/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^6))
proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^4, 3 * nat(1 + 2 * Arg_1 + -2 * Arg_3) * nat(2 * max(2, 2 + 2 * Arg_1 * max(2, 3 + 2 * Arg_1) + max(2, 3 + 2 * Arg_1)) * nat(2 + 2 * Arg_1 + max(-4, min(-4, -6 + -4 * Arg_1))) + nat(2 + 4 * Arg_1 + -4 * Arg_3) + max(4, 5 + 2 * Arg_1)) + 5 * max(2, 2 + 2 * Arg_1 * max(2, 3 + 2 * Arg_1) + max(2, 3 + 2 * Arg_1)) * nat(2 + 2 * Arg_1 + max(-4, min(-4, -6 + -4 * Arg_1))) + 3 * max(2, 2 + 2 * Arg_1 * max(2, 3 + 2 * Arg_1) + max(2, 3 + 2 * Arg_1)) * nat(2 + 2 * Arg_1 + max(-4, min(-4, -6 + -4 * Arg_1))) * nat(max(4, 5 + 2 * Arg_1) + 2 * max(2, 2 + 2 * Arg_1 * max(2, 3 + 2 * Arg_1) + max(2, 3 + 2 * Arg_1)) * nat(2 + 2 * Arg_1 + max(-4, min(-4, -6 + -4 * Arg_1))) + nat(2 + 4 * Arg_1 + -4 * Arg_3)) + 3 * max(2, 2 + 2 * Arg_1 * max(2, 3 + 2 * Arg_1) + max(2, 3 + 2 * Arg_1)) * nat(max(3, 4 + 2 * Arg_1) + max(-1 * Arg_4, -1)) + max(1, 2 + 2 * Arg_1) + nat(5 + 10 * Arg_1 + -10 * Arg_3) + nat(3 + 3 * Arg_1 + -3 * Arg_4) + nat(1 + 2 * Arg_1) + max(12 + 6 * Arg_1 * max(2, 3 + 2 * Arg_1) + max(9 + 6 * Arg_1, 6), 12)).

(0) CpxIntTrs
(1) Koat2 Proof [FINISHED, 11.9 s]
(2) BOUNDS(1, 3 * nat(1 + 2 * Arg_1 + -2 * Arg_3) * nat(2 * max(2, 2 + 2 * Arg_1 * max(2, 3 + 2 * Arg_1) + max(2, 3 + 2 * Arg_1)) * nat(2 + 2 * Arg_1 + max(-4, min(-4, -6 + -4 * Arg_1))) + nat(2 + 4 * Arg_1 + -4 * Arg_3) + max(4, 5 + 2 * Arg_1)) + 5 * max(2, 2 + 2 * Arg_1 * max(2, 3 + 2 * Arg_1) + max(2, 3 + 2 * Arg_1)) * nat(2 + 2 * Arg_1 + max(-4, min(-4, -6 + -4 * Arg_1))) + 3 * max(2, 2 + 2 * Arg_1 * max(2, 3 + 2 * Arg_1) + max(2, 3 + 2 * Arg_1)) * nat(2 + 2 * Arg_1 + max(-4, min(-4, -6 + -4 * Arg_1))) * nat(max(4, 5 + 2 * Arg_1) + 2 * max(2, 2 + 2 * Arg_1 * max(2, 3 + 2 * Arg_1) + max(2, 3 + 2 * Arg_1)) * nat(2 + 2 * Arg_1 + max(-4, min(-4, -6 + -4 * Arg_1))) + nat(2 + 4 * Arg_1 + -4 * Arg_3)) + 3 * max(2, 2 + 2 * Arg_1 * max(2, 3 + 2 * Arg_1) + max(2, 3 + 2 * Arg_1)) * nat(max(3, 4 + 2 * Arg_1) + max(-1 * Arg_4, -1)) + max(1, 2 + 2 * Arg_1) + nat(5 + 10 * Arg_1 + -10 * Arg_3) + nat(3 + 3 * Arg_1 + -3 * Arg_4) + nat(1 + 2 * Arg_1) + max(12 + 6 * Arg_1 * max(2, 3 + 2 * Arg_1) + max(9 + 6 * Arg_1, 6), 12))
(3) Loat Proof [FINISHED, 1548 ms]
(4) BOUNDS(n^4, INF)


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

(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(1, B, C, D, E)) :|: TRUE
evalfbb10in(A, B, C, D, E) -> Com_1(evalfbb8in(A, B, 1, D, E)) :|: B >= A
evalfbb10in(A, B, C, D, E) -> Com_1(evalfreturnin(A, B, C, D, E)) :|: A >= B + 1
evalfbb8in(A, B, C, D, E) -> Com_1(evalfbb6in(A, B, C, A + 1, E)) :|: A >= C
evalfbb8in(A, B, C, D, E) -> Com_1(evalfbb10in(A + 1, B, C, D, E)) :|: C >= A + 1
evalfbb6in(A, B, C, D, E) -> Com_1(evalfbb4in(A, B, C, D, 1)) :|: B >= D
evalfbb6in(A, B, C, D, E) -> Com_1(evalfbb7in(A, B, C, D, E)) :|: D >= B + 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
evalfreturnin(A, B, C, D, E) -> Com_1(evalfstop(A, B, C, D, E)) :|: TRUE

The start-symbols are:[evalfstart_5]


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

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



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, evalfentryin, evalfreturnin, evalfstart, evalfstop  

  Transitions:

  2: evalfbb10in->evalfbb8in

  3: evalfbb10in->evalfreturnin

  10: evalfbb3in->evalfbb4in

  8: evalfbb4in->evalfbb3in

  9: evalfbb4in->evalfbb5in

  11: evalfbb5in->evalfbb6in

  6: evalfbb6in->evalfbb4in

  7: evalfbb6in->evalfbb7in

  12: evalfbb7in->evalfbb8in

  5: evalfbb8in->evalfbb10in

  4: evalfbb8in->evalfbb6in

  1: evalfentryin->evalfbb10in

  13: evalfreturnin->evalfstop

  0: evalfstart->evalfentryin  



Timebounds: 

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

  2: evalfbb10in->evalfbb8in: max([0, 1+2*Arg_1]) {O(n)}

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

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

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

  9: evalfbb4in->evalfbb5in: 1+2*(max([2, 2+(1+2*Arg_1)*max([2, 3+2*Arg_1])])*max([0, 1+1+2*Arg_1+max([-4, -2*max([2, 3+2*Arg_1])])])+max([0, 1+2*Arg_1+-2*Arg_3])) {O(n^3)}

  11: evalfbb5in->evalfbb6in: 1+2*(max([2, 2+(1+2*Arg_1)*max([2, 3+2*Arg_1])])*max([0, 1+1+2*Arg_1+max([-4, -2*max([2, 3+2*Arg_1])])])+max([0, 1+2*Arg_1+-2*Arg_3])) {O(n^3)}

  6: evalfbb6in->evalfbb4in: max([2, 2+(1+2*Arg_1)*max([2, 3+2*Arg_1])])*max([0, 1+1+2*Arg_1+max([-4, -2*max([2, 3+2*Arg_1])])])+max([0, 1+2*Arg_1+-2*Arg_3]) {O(n^3)}

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

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

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

  5: evalfbb8in->evalfbb10in: max([0, 1+2*Arg_1]) {O(n)}

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

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

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



Costbounds:

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

  2: evalfbb10in->evalfbb8in: max([0, 1+2*Arg_1]) {O(n)}

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

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

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

  9: evalfbb4in->evalfbb5in: 1+2*(max([2, 2+(1+2*Arg_1)*max([2, 3+2*Arg_1])])*max([0, 1+1+2*Arg_1+max([-4, -2*max([2, 3+2*Arg_1])])])+max([0, 1+2*Arg_1+-2*Arg_3])) {O(n^3)}

  11: evalfbb5in->evalfbb6in: 1+2*(max([2, 2+(1+2*Arg_1)*max([2, 3+2*Arg_1])])*max([0, 1+1+2*Arg_1+max([-4, -2*max([2, 3+2*Arg_1])])])+max([0, 1+2*Arg_1+-2*Arg_3])) {O(n^3)}

  6: evalfbb6in->evalfbb4in: max([2, 2+(1+2*Arg_1)*max([2, 3+2*Arg_1])])*max([0, 1+1+2*Arg_1+max([-4, -2*max([2, 3+2*Arg_1])])])+max([0, 1+2*Arg_1+-2*Arg_3]) {O(n^3)}

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

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

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

  5: evalfbb8in->evalfbb10in: max([0, 1+2*Arg_1]) {O(n)}

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

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

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



Sizebounds:

`Lower:

  2: evalfbb10in->evalfbb8in, Arg_0: 1 {O(1)}

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

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

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

  2: evalfbb10in->evalfbb8in, Arg_4: min([1, Arg_4]) {O(n)}

  3: evalfbb10in->evalfreturnin, Arg_0: 1 {O(1)}

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

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

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

  3: evalfbb10in->evalfreturnin, Arg_4: min([1, Arg_4]) {O(n)}

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

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

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

  10: evalfbb3in->evalfbb4in, Arg_3: 2 {O(1)}

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

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

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

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

  8: evalfbb4in->evalfbb3in, Arg_3: 2 {O(1)}

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

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

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

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

  9: evalfbb4in->evalfbb5in, Arg_3: 2 {O(1)}

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

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

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

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

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

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

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

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

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

  6: evalfbb6in->evalfbb4in, Arg_3: 2 {O(1)}

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

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

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

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

  7: evalfbb6in->evalfbb7in, Arg_3: 2 {O(1)}

  7: evalfbb6in->evalfbb7in, Arg_4: min([1, Arg_4]) {O(n)}

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

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

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

  12: evalfbb7in->evalfbb8in, Arg_3: 2 {O(1)}

  12: evalfbb7in->evalfbb8in, Arg_4: min([1, Arg_4]) {O(n)}

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

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

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

  4: evalfbb8in->evalfbb6in, Arg_3: 2 {O(1)}

  4: evalfbb8in->evalfbb6in, Arg_4: min([1, Arg_4]) {O(n)}

  5: evalfbb8in->evalfbb10in, Arg_0: 1 {O(1)}

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

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

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

  5: evalfbb8in->evalfbb10in, Arg_4: min([1, Arg_4]) {O(n)}

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

  1: evalfentryin->evalfbb10in, Arg_1: Arg_1 {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)}

  13: evalfreturnin->evalfstop, Arg_0: 1 {O(1)}

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

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

  13: evalfreturnin->evalfstop, Arg_3: min([2, Arg_3]) {O(n)}

  13: evalfreturnin->evalfstop, Arg_4: min([1, 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: max([1, 2+2*Arg_1]) {O(n)}

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

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

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

  2: evalfbb10in->evalfbb8in, Arg_4: max([1, max([Arg_4, 2+2*((max([2, 2+(1+2*Arg_1)*max([2, 3+2*Arg_1])])*max([0, 1+1+2*Arg_1+max([-4, -2*max([2, 3+2*Arg_1])])])+max([0, 1+2*Arg_1+-2*Arg_3]))*max([0, 2+2*(max([2, 2+(1+2*Arg_1)*max([2, 3+2*Arg_1])])*max([0, 1+1+2*Arg_1+max([-4, -2*max([2, 3+2*Arg_1])])])+max([0, 1+2*Arg_1+-2*Arg_3]))+max([2, 3+2*Arg_1])])+max([2, 2+(1+2*Arg_1)*max([2, 3+2*Arg_1])])*max([0, 1+max([2, 3+2*Arg_1])+max([-1, -(Arg_4)])])+max([0, 1+Arg_1-Arg_4]))])]) {O(n^6)}

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

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

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

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

  3: evalfbb10in->evalfreturnin, Arg_4: max([1, max([Arg_4, max([Arg_4, 2+2*((max([2, 2+(1+2*Arg_1)*max([2, 3+2*Arg_1])])*max([0, 1+1+2*Arg_1+max([-4, -2*max([2, 3+2*Arg_1])])])+max([0, 1+2*Arg_1+-2*Arg_3]))*max([0, 2+2*(max([2, 2+(1+2*Arg_1)*max([2, 3+2*Arg_1])])*max([0, 1+1+2*Arg_1+max([-4, -2*max([2, 3+2*Arg_1])])])+max([0, 1+2*Arg_1+-2*Arg_3]))+max([2, 3+2*Arg_1])])+max([2, 2+(1+2*Arg_1)*max([2, 3+2*Arg_1])])*max([0, 1+max([2, 3+2*Arg_1])+max([-1, -(Arg_4)])])+max([0, 1+Arg_1-Arg_4]))])])]) {O(n^6)}

  10: evalfbb3in->evalfbb4in, Arg_0: max([1, 2+2*Arg_1]) {O(n)}

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

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

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

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

  8: evalfbb4in->evalfbb3in, Arg_0: max([1, 2+2*Arg_1]) {O(n)}

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

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

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

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

  9: evalfbb4in->evalfbb5in, Arg_0: max([1, 2+2*Arg_1]) {O(n)}

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

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

  9: evalfbb4in->evalfbb5in, Arg_3: 1+2*(max([2, 2+(1+2*Arg_1)*max([2, 3+2*Arg_1])])*max([0, 1+1+2*Arg_1+max([-4, -2*max([2, 3+2*Arg_1])])])+max([0, 1+2*Arg_1+-2*Arg_3]))+max([2, 3+2*Arg_1]) {O(n^3)}

  9: evalfbb4in->evalfbb5in, Arg_4: max([1, 2+2*((max([2, 2+(1+2*Arg_1)*max([2, 3+2*Arg_1])])*max([0, 1+1+2*Arg_1+max([-4, -2*max([2, 3+2*Arg_1])])])+max([0, 1+2*Arg_1+-2*Arg_3]))*max([0, 2+2*(max([2, 2+(1+2*Arg_1)*max([2, 3+2*Arg_1])])*max([0, 1+1+2*Arg_1+max([-4, -2*max([2, 3+2*Arg_1])])])+max([0, 1+2*Arg_1+-2*Arg_3]))+max([2, 3+2*Arg_1])])+max([2, 2+(1+2*Arg_1)*max([2, 3+2*Arg_1])])*max([0, 1+max([2, 3+2*Arg_1])+max([-1, -(Arg_4)])])+max([0, 1+Arg_1-Arg_4]))]) {O(n^6)}

  11: evalfbb5in->evalfbb6in, Arg_0: max([1, 2+2*Arg_1]) {O(n)}

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

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

  11: evalfbb5in->evalfbb6in, Arg_3: 1+2*(max([2, 2+(1+2*Arg_1)*max([2, 3+2*Arg_1])])*max([0, 1+1+2*Arg_1+max([-4, -2*max([2, 3+2*Arg_1])])])+max([0, 1+2*Arg_1+-2*Arg_3]))+max([2, 3+2*Arg_1]) {O(n^3)}

  11: evalfbb5in->evalfbb6in, Arg_4: max([1, 2+2*((max([2, 2+(1+2*Arg_1)*max([2, 3+2*Arg_1])])*max([0, 1+1+2*Arg_1+max([-4, -2*max([2, 3+2*Arg_1])])])+max([0, 1+2*Arg_1+-2*Arg_3]))*max([0, 2+2*(max([2, 2+(1+2*Arg_1)*max([2, 3+2*Arg_1])])*max([0, 1+1+2*Arg_1+max([-4, -2*max([2, 3+2*Arg_1])])])+max([0, 1+2*Arg_1+-2*Arg_3]))+max([2, 3+2*Arg_1])])+max([2, 2+(1+2*Arg_1)*max([2, 3+2*Arg_1])])*max([0, 1+max([2, 3+2*Arg_1])+max([-1, -(Arg_4)])])+max([0, 1+Arg_1-Arg_4]))]) {O(n^6)}

  6: evalfbb6in->evalfbb4in, Arg_0: max([1, 2+2*Arg_1]) {O(n)}

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

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

  6: evalfbb6in->evalfbb4in, Arg_3: 1+2*(max([2, 2+(1+2*Arg_1)*max([2, 3+2*Arg_1])])*max([0, 1+1+2*Arg_1+max([-4, -2*max([2, 3+2*Arg_1])])])+max([0, 1+2*Arg_1+-2*Arg_3]))+max([2, 3+2*Arg_1]) {O(n^3)}

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

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

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

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

  7: evalfbb6in->evalfbb7in, Arg_3: max([2, max([1+2*(max([2, 2+(1+2*Arg_1)*max([2, 3+2*Arg_1])])*max([0, 1+1+2*Arg_1+max([-4, -2*max([2, 3+2*Arg_1])])])+max([0, 1+2*Arg_1+-2*Arg_3]))+max([2, 3+2*Arg_1]), 3+2*Arg_1])]) {O(n^3)}

  7: evalfbb6in->evalfbb7in, Arg_4: max([1, max([Arg_4, 2+2*((max([2, 2+(1+2*Arg_1)*max([2, 3+2*Arg_1])])*max([0, 1+1+2*Arg_1+max([-4, -2*max([2, 3+2*Arg_1])])])+max([0, 1+2*Arg_1+-2*Arg_3]))*max([0, 2+2*(max([2, 2+(1+2*Arg_1)*max([2, 3+2*Arg_1])])*max([0, 1+1+2*Arg_1+max([-4, -2*max([2, 3+2*Arg_1])])])+max([0, 1+2*Arg_1+-2*Arg_3]))+max([2, 3+2*Arg_1])])+max([2, 2+(1+2*Arg_1)*max([2, 3+2*Arg_1])])*max([0, 1+max([2, 3+2*Arg_1])+max([-1, -(Arg_4)])])+max([0, 1+Arg_1-Arg_4]))])]) {O(n^6)}

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

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

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

  12: evalfbb7in->evalfbb8in, Arg_3: max([2, max([1+2*(max([2, 2+(1+2*Arg_1)*max([2, 3+2*Arg_1])])*max([0, 1+1+2*Arg_1+max([-4, -2*max([2, 3+2*Arg_1])])])+max([0, 1+2*Arg_1+-2*Arg_3]))+max([2, 3+2*Arg_1]), 3+2*Arg_1])]) {O(n^3)}

  12: evalfbb7in->evalfbb8in, Arg_4: max([1, max([Arg_4, 2+2*((max([2, 2+(1+2*Arg_1)*max([2, 3+2*Arg_1])])*max([0, 1+1+2*Arg_1+max([-4, -2*max([2, 3+2*Arg_1])])])+max([0, 1+2*Arg_1+-2*Arg_3]))*max([0, 2+2*(max([2, 2+(1+2*Arg_1)*max([2, 3+2*Arg_1])])*max([0, 1+1+2*Arg_1+max([-4, -2*max([2, 3+2*Arg_1])])])+max([0, 1+2*Arg_1+-2*Arg_3]))+max([2, 3+2*Arg_1])])+max([2, 2+(1+2*Arg_1)*max([2, 3+2*Arg_1])])*max([0, 1+max([2, 3+2*Arg_1])+max([-1, -(Arg_4)])])+max([0, 1+Arg_1-Arg_4]))])]) {O(n^6)}

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

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

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

  4: evalfbb8in->evalfbb6in, Arg_3: max([2, 3+2*Arg_1]) {O(n)}

  4: evalfbb8in->evalfbb6in, Arg_4: max([1, max([Arg_4, 2+2*((max([2, 2+(1+2*Arg_1)*max([2, 3+2*Arg_1])])*max([0, 1+1+2*Arg_1+max([-4, -2*max([2, 3+2*Arg_1])])])+max([0, 1+2*Arg_1+-2*Arg_3]))*max([0, 2+2*(max([2, 2+(1+2*Arg_1)*max([2, 3+2*Arg_1])])*max([0, 1+1+2*Arg_1+max([-4, -2*max([2, 3+2*Arg_1])])])+max([0, 1+2*Arg_1+-2*Arg_3]))+max([2, 3+2*Arg_1])])+max([2, 2+(1+2*Arg_1)*max([2, 3+2*Arg_1])])*max([0, 1+max([2, 3+2*Arg_1])+max([-1, -(Arg_4)])])+max([0, 1+Arg_1-Arg_4]))])]) {O(n^6)}

  5: evalfbb8in->evalfbb10in, Arg_0: max([1, 2+2*Arg_1]) {O(n)}

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

  5: evalfbb8in->evalfbb10in, Arg_2: max([3, 3+(1+2*Arg_1)*max([2, 3+2*Arg_1])]) {O(n^2)}

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

  5: evalfbb8in->evalfbb10in, Arg_4: max([1, max([Arg_4, 2+2*((max([2, 2+(1+2*Arg_1)*max([2, 3+2*Arg_1])])*max([0, 1+1+2*Arg_1+max([-4, -2*max([2, 3+2*Arg_1])])])+max([0, 1+2*Arg_1+-2*Arg_3]))*max([0, 2+2*(max([2, 2+(1+2*Arg_1)*max([2, 3+2*Arg_1])])*max([0, 1+1+2*Arg_1+max([-4, -2*max([2, 3+2*Arg_1])])])+max([0, 1+2*Arg_1+-2*Arg_3]))+max([2, 3+2*Arg_1])])+max([2, 2+(1+2*Arg_1)*max([2, 3+2*Arg_1])])*max([0, 1+max([2, 3+2*Arg_1])+max([-1, -(Arg_4)])])+max([0, 1+Arg_1-Arg_4]))])]) {O(n^6)}

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

  1: evalfentryin->evalfbb10in, Arg_1: Arg_1 {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)}

  13: evalfreturnin->evalfstop, Arg_0: max([1, max([1, 2+2*Arg_1])]) {O(n)}

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

  13: evalfreturnin->evalfstop, Arg_2: max([3, max([Arg_2, 3+(1+2*Arg_1)*max([2, 3+2*Arg_1])])]) {O(n^2)}

  13: evalfreturnin->evalfstop, Arg_3: max([2, max([Arg_3, max([Arg_3, max([1+2*(max([2, 2+(1+2*Arg_1)*max([2, 3+2*Arg_1])])*max([0, 1+1+2*Arg_1+max([-4, -2*max([2, 3+2*Arg_1])])])+max([0, 1+2*Arg_1+-2*Arg_3]))+max([2, 3+2*Arg_1]), 3+2*Arg_1])])])]) {O(n^3)}

  13: evalfreturnin->evalfstop, Arg_4: max([1, max([Arg_4, max([Arg_4, 2+2*((max([2, 2+(1+2*Arg_1)*max([2, 3+2*Arg_1])])*max([0, 1+1+2*Arg_1+max([-4, -2*max([2, 3+2*Arg_1])])])+max([0, 1+2*Arg_1+-2*Arg_3]))*max([0, 2+2*(max([2, 2+(1+2*Arg_1)*max([2, 3+2*Arg_1])])*max([0, 1+1+2*Arg_1+max([-4, -2*max([2, 3+2*Arg_1])])])+max([0, 1+2*Arg_1+-2*Arg_3]))+max([2, 3+2*Arg_1])])+max([2, 2+(1+2*Arg_1)*max([2, 3+2*Arg_1])])*max([0, 1+max([2, 3+2*Arg_1])+max([-1, -(Arg_4)])])+max([0, 1+Arg_1-Arg_4]))])])]) {O(n^6)}

  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, 3 * nat(1 + 2 * Arg_1 + -2 * Arg_3) * nat(2 * max(2, 2 + 2 * Arg_1 * max(2, 3 + 2 * Arg_1) + max(2, 3 + 2 * Arg_1)) * nat(2 + 2 * Arg_1 + max(-4, min(-4, -6 + -4 * Arg_1))) + nat(2 + 4 * Arg_1 + -4 * Arg_3) + max(4, 5 + 2 * Arg_1)) + 5 * max(2, 2 + 2 * Arg_1 * max(2, 3 + 2 * Arg_1) + max(2, 3 + 2 * Arg_1)) * nat(2 + 2 * Arg_1 + max(-4, min(-4, -6 + -4 * Arg_1))) + 3 * max(2, 2 + 2 * Arg_1 * max(2, 3 + 2 * Arg_1) + max(2, 3 + 2 * Arg_1)) * nat(2 + 2 * Arg_1 + max(-4, min(-4, -6 + -4 * Arg_1))) * nat(max(4, 5 + 2 * Arg_1) + 2 * max(2, 2 + 2 * Arg_1 * max(2, 3 + 2 * Arg_1) + max(2, 3 + 2 * Arg_1)) * nat(2 + 2 * Arg_1 + max(-4, min(-4, -6 + -4 * Arg_1))) + nat(2 + 4 * Arg_1 + -4 * Arg_3)) + 3 * max(2, 2 + 2 * Arg_1 * max(2, 3 + 2 * Arg_1) + max(2, 3 + 2 * Arg_1)) * nat(max(3, 4 + 2 * Arg_1) + max(-1 * Arg_4, -1)) + max(1, 2 + 2 * Arg_1) + nat(5 + 10 * Arg_1 + -10 * Arg_3) + nat(3 + 3 * Arg_1 + -3 * Arg_4) + nat(1 + 2 * Arg_1) + max(12 + 6 * Arg_1 * max(2, 3 + 2 * Arg_1) + max(9 + 6 * Arg_1, 6), 12))

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

(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'=1, [], cost: 1

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

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

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

      5: evalfbb8in -> evalfbb10in : A'=1+A, [ C>=1+A ], cost: 1

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

      7: evalfbb6in -> evalfbb7in : [ D>=1+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: evalfreturnin -> evalfstop : [], cost: 1



Checking for constant complexity:

   The following rule is satisfiable with cost >= 1, yielding constant complexity:

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



Removed unreachable and leaf rules:

   Start location: evalfstart

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

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

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

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

      5: evalfbb8in -> evalfbb10in : A'=1+A, [ C>=1+A ], cost: 1

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

      7: evalfbb6in -> evalfbb7in : [ D>=1+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



### Simplification by acceleration and chaining ###



Eliminated locations (on linear paths):

   Start location: evalfstart

     14: evalfstart -> evalfbb10in : A'=1, [], cost: 2

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

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

      5: evalfbb8in -> evalfbb10in : A'=1+A, [ C>=1+A ], cost: 1

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

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

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

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



Accelerating simple loops of location 5.

   Accelerating the following rules:

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



   Accelerated rule 16 with metering function 1+D-E, yielding the new rule 18.

   Removing the simple loops: 16.



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

   Start location: evalfstart

     14: evalfstart -> evalfbb10in : A'=1, [], cost: 2

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

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

      5: evalfbb8in -> evalfbb10in : A'=1+A, [ C>=1+A ], cost: 1

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

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

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

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



Chained accelerated rules (with incoming rules):

   Start location: evalfstart

     14: evalfstart -> evalfbb10in : A'=1, [], cost: 2

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

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

      5: evalfbb8in -> evalfbb10in : A'=1+A, [ C>=1+A ], cost: 1

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

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

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

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



Eliminated locations (on tree-shaped paths):

   Start location: evalfstart

     14: evalfstart -> evalfbb10in : A'=1, [], cost: 2

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

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

      5: evalfbb8in -> evalfbb10in : A'=1+A, [ C>=1+A ], cost: 1

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

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

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



Accelerating simple loops of location 4.

   Accelerating the following rules:

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

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



   Found no metering function for rule 20.

   Accelerated rule 21 with metering function 1-D+B, yielding the new rule 22.

   Removing the simple loops: 21.



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

   Start location: evalfstart

     14: evalfstart -> evalfbb10in : A'=1, [], cost: 2

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

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

      5: evalfbb8in -> evalfbb10in : A'=1+A, [ C>=1+A ], cost: 1

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

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

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



Chained accelerated rules (with incoming rules):

   Start location: evalfstart

     14: evalfstart -> evalfbb10in : A'=1, [], cost: 2

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

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

      5: evalfbb8in -> evalfbb10in : A'=1+A, [ C>=1+A ], cost: 1

     23: evalfbb8in -> evalfbb6in : D'=2+A, E'=1, [ A>=C && B>=1+A && 1>=2+A ], cost: 4

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

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



Eliminated locations (on tree-shaped paths):

   Start location: evalfstart

     14: evalfstart -> evalfbb10in : A'=1, [], cost: 2

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

      5: evalfbb8in -> evalfbb10in : A'=1+A, [ C>=1+A ], cost: 1

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

     26: evalfbb8in -> evalfbb8in : C'=1+C, D'=2+A, E'=1, [ A>=C && B>=1+A && 1>=2+A && 2+A>=1+B ], cost: 6

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



Accelerating simple loops of location 3.

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

   Accelerating the following rules:

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

     26: evalfbb8in -> evalfbb8in : C'=1+C, D'=2+A, E'=1, [ A>=C && 1+A-B==0 && 1>=2+A ], cost: 6

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



   Accelerated rule 25 with metering function 1-C+A, yielding the new rule 28.

   Accelerated rule 26 with metering function 1-C+A, yielding the new rule 29.

   Accelerated rule 27 with metering function 1-C+A, yielding the new rule 30.

   Removing the simple loops: 25 26 27.



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

   Start location: evalfstart

     14: evalfstart -> evalfbb10in : A'=1, [], cost: 2

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

      5: evalfbb8in -> evalfbb10in : A'=1+A, [ C>=1+A ], cost: 1

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

     29: evalfbb8in -> evalfbb8in : C'=1+A, D'=2+A, E'=1, [ A>=C && 1+A-B==0 && 1>=2+A ], cost: 6-6*C+6*A

     30: evalfbb8in -> evalfbb8in : C'=1+A, D'=1+B, E'=1+B, [ A>=C && B>=1+A && 1+A>=1 ], cost: 3-4*(-1+C-A)*B-3*C+A^2*(-1+C-A)-(-1+C-A)*B^2+3*A+4*A*(-1+C-A)



Chained accelerated rules (with incoming rules):

   Start location: evalfstart

     14: evalfstart -> evalfbb10in : A'=1, [], cost: 2

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

     31: evalfbb10in -> evalfbb8in : C'=1+A, D'=1+A, [ A-B==0 && A>=1 ], cost: 1+3*A

     32: evalfbb10in -> evalfbb8in : C'=1+A, D'=1+B, E'=1+B, [ A>=1 && B>=1+A ], cost: 1+4*A*B+A*B^2+3*A-4*A^2-A^3

      5: evalfbb8in -> evalfbb10in : A'=1+A, [ C>=1+A ], cost: 1



Eliminated locations (on tree-shaped paths):

   Start location: evalfstart

     14: evalfstart -> evalfbb10in : A'=1, [], cost: 2

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

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

     35: evalfbb10in -> evalfbb10in : A'=1+A, C'=1+A, D'=1+B, E'=1+B, [ A>=1 && B>=1+A ], cost: 2+4*A*B+A*B^2+3*A-4*A^2-A^3



Accelerating simple loops of location 2.

   Accelerating the following rules:

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

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

     35: evalfbb10in -> evalfbb10in : A'=1+A, C'=1+A, D'=1+B, E'=1+B, [ A>=1 && B>=1+A ], cost: 2+4*A*B+A*B^2+3*A-4*A^2-A^3



   Found no metering function for rule 33.

   Accelerated rule 34 with metering function 1-A+B, yielding the new rule 36.

   Accelerated rule 35 with metering function -A+B, yielding the new rule 37.

   Nested simple loops 35 (outer loop) and 36 (inner loop) with metering function meter_1 (where 2*meter_1==-A+B), resulting in the new rules: 38.

   Removing the simple loops: 34 35.



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

   Start location: evalfstart

     14: evalfstart -> evalfbb10in : A'=1, [], cost: 2

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

     36: evalfbb10in -> evalfbb10in : A'=1+B, C'=1+B, D'=1+B, [ A-B==0 && A>=1 ], cost: 1/2-1/2*A+3/2*(-1+A-B)^2+1/2*B-3*(-1+A-B)*A

     37: evalfbb10in -> evalfbb10in : A'=B, C'=B, D'=1+B, E'=1+B, [ A>=1 && B>=1+A ], cost: 2*(A-B)^2*B+A^3*(A-B)-3/2*A^2*(A-B)^2+5/6*(A-B)^3+5/2*A^2*(A-B)+13/4*(A-B)^2+1/2*(A-B)^2*B^2+1/6*A+1/2*(A-B)*B^2-A*(A-B)*B^2-13/2*A*(A-B)-1/4*(A-B)^4-5/2*A*(A-B)^2-1/6*B-4*A*(A-B)*B+A*(A-B)^3+2*(A-B)*B

     38: evalfbb10in -> evalfbb10in : A'=1+B, C'=1+B, D'=1+B, E'=1+B, [ A>=1 && 1+A-B==0 && 2*meter_1==-A+B && meter_1>=1 ], cost: -7*meter_1*B-2*meter_1*B^2-5*meter_1



Chained accelerated rules (with incoming rules):

   Start location: evalfstart

     14: evalfstart -> evalfbb10in : A'=1, [], cost: 2

     39: evalfstart -> evalfbb10in : A'=1+B, C'=1+B, D'=1+B, [ 1-B==0 ], cost: 2+7/2*B+3/2*B^2

     40: evalfstart -> evalfbb10in : A'=B, C'=B, D'=1+B, E'=1+B, [ B>=2 ], cost: -5/6-1/4*(-1+B)^4+1/2*(-1+B)^2*B^2+2*(-1+B)^2*B+2*(-1+B)*B+17/6*B-3/4*(-1+B)^2+1/2*(-1+B)*B^2-11/6*(-1+B)^3



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

   Start location: evalfstart

     39: evalfstart -> evalfbb10in : A'=1+B, C'=1+B, D'=1+B, [ 1-B==0 ], cost: 2+7/2*B+3/2*B^2

     40: evalfstart -> evalfbb10in : A'=B, C'=B, D'=1+B, E'=1+B, [ B>=2 ], cost: -5/6-1/4*(-1+B)^4+1/2*(-1+B)^2*B^2+2*(-1+B)^2*B+2*(-1+B)*B+17/6*B-3/4*(-1+B)^2+1/2*(-1+B)*B^2-11/6*(-1+B)^3



### Computing asymptotic complexity ###



Fully simplified ITS problem

   Start location: evalfstart

     39: evalfstart -> evalfbb10in : A'=1+B, C'=1+B, D'=1+B, [ 1-B==0 ], cost: 2+7/2*B+3/2*B^2

     40: evalfstart -> evalfbb10in : A'=B, C'=B, D'=1+B, E'=1+B, [ B>=2 ], cost: -5/6-1/4*(-1+B)^4+1/2*(-1+B)^2*B^2+2*(-1+B)^2*B+2*(-1+B)*B+17/6*B-3/4*(-1+B)^2+1/2*(-1+B)*B^2-11/6*(-1+B)^3



Computing asymptotic complexity for rule 39

   Could not solve the limit problem.

   Resulting cost 0 has complexity: Unknown



Computing asymptotic complexity for rule 40

   Solved the limit problem by the following transformations:

      Created initial limit problem:

      1/4*B^4+2/3*B^3-1/6*B+5/4*B^2 (+), -1+B (+/+!) [not solved]



      removing all constraints (solved by SMT)

      resulting limit problem: [solved]



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

      resulting limit problem:

      [solved]



   Solution:

      B / 1+n

   Resulting cost 2+1/4*n^4+19/4*n^2+16/3*n+5/3*n^3 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+1/4*n^4+19/4*n^2+16/3*n+5/3*n^3

   Rule cost:   -5/6-1/4*(-1+B)^4+1/2*(-1+B)^2*B^2+2*(-1+B)^2*B+2*(-1+B)*B+17/6*B-3/4*(-1+B)^2+1/2*(-1+B)*B^2-11/6*(-1+B)^3

   Rule guard:  [ B>=2 ]



WORST_CASE(Omega(n^4),?)


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

(4)
BOUNDS(n^4, INF)