details

property	value
status	complete
benchmark	otto02.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	AProVE_07

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.648 seconds
cpu usage	1110.66
user time	1100.55
system time	10.105
max virtual memory	3.8089736E7
max residence set size	5750524.0

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^1), O(n^2))

output

WORST_CASE(Omega(n^1), O(n^2)) proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). (0) CpxTRS (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxWeightedTrs (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CpxTypedWeightedTrs (5) CompletionProof [UPPER BOUND(ID), 0 ms] (6) CpxTypedWeightedCompleteTrs (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (8) CpxRNTS (9) CompleteCoflocoProof [FINISHED, 1158 ms] (10) BOUNDS(1, n^2) (11) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CpxTRS (13) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (14) typed CpxTrs (15) OrderProof [LOWER BOUND(ID), 0 ms] (16) typed CpxTrs (17) RewriteLemmaProof [LOWER BOUND(ID), 255 ms] (18) BEST (19) proven lower bound (20) LowerBoundPropagationProof [FINISHED, 0 ms] (21) BOUNDS(n^1, INF) (22) typed CpxTrs (23) RewriteLemmaProof [LOWER BOUND(ID), 16 ms] (24) typed CpxTrs (25) RewriteLemmaProof [LOWER BOUND(ID), 57 ms] (26) typed CpxTrs (27) RewriteLemmaProof [LOWER BOUND(ID), 39 ms] (28) typed CpxTrs ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). The TRS R consists of the following rules: app(x, y) -> helpa(0, plus(length(x), length(y)), x, y) plus(x, 0) -> x plus(x, s(y)) -> s(plus(x, y)) length(nil) -> 0 length(cons(x, y)) -> s(length(y)) helpa(c, l, ys, zs) -> if(ge(c, l), c, l, ys, zs) ge(x, 0) -> true ge(0, s(x)) -> false ge(s(x), s(y)) -> ge(x, y) if(true, c, l, ys, zs) -> nil if(false, c, l, ys, zs) -> helpb(c, l, ys, zs) take(0, cons(x, xs), ys) -> x take(0, nil, cons(y, ys)) -> y take(s(c), cons(x, xs), ys) -> take(c, xs, ys) take(s(c), nil, cons(y, ys)) -> take(c, nil, ys) helpb(c, l, ys, zs) -> cons(take(c, ys, zs), helpa(s(c), l, ys, zs)) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). The TRS R consists of the following rules: app(x, y) -> helpa(0, plus(length(x), length(y)), x, y) [1] plus(x, 0) -> x [1] plus(x, s(y)) -> s(plus(x, y)) [1] length(nil) -> 0 [1] length(cons(x, y)) -> s(length(y)) [1] helpa(c, l, ys, zs) -> if(ge(c, l), c, l, ys, zs) [1] ge(x, 0) -> true [1] ge(0, s(x)) -> false [1] ge(s(x), s(y)) -> ge(x, y) [1] if(true, c, l, ys, zs) -> nil [1] if(false, c, l, ys, zs) -> helpb(c, l, ys, zs) [1] take(0, cons(x, xs), ys) -> x [1] take(0, nil, cons(y, ys)) -> y [1] take(s(c), cons(x, xs), ys) -> take(c, xs, ys) [1] take(s(c), nil, cons(y, ys)) -> take(c, nil, ys) [1] helpb(c, l, ys, zs) -> cons(take(c, ys, zs), helpa(s(c), l, ys, zs)) [1] Rewrite Strategy: INNERMOST ---------------------------------------- (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) popout

output may be truncated. 'popout' for the full output.

job log

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actions

all output return to Runtime Complexity: TRS Innermost