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Complexity_ITS 2019-03-21 04.46 pair #429991100
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
n004.star.cs.uiowa.edu
space
WTC
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
11.9425 seconds
cpu usage
15.1601
user time
14.6033
system time
0.556782
max virtual memory
1.8814536E7
max residence set size
229608.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), O(n^2))
output
15.04/10.73 WORST_CASE(Omega(n^2), O(n^2)) 15.04/10.74 proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat 15.04/10.74 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 15.04/10.74 15.04/10.74 15.04/10.74 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^2, max(2, 2 + 12 * Arg_0) * nat(3 *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)). 15.04/10.74 15.04/10.74 (0) CpxIntTrs 15.04/10.74 (1) Koat2 Proof [FINISHED, 9035 ms] 15.04/10.74 (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)) 15.04/10.74 (3) Loat Proof [FINISHED, 1122 ms] 15.04/10.74 (4) BOUNDS(n^2, INF) 15.04/10.74 15.04/10.74 15.04/10.74 ---------------------------------------- 15.04/10.74 15.04/10.74 (0) 15.04/10.74 Obligation: 15.04/10.74 Complexity Int TRS consisting of the following rules: 15.04/10.74 evalnestedLoopstart(A, B, C, D, E, F, G, H) -> Com_1(evalnestedLoopentryin(A, B, C, D, E, F, G, H)) :|: TRUE 15.04/10.74 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 15.04/10.74 evalnestedLoopentryin(A, B, C, D, E, F, G, H) -> Com_1(evalnestedLoopreturnin(A, B, C, D, E, F, G, H)) :|: 0 >= A + 1 15.04/10.74 evalnestedLoopentryin(A, B, C, D, E, F, G, H) -> Com_1(evalnestedLoopreturnin(A, B, C, D, E, F, G, H)) :|: 0 >= B + 1 15.04/10.74 evalnestedLoopentryin(A, B, C, D, E, F, G, H) -> Com_1(evalnestedLoopreturnin(A, B, C, D, E, F, G, H)) :|: 0 >= C + 1 15.04/10.74 evalnestedLoopbb9in(A, B, C, D, E, F, G, H) -> Com_1(evalnestedLoopbb7in(A, B, C, D, 0, D, G, H)) :|: A >= D + 1 15.04/10.74 evalnestedLoopbb9in(A, B, C, D, E, F, G, H) -> Com_1(evalnestedLoopreturnin(A, B, C, D, E, F, G, H)) :|: D >= A 15.04/10.74 evalnestedLoopbb7in(A, B, C, D, E, F, G, H) -> Com_1(evalnestedLoopbb4in(A, B, C, D, E, F, G, H)) :|: B >= E + 1 15.04/10.74 evalnestedLoopbb7in(A, B, C, D, E, F, G, H) -> Com_1(evalnestedLoopbb8in(A, B, C, D, E, F, G, H)) :|: E >= B 15.04/10.74 evalnestedLoopbb4in(A, B, C, D, E, F, G, H) -> Com_1(evalnestedLoopbb6in(A, B, C, D, E, F, E + 1, F)) :|: TRUE 15.04/10.74 evalnestedLoopbb6in(A, B, C, D, E, F, G, H) -> Com_1(evalnestedLoopbb5in(A, B, C, D, E, F, G, H)) :|: C >= H + 1 15.04/10.74 evalnestedLoopbb6in(A, B, C, D, E, F, G, H) -> Com_1(evalnestedLoopbb7in(A, B, C, D, G, H, G, H)) :|: H >= C 15.04/10.74 evalnestedLoopbb5in(A, B, C, D, E, F, G, H) -> Com_1(evalnestedLoopbb6in(A, B, C, D, E, F, G, H + 1)) :|: TRUE 15.04/10.74 evalnestedLoopbb8in(A, B, C, D, E, F, G, H) -> Com_1(evalnestedLoopbb9in(A, B, C, F + 1, E, F, G, H)) :|: TRUE 15.04/10.74 evalnestedLoopreturnin(A, B, C, D, E, F, G, H) -> Com_1(evalnestedLoopstop(A, B, C, D, E, F, G, H)) :|: TRUE 15.04/10.74 15.04/10.74 The start-symbols are:[evalnestedLoopstart_8] 15.04/10.74 15.04/10.74 15.04/10.74 ---------------------------------------- 15.04/10.74 15.04/10.74 (1) Koat2 Proof (FINISHED) 15.04/10.74 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)}) 15.04/10.74 15.04/10.74 15.04/10.74 15.04/10.74 Initial Complexity Problem: 15.04/10.74 15.04/10.74 Start: evalnestedLoopstart 15.04/10.74 15.04/10.74 Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4, Arg_5, Arg_6, Arg_7 15.04/10.74 15.04/10.74 Temp_Vars: 15.04/10.74 15.04/10.74 Locations: evalnestedLoopbb4in, evalnestedLoopbb5in, evalnestedLoopbb6in, evalnestedLoopbb7in, evalnestedLoopbb8in, evalnestedLoopbb9in, evalnestedLoopentryin, evalnestedLoopreturnin, evalnestedLoopstart, evalnestedLoopstop 15.04/10.74 15.04/10.74 Transitions: 15.04/10.74 15.04/10.74 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 15.04/10.74 15.04/10.74 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 15.04/10.74 15.04/10.74 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 15.04/10.74 15.04/10.74 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 15.04/10.74 15.04/10.74 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 15.04/10.74 15.04/10.74 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 15.04/10.74 15.04/10.74 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 15.04/10.74 15.04/10.74 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 15.04/10.74 15.04/10.74 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 15.04/10.74 15.04/10.74 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 15.04/10.74 15.04/10.74 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 15.04/10.74 15.04/10.74 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 15.04/10.74 15.04/10.74 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 15.04/10.74 15.04/10.74 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):|: 15.04/10.74 15.04/10.74 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):|: 15.04/10.74 15.04/10.74 15.04/10.74 15.04/10.74 Timebounds: 15.04/10.74 15.04/10.74 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)} 15.04/10.74 15.04/10.74 9: evalnestedLoopbb4in->evalnestedLoopbb6in: max([1, 1+6*Arg_0])*max([0, 3*Arg_1]) {O(n^2)} 15.04/10.74 15.04/10.74 12: evalnestedLoopbb5in->evalnestedLoopbb6in: max([0, Arg_2]) {O(n)} 15.04/10.74 15.04/10.74 10: evalnestedLoopbb6in->evalnestedLoopbb5in: max([0, 3*Arg_2]) {O(n)} 15.04/10.74 15.04/10.74 11: evalnestedLoopbb6in->evalnestedLoopbb7in: max([1, 1+6*Arg_0])*max([0, 3*Arg_1]) {O(n^2)}
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