/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.koat /export/starexec/sandbox2/output/output_files


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WORST_CASE(Omega(n^4), O(n^7))
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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(n^4, nat(3 * Arg_0 * max(min(3, 3 * Arg_1), 3 * Arg_1)) * nat(Arg_0 + Arg_1) + 2 * nat(3 * Arg_0 * max(min(3, 3 * Arg_1), 3 * Arg_1)) * nat(Arg_0 + Arg_1) * nat(Arg_1) + nat(3 * Arg_0 * max(min(3, 3 * Arg_1), 3 * Arg_1)) * nat(Arg_0 + Arg_1) * max(4, -2 + 6 * Arg_0 + 6 * nat(3 * Arg_0 * max(min(3, 3 * Arg_1), 3 * Arg_1)) * nat(Arg_0 + Arg_1) * nat(Arg_1) + 6 * nat(3 * Arg_1) * nat(Arg_0 + Arg_1) * nat(Arg_1) + 6 * nat(-10 * Arg_3) * nat(Arg_1)) + nat(3 * Arg_0 * max(min(3, 3 * Arg_1), 3 * Arg_1)) * nat(Arg_0 + Arg_1) * max(1, -1 + 2 * Arg_0 + 2 * nat(3 * Arg_1) * nat(Arg_0 + Arg_1) * nat(Arg_1) + 2 * nat(3 * Arg_0 * max(min(3, 3 * Arg_1), 3 * Arg_1)) * nat(Arg_0 + Arg_1) * nat(Arg_1) + 2 * nat(-10 * Arg_3) * nat(Arg_1)) + 2 * nat(3 * Arg_1) * nat(Arg_0 + Arg_1) * nat(Arg_1) + nat(3 * Arg_1) * nat(Arg_0 + Arg_1) + nat(3 * Arg_1) * nat(Arg_0 + Arg_1) * max(1, -1 + 2 * Arg_0 + 2 * nat(3 * Arg_1) * nat(Arg_0 + Arg_1) * nat(Arg_1) + 2 * nat(3 * Arg_0 * max(min(3, 3 * Arg_1), 3 * Arg_1)) * nat(Arg_0 + Arg_1) * nat(Arg_1) + 2 * nat(-10 * Arg_3) * nat(Arg_1)) + nat(3 * Arg_1) * nat(Arg_0 + Arg_1) * max(4, -2 + 6 * Arg_0 + 6 * nat(3 * Arg_1) * nat(Arg_0 + Arg_1) * nat(Arg_1) + 6 * nat(3 * Arg_0 * max(3 * Arg_1, min(3, 3 * Arg_1))) * nat(Arg_0 + Arg_1) * nat(Arg_1) + 6 * nat(-10 * Arg_3) * nat(Arg_1)) + 2 * nat(-10 * Arg_3) * nat(Arg_1) + nat(-10 * Arg_3) + nat(-10 * Arg_3) * max(1, -1 + 2 * Arg_0 + 2 * nat(3 * Arg_1) * nat(Arg_0 + Arg_1) * nat(Arg_1) + 2 * nat(3 * Arg_0 * max(min(3, 3 * Arg_1), 3 * Arg_1)) * nat(Arg_0 + Arg_1) * nat(Arg_1) + 2 * nat(-10 * Arg_3) * nat(Arg_1)) + nat(-10 * Arg_3) * max(4, -2 + 6 * Arg_0 + 6 * nat(3 * Arg_1) * nat(Arg_0 + Arg_1) * nat(Arg_1) + 6 * nat(3 * Arg_0 * max(3 * Arg_1, min(3, 3 * Arg_1))) * nat(Arg_0 + Arg_1) * nat(Arg_1) + 6 * nat(-10 * Arg_3) * nat(Arg_1)) + nat(6 * Arg_0) + nat(-2 * Arg_4) + nat(3 * Arg_0 * max(4 * Arg_1, min(4, 4 * Arg_1))) + nat(4 * Arg_1) + max(1, 2 + Arg_0) + nat(-9 * Arg_4) + max(3, 3 + 6 * Arg_1) + nat(6 * Arg_0 * max(3 * Arg_1, min(3, 3 * Arg_1)))).

(0) CpxIntTrs
(1) Koat2 Proof [FINISHED, 8967 ms]
(2) BOUNDS(1, nat(3 * Arg_0 * max(min(3, 3 * Arg_1), 3 * Arg_1)) * nat(Arg_0 + Arg_1) + 2 * nat(3 * Arg_0 * max(min(3, 3 * Arg_1), 3 * Arg_1)) * nat(Arg_0 + Arg_1) * nat(Arg_1) + nat(3 * Arg_0 * max(min(3, 3 * Arg_1), 3 * Arg_1)) * nat(Arg_0 + Arg_1) * max(4, -2 + 6 * Arg_0 + 6 * nat(3 * Arg_0 * max(min(3, 3 * Arg_1), 3 * Arg_1)) * nat(Arg_0 + Arg_1) * nat(Arg_1) + 6 * nat(3 * Arg_1) * nat(Arg_0 + Arg_1) * nat(Arg_1) + 6 * nat(-10 * Arg_3) * nat(Arg_1)) + nat(3 * Arg_0 * max(min(3, 3 * Arg_1), 3 * Arg_1)) * nat(Arg_0 + Arg_1) * max(1, -1 + 2 * Arg_0 + 2 * nat(3 * Arg_1) * nat(Arg_0 + Arg_1) * nat(Arg_1) + 2 * nat(3 * Arg_0 * max(min(3, 3 * Arg_1), 3 * Arg_1)) * nat(Arg_0 + Arg_1) * nat(Arg_1) + 2 * nat(-10 * Arg_3) * nat(Arg_1)) + 2 * nat(3 * Arg_1) * nat(Arg_0 + Arg_1) * nat(Arg_1) + nat(3 * Arg_1) * nat(Arg_0 + Arg_1) + nat(3 * Arg_1) * nat(Arg_0 + Arg_1) * max(1, -1 + 2 * Arg_0 + 2 * nat(3 * Arg_1) * nat(Arg_0 + Arg_1) * nat(Arg_1) + 2 * nat(3 * Arg_0 * max(min(3, 3 * Arg_1), 3 * Arg_1)) * nat(Arg_0 + Arg_1) * nat(Arg_1) + 2 * nat(-10 * Arg_3) * nat(Arg_1)) + nat(3 * Arg_1) * nat(Arg_0 + Arg_1) * max(4, -2 + 6 * Arg_0 + 6 * nat(3 * Arg_1) * nat(Arg_0 + Arg_1) * nat(Arg_1) + 6 * nat(3 * Arg_0 * max(3 * Arg_1, min(3, 3 * Arg_1))) * nat(Arg_0 + Arg_1) * nat(Arg_1) + 6 * nat(-10 * Arg_3) * nat(Arg_1)) + 2 * nat(-10 * Arg_3) * nat(Arg_1) + nat(-10 * Arg_3) + nat(-10 * Arg_3) * max(1, -1 + 2 * Arg_0 + 2 * nat(3 * Arg_1) * nat(Arg_0 + Arg_1) * nat(Arg_1) + 2 * nat(3 * Arg_0 * max(min(3, 3 * Arg_1), 3 * Arg_1)) * nat(Arg_0 + Arg_1) * nat(Arg_1) + 2 * nat(-10 * Arg_3) * nat(Arg_1)) + nat(-10 * Arg_3) * max(4, -2 + 6 * Arg_0 + 6 * nat(3 * Arg_1) * nat(Arg_0 + Arg_1) * nat(Arg_1) + 6 * nat(3 * Arg_0 * max(3 * Arg_1, min(3, 3 * Arg_1))) * nat(Arg_0 + Arg_1) * nat(Arg_1) + 6 * nat(-10 * Arg_3) * nat(Arg_1)) + nat(6 * Arg_0) + nat(-2 * Arg_4) + nat(3 * Arg_0 * max(4 * Arg_1, min(4, 4 * Arg_1))) + nat(4 * Arg_1) + max(1, 2 + Arg_0) + nat(-9 * Arg_4) + max(3, 3 + 6 * Arg_1) + nat(6 * Arg_0 * max(3 * Arg_1, min(3, 3 * Arg_1))))
(3) Loat Proof [FINISHED, 2151 ms]
(4) BOUNDS(n^4, INF)


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(0)
Obligation:
Complexity Int TRS consisting of the following rules:
evalfstart(A, B, C, D, E) -> Com_1(evalfentryin(A, B, C, D, E)) :|: TRUE
evalfentryin(A, B, C, D, E) -> Com_1(evalfbb10in(B, A, C, D, E)) :|: TRUE
evalfbb10in(A, B, C, D, E) -> Com_1(evalfbb8in(A, B, 1, D, E)) :|: B >= 1
evalfbb10in(A, B, C, D, E) -> Com_1(evalfreturnin(A, B, C, D, E)) :|: 0 >= B
evalfbb8in(A, B, C, D, E) -> Com_1(evalfbb6in(A, B, C, B, E)) :|: A >= C
evalfbb8in(A, B, C, D, E) -> Com_1(evalfbb9in(A, B, C, D, E)) :|: C >= A + 1
evalfbb6in(A, B, C, D, E) -> Com_1(evalfbb4in(A, B, C, D, 1)) :|: B + C >= D
evalfbb6in(A, B, C, D, E) -> Com_1(evalfbb7in(A, B, C, D, E)) :|: D >= B + C + 1
evalfbb4in(A, B, C, D, E) -> Com_1(evalfbb3in(A, B, C, D, E)) :|: D >= E
evalfbb4in(A, B, C, D, E) -> Com_1(evalfbb5in(A, B, C, D, E)) :|: E >= D + 1
evalfbb3in(A, B, C, D, E) -> Com_1(evalfbb4in(A, B, C, D, E + 1)) :|: TRUE
evalfbb5in(A, B, C, D, E) -> Com_1(evalfbb6in(A, B, C, D + 1, E)) :|: TRUE
evalfbb7in(A, B, C, D, E) -> Com_1(evalfbb8in(A, B, C + 1, D, E)) :|: TRUE
evalfbb9in(A, B, C, D, E) -> Com_1(evalfbb10in(A, B - 1, C, D, E)) :|: TRUE
evalfreturnin(A, B, C, D, E) -> Com_1(evalfstop(A, B, C, D, E)) :|: TRUE

The start-symbols are:[evalfstart_5]


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(1) Koat2 Proof (FINISHED)
YES( ?, 3+(max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+2*((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([0, Arg_1])+((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([4, -2+6*(Arg_0+((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([0, Arg_1]))])+((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([1, -1+2*(Arg_0+((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([0, Arg_1]))])+max([0, 3*Arg_0])+max([0, -2*Arg_4])+max([0, 3*Arg_0])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])])+max([0, 3*Arg_1])+max([0, 3*Arg_0*max([4*min([1, Arg_1]), 4*Arg_1])])+max([0, 4*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])])+max([0, 3*Arg_1])+max([0, -10*Arg_3])+max([1, 2+Arg_0])+max([0, -9*Arg_4]) {O(n^7)})



Initial Complexity Problem:

  Start:  evalfstart  

  Program_Vars:  Arg_0, Arg_1, Arg_2, Arg_3, Arg_4  

  Temp_Vars:    

  Locations:  evalfbb10in, evalfbb3in, evalfbb4in, evalfbb5in, evalfbb6in, evalfbb7in, evalfbb8in, evalfbb9in, evalfentryin, evalfreturnin, evalfstart, evalfstop  

  Transitions:

  evalfbb10in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb8in(Arg_0,Arg_1,1,Arg_3,Arg_4):|:1 <= Arg_1

  evalfbb10in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfreturnin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_1 <= 0

  evalfbb3in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb4in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4+1):|:Arg_4 <= Arg_3 && 1 <= Arg_4 && 2 <= Arg_3+Arg_4 && 2 <= Arg_2+Arg_4 && 2 <= Arg_1+Arg_4 && 2 <= Arg_0+Arg_4 && 1 <= Arg_3 && 2 <= Arg_2+Arg_3 && 2 <= Arg_1+Arg_3 && Arg_1 <= Arg_3 && 2 <= Arg_0+Arg_3 && Arg_2 <= Arg_0 && 1 <= Arg_2 && 2 <= Arg_1+Arg_2 && 2 <= Arg_0+Arg_2 && 1 <= Arg_1 && 2 <= Arg_0+Arg_1 && 1 <= Arg_0

  evalfbb4in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb3in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:1 <= Arg_4 && 2 <= Arg_3+Arg_4 && 2 <= Arg_2+Arg_4 && 2 <= Arg_1+Arg_4 && 2 <= Arg_0+Arg_4 && 1 <= Arg_3 && 2 <= Arg_2+Arg_3 && 2 <= Arg_1+Arg_3 && Arg_1 <= Arg_3 && 2 <= Arg_0+Arg_3 && Arg_2 <= Arg_0 && 1 <= Arg_2 && 2 <= Arg_1+Arg_2 && 2 <= Arg_0+Arg_2 && 1 <= Arg_1 && 2 <= Arg_0+Arg_1 && 1 <= Arg_0 && Arg_4 <= Arg_3

  evalfbb4in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb5in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:1 <= Arg_4 && 2 <= Arg_3+Arg_4 && 2 <= Arg_2+Arg_4 && 2 <= Arg_1+Arg_4 && 2 <= Arg_0+Arg_4 && 1 <= Arg_3 && 2 <= Arg_2+Arg_3 && 2 <= Arg_1+Arg_3 && Arg_1 <= Arg_3 && 2 <= Arg_0+Arg_3 && Arg_2 <= Arg_0 && 1 <= Arg_2 && 2 <= Arg_1+Arg_2 && 2 <= Arg_0+Arg_2 && 1 <= Arg_1 && 2 <= Arg_0+Arg_1 && 1 <= Arg_0 && Arg_3+1 <= Arg_4

  evalfbb5in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb6in(Arg_0,Arg_1,Arg_2,Arg_3+1,Arg_4):|:2 <= Arg_4 && 3 <= Arg_3+Arg_4 && 1+Arg_3 <= Arg_4 && 3 <= Arg_2+Arg_4 && 3 <= Arg_1+Arg_4 && 1+Arg_1 <= Arg_4 && 3 <= Arg_0+Arg_4 && 1 <= Arg_3 && 2 <= Arg_2+Arg_3 && 2 <= Arg_1+Arg_3 && Arg_1 <= Arg_3 && 2 <= Arg_0+Arg_3 && Arg_2 <= Arg_0 && 1 <= Arg_2 && 2 <= Arg_1+Arg_2 && 2 <= Arg_0+Arg_2 && 1 <= Arg_1 && 2 <= Arg_0+Arg_1 && 1 <= Arg_0

  evalfbb6in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb4in(Arg_0,Arg_1,Arg_2,Arg_3,1):|:1 <= Arg_3 && 2 <= Arg_2+Arg_3 && 2 <= Arg_1+Arg_3 && Arg_1 <= Arg_3 && 2 <= Arg_0+Arg_3 && Arg_2 <= Arg_0 && 1 <= Arg_2 && 2 <= Arg_1+Arg_2 && 2 <= Arg_0+Arg_2 && 1 <= Arg_1 && 2 <= Arg_0+Arg_1 && 1 <= Arg_0 && Arg_3 <= Arg_1+Arg_2

  evalfbb6in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb7in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:1 <= Arg_3 && 2 <= Arg_2+Arg_3 && 2 <= Arg_1+Arg_3 && Arg_1 <= Arg_3 && 2 <= Arg_0+Arg_3 && Arg_2 <= Arg_0 && 1 <= Arg_2 && 2 <= Arg_1+Arg_2 && 2 <= Arg_0+Arg_2 && 1 <= Arg_1 && 2 <= Arg_0+Arg_1 && 1 <= Arg_0 && Arg_1+Arg_2+1 <= Arg_3

  evalfbb7in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb8in(Arg_0,Arg_1,Arg_2+1,Arg_3,Arg_4):|:3 <= Arg_3 && 4 <= Arg_2+Arg_3 && 2+Arg_2 <= Arg_3 && 4 <= Arg_1+Arg_3 && 2+Arg_1 <= Arg_3 && 4 <= Arg_0+Arg_3 && Arg_2 <= Arg_0 && 1 <= Arg_2 && 2 <= Arg_1+Arg_2 && 2 <= Arg_0+Arg_2 && 1 <= Arg_1 && 2 <= Arg_0+Arg_1 && 1 <= Arg_0

  evalfbb8in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb6in(Arg_0,Arg_1,Arg_2,Arg_1,Arg_4):|:1 <= Arg_2 && 2 <= Arg_1+Arg_2 && 1 <= Arg_1 && Arg_2 <= Arg_0

  evalfbb8in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb9in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:1 <= Arg_2 && 2 <= Arg_1+Arg_2 && 1 <= Arg_1 && Arg_0+1 <= Arg_2

  evalfbb9in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb10in(Arg_0,Arg_1-1,Arg_2,Arg_3,Arg_4):|:1 <= Arg_2 && 2 <= Arg_1+Arg_2 && 1+Arg_0 <= Arg_2 && 1 <= Arg_1

  evalfentryin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb10in(Arg_1,Arg_0,Arg_2,Arg_3,Arg_4):|:

  evalfreturnin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfstop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_1 <= 0

  evalfstart(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfentryin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:  



Timebounds: 

  Overall timebound: 3+(max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+2*((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([0, Arg_1])+((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([4, -2+6*(Arg_0+((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([0, Arg_1]))])+((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([1, -1+2*(Arg_0+((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([0, Arg_1]))])+max([0, 3*Arg_0])+max([0, -2*Arg_4])+max([0, 3*Arg_0])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])])+max([0, 3*Arg_1])+max([0, 3*Arg_0*max([4*min([1, Arg_1]), 4*Arg_1])])+max([0, 4*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])])+max([0, 3*Arg_1])+max([0, -10*Arg_3])+max([1, 2+Arg_0])+max([0, -9*Arg_4]) {O(n^7)}

  2: evalfbb10in->evalfbb8in: max([0, 1+Arg_0]) {O(n)}

  3: evalfbb10in->evalfreturnin: 1 {O(1)}

  10: evalfbb3in->evalfbb4in: ((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([1, -1+2*(Arg_0+((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([0, Arg_1]))])+max([0, -9*Arg_4]) {O(n^7)}

  8: evalfbb4in->evalfbb3in: ((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([4, -2+6*(Arg_0+((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([0, Arg_1]))])+max([0, -2*Arg_4]) {O(n^7)}

  9: evalfbb4in->evalfbb5in: ((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([0, Arg_1]) {O(n^4)}

  11: evalfbb5in->evalfbb6in: ((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([0, Arg_1]) {O(n^4)}

  6: evalfbb6in->evalfbb4in: (max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]) {O(n^3)}

  7: evalfbb6in->evalfbb7in: max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]) {O(n^2)}

  12: evalfbb7in->evalfbb8in: max([0, 4*Arg_1])+max([0, 3*Arg_0*max([4*min([1, Arg_1]), 4*Arg_1])]) {O(n^2)}

  4: evalfbb8in->evalfbb6in: max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]) {O(n^2)}

  5: evalfbb8in->evalfbb9in: max([0, 3*Arg_0]) {O(n)}

  13: evalfbb9in->evalfbb10in: max([0, 3*Arg_0]) {O(n)}

  1: evalfentryin->evalfbb10in: 1 {O(1)}

  14: evalfreturnin->evalfstop: 1 {O(1)}

  0: evalfstart->evalfentryin: 1 {O(1)}



Costbounds:

  Overall costbound: 3+(max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+2*((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([0, Arg_1])+((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([4, -2+6*(Arg_0+((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([0, Arg_1]))])+((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([1, -1+2*(Arg_0+((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([0, Arg_1]))])+max([0, 3*Arg_0])+max([0, -2*Arg_4])+max([0, 3*Arg_0])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])])+max([0, 3*Arg_1])+max([0, 3*Arg_0*max([4*min([1, Arg_1]), 4*Arg_1])])+max([0, 4*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])])+max([0, 3*Arg_1])+max([0, -10*Arg_3])+max([1, 2+Arg_0])+max([0, -9*Arg_4]) {O(n^7)}

  2: evalfbb10in->evalfbb8in: max([0, 1+Arg_0]) {O(n)}

  3: evalfbb10in->evalfreturnin: 1 {O(1)}

  10: evalfbb3in->evalfbb4in: ((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([1, -1+2*(Arg_0+((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([0, Arg_1]))])+max([0, -9*Arg_4]) {O(n^7)}

  8: evalfbb4in->evalfbb3in: ((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([4, -2+6*(Arg_0+((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([0, Arg_1]))])+max([0, -2*Arg_4]) {O(n^7)}

  9: evalfbb4in->evalfbb5in: ((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([0, Arg_1]) {O(n^4)}

  11: evalfbb5in->evalfbb6in: ((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([0, Arg_1]) {O(n^4)}

  6: evalfbb6in->evalfbb4in: (max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]) {O(n^3)}

  7: evalfbb6in->evalfbb7in: max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]) {O(n^2)}

  12: evalfbb7in->evalfbb8in: max([0, 4*Arg_1])+max([0, 3*Arg_0*max([4*min([1, Arg_1]), 4*Arg_1])]) {O(n^2)}

  4: evalfbb8in->evalfbb6in: max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]) {O(n^2)}

  5: evalfbb8in->evalfbb9in: max([0, 3*Arg_0]) {O(n)}

  13: evalfbb9in->evalfbb10in: max([0, 3*Arg_0]) {O(n)}

  1: evalfentryin->evalfbb10in: 1 {O(1)}

  14: evalfreturnin->evalfstop: 1 {O(1)}

  0: evalfstart->evalfentryin: 1 {O(1)}



Sizebounds:

`Lower:

  2: evalfbb10in->evalfbb8in, Arg_0: min([1, Arg_1]) {O(n)}

  2: evalfbb10in->evalfbb8in, Arg_1: 1 {O(1)}

  2: evalfbb10in->evalfbb8in, Arg_2: 1 {O(1)}

  2: evalfbb10in->evalfbb8in, Arg_3: min([3, Arg_3]) {O(n)}

  2: evalfbb10in->evalfbb8in, Arg_4: min([2, Arg_4]) {O(n)}

  3: evalfbb10in->evalfreturnin, Arg_0: min([1, Arg_1]) {O(n)}

  3: evalfbb10in->evalfreturnin, Arg_1: min([0, Arg_0]) {O(n)}

  3: evalfbb10in->evalfreturnin, Arg_2: min([1, Arg_2]) {O(n)}

  3: evalfbb10in->evalfreturnin, Arg_3: min([3, Arg_3]) {O(n)}

  3: evalfbb10in->evalfreturnin, Arg_4: min([2, Arg_4]) {O(n)}

  10: evalfbb3in->evalfbb4in, Arg_0: 1 {O(1)}

  10: evalfbb3in->evalfbb4in, Arg_1: 1 {O(1)}

  10: evalfbb3in->evalfbb4in, Arg_2: 1 {O(1)}

  10: evalfbb3in->evalfbb4in, Arg_3: 1 {O(1)}

  10: evalfbb3in->evalfbb4in, Arg_4: 2 {O(1)}

  8: evalfbb4in->evalfbb3in, Arg_0: 1 {O(1)}

  8: evalfbb4in->evalfbb3in, Arg_1: 1 {O(1)}

  8: evalfbb4in->evalfbb3in, Arg_2: 1 {O(1)}

  8: evalfbb4in->evalfbb3in, Arg_3: 1 {O(1)}

  8: evalfbb4in->evalfbb3in, Arg_4: 1 {O(1)}

  9: evalfbb4in->evalfbb5in, Arg_0: 1 {O(1)}

  9: evalfbb4in->evalfbb5in, Arg_1: 1 {O(1)}

  9: evalfbb4in->evalfbb5in, Arg_2: 1 {O(1)}

  9: evalfbb4in->evalfbb5in, Arg_3: 1 {O(1)}

  9: evalfbb4in->evalfbb5in, Arg_4: 2 {O(1)}

  11: evalfbb5in->evalfbb6in, Arg_0: 1 {O(1)}

  11: evalfbb5in->evalfbb6in, Arg_1: 1 {O(1)}

  11: evalfbb5in->evalfbb6in, Arg_2: 1 {O(1)}

  11: evalfbb5in->evalfbb6in, Arg_3: 2 {O(1)}

  11: evalfbb5in->evalfbb6in, Arg_4: 2 {O(1)}

  6: evalfbb6in->evalfbb4in, Arg_0: 1 {O(1)}

  6: evalfbb6in->evalfbb4in, Arg_1: 1 {O(1)}

  6: evalfbb6in->evalfbb4in, Arg_2: 1 {O(1)}

  6: evalfbb6in->evalfbb4in, Arg_3: 1 {O(1)}

  6: evalfbb6in->evalfbb4in, Arg_4: 1 {O(1)}

  7: evalfbb6in->evalfbb7in, Arg_0: 1 {O(1)}

  7: evalfbb6in->evalfbb7in, Arg_1: 1 {O(1)}

  7: evalfbb6in->evalfbb7in, Arg_2: 1 {O(1)}

  7: evalfbb6in->evalfbb7in, Arg_3: 3 {O(1)}

  7: evalfbb6in->evalfbb7in, Arg_4: 2 {O(1)}

  12: evalfbb7in->evalfbb8in, Arg_0: 1 {O(1)}

  12: evalfbb7in->evalfbb8in, Arg_1: 1 {O(1)}

  12: evalfbb7in->evalfbb8in, Arg_2: 2 {O(1)}

  12: evalfbb7in->evalfbb8in, Arg_3: 3 {O(1)}

  12: evalfbb7in->evalfbb8in, Arg_4: 2 {O(1)}

  4: evalfbb8in->evalfbb6in, Arg_0: 1 {O(1)}

  4: evalfbb8in->evalfbb6in, Arg_1: 1 {O(1)}

  4: evalfbb8in->evalfbb6in, Arg_2: 1 {O(1)}

  4: evalfbb8in->evalfbb6in, Arg_3: 1 {O(1)}

  4: evalfbb8in->evalfbb6in, Arg_4: min([2, min([2, Arg_4])]) {O(n)}

  5: evalfbb8in->evalfbb9in, Arg_0: min([1, Arg_1]) {O(n)}

  5: evalfbb8in->evalfbb9in, Arg_1: 1 {O(1)}

  5: evalfbb8in->evalfbb9in, Arg_2: 1 {O(1)}

  5: evalfbb8in->evalfbb9in, Arg_3: min([3, Arg_3]) {O(n)}

  5: evalfbb8in->evalfbb9in, Arg_4: min([2, Arg_4]) {O(n)}

  13: evalfbb9in->evalfbb10in, Arg_0: min([1, Arg_1]) {O(n)}

  13: evalfbb9in->evalfbb10in, Arg_1: 0 {O(1)}

  13: evalfbb9in->evalfbb10in, Arg_2: 1 {O(1)}

  13: evalfbb9in->evalfbb10in, Arg_3: min([3, Arg_3]) {O(n)}

  13: evalfbb9in->evalfbb10in, Arg_4: min([2, Arg_4]) {O(n)}

  1: evalfentryin->evalfbb10in, Arg_0: Arg_1 {O(n)}

  1: evalfentryin->evalfbb10in, Arg_1: Arg_0 {O(n)}

  1: evalfentryin->evalfbb10in, Arg_2: Arg_2 {O(n)}

  1: evalfentryin->evalfbb10in, Arg_3: Arg_3 {O(n)}

  1: evalfentryin->evalfbb10in, Arg_4: Arg_4 {O(n)}

  14: evalfreturnin->evalfstop, Arg_0: min([1, Arg_1]) {O(n)}

  14: evalfreturnin->evalfstop, Arg_1: min([0, Arg_0]) {O(n)}

  14: evalfreturnin->evalfstop, Arg_2: min([1, Arg_2]) {O(n)}

  14: evalfreturnin->evalfstop, Arg_3: min([3, Arg_3]) {O(n)}

  14: evalfreturnin->evalfstop, Arg_4: min([2, Arg_4]) {O(n)}

  0: evalfstart->evalfentryin, Arg_0: Arg_0 {O(n)}

  0: evalfstart->evalfentryin, Arg_1: Arg_1 {O(n)}

  0: evalfstart->evalfentryin, Arg_2: Arg_2 {O(n)}

  0: evalfstart->evalfentryin, Arg_3: Arg_3 {O(n)}

  0: evalfstart->evalfentryin, Arg_4: Arg_4 {O(n)}

`Upper:

  2: evalfbb10in->evalfbb8in, Arg_0: Arg_1 {O(n)}

  2: evalfbb10in->evalfbb8in, Arg_1: Arg_0 {O(n)}

  2: evalfbb10in->evalfbb8in, Arg_2: 1 {O(1)}

  2: evalfbb10in->evalfbb8in, Arg_3: max([Arg_3, Arg_0+((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([0, Arg_1])]) {O(n^4)}

  2: evalfbb10in->evalfbb8in, Arg_4: max([Arg_4, 1+((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([1, -1+2*(Arg_0+((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([0, Arg_1]))])+max([0, -9*Arg_4])]) {O(n^7)}

  3: evalfbb10in->evalfreturnin, Arg_0: Arg_1 {O(n)}

  3: evalfbb10in->evalfreturnin, Arg_1: 0 {O(1)}

  3: evalfbb10in->evalfreturnin, Arg_2: max([1, max([Arg_2, 1+max([0, 4*Arg_1])+max([0, 3*Arg_0*max([4*min([1, Arg_1]), 4*Arg_1])])])]) {O(n^2)}

  3: evalfbb10in->evalfreturnin, Arg_3: max([Arg_3, max([Arg_3, Arg_0+((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([0, Arg_1])])]) {O(n^4)}

  3: evalfbb10in->evalfreturnin, Arg_4: max([Arg_4, max([Arg_4, 1+((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([1, -1+2*(Arg_0+((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([0, Arg_1]))])+max([0, -9*Arg_4])])]) {O(n^7)}

  10: evalfbb3in->evalfbb4in, Arg_0: Arg_1 {O(n)}

  10: evalfbb3in->evalfbb4in, Arg_1: Arg_0 {O(n)}

  10: evalfbb3in->evalfbb4in, Arg_2: 1+max([0, 4*Arg_1])+max([0, 3*Arg_0*max([4*min([1, Arg_1]), 4*Arg_1])]) {O(n^2)}

  10: evalfbb3in->evalfbb4in, Arg_3: Arg_0+((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([0, Arg_1]) {O(n^4)}

  10: evalfbb3in->evalfbb4in, Arg_4: 1+((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([1, -1+2*(Arg_0+((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([0, Arg_1]))])+max([0, -9*Arg_4]) {O(n^7)}

  8: evalfbb4in->evalfbb3in, Arg_0: Arg_1 {O(n)}

  8: evalfbb4in->evalfbb3in, Arg_1: Arg_0 {O(n)}

  8: evalfbb4in->evalfbb3in, Arg_2: 1+max([0, 4*Arg_1])+max([0, 3*Arg_0*max([4*min([1, Arg_1]), 4*Arg_1])]) {O(n^2)}

  8: evalfbb4in->evalfbb3in, Arg_3: Arg_0+((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([0, Arg_1]) {O(n^4)}

  8: evalfbb4in->evalfbb3in, Arg_4: 1+((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([1, -1+2*(Arg_0+((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([0, Arg_1]))])+max([0, -9*Arg_4]) {O(n^7)}

  9: evalfbb4in->evalfbb5in, Arg_0: Arg_1 {O(n)}

  9: evalfbb4in->evalfbb5in, Arg_1: Arg_0 {O(n)}

  9: evalfbb4in->evalfbb5in, Arg_2: 1+max([0, 4*Arg_1])+max([0, 3*Arg_0*max([4*min([1, Arg_1]), 4*Arg_1])]) {O(n^2)}

  9: evalfbb4in->evalfbb5in, Arg_3: Arg_0+((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([0, Arg_1]) {O(n^4)}

  9: evalfbb4in->evalfbb5in, Arg_4: 1+((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([1, -1+2*(Arg_0+((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([0, Arg_1]))])+max([0, -9*Arg_4]) {O(n^7)}

  11: evalfbb5in->evalfbb6in, Arg_0: Arg_1 {O(n)}

  11: evalfbb5in->evalfbb6in, Arg_1: Arg_0 {O(n)}

  11: evalfbb5in->evalfbb6in, Arg_2: 1+max([0, 4*Arg_1])+max([0, 3*Arg_0*max([4*min([1, Arg_1]), 4*Arg_1])]) {O(n^2)}

  11: evalfbb5in->evalfbb6in, Arg_3: Arg_0+((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([0, Arg_1]) {O(n^4)}

  11: evalfbb5in->evalfbb6in, Arg_4: 1+((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([1, -1+2*(Arg_0+((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([0, Arg_1]))])+max([0, -9*Arg_4]) {O(n^7)}

  6: evalfbb6in->evalfbb4in, Arg_0: Arg_1 {O(n)}

  6: evalfbb6in->evalfbb4in, Arg_1: Arg_0 {O(n)}

  6: evalfbb6in->evalfbb4in, Arg_2: 1+max([0, 4*Arg_1])+max([0, 3*Arg_0*max([4*min([1, Arg_1]), 4*Arg_1])]) {O(n^2)}

  6: evalfbb6in->evalfbb4in, Arg_3: Arg_0+((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([0, Arg_1]) {O(n^4)}

  6: evalfbb6in->evalfbb4in, Arg_4: 1 {O(1)}

  7: evalfbb6in->evalfbb7in, Arg_0: Arg_1 {O(n)}

  7: evalfbb6in->evalfbb7in, Arg_1: Arg_0 {O(n)}

  7: evalfbb6in->evalfbb7in, Arg_2: 1+max([0, 4*Arg_1])+max([0, 3*Arg_0*max([4*min([1, Arg_1]), 4*Arg_1])]) {O(n^2)}

  7: evalfbb6in->evalfbb7in, Arg_3: Arg_0+((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([0, Arg_1]) {O(n^4)}

  7: evalfbb6in->evalfbb7in, Arg_4: 1+((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([1, -1+2*(Arg_0+((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([0, Arg_1]))])+max([0, -9*Arg_4]) {O(n^7)}

  12: evalfbb7in->evalfbb8in, Arg_0: Arg_1 {O(n)}

  12: evalfbb7in->evalfbb8in, Arg_1: Arg_0 {O(n)}

  12: evalfbb7in->evalfbb8in, Arg_2: 1+max([0, 4*Arg_1])+max([0, 3*Arg_0*max([4*min([1, Arg_1]), 4*Arg_1])]) {O(n^2)}

  12: evalfbb7in->evalfbb8in, Arg_3: Arg_0+((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([0, Arg_1]) {O(n^4)}

  12: evalfbb7in->evalfbb8in, Arg_4: 1+((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([1, -1+2*(Arg_0+((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([0, Arg_1]))])+max([0, -9*Arg_4]) {O(n^7)}

  4: evalfbb8in->evalfbb6in, Arg_0: Arg_1 {O(n)}

  4: evalfbb8in->evalfbb6in, Arg_1: Arg_0 {O(n)}

  4: evalfbb8in->evalfbb6in, Arg_2: 1+max([0, 4*Arg_1])+max([0, 3*Arg_0*max([4*min([1, Arg_1]), 4*Arg_1])]) {O(n^2)}

  4: evalfbb8in->evalfbb6in, Arg_3: Arg_0 {O(n)}

  4: evalfbb8in->evalfbb6in, Arg_4: max([Arg_4, 1+((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([1, -1+2*(Arg_0+((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([0, Arg_1]))])+max([0, -9*Arg_4])]) {O(n^7)}

  5: evalfbb8in->evalfbb9in, Arg_0: Arg_1 {O(n)}

  5: evalfbb8in->evalfbb9in, Arg_1: Arg_0 {O(n)}

  5: evalfbb8in->evalfbb9in, Arg_2: max([1, 1+max([0, 4*Arg_1])+max([0, 3*Arg_0*max([4*min([1, Arg_1]), 4*Arg_1])])]) {O(n^2)}

  5: evalfbb8in->evalfbb9in, Arg_3: max([Arg_3, Arg_0+((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([0, Arg_1])]) {O(n^4)}

  5: evalfbb8in->evalfbb9in, Arg_4: max([Arg_4, 1+((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([1, -1+2*(Arg_0+((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([0, Arg_1]))])+max([0, -9*Arg_4])]) {O(n^7)}

  13: evalfbb9in->evalfbb10in, Arg_0: Arg_1 {O(n)}

  13: evalfbb9in->evalfbb10in, Arg_1: Arg_0 {O(n)}

  13: evalfbb9in->evalfbb10in, Arg_2: max([1, 1+max([0, 4*Arg_1])+max([0, 3*Arg_0*max([4*min([1, Arg_1]), 4*Arg_1])])]) {O(n^2)}

  13: evalfbb9in->evalfbb10in, Arg_3: max([Arg_3, Arg_0+((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([0, Arg_1])]) {O(n^4)}

  13: evalfbb9in->evalfbb10in, Arg_4: max([Arg_4, 1+((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([1, -1+2*(Arg_0+((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([0, Arg_1]))])+max([0, -9*Arg_4])]) {O(n^7)}

  1: evalfentryin->evalfbb10in, Arg_0: Arg_1 {O(n)}

  1: evalfentryin->evalfbb10in, Arg_1: Arg_0 {O(n)}

  1: evalfentryin->evalfbb10in, Arg_2: Arg_2 {O(n)}

  1: evalfentryin->evalfbb10in, Arg_3: Arg_3 {O(n)}

  1: evalfentryin->evalfbb10in, Arg_4: Arg_4 {O(n)}

  14: evalfreturnin->evalfstop, Arg_0: Arg_1 {O(n)}

  14: evalfreturnin->evalfstop, Arg_1: 0 {O(1)}

  14: evalfreturnin->evalfstop, Arg_2: max([1, max([Arg_2, 1+max([0, 4*Arg_1])+max([0, 3*Arg_0*max([4*min([1, Arg_1]), 4*Arg_1])])])]) {O(n^2)}

  14: evalfreturnin->evalfstop, Arg_3: max([Arg_3, max([Arg_3, Arg_0+((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([0, Arg_1])])]) {O(n^4)}

  14: evalfreturnin->evalfstop, Arg_4: max([Arg_4, max([Arg_4, 1+((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([1, -1+2*(Arg_0+((max([0, 3*Arg_1])+max([0, 3*Arg_0*max([3*min([1, Arg_1]), 3*Arg_1])]))*max([0, Arg_0+Arg_1])+max([0, -10*Arg_3]))*max([0, Arg_1]))])+max([0, -9*Arg_4])])]) {O(n^7)}

  0: evalfstart->evalfentryin, Arg_0: Arg_0 {O(n)}

  0: evalfstart->evalfentryin, Arg_1: Arg_1 {O(n)}

  0: evalfstart->evalfentryin, Arg_2: Arg_2 {O(n)}

  0: evalfstart->evalfentryin, Arg_3: Arg_3 {O(n)}

  0: evalfstart->evalfentryin, Arg_4: Arg_4 {O(n)}


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

(2)
BOUNDS(1, nat(3 * Arg_0 * max(min(3, 3 * Arg_1), 3 * Arg_1)) * nat(Arg_0 + Arg_1) + 2 * nat(3 * Arg_0 * max(min(3, 3 * Arg_1), 3 * Arg_1)) * nat(Arg_0 + Arg_1) * nat(Arg_1) + nat(3 * Arg_0 * max(min(3, 3 * Arg_1), 3 * Arg_1)) * nat(Arg_0 + Arg_1) * max(4, -2 + 6 * Arg_0 + 6 * nat(3 * Arg_0 * max(min(3, 3 * Arg_1), 3 * Arg_1)) * nat(Arg_0 + Arg_1) * nat(Arg_1) + 6 * nat(3 * Arg_1) * nat(Arg_0 + Arg_1) * nat(Arg_1) + 6 * nat(-10 * Arg_3) * nat(Arg_1)) + nat(3 * Arg_0 * max(min(3, 3 * Arg_1), 3 * Arg_1)) * nat(Arg_0 + Arg_1) * max(1, -1 + 2 * Arg_0 + 2 * nat(3 * Arg_1) * nat(Arg_0 + Arg_1) * nat(Arg_1) + 2 * nat(3 * Arg_0 * max(min(3, 3 * Arg_1), 3 * Arg_1)) * nat(Arg_0 + Arg_1) * nat(Arg_1) + 2 * nat(-10 * Arg_3) * nat(Arg_1)) + 2 * nat(3 * Arg_1) * nat(Arg_0 + Arg_1) * nat(Arg_1) + nat(3 * Arg_1) * nat(Arg_0 + Arg_1) + nat(3 * Arg_1) * nat(Arg_0 + Arg_1) * max(1, -1 + 2 * Arg_0 + 2 * nat(3 * Arg_1) * nat(Arg_0 + Arg_1) * nat(Arg_1) + 2 * nat(3 * Arg_0 * max(min(3, 3 * Arg_1), 3 * Arg_1)) * nat(Arg_0 + Arg_1) * nat(Arg_1) + 2 * nat(-10 * Arg_3) * nat(Arg_1)) + nat(3 * Arg_1) * nat(Arg_0 + Arg_1) * max(4, -2 + 6 * Arg_0 + 6 * nat(3 * Arg_1) * nat(Arg_0 + Arg_1) * nat(Arg_1) + 6 * nat(3 * Arg_0 * max(3 * Arg_1, min(3, 3 * Arg_1))) * nat(Arg_0 + Arg_1) * nat(Arg_1) + 6 * nat(-10 * Arg_3) * nat(Arg_1)) + 2 * nat(-10 * Arg_3) * nat(Arg_1) + nat(-10 * Arg_3) + nat(-10 * Arg_3) * max(1, -1 + 2 * Arg_0 + 2 * nat(3 * Arg_1) * nat(Arg_0 + Arg_1) * nat(Arg_1) + 2 * nat(3 * Arg_0 * max(min(3, 3 * Arg_1), 3 * Arg_1)) * nat(Arg_0 + Arg_1) * nat(Arg_1) + 2 * nat(-10 * Arg_3) * nat(Arg_1)) + nat(-10 * Arg_3) * max(4, -2 + 6 * Arg_0 + 6 * nat(3 * Arg_1) * nat(Arg_0 + Arg_1) * nat(Arg_1) + 6 * nat(3 * Arg_0 * max(3 * Arg_1, min(3, 3 * Arg_1))) * nat(Arg_0 + Arg_1) * nat(Arg_1) + 6 * nat(-10 * Arg_3) * nat(Arg_1)) + nat(6 * Arg_0) + nat(-2 * Arg_4) + nat(3 * Arg_0 * max(4 * Arg_1, min(4, 4 * Arg_1))) + nat(4 * Arg_1) + max(1, 2 + Arg_0) + nat(-9 * Arg_4) + max(3, 3 + 6 * Arg_1) + nat(6 * Arg_0 * max(3 * Arg_1, min(3, 3 * Arg_1))))

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

(3) Loat Proof (FINISHED)


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



Initial linear ITS problem

   Start location: evalfstart

      0: evalfstart -> evalfentryin : [], cost: 1

      1: evalfentryin -> evalfbb10in : A'=B, B'=A, [], cost: 1

      2: evalfbb10in -> evalfbb8in : C'=1, [ B>=1 ], cost: 1

      3: evalfbb10in -> evalfreturnin : [ 0>=B ], cost: 1

      4: evalfbb8in -> evalfbb6in : D'=B, [ A>=C ], cost: 1

      5: evalfbb8in -> evalfbb9in : [ C>=1+A ], cost: 1

      6: evalfbb6in -> evalfbb4in : E'=1, [ C+B>=D ], cost: 1

      7: evalfbb6in -> evalfbb7in : [ D>=1+C+B ], cost: 1

      8: evalfbb4in -> evalfbb3in : [ D>=E ], cost: 1

      9: evalfbb4in -> evalfbb5in : [ E>=1+D ], cost: 1

     10: evalfbb3in -> evalfbb4in : E'=1+E, [], cost: 1

     11: evalfbb5in -> evalfbb6in : D'=1+D, [], cost: 1

     12: evalfbb7in -> evalfbb8in : C'=1+C, [], cost: 1

     13: evalfbb9in -> evalfbb10in : B'=-1+B, [], cost: 1

     14: evalfreturnin -> evalfstop : [], cost: 1



Removed unreachable and leaf rules:

   Start location: evalfstart

      0: evalfstart -> evalfentryin : [], cost: 1

      1: evalfentryin -> evalfbb10in : A'=B, B'=A, [], cost: 1

      2: evalfbb10in -> evalfbb8in : C'=1, [ B>=1 ], cost: 1

      4: evalfbb8in -> evalfbb6in : D'=B, [ A>=C ], cost: 1

      5: evalfbb8in -> evalfbb9in : [ C>=1+A ], cost: 1

      6: evalfbb6in -> evalfbb4in : E'=1, [ C+B>=D ], cost: 1

      7: evalfbb6in -> evalfbb7in : [ D>=1+C+B ], cost: 1

      8: evalfbb4in -> evalfbb3in : [ D>=E ], cost: 1

      9: evalfbb4in -> evalfbb5in : [ E>=1+D ], cost: 1

     10: evalfbb3in -> evalfbb4in : E'=1+E, [], cost: 1

     11: evalfbb5in -> evalfbb6in : D'=1+D, [], cost: 1

     12: evalfbb7in -> evalfbb8in : C'=1+C, [], cost: 1

     13: evalfbb9in -> evalfbb10in : B'=-1+B, [], cost: 1



### Simplification by acceleration and chaining ###



Eliminated locations (on linear paths):

   Start location: evalfstart

     15: evalfstart -> evalfbb10in : A'=B, B'=A, [], cost: 2

      2: evalfbb10in -> evalfbb8in : C'=1, [ B>=1 ], cost: 1

      4: evalfbb8in -> evalfbb6in : D'=B, [ A>=C ], cost: 1

     16: evalfbb8in -> evalfbb10in : B'=-1+B, [ C>=1+A ], cost: 2

      6: evalfbb6in -> evalfbb4in : E'=1, [ C+B>=D ], cost: 1

     17: evalfbb6in -> evalfbb8in : C'=1+C, [ D>=1+C+B ], cost: 2

     18: evalfbb4in -> evalfbb4in : E'=1+E, [ D>=E ], cost: 2

     19: evalfbb4in -> evalfbb6in : D'=1+D, [ E>=1+D ], cost: 2



Accelerating simple loops of location 5.

   Accelerating the following rules:

     18: evalfbb4in -> evalfbb4in : E'=1+E, [ D>=E ], cost: 2



   Accelerated rule 18 with metering function 1+D-E, yielding the new rule 20.

   Removing the simple loops: 18.



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

   Start location: evalfstart

     15: evalfstart -> evalfbb10in : A'=B, B'=A, [], cost: 2

      2: evalfbb10in -> evalfbb8in : C'=1, [ B>=1 ], cost: 1

      4: evalfbb8in -> evalfbb6in : D'=B, [ A>=C ], cost: 1

     16: evalfbb8in -> evalfbb10in : B'=-1+B, [ C>=1+A ], cost: 2

      6: evalfbb6in -> evalfbb4in : E'=1, [ C+B>=D ], cost: 1

     17: evalfbb6in -> evalfbb8in : C'=1+C, [ D>=1+C+B ], cost: 2

     19: evalfbb4in -> evalfbb6in : D'=1+D, [ E>=1+D ], cost: 2

     20: evalfbb4in -> evalfbb4in : E'=1+D, [ D>=E ], cost: 2+2*D-2*E



Chained accelerated rules (with incoming rules):

   Start location: evalfstart

     15: evalfstart -> evalfbb10in : A'=B, B'=A, [], cost: 2

      2: evalfbb10in -> evalfbb8in : C'=1, [ B>=1 ], cost: 1

      4: evalfbb8in -> evalfbb6in : D'=B, [ A>=C ], cost: 1

     16: evalfbb8in -> evalfbb10in : B'=-1+B, [ C>=1+A ], cost: 2

      6: evalfbb6in -> evalfbb4in : E'=1, [ C+B>=D ], cost: 1

     17: evalfbb6in -> evalfbb8in : C'=1+C, [ D>=1+C+B ], cost: 2

     21: evalfbb6in -> evalfbb4in : E'=1+D, [ C+B>=D && D>=1 ], cost: 1+2*D

     19: evalfbb4in -> evalfbb6in : D'=1+D, [ E>=1+D ], cost: 2



Eliminated locations (on tree-shaped paths):

   Start location: evalfstart

     15: evalfstart -> evalfbb10in : A'=B, B'=A, [], cost: 2

      2: evalfbb10in -> evalfbb8in : C'=1, [ B>=1 ], cost: 1

      4: evalfbb8in -> evalfbb6in : D'=B, [ A>=C ], cost: 1

     16: evalfbb8in -> evalfbb10in : B'=-1+B, [ C>=1+A ], cost: 2

     17: evalfbb6in -> evalfbb8in : C'=1+C, [ D>=1+C+B ], cost: 2

     22: evalfbb6in -> evalfbb6in : D'=1+D, E'=1, [ C+B>=D && 1>=1+D ], cost: 3

     23: evalfbb6in -> evalfbb6in : D'=1+D, E'=1+D, [ C+B>=D && D>=1 ], cost: 3+2*D



Accelerating simple loops of location 4.

   Accelerating the following rules:

     22: evalfbb6in -> evalfbb6in : D'=1+D, E'=1, [ C+B>=D && 1>=1+D ], cost: 3

     23: evalfbb6in -> evalfbb6in : D'=1+D, E'=1+D, [ C+B>=D && D>=1 ], cost: 3+2*D



   Accelerated rule 22 with backward acceleration, yielding the new rule 24.

   Accelerated rule 22 with backward acceleration, yielding the new rule 25.

   Accelerated rule 23 with metering function 1+C-D+B, yielding the new rule 26.

   Removing the simple loops: 22 23.



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

   Start location: evalfstart

     15: evalfstart -> evalfbb10in : A'=B, B'=A, [], cost: 2

      2: evalfbb10in -> evalfbb8in : C'=1, [ B>=1 ], cost: 1

      4: evalfbb8in -> evalfbb6in : D'=B, [ A>=C ], cost: 1

     16: evalfbb8in -> evalfbb10in : B'=-1+B, [ C>=1+A ], cost: 2

     17: evalfbb6in -> evalfbb8in : C'=1+C, [ D>=1+C+B ], cost: 2

     24: evalfbb6in -> evalfbb6in : D'=1+C+B, E'=1, [ C+B>=D && 1>=1+D && 1>=1+C+B ], cost: 3+3*C-3*D+3*B

     25: evalfbb6in -> evalfbb6in : D'=1, E'=1, [ C+B>=D && 1>=1+D && C+B>=0 ], cost: 3-3*D

     26: evalfbb6in -> evalfbb6in : D'=1+C+B, E'=1+C+B, [ C+B>=D && D>=1 ], cost: 2+2*C+(1+C-D+B)^2-2*D+2*(1+C-D+B)*D+2*B



Chained accelerated rules (with incoming rules):

   Start location: evalfstart

     15: evalfstart -> evalfbb10in : A'=B, B'=A, [], cost: 2

      2: evalfbb10in -> evalfbb8in : C'=1, [ B>=1 ], cost: 1

      4: evalfbb8in -> evalfbb6in : D'=B, [ A>=C ], cost: 1

     16: evalfbb8in -> evalfbb10in : B'=-1+B, [ C>=1+A ], cost: 2

     27: evalfbb8in -> evalfbb6in : D'=1+C+B, E'=1, [ A>=C && C+B>=B && 1>=1+B && 1>=1+C+B ], cost: 4+3*C

     28: evalfbb8in -> evalfbb6in : D'=1, E'=1, [ A>=C && C+B>=B && 1>=1+B && C+B>=0 ], cost: 4-3*B

     29: evalfbb8in -> evalfbb6in : D'=1+C+B, E'=1+C+B, [ A>=C && C+B>=B && B>=1 ], cost: 3+2*C+2*(1+C)*B+(1+C)^2

     17: evalfbb6in -> evalfbb8in : C'=1+C, [ D>=1+C+B ], cost: 2



Eliminated locations (on tree-shaped paths):

   Start location: evalfstart

     15: evalfstart -> evalfbb10in : A'=B, B'=A, [], cost: 2

      2: evalfbb10in -> evalfbb8in : C'=1, [ B>=1 ], cost: 1

     16: evalfbb8in -> evalfbb10in : B'=-1+B, [ C>=1+A ], cost: 2

     30: evalfbb8in -> evalfbb8in : C'=1+C, D'=B, [ A>=C && B>=1+C+B ], cost: 3

     31: evalfbb8in -> evalfbb8in : C'=1+C, D'=1+C+B, E'=1, [ A>=C && C+B>=B && 1>=1+B && 1>=1+C+B ], cost: 6+3*C

     32: evalfbb8in -> evalfbb8in : C'=1+C, D'=1, E'=1, [ A>=C && C+B>=B && 1>=1+B && C+B>=0 && 1>=1+C+B ], cost: 6-3*B

     33: evalfbb8in -> evalfbb8in : C'=1+C, D'=1+C+B, E'=1+C+B, [ A>=C && C+B>=B && B>=1 ], cost: 5+2*C+2*(1+C)*B+(1+C)^2



Accelerating simple loops of location 3.

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

   Accelerating the following rules:

     30: evalfbb8in -> evalfbb8in : C'=1+C, D'=B, [ A>=C && B>=1+C+B ], cost: 3

     31: evalfbb8in -> evalfbb8in : C'=1+C, D'=1+C+B, E'=1, [ A>=C && C+B>=B && 1>=1+B && 1>=1+C+B ], cost: 6+3*C

     32: evalfbb8in -> evalfbb8in : C'=1+C, D'=1, E'=1, [ A>=C && C+B>=B && 1>=1+B && -C-B==0 ], cost: 6-3*B

     33: evalfbb8in -> evalfbb8in : C'=1+C, D'=1+C+B, E'=1+C+B, [ A>=C && C+B>=B && B>=1 ], cost: 5+2*C+2*(1+C)*B+(1+C)^2



   Accelerated rule 30 with backward acceleration, yielding the new rule 34.

   Accelerated rule 30 with backward acceleration, yielding the new rule 35.

   Accelerated rule 31 with backward acceleration, yielding the new rule 36.

   Accelerated rule 31 with backward acceleration, yielding the new rule 37.

   Accelerated rule 32 with metering function -C-B, yielding the new rule 38.

   Accelerated rule 33 with metering function 1-C+A, yielding the new rule 39.

   Nested simple loops 32 (outer loop) and 35 (inner loop) with metering function -B, resulting in the new rules: 40.

   Removing the simple loops: 30 31 32 33.



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

   Start location: evalfstart

     15: evalfstart -> evalfbb10in : A'=B, B'=A, [], cost: 2

      2: evalfbb10in -> evalfbb8in : C'=1, [ B>=1 ], cost: 1

     16: evalfbb8in -> evalfbb10in : B'=-1+B, [ C>=1+A ], cost: 2

     34: evalfbb8in -> evalfbb8in : C'=1+A, D'=B, [ A>=C && B>=1+C+B && B>=1+A+B ], cost: 3-3*C+3*A

     35: evalfbb8in -> evalfbb8in : C'=0, D'=B, [ A>=C && B>=1+C+B && A>=-1 ], cost: -3*C

     36: evalfbb8in -> evalfbb8in : C'=1+A, D'=1+A+B, E'=1, [ A>=C && C+B>=B && 1>=1+B && 1>=1+C+B && A+B>=B && 1>=1+A+B ], cost: 9/2-3*(-1+C-A)*C-9/2*C+3/2*(-1+C-A)^2+9/2*A

     37: evalfbb8in -> evalfbb8in : C'=1-B, D'=1, E'=1, [ A>=C && C+B>=B && 1>=1+B && 1>=1+C+B && A>=-B ], cost: 9/2-9/2*C+3/2*(-1+C+B)^2-3*C*(-1+C+B)-9/2*B

     38: evalfbb8in -> evalfbb8in : C'=-B, D'=1, E'=1, [ A>=C && C+B>=B && 1>=1+B && -C-B==0 && -C-B>=1 ], cost: -6*C+3*(C+B)*B-6*B

     39: evalfbb8in -> evalfbb8in : C'=1+A, D'=1+A+B, E'=1+A+B, [ A>=C && C+B>=B && B>=1 ], cost: 25/6-3*(-1+C-A)*C-(-1+C-A)*C^2-25/6*C-(-1+C-A)*B+3/2*(-1+C-A)^2+25/6*A+(-1+C-A)^2*B-1/3*(-1+C-A)^3-2*(-1+C-A)*C*B+(-1+C-A)^2*C

     40: evalfbb8in -> evalfbb8in : C'=1, D'=1, E'=1, [ A>=C && B>=1+C+B && A>=0 && -B==0 && -B>=1 ], cost: 3*B^2-3*B



Chained accelerated rules (with incoming rules):

   Start location: evalfstart

     15: evalfstart -> evalfbb10in : A'=B, B'=A, [], cost: 2

      2: evalfbb10in -> evalfbb8in : C'=1, [ B>=1 ], cost: 1

     41: evalfbb10in -> evalfbb8in : C'=1+A, D'=1+A+B, E'=1+A+B, [ B>=1 && A>=1 ], cost: 1+A^2*B+49/6*A+3*A*B+5/2*A^2+1/3*A^3

     16: evalfbb8in -> evalfbb10in : B'=-1+B, [ C>=1+A ], cost: 2



Eliminated locations (on tree-shaped paths):

   Start location: evalfstart

     15: evalfstart -> evalfbb10in : A'=B, B'=A, [], cost: 2

     42: evalfbb10in -> evalfbb10in : B'=-1+B, C'=1, [ B>=1 && 1>=1+A ], cost: 3

     43: evalfbb10in -> evalfbb10in : B'=-1+B, C'=1+A, D'=1+A+B, E'=1+A+B, [ B>=1 && A>=1 ], cost: 3+A^2*B+49/6*A+3*A*B+5/2*A^2+1/3*A^3



Accelerating simple loops of location 2.

   Accelerating the following rules:

     42: evalfbb10in -> evalfbb10in : B'=-1+B, C'=1, [ B>=1 && 1>=1+A ], cost: 3

     43: evalfbb10in -> evalfbb10in : B'=-1+B, C'=1+A, D'=1+A+B, E'=1+A+B, [ B>=1 && A>=1 ], cost: 3+A^2*B+49/6*A+3*A*B+5/2*A^2+1/3*A^3



   Accelerated rule 42 with metering function B, yielding the new rule 44.

   Accelerated rule 43 with metering function B, yielding the new rule 45.

   Removing the simple loops: 42 43.



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

   Start location: evalfstart

     15: evalfstart -> evalfbb10in : A'=B, B'=A, [], cost: 2

     44: evalfbb10in -> evalfbb10in : B'=0, C'=1, [ B>=1 && 1>=1+A ], cost: 3*B

     45: evalfbb10in -> evalfbb10in : B'=0, C'=1+A, D'=2+A, E'=2+A, [ B>=1 && A>=1 ], cost: 3*A^2*B+1/2*A^2*B^2+1/3*A^3*B+3/2*A*B^2+29/3*A*B+3*B



Chained accelerated rules (with incoming rules):

   Start location: evalfstart

     15: evalfstart -> evalfbb10in : A'=B, B'=A, [], cost: 2

     46: evalfstart -> evalfbb10in : A'=B, B'=0, C'=1, [ A>=1 && 1>=1+B ], cost: 2+3*A

     47: evalfstart -> evalfbb10in : A'=B, B'=0, C'=1+B, D'=2+B, E'=2+B, [ A>=1 && B>=1 ], cost: 2+3/2*A^2*B+1/2*A^2*B^2+1/3*A*B^3+3*A*B^2+3*A+29/3*A*B



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

   Start location: evalfstart

     46: evalfstart -> evalfbb10in : A'=B, B'=0, C'=1, [ A>=1 && 1>=1+B ], cost: 2+3*A

     47: evalfstart -> evalfbb10in : A'=B, B'=0, C'=1+B, D'=2+B, E'=2+B, [ A>=1 && B>=1 ], cost: 2+3/2*A^2*B+1/2*A^2*B^2+1/3*A*B^3+3*A*B^2+3*A+29/3*A*B



### Computing asymptotic complexity ###



Fully simplified ITS problem

   Start location: evalfstart

     46: evalfstart -> evalfbb10in : A'=B, B'=0, C'=1, [ A>=1 && 1>=1+B ], cost: 2+3*A

     47: evalfstart -> evalfbb10in : A'=B, B'=0, C'=1+B, D'=2+B, E'=2+B, [ A>=1 && B>=1 ], cost: 2+3/2*A^2*B+1/2*A^2*B^2+1/3*A*B^3+3*A*B^2+3*A+29/3*A*B



Computing asymptotic complexity for rule 46

   Solved the limit problem by the following transformations:

      Created initial limit problem:

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



      removing all constraints (solved by SMT)

      resulting limit problem: [solved]



      applying transformation rule (C) using substitution {A==n,B==0}

      resulting limit problem:

      [solved]



   Solution:

      A / n

      B / 0

   Resulting cost 2+3*n has complexity: Poly(n^1)



Found new complexity Poly(n^1).



Computing asymptotic complexity for rule 47

   Solved the limit problem by the following transformations:

      Created initial limit problem:

      2+3/2*A^2*B+1/2*A^2*B^2+1/3*A*B^3+3*A*B^2+3*A+29/3*A*B (+), A (+/+!), 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:

      A / n

      B / n

   Resulting cost 2+9/2*n^3+29/3*n^2+5/6*n^4+3*n has complexity: Poly(n^4)



Found new complexity Poly(n^4).



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

   Complexity:  Poly(n^4)

   Cpx degree:  4

   Solved cost: 2+9/2*n^3+29/3*n^2+5/6*n^4+3*n

   Rule cost:   2+3/2*A^2*B+1/2*A^2*B^2+1/3*A*B^3+3*A*B^2+3*A+29/3*A*B

   Rule guard:  [ A>=1 && B>=1 ]



WORST_CASE(Omega(n^4),?)


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

(4)
BOUNDS(n^4, INF)