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Runtime Complexity: TRS Innermost pair #487112672
details
property
value
status
complete
benchmark
gcd2.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n144.star.cs.uiowa.edu
space
Frederiksen_Glenstrup
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
298.895 seconds
cpu usage
1115.92
user time
1104.39
system time
11.5284
max virtual memory
1.961128E7
max residence set size
1.5336648E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^3))
output
WORST_CASE(Omega(n^1), O(n^3)) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^3). (0) CpxRelTRS (1) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 211 ms] (2) CpxRelTRS (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), 11 ms] (10) CpxRNTS (11) CompleteCoflocoProof [FINISHED, 108.8 s] (12) BOUNDS(1, n^3) (13) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (14) CpxRelTRS (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), 278 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), 49 ms] (26) typed CpxTrs (27) RewriteLemmaProof [LOWER BOUND(ID), 42 ms] (28) typed CpxTrs (29) RewriteLemmaProof [LOWER BOUND(ID), 27 ms] (30) typed CpxTrs ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^3). The TRS R consists of the following rules: @(Cons(x, xs), ys) -> Cons(x, @(xs, ys)) @(Nil, ys) -> ys gt0(Cons(x, xs), Nil) -> True gt0(Cons(x', xs'), Cons(x, xs)) -> gt0(xs', xs) gcd(Nil, Nil) -> Nil gcd(Nil, Cons(x, xs)) -> Nil gcd(Cons(x, xs), Nil) -> Nil gcd(Cons(x', xs'), Cons(x, xs)) -> gcd[Ite](eqList(Cons(x', xs'), Cons(x, xs)), Cons(x', xs'), Cons(x, xs)) lgth(Cons(x, xs)) -> @(Cons(Nil, Nil), lgth(xs)) eqList(Cons(x, xs), Cons(y, ys)) -> and(eqList(x, y), eqList(xs, ys)) eqList(Cons(x, xs), Nil) -> False eqList(Nil, Cons(y, ys)) -> False eqList(Nil, Nil) -> True lgth(Nil) -> Nil gt0(Nil, y) -> False monus(x, y) -> monus[Ite](eqList(lgth(y), Cons(Nil, Nil)), x, y) goal(x, y) -> gcd(x, y) The (relative) TRS S consists of the following rules: and(False, False) -> False and(True, False) -> False and(False, True) -> False and(True, True) -> True monus[Ite](False, Cons(x', xs'), Cons(x, xs)) -> monus(xs', xs) monus[Ite](True, Cons(x, xs), y) -> xs gcd[Ite](False, x, y) -> gcd[False][Ite](gt0(x, y), x, y) gcd[Ite](True, x, y) -> x gcd[False][Ite](False, x, y) -> gcd(monus(y, x), x) gcd[False][Ite](True, x, y) -> gcd(y, monus(x, y)) Rewrite Strategy: INNERMOST ---------------------------------------- (1) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved innermost termination of relative rules ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^3). The TRS R consists of the following rules: @(Cons(x, xs), ys) -> Cons(x, @(xs, ys)) @(Nil, ys) -> ys gt0(Cons(x, xs), Nil) -> True gt0(Cons(x', xs'), Cons(x, xs)) -> gt0(xs', xs) gcd(Nil, Nil) -> Nil gcd(Nil, Cons(x, xs)) -> Nil
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