details

property	value
status	complete
benchmark	otto09.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n140.star.cs.uiowa.edu
space	AProVE_07

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	292.816 seconds
cpu usage	307.91
user time	305.935
system time	1.97507
max virtual memory	1.8414776E7
max residence set size	5279776.0

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^1), ?)

output

WORST_CASE(Omega(n^1), ?) proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).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), 288 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), 37 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: lt(x, 0) -> false lt(0, s(y)) -> true lt(s(x), s(y)) -> lt(x, y) plus(x, 0) -> x plus(x, s(y)) -> s(plus(x, y)) quot(x, s(y)) -> help(x, s(y), 0) help(x, s(y), c) -> if(lt(c, x), x, s(y), c) if(true, x, s(y), c) -> s(help(x, s(y), plus(c, s(y)))) if(false, x, s(y), c) -> 0 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: lt(x, 0') -> false lt(0', s(y)) -> true lt(s(x), s(y)) -> lt(x, y) plus(x, 0') -> x plus(x, s(y)) -> s(plus(x, y)) quot(x, s(y)) -> help(x, s(y), 0') help(x, s(y), c) -> if(lt(c, x), x, s(y), c) if(true, x, s(y), c) -> s(help(x, s(y), plus(c, s(y)))) if(false, x, s(y), c) -> 0' S is empty. Rewrite Strategy: FULL ---------------------------------------- (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (4) Obligation: TRS: Rules: lt(x, 0') -> false lt(0', s(y)) -> true lt(s(x), s(y)) -> lt(x, y) plus(x, 0') -> x plus(x, s(y)) -> s(plus(x, y)) quot(x, s(y)) -> help(x, s(y), 0') help(x, s(y), c) -> if(lt(c, x), x, s(y), c) if(true, x, s(y), c) -> s(help(x, s(y), plus(c, s(y)))) if(false, x, s(y), c) -> 0' Types: lt :: 0':s -> 0':s -> false:true 0' :: 0':s false :: false:true s :: 0':s -> 0':s true :: false:true plus :: 0':s -> 0':s -> 0':s quot :: 0':s -> 0':s -> 0':s help :: 0':s -> 0':s -> 0':s -> 0':s if :: false:true -> 0':s -> 0':s -> 0':s -> 0':s popout

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actions

all output return to Runtime Complexity: TRS