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Runti Compl Inner Rewri 22807 pair #381904368
details
property
value
status
complete
benchmark
rta3.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n072.star.cs.uiowa.edu
space
AProVE_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
292.208420038 seconds
cpu usage
984.751117403
max memory
7.495806976E9
stage attributes
key
value
output-size
5419
starexec-result
WORST_CASE(Omega(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), ?) 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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).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), 993 ms] (8) BEST (9) proven lower bound (10) LowerBoundPropagationProof [FINISHED, 0 ms] (11) BOUNDS(n^1, INF) (12) typed CpxTrs ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: ack(0, y) -> s(y) ack(s(x), 0) -> ack(x, s(0)) ack(s(x), s(y)) -> ack(x, ack(s(x), y)) f(s(x), y) -> f(x, s(x)) f(x, s(y)) -> f(y, x) f(x, y) -> ack(x, y) ack(s(x), y) -> f(x, x) 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^1, INF). The TRS R consists of the following rules: ack(0', y) -> s(y) ack(s(x), 0') -> ack(x, s(0')) ack(s(x), s(y)) -> ack(x, ack(s(x), y)) f(s(x), y) -> f(x, s(x)) f(x, s(y)) -> f(y, x) f(x, y) -> ack(x, y) ack(s(x), y) -> f(x, x) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (4) Obligation: Innermost TRS: Rules: ack(0', y) -> s(y) ack(s(x), 0') -> ack(x, s(0')) ack(s(x), s(y)) -> ack(x, ack(s(x), y)) f(s(x), y) -> f(x, s(x)) f(x, s(y)) -> f(y, x) f(x, y) -> ack(x, y) ack(s(x), y) -> f(x, x) Types: ack :: 0':s -> 0':s -> 0':s 0' :: 0':s s :: 0':s -> 0':s f :: 0':s -> 0':s -> 0':s hole_0':s1_0 :: 0':s gen_0':s2_0 :: Nat -> 0':s ---------------------------------------- (5) OrderProof (LOWER BOUND(ID)) Heuristically decided to analyse the following defined symbols:
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