max residence set size
4263472.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
49.01/14.36 WORST_CASE(Omega(n^1), O(n^1)) 49.01/14.37 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 49.01/14.37 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 49.01/14.37 49.01/14.37 49.01/14.37 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 49.01/14.37 49.01/14.37 (0) CpxTRS 49.01/14.37 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 49.01/14.37 (2) CpxWeightedTrs 49.01/14.37 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 49.01/14.37 (4) CpxTypedWeightedTrs 49.01/14.37 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 49.01/14.37 (6) CpxTypedWeightedCompleteTrs 49.01/14.37 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 4 ms] 49.01/14.37 (8) CpxRNTS 49.01/14.37 (9) CompleteCoflocoProof [FINISHED, 307 ms] 49.01/14.37 (10) BOUNDS(1, n^1) 49.01/14.37 (11) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 49.01/14.37 (12) CpxTRS 49.01/14.37 (13) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 49.01/14.37 (14) typed CpxTrs 49.01/14.37 (15) OrderProof [LOWER BOUND(ID), 0 ms] 49.01/14.37 (16) typed CpxTrs 49.01/14.37 (17) RewriteLemmaProof [LOWER BOUND(ID), 287 ms] 49.01/14.37 (18) BEST 49.01/14.37 (19) proven lower bound 49.01/14.37 (20) LowerBoundPropagationProof [FINISHED, 0 ms] 49.01/14.37 (21) BOUNDS(n^1, INF) 49.01/14.37 (22) typed CpxTrs 49.01/14.37 49.01/14.37 49.01/14.37 ---------------------------------------- 49.01/14.37 49.01/14.37 (0) 49.01/14.37 Obligation: 49.01/14.37 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 49.01/14.37 49.01/14.37 49.01/14.37 The TRS R consists of the following rules: 49.01/14.37 49.01/14.37 half(x) -> if(ge(x, s(s(0))), x) 49.01/14.37 if(false, x) -> 0 49.01/14.37 if(true, x) -> s(half(p(p(x)))) 49.01/14.37 p(0) -> 0 49.01/14.37 p(s(x)) -> x 49.01/14.37 ge(x, 0) -> true 49.01/14.37 ge(0, s(x)) -> false 49.01/14.37 ge(s(x), s(y)) -> ge(x, y) 49.01/14.37 log(0) -> 0 49.01/14.37 log(s(x)) -> s(log(half(s(x)))) 49.01/14.37 49.01/14.37 S is empty. 49.01/14.37 Rewrite Strategy: INNERMOST 49.01/14.37 ---------------------------------------- 49.01/14.37 49.01/14.37 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 49.01/14.37 Transformed relative TRS to weighted TRS 49.01/14.37 ---------------------------------------- 49.01/14.37 49.01/14.37 (2) 49.01/14.37 Obligation: 49.01/14.37 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1). 49.01/14.37 49.01/14.37 49.01/14.37 The TRS R consists of the following rules: 49.01/14.37 49.01/14.37 half(x) -> if(ge(x, s(s(0))), x) [1] 49.01/14.37 if(false, x) -> 0 [1] 49.01/14.37 if(true, x) -> s(half(p(p(x)))) [1] 49.01/14.37 p(0) -> 0 [1] 49.01/14.37 p(s(x)) -> x [1] 49.01/14.37 ge(x, 0) -> true [1] 49.01/14.37 ge(0, s(x)) -> false [1] 49.01/14.37 ge(s(x), s(y)) -> ge(x, y) [1] 49.01/14.37 log(0) -> 0 [1] 49.01/14.37 log(s(x)) -> s(log(half(s(x)))) [1] 49.01/14.37 49.01/14.37 Rewrite Strategy: INNERMOST 49.01/14.37 ---------------------------------------- 49.01/14.37 49.01/14.37 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 49.01/14.37 Infered types. 49.01/14.37 ---------------------------------------- 49.01/14.37 49.01/14.37 (4) 49.01/14.37 Obligation: 49.01/14.37 Runtime Complexity Weighted TRS with Types. 49.01/14.37 The TRS R consists of the following rules: 49.01/14.37 49.01/14.37 half(x) -> if(ge(x, s(s(0))), x) [1] 49.01/14.37 if(false, x) -> 0 [1] 49.01/14.37 if(true, x) -> s(half(p(p(x)))) [1] 49.01/14.37 p(0) -> 0 [1] 49.01/14.37 p(s(x)) -> x [1] 49.01/14.37 ge(x, 0) -> true [1] 49.01/14.37 ge(0, s(x)) -> false [1] 49.01/14.37 ge(s(x), s(y)) -> ge(x, y) [1] 49.01/14.37 log(0) -> 0 [1] 49.01/14.37 log(s(x)) -> s(log(half(s(x)))) [1]
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