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Runti Compl Inner Rewri 22807 pair #381904270
details
property
value
status
complete
benchmark
fact-hard.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n049.star.cs.uiowa.edu
space
CiME_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
292.597991943 seconds
cpu usage
1138.55036716
max memory
1.3075275776E10
stage attributes
key
value
output-size
14108
starexec-result
WORST_CASE(Omega(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^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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF).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), 285 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), 85 ms] (14) BEST (15) proven lower bound (16) LowerBoundPropagationProof [FINISHED, 0 ms] (17) BOUNDS(n^2, INF) (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 17 ms] (20) typed CpxTrs (21) RewriteLemmaProof [LOWER BOUND(ID), 51 ms] (22) typed CpxTrs ---------------------------------------- (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: +(x, 0) -> x +(x, s(y)) -> s(+(x, y)) *(x, 0) -> 0 *(x, s(y)) -> +(*(x, y), x) ge(x, 0) -> true ge(0, s(y)) -> false ge(s(x), s(y)) -> ge(x, y) -(x, 0) -> x -(s(x), s(y)) -> -(x, y) fact(x) -> iffact(x, ge(x, s(s(0)))) iffact(x, true) -> *(x, fact(-(x, s(0)))) iffact(x, false) -> s(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: +'(x, 0') -> x +'(x, s(y)) -> s(+'(x, y)) *'(x, 0') -> 0' *'(x, s(y)) -> +'(*'(x, y), x) ge(x, 0') -> true ge(0', s(y)) -> false ge(s(x), s(y)) -> ge(x, y) -(x, 0') -> x -(s(x), s(y)) -> -(x, y) fact(x) -> iffact(x, ge(x, s(s(0')))) iffact(x, true) -> *'(x, fact(-(x, s(0')))) iffact(x, false) -> s(0') S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (4) Obligation: Innermost TRS: Rules:
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