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Runti Compl Inner Rewri 22807 pair #381904047
details
property
value
status
complete
benchmark
otto06.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n053.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
294.344651937 seconds
cpu usage
1151.2269199
max memory
9.687896064E9
stage attributes
key
value
output-size
72389
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^2)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2).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, 7668 ms] (10) BOUNDS(1, n^2) (11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (12) TRS for Loop Detection (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (14) BEST (15) proven lower bound (16) LowerBoundPropagationProof [FINISHED, 0 ms] (17) BOUNDS(n^1, INF) (18) TRS for Loop Detection ---------------------------------------- (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, greater(ys, zs), smaller(ys, zs)) greater(ys, zs) -> helpc(ge(length(ys), length(zs)), ys, zs) smaller(ys, zs) -> helpc(ge(length(ys), length(zs)), zs, ys) helpc(true, ys, zs) -> ys helpc(false, ys, zs) -> zs helpb(c, l, cons(y, ys), zs) -> cons(y, 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, greater(ys, zs), smaller(ys, zs)) [1] greater(ys, zs) -> helpc(ge(length(ys), length(zs)), ys, zs) [1] smaller(ys, zs) -> helpc(ge(length(ys), length(zs)), zs, ys) [1] helpc(true, ys, zs) -> ys [1] helpc(false, ys, zs) -> zs [1] helpb(c, l, cons(y, ys), zs) -> cons(y, helpa(s(c), l, ys, zs)) [1] Rewrite Strategy: INNERMOST ---------------------------------------- (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (4)
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