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Runtime Complexity: TRS pair #487111578
details
property
value
status
complete
benchmark
cade16.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n146.star.cs.uiowa.edu
space
GTSSK07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
294.275 seconds
cpu usage
1133.57
user time
1119.47
system time
14.0992
max virtual memory
3.791046E7
max residence set size
1.514842E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
WORST_CASE(Omega(n^1), O(n^2)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). (0) CpxTRS (1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CpxWeightedTrs (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxTypedWeightedTrs (7) CompletionProof [UPPER BOUND(ID), 0 ms] (8) CpxTypedWeightedCompleteTrs (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (10) CpxRNTS (11) CompleteCoflocoProof [FINISHED, 360 ms] (12) BOUNDS(1, n^2) (13) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (14) CpxTRS (15) SlicingProof [LOWER BOUND(ID), 0 ms] (16) CpxTRS (17) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (18) typed CpxTrs (19) OrderProof [LOWER BOUND(ID), 0 ms] (20) typed CpxTrs (21) RewriteLemmaProof [LOWER BOUND(ID), 248 ms] (22) BEST (23) proven lower bound (24) LowerBoundPropagationProof [FINISHED, 0 ms] (25) BOUNDS(n^1, INF) (26) typed CpxTrs (27) RewriteLemmaProof [LOWER BOUND(ID), 8 ms] (28) typed CpxTrs ---------------------------------------- (0) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). The TRS R consists of the following rules: nthtail(n, l) -> cond(ge(n, length(l)), n, l) cond(true, n, l) -> l cond(false, n, l) -> tail(nthtail(s(n), l)) tail(nil) -> nil tail(cons(x, l)) -> l length(nil) -> 0 length(cons(x, l)) -> s(length(l)) ge(u, 0) -> true ge(0, s(v)) -> false ge(s(u), s(v)) -> ge(u, v) S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) RcToIrcProof (BOTH BOUNDS(ID, ID)) Converted rc-obligation to irc-obligation. The duplicating contexts are: nthtail([], l) nthtail(n, []) The defined contexts are: tail([]) cond([], x1, x2) ge(x0, []) As the TRS is an overlay system and the defined contexts and the duplicating contexts don't overlap, we have rc = irc. ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^2). The TRS R consists of the following rules: nthtail(n, l) -> cond(ge(n, length(l)), n, l) cond(true, n, l) -> l cond(false, n, l) -> tail(nthtail(s(n), l)) tail(nil) -> nil tail(cons(x, l)) -> l length(nil) -> 0 length(cons(x, l)) -> s(length(l)) ge(u, 0) -> true ge(0, s(v)) -> false ge(s(u), s(v)) -> ge(u, v) S is empty. Rewrite Strategy: INNERMOST ----------------------------------------
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