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Runti Compl Inner Rewri 22807 pair #381903990
details
property
value
status
complete
benchmark
zerolist.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n034.star.cs.uiowa.edu
space
AProVE_09_Inductive
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.491071939 seconds
cpu usage
921.030767267
max memory
8.00831488E9
stage attributes
key
value
output-size
13871
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
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^2)) 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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). (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), 0 ms] (8) CpxRNTS (9) CompleteCoflocoProof [FINISHED, 270 ms] (10) BOUNDS(1, n^2) (11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (12) TRS for Loop Detection (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (14) BEST (15) proven lower bound (16) LowerBoundPropagationProof [FINISHED, 0 ms] (17) BOUNDS(n^1, INF) (18) TRS for Loop Detection ---------------------------------------- (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: sub(0, 0) -> 0 sub(s(x), 0) -> s(x) sub(0, s(x)) -> 0 sub(s(x), s(y)) -> sub(x, y) zero(nil) -> zero2(0, nil) zero(cons(x, xs)) -> zero2(sub(x, x), cons(x, xs)) zero2(0, nil) -> nil zero2(0, cons(x, xs)) -> cons(sub(x, x), zero(xs)) zero2(s(y), nil) -> zero(nil) zero2(s(y), cons(x, xs)) -> zero(cons(x, xs)) 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: sub(0, 0) -> 0 [1] sub(s(x), 0) -> s(x) [1] sub(0, s(x)) -> 0 [1] sub(s(x), s(y)) -> sub(x, y) [1] zero(nil) -> zero2(0, nil) [1] zero(cons(x, xs)) -> zero2(sub(x, x), cons(x, xs)) [1] zero2(0, nil) -> nil [1] zero2(0, cons(x, xs)) -> cons(sub(x, x), zero(xs)) [1] zero2(s(y), nil) -> zero(nil) [1] zero2(s(y), cons(x, xs)) -> zero(cons(x, xs)) [1] Rewrite Strategy: INNERMOST ---------------------------------------- (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (4) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: sub(0, 0) -> 0 [1] sub(s(x), 0) -> s(x) [1] sub(0, s(x)) -> 0 [1] sub(s(x), s(y)) -> sub(x, y) [1] zero(nil) -> zero2(0, nil) [1] zero(cons(x, xs)) -> zero2(sub(x, x), cons(x, xs)) [1] zero2(0, nil) -> nil [1] zero2(0, cons(x, xs)) -> cons(sub(x, x), zero(xs)) [1]
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