/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.koat /export/starexec/sandbox/output/output_files


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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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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]


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(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)}

  12: evalnestedLoopbb5in->evalnestedLoopbb6in: max([0, Arg_2]) {O(n)}

  10: evalnestedLoopbb6in->evalnestedLoopbb5in: max([0, 3*Arg_2]) {O(n)}

  11: evalnestedLoopbb6in->evalnestedLoopbb7in: max([1, 1+6*Arg_0])*max([0, 3*Arg_1]) {O(n^2)}

  7: evalnestedLoopbb7in->evalnestedLoopbb4in: max([1, 1+6*Arg_0])*max([0, 2*Arg_1]) {O(n^2)}

  8: evalnestedLoopbb7in->evalnestedLoopbb8in: max([0, 4*Arg_0]) {O(n)}

  13: evalnestedLoopbb8in->evalnestedLoopbb9in: max([0, Arg_0]) {O(n)}

  5: evalnestedLoopbb9in->evalnestedLoopbb7in: max([1, 1+6*Arg_0]) {O(n)}

  6: evalnestedLoopbb9in->evalnestedLoopreturnin: 1 {O(1)}

  1: evalnestedLoopentryin->evalnestedLoopbb9in: 1 {O(1)}

  2: evalnestedLoopentryin->evalnestedLoopreturnin: 1 {O(1)}

  3: evalnestedLoopentryin->evalnestedLoopreturnin: 1 {O(1)}

  4: evalnestedLoopentryin->evalnestedLoopreturnin: 1 {O(1)}

  14: evalnestedLoopreturnin->evalnestedLoopstop: 1 {O(1)}

  0: evalnestedLoopstart->evalnestedLoopentryin: 1 {O(1)}



Costbounds:

  Overall costbound: 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)}

  12: evalnestedLoopbb5in->evalnestedLoopbb6in: max([0, Arg_2]) {O(n)}

  10: evalnestedLoopbb6in->evalnestedLoopbb5in: max([0, 3*Arg_2]) {O(n)}

  11: evalnestedLoopbb6in->evalnestedLoopbb7in: max([1, 1+6*Arg_0])*max([0, 3*Arg_1]) {O(n^2)}

  7: evalnestedLoopbb7in->evalnestedLoopbb4in: max([1, 1+6*Arg_0])*max([0, 2*Arg_1]) {O(n^2)}

  8: evalnestedLoopbb7in->evalnestedLoopbb8in: max([0, 4*Arg_0]) {O(n)}

  13: evalnestedLoopbb8in->evalnestedLoopbb9in: max([0, Arg_0]) {O(n)}

  5: evalnestedLoopbb9in->evalnestedLoopbb7in: max([1, 1+6*Arg_0]) {O(n)}

  6: evalnestedLoopbb9in->evalnestedLoopreturnin: 1 {O(1)}

  1: evalnestedLoopentryin->evalnestedLoopbb9in: 1 {O(1)}

  2: evalnestedLoopentryin->evalnestedLoopreturnin: 1 {O(1)}

  3: evalnestedLoopentryin->evalnestedLoopreturnin: 1 {O(1)}

  4: evalnestedLoopentryin->evalnestedLoopreturnin: 1 {O(1)}

  14: evalnestedLoopreturnin->evalnestedLoopstop: 1 {O(1)}

  0: evalnestedLoopstart->evalnestedLoopentryin: 1 {O(1)}



Sizebounds:

`Lower:

  9: evalnestedLoopbb4in->evalnestedLoopbb6in, Arg_0: 1 {O(1)}

  9: evalnestedLoopbb4in->evalnestedLoopbb6in, Arg_1: 1 {O(1)}

  9: evalnestedLoopbb4in->evalnestedLoopbb6in, Arg_2: 0 {O(1)}

  9: evalnestedLoopbb4in->evalnestedLoopbb6in, Arg_3: 0 {O(1)}

  9: evalnestedLoopbb4in->evalnestedLoopbb6in, Arg_4: 0 {O(1)}

  9: evalnestedLoopbb4in->evalnestedLoopbb6in, Arg_5: 0 {O(1)}

  9: evalnestedLoopbb4in->evalnestedLoopbb6in, Arg_6: 1 {O(1)}

  9: evalnestedLoopbb4in->evalnestedLoopbb6in, Arg_7: 0 {O(1)}

  12: evalnestedLoopbb5in->evalnestedLoopbb6in, Arg_0: 1 {O(1)}

  12: evalnestedLoopbb5in->evalnestedLoopbb6in, Arg_1: 1 {O(1)}

  12: evalnestedLoopbb5in->evalnestedLoopbb6in, Arg_2: 1 {O(1)}

  12: evalnestedLoopbb5in->evalnestedLoopbb6in, Arg_3: 0 {O(1)}

  12: evalnestedLoopbb5in->evalnestedLoopbb6in, Arg_4: 0 {O(1)}

  12: evalnestedLoopbb5in->evalnestedLoopbb6in, Arg_5: 0 {O(1)}

  12: evalnestedLoopbb5in->evalnestedLoopbb6in, Arg_6: 1 {O(1)}

  12: evalnestedLoopbb5in->evalnestedLoopbb6in, Arg_7: 1 {O(1)}

  10: evalnestedLoopbb6in->evalnestedLoopbb5in, Arg_0: 1 {O(1)}

  10: evalnestedLoopbb6in->evalnestedLoopbb5in, Arg_1: 1 {O(1)}

  10: evalnestedLoopbb6in->evalnestedLoopbb5in, Arg_2: 1 {O(1)}

  10: evalnestedLoopbb6in->evalnestedLoopbb5in, Arg_3: 0 {O(1)}

  10: evalnestedLoopbb6in->evalnestedLoopbb5in, Arg_4: 0 {O(1)}

  10: evalnestedLoopbb6in->evalnestedLoopbb5in, Arg_5: 0 {O(1)}

  10: evalnestedLoopbb6in->evalnestedLoopbb5in, Arg_6: 1 {O(1)}

  10: evalnestedLoopbb6in->evalnestedLoopbb5in, Arg_7: 0 {O(1)}

  11: evalnestedLoopbb6in->evalnestedLoopbb7in, Arg_0: 1 {O(1)}

  11: evalnestedLoopbb6in->evalnestedLoopbb7in, Arg_1: 1 {O(1)}

  11: evalnestedLoopbb6in->evalnestedLoopbb7in, Arg_2: 0 {O(1)}

  11: evalnestedLoopbb6in->evalnestedLoopbb7in, Arg_3: 0 {O(1)}

  11: evalnestedLoopbb6in->evalnestedLoopbb7in, Arg_4: 1 {O(1)}

  11: evalnestedLoopbb6in->evalnestedLoopbb7in, Arg_5: 0 {O(1)}

  11: evalnestedLoopbb6in->evalnestedLoopbb7in, Arg_6: 1 {O(1)}

  11: evalnestedLoopbb6in->evalnestedLoopbb7in, Arg_7: 0 {O(1)}

  7: evalnestedLoopbb7in->evalnestedLoopbb4in, Arg_0: 1 {O(1)}

  7: evalnestedLoopbb7in->evalnestedLoopbb4in, Arg_1: 1 {O(1)}

  7: evalnestedLoopbb7in->evalnestedLoopbb4in, Arg_2: 0 {O(1)}

  7: evalnestedLoopbb7in->evalnestedLoopbb4in, Arg_3: 0 {O(1)}

  7: evalnestedLoopbb7in->evalnestedLoopbb4in, Arg_4: 0 {O(1)}

  7: evalnestedLoopbb7in->evalnestedLoopbb4in, Arg_5: 0 {O(1)}

  7: evalnestedLoopbb7in->evalnestedLoopbb4in, Arg_6: min([1, Arg_6]) {O(n)}

  7: evalnestedLoopbb7in->evalnestedLoopbb4in, Arg_7: min([0, Arg_7]) {O(n)}

  8: evalnestedLoopbb7in->evalnestedLoopbb8in, Arg_0: 1 {O(1)}

  8: evalnestedLoopbb7in->evalnestedLoopbb8in, Arg_1: 0 {O(1)}

  8: evalnestedLoopbb7in->evalnestedLoopbb8in, Arg_2: 0 {O(1)}

  8: evalnestedLoopbb7in->evalnestedLoopbb8in, Arg_3: 0 {O(1)}

  8: evalnestedLoopbb7in->evalnestedLoopbb8in, Arg_4: 0 {O(1)}

  8: evalnestedLoopbb7in->evalnestedLoopbb8in, Arg_5: 0 {O(1)}

  8: evalnestedLoopbb7in->evalnestedLoopbb8in, Arg_6: min([1, Arg_6]) {O(n)}

  8: evalnestedLoopbb7in->evalnestedLoopbb8in, Arg_7: min([0, Arg_7]) {O(n)}

  13: evalnestedLoopbb8in->evalnestedLoopbb9in, Arg_0: 1 {O(1)}

  13: evalnestedLoopbb8in->evalnestedLoopbb9in, Arg_1: 0 {O(1)}

  13: evalnestedLoopbb8in->evalnestedLoopbb9in, Arg_2: 0 {O(1)}

  13: evalnestedLoopbb8in->evalnestedLoopbb9in, Arg_3: 1 {O(1)}

  13: evalnestedLoopbb8in->evalnestedLoopbb9in, Arg_4: 0 {O(1)}

  13: evalnestedLoopbb8in->evalnestedLoopbb9in, Arg_5: 0 {O(1)}

  13: evalnestedLoopbb8in->evalnestedLoopbb9in, Arg_6: min([1, Arg_6]) {O(n)}

  13: evalnestedLoopbb8in->evalnestedLoopbb9in, Arg_7: min([0, Arg_7]) {O(n)}

  5: evalnestedLoopbb9in->evalnestedLoopbb7in, Arg_0: 1 {O(1)}

  5: evalnestedLoopbb9in->evalnestedLoopbb7in, Arg_1: 0 {O(1)}

  5: evalnestedLoopbb9in->evalnestedLoopbb7in, Arg_2: 0 {O(1)}

  5: evalnestedLoopbb9in->evalnestedLoopbb7in, Arg_3: 0 {O(1)}

  5: evalnestedLoopbb9in->evalnestedLoopbb7in, Arg_4: 0 {O(1)}

  5: evalnestedLoopbb9in->evalnestedLoopbb7in, Arg_5: 0 {O(1)}

  5: evalnestedLoopbb9in->evalnestedLoopbb7in, Arg_6: min([1, Arg_6]) {O(n)}

  5: evalnestedLoopbb9in->evalnestedLoopbb7in, Arg_7: min([0, Arg_7]) {O(n)}

  6: evalnestedLoopbb9in->evalnestedLoopreturnin, Arg_0: 0 {O(1)}

  6: evalnestedLoopbb9in->evalnestedLoopreturnin, Arg_1: 0 {O(1)}

  6: evalnestedLoopbb9in->evalnestedLoopreturnin, Arg_2: 0 {O(1)}

  6: evalnestedLoopbb9in->evalnestedLoopreturnin, Arg_3: 0 {O(1)}

  6: evalnestedLoopbb9in->evalnestedLoopreturnin, Arg_4: min([0, Arg_4]) {O(n)}

  6: evalnestedLoopbb9in->evalnestedLoopreturnin, Arg_5: min([0, Arg_5]) {O(n)}

  6: evalnestedLoopbb9in->evalnestedLoopreturnin, Arg_6: min([1, Arg_6]) {O(n)}

  6: evalnestedLoopbb9in->evalnestedLoopreturnin, Arg_7: min([0, Arg_7]) {O(n)}

  1: evalnestedLoopentryin->evalnestedLoopbb9in, Arg_0: 0 {O(1)}

  1: evalnestedLoopentryin->evalnestedLoopbb9in, Arg_1: 0 {O(1)}

  1: evalnestedLoopentryin->evalnestedLoopbb9in, Arg_2: 0 {O(1)}

  1: evalnestedLoopentryin->evalnestedLoopbb9in, Arg_3: 0 {O(1)}

  1: evalnestedLoopentryin->evalnestedLoopbb9in, Arg_4: Arg_4 {O(n)}

  1: evalnestedLoopentryin->evalnestedLoopbb9in, Arg_5: Arg_5 {O(n)}

  1: evalnestedLoopentryin->evalnestedLoopbb9in, Arg_6: Arg_6 {O(n)}

  1: evalnestedLoopentryin->evalnestedLoopbb9in, Arg_7: Arg_7 {O(n)}

  2: evalnestedLoopentryin->evalnestedLoopreturnin, Arg_0: Arg_0 {O(n)}

  2: evalnestedLoopentryin->evalnestedLoopreturnin, Arg_1: Arg_1 {O(n)}

  2: evalnestedLoopentryin->evalnestedLoopreturnin, Arg_2: Arg_2 {O(n)}

  2: evalnestedLoopentryin->evalnestedLoopreturnin, Arg_3: Arg_3 {O(n)}

  2: evalnestedLoopentryin->evalnestedLoopreturnin, Arg_4: Arg_4 {O(n)}

  2: evalnestedLoopentryin->evalnestedLoopreturnin, Arg_5: Arg_5 {O(n)}

  2: evalnestedLoopentryin->evalnestedLoopreturnin, Arg_6: Arg_6 {O(n)}

  2: evalnestedLoopentryin->evalnestedLoopreturnin, Arg_7: Arg_7 {O(n)}

  3: evalnestedLoopentryin->evalnestedLoopreturnin, Arg_0: Arg_0 {O(n)}

  3: evalnestedLoopentryin->evalnestedLoopreturnin, Arg_1: Arg_1 {O(n)}

  3: evalnestedLoopentryin->evalnestedLoopreturnin, Arg_2: Arg_2 {O(n)}

  3: evalnestedLoopentryin->evalnestedLoopreturnin, Arg_3: Arg_3 {O(n)}

  3: evalnestedLoopentryin->evalnestedLoopreturnin, Arg_4: Arg_4 {O(n)}

  3: evalnestedLoopentryin->evalnestedLoopreturnin, Arg_5: Arg_5 {O(n)}

  3: evalnestedLoopentryin->evalnestedLoopreturnin, Arg_6: Arg_6 {O(n)}

  3: evalnestedLoopentryin->evalnestedLoopreturnin, Arg_7: Arg_7 {O(n)}

  4: evalnestedLoopentryin->evalnestedLoopreturnin, Arg_0: Arg_0 {O(n)}

  4: evalnestedLoopentryin->evalnestedLoopreturnin, Arg_1: Arg_1 {O(n)}

  4: evalnestedLoopentryin->evalnestedLoopreturnin, Arg_2: Arg_2 {O(n)}

  4: evalnestedLoopentryin->evalnestedLoopreturnin, Arg_3: Arg_3 {O(n)}

  4: evalnestedLoopentryin->evalnestedLoopreturnin, Arg_4: Arg_4 {O(n)}

  4: evalnestedLoopentryin->evalnestedLoopreturnin, Arg_5: Arg_5 {O(n)}

  4: evalnestedLoopentryin->evalnestedLoopreturnin, Arg_6: Arg_6 {O(n)}

  4: evalnestedLoopentryin->evalnestedLoopreturnin, Arg_7: Arg_7 {O(n)}

  14: evalnestedLoopreturnin->evalnestedLoopstop, Arg_0: min([0, Arg_0]) {O(n)}

  14: evalnestedLoopreturnin->evalnestedLoopstop, Arg_1: min([0, Arg_1]) {O(n)}

  14: evalnestedLoopreturnin->evalnestedLoopstop, Arg_2: min([0, Arg_2]) {O(n)}

  14: evalnestedLoopreturnin->evalnestedLoopstop, Arg_3: min([0, Arg_3]) {O(n)}

  14: evalnestedLoopreturnin->evalnestedLoopstop, Arg_4: min([0, Arg_4]) {O(n)}

  14: evalnestedLoopreturnin->evalnestedLoopstop, Arg_5: min([0, Arg_5]) {O(n)}

  14: evalnestedLoopreturnin->evalnestedLoopstop, Arg_6: min([1, Arg_6]) {O(n)}

  14: evalnestedLoopreturnin->evalnestedLoopstop, Arg_7: min([0, Arg_7]) {O(n)}

  0: evalnestedLoopstart->evalnestedLoopentryin, Arg_0: Arg_0 {O(n)}

  0: evalnestedLoopstart->evalnestedLoopentryin, Arg_1: Arg_1 {O(n)}

  0: evalnestedLoopstart->evalnestedLoopentryin, Arg_2: Arg_2 {O(n)}

  0: evalnestedLoopstart->evalnestedLoopentryin, Arg_3: Arg_3 {O(n)}

  0: evalnestedLoopstart->evalnestedLoopentryin, Arg_4: Arg_4 {O(n)}

  0: evalnestedLoopstart->evalnestedLoopentryin, Arg_5: Arg_5 {O(n)}

  0: evalnestedLoopstart->evalnestedLoopentryin, Arg_6: Arg_6 {O(n)}

  0: evalnestedLoopstart->evalnestedLoopentryin, Arg_7: Arg_7 {O(n)}

`Upper:

  9: evalnestedLoopbb4in->evalnestedLoopbb6in, Arg_0: Arg_0 {O(n)}

  9: evalnestedLoopbb4in->evalnestedLoopbb6in, Arg_1: Arg_1 {O(n)}

  9: evalnestedLoopbb4in->evalnestedLoopbb6in, Arg_2: Arg_2 {O(n)}

  9: evalnestedLoopbb4in->evalnestedLoopbb6in, Arg_3: max([0, max([0, Arg_0])+max([0, Arg_2])]) {O(n)}

  9: evalnestedLoopbb4in->evalnestedLoopbb6in, Arg_4: max([1, 1+6*Arg_0])*max([0, 3*Arg_1]) {O(n^2)}

  9: evalnestedLoopbb4in->evalnestedLoopbb6in, Arg_5: max([0, Arg_0])+max([0, Arg_2]) {O(n)}

  9: evalnestedLoopbb4in->evalnestedLoopbb6in, Arg_6: max([1, 1+6*Arg_0])*max([0, 3*Arg_1]) {O(n^2)}

  9: evalnestedLoopbb4in->evalnestedLoopbb6in, Arg_7: max([0, Arg_0])+max([0, Arg_2]) {O(n)}

  12: evalnestedLoopbb5in->evalnestedLoopbb6in, Arg_0: Arg_0 {O(n)}

  12: evalnestedLoopbb5in->evalnestedLoopbb6in, Arg_1: Arg_1 {O(n)}

  12: evalnestedLoopbb5in->evalnestedLoopbb6in, Arg_2: Arg_2 {O(n)}

  12: evalnestedLoopbb5in->evalnestedLoopbb6in, Arg_3: max([0, max([0, Arg_0])+max([0, Arg_2])]) {O(n)}

  12: evalnestedLoopbb5in->evalnestedLoopbb6in, Arg_4: max([1, 1+6*Arg_0])*max([0, 3*Arg_1]) {O(n^2)}

  12: evalnestedLoopbb5in->evalnestedLoopbb6in, Arg_5: max([0, Arg_0])+max([0, Arg_2]) {O(n)}

  12: evalnestedLoopbb5in->evalnestedLoopbb6in, Arg_6: max([1, 1+6*Arg_0])*max([0, 3*Arg_1]) {O(n^2)}

  12: evalnestedLoopbb5in->evalnestedLoopbb6in, Arg_7: max([0, Arg_0])+max([0, Arg_2]) {O(n)}

  10: evalnestedLoopbb6in->evalnestedLoopbb5in, Arg_0: Arg_0 {O(n)}

  10: evalnestedLoopbb6in->evalnestedLoopbb5in, Arg_1: Arg_1 {O(n)}

  10: evalnestedLoopbb6in->evalnestedLoopbb5in, Arg_2: Arg_2 {O(n)}

  10: evalnestedLoopbb6in->evalnestedLoopbb5in, Arg_3: max([0, max([0, Arg_0])+max([0, Arg_2])]) {O(n)}

  10: evalnestedLoopbb6in->evalnestedLoopbb5in, Arg_4: max([1, 1+6*Arg_0])*max([0, 3*Arg_1]) {O(n^2)}

  10: evalnestedLoopbb6in->evalnestedLoopbb5in, Arg_5: max([0, Arg_0])+max([0, Arg_2]) {O(n)}

  10: evalnestedLoopbb6in->evalnestedLoopbb5in, Arg_6: max([1, 1+6*Arg_0])*max([0, 3*Arg_1]) {O(n^2)}

  10: evalnestedLoopbb6in->evalnestedLoopbb5in, Arg_7: max([0, Arg_0])+max([0, Arg_2]) {O(n)}

  11: evalnestedLoopbb6in->evalnestedLoopbb7in, Arg_0: Arg_0 {O(n)}

  11: evalnestedLoopbb6in->evalnestedLoopbb7in, Arg_1: Arg_1 {O(n)}

  11: evalnestedLoopbb6in->evalnestedLoopbb7in, Arg_2: Arg_2 {O(n)}

  11: evalnestedLoopbb6in->evalnestedLoopbb7in, Arg_3: max([0, max([0, Arg_0])+max([0, Arg_2])]) {O(n)}

  11: evalnestedLoopbb6in->evalnestedLoopbb7in, Arg_4: max([1, 1+6*Arg_0])*max([0, 3*Arg_1]) {O(n^2)}

  11: evalnestedLoopbb6in->evalnestedLoopbb7in, Arg_5: max([0, Arg_0])+max([0, Arg_2]) {O(n)}

  11: evalnestedLoopbb6in->evalnestedLoopbb7in, Arg_6: max([1, 1+6*Arg_0])*max([0, 3*Arg_1]) {O(n^2)}

  11: evalnestedLoopbb6in->evalnestedLoopbb7in, Arg_7: max([0, Arg_0])+max([0, Arg_2]) {O(n)}

  7: evalnestedLoopbb7in->evalnestedLoopbb4in, Arg_0: Arg_0 {O(n)}

  7: evalnestedLoopbb7in->evalnestedLoopbb4in, Arg_1: Arg_1 {O(n)}

  7: evalnestedLoopbb7in->evalnestedLoopbb4in, Arg_2: Arg_2 {O(n)}

  7: evalnestedLoopbb7in->evalnestedLoopbb4in, Arg_3: max([0, max([0, Arg_0])+max([0, Arg_2])]) {O(n)}

  7: evalnestedLoopbb7in->evalnestedLoopbb4in, Arg_4: max([1, 1+6*Arg_0])*max([0, 3*Arg_1]) {O(n^2)}

  7: evalnestedLoopbb7in->evalnestedLoopbb4in, Arg_5: max([0, Arg_0])+max([0, Arg_2]) {O(n)}

  7: evalnestedLoopbb7in->evalnestedLoopbb4in, Arg_6: max([Arg_6, max([1, 1+6*Arg_0])*max([0, 3*Arg_1])]) {O(n^2)}

  7: evalnestedLoopbb7in->evalnestedLoopbb4in, Arg_7: max([Arg_7, max([0, Arg_0])+max([0, Arg_2])]) {O(n)}

  8: evalnestedLoopbb7in->evalnestedLoopbb8in, Arg_0: Arg_0 {O(n)}

  8: evalnestedLoopbb7in->evalnestedLoopbb8in, Arg_1: Arg_1 {O(n)}

  8: evalnestedLoopbb7in->evalnestedLoopbb8in, Arg_2: Arg_2 {O(n)}

  8: evalnestedLoopbb7in->evalnestedLoopbb8in, Arg_3: max([0, max([0, Arg_0])+max([0, Arg_2])]) {O(n)}

  8: evalnestedLoopbb7in->evalnestedLoopbb8in, Arg_4: max([0, max([1, 1+6*Arg_0])*max([0, 3*Arg_1])]) {O(n^2)}

  8: evalnestedLoopbb7in->evalnestedLoopbb8in, Arg_5: max([0, Arg_0])+max([0, Arg_2]) {O(n)}

  8: evalnestedLoopbb7in->evalnestedLoopbb8in, Arg_6: max([Arg_6, max([1, 1+6*Arg_0])*max([0, 3*Arg_1])]) {O(n^2)}

  8: evalnestedLoopbb7in->evalnestedLoopbb8in, Arg_7: max([Arg_7, max([0, Arg_0])+max([0, Arg_2])]) {O(n)}

  13: evalnestedLoopbb8in->evalnestedLoopbb9in, Arg_0: Arg_0 {O(n)}

  13: evalnestedLoopbb8in->evalnestedLoopbb9in, Arg_1: Arg_1 {O(n)}

  13: evalnestedLoopbb8in->evalnestedLoopbb9in, Arg_2: Arg_2 {O(n)}

  13: evalnestedLoopbb8in->evalnestedLoopbb9in, Arg_3: max([0, Arg_0])+max([0, Arg_2]) {O(n)}

  13: evalnestedLoopbb8in->evalnestedLoopbb9in, Arg_4: max([0, max([1, 1+6*Arg_0])*max([0, 3*Arg_1])]) {O(n^2)}

  13: evalnestedLoopbb8in->evalnestedLoopbb9in, Arg_5: max([0, Arg_0])+max([0, Arg_2]) {O(n)}

  13: evalnestedLoopbb8in->evalnestedLoopbb9in, Arg_6: max([Arg_6, max([1, 1+6*Arg_0])*max([0, 3*Arg_1])]) {O(n^2)}

  13: evalnestedLoopbb8in->evalnestedLoopbb9in, Arg_7: max([Arg_7, max([0, Arg_0])+max([0, Arg_2])]) {O(n)}

  5: evalnestedLoopbb9in->evalnestedLoopbb7in, Arg_0: Arg_0 {O(n)}

  5: evalnestedLoopbb9in->evalnestedLoopbb7in, Arg_1: Arg_1 {O(n)}

  5: evalnestedLoopbb9in->evalnestedLoopbb7in, Arg_2: Arg_2 {O(n)}

  5: evalnestedLoopbb9in->evalnestedLoopbb7in, Arg_3: max([0, max([0, Arg_0])+max([0, Arg_2])]) {O(n)}

  5: evalnestedLoopbb9in->evalnestedLoopbb7in, Arg_4: 0 {O(1)}

  5: evalnestedLoopbb9in->evalnestedLoopbb7in, Arg_5: max([0, Arg_0])+max([0, Arg_2]) {O(n)}

  5: evalnestedLoopbb9in->evalnestedLoopbb7in, Arg_6: max([Arg_6, max([1, 1+6*Arg_0])*max([0, 3*Arg_1])]) {O(n^2)}

  5: evalnestedLoopbb9in->evalnestedLoopbb7in, Arg_7: max([Arg_7, max([0, Arg_0])+max([0, Arg_2])]) {O(n)}

  6: evalnestedLoopbb9in->evalnestedLoopreturnin, Arg_0: Arg_0 {O(n)}

  6: evalnestedLoopbb9in->evalnestedLoopreturnin, Arg_1: Arg_1 {O(n)}

  6: evalnestedLoopbb9in->evalnestedLoopreturnin, Arg_2: Arg_2 {O(n)}

  6: evalnestedLoopbb9in->evalnestedLoopreturnin, Arg_3: max([0, max([0, Arg_0])+max([0, Arg_2])]) {O(n)}

  6: evalnestedLoopbb9in->evalnestedLoopreturnin, Arg_4: max([0, max([Arg_4, max([1, 1+6*Arg_0])*max([0, 3*Arg_1])])]) {O(n^2)}

  6: evalnestedLoopbb9in->evalnestedLoopreturnin, Arg_5: max([Arg_5, max([0, Arg_0])+max([0, Arg_2])]) {O(n)}

  6: evalnestedLoopbb9in->evalnestedLoopreturnin, Arg_6: max([Arg_6, max([Arg_6, max([1, 1+6*Arg_0])*max([0, 3*Arg_1])])]) {O(n^2)}

  6: evalnestedLoopbb9in->evalnestedLoopreturnin, Arg_7: max([Arg_7, max([Arg_7, max([0, Arg_0])+max([0, Arg_2])])]) {O(n)}

  1: evalnestedLoopentryin->evalnestedLoopbb9in, Arg_0: Arg_0 {O(n)}

  1: evalnestedLoopentryin->evalnestedLoopbb9in, Arg_1: Arg_1 {O(n)}

  1: evalnestedLoopentryin->evalnestedLoopbb9in, Arg_2: Arg_2 {O(n)}

  1: evalnestedLoopentryin->evalnestedLoopbb9in, Arg_3: 0 {O(1)}

  1: evalnestedLoopentryin->evalnestedLoopbb9in, Arg_4: Arg_4 {O(n)}

  1: evalnestedLoopentryin->evalnestedLoopbb9in, Arg_5: Arg_5 {O(n)}

  1: evalnestedLoopentryin->evalnestedLoopbb9in, Arg_6: Arg_6 {O(n)}

  1: evalnestedLoopentryin->evalnestedLoopbb9in, Arg_7: Arg_7 {O(n)}

  2: evalnestedLoopentryin->evalnestedLoopreturnin, Arg_0: -1 {O(1)}

  2: evalnestedLoopentryin->evalnestedLoopreturnin, Arg_1: Arg_1 {O(n)}

  2: evalnestedLoopentryin->evalnestedLoopreturnin, Arg_2: Arg_2 {O(n)}

  2: evalnestedLoopentryin->evalnestedLoopreturnin, Arg_3: Arg_3 {O(n)}

  2: evalnestedLoopentryin->evalnestedLoopreturnin, Arg_4: Arg_4 {O(n)}

  2: evalnestedLoopentryin->evalnestedLoopreturnin, Arg_5: Arg_5 {O(n)}

  2: evalnestedLoopentryin->evalnestedLoopreturnin, Arg_6: Arg_6 {O(n)}

  2: evalnestedLoopentryin->evalnestedLoopreturnin, Arg_7: Arg_7 {O(n)}

  3: evalnestedLoopentryin->evalnestedLoopreturnin, Arg_0: Arg_0 {O(n)}

  3: evalnestedLoopentryin->evalnestedLoopreturnin, Arg_1: -1 {O(1)}

  3: evalnestedLoopentryin->evalnestedLoopreturnin, Arg_2: Arg_2 {O(n)}

  3: evalnestedLoopentryin->evalnestedLoopreturnin, Arg_3: Arg_3 {O(n)}

  3: evalnestedLoopentryin->evalnestedLoopreturnin, Arg_4: Arg_4 {O(n)}

  3: evalnestedLoopentryin->evalnestedLoopreturnin, Arg_5: Arg_5 {O(n)}

  3: evalnestedLoopentryin->evalnestedLoopreturnin, Arg_6: Arg_6 {O(n)}

  3: evalnestedLoopentryin->evalnestedLoopreturnin, Arg_7: Arg_7 {O(n)}

  4: evalnestedLoopentryin->evalnestedLoopreturnin, Arg_0: Arg_0 {O(n)}

  4: evalnestedLoopentryin->evalnestedLoopreturnin, Arg_1: Arg_1 {O(n)}

  4: evalnestedLoopentryin->evalnestedLoopreturnin, Arg_2: -1 {O(1)}

  4: evalnestedLoopentryin->evalnestedLoopreturnin, Arg_3: Arg_3 {O(n)}

  4: evalnestedLoopentryin->evalnestedLoopreturnin, Arg_4: Arg_4 {O(n)}

  4: evalnestedLoopentryin->evalnestedLoopreturnin, Arg_5: Arg_5 {O(n)}

  4: evalnestedLoopentryin->evalnestedLoopreturnin, Arg_6: Arg_6 {O(n)}

  4: evalnestedLoopentryin->evalnestedLoopreturnin, Arg_7: Arg_7 {O(n)}

  14: evalnestedLoopreturnin->evalnestedLoopstop, Arg_0: max([-1, Arg_0]) {O(n)}

  14: evalnestedLoopreturnin->evalnestedLoopstop, Arg_1: max([-1, Arg_1]) {O(n)}

  14: evalnestedLoopreturnin->evalnestedLoopstop, Arg_2: max([-1, Arg_2]) {O(n)}

  14: evalnestedLoopreturnin->evalnestedLoopstop, Arg_3: max([0, max([Arg_3, max([0, Arg_0])+max([0, Arg_2])])]) {O(n)}

  14: evalnestedLoopreturnin->evalnestedLoopstop, Arg_4: max([0, max([Arg_4, max([Arg_4, max([1, 1+6*Arg_0])*max([0, 3*Arg_1])])])]) {O(n^2)}

  14: evalnestedLoopreturnin->evalnestedLoopstop, Arg_5: max([Arg_5, max([Arg_5, max([0, Arg_0])+max([0, Arg_2])])]) {O(n)}

  14: evalnestedLoopreturnin->evalnestedLoopstop, Arg_6: max([Arg_6, max([Arg_6, max([Arg_6, max([1, 1+6*Arg_0])*max([0, 3*Arg_1])])])]) {O(n^2)}

  14: evalnestedLoopreturnin->evalnestedLoopstop, Arg_7: max([Arg_7, max([Arg_7, max([Arg_7, max([0, Arg_0])+max([0, Arg_2])])])]) {O(n)}

  0: evalnestedLoopstart->evalnestedLoopentryin, Arg_0: Arg_0 {O(n)}

  0: evalnestedLoopstart->evalnestedLoopentryin, Arg_1: Arg_1 {O(n)}

  0: evalnestedLoopstart->evalnestedLoopentryin, Arg_2: Arg_2 {O(n)}

  0: evalnestedLoopstart->evalnestedLoopentryin, Arg_3: Arg_3 {O(n)}

  0: evalnestedLoopstart->evalnestedLoopentryin, Arg_4: Arg_4 {O(n)}

  0: evalnestedLoopstart->evalnestedLoopentryin, Arg_5: Arg_5 {O(n)}

  0: evalnestedLoopstart->evalnestedLoopentryin, Arg_6: Arg_6 {O(n)}

  0: evalnestedLoopstart->evalnestedLoopentryin, Arg_7: Arg_7 {O(n)}


----------------------------------------

(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)


### Pre-processing the ITS problem ###



Initial linear ITS problem

   Start location: evalnestedLoopstart

      0: evalnestedLoopstart -> evalnestedLoopentryin : [], cost: 1

      1: evalnestedLoopentryin -> evalnestedLoopbb9in : D'=0, [ A>=0 && B>=0 && C>=0 ], cost: 1

      2: evalnestedLoopentryin -> evalnestedLoopreturnin : [ 0>=1+A ], cost: 1

      3: evalnestedLoopentryin -> evalnestedLoopreturnin : [ 0>=1+B ], cost: 1

      4: evalnestedLoopentryin -> evalnestedLoopreturnin : [ 0>=1+C ], cost: 1

      5: evalnestedLoopbb9in -> evalnestedLoopbb7in : E'=0, F'=D, [ A>=1+D ], cost: 1

      6: evalnestedLoopbb9in -> evalnestedLoopreturnin : [ D>=A ], cost: 1

      7: evalnestedLoopbb7in -> evalnestedLoopbb4in : [ B>=1+E ], cost: 1

      8: evalnestedLoopbb7in -> evalnestedLoopbb8in : [ E>=B ], cost: 1

      9: evalnestedLoopbb4in -> evalnestedLoopbb6in : G'=1+E, H'=F, [], cost: 1

     10: evalnestedLoopbb6in -> evalnestedLoopbb5in : [ C>=1+H ], cost: 1

     11: evalnestedLoopbb6in -> evalnestedLoopbb7in : E'=G, F'=H, [ H>=C ], cost: 1

     12: evalnestedLoopbb5in -> evalnestedLoopbb6in : H'=1+H, [], cost: 1

     13: evalnestedLoopbb8in -> evalnestedLoopbb9in : D'=1+F, [], cost: 1

     14: evalnestedLoopreturnin -> evalnestedLoopstop : [], cost: 1



Removed unreachable and leaf rules:

   Start location: evalnestedLoopstart

      0: evalnestedLoopstart -> evalnestedLoopentryin : [], cost: 1

      1: evalnestedLoopentryin -> evalnestedLoopbb9in : D'=0, [ A>=0 && B>=0 && C>=0 ], cost: 1

      5: evalnestedLoopbb9in -> evalnestedLoopbb7in : E'=0, F'=D, [ A>=1+D ], cost: 1

      7: evalnestedLoopbb7in -> evalnestedLoopbb4in : [ B>=1+E ], cost: 1

      8: evalnestedLoopbb7in -> evalnestedLoopbb8in : [ E>=B ], cost: 1

      9: evalnestedLoopbb4in -> evalnestedLoopbb6in : G'=1+E, H'=F, [], cost: 1

     10: evalnestedLoopbb6in -> evalnestedLoopbb5in : [ C>=1+H ], cost: 1

     11: evalnestedLoopbb6in -> evalnestedLoopbb7in : E'=G, F'=H, [ H>=C ], cost: 1

     12: evalnestedLoopbb5in -> evalnestedLoopbb6in : H'=1+H, [], cost: 1

     13: evalnestedLoopbb8in -> evalnestedLoopbb9in : D'=1+F, [], cost: 1



### Simplification by acceleration and chaining ###



Eliminated locations (on linear paths):

   Start location: evalnestedLoopstart

     15: evalnestedLoopstart -> evalnestedLoopbb9in : D'=0, [ A>=0 && B>=0 && C>=0 ], cost: 2

      5: evalnestedLoopbb9in -> evalnestedLoopbb7in : E'=0, F'=D, [ A>=1+D ], cost: 1

     16: evalnestedLoopbb7in -> evalnestedLoopbb6in : G'=1+E, H'=F, [ B>=1+E ], cost: 2

     17: evalnestedLoopbb7in -> evalnestedLoopbb9in : D'=1+F, [ E>=B ], cost: 2

     11: evalnestedLoopbb6in -> evalnestedLoopbb7in : E'=G, F'=H, [ H>=C ], cost: 1

     18: evalnestedLoopbb6in -> evalnestedLoopbb6in : H'=1+H, [ C>=1+H ], cost: 2



Accelerating simple loops of location 5.

   Accelerating the following rules:

     18: evalnestedLoopbb6in -> evalnestedLoopbb6in : H'=1+H, [ C>=1+H ], cost: 2



   Accelerated rule 18 with metering function C-H, yielding the new rule 19.

   Removing the simple loops: 18.



Accelerated all simple loops using metering functions (where possible):

   Start location: evalnestedLoopstart

     15: evalnestedLoopstart -> evalnestedLoopbb9in : D'=0, [ A>=0 && B>=0 && C>=0 ], cost: 2

      5: evalnestedLoopbb9in -> evalnestedLoopbb7in : E'=0, F'=D, [ A>=1+D ], cost: 1

     16: evalnestedLoopbb7in -> evalnestedLoopbb6in : G'=1+E, H'=F, [ B>=1+E ], cost: 2

     17: evalnestedLoopbb7in -> evalnestedLoopbb9in : D'=1+F, [ E>=B ], cost: 2

     11: evalnestedLoopbb6in -> evalnestedLoopbb7in : E'=G, F'=H, [ H>=C ], cost: 1

     19: evalnestedLoopbb6in -> evalnestedLoopbb6in : H'=C, [ C>=1+H ], cost: 2*C-2*H



Chained accelerated rules (with incoming rules):

   Start location: evalnestedLoopstart

     15: evalnestedLoopstart -> evalnestedLoopbb9in : D'=0, [ A>=0 && B>=0 && C>=0 ], cost: 2

      5: evalnestedLoopbb9in -> evalnestedLoopbb7in : E'=0, F'=D, [ A>=1+D ], cost: 1

     16: evalnestedLoopbb7in -> evalnestedLoopbb6in : G'=1+E, H'=F, [ B>=1+E ], cost: 2

     17: evalnestedLoopbb7in -> evalnestedLoopbb9in : D'=1+F, [ E>=B ], cost: 2

     20: evalnestedLoopbb7in -> evalnestedLoopbb6in : G'=1+E, H'=C, [ B>=1+E && C>=1+F ], cost: 2-2*F+2*C

     11: evalnestedLoopbb6in -> evalnestedLoopbb7in : E'=G, F'=H, [ H>=C ], cost: 1



Eliminated locations (on tree-shaped paths):

   Start location: evalnestedLoopstart

     15: evalnestedLoopstart -> evalnestedLoopbb9in : D'=0, [ A>=0 && B>=0 && C>=0 ], cost: 2

      5: evalnestedLoopbb9in -> evalnestedLoopbb7in : E'=0, F'=D, [ A>=1+D ], cost: 1

     17: evalnestedLoopbb7in -> evalnestedLoopbb9in : D'=1+F, [ E>=B ], cost: 2

     21: evalnestedLoopbb7in -> evalnestedLoopbb7in : E'=1+E, F'=F, G'=1+E, H'=F, [ B>=1+E && F>=C ], cost: 3

     22: evalnestedLoopbb7in -> evalnestedLoopbb7in : E'=1+E, F'=C, G'=1+E, H'=C, [ B>=1+E && C>=1+F ], cost: 3-2*F+2*C



Accelerating simple loops of location 3.

   Simplified some of the simple loops (and removed duplicate rules).

   Accelerating the following rules:

     21: evalnestedLoopbb7in -> evalnestedLoopbb7in : E'=1+E, G'=1+E, H'=F, [ B>=1+E && F>=C ], cost: 3

     22: evalnestedLoopbb7in -> evalnestedLoopbb7in : E'=1+E, F'=C, G'=1+E, H'=C, [ B>=1+E && C>=1+F ], cost: 3-2*F+2*C



   Accelerated rule 21 with metering function -E+B, yielding the new rule 23.

   Found no metering function for rule 22.

   Removing the simple loops: 21.



Accelerated all simple loops using metering functions (where possible):

   Start location: evalnestedLoopstart

     15: evalnestedLoopstart -> evalnestedLoopbb9in : D'=0, [ A>=0 && B>=0 && C>=0 ], cost: 2

      5: evalnestedLoopbb9in -> evalnestedLoopbb7in : E'=0, F'=D, [ A>=1+D ], cost: 1

     17: evalnestedLoopbb7in -> evalnestedLoopbb9in : D'=1+F, [ E>=B ], cost: 2

     22: evalnestedLoopbb7in -> evalnestedLoopbb7in : E'=1+E, F'=C, G'=1+E, H'=C, [ B>=1+E && C>=1+F ], cost: 3-2*F+2*C

     23: evalnestedLoopbb7in -> evalnestedLoopbb7in : E'=B, G'=B, H'=F, [ B>=1+E && F>=C ], cost: -3*E+3*B



Chained accelerated rules (with incoming rules):

   Start location: evalnestedLoopstart

     15: evalnestedLoopstart -> evalnestedLoopbb9in : D'=0, [ A>=0 && B>=0 && C>=0 ], cost: 2

      5: evalnestedLoopbb9in -> evalnestedLoopbb7in : E'=0, F'=D, [ A>=1+D ], cost: 1

     24: evalnestedLoopbb9in -> evalnestedLoopbb7in : E'=1, F'=C, G'=1, H'=C, [ A>=1+D && B>=1 && C>=1+D ], cost: 4+2*C-2*D

     25: evalnestedLoopbb9in -> evalnestedLoopbb7in : E'=B, F'=D, G'=B, H'=D, [ A>=1+D && B>=1 && D>=C ], cost: 1+3*B

     17: evalnestedLoopbb7in -> evalnestedLoopbb9in : D'=1+F, [ E>=B ], cost: 2



Eliminated locations (on tree-shaped paths):

   Start location: evalnestedLoopstart

     15: evalnestedLoopstart -> evalnestedLoopbb9in : D'=0, [ A>=0 && B>=0 && C>=0 ], cost: 2

     26: evalnestedLoopbb9in -> evalnestedLoopbb9in : D'=1+D, E'=0, F'=D, [ A>=1+D && 0>=B ], cost: 3

     27: evalnestedLoopbb9in -> evalnestedLoopbb9in : D'=1+C, E'=1, F'=C, G'=1, H'=C, [ A>=1+D && B>=1 && C>=1+D && 1>=B ], cost: 6+2*C-2*D

     28: evalnestedLoopbb9in -> evalnestedLoopbb9in : D'=1+D, E'=B, F'=D, G'=B, H'=D, [ A>=1+D && B>=1 && D>=C ], cost: 3+3*B



Accelerating simple loops of location 2.

   Simplified some of the simple loops (and removed duplicate rules).

   Accelerating the following rules:

     26: evalnestedLoopbb9in -> evalnestedLoopbb9in : D'=1+D, E'=0, F'=D, [ A>=1+D && 0>=B ], cost: 3

     27: evalnestedLoopbb9in -> evalnestedLoopbb9in : D'=1+C, E'=1, F'=C, G'=1, H'=C, [ A>=1+D && 1-B==0 && C>=1+D ], cost: 6+2*C-2*D

     28: evalnestedLoopbb9in -> evalnestedLoopbb9in : D'=1+D, E'=B, F'=D, G'=B, H'=D, [ A>=1+D && B>=1 && D>=C ], cost: 3+3*B



   Accelerated rule 26 with metering function -D+A, yielding the new rule 29.

   Found no metering function for rule 27.

   Accelerated rule 28 with metering function -D+A, yielding the new rule 30.

   Removing the simple loops: 26 28.



Accelerated all simple loops using metering functions (where possible):

   Start location: evalnestedLoopstart

     15: evalnestedLoopstart -> evalnestedLoopbb9in : D'=0, [ A>=0 && B>=0 && C>=0 ], cost: 2

     27: evalnestedLoopbb9in -> evalnestedLoopbb9in : D'=1+C, E'=1, F'=C, G'=1, H'=C, [ A>=1+D && 1-B==0 && C>=1+D ], cost: 6+2*C-2*D

     29: evalnestedLoopbb9in -> evalnestedLoopbb9in : D'=A, E'=0, F'=-1+A, [ A>=1+D && 0>=B ], cost: -3*D+3*A

     30: evalnestedLoopbb9in -> evalnestedLoopbb9in : D'=A, E'=B, F'=-1+A, G'=B, H'=-1+A, [ A>=1+D && B>=1 && D>=C ], cost: -3*(D-A)*B-3*D+3*A



Chained accelerated rules (with incoming rules):

   Start location: evalnestedLoopstart

     15: evalnestedLoopstart -> evalnestedLoopbb9in : D'=0, [ A>=0 && B>=0 && C>=0 ], cost: 2

     31: evalnestedLoopstart -> evalnestedLoopbb9in : D'=1+C, E'=1, F'=C, G'=1, H'=C, [ A>=1 && 1-B==0 && C>=1 ], cost: 8+2*C

     32: evalnestedLoopstart -> evalnestedLoopbb9in : D'=A, E'=0, F'=-1+A, [ -B==0 && C>=0 && A>=1 ], cost: 2+3*A

     33: evalnestedLoopstart -> evalnestedLoopbb9in : D'=A, E'=B, F'=-1+A, G'=B, H'=-1+A, [ -C==0 && A>=1 && B>=1 ], cost: 2+3*A+3*A*B



Removed unreachable locations (and leaf rules with constant cost):

   Start location: evalnestedLoopstart

     31: evalnestedLoopstart -> evalnestedLoopbb9in : D'=1+C, E'=1, F'=C, G'=1, H'=C, [ A>=1 && 1-B==0 && C>=1 ], cost: 8+2*C

     32: evalnestedLoopstart -> evalnestedLoopbb9in : D'=A, E'=0, F'=-1+A, [ -B==0 && C>=0 && A>=1 ], cost: 2+3*A

     33: evalnestedLoopstart -> evalnestedLoopbb9in : D'=A, E'=B, F'=-1+A, G'=B, H'=-1+A, [ -C==0 && A>=1 && B>=1 ], cost: 2+3*A+3*A*B



### Computing asymptotic complexity ###



Fully simplified ITS problem

   Start location: evalnestedLoopstart

     31: evalnestedLoopstart -> evalnestedLoopbb9in : D'=1+C, E'=1, F'=C, G'=1, H'=C, [ A>=1 && 1-B==0 && C>=1 ], cost: 8+2*C

     32: evalnestedLoopstart -> evalnestedLoopbb9in : D'=A, E'=0, F'=-1+A, [ -B==0 && C>=0 && A>=1 ], cost: 2+3*A

     33: evalnestedLoopstart -> evalnestedLoopbb9in : D'=A, E'=B, F'=-1+A, G'=B, H'=-1+A, [ -C==0 && A>=1 && B>=1 ], cost: 2+3*A+3*A*B



Computing asymptotic complexity for rule 31

   Solved the limit problem by the following transformations:

      Created initial limit problem:

      C (+/+!), 8+2*C (+), A (+/+!), 2-B (+/+!), B (+/+!) [not solved]



      applying transformation rule (C) using substitution {B==1}

      resulting limit problem:

      1 (+/+!), C (+/+!), 8+2*C (+), A (+/+!) [not solved]



      applying transformation rule (B), deleting 1 (+/+!)

      resulting limit problem:

      C (+/+!), 8+2*C (+), A (+/+!) [not solved]



      removing all constraints (solved by SMT)

      resulting limit problem: [solved]



      applying transformation rule (C) using substitution {C==n,A==n}

      resulting limit problem:

      [solved]



   Solution:

      C / n

      A / n

      B / 1

   Resulting cost 8+2*n has complexity: Poly(n^1)



Found new complexity Poly(n^1).



Computing asymptotic complexity for rule 33

   Solved the limit problem by the following transformations:

      Created initial limit problem:

      1+C (+/+!), A (+/+!), 2+3*A+3*A*B (+), 1-C (+/+!), B (+/+!) [not solved]



      applying transformation rule (C) using substitution {C==0}

      resulting limit problem:

      1 (+/+!), A (+/+!), 2+3*A+3*A*B (+), B (+/+!) [not solved]



      applying transformation rule (B), deleting 1 (+/+!)

      resulting limit problem:

      A (+/+!), 2+3*A+3*A*B (+), B (+/+!) [not solved]



      removing all constraints (solved by SMT)

      resulting limit problem: [solved]



      applying transformation rule (C) using substitution {A==n,B==n}

      resulting limit problem:

      [solved]



   Solution:

      C / 0

      A / n

      B / n

   Resulting cost 2+3*n^2+3*n has complexity: Poly(n^2)



Found new complexity Poly(n^2).



Obtained the following overall complexity (w.r.t. the length of the input n):

   Complexity:  Poly(n^2)

   Cpx degree:  2

   Solved cost: 2+3*n^2+3*n

   Rule cost:   2+3*A+3*A*B

   Rule guard:  [ -C==0 && A>=1 && B>=1 ]



WORST_CASE(Omega(n^2),?)


----------------------------------------

(4)
BOUNDS(n^2, INF)