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Runti Compl Inner Rewri 22807 pair #381905039
details
property
value
status
complete
benchmark
Ex1_GL02a_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n039.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
5.56667804718 seconds
cpu usage
16.351658704
max memory
2.997907456E9
stage attributes
key
value
output-size
34043
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). (0) CpxTRS (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxWeightedTrs (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CpxTypedWeightedTrs (5) CompletionProof [UPPER BOUND(ID), 0 ms] (6) CpxTypedWeightedCompleteTrs (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 8 ms] (8) CpxRNTS (9) CompleteCoflocoProof [FINISHED, 450 ms] (10) BOUNDS(1, n^1) (11) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CpxTRS (13) SlicingProof [LOWER BOUND(ID), 0 ms] (14) CpxTRS (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), 294 ms] (20) BEST (21) proven lower bound (22) LowerBoundPropagationProof [FINISHED, 0 ms] (23) BOUNDS(n^1, INF) (24) typed CpxTrs ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: a__eq(0, 0) -> true a__eq(s(X), s(Y)) -> a__eq(X, Y) a__eq(X, Y) -> false a__inf(X) -> cons(X, inf(s(X))) a__take(0, X) -> nil a__take(s(X), cons(Y, L)) -> cons(Y, take(X, L)) a__length(nil) -> 0 a__length(cons(X, L)) -> s(length(L)) mark(eq(X1, X2)) -> a__eq(X1, X2) mark(inf(X)) -> a__inf(mark(X)) mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) mark(length(X)) -> a__length(mark(X)) mark(0) -> 0 mark(true) -> true mark(s(X)) -> s(X) mark(false) -> false mark(cons(X1, X2)) -> cons(X1, X2) mark(nil) -> nil a__eq(X1, X2) -> eq(X1, X2) a__inf(X) -> inf(X) a__take(X1, X2) -> take(X1, X2) a__length(X) -> length(X) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: a__eq(0, 0) -> true [1] a__eq(s(X), s(Y)) -> a__eq(X, Y) [1] a__eq(X, Y) -> false [1] a__inf(X) -> cons(X, inf(s(X))) [1] a__take(0, X) -> nil [1] a__take(s(X), cons(Y, L)) -> cons(Y, take(X, L)) [1] a__length(nil) -> 0 [1] a__length(cons(X, L)) -> s(length(L)) [1] mark(eq(X1, X2)) -> a__eq(X1, X2) [1] mark(inf(X)) -> a__inf(mark(X)) [1] mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) [1] mark(length(X)) -> a__length(mark(X)) [1] mark(0) -> 0 [1]
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