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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307867
details
property
value
status
complete
benchmark
reverse.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n135.star.cs.uiowa.edu
space
Secret_06_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.517 seconds
cpu usage
319.71
user time
317.5
system time
2.21
max virtual memory
1.8281764E7
max residence set size
5523244.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), ?)
output
319.59/291.48 WORST_CASE(Omega(n^2), ?) 319.69/291.49 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 319.69/291.49 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 319.69/291.49 319.69/291.49 319.69/291.49 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 319.69/291.49 319.69/291.49 (0) CpxTRS 319.69/291.49 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 319.69/291.49 (2) CpxTRS 319.69/291.49 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 319.69/291.49 (4) typed CpxTrs 319.69/291.49 (5) OrderProof [LOWER BOUND(ID), 0 ms] 319.69/291.49 (6) typed CpxTrs 319.69/291.49 (7) RewriteLemmaProof [LOWER BOUND(ID), 218 ms] 319.69/291.49 (8) BEST 319.69/291.49 (9) proven lower bound 319.69/291.49 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 319.69/291.49 (11) BOUNDS(n^1, INF) 319.69/291.49 (12) typed CpxTrs 319.69/291.49 (13) RewriteLemmaProof [LOWER BOUND(ID), 74 ms] 319.69/291.49 (14) typed CpxTrs 319.69/291.49 (15) RewriteLemmaProof [LOWER BOUND(ID), 46 ms] 319.69/291.49 (16) typed CpxTrs 319.69/291.49 (17) RewriteLemmaProof [LOWER BOUND(ID), 247 ms] 319.69/291.49 (18) proven lower bound 319.69/291.49 (19) LowerBoundPropagationProof [FINISHED, 0 ms] 319.69/291.49 (20) BOUNDS(n^2, INF) 319.69/291.49 319.69/291.49 319.69/291.49 ---------------------------------------- 319.69/291.49 319.69/291.49 (0) 319.69/291.49 Obligation: 319.69/291.49 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 319.69/291.49 319.69/291.49 319.69/291.49 The TRS R consists of the following rules: 319.69/291.49 319.69/291.49 isEmpty(nil) -> true 319.69/291.49 isEmpty(cons(x, xs)) -> false 319.69/291.49 last(cons(x, nil)) -> x 319.69/291.49 last(cons(x, cons(y, ys))) -> last(cons(y, ys)) 319.69/291.49 dropLast(nil) -> nil 319.69/291.49 dropLast(cons(x, nil)) -> nil 319.69/291.49 dropLast(cons(x, cons(y, ys))) -> cons(x, dropLast(cons(y, ys))) 319.69/291.49 append(nil, ys) -> ys 319.69/291.49 append(cons(x, xs), ys) -> cons(x, append(xs, ys)) 319.69/291.49 reverse(xs) -> rev(xs, nil) 319.69/291.49 rev(xs, ys) -> if(isEmpty(xs), dropLast(xs), append(ys, last(xs)), ys) 319.69/291.49 if(true, xs, ys, zs) -> zs 319.69/291.49 if(false, xs, ys, zs) -> rev(xs, ys) 319.69/291.49 319.69/291.49 S is empty. 319.69/291.49 Rewrite Strategy: FULL 319.69/291.49 ---------------------------------------- 319.69/291.49 319.69/291.49 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 319.69/291.49 Renamed function symbols to avoid clashes with predefined symbol. 319.69/291.49 ---------------------------------------- 319.69/291.49 319.69/291.49 (2) 319.69/291.49 Obligation: 319.69/291.49 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 319.69/291.49 319.69/291.49 319.69/291.49 The TRS R consists of the following rules: 319.69/291.49 319.69/291.49 isEmpty(nil) -> true 319.69/291.49 isEmpty(cons(x, xs)) -> false 319.69/291.49 last(cons(x, nil)) -> x 319.69/291.49 last(cons(x, cons(y, ys))) -> last(cons(y, ys)) 319.69/291.49 dropLast(nil) -> nil 319.69/291.49 dropLast(cons(x, nil)) -> nil 319.69/291.49 dropLast(cons(x, cons(y, ys))) -> cons(x, dropLast(cons(y, ys))) 319.69/291.49 append(nil, ys) -> ys 319.69/291.49 append(cons(x, xs), ys) -> cons(x, append(xs, ys)) 319.69/291.49 reverse(xs) -> rev(xs, nil) 319.69/291.49 rev(xs, ys) -> if(isEmpty(xs), dropLast(xs), append(ys, last(xs)), ys) 319.69/291.49 if(true, xs, ys, zs) -> zs 319.69/291.49 if(false, xs, ys, zs) -> rev(xs, ys) 319.69/291.49 319.69/291.49 S is empty. 319.69/291.49 Rewrite Strategy: FULL 319.69/291.49 ---------------------------------------- 319.69/291.49 319.69/291.49 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 319.69/291.49 Infered types. 319.69/291.49 ---------------------------------------- 319.69/291.49 319.69/291.49 (4) 319.69/291.49 Obligation: 319.69/291.49 TRS: 319.69/291.49 Rules: 319.69/291.49 isEmpty(nil) -> true 319.69/291.49 isEmpty(cons(x, xs)) -> false 319.69/291.49 last(cons(x, nil)) -> x 319.69/291.49 last(cons(x, cons(y, ys))) -> last(cons(y, ys)) 319.69/291.49 dropLast(nil) -> nil 319.69/291.49 dropLast(cons(x, nil)) -> nil
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