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Runti Compl Inner Rewri 22807 pair #381904997
details
property
value
status
complete
benchmark
select.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n027.star.cs.uiowa.edu
space
Frederiksen_Glenstrup
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.474283934 seconds
cpu usage
349.295572254
max memory
5.817536512E9
stage attributes
key
value
output-size
25441
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^2)) proof of /export/starexec/sandbox2/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). (0) CpxTRS (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxWeightedTrs (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 1 ms] (4) CpxTypedWeightedTrs (5) CompletionProof [UPPER BOUND(ID), 0 ms] (6) CpxTypedWeightedCompleteTrs (7) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxTypedWeightedCompleteTrs (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 8 ms] (10) CpxRNTS (11) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CpxRNTS (13) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] (14) CpxRNTS (15) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (16) CpxRNTS (17) IntTrsBoundProof [UPPER BOUND(ID), 438 ms] (18) CpxRNTS (19) IntTrsBoundProof [UPPER BOUND(ID), 127 ms] (20) CpxRNTS (21) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (22) CpxRNTS (23) IntTrsBoundProof [UPPER BOUND(ID), 716 ms] (24) CpxRNTS (25) IntTrsBoundProof [UPPER BOUND(ID), 266 ms] (26) CpxRNTS (27) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (28) CpxRNTS (29) IntTrsBoundProof [UPPER BOUND(ID), 808 ms] (30) CpxRNTS (31) IntTrsBoundProof [UPPER BOUND(ID), 2 ms] (32) CpxRNTS (33) FinalProof [FINISHED, 0 ms] (34) BOUNDS(1, n^2) (35) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (36) CpxTRS (37) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (38) typed CpxTrs (39) OrderProof [LOWER BOUND(ID), 0 ms] (40) typed CpxTrs (41) RewriteLemmaProof [LOWER BOUND(ID), 299 ms] (42) BEST (43) proven lower bound (44) LowerBoundPropagationProof [FINISHED, 0 ms] (45) BOUNDS(n^1, INF) (46) typed CpxTrs ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). The TRS R consists of the following rules: selects(x', revprefix, Cons(x, xs)) -> Cons(Cons(x', revapp(revprefix, Cons(x, xs))), selects(x, Cons(x', revprefix), xs)) select(Cons(x, xs)) -> selects(x, Nil, xs) revapp(Cons(x, xs), rest) -> revapp(xs, Cons(x, rest)) selects(x, revprefix, Nil) -> Cons(Cons(x, revapp(revprefix, Nil)), Nil) select(Nil) -> Nil revapp(Nil, rest) -> rest 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^2). The TRS R consists of the following rules: selects(x', revprefix, Cons(x, xs)) -> Cons(Cons(x', revapp(revprefix, Cons(x, xs))), selects(x, Cons(x', revprefix), xs)) [1] select(Cons(x, xs)) -> selects(x, Nil, xs) [1] revapp(Cons(x, xs), rest) -> revapp(xs, Cons(x, rest)) [1] selects(x, revprefix, Nil) -> Cons(Cons(x, revapp(revprefix, Nil)), Nil) [1] select(Nil) -> Nil [1] revapp(Nil, rest) -> rest [1]
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