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Runtime Complexity: TRS Innermost pair #487111886
details
property
value
status
complete
benchmark
inssort.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n150.star.cs.uiowa.edu
space
Frederiksen_Others
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.748 seconds
cpu usage
331.074
user time
328.015
system time
3.05875
max virtual memory
3.791824E7
max residence set size
5628560.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2). (0) CpxRelTRS (1) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 165 ms] (2) CpxRelTRS (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CpxWeightedTrs (5) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxWeightedTrs (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxTypedWeightedTrs (9) CompletionProof [UPPER BOUND(ID), 0 ms] (10) CpxTypedWeightedCompleteTrs (11) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (12) CpxRNTS (13) CompleteCoflocoProof [FINISHED, 233 ms] (14) BOUNDS(1, n^2) (15) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (16) CpxRelTRS (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) typed CpxTrs (23) RewriteLemmaProof [LOWER BOUND(ID), 476 ms] (24) BEST (25) proven lower bound (26) LowerBoundPropagationProof [FINISHED, 0 ms] (27) BOUNDS(n^1, INF) (28) typed CpxTrs ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2). The TRS R consists of the following rules: isort(Cons(x, xs), r) -> isort(xs, insert(x, r)) isort(Nil, r) -> Nil insert(S(x), r) -> insert[Ite](<(S(x), x), S(x), r) inssort(xs) -> isort(xs, Nil) The (relative) TRS S consists of the following rules: <(S(x), S(y)) -> <(x, y) <(0, S(y)) -> True <(x, 0) -> False insert[Ite](False, x', Cons(x, xs)) -> Cons(x, insert(x', xs)) insert[Ite](True, x, r) -> Cons(x, r) 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^2). The TRS R consists of the following rules: isort(Cons(x, xs), r) -> isort(xs, insert(x, r)) isort(Nil, r) -> Nil insert(S(x), r) -> insert[Ite](<(S(x), x), S(x), r) inssort(xs) -> isort(xs, Nil) The (relative) TRS S consists of the following rules: <(S(x), S(y)) -> <(x, y) <(0, S(y)) -> True <(x, 0) -> False insert[Ite](False, x', Cons(x, xs)) -> Cons(x, insert(x', xs)) insert[Ite](True, x, r) -> Cons(x, r) Rewrite Strategy: INNERMOST ---------------------------------------- (3) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (4) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). The TRS R consists of the following rules:
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