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Compl Integ Trans Syste 26843 pair #381744289
details
property
value
status
complete
benchmark
nestedLoop.koat
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n108.star.cs.uiowa.edu
space
WTC
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
10.5689580441 seconds
cpu usage
14.778088589
max memory
3.66092288E8
stage attributes
key
value
output-size
44354
starexec-result
WORST_CASE(Omega(n^2), O(n^2))
output
/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.koat /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^2), O(n^2)) proof of /export/starexec/sandbox/benchmark/theBenchmark.koat # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^2, max(2, 2 + 12 * Arg_0) * nat(3 * Arg_1) + nat(Arg_2) + nat(Arg_0) + nat(3 * Arg_2) + nat(4 * Arg_0) + max(8, 8 + 6 * Arg_0) + max(1, 1 + 6 * Arg_0) * nat(2 * Arg_1)). (0) CpxIntTrs (1) Koat2 Proof [FINISHED, 8883 ms] (2) BOUNDS(1, max(2, 2 + 12 * Arg_0) * nat(3 * Arg_1) + nat(Arg_2) + nat(Arg_0) + nat(3 * Arg_2) + nat(4 * Arg_0) + max(8, 8 + 6 * Arg_0) + max(1, 1 + 6 * Arg_0) * nat(2 * Arg_1)) (3) Loat Proof [FINISHED, 1116 ms] (4) BOUNDS(n^2, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: evalnestedLoopstart(A, B, C, D, E, F, G, H) -> Com_1(evalnestedLoopentryin(A, B, C, D, E, F, G, H)) :|: TRUE evalnestedLoopentryin(A, B, C, D, E, F, G, H) -> Com_1(evalnestedLoopbb9in(A, B, C, 0, E, F, G, H)) :|: A >= 0 && B >= 0 && C >= 0 evalnestedLoopentryin(A, B, C, D, E, F, G, H) -> Com_1(evalnestedLoopreturnin(A, B, C, D, E, F, G, H)) :|: 0 >= A + 1 evalnestedLoopentryin(A, B, C, D, E, F, G, H) -> Com_1(evalnestedLoopreturnin(A, B, C, D, E, F, G, H)) :|: 0 >= B + 1 evalnestedLoopentryin(A, B, C, D, E, F, G, H) -> Com_1(evalnestedLoopreturnin(A, B, C, D, E, F, G, H)) :|: 0 >= C + 1 evalnestedLoopbb9in(A, B, C, D, E, F, G, H) -> Com_1(evalnestedLoopbb7in(A, B, C, D, 0, D, G, H)) :|: A >= D + 1 evalnestedLoopbb9in(A, B, C, D, E, F, G, H) -> Com_1(evalnestedLoopreturnin(A, B, C, D, E, F, G, H)) :|: D >= A evalnestedLoopbb7in(A, B, C, D, E, F, G, H) -> Com_1(evalnestedLoopbb4in(A, B, C, D, E, F, G, H)) :|: B >= E + 1 evalnestedLoopbb7in(A, B, C, D, E, F, G, H) -> Com_1(evalnestedLoopbb8in(A, B, C, D, E, F, G, H)) :|: E >= B evalnestedLoopbb4in(A, B, C, D, E, F, G, H) -> Com_1(evalnestedLoopbb6in(A, B, C, D, E, F, E + 1, F)) :|: TRUE evalnestedLoopbb6in(A, B, C, D, E, F, G, H) -> Com_1(evalnestedLoopbb5in(A, B, C, D, E, F, G, H)) :|: C >= H + 1 evalnestedLoopbb6in(A, B, C, D, E, F, G, H) -> Com_1(evalnestedLoopbb7in(A, B, C, D, G, H, G, H)) :|: H >= C evalnestedLoopbb5in(A, B, C, D, E, F, G, H) -> Com_1(evalnestedLoopbb6in(A, B, C, D, E, F, G, H + 1)) :|: TRUE evalnestedLoopbb8in(A, B, C, D, E, F, G, H) -> Com_1(evalnestedLoopbb9in(A, B, C, F + 1, E, F, G, H)) :|: TRUE evalnestedLoopreturnin(A, B, C, D, E, F, G, H) -> Com_1(evalnestedLoopstop(A, B, C, D, E, F, G, H)) :|: TRUE The start-symbols are:[evalnestedLoopstart_8] ---------------------------------------- (1) Koat2 Proof (FINISHED) YES( ?, 7+max([1, 1+6*Arg_0])*max([0, 2*Arg_1])+2*max([1, 1+6*Arg_0])*max([0, 3*Arg_1])+max([1, 1+6*Arg_0])+max([0, Arg_2])+max([0, Arg_0])+max([0, 3*Arg_2])+max([0, 4*Arg_0]) {O(n^2)}) Initial Complexity Problem: Start: evalnestedLoopstart Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4, Arg_5, Arg_6, Arg_7 Temp_Vars: Locations: evalnestedLoopbb4in, evalnestedLoopbb5in, evalnestedLoopbb6in, evalnestedLoopbb7in, evalnestedLoopbb8in, evalnestedLoopbb9in, evalnestedLoopentryin, evalnestedLoopreturnin, evalnestedLoopstart, evalnestedLoopstop Transitions: evalnestedLoopbb4in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> evalnestedLoopbb6in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_4+1,Arg_5):|:0 <= Arg_5 && 0 <= Arg_4+Arg_5 && 0 <= Arg_3+Arg_5 && Arg_3 <= Arg_5 && 0 <= Arg_2+Arg_5 && 1 <= Arg_1+Arg_5 && 1 <= Arg_0+Arg_5 && 1+Arg_4 <= Arg_1 && 0 <= Arg_4 && 0 <= Arg_3+Arg_4 && 0 <= Arg_2+Arg_4 && 1 <= Arg_1+Arg_4 && 1 <= Arg_0+Arg_4 && 1+Arg_3 <= Arg_0 && 0 <= Arg_3 && 0 <= Arg_2+Arg_3 && 1 <= Arg_1+Arg_3 && 1 <= Arg_0+Arg_3 && 0 <= Arg_2 && 1 <= Arg_1+Arg_2 && 1 <= Arg_0+Arg_2 && 1 <= Arg_1 && 2 <= Arg_0+Arg_1 && 1 <= Arg_0 evalnestedLoopbb5in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> evalnestedLoopbb6in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7+1):|:1+Arg_7 <= Arg_2 && 0 <= Arg_7 && 1 <= Arg_6+Arg_7 && 0 <= Arg_5+Arg_7 && Arg_5 <= Arg_7 && 0 <= Arg_4+Arg_7 && 0 <= Arg_3+Arg_7 && Arg_3 <= Arg_7 && 1 <= Arg_2+Arg_7 && 1 <= Arg_1+Arg_7 && 1 <= Arg_0+Arg_7 && Arg_6 <= 1+Arg_4 && Arg_6 <= Arg_1 && 1 <= Arg_6 && 1 <= Arg_5+Arg_6 && 1 <= Arg_4+Arg_6 && 1+Arg_4 <= Arg_6 && 1 <= Arg_3+Arg_6 && 2 <= Arg_2+Arg_6 && 2 <= Arg_1+Arg_6 && 2 <= Arg_0+Arg_6 && 1+Arg_5 <= Arg_2 && 0 <= Arg_5 && 0 <= Arg_4+Arg_5 && 0 <= Arg_3+Arg_5 && Arg_3 <= Arg_5 && 1 <= Arg_2+Arg_5 && 1 <= Arg_1+Arg_5 && 1 <= Arg_0+Arg_5 && 1+Arg_4 <= Arg_1 && 0 <= Arg_4 && 0 <= Arg_3+Arg_4 && 1 <= Arg_2+Arg_4 && 1 <= Arg_1+Arg_4 && 1 <= Arg_0+Arg_4 && 1+Arg_3 <= Arg_2 && 1+Arg_3 <= Arg_0 && 0 <= Arg_3 && 1 <= Arg_2+Arg_3 && 1 <= Arg_1+Arg_3 && 1 <= Arg_0+Arg_3 && 1 <= Arg_2 && 2 <= Arg_1+Arg_2 && 2 <= Arg_0+Arg_2 && 1 <= Arg_1 && 2 <= Arg_0+Arg_1 && 1 <= Arg_0 evalnestedLoopbb6in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> evalnestedLoopbb5in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|:0 <= Arg_7 && 1 <= Arg_6+Arg_7 && 0 <= Arg_5+Arg_7 && Arg_5 <= Arg_7 && 0 <= Arg_4+Arg_7 && 0 <= Arg_3+Arg_7 && Arg_3 <= Arg_7 && 0 <= Arg_2+Arg_7 && 1 <= Arg_1+Arg_7 && 1 <= Arg_0+Arg_7 && Arg_6 <= 1+Arg_4 && Arg_6 <= Arg_1 && 1 <= Arg_6 && 1 <= Arg_5+Arg_6 && 1 <= Arg_4+Arg_6 && 1+Arg_4 <= Arg_6 && 1 <= Arg_3+Arg_6 && 1 <= Arg_2+Arg_6 && 2 <= Arg_1+Arg_6 && 2 <= Arg_0+Arg_6 && 0 <= Arg_5 && 0 <= Arg_4+Arg_5 && 0 <= Arg_3+Arg_5 && Arg_3 <= Arg_5 && 0 <= Arg_2+Arg_5 && 1 <= Arg_1+Arg_5 && 1 <= Arg_0+Arg_5 && 1+Arg_4 <= Arg_1 && 0 <= Arg_4 && 0 <= Arg_3+Arg_4 && 0 <= Arg_2+Arg_4 && 1 <= Arg_1+Arg_4 && 1 <= Arg_0+Arg_4 && 1+Arg_3 <= Arg_0 && 0 <= Arg_3 && 0 <= Arg_2+Arg_3 && 1 <= Arg_1+Arg_3 && 1 <= Arg_0+Arg_3 && 0 <= Arg_2 && 1 <= Arg_1+Arg_2 && 1 <= Arg_0+Arg_2 && 1 <= Arg_1 && 2 <= Arg_0+Arg_1 && 1 <= Arg_0 && Arg_7+1 <= Arg_2 evalnestedLoopbb6in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> evalnestedLoopbb7in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_6,Arg_7,Arg_6,Arg_7):|:0 <= Arg_7 && 1 <= Arg_6+Arg_7 && 0 <= Arg_5+Arg_7 && Arg_5 <= Arg_7 && 0 <= Arg_4+Arg_7 && 0 <= Arg_3+Arg_7 && Arg_3 <= Arg_7 && 0 <= Arg_2+Arg_7 && 1 <= Arg_1+Arg_7 && 1 <= Arg_0+Arg_7 && Arg_6 <= 1+Arg_4 && Arg_6 <= Arg_1 && 1 <= Arg_6 && 1 <= Arg_5+Arg_6 && 1 <= Arg_4+Arg_6 && 1+Arg_4 <= Arg_6 && 1 <= Arg_3+Arg_6 && 1 <= Arg_2+Arg_6 && 2 <= Arg_1+Arg_6 && 2 <= Arg_0+Arg_6 && 0 <= Arg_5 && 0 <= Arg_4+Arg_5 && 0 <= Arg_3+Arg_5 && Arg_3 <= Arg_5 && 0 <= Arg_2+Arg_5 && 1 <= Arg_1+Arg_5 && 1 <= Arg_0+Arg_5 && 1+Arg_4 <= Arg_1 && 0 <= Arg_4 && 0 <= Arg_3+Arg_4 && 0 <= Arg_2+Arg_4 && 1 <= Arg_1+Arg_4 && 1 <= Arg_0+Arg_4 && 1+Arg_3 <= Arg_0 && 0 <= Arg_3 && 0 <= Arg_2+Arg_3 && 1 <= Arg_1+Arg_3 && 1 <= Arg_0+Arg_3 && 0 <= Arg_2 && 1 <= Arg_1+Arg_2 && 1 <= Arg_0+Arg_2 && 1 <= Arg_1 && 2 <= Arg_0+Arg_1 && 1 <= Arg_0 && Arg_2 <= Arg_7 evalnestedLoopbb7in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> evalnestedLoopbb4in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|:0 <= Arg_5 && 0 <= Arg_4+Arg_5 && 0 <= Arg_3+Arg_5 && Arg_3 <= Arg_5 && 0 <= Arg_2+Arg_5 && 0 <= Arg_1+Arg_5 && 1 <= Arg_0+Arg_5 && Arg_4 <= Arg_1 && 0 <= Arg_4 && 0 <= Arg_3+Arg_4 && 0 <= Arg_2+Arg_4 && 0 <= Arg_1+Arg_4 && 1 <= Arg_0+Arg_4 && 1+Arg_3 <= Arg_0 && 0 <= Arg_3 && 0 <= Arg_2+Arg_3 && 0 <= Arg_1+Arg_3 && 1 <= Arg_0+Arg_3 && 0 <= Arg_2 && 0 <= Arg_1+Arg_2 && 1 <= Arg_0+Arg_2 && 0 <= Arg_1 && 1 <= Arg_0+Arg_1 && 1 <= Arg_0 && Arg_4+1 <= Arg_1 evalnestedLoopbb7in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> evalnestedLoopbb8in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|:0 <= Arg_5 && 0 <= Arg_4+Arg_5 && 0 <= Arg_3+Arg_5 && Arg_3 <= Arg_5 && 0 <= Arg_2+Arg_5 && 0 <= Arg_1+Arg_5 && 1 <= Arg_0+Arg_5 && Arg_4 <= Arg_1 && 0 <= Arg_4 && 0 <= Arg_3+Arg_4 && 0 <= Arg_2+Arg_4 && 0 <= Arg_1+Arg_4 && 1 <= Arg_0+Arg_4 && 1+Arg_3 <= Arg_0 && 0 <= Arg_3 && 0 <= Arg_2+Arg_3 && 0 <= Arg_1+Arg_3 && 1 <= Arg_0+Arg_3 && 0 <= Arg_2 && 0 <= Arg_1+Arg_2 && 1 <= Arg_0+Arg_2 && 0 <= Arg_1 && 1 <= Arg_0+Arg_1 && 1 <= Arg_0 && Arg_1 <= Arg_4 evalnestedLoopbb8in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> evalnestedLoopbb9in(Arg_0,Arg_1,Arg_2,Arg_5+1,Arg_4,Arg_5,Arg_6,Arg_7):|:0 <= Arg_5 && 0 <= Arg_4+Arg_5 && 0 <= Arg_3+Arg_5 && Arg_3 <= Arg_5 && 0 <= Arg_2+Arg_5 && 0 <= Arg_1+Arg_5 && 1 <= Arg_0+Arg_5 && Arg_4 <= Arg_1 && 0 <= Arg_4 && 0 <= Arg_3+Arg_4 && 0 <= Arg_2+Arg_4 && 0 <= Arg_1+Arg_4 && Arg_1 <= Arg_4 && 1 <= Arg_0+Arg_4 && 1+Arg_3 <= Arg_0 && 0 <= Arg_3 && 0 <= Arg_2+Arg_3 && 0 <= Arg_1+Arg_3 && 1 <= Arg_0+Arg_3 && 0 <= Arg_2 && 0 <= Arg_1+Arg_2 && 1 <= Arg_0+Arg_2 && 0 <= Arg_1 && 1 <= Arg_0+Arg_1 && 1 <= Arg_0 evalnestedLoopbb9in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> evalnestedLoopbb7in(Arg_0,Arg_1,Arg_2,Arg_3,0,Arg_3,Arg_6,Arg_7):|:0 <= Arg_3 && 0 <= Arg_2+Arg_3 && 0 <= Arg_1+Arg_3 && 0 <= Arg_0+Arg_3 && 0 <= Arg_2 && 0 <= Arg_1+Arg_2 && 0 <= Arg_0+Arg_2 && 0 <= Arg_1 && 0 <= Arg_0+Arg_1 && 0 <= Arg_0 && Arg_3+1 <= Arg_0 evalnestedLoopbb9in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> evalnestedLoopreturnin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|:0 <= Arg_3 && 0 <= Arg_2+Arg_3 && 0 <= Arg_1+Arg_3 && 0 <= Arg_0+Arg_3 && 0 <= Arg_2 && 0 <= Arg_1+Arg_2 && 0 <= Arg_0+Arg_2 && 0 <= Arg_1 && 0 <= Arg_0+Arg_1 && 0 <= Arg_0 && Arg_0 <= Arg_3 evalnestedLoopentryin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> evalnestedLoopbb9in(Arg_0,Arg_1,Arg_2,0,Arg_4,Arg_5,Arg_6,Arg_7):|:0 <= Arg_0 && 0 <= Arg_1 && 0 <= Arg_2 evalnestedLoopentryin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> evalnestedLoopreturnin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|:Arg_0+1 <= 0 evalnestedLoopentryin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> evalnestedLoopreturnin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|:Arg_1+1 <= 0 evalnestedLoopentryin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> evalnestedLoopreturnin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|:Arg_2+1 <= 0 evalnestedLoopreturnin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> evalnestedLoopstop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|: evalnestedLoopstart(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> evalnestedLoopentryin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|: Timebounds: Overall timebound: 7+max([1, 1+6*Arg_0])*max([0, 2*Arg_1])+2*max([1, 1+6*Arg_0])*max([0, 3*Arg_1])+max([1, 1+6*Arg_0])+max([0, Arg_2])+max([0, Arg_0])+max([0, 3*Arg_2])+max([0, 4*Arg_0]) {O(n^2)} 9: evalnestedLoopbb4in->evalnestedLoopbb6in: max([1, 1+6*Arg_0])*max([0, 3*Arg_1]) {O(n^2)}
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