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Runtime Complexity: TRS Innermost pair #487112900
details
property
value
status
complete
benchmark
quick.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n143.star.cs.uiowa.edu
space
Rubio_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
295.728 seconds
cpu usage
1137.45
user time
1124.32
system time
13.1292
max virtual memory
3.7508396E7
max residence set size
1.4976972E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), ?)
output
WORST_CASE(Omega(n^2), ?) 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). (0) CpxTRS (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (4) typed CpxTrs (5) OrderProof [LOWER BOUND(ID), 0 ms] (6) typed CpxTrs (7) RewriteLemmaProof [LOWER BOUND(ID), 252 ms] (8) BEST (9) proven lower bound (10) LowerBoundPropagationProof [FINISHED, 0 ms] (11) BOUNDS(n^1, INF) (12) typed CpxTrs (13) RewriteLemmaProof [LOWER BOUND(ID), 64 ms] (14) typed CpxTrs (15) RewriteLemmaProof [LOWER BOUND(ID), 43 ms] (16) typed CpxTrs (17) RewriteLemmaProof [LOWER BOUND(ID), 29 ms] (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 80 ms] (20) proven lower bound (21) LowerBoundPropagationProof [FINISHED, 0 ms] (22) BOUNDS(n^2, INF) ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). The TRS R consists of the following rules: le(0, Y) -> true le(s(X), 0) -> false le(s(X), s(Y)) -> le(X, Y) app(nil, Y) -> Y app(cons(N, L), Y) -> cons(N, app(L, Y)) low(N, nil) -> nil low(N, cons(M, L)) -> iflow(le(M, N), N, cons(M, L)) iflow(true, N, cons(M, L)) -> cons(M, low(N, L)) iflow(false, N, cons(M, L)) -> low(N, L) high(N, nil) -> nil high(N, cons(M, L)) -> ifhigh(le(M, N), N, cons(M, L)) ifhigh(true, N, cons(M, L)) -> high(N, L) ifhigh(false, N, cons(M, L)) -> cons(M, high(N, L)) quicksort(nil) -> nil quicksort(cons(N, L)) -> app(quicksort(low(N, L)), cons(N, quicksort(high(N, L)))) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). The TRS R consists of the following rules: le(0', Y) -> true le(s(X), 0') -> false le(s(X), s(Y)) -> le(X, Y) app(nil, Y) -> Y app(cons(N, L), Y) -> cons(N, app(L, Y)) low(N, nil) -> nil low(N, cons(M, L)) -> iflow(le(M, N), N, cons(M, L)) iflow(true, N, cons(M, L)) -> cons(M, low(N, L)) iflow(false, N, cons(M, L)) -> low(N, L) high(N, nil) -> nil high(N, cons(M, L)) -> ifhigh(le(M, N), N, cons(M, L)) ifhigh(true, N, cons(M, L)) -> high(N, L) ifhigh(false, N, cons(M, L)) -> cons(M, high(N, L)) quicksort(nil) -> nil quicksort(cons(N, L)) -> app(quicksort(low(N, L)), cons(N, quicksort(high(N, L)))) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (4) Obligation: Innermost TRS: Rules:
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