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Runti Compl Inner Rewri 22807 pair #381904577
details
property
value
status
complete
benchmark
sumList.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n033.star.cs.uiowa.edu
space
Secret_06_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.487272978 seconds
cpu usage
1129.3246879
max memory
1.5486656512E10
stage attributes
key
value
output-size
16404
starexec-result
WORST_CASE(Omega(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^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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). (0) CpxTRS (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (4) typed CpxTrs (5) OrderProof [LOWER BOUND(ID), 0 ms] (6) typed CpxTrs (7) RewriteLemmaProof [LOWER BOUND(ID), 300 ms] (8) BEST (9) proven lower bound (10) LowerBoundPropagationProof [FINISHED, 0 ms] (11) BOUNDS(n^1, INF) (12) typed CpxTrs (13) RewriteLemmaProof [LOWER BOUND(ID), 36 ms] (14) typed CpxTrs (15) RewriteLemmaProof [LOWER BOUND(ID), 136 ms] (16) proven lower bound (17) LowerBoundPropagationProof [FINISHED, 0 ms] (18) BOUNDS(n^2, INF) ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). The TRS R consists of the following rules: isEmpty(cons(x, xs)) -> false isEmpty(nil) -> true isZero(0) -> true isZero(s(x)) -> false head(cons(x, xs)) -> x tail(cons(x, xs)) -> xs tail(nil) -> nil p(s(s(x))) -> s(p(s(x))) p(s(0)) -> 0 p(0) -> 0 inc(s(x)) -> s(inc(x)) inc(0) -> s(0) sumList(xs, y) -> if(isEmpty(xs), isZero(head(xs)), y, tail(xs), cons(p(head(xs)), tail(xs)), inc(y)) if(true, b, y, xs, ys, x) -> y if(false, true, y, xs, ys, x) -> sumList(xs, y) if(false, false, y, xs, ys, x) -> sumList(ys, x) sum(xs) -> sumList(xs, 0) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). The TRS R consists of the following rules: isEmpty(cons(x, xs)) -> false isEmpty(nil) -> true isZero(0') -> true isZero(s(x)) -> false head(cons(x, xs)) -> x tail(cons(x, xs)) -> xs tail(nil) -> nil p(s(s(x))) -> s(p(s(x))) p(s(0')) -> 0' p(0') -> 0' inc(s(x)) -> s(inc(x)) inc(0') -> s(0') sumList(xs, y) -> if(isEmpty(xs), isZero(head(xs)), y, tail(xs), cons(p(head(xs)), tail(xs)), inc(y)) if(true, b, y, xs, ys, x) -> y if(false, true, y, xs, ys, x) -> sumList(xs, y) if(false, false, y, xs, ys, x) -> sumList(ys, x) sum(xs) -> sumList(xs, 0') S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types.
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