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Runtime Complexity: TRS pair #487111100
details
property
value
status
complete
benchmark
aprove02.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n142.star.cs.uiowa.edu
space
Secret_07_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.511 seconds
cpu usage
312.425
user time
310.029
system time
2.39583
max virtual memory
1.8279408E7
max residence set size
5328848.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
WORST_CASE(Omega(n^1), ?) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).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), 234 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), 40 ms] (14) typed CpxTrs (15) RewriteLemmaProof [LOWER BOUND(ID), 148 ms] (16) typed CpxTrs (17) RewriteLemmaProof [LOWER BOUND(ID), 48 ms] (18) typed CpxTrs ---------------------------------------- (0) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: plus(x, y) -> ifPlus(isZero(x), x, inc(y)) ifPlus(true, x, y) -> p(y) ifPlus(false, x, y) -> plus(p(x), y) times(x, y) -> timesIter(0, x, y, 0) timesIter(i, x, y, z) -> ifTimes(ge(i, x), i, x, y, z) ifTimes(true, i, x, y, z) -> z ifTimes(false, i, x, y, z) -> timesIter(inc(i), x, y, plus(z, y)) isZero(0) -> true isZero(s(0)) -> false isZero(s(s(x))) -> isZero(s(x)) inc(0) -> s(0) inc(s(x)) -> s(inc(x)) inc(x) -> s(x) p(0) -> 0 p(s(x)) -> x p(s(s(x))) -> s(p(s(x))) ge(x, 0) -> true ge(0, s(y)) -> false ge(s(x), s(y)) -> ge(x, y) f0(0, y, x) -> f1(x, y, x) f1(x, y, z) -> f2(x, y, z) f2(x, 1, z) -> f0(x, z, z) f0(x, y, z) -> d f1(x, y, z) -> c S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (2) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: plus(x, y) -> ifPlus(isZero(x), x, inc(y)) ifPlus(true, x, y) -> p(y) ifPlus(false, x, y) -> plus(p(x), y) times(x, y) -> timesIter(0', x, y, 0') timesIter(i, x, y, z) -> ifTimes(ge(i, x), i, x, y, z) ifTimes(true, i, x, y, z) -> z ifTimes(false, i, x, y, z) -> timesIter(inc(i), x, y, plus(z, y)) isZero(0') -> true isZero(s(0')) -> false isZero(s(s(x))) -> isZero(s(x)) inc(0') -> s(0') inc(s(x)) -> s(inc(x)) inc(x) -> s(x) p(0') -> 0' p(s(x)) -> x p(s(s(x))) -> s(p(s(x))) ge(x, 0') -> true ge(0', s(y)) -> false ge(s(x), s(y)) -> ge(x, y) f0(0', y, x) -> f1(x, y, x) f1(x, y, z) -> f2(x, y, z) f2(x, 1', z) -> f0(x, z, z) f0(x, y, z) -> d
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