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	n147.star.cs.uiowa.edu
space	GTSSK07

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.545 seconds
cpu usage	1062.37
user time	1057.3
system time	5.06911
max virtual memory	3.764564E7
max residence set size	5748612.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).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), 280 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), 53 ms] (14) 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: 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: 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: 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: INNERMOST ---------------------------------------- (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (4) Obligation: Innermost 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 popout

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actions

all output return to Runtime Complexity: TRS Innermost