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Runtime Complexity: TRS pair #487111588
details
property
value
status
complete
benchmark
cade13t.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n141.star.cs.uiowa.edu
space
GTSSK07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.484 seconds
cpu usage
314.73
user time
312.626
system time
2.10395
max virtual memory
1.8283336E7
max residence set size
5393640.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).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), 282 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), 30 ms] (14) 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: div(x, s(y)) -> d(x, s(y), 0) d(x, s(y), z) -> cond(ge(x, z), x, y, z) cond(true, x, y, z) -> s(d(x, s(y), plus(s(y), z))) cond(false, x, y, z) -> 0 ge(u, 0) -> true ge(0, s(v)) -> false ge(s(u), s(v)) -> ge(u, v) plus(n, 0) -> n plus(n, s(m)) -> s(plus(n, m)) 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: div(x, s(y)) -> d(x, s(y), 0') d(x, s(y), z) -> cond(ge(x, z), x, y, z) cond(true, x, y, z) -> s(d(x, s(y), plus(s(y), z))) cond(false, x, y, z) -> 0' ge(u, 0') -> true ge(0', s(v)) -> false ge(s(u), s(v)) -> ge(u, v) plus(n, 0') -> n plus(n, s(m)) -> s(plus(n, m)) S is empty. Rewrite Strategy: FULL ---------------------------------------- (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (4) Obligation: TRS: Rules: div(x, s(y)) -> d(x, s(y), 0') d(x, s(y), z) -> cond(ge(x, z), x, y, z) cond(true, x, y, z) -> s(d(x, s(y), plus(s(y), z))) cond(false, x, y, z) -> 0' ge(u, 0') -> true ge(0', s(v)) -> false ge(s(u), s(v)) -> ge(u, v) plus(n, 0') -> n plus(n, s(m)) -> s(plus(n, m)) Types: div :: s:0' -> s:0' -> s:0' s :: s:0' -> s:0' d :: s:0' -> s:0' -> s:0' -> s:0' 0' :: s:0' cond :: true:false -> s:0' -> s:0' -> s:0' -> s:0' ge :: s:0' -> s:0' -> true:false true :: true:false plus :: s:0' -> s:0' -> s:0' false :: true:false
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