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Compl Integ Trans Syste 26843 pair #381744446
details
property
value
status
complete
benchmark
realheapsort.koat
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n106.star.cs.uiowa.edu
space
WTC
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
42.2538809776 seconds
cpu usage
56.885408199
max memory
5.17971968E8
stage attributes
key
value
output-size
172095
starexec-result
WORST_CASE(?, O(n^2))
output
/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.koat /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?, O(n^2)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2). (0) CpxIntTrs (1) Koat Proof [FINISHED, 1300 ms] (2) BOUNDS(1, n^2) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: evalrealheapsortstart(A, B, C, D) -> Com_1(evalrealheapsortentryin(A, B, C, D)) :|: TRUE evalrealheapsortentryin(A, B, C, D) -> Com_1(evalrealheapsortbb6in(A, 1, C, D)) :|: A >= 3 evalrealheapsortentryin(A, B, C, D) -> Com_1(evalrealheapsortreturnin(A, B, C, D)) :|: 2 >= A evalrealheapsortbb6in(A, B, C, D) -> Com_1(evalrealheapsortbb3in(A, B, B, D)) :|: A >= 1 + B evalrealheapsortbb6in(A, B, C, D) -> Com_1(evalrealheapsortbb7in(A, B, C, D)) :|: B >= A evalrealheapsortbb3in(A, B, C, D) -> Com_1(evalrealheapsortbb5in(A, B, C, D)) :|: 0 >= C evalrealheapsortbb3in(A, B, C, D) -> Com_1(evalrealheapsortbb4in(A, B, C, D)) :|: C >= 1 evalrealheapsortbb4in(A, B, C, D) -> Com_1(evalrealheapsortbb2in(A, B, C, D)) :|: C + 1 >= 0 && C + 1 <= 0 evalrealheapsortbb4in(A, B, C, D) -> Com_1(evalrealheapsortbb2in(A, B, C, D)) :|: C >= 0 && E >= 0 && C + 1 >= 2 * E && 2 * E >= C evalrealheapsortbb4in(A, B, C, D) -> Com_1(evalrealheapsortbb2in(A, B, C, D)) :|: 0 >= C + 2 && 0 >= E && 2 * E >= C + 1 && 2 + C >= 2 * E evalrealheapsortbb4in(A, B, C, D) -> Com_1(evalrealheapsortbb5in(A, B, C, D)) :|: C + 1 >= 0 && C + 1 <= 0 evalrealheapsortbb4in(A, B, C, D) -> Com_1(evalrealheapsortbb5in(A, B, C, D)) :|: C >= 0 && E >= 0 && C + 1 >= 2 * E && 2 * E >= C evalrealheapsortbb4in(A, B, C, D) -> Com_1(evalrealheapsortbb5in(A, B, C, D)) :|: 0 >= C + 2 && 0 >= E && 2 * E >= C + 1 && 2 + C >= 2 * E evalrealheapsortbb2in(A, B, C, D) -> Com_1(evalrealheapsortbb3in(A, B, -(1), D)) :|: C + 1 >= 0 && C + 1 <= 0 evalrealheapsortbb2in(A, B, C, D) -> Com_1(evalrealheapsortbb3in(A, B, E - 1, D)) :|: 0 >= 1 && E >= 0 && 0 >= 2 * E && 1 + 2 * E >= 0 && C + 1 >= 0 && C + 1 <= 0 evalrealheapsortbb2in(A, B, C, D) -> Com_1(evalrealheapsortbb3in(A, B, E - 1, D)) :|: 0 >= 1 && 0 >= E && C + 1 >= 0 && C + 1 <= 0 && 2 * E >= C + 1 && 2 + C >= 2 * E evalrealheapsortbb2in(A, B, C, D) -> Com_1(evalrealheapsortbb3in(A, B, -(1), D)) :|: 0 >= 1 && E >= 0 && 0 >= 2 * E && 1 + 2 * E >= 0 && C + 1 >= 0 && C + 1 <= 0 evalrealheapsortbb2in(A, B, C, D) -> Com_1(evalrealheapsortbb3in(A, B, E - 1, D)) :|: 0 >= 1 && F >= 0 && 0 >= 2 * F && 1 + 2 * F >= 0 && E >= 0 && 0 >= 2 * E && 1 + 2 * E >= 0 && C + 1 >= 0 && C + 1 <= 0 evalrealheapsortbb2in(A, B, C, D) -> Com_1(evalrealheapsortbb3in(A, B, E - 1, D)) :|: 0 >= 1 && F >= 0 && 0 >= 2 * F && 1 + 2 * F >= 0 && 0 >= E && C + 1 >= 0 && C + 1 <= 0 && 2 * E >= C + 1 && 2 + C >= 2 * E evalrealheapsortbb2in(A, B, C, D) -> Com_1(evalrealheapsortbb3in(A, B, -(1), D)) :|: 0 >= 1 && 0 >= E && C + 1 >= 0 && C + 1 <= 0 && 2 * E >= C + 1 && 2 + C >= 2 * E evalrealheapsortbb2in(A, B, C, D) -> Com_1(evalrealheapsortbb3in(A, B, E - 1, D)) :|: 0 >= 1 && 0 >= F && E >= 0 && 0 >= 2 * E && 1 + 2 * E >= 0 && C + 1 >= 0 && C + 1 <= 0 && 2 * F >= C + 1 && 2 + C >= 2 * F evalrealheapsortbb2in(A, B, C, D) -> Com_1(evalrealheapsortbb3in(A, B, E - 1, D)) :|: 0 >= 1 && 0 >= F && 0 >= E && C + 1 >= 0 && C + 1 <= 0 && 2 * F >= C + 1 && 2 + C >= 2 * F && 2 * E >= C + 1 && 2 + C >= 2 * E evalrealheapsortbb2in(A, B, C, D) -> Com_1(evalrealheapsortbb3in(A, B, -(1), D)) :|: 0 >= 1 && E >= 0 && 0 >= 2 * E && 1 + 2 * E >= 0 && F >= 0 && 0 >= 2 * F && 1 + 2 * F >= 0 && C + 1 >= 0 && C + 1 <= 0 evalrealheapsortbb2in(A, B, C, D) -> Com_1(evalrealheapsortbb3in(A, B, E - 1, D)) :|: C >= 0 && F >= 0 && C + 1 >= 2 * F && 2 * F >= C && G >= 0 && C + 1 >= 2 * G && 2 * G >= C && E >= 0 && C + 1 >= 2 * E && 2 * E >= C evalrealheapsortbb2in(A, B, C, D) -> Com_1(evalrealheapsortbb3in(A, B, E - 1, D)) :|: C >= 0 && F >= 0 && C + 1 >= 2 * F && 2 * F >= C && G >= 0 && C + 1 >= 2 * G && 2 * G >= C && 0 >= C + 2 && 0 >= E && 2 * E >= C + 1 && 2 + C >= 2 * E evalrealheapsortbb2in(A, B, C, D) -> Com_1(evalrealheapsortbb3in(A, B, -(1), D)) :|: 0 >= 1 && E >= 0 && 0 >= 2 * E && 1 + 2 * E >= 0 && 0 >= F && C + 1 >= 0 && C + 1 <= 0 && 2 * F >= C + 1 && 2 + C >= 2 * F evalrealheapsortbb2in(A, B, C, D) -> Com_1(evalrealheapsortbb3in(A, B, E - 1, D)) :|: C >= 0 && F >= 0 && C + 1 >= 2 * F && 2 * F >= C && 0 >= C + 2 && 0 >= G && E >= 0 && C + 1 >= 2 * E && 2 * E >= C && 2 * G >= C + 1 && 2 + C >= 2 * G evalrealheapsortbb2in(A, B, C, D) -> Com_1(evalrealheapsortbb3in(A, B, E - 1, D)) :|: C >= 0 && F >= 0 && C + 1 >= 2 * F && 2 * F >= C && 0 >= C + 2 && 0 >= G && 0 >= E && 2 * G >= C + 1 && 2 + C >= 2 * G && 2 * E >= C + 1 && 2 + C >= 2 * E evalrealheapsortbb2in(A, B, C, D) -> Com_1(evalrealheapsortbb3in(A, B, -(1), D)) :|: 0 >= 1 && 0 >= E && F >= 0 && 0 >= 2 * F && 1 + 2 * F >= 0 && C + 1 >= 0 && C + 1 <= 0 && 2 * E >= C + 1 && 2 + C >= 2 * E evalrealheapsortbb2in(A, B, C, D) -> Com_1(evalrealheapsortbb3in(A, B, E - 1, D)) :|: 0 >= C + 2 && 0 >= F && C >= 0 && G >= 0 && C + 1 >= 2 * G && 2 * G >= C && E >= 0 && C + 1 >= 2 * E && 2 * E >= C && 2 * F >= C + 1 && 2 + C >= 2 * F evalrealheapsortbb2in(A, B, C, D) -> Com_1(evalrealheapsortbb3in(A, B, E - 1, D)) :|: 0 >= C + 2 && 0 >= F && C >= 0 && G >= 0 && C + 1 >= 2 * G && 2 * G >= C && 0 >= E && 2 * F >= C + 1 && 2 + C >= 2 * F && 2 * E >= C + 1 && 2 + C >= 2 * E evalrealheapsortbb2in(A, B, C, D) -> Com_1(evalrealheapsortbb3in(A, B, -(1), D)) :|: 0 >= 1 && 0 >= E && 0 >= F && C + 1 >= 0 && C + 1 <= 0 && 2 * E >= C + 1 && 2 + C >= 2 * E && 2 * F >= C + 1 && 2 + C >= 2 * F evalrealheapsortbb2in(A, B, C, D) -> Com_1(evalrealheapsortbb3in(A, B, E - 1, D)) :|: 0 >= C + 2 && 0 >= F && 0 >= G && C >= 0 && E >= 0 && C + 1 >= 2 * E && 2 * E >= C && 2 * F >= C + 1 && 2 + C >= 2 * F && 2 * G >= C + 1 && 2 + C >= 2 * G evalrealheapsortbb2in(A, B, C, D) -> Com_1(evalrealheapsortbb3in(A, B, E - 1, D)) :|: 0 >= C + 2 && 0 >= F && 0 >= G && 0 >= E && 2 * F >= C + 1 && 2 + C >= 2 * F && 2 * G >= C + 1 && 2 + C >= 2 * G && 2 * E >= C + 1 && 2 + C >= 2 * E evalrealheapsortbb5in(A, B, C, D) -> Com_1(evalrealheapsortbb6in(A, B + 1, C, D)) :|: TRUE evalrealheapsortbb7in(A, B, C, D) -> Com_1(evalrealheapsortbb18in(A, 0, C, D)) :|: TRUE evalrealheapsortbb18in(A, B, C, D) -> Com_1(evalrealheapsortbb8in(A, B, C, D)) :|: A >= 2 + B evalrealheapsortbb18in(A, B, C, D) -> Com_1(evalrealheapsortreturnin(A, B, C, D)) :|: B + 1 >= A evalrealheapsortbb8in(A, B, C, D) -> Com_1(evalrealheapsortbb16in(A, B, 0, D)) :|: TRUE evalrealheapsortbb16in(A, B, C, D) -> Com_1(evalrealheapsortbb9in(A, B, C, D)) :|: A >= B + 3 + 2 * C evalrealheapsortbb16in(A, B, C, D) -> Com_1(evalrealheapsortbb17in(A, B, C, D)) :|: 2 * C + 2 + B >= A evalrealheapsortbb9in(A, B, C, D) -> Com_1(evalrealheapsortbb11in(A, B, C, D)) :|: A >= 2 * C + 3 + B && A <= 2 * C + 3 + B evalrealheapsortbb9in(A, B, C, D) -> Com_1(evalrealheapsortbb10in(A, B, C, D)) :|: A >= B + 4 + 2 * C evalrealheapsortbb9in(A, B, C, D) -> Com_1(evalrealheapsortbb10in(A, B, C, D)) :|: 2 * C + 2 + B >= A evalrealheapsortbb10in(A, B, C, D) -> Com_1(evalrealheapsortbb11in(A, B, C, D)) :|: TRUE evalrealheapsortbb10in(A, B, C, D) -> Com_1(evalrealheapsortbb12in(A, B, C, D)) :|: TRUE evalrealheapsortbb11in(A, B, C, D) -> Com_1(evalrealheapsortbb13in(A, B, C, 2 * C + 1)) :|: TRUE evalrealheapsortbb12in(A, B, C, D) -> Com_1(evalrealheapsortbb13in(A, B, C, 2 * C + 2)) :|: TRUE evalrealheapsortbb13in(A, B, C, D) -> Com_1(evalrealheapsortbb14in(A, B, C, D)) :|: TRUE evalrealheapsortbb13in(A, B, C, D) -> Com_1(evalrealheapsortbb16in(A, B, A, D)) :|: TRUE evalrealheapsortbb14in(A, B, C, D) -> Com_1(evalrealheapsortbb16in(A, B, D, D)) :|: TRUE evalrealheapsortbb17in(A, B, C, D) -> Com_1(evalrealheapsortbb18in(A, B + 1, C, D)) :|: TRUE evalrealheapsortreturnin(A, B, C, D) -> Com_1(evalrealheapsortstop(A, B, C, D)) :|: TRUE The start-symbols are:[evalrealheapsortstart_4] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 18004615*ar_0 + 2100*ar_0^2 + 21602533) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalrealheapsortstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortentryin(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalrealheapsortentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortbb6in(ar_0, 1, ar_2, ar_3)) [ ar_0 >= 3 ] (Comp: ?, Cost: 1) evalrealheapsortentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortreturnin(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_0 ] (Comp: ?, Cost: 1) evalrealheapsortbb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortbb3in(ar_0, ar_1, ar_1, ar_3)) [ ar_0 >= ar_1 + 1 ] (Comp: ?, Cost: 1) evalrealheapsortbb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortbb7in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 ]
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