/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(?, O(n^1))
proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, max(7, 9 + 2 * Arg_0) + max(2, 4 + 2 * Arg_0) + max(16 + 6 * Arg_0, 10) + nat(1 + Arg_0)).

(0) CpxIntTrs
(1) Koat2 Proof [FINISHED, 2249 ms]
(2) BOUNDS(1, max(7, 9 + 2 * Arg_0) + max(2, 4 + 2 * Arg_0) + max(16 + 6 * Arg_0, 10) + nat(1 + Arg_0))


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

(0)
Obligation:
Complexity Int TRS consisting of the following rules:
eval_wcet0_start(v_1, v_i_0, v_j_0, v_j_3, v_n) -> Com_1(eval_wcet0_bb0_in(v_1, v_i_0, v_j_0, v_j_3, v_n)) :|: TRUE
eval_wcet0_bb0_in(v_1, v_i_0, v_j_0, v_j_3, v_n) -> Com_1(eval_wcet0_0(v_1, v_i_0, v_j_0, v_j_3, v_n)) :|: TRUE
eval_wcet0_0(v_1, v_i_0, v_j_0, v_j_3, v_n) -> Com_1(eval_wcet0_1(v_1, v_i_0, v_j_0, v_j_3, v_n)) :|: TRUE
eval_wcet0_1(v_1, v_i_0, v_j_0, v_j_3, v_n) -> Com_1(eval_wcet0_2(v_1, v_i_0, v_j_0, v_j_3, v_n)) :|: TRUE
eval_wcet0_2(v_1, v_i_0, v_j_0, v_j_3, v_n) -> Com_1(eval_wcet0_3(v_1, v_i_0, v_j_0, v_j_3, v_n)) :|: TRUE
eval_wcet0_3(v_1, v_i_0, v_j_0, v_j_3, v_n) -> Com_1(eval_wcet0_bb1_in(v_1, v_n, 0, v_j_3, v_n)) :|: v_n >= 1
eval_wcet0_3(v_1, v_i_0, v_j_0, v_j_3, v_n) -> Com_1(eval_wcet0_bb5_in(v_1, v_i_0, v_j_0, v_j_3, v_n)) :|: v_n < 1
eval_wcet0_bb1_in(v_1, v_i_0, v_j_0, v_j_3, v_n) -> Com_1(eval_wcet0_4(v_1, v_i_0, v_j_0, v_j_3, v_n)) :|: TRUE
eval_wcet0_4(v_1, v_i_0, v_j_0, v_j_3, v_n) -> Com_1(eval_wcet0_5(nondef_0, v_i_0, v_j_0, v_j_3, v_n)) :|: TRUE
eval_wcet0_5(v_1, v_i_0, v_j_0, v_j_3, v_n) -> Com_1(eval_wcet0_bb2_in(v_1, v_i_0, v_j_0, v_j_3, v_n)) :|: v_1 > 0
eval_wcet0_5(v_1, v_i_0, v_j_0, v_j_3, v_n) -> Com_1(eval_wcet0_bb3_in(v_1, v_i_0, v_j_0, v_j_3, v_n)) :|: v_1 <= 0
eval_wcet0_bb2_in(v_1, v_i_0, v_j_0, v_j_3, v_n) -> Com_1(eval_wcet0_bb4_in(v_1, v_i_0, v_j_0, 0, v_n)) :|: v_j_0 + 1 >= v_n
eval_wcet0_bb2_in(v_1, v_i_0, v_j_0, v_j_3, v_n) -> Com_1(eval_wcet0_bb4_in(v_1, v_i_0, v_j_0, v_j_0 + 1, v_n)) :|: v_j_0 + 1 < v_n
eval_wcet0_bb3_in(v_1, v_i_0, v_j_0, v_j_3, v_n) -> Com_1(eval_wcet0_bb4_in(v_1, v_i_0, v_j_0, 0, v_n)) :|: v_j_0 - 1 <= -(v_n)
eval_wcet0_bb3_in(v_1, v_i_0, v_j_0, v_j_3, v_n) -> Com_1(eval_wcet0_bb4_in(v_1, v_i_0, v_j_0, v_j_0 - 1, v_n)) :|: v_j_0 - 1 > -(v_n)
eval_wcet0_bb4_in(v_1, v_i_0, v_j_0, v_j_3, v_n) -> Com_1(eval_wcet0_bb1_in(v_1, v_i_0 - 1, v_j_3, v_j_3, v_n)) :|: v_i_0 - 1 > 0
eval_wcet0_bb4_in(v_1, v_i_0, v_j_0, v_j_3, v_n) -> Com_1(eval_wcet0_bb5_in(v_1, v_i_0, v_j_0, v_j_3, v_n)) :|: v_i_0 - 1 <= 0
eval_wcet0_bb5_in(v_1, v_i_0, v_j_0, v_j_3, v_n) -> Com_1(eval_wcet0_stop(v_1, v_i_0, v_j_0, v_j_3, v_n)) :|: TRUE

The start-symbols are:[eval_wcet0_start_5]


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

(1) Koat2 Proof (FINISHED)
YES( ?, 4+2*2*max([1, 2+Arg_0])+max([0, 1+Arg_0])+max([7, 7+2*(1+Arg_0)])+max([1, 2+Arg_0])+max([2, 2+2*(1+Arg_0)])+max([1, 2+Arg_0]) {O(n)})



Initial Complexity Problem:

  Start:  evalwcet0start  

  Program_Vars:  Arg_0, Arg_1, Arg_2, Arg_3, Arg_4  

  Temp_Vars:  F  

  Locations:  evalwcet00, evalwcet01, evalwcet02, evalwcet03, evalwcet04, evalwcet05, evalwcet0bb0in, evalwcet0bb1in, evalwcet0bb2in, evalwcet0bb3in, evalwcet0bb4in, evalwcet0bb5in, evalwcet0start, evalwcet0stop  

  Transitions:

  2: evalwcet00->evalwcet01

  3: evalwcet01->evalwcet02

  4: evalwcet02->evalwcet03

  5: evalwcet03->evalwcet0bb1in

  6: evalwcet03->evalwcet0bb5in

  8: evalwcet04->evalwcet05

  9: evalwcet05->evalwcet0bb2in

  10: evalwcet05->evalwcet0bb3in

  1: evalwcet0bb0in->evalwcet00

  7: evalwcet0bb1in->evalwcet04

  11: evalwcet0bb2in->evalwcet0bb4in

  12: evalwcet0bb2in->evalwcet0bb4in

  13: evalwcet0bb3in->evalwcet0bb4in

  14: evalwcet0bb3in->evalwcet0bb4in

  15: evalwcet0bb4in->evalwcet0bb1in

  16: evalwcet0bb4in->evalwcet0bb5in

  17: evalwcet0bb5in->evalwcet0stop

  0: evalwcet0start->evalwcet0bb0in  



Timebounds: 

  Overall timebound: 4+2*2*max([1, 2+Arg_0])+max([0, 1+Arg_0])+max([7, 7+2*(1+Arg_0)])+max([1, 2+Arg_0])+max([2, 2+2*(1+Arg_0)])+max([1, 2+Arg_0]) {O(n)}

  2: evalwcet00->evalwcet01: 1 {O(1)}

  3: evalwcet01->evalwcet02: 1 {O(1)}

  4: evalwcet02->evalwcet03: 1 {O(1)}

  5: evalwcet03->evalwcet0bb1in: 1 {O(1)}

  6: evalwcet03->evalwcet0bb5in: 1 {O(1)}

  8: evalwcet04->evalwcet05: max([2, 2+2*(1+Arg_0)]) {O(n)}

  9: evalwcet05->evalwcet0bb2in: max([1, 2+Arg_0]) {O(n)}

  10: evalwcet05->evalwcet0bb3in: max([1, 2+Arg_0]) {O(n)}

  1: evalwcet0bb0in->evalwcet00: 1 {O(1)}

  7: evalwcet0bb1in->evalwcet04: max([2, 2+2*(1+Arg_0)]) {O(n)}

  11: evalwcet0bb2in->evalwcet0bb4in: max([1, 2+Arg_0]) {O(n)}

  12: evalwcet0bb2in->evalwcet0bb4in: max([1, 2+Arg_0]) {O(n)}

  13: evalwcet0bb3in->evalwcet0bb4in: max([1, 2+Arg_0]) {O(n)}

  14: evalwcet0bb3in->evalwcet0bb4in: max([1, 2+Arg_0]) {O(n)}

  15: evalwcet0bb4in->evalwcet0bb1in: max([0, 1+Arg_0]) {O(n)}

  16: evalwcet0bb4in->evalwcet0bb5in: 1 {O(1)}

  17: evalwcet0bb5in->evalwcet0stop: 1 {O(1)}

  0: evalwcet0start->evalwcet0bb0in: 1 {O(1)}



Costbounds:

  Overall costbound: 4+2*2*max([1, 2+Arg_0])+max([0, 1+Arg_0])+max([7, 7+2*(1+Arg_0)])+max([1, 2+Arg_0])+max([2, 2+2*(1+Arg_0)])+max([1, 2+Arg_0]) {O(n)}

  2: evalwcet00->evalwcet01: 1 {O(1)}

  3: evalwcet01->evalwcet02: 1 {O(1)}

  4: evalwcet02->evalwcet03: 1 {O(1)}

  5: evalwcet03->evalwcet0bb1in: 1 {O(1)}

  6: evalwcet03->evalwcet0bb5in: 1 {O(1)}

  8: evalwcet04->evalwcet05: max([2, 2+2*(1+Arg_0)]) {O(n)}

  9: evalwcet05->evalwcet0bb2in: max([1, 2+Arg_0]) {O(n)}

  10: evalwcet05->evalwcet0bb3in: max([1, 2+Arg_0]) {O(n)}

  1: evalwcet0bb0in->evalwcet00: 1 {O(1)}

  7: evalwcet0bb1in->evalwcet04: max([2, 2+2*(1+Arg_0)]) {O(n)}

  11: evalwcet0bb2in->evalwcet0bb4in: max([1, 2+Arg_0]) {O(n)}

  12: evalwcet0bb2in->evalwcet0bb4in: max([1, 2+Arg_0]) {O(n)}

  13: evalwcet0bb3in->evalwcet0bb4in: max([1, 2+Arg_0]) {O(n)}

  14: evalwcet0bb3in->evalwcet0bb4in: max([1, 2+Arg_0]) {O(n)}

  15: evalwcet0bb4in->evalwcet0bb1in: max([0, 1+Arg_0]) {O(n)}

  16: evalwcet0bb4in->evalwcet0bb5in: 1 {O(1)}

  17: evalwcet0bb5in->evalwcet0stop: 1 {O(1)}

  0: evalwcet0start->evalwcet0bb0in: 1 {O(1)}



Sizebounds:

`Lower:

  2: evalwcet00->evalwcet01, Arg_0: Arg_0 {O(n)}

  2: evalwcet00->evalwcet01, Arg_1: Arg_1 {O(n)}

  2: evalwcet00->evalwcet01, Arg_2: Arg_2 {O(n)}

  2: evalwcet00->evalwcet01, Arg_3: Arg_3 {O(n)}

  2: evalwcet00->evalwcet01, Arg_4: Arg_4 {O(n)}

  3: evalwcet01->evalwcet02, Arg_0: Arg_0 {O(n)}

  3: evalwcet01->evalwcet02, Arg_1: Arg_1 {O(n)}

  3: evalwcet01->evalwcet02, Arg_2: Arg_2 {O(n)}

  3: evalwcet01->evalwcet02, Arg_3: Arg_3 {O(n)}

  3: evalwcet01->evalwcet02, Arg_4: Arg_4 {O(n)}

  4: evalwcet02->evalwcet03, Arg_0: Arg_0 {O(n)}

  4: evalwcet02->evalwcet03, Arg_1: Arg_1 {O(n)}

  4: evalwcet02->evalwcet03, Arg_2: Arg_2 {O(n)}

  4: evalwcet02->evalwcet03, Arg_3: Arg_3 {O(n)}

  4: evalwcet02->evalwcet03, Arg_4: Arg_4 {O(n)}

  5: evalwcet03->evalwcet0bb1in, Arg_0: 1 {O(1)}

  5: evalwcet03->evalwcet0bb1in, Arg_1: 1 {O(1)}

  5: evalwcet03->evalwcet0bb1in, Arg_2: 0 {O(1)}

  5: evalwcet03->evalwcet0bb1in, Arg_3: Arg_3 {O(n)}

  5: evalwcet03->evalwcet0bb1in, Arg_4: Arg_4 {O(n)}

  6: evalwcet03->evalwcet0bb5in, Arg_0: Arg_0 {O(n)}

  6: evalwcet03->evalwcet0bb5in, Arg_1: Arg_1 {O(n)}

  6: evalwcet03->evalwcet0bb5in, Arg_2: Arg_2 {O(n)}

  6: evalwcet03->evalwcet0bb5in, Arg_3: Arg_3 {O(n)}

  6: evalwcet03->evalwcet0bb5in, Arg_4: Arg_4 {O(n)}

  8: evalwcet04->evalwcet05, Arg_0: 1 {O(1)}

  8: evalwcet04->evalwcet05, Arg_1: 1 {O(1)}

  8: evalwcet04->evalwcet05, Arg_2: min([-1, -(2+Arg_0)]) {O(n)}

  8: evalwcet04->evalwcet05, Arg_4: min([-1, min([Arg_4, -(2+Arg_0)])]) {O(n)}

  9: evalwcet05->evalwcet0bb2in, Arg_0: 1 {O(1)}

  9: evalwcet05->evalwcet0bb2in, Arg_1: 1 {O(1)}

  9: evalwcet05->evalwcet0bb2in, Arg_2: min([-1, -(2+Arg_0)]) {O(n)}

  9: evalwcet05->evalwcet0bb2in, Arg_3: 1 {O(1)}

  9: evalwcet05->evalwcet0bb2in, Arg_4: min([-1, min([Arg_4, -(2+Arg_0)])]) {O(n)}

  10: evalwcet05->evalwcet0bb3in, Arg_0: 1 {O(1)}

  10: evalwcet05->evalwcet0bb3in, Arg_1: 1 {O(1)}

  10: evalwcet05->evalwcet0bb3in, Arg_2: min([-1, -(2+Arg_0)]) {O(n)}

  10: evalwcet05->evalwcet0bb3in, Arg_4: min([-1, min([Arg_4, -(2+Arg_0)])]) {O(n)}

  1: evalwcet0bb0in->evalwcet00, Arg_0: Arg_0 {O(n)}

  1: evalwcet0bb0in->evalwcet00, Arg_1: Arg_1 {O(n)}

  1: evalwcet0bb0in->evalwcet00, Arg_2: Arg_2 {O(n)}

  1: evalwcet0bb0in->evalwcet00, Arg_3: Arg_3 {O(n)}

  1: evalwcet0bb0in->evalwcet00, Arg_4: Arg_4 {O(n)}

  7: evalwcet0bb1in->evalwcet04, Arg_0: 1 {O(1)}

  7: evalwcet0bb1in->evalwcet04, Arg_1: 1 {O(1)}

  7: evalwcet0bb1in->evalwcet04, Arg_2: min([-1, -(2+Arg_0)]) {O(n)}

  7: evalwcet0bb1in->evalwcet04, Arg_4: min([-1, min([Arg_4, -(2+Arg_0)])]) {O(n)}

  11: evalwcet0bb2in->evalwcet0bb4in, Arg_0: 1 {O(1)}

  11: evalwcet0bb2in->evalwcet0bb4in, Arg_1: 1 {O(1)}

  11: evalwcet0bb2in->evalwcet0bb4in, Arg_2: min([-1, -(2+Arg_0)]) {O(n)}

  11: evalwcet0bb2in->evalwcet0bb4in, Arg_3: 1 {O(1)}

  11: evalwcet0bb2in->evalwcet0bb4in, Arg_4: 0 {O(1)}

  12: evalwcet0bb2in->evalwcet0bb4in, Arg_0: 1 {O(1)}

  12: evalwcet0bb2in->evalwcet0bb4in, Arg_1: 1 {O(1)}

  12: evalwcet0bb2in->evalwcet0bb4in, Arg_2: min([-1, -(2+Arg_0)]) {O(n)}

  12: evalwcet0bb2in->evalwcet0bb4in, Arg_3: 1 {O(1)}

  12: evalwcet0bb2in->evalwcet0bb4in, Arg_4: min([-1, -(2+Arg_0)]) {O(n)}

  13: evalwcet0bb3in->evalwcet0bb4in, Arg_0: 1 {O(1)}

  13: evalwcet0bb3in->evalwcet0bb4in, Arg_1: 1 {O(1)}

  13: evalwcet0bb3in->evalwcet0bb4in, Arg_2: min([-1, -(2+Arg_0)]) {O(n)}

  13: evalwcet0bb3in->evalwcet0bb4in, Arg_4: 0 {O(1)}

  14: evalwcet0bb3in->evalwcet0bb4in, Arg_0: 1 {O(1)}

  14: evalwcet0bb3in->evalwcet0bb4in, Arg_1: 1 {O(1)}

  14: evalwcet0bb3in->evalwcet0bb4in, Arg_2: min([-1, -(2+Arg_0)]) {O(n)}

  14: evalwcet0bb3in->evalwcet0bb4in, Arg_4: min([-1, -(2+Arg_0)]) {O(n)}

  15: evalwcet0bb4in->evalwcet0bb1in, Arg_0: 1 {O(1)}

  15: evalwcet0bb4in->evalwcet0bb1in, Arg_1: 1 {O(1)}

  15: evalwcet0bb4in->evalwcet0bb1in, Arg_2: min([-1, -(2+Arg_0)]) {O(n)}

  15: evalwcet0bb4in->evalwcet0bb1in, Arg_4: min([-1, -(2+Arg_0)]) {O(n)}

  16: evalwcet0bb4in->evalwcet0bb5in, Arg_0: 1 {O(1)}

  16: evalwcet0bb4in->evalwcet0bb5in, Arg_1: 1 {O(1)}

  16: evalwcet0bb4in->evalwcet0bb5in, Arg_2: min([-1, -(2+Arg_0)]) {O(n)}

  16: evalwcet0bb4in->evalwcet0bb5in, Arg_4: min([-1, -(2+Arg_0)]) {O(n)}

  17: evalwcet0bb5in->evalwcet0stop, Arg_0: min([1, Arg_0]) {O(n)}

  17: evalwcet0bb5in->evalwcet0stop, Arg_1: min([1, Arg_1]) {O(n)}

  17: evalwcet0bb5in->evalwcet0stop, Arg_2: min([-1, min([Arg_2, -(2+Arg_0)])]) {O(n)}

  17: evalwcet0bb5in->evalwcet0stop, Arg_4: min([-1, min([Arg_4, -(2+Arg_0)])]) {O(n)}

  0: evalwcet0start->evalwcet0bb0in, Arg_0: Arg_0 {O(n)}

  0: evalwcet0start->evalwcet0bb0in, Arg_1: Arg_1 {O(n)}

  0: evalwcet0start->evalwcet0bb0in, Arg_2: Arg_2 {O(n)}

  0: evalwcet0start->evalwcet0bb0in, Arg_3: Arg_3 {O(n)}

  0: evalwcet0start->evalwcet0bb0in, Arg_4: Arg_4 {O(n)}

`Upper:

  2: evalwcet00->evalwcet01, Arg_0: Arg_0 {O(n)}

  2: evalwcet00->evalwcet01, Arg_1: Arg_1 {O(n)}

  2: evalwcet00->evalwcet01, Arg_2: Arg_2 {O(n)}

  2: evalwcet00->evalwcet01, Arg_3: Arg_3 {O(n)}

  2: evalwcet00->evalwcet01, Arg_4: Arg_4 {O(n)}

  3: evalwcet01->evalwcet02, Arg_0: Arg_0 {O(n)}

  3: evalwcet01->evalwcet02, Arg_1: Arg_1 {O(n)}

  3: evalwcet01->evalwcet02, Arg_2: Arg_2 {O(n)}

  3: evalwcet01->evalwcet02, Arg_3: Arg_3 {O(n)}

  3: evalwcet01->evalwcet02, Arg_4: Arg_4 {O(n)}

  4: evalwcet02->evalwcet03, Arg_0: Arg_0 {O(n)}

  4: evalwcet02->evalwcet03, Arg_1: Arg_1 {O(n)}

  4: evalwcet02->evalwcet03, Arg_2: Arg_2 {O(n)}

  4: evalwcet02->evalwcet03, Arg_3: Arg_3 {O(n)}

  4: evalwcet02->evalwcet03, Arg_4: Arg_4 {O(n)}

  5: evalwcet03->evalwcet0bb1in, Arg_0: Arg_0 {O(n)}

  5: evalwcet03->evalwcet0bb1in, Arg_1: Arg_0 {O(n)}

  5: evalwcet03->evalwcet0bb1in, Arg_2: 0 {O(1)}

  5: evalwcet03->evalwcet0bb1in, Arg_3: Arg_3 {O(n)}

  5: evalwcet03->evalwcet0bb1in, Arg_4: Arg_4 {O(n)}

  6: evalwcet03->evalwcet0bb5in, Arg_0: 0 {O(1)}

  6: evalwcet03->evalwcet0bb5in, Arg_1: Arg_1 {O(n)}

  6: evalwcet03->evalwcet0bb5in, Arg_2: Arg_2 {O(n)}

  6: evalwcet03->evalwcet0bb5in, Arg_3: Arg_3 {O(n)}

  6: evalwcet03->evalwcet0bb5in, Arg_4: Arg_4 {O(n)}

  8: evalwcet04->evalwcet05, Arg_0: Arg_0 {O(n)}

  8: evalwcet04->evalwcet05, Arg_1: Arg_0 {O(n)}

  8: evalwcet04->evalwcet05, Arg_2: max([1, 2+Arg_0]) {O(n)}

  8: evalwcet04->evalwcet05, Arg_4: max([1, max([Arg_4, 2+Arg_0])]) {O(n)}

  9: evalwcet05->evalwcet0bb2in, Arg_0: Arg_0 {O(n)}

  9: evalwcet05->evalwcet0bb2in, Arg_1: Arg_0 {O(n)}

  9: evalwcet05->evalwcet0bb2in, Arg_2: max([1, 2+Arg_0]) {O(n)}

  9: evalwcet05->evalwcet0bb2in, Arg_4: max([1, max([Arg_4, 2+Arg_0])]) {O(n)}

  10: evalwcet05->evalwcet0bb3in, Arg_0: Arg_0 {O(n)}

  10: evalwcet05->evalwcet0bb3in, Arg_1: Arg_0 {O(n)}

  10: evalwcet05->evalwcet0bb3in, Arg_2: max([1, 2+Arg_0]) {O(n)}

  10: evalwcet05->evalwcet0bb3in, Arg_3: 0 {O(1)}

  10: evalwcet05->evalwcet0bb3in, Arg_4: max([1, max([Arg_4, 2+Arg_0])]) {O(n)}

  1: evalwcet0bb0in->evalwcet00, Arg_0: Arg_0 {O(n)}

  1: evalwcet0bb0in->evalwcet00, Arg_1: Arg_1 {O(n)}

  1: evalwcet0bb0in->evalwcet00, Arg_2: Arg_2 {O(n)}

  1: evalwcet0bb0in->evalwcet00, Arg_3: Arg_3 {O(n)}

  1: evalwcet0bb0in->evalwcet00, Arg_4: Arg_4 {O(n)}

  7: evalwcet0bb1in->evalwcet04, Arg_0: Arg_0 {O(n)}

  7: evalwcet0bb1in->evalwcet04, Arg_1: Arg_0 {O(n)}

  7: evalwcet0bb1in->evalwcet04, Arg_2: max([1, 2+Arg_0]) {O(n)}

  7: evalwcet0bb1in->evalwcet04, Arg_4: max([1, max([Arg_4, 2+Arg_0])]) {O(n)}

  11: evalwcet0bb2in->evalwcet0bb4in, Arg_0: Arg_0 {O(n)}

  11: evalwcet0bb2in->evalwcet0bb4in, Arg_1: Arg_0 {O(n)}

  11: evalwcet0bb2in->evalwcet0bb4in, Arg_2: max([1, 2+Arg_0]) {O(n)}

  11: evalwcet0bb2in->evalwcet0bb4in, Arg_4: 0 {O(1)}

  12: evalwcet0bb2in->evalwcet0bb4in, Arg_0: Arg_0 {O(n)}

  12: evalwcet0bb2in->evalwcet0bb4in, Arg_1: Arg_0 {O(n)}

  12: evalwcet0bb2in->evalwcet0bb4in, Arg_2: max([1, 2+Arg_0]) {O(n)}

  12: evalwcet0bb2in->evalwcet0bb4in, Arg_4: max([1, 2+Arg_0]) {O(n)}

  13: evalwcet0bb3in->evalwcet0bb4in, Arg_0: Arg_0 {O(n)}

  13: evalwcet0bb3in->evalwcet0bb4in, Arg_1: Arg_0 {O(n)}

  13: evalwcet0bb3in->evalwcet0bb4in, Arg_2: max([1, 2+Arg_0]) {O(n)}

  13: evalwcet0bb3in->evalwcet0bb4in, Arg_3: 0 {O(1)}

  13: evalwcet0bb3in->evalwcet0bb4in, Arg_4: 0 {O(1)}

  14: evalwcet0bb3in->evalwcet0bb4in, Arg_0: Arg_0 {O(n)}

  14: evalwcet0bb3in->evalwcet0bb4in, Arg_1: Arg_0 {O(n)}

  14: evalwcet0bb3in->evalwcet0bb4in, Arg_2: max([1, 2+Arg_0]) {O(n)}

  14: evalwcet0bb3in->evalwcet0bb4in, Arg_3: 0 {O(1)}

  14: evalwcet0bb3in->evalwcet0bb4in, Arg_4: max([1, 2+Arg_0]) {O(n)}

  15: evalwcet0bb4in->evalwcet0bb1in, Arg_0: Arg_0 {O(n)}

  15: evalwcet0bb4in->evalwcet0bb1in, Arg_1: Arg_0 {O(n)}

  15: evalwcet0bb4in->evalwcet0bb1in, Arg_2: max([1, 2+Arg_0]) {O(n)}

  15: evalwcet0bb4in->evalwcet0bb1in, Arg_4: max([1, 2+Arg_0]) {O(n)}

  16: evalwcet0bb4in->evalwcet0bb5in, Arg_0: Arg_0 {O(n)}

  16: evalwcet0bb4in->evalwcet0bb5in, Arg_1: 1 {O(1)}

  16: evalwcet0bb4in->evalwcet0bb5in, Arg_2: max([1, 2+Arg_0]) {O(n)}

  16: evalwcet0bb4in->evalwcet0bb5in, Arg_4: max([1, 2+Arg_0]) {O(n)}

  17: evalwcet0bb5in->evalwcet0stop, Arg_0: max([0, Arg_0]) {O(n)}

  17: evalwcet0bb5in->evalwcet0stop, Arg_1: max([1, Arg_1]) {O(n)}

  17: evalwcet0bb5in->evalwcet0stop, Arg_2: max([1, max([Arg_2, 2+Arg_0])]) {O(n)}

  17: evalwcet0bb5in->evalwcet0stop, Arg_4: max([1, max([Arg_4, 2+Arg_0])]) {O(n)}

  0: evalwcet0start->evalwcet0bb0in, Arg_0: Arg_0 {O(n)}

  0: evalwcet0start->evalwcet0bb0in, Arg_1: Arg_1 {O(n)}

  0: evalwcet0start->evalwcet0bb0in, Arg_2: Arg_2 {O(n)}

  0: evalwcet0start->evalwcet0bb0in, Arg_3: Arg_3 {O(n)}

  0: evalwcet0start->evalwcet0bb0in, Arg_4: Arg_4 {O(n)}


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

(2)
BOUNDS(1, max(7, 9 + 2 * Arg_0) + max(2, 4 + 2 * Arg_0) + max(16 + 6 * Arg_0, 10) + nat(1 + Arg_0))