Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
Runtime Complexity: TRS Innermost pair #487112444
details
property
value
status
complete
benchmark
#3.53.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n147.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
7.4192 seconds
cpu usage
25.1332
user time
23.6411
system time
1.49208
max virtual memory
1.9275848E7
max residence set size
3651292.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^3), O(n^3))
output
WORST_CASE(Omega(n^3), O(n^3)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^3, n^3). (0) CpxTRS (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxWeightedTrs (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CpxTypedWeightedTrs (5) CompletionProof [UPPER BOUND(ID), 0 ms] (6) CpxTypedWeightedCompleteTrs (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (8) CpxRNTS (9) CompleteCoflocoProof [FINISHED, 442 ms] (10) BOUNDS(1, n^3) (11) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CpxTRS (13) SlicingProof [LOWER BOUND(ID), 0 ms] (14) CpxTRS (15) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (16) typed CpxTrs (17) OrderProof [LOWER BOUND(ID), 0 ms] (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 283 ms] (20) BEST (21) proven lower bound (22) LowerBoundPropagationProof [FINISHED, 0 ms] (23) BOUNDS(n^1, INF) (24) typed CpxTrs (25) RewriteLemmaProof [LOWER BOUND(ID), 55 ms] (26) typed CpxTrs (27) RewriteLemmaProof [LOWER BOUND(ID), 18 ms] (28) BEST (29) proven lower bound (30) LowerBoundPropagationProof [FINISHED, 0 ms] (31) BOUNDS(n^2, INF) (32) typed CpxTrs (33) RewriteLemmaProof [LOWER BOUND(ID), 0 ms] (34) BEST (35) proven lower bound (36) LowerBoundPropagationProof [FINISHED, 0 ms] (37) BOUNDS(n^3, INF) (38) typed CpxTrs (39) RewriteLemmaProof [LOWER BOUND(ID), 0 ms] (40) typed CpxTrs (41) RewriteLemmaProof [LOWER BOUND(ID), 30 ms] (42) BOUNDS(1, INF) ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^3, n^3). The TRS R consists of the following rules: minus(x, 0) -> x minus(s(x), s(y)) -> minus(x, y) quot(0, s(y)) -> 0 quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) app(nil, y) -> y app(add(n, x), y) -> add(n, app(x, y)) reverse(nil) -> nil reverse(add(n, x)) -> app(reverse(x), add(n, nil)) shuffle(nil) -> nil shuffle(add(n, x)) -> add(n, shuffle(reverse(x))) concat(leaf, y) -> y concat(cons(u, v), y) -> cons(u, concat(v, y)) less_leaves(x, leaf) -> false less_leaves(leaf, cons(w, z)) -> true less_leaves(cons(u, v), cons(w, z)) -> less_leaves(concat(u, v), concat(w, z)) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^3). The TRS R consists of the following rules: minus(x, 0) -> x [1] minus(s(x), s(y)) -> minus(x, y) [1] quot(0, s(y)) -> 0 [1] quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) [1] app(nil, y) -> y [1] app(add(n, x), y) -> add(n, app(x, y)) [1] reverse(nil) -> nil [1] reverse(add(n, x)) -> app(reverse(x), add(n, nil)) [1]
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to Runtime Complexity: TRS Innermost