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


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WORST_CASE(Omega(n^1), 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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(n^1, nat(1 + Arg_0) + nat(2 * Arg_0) + max(34, 32 + 2 * Arg_0) + nat(Arg_1) + max(8 + Arg_1, 9)).

(0) CpxIntTrs
(1) Koat2 Proof [FINISHED, 12.0 s]
(2) BOUNDS(1, nat(1 + Arg_0) + nat(2 * Arg_0) + max(34, 32 + 2 * Arg_0) + nat(Arg_1) + max(8 + Arg_1, 9))
(3) Loat Proof [FINISHED, 807 ms]
(4) BOUNDS(n^1, INF)


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

(0)
Obligation:
Complexity Int TRS consisting of the following rules:
eval_start_start(v_dir, v_i_0, v_m, v_n) -> Com_1(eval_start_bb0_in(v_dir, v_i_0, v_m, v_n)) :|: TRUE
eval_start_bb0_in(v_dir, v_i_0, v_m, v_n) -> Com_1(eval_start_0(v_dir, v_i_0, v_m, v_n)) :|: TRUE
eval_start_0(v_dir, v_i_0, v_m, v_n) -> Com_1(eval_start_1(v_dir, v_i_0, v_m, v_n)) :|: TRUE
eval_start_1(v_dir, v_i_0, v_m, v_n) -> Com_1(eval_start_2(v_dir, v_i_0, v_m, v_n)) :|: TRUE
eval_start_2(v_dir, v_i_0, v_m, v_n) -> Com_1(eval_start_3(v_dir, v_i_0, v_m, v_n)) :|: TRUE
eval_start_3(v_dir, v_i_0, v_m, v_n) -> Com_1(eval_start_bb1_in(v_dir, v_i_0, v_m, v_n)) :|: 0 < v_m
eval_start_3(v_dir, v_i_0, v_m, v_n) -> Com_1(eval_start_bb6_in(v_dir, v_i_0, v_m, v_n)) :|: 0 >= v_m
eval_start_bb1_in(v_dir, v_i_0, v_m, v_n) -> Com_1(eval_start_bb2_in(v_dir, v_m, v_m, v_n)) :|: v_m < v_n
eval_start_bb1_in(v_dir, v_i_0, v_m, v_n) -> Com_1(eval_start_bb5_in(v_dir, v_i_0, v_m, v_n)) :|: v_m >= v_n
eval_start_bb2_in(v_dir, v_i_0, v_m, v_n) -> Com_1(eval_start_bb3_in(v_dir, v_i_0, v_m, v_n)) :|: 0 < v_i_0 && v_i_0 < v_n
eval_start_bb2_in(v_dir, v_i_0, v_m, v_n) -> Com_1(eval_start_bb4_in(v_dir, v_i_0, v_m, v_n)) :|: 0 >= v_i_0
eval_start_bb2_in(v_dir, v_i_0, v_m, v_n) -> Com_1(eval_start_bb4_in(v_dir, v_i_0, v_m, v_n)) :|: v_i_0 >= v_n
eval_start_bb3_in(v_dir, v_i_0, v_m, v_n) -> Com_1(eval_start_bb2_in(v_dir, v_i_0 + 1, v_m, v_n)) :|: v_dir >= 1 && v_dir <= 1
eval_start_bb3_in(v_dir, v_i_0, v_m, v_n) -> Com_1(eval_start_bb2_in(v_dir, v_i_0 - 1, v_m, v_n)) :|: v_dir < 1
eval_start_bb3_in(v_dir, v_i_0, v_m, v_n) -> Com_1(eval_start_bb2_in(v_dir, v_i_0 - 1, v_m, v_n)) :|: v_dir > 1
eval_start_bb4_in(v_dir, v_i_0, v_m, v_n) -> Com_1(eval_start_stop(v_dir, v_i_0, v_m, v_n)) :|: TRUE
eval_start_bb5_in(v_dir, v_i_0, v_m, v_n) -> Com_1(eval_start_8(v_dir, v_i_0, v_m, v_n)) :|: TRUE
eval_start_8(v_dir, v_i_0, v_m, v_n) -> Com_1(eval_start_9(v_dir, v_i_0, v_m, v_n)) :|: TRUE
eval_start_9(v_dir, v_i_0, v_m, v_n) -> Com_1(eval_start_stop(v_dir, v_i_0, v_m, v_n)) :|: TRUE
eval_start_bb6_in(v_dir, v_i_0, v_m, v_n) -> Com_1(eval_start_10(v_dir, v_i_0, v_m, v_n)) :|: TRUE
eval_start_10(v_dir, v_i_0, v_m, v_n) -> Com_1(eval_start_11(v_dir, v_i_0, v_m, v_n)) :|: TRUE
eval_start_11(v_dir, v_i_0, v_m, v_n) -> Com_1(eval_start_stop(v_dir, v_i_0, v_m, v_n)) :|: TRUE

The start-symbols are:[eval_start_start_4]


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

(1) Koat2 Proof (FINISHED)
YES( ?, 9+max([0, -1+Arg_1])+max([0, 1+Arg_0])+max([0, Arg_0])+max([34, 34+2*(-1+Arg_0)])+max([0, Arg_0])+max([0, Arg_1]) {O(n)})



Initial Complexity Problem:

  Start:  evalstartstart  

  Program_Vars:  Arg_0, Arg_1, Arg_2, Arg_3  

  Temp_Vars:    

  Locations:  evalstart0, evalstart1, evalstart10, evalstart11, evalstart2, evalstart3, evalstart8, evalstart9, evalstartbb0in, evalstartbb1in, evalstartbb2in, evalstartbb4in, evalstartbb5in, evalstartbb6in, evalstartstart, evalstartstop, n_evalstartbb2in___4, n_evalstartbb2in___5, n_evalstartbb2in___6, n_evalstartbb3in___1, n_evalstartbb3in___2, n_evalstartbb3in___3, n_evalstartbb3in___7  

  Transitions:

  2: evalstart0->evalstart1

  3: evalstart1->evalstart2

  20: evalstart10->evalstart11

  21: evalstart11->evalstartstop

  4: evalstart2->evalstart3

  5: evalstart3->evalstartbb1in

  6: evalstart3->evalstartbb6in

  17: evalstart8->evalstart9

  18: evalstart9->evalstartstop

  1: evalstartbb0in->evalstart0

  7: evalstartbb1in->evalstartbb2in

  8: evalstartbb1in->evalstartbb5in

  10: evalstartbb2in->evalstartbb4in

  11: evalstartbb2in->evalstartbb4in

  977: evalstartbb2in->n_evalstartbb3in___7

  15: evalstartbb4in->evalstartstop

  16: evalstartbb5in->evalstart8

  19: evalstartbb6in->evalstart10

  0: evalstartstart->evalstartbb0in

  997: n_evalstartbb2in___4->evalstartbb4in

  1000: n_evalstartbb2in___4->evalstartbb4in

  1003: n_evalstartbb2in___4->evalstartbb4in

  1006: n_evalstartbb2in___4->evalstartbb4in

  1009: n_evalstartbb2in___4->evalstartbb4in

  1012: n_evalstartbb2in___4->evalstartbb4in

  974: n_evalstartbb2in___4->n_evalstartbb3in___1

  998: n_evalstartbb2in___5->evalstartbb4in

  1001: n_evalstartbb2in___5->evalstartbb4in

  1004: n_evalstartbb2in___5->evalstartbb4in

  1007: n_evalstartbb2in___5->evalstartbb4in

  1010: n_evalstartbb2in___5->evalstartbb4in

  1013: n_evalstartbb2in___5->evalstartbb4in

  975: n_evalstartbb2in___5->n_evalstartbb3in___2

  999: n_evalstartbb2in___6->evalstartbb4in

  1002: n_evalstartbb2in___6->evalstartbb4in

  1005: n_evalstartbb2in___6->evalstartbb4in

  1008: n_evalstartbb2in___6->evalstartbb4in

  1011: n_evalstartbb2in___6->evalstartbb4in

  1014: n_evalstartbb2in___6->evalstartbb4in

  976: n_evalstartbb2in___6->n_evalstartbb3in___3

  978: n_evalstartbb3in___1->n_evalstartbb2in___4

  979: n_evalstartbb3in___2->n_evalstartbb2in___5

  980: n_evalstartbb3in___3->n_evalstartbb2in___6

  981: n_evalstartbb3in___7->n_evalstartbb2in___4

  982: n_evalstartbb3in___7->n_evalstartbb2in___5

  983: n_evalstartbb3in___7->n_evalstartbb2in___6  



Timebounds: 

  Overall timebound: 9+max([0, -1+Arg_1])+max([0, 1+Arg_0])+max([0, Arg_0])+max([34, 34+2*(-1+Arg_0)])+max([0, Arg_0])+max([0, Arg_1]) {O(n)}

  2: evalstart0->evalstart1: 1 {O(1)}

  3: evalstart1->evalstart2: 1 {O(1)}

  20: evalstart10->evalstart11: 1 {O(1)}

  21: evalstart11->evalstartstop: 1 {O(1)}

  4: evalstart2->evalstart3: 1 {O(1)}

  5: evalstart3->evalstartbb1in: 1 {O(1)}

  6: evalstart3->evalstartbb6in: 1 {O(1)}

  17: evalstart8->evalstart9: 1 {O(1)}

  18: evalstart9->evalstartstop: 1 {O(1)}

  1: evalstartbb0in->evalstart0: 1 {O(1)}

  7: evalstartbb1in->evalstartbb2in: 1 {O(1)}

  8: evalstartbb1in->evalstartbb5in: 1 {O(1)}

  10: evalstartbb2in->evalstartbb4in: 1 {O(1)}

  11: evalstartbb2in->evalstartbb4in: 1 {O(1)}

  977: evalstartbb2in->n_evalstartbb3in___7: 1 {O(1)}

  15: evalstartbb4in->evalstartstop: 1 {O(1)}

  16: evalstartbb5in->evalstart8: 1 {O(1)}

  19: evalstartbb6in->evalstart10: 1 {O(1)}

  0: evalstartstart->evalstartbb0in: 1 {O(1)}

  974: n_evalstartbb2in___4->n_evalstartbb3in___1: max([3, 3+2*(-1+Arg_0)]) {O(n)}

  997: n_evalstartbb2in___4->evalstartbb4in: 1 {O(1)}

  1000: n_evalstartbb2in___4->evalstartbb4in: 1 {O(1)}

  1003: n_evalstartbb2in___4->evalstartbb4in: 1 {O(1)}

  1006: n_evalstartbb2in___4->evalstartbb4in: 1 {O(1)}

  1009: n_evalstartbb2in___4->evalstartbb4in: 1 {O(1)}

  1012: n_evalstartbb2in___4->evalstartbb4in: 1 {O(1)}

  975: n_evalstartbb2in___5->n_evalstartbb3in___2: max([0, 1+Arg_0]) {O(n)}

  998: n_evalstartbb2in___5->evalstartbb4in: 1 {O(1)}

  1001: n_evalstartbb2in___5->evalstartbb4in: 1 {O(1)}

  1004: n_evalstartbb2in___5->evalstartbb4in: 1 {O(1)}

  1007: n_evalstartbb2in___5->evalstartbb4in: 1 {O(1)}

  1010: n_evalstartbb2in___5->evalstartbb4in: 1 {O(1)}

  1013: n_evalstartbb2in___5->evalstartbb4in: 1 {O(1)}

  976: n_evalstartbb2in___6->n_evalstartbb3in___3: max([0, Arg_1]) {O(n)}

  999: n_evalstartbb2in___6->evalstartbb4in: 1 {O(1)}

  1002: n_evalstartbb2in___6->evalstartbb4in: 1 {O(1)}

  1005: n_evalstartbb2in___6->evalstartbb4in: 1 {O(1)}

  1008: n_evalstartbb2in___6->evalstartbb4in: 1 {O(1)}

  1011: n_evalstartbb2in___6->evalstartbb4in: 1 {O(1)}

  1014: n_evalstartbb2in___6->evalstartbb4in: 1 {O(1)}

  978: n_evalstartbb3in___1->n_evalstartbb2in___4: max([0, Arg_0]) {O(n)}

  979: n_evalstartbb3in___2->n_evalstartbb2in___5: max([0, Arg_0]) {O(n)}

  980: n_evalstartbb3in___3->n_evalstartbb2in___6: max([0, -1+Arg_1]) {O(n)}

  981: n_evalstartbb3in___7->n_evalstartbb2in___4: 1 {O(1)}

  982: n_evalstartbb3in___7->n_evalstartbb2in___5: 1 {O(1)}

  983: n_evalstartbb3in___7->n_evalstartbb2in___6: 1 {O(1)}



Costbounds:

  Overall costbound: 9+max([0, -1+Arg_1])+max([0, 1+Arg_0])+max([0, Arg_0])+max([34, 34+2*(-1+Arg_0)])+max([0, Arg_0])+max([0, Arg_1]) {O(n)}

  2: evalstart0->evalstart1: 1 {O(1)}

  3: evalstart1->evalstart2: 1 {O(1)}

  20: evalstart10->evalstart11: 1 {O(1)}

  21: evalstart11->evalstartstop: 1 {O(1)}

  4: evalstart2->evalstart3: 1 {O(1)}

  5: evalstart3->evalstartbb1in: 1 {O(1)}

  6: evalstart3->evalstartbb6in: 1 {O(1)}

  17: evalstart8->evalstart9: 1 {O(1)}

  18: evalstart9->evalstartstop: 1 {O(1)}

  1: evalstartbb0in->evalstart0: 1 {O(1)}

  7: evalstartbb1in->evalstartbb2in: 1 {O(1)}

  8: evalstartbb1in->evalstartbb5in: 1 {O(1)}

  10: evalstartbb2in->evalstartbb4in: 1 {O(1)}

  11: evalstartbb2in->evalstartbb4in: 1 {O(1)}

  977: evalstartbb2in->n_evalstartbb3in___7: 1 {O(1)}

  15: evalstartbb4in->evalstartstop: 1 {O(1)}

  16: evalstartbb5in->evalstart8: 1 {O(1)}

  19: evalstartbb6in->evalstart10: 1 {O(1)}

  0: evalstartstart->evalstartbb0in: 1 {O(1)}

  974: n_evalstartbb2in___4->n_evalstartbb3in___1: max([3, 3+2*(-1+Arg_0)]) {O(n)}

  997: n_evalstartbb2in___4->evalstartbb4in: 1 {O(1)}

  1000: n_evalstartbb2in___4->evalstartbb4in: 1 {O(1)}

  1003: n_evalstartbb2in___4->evalstartbb4in: 1 {O(1)}

  1006: n_evalstartbb2in___4->evalstartbb4in: 1 {O(1)}

  1009: n_evalstartbb2in___4->evalstartbb4in: 1 {O(1)}

  1012: n_evalstartbb2in___4->evalstartbb4in: 1 {O(1)}

  975: n_evalstartbb2in___5->n_evalstartbb3in___2: max([0, 1+Arg_0]) {O(n)}

  998: n_evalstartbb2in___5->evalstartbb4in: 1 {O(1)}

  1001: n_evalstartbb2in___5->evalstartbb4in: 1 {O(1)}

  1004: n_evalstartbb2in___5->evalstartbb4in: 1 {O(1)}

  1007: n_evalstartbb2in___5->evalstartbb4in: 1 {O(1)}

  1010: n_evalstartbb2in___5->evalstartbb4in: 1 {O(1)}

  1013: n_evalstartbb2in___5->evalstartbb4in: 1 {O(1)}

  976: n_evalstartbb2in___6->n_evalstartbb3in___3: max([0, Arg_1]) {O(n)}

  999: n_evalstartbb2in___6->evalstartbb4in: 1 {O(1)}

  1002: n_evalstartbb2in___6->evalstartbb4in: 1 {O(1)}

  1005: n_evalstartbb2in___6->evalstartbb4in: 1 {O(1)}

  1008: n_evalstartbb2in___6->evalstartbb4in: 1 {O(1)}

  1011: n_evalstartbb2in___6->evalstartbb4in: 1 {O(1)}

  1014: n_evalstartbb2in___6->evalstartbb4in: 1 {O(1)}

  978: n_evalstartbb3in___1->n_evalstartbb2in___4: max([0, Arg_0]) {O(n)}

  979: n_evalstartbb3in___2->n_evalstartbb2in___5: max([0, Arg_0]) {O(n)}

  980: n_evalstartbb3in___3->n_evalstartbb2in___6: max([0, -1+Arg_1]) {O(n)}

  981: n_evalstartbb3in___7->n_evalstartbb2in___4: 1 {O(1)}

  982: n_evalstartbb3in___7->n_evalstartbb2in___5: 1 {O(1)}

  983: n_evalstartbb3in___7->n_evalstartbb2in___6: 1 {O(1)}



Sizebounds:

`Lower:

  2: evalstart0->evalstart1, Arg_0: Arg_0 {O(n)}

  2: evalstart0->evalstart1, Arg_1: Arg_1 {O(n)}

  2: evalstart0->evalstart1, Arg_2: Arg_2 {O(n)}

  2: evalstart0->evalstart1, Arg_3: Arg_3 {O(n)}

  3: evalstart1->evalstart2, Arg_0: Arg_0 {O(n)}

  3: evalstart1->evalstart2, Arg_1: Arg_1 {O(n)}

  3: evalstart1->evalstart2, Arg_2: Arg_2 {O(n)}

  3: evalstart1->evalstart2, Arg_3: Arg_3 {O(n)}

  20: evalstart10->evalstart11, Arg_0: Arg_0 {O(n)}

  20: evalstart10->evalstart11, Arg_1: Arg_1 {O(n)}

  20: evalstart10->evalstart11, Arg_2: Arg_2 {O(n)}

  20: evalstart10->evalstart11, Arg_3: Arg_3 {O(n)}

  21: evalstart11->evalstartstop, Arg_0: Arg_0 {O(n)}

  21: evalstart11->evalstartstop, Arg_1: Arg_1 {O(n)}

  21: evalstart11->evalstartstop, Arg_2: Arg_2 {O(n)}

  21: evalstart11->evalstartstop, Arg_3: Arg_3 {O(n)}

  4: evalstart2->evalstart3, Arg_0: Arg_0 {O(n)}

  4: evalstart2->evalstart3, Arg_1: Arg_1 {O(n)}

  4: evalstart2->evalstart3, Arg_2: Arg_2 {O(n)}

  4: evalstart2->evalstart3, Arg_3: Arg_3 {O(n)}

  5: evalstart3->evalstartbb1in, Arg_0: 1 {O(1)}

  5: evalstart3->evalstartbb1in, Arg_1: Arg_1 {O(n)}

  5: evalstart3->evalstartbb1in, Arg_2: Arg_2 {O(n)}

  5: evalstart3->evalstartbb1in, Arg_3: Arg_3 {O(n)}

  6: evalstart3->evalstartbb6in, Arg_0: Arg_0 {O(n)}

  6: evalstart3->evalstartbb6in, Arg_1: Arg_1 {O(n)}

  6: evalstart3->evalstartbb6in, Arg_2: Arg_2 {O(n)}

  6: evalstart3->evalstartbb6in, Arg_3: Arg_3 {O(n)}

  17: evalstart8->evalstart9, Arg_0: 1 {O(1)}

  17: evalstart8->evalstart9, Arg_1: Arg_1 {O(n)}

  17: evalstart8->evalstart9, Arg_2: Arg_2 {O(n)}

  17: evalstart8->evalstart9, Arg_3: Arg_3 {O(n)}

  18: evalstart9->evalstartstop, Arg_0: 1 {O(1)}

  18: evalstart9->evalstartstop, Arg_1: Arg_1 {O(n)}

  18: evalstart9->evalstartstop, Arg_2: Arg_2 {O(n)}

  18: evalstart9->evalstartstop, Arg_3: Arg_3 {O(n)}

  1: evalstartbb0in->evalstart0, Arg_0: Arg_0 {O(n)}

  1: evalstartbb0in->evalstart0, Arg_1: Arg_1 {O(n)}

  1: evalstartbb0in->evalstart0, Arg_2: Arg_2 {O(n)}

  1: evalstartbb0in->evalstart0, Arg_3: Arg_3 {O(n)}

  7: evalstartbb1in->evalstartbb2in, Arg_0: 1 {O(1)}

  7: evalstartbb1in->evalstartbb2in, Arg_1: Arg_1 {O(n)}

  7: evalstartbb1in->evalstartbb2in, Arg_2: 1 {O(1)}

  7: evalstartbb1in->evalstartbb2in, Arg_3: Arg_3 {O(n)}

  8: evalstartbb1in->evalstartbb5in, Arg_0: 1 {O(1)}

  8: evalstartbb1in->evalstartbb5in, Arg_1: Arg_1 {O(n)}

  8: evalstartbb1in->evalstartbb5in, Arg_2: Arg_2 {O(n)}

  8: evalstartbb1in->evalstartbb5in, Arg_3: Arg_3 {O(n)}

  10: evalstartbb2in->evalstartbb4in, Arg_0: 1 {O(1)}

  10: evalstartbb2in->evalstartbb4in, Arg_1: max([Arg_1, max([Arg_1, max([Arg_1, max([Arg_1, max([Arg_1, max([Arg_1, min([2, Arg_1])])])])])])]) {O(n)}

  10: evalstartbb2in->evalstartbb4in, Arg_2: 1 {O(1)}

  10: evalstartbb2in->evalstartbb4in, Arg_3: max([Arg_3, max([Arg_3, max([Arg_3, max([Arg_3, max([Arg_3, max([Arg_3, min([1, Arg_3])])])])])])]) {O(n)}

  11: evalstartbb2in->evalstartbb4in, Arg_0: inf {Infinity}

  11: evalstartbb2in->evalstartbb4in, Arg_1: inf {Infinity}

  11: evalstartbb2in->evalstartbb4in, Arg_2: inf {Infinity}

  11: evalstartbb2in->evalstartbb4in, Arg_3: inf {Infinity}

  977: evalstartbb2in->n_evalstartbb3in___7, Arg_0: 1 {O(1)}

  977: evalstartbb2in->n_evalstartbb3in___7, Arg_1: 2 {O(1)}

  977: evalstartbb2in->n_evalstartbb3in___7, Arg_2: 1 {O(1)}

  977: evalstartbb2in->n_evalstartbb3in___7, Arg_3: Arg_3 {O(n)}

  15: evalstartbb4in->evalstartstop, Arg_0: 1 {O(1)}

  15: evalstartbb4in->evalstartstop, Arg_1: max([min([2, max([Arg_1, max([Arg_1, max([Arg_1, max([Arg_1, max([Arg_1, max([Arg_1, min([2, Arg_1])])])])])])])]), max([min([2, max([Arg_1, max([Arg_1, max([Arg_1, max([Arg_1, max([Arg_1, min([2, Arg_1])])])])])])]), max([min([2, max([Arg_1, max([Arg_1, max([Arg_1, max([Arg_1, min([2, Arg_1])])])])])]), max([min([2, max([Arg_1, max([Arg_1, max([Arg_1, min([2, Arg_1])])])])]), max([min([2, max([Arg_1, max([Arg_1, min([2, Arg_1])])])]), max([min([2, max([Arg_1, min([2, Arg_1])])]), min([2, min([2, Arg_1])])])])])])])]) {O(n)}

  15: evalstartbb4in->evalstartstop, Arg_2: 0 {O(1)}

  15: evalstartbb4in->evalstartstop, Arg_3: max([min([1, min([max([Arg_3, max([Arg_3, max([Arg_3, max([Arg_3, max([Arg_3, max([Arg_3, min([1, Arg_3])])])])])])]), Arg_3])]), max([min([1, min([max([Arg_3, max([Arg_3, max([Arg_3, max([Arg_3, max([Arg_3, min([1, Arg_3])])])])])]), Arg_3])]), max([min([1, min([max([Arg_3, max([Arg_3, max([Arg_3, max([Arg_3, min([1, Arg_3])])])])]), Arg_3])]), max([min([1, min([max([Arg_3, max([Arg_3, max([Arg_3, min([1, Arg_3])])])]), Arg_3])]), max([min([1, min([max([Arg_3, max([Arg_3, min([1, Arg_3])])]), Arg_3])]), max([min([1, min([max([Arg_3, min([1, Arg_3])]), Arg_3])]), min([1, min([1, Arg_3])])])])])])])]) {O(n)}

  16: evalstartbb5in->evalstart8, Arg_0: 1 {O(1)}

  16: evalstartbb5in->evalstart8, Arg_1: Arg_1 {O(n)}

  16: evalstartbb5in->evalstart8, Arg_2: Arg_2 {O(n)}

  16: evalstartbb5in->evalstart8, Arg_3: Arg_3 {O(n)}

  19: evalstartbb6in->evalstart10, Arg_0: Arg_0 {O(n)}

  19: evalstartbb6in->evalstart10, Arg_1: Arg_1 {O(n)}

  19: evalstartbb6in->evalstart10, Arg_2: Arg_2 {O(n)}

  19: evalstartbb6in->evalstart10, Arg_3: Arg_3 {O(n)}

  0: evalstartstart->evalstartbb0in, Arg_0: Arg_0 {O(n)}

  0: evalstartstart->evalstartbb0in, Arg_1: Arg_1 {O(n)}

  0: evalstartstart->evalstartbb0in, Arg_2: Arg_2 {O(n)}

  0: evalstartstart->evalstartbb0in, Arg_3: Arg_3 {O(n)}

  974: n_evalstartbb2in___4->n_evalstartbb3in___1, Arg_0: 1 {O(1)}

  974: n_evalstartbb2in___4->n_evalstartbb3in___1, Arg_1: 2 {O(1)}

  974: n_evalstartbb2in___4->n_evalstartbb3in___1, Arg_2: 1 {O(1)}

  974: n_evalstartbb2in___4->n_evalstartbb3in___1, Arg_3: 2 {O(1)}

  997: n_evalstartbb2in___4->evalstartbb4in, Arg_0: 1 {O(1)}

  997: n_evalstartbb2in___4->evalstartbb4in, Arg_1: 2 {O(1)}

  997: n_evalstartbb2in___4->evalstartbb4in, Arg_2: 0 {O(1)}

  997: n_evalstartbb2in___4->evalstartbb4in, Arg_3: 2 {O(1)}

  1000: n_evalstartbb2in___4->evalstartbb4in, Arg_0: inf {Infinity}

  1000: n_evalstartbb2in___4->evalstartbb4in, Arg_1: inf {Infinity}

  1000: n_evalstartbb2in___4->evalstartbb4in, Arg_2: inf {Infinity}

  1000: n_evalstartbb2in___4->evalstartbb4in, Arg_3: inf {Infinity}

  1003: n_evalstartbb2in___4->evalstartbb4in, Arg_0: 1 {O(1)}

  1003: n_evalstartbb2in___4->evalstartbb4in, Arg_1: 2 {O(1)}

  1003: n_evalstartbb2in___4->evalstartbb4in, Arg_2: 0 {O(1)}

  1003: n_evalstartbb2in___4->evalstartbb4in, Arg_3: 2 {O(1)}

  1006: n_evalstartbb2in___4->evalstartbb4in, Arg_0: inf {Infinity}

  1006: n_evalstartbb2in___4->evalstartbb4in, Arg_1: inf {Infinity}

  1006: n_evalstartbb2in___4->evalstartbb4in, Arg_2: inf {Infinity}

  1006: n_evalstartbb2in___4->evalstartbb4in, Arg_3: inf {Infinity}

  1009: n_evalstartbb2in___4->evalstartbb4in, Arg_0: 1 {O(1)}

  1009: n_evalstartbb2in___4->evalstartbb4in, Arg_1: 2 {O(1)}

  1009: n_evalstartbb2in___4->evalstartbb4in, Arg_2: 0 {O(1)}

  1009: n_evalstartbb2in___4->evalstartbb4in, Arg_3: 2 {O(1)}

  1012: n_evalstartbb2in___4->evalstartbb4in, Arg_0: inf {Infinity}

  1012: n_evalstartbb2in___4->evalstartbb4in, Arg_1: inf {Infinity}

  1012: n_evalstartbb2in___4->evalstartbb4in, Arg_2: inf {Infinity}

  1012: n_evalstartbb2in___4->evalstartbb4in, Arg_3: inf {Infinity}

  975: n_evalstartbb2in___5->n_evalstartbb3in___2, Arg_0: 1 {O(1)}

  975: n_evalstartbb2in___5->n_evalstartbb3in___2, Arg_1: 2 {O(1)}

  975: n_evalstartbb2in___5->n_evalstartbb3in___2, Arg_2: 1 {O(1)}

  975: n_evalstartbb2in___5->n_evalstartbb3in___2, Arg_3: Arg_3 {O(n)}

  998: n_evalstartbb2in___5->evalstartbb4in, Arg_0: 1 {O(1)}

  998: n_evalstartbb2in___5->evalstartbb4in, Arg_1: 2 {O(1)}

  998: n_evalstartbb2in___5->evalstartbb4in, Arg_2: 0 {O(1)}

  998: n_evalstartbb2in___5->evalstartbb4in, Arg_3: Arg_3 {O(n)}

  1001: n_evalstartbb2in___5->evalstartbb4in, Arg_0: inf {Infinity}

  1001: n_evalstartbb2in___5->evalstartbb4in, Arg_1: inf {Infinity}

  1001: n_evalstartbb2in___5->evalstartbb4in, Arg_2: inf {Infinity}

  1001: n_evalstartbb2in___5->evalstartbb4in, Arg_3: inf {Infinity}

  1004: n_evalstartbb2in___5->evalstartbb4in, Arg_0: 1 {O(1)}

  1004: n_evalstartbb2in___5->evalstartbb4in, Arg_1: 2 {O(1)}

  1004: n_evalstartbb2in___5->evalstartbb4in, Arg_2: 0 {O(1)}

  1004: n_evalstartbb2in___5->evalstartbb4in, Arg_3: Arg_3 {O(n)}

  1007: n_evalstartbb2in___5->evalstartbb4in, Arg_0: inf {Infinity}

  1007: n_evalstartbb2in___5->evalstartbb4in, Arg_1: inf {Infinity}

  1007: n_evalstartbb2in___5->evalstartbb4in, Arg_2: inf {Infinity}

  1007: n_evalstartbb2in___5->evalstartbb4in, Arg_3: inf {Infinity}

  1010: n_evalstartbb2in___5->evalstartbb4in, Arg_0: 1 {O(1)}

  1010: n_evalstartbb2in___5->evalstartbb4in, Arg_1: 2 {O(1)}

  1010: n_evalstartbb2in___5->evalstartbb4in, Arg_2: 0 {O(1)}

  1010: n_evalstartbb2in___5->evalstartbb4in, Arg_3: Arg_3 {O(n)}

  1013: n_evalstartbb2in___5->evalstartbb4in, Arg_0: inf {Infinity}

  1013: n_evalstartbb2in___5->evalstartbb4in, Arg_1: inf {Infinity}

  1013: n_evalstartbb2in___5->evalstartbb4in, Arg_2: inf {Infinity}

  1013: n_evalstartbb2in___5->evalstartbb4in, Arg_3: inf {Infinity}

  976: n_evalstartbb2in___6->n_evalstartbb3in___3, Arg_0: 1 {O(1)}

  976: n_evalstartbb2in___6->n_evalstartbb3in___3, Arg_1: 2 {O(1)}

  976: n_evalstartbb2in___6->n_evalstartbb3in___3, Arg_2: 1 {O(1)}

  976: n_evalstartbb2in___6->n_evalstartbb3in___3, Arg_3: 1 {O(1)}

  999: n_evalstartbb2in___6->evalstartbb4in, Arg_0: inf {Infinity}

  999: n_evalstartbb2in___6->evalstartbb4in, Arg_1: inf {Infinity}

  999: n_evalstartbb2in___6->evalstartbb4in, Arg_2: inf {Infinity}

  999: n_evalstartbb2in___6->evalstartbb4in, Arg_3: inf {Infinity}

  1002: n_evalstartbb2in___6->evalstartbb4in, Arg_0: 1 {O(1)}

  1002: n_evalstartbb2in___6->evalstartbb4in, Arg_1: 2 {O(1)}

  1002: n_evalstartbb2in___6->evalstartbb4in, Arg_2: 2 {O(1)}

  1002: n_evalstartbb2in___6->evalstartbb4in, Arg_3: 1 {O(1)}

  1005: n_evalstartbb2in___6->evalstartbb4in, Arg_0: inf {Infinity}

  1005: n_evalstartbb2in___6->evalstartbb4in, Arg_1: inf {Infinity}

  1005: n_evalstartbb2in___6->evalstartbb4in, Arg_2: inf {Infinity}

  1005: n_evalstartbb2in___6->evalstartbb4in, Arg_3: inf {Infinity}

  1008: n_evalstartbb2in___6->evalstartbb4in, Arg_0: 1 {O(1)}

  1008: n_evalstartbb2in___6->evalstartbb4in, Arg_1: 2 {O(1)}

  1008: n_evalstartbb2in___6->evalstartbb4in, Arg_2: 2 {O(1)}

  1008: n_evalstartbb2in___6->evalstartbb4in, Arg_3: 1 {O(1)}

  1011: n_evalstartbb2in___6->evalstartbb4in, Arg_0: inf {Infinity}

  1011: n_evalstartbb2in___6->evalstartbb4in, Arg_1: inf {Infinity}

  1011: n_evalstartbb2in___6->evalstartbb4in, Arg_2: inf {Infinity}

  1011: n_evalstartbb2in___6->evalstartbb4in, Arg_3: inf {Infinity}

  1014: n_evalstartbb2in___6->evalstartbb4in, Arg_0: 1 {O(1)}

  1014: n_evalstartbb2in___6->evalstartbb4in, Arg_1: 2 {O(1)}

  1014: n_evalstartbb2in___6->evalstartbb4in, Arg_2: 2 {O(1)}

  1014: n_evalstartbb2in___6->evalstartbb4in, Arg_3: 1 {O(1)}

  978: n_evalstartbb3in___1->n_evalstartbb2in___4, Arg_0: 1 {O(1)}

  978: n_evalstartbb3in___1->n_evalstartbb2in___4, Arg_1: 2 {O(1)}

  978: n_evalstartbb3in___1->n_evalstartbb2in___4, Arg_2: 0 {O(1)}

  978: n_evalstartbb3in___1->n_evalstartbb2in___4, Arg_3: 2 {O(1)}

  979: n_evalstartbb3in___2->n_evalstartbb2in___5, Arg_0: 1 {O(1)}

  979: n_evalstartbb3in___2->n_evalstartbb2in___5, Arg_1: 2 {O(1)}

  979: n_evalstartbb3in___2->n_evalstartbb2in___5, Arg_2: 0 {O(1)}

  979: n_evalstartbb3in___2->n_evalstartbb2in___5, Arg_3: Arg_3 {O(n)}

  980: n_evalstartbb3in___3->n_evalstartbb2in___6, Arg_0: 1 {O(1)}

  980: n_evalstartbb3in___3->n_evalstartbb2in___6, Arg_1: 2 {O(1)}

  980: n_evalstartbb3in___3->n_evalstartbb2in___6, Arg_2: 2 {O(1)}

  980: n_evalstartbb3in___3->n_evalstartbb2in___6, Arg_3: 1 {O(1)}

  981: n_evalstartbb3in___7->n_evalstartbb2in___4, Arg_0: 1 {O(1)}

  981: n_evalstartbb3in___7->n_evalstartbb2in___4, Arg_1: 2 {O(1)}

  981: n_evalstartbb3in___7->n_evalstartbb2in___4, Arg_2: 0 {O(1)}

  981: n_evalstartbb3in___7->n_evalstartbb2in___4, Arg_3: 2 {O(1)}

  982: n_evalstartbb3in___7->n_evalstartbb2in___5, Arg_0: 1 {O(1)}

  982: n_evalstartbb3in___7->n_evalstartbb2in___5, Arg_1: 2 {O(1)}

  982: n_evalstartbb3in___7->n_evalstartbb2in___5, Arg_2: 0 {O(1)}

  982: n_evalstartbb3in___7->n_evalstartbb2in___5, Arg_3: Arg_3 {O(n)}

  983: n_evalstartbb3in___7->n_evalstartbb2in___6, Arg_0: 1 {O(1)}

  983: n_evalstartbb3in___7->n_evalstartbb2in___6, Arg_1: 2 {O(1)}

  983: n_evalstartbb3in___7->n_evalstartbb2in___6, Arg_2: 2 {O(1)}

  983: n_evalstartbb3in___7->n_evalstartbb2in___6, Arg_3: 1 {O(1)}

`Upper:

  2: evalstart0->evalstart1, Arg_0: Arg_0 {O(n)}

  2: evalstart0->evalstart1, Arg_1: Arg_1 {O(n)}

  2: evalstart0->evalstart1, Arg_2: Arg_2 {O(n)}

  2: evalstart0->evalstart1, Arg_3: Arg_3 {O(n)}

  3: evalstart1->evalstart2, Arg_0: Arg_0 {O(n)}

  3: evalstart1->evalstart2, Arg_1: Arg_1 {O(n)}

  3: evalstart1->evalstart2, Arg_2: Arg_2 {O(n)}

  3: evalstart1->evalstart2, Arg_3: Arg_3 {O(n)}

  20: evalstart10->evalstart11, Arg_0: 0 {O(1)}

  20: evalstart10->evalstart11, Arg_1: Arg_1 {O(n)}

  20: evalstart10->evalstart11, Arg_2: Arg_2 {O(n)}

  20: evalstart10->evalstart11, Arg_3: Arg_3 {O(n)}

  21: evalstart11->evalstartstop, Arg_0: 0 {O(1)}

  21: evalstart11->evalstartstop, Arg_1: Arg_1 {O(n)}

  21: evalstart11->evalstartstop, Arg_2: Arg_2 {O(n)}

  21: evalstart11->evalstartstop, Arg_3: Arg_3 {O(n)}

  4: evalstart2->evalstart3, Arg_0: Arg_0 {O(n)}

  4: evalstart2->evalstart3, Arg_1: Arg_1 {O(n)}

  4: evalstart2->evalstart3, Arg_2: Arg_2 {O(n)}

  4: evalstart2->evalstart3, Arg_3: Arg_3 {O(n)}

  5: evalstart3->evalstartbb1in, Arg_0: Arg_0 {O(n)}

  5: evalstart3->evalstartbb1in, Arg_1: Arg_1 {O(n)}

  5: evalstart3->evalstartbb1in, Arg_2: Arg_2 {O(n)}

  5: evalstart3->evalstartbb1in, Arg_3: Arg_3 {O(n)}

  6: evalstart3->evalstartbb6in, Arg_0: 0 {O(1)}

  6: evalstart3->evalstartbb6in, Arg_1: Arg_1 {O(n)}

  6: evalstart3->evalstartbb6in, Arg_2: Arg_2 {O(n)}

  6: evalstart3->evalstartbb6in, Arg_3: Arg_3 {O(n)}

  17: evalstart8->evalstart9, Arg_0: Arg_0 {O(n)}

  17: evalstart8->evalstart9, Arg_1: Arg_1 {O(n)}

  17: evalstart8->evalstart9, Arg_2: Arg_2 {O(n)}

  17: evalstart8->evalstart9, Arg_3: Arg_3 {O(n)}

  18: evalstart9->evalstartstop, Arg_0: Arg_0 {O(n)}

  18: evalstart9->evalstartstop, Arg_1: Arg_1 {O(n)}

  18: evalstart9->evalstartstop, Arg_2: Arg_2 {O(n)}

  18: evalstart9->evalstartstop, Arg_3: Arg_3 {O(n)}

  1: evalstartbb0in->evalstart0, Arg_0: Arg_0 {O(n)}

  1: evalstartbb0in->evalstart0, Arg_1: Arg_1 {O(n)}

  1: evalstartbb0in->evalstart0, Arg_2: Arg_2 {O(n)}

  1: evalstartbb0in->evalstart0, Arg_3: Arg_3 {O(n)}

  7: evalstartbb1in->evalstartbb2in, Arg_0: Arg_0 {O(n)}

  7: evalstartbb1in->evalstartbb2in, Arg_1: Arg_1 {O(n)}

  7: evalstartbb1in->evalstartbb2in, Arg_2: Arg_0 {O(n)}

  7: evalstartbb1in->evalstartbb2in, Arg_3: Arg_3 {O(n)}

  8: evalstartbb1in->evalstartbb5in, Arg_0: Arg_0 {O(n)}

  8: evalstartbb1in->evalstartbb5in, Arg_1: Arg_1 {O(n)}

  8: evalstartbb1in->evalstartbb5in, Arg_2: Arg_2 {O(n)}

  8: evalstartbb1in->evalstartbb5in, Arg_3: Arg_3 {O(n)}

  10: evalstartbb2in->evalstartbb4in, Arg_0: Arg_0 {O(n)}

  10: evalstartbb2in->evalstartbb4in, Arg_1: Arg_1 {O(n)}

  10: evalstartbb2in->evalstartbb4in, Arg_2: 0 {O(1)}

  10: evalstartbb2in->evalstartbb4in, Arg_3: min([Arg_3, min([Arg_3, min([Arg_3, min([Arg_3, min([Arg_3, min([Arg_3, max([1, Arg_3])])])])])])]) {O(n)}

  11: evalstartbb2in->evalstartbb4in, Arg_0: -(inf) {Infinity}

  11: evalstartbb2in->evalstartbb4in, Arg_1: -(inf) {Infinity}

  11: evalstartbb2in->evalstartbb4in, Arg_2: -(inf) {Infinity}

  11: evalstartbb2in->evalstartbb4in, Arg_3: -(inf) {Infinity}

  977: evalstartbb2in->n_evalstartbb3in___7, Arg_0: Arg_0 {O(n)}

  977: evalstartbb2in->n_evalstartbb3in___7, Arg_1: Arg_1 {O(n)}

  977: evalstartbb2in->n_evalstartbb3in___7, Arg_2: Arg_0 {O(n)}

  977: evalstartbb2in->n_evalstartbb3in___7, Arg_3: Arg_3 {O(n)}

  15: evalstartbb4in->evalstartstop, Arg_0: Arg_0 {O(n)}

  15: evalstartbb4in->evalstartstop, Arg_1: Arg_1 {O(n)}

  15: evalstartbb4in->evalstartstop, Arg_2: max([0, max([1+Arg_0+max([0, -1+Arg_1]), 1+Arg_0])]) {O(n)}

  15: evalstartbb4in->evalstartstop, Arg_3: min([max([1, max([Arg_3, min([Arg_3, min([Arg_3, min([Arg_3, min([Arg_3, min([Arg_3, min([Arg_3, max([1, Arg_3])])])])])])])])]), min([max([1, max([Arg_3, min([Arg_3, min([Arg_3, min([Arg_3, min([Arg_3, min([Arg_3, max([1, Arg_3])])])])])])])]), min([max([1, max([Arg_3, min([Arg_3, min([Arg_3, min([Arg_3, min([Arg_3, max([1, Arg_3])])])])])])]), min([max([1, max([Arg_3, min([Arg_3, min([Arg_3, min([Arg_3, max([1, Arg_3])])])])])]), min([max([1, max([Arg_3, min([Arg_3, min([Arg_3, max([1, Arg_3])])])])]), min([max([1, max([Arg_3, min([Arg_3, max([1, Arg_3])])])]), max([1, Arg_3])])])])])])]) {O(n)}

  16: evalstartbb5in->evalstart8, Arg_0: Arg_0 {O(n)}

  16: evalstartbb5in->evalstart8, Arg_1: Arg_1 {O(n)}

  16: evalstartbb5in->evalstart8, Arg_2: Arg_2 {O(n)}

  16: evalstartbb5in->evalstart8, Arg_3: Arg_3 {O(n)}

  19: evalstartbb6in->evalstart10, Arg_0: 0 {O(1)}

  19: evalstartbb6in->evalstart10, Arg_1: Arg_1 {O(n)}

  19: evalstartbb6in->evalstart10, Arg_2: Arg_2 {O(n)}

  19: evalstartbb6in->evalstart10, Arg_3: Arg_3 {O(n)}

  0: evalstartstart->evalstartbb0in, Arg_0: Arg_0 {O(n)}

  0: evalstartstart->evalstartbb0in, Arg_1: Arg_1 {O(n)}

  0: evalstartstart->evalstartbb0in, Arg_2: Arg_2 {O(n)}

  0: evalstartstart->evalstartbb0in, Arg_3: Arg_3 {O(n)}

  974: n_evalstartbb2in___4->n_evalstartbb3in___1, Arg_0: Arg_0 {O(n)}

  974: n_evalstartbb2in___4->n_evalstartbb3in___1, Arg_1: Arg_1 {O(n)}

  974: n_evalstartbb2in___4->n_evalstartbb3in___1, Arg_2: -1+Arg_0 {O(n)}

  974: n_evalstartbb2in___4->n_evalstartbb3in___1, Arg_3: Arg_3 {O(n)}

  997: n_evalstartbb2in___4->evalstartbb4in, Arg_0: Arg_0 {O(n)}

  997: n_evalstartbb2in___4->evalstartbb4in, Arg_1: Arg_1 {O(n)}

  997: n_evalstartbb2in___4->evalstartbb4in, Arg_2: 0 {O(1)}

  997: n_evalstartbb2in___4->evalstartbb4in, Arg_3: Arg_3 {O(n)}

  1000: n_evalstartbb2in___4->evalstartbb4in, Arg_0: -(inf) {Infinity}

  1000: n_evalstartbb2in___4->evalstartbb4in, Arg_1: -(inf) {Infinity}

  1000: n_evalstartbb2in___4->evalstartbb4in, Arg_2: -(inf) {Infinity}

  1000: n_evalstartbb2in___4->evalstartbb4in, Arg_3: -(inf) {Infinity}

  1003: n_evalstartbb2in___4->evalstartbb4in, Arg_0: Arg_0 {O(n)}

  1003: n_evalstartbb2in___4->evalstartbb4in, Arg_1: Arg_1 {O(n)}

  1003: n_evalstartbb2in___4->evalstartbb4in, Arg_2: 0 {O(1)}

  1003: n_evalstartbb2in___4->evalstartbb4in, Arg_3: Arg_3 {O(n)}

  1006: n_evalstartbb2in___4->evalstartbb4in, Arg_0: -(inf) {Infinity}

  1006: n_evalstartbb2in___4->evalstartbb4in, Arg_1: -(inf) {Infinity}

  1006: n_evalstartbb2in___4->evalstartbb4in, Arg_2: -(inf) {Infinity}

  1006: n_evalstartbb2in___4->evalstartbb4in, Arg_3: -(inf) {Infinity}

  1009: n_evalstartbb2in___4->evalstartbb4in, Arg_0: Arg_0 {O(n)}

  1009: n_evalstartbb2in___4->evalstartbb4in, Arg_1: Arg_1 {O(n)}

  1009: n_evalstartbb2in___4->evalstartbb4in, Arg_2: 0 {O(1)}

  1009: n_evalstartbb2in___4->evalstartbb4in, Arg_3: Arg_3 {O(n)}

  1012: n_evalstartbb2in___4->evalstartbb4in, Arg_0: -(inf) {Infinity}

  1012: n_evalstartbb2in___4->evalstartbb4in, Arg_1: -(inf) {Infinity}

  1012: n_evalstartbb2in___4->evalstartbb4in, Arg_2: -(inf) {Infinity}

  1012: n_evalstartbb2in___4->evalstartbb4in, Arg_3: -(inf) {Infinity}

  975: n_evalstartbb2in___5->n_evalstartbb3in___2, Arg_0: Arg_0 {O(n)}

  975: n_evalstartbb2in___5->n_evalstartbb3in___2, Arg_1: Arg_1 {O(n)}

  975: n_evalstartbb2in___5->n_evalstartbb3in___2, Arg_2: -1+Arg_0 {O(n)}

  975: n_evalstartbb2in___5->n_evalstartbb3in___2, Arg_3: 0 {O(1)}

  998: n_evalstartbb2in___5->evalstartbb4in, Arg_0: Arg_0 {O(n)}

  998: n_evalstartbb2in___5->evalstartbb4in, Arg_1: Arg_1 {O(n)}

  998: n_evalstartbb2in___5->evalstartbb4in, Arg_2: 0 {O(1)}

  998: n_evalstartbb2in___5->evalstartbb4in, Arg_3: 0 {O(1)}

  1001: n_evalstartbb2in___5->evalstartbb4in, Arg_0: -(inf) {Infinity}

  1001: n_evalstartbb2in___5->evalstartbb4in, Arg_1: -(inf) {Infinity}

  1001: n_evalstartbb2in___5->evalstartbb4in, Arg_2: -(inf) {Infinity}

  1001: n_evalstartbb2in___5->evalstartbb4in, Arg_3: -(inf) {Infinity}

  1004: n_evalstartbb2in___5->evalstartbb4in, Arg_0: Arg_0 {O(n)}

  1004: n_evalstartbb2in___5->evalstartbb4in, Arg_1: Arg_1 {O(n)}

  1004: n_evalstartbb2in___5->evalstartbb4in, Arg_2: 0 {O(1)}

  1004: n_evalstartbb2in___5->evalstartbb4in, Arg_3: 0 {O(1)}

  1007: n_evalstartbb2in___5->evalstartbb4in, Arg_0: -(inf) {Infinity}

  1007: n_evalstartbb2in___5->evalstartbb4in, Arg_1: -(inf) {Infinity}

  1007: n_evalstartbb2in___5->evalstartbb4in, Arg_2: -(inf) {Infinity}

  1007: n_evalstartbb2in___5->evalstartbb4in, Arg_3: -(inf) {Infinity}

  1010: n_evalstartbb2in___5->evalstartbb4in, Arg_0: Arg_0 {O(n)}

  1010: n_evalstartbb2in___5->evalstartbb4in, Arg_1: Arg_1 {O(n)}

  1010: n_evalstartbb2in___5->evalstartbb4in, Arg_2: 0 {O(1)}

  1010: n_evalstartbb2in___5->evalstartbb4in, Arg_3: 0 {O(1)}

  1013: n_evalstartbb2in___5->evalstartbb4in, Arg_0: -(inf) {Infinity}

  1013: n_evalstartbb2in___5->evalstartbb4in, Arg_1: -(inf) {Infinity}

  1013: n_evalstartbb2in___5->evalstartbb4in, Arg_2: -(inf) {Infinity}

  1013: n_evalstartbb2in___5->evalstartbb4in, Arg_3: -(inf) {Infinity}

  976: n_evalstartbb2in___6->n_evalstartbb3in___3, Arg_0: Arg_0 {O(n)}

  976: n_evalstartbb2in___6->n_evalstartbb3in___3, Arg_1: Arg_1 {O(n)}

  976: n_evalstartbb2in___6->n_evalstartbb3in___3, Arg_2: 1+Arg_0+max([0, -1+Arg_1]) {O(n)}

  976: n_evalstartbb2in___6->n_evalstartbb3in___3, Arg_3: 1 {O(1)}

  999: n_evalstartbb2in___6->evalstartbb4in, Arg_0: -(inf) {Infinity}

  999: n_evalstartbb2in___6->evalstartbb4in, Arg_1: -(inf) {Infinity}

  999: n_evalstartbb2in___6->evalstartbb4in, Arg_2: -(inf) {Infinity}

  999: n_evalstartbb2in___6->evalstartbb4in, Arg_3: -(inf) {Infinity}

  1002: n_evalstartbb2in___6->evalstartbb4in, Arg_0: Arg_0 {O(n)}

  1002: n_evalstartbb2in___6->evalstartbb4in, Arg_1: Arg_1 {O(n)}

  1002: n_evalstartbb2in___6->evalstartbb4in, Arg_2: max([1+Arg_0, 1+Arg_0+max([0, -1+Arg_1])]) {O(n)}

  1002: n_evalstartbb2in___6->evalstartbb4in, Arg_3: 1 {O(1)}

  1005: n_evalstartbb2in___6->evalstartbb4in, Arg_0: -(inf) {Infinity}

  1005: n_evalstartbb2in___6->evalstartbb4in, Arg_1: -(inf) {Infinity}

  1005: n_evalstartbb2in___6->evalstartbb4in, Arg_2: -(inf) {Infinity}

  1005: n_evalstartbb2in___6->evalstartbb4in, Arg_3: -(inf) {Infinity}

  1008: n_evalstartbb2in___6->evalstartbb4in, Arg_0: Arg_0 {O(n)}

  1008: n_evalstartbb2in___6->evalstartbb4in, Arg_1: Arg_1 {O(n)}

  1008: n_evalstartbb2in___6->evalstartbb4in, Arg_2: max([1+Arg_0, 1+Arg_0+max([0, -1+Arg_1])]) {O(n)}

  1008: n_evalstartbb2in___6->evalstartbb4in, Arg_3: 1 {O(1)}

  1011: n_evalstartbb2in___6->evalstartbb4in, Arg_0: -(inf) {Infinity}

  1011: n_evalstartbb2in___6->evalstartbb4in, Arg_1: -(inf) {Infinity}

  1011: n_evalstartbb2in___6->evalstartbb4in, Arg_2: -(inf) {Infinity}

  1011: n_evalstartbb2in___6->evalstartbb4in, Arg_3: -(inf) {Infinity}

  1014: n_evalstartbb2in___6->evalstartbb4in, Arg_0: Arg_0 {O(n)}

  1014: n_evalstartbb2in___6->evalstartbb4in, Arg_1: Arg_1 {O(n)}

  1014: n_evalstartbb2in___6->evalstartbb4in, Arg_2: max([1+Arg_0, 1+Arg_0+max([0, -1+Arg_1])]) {O(n)}

  1014: n_evalstartbb2in___6->evalstartbb4in, Arg_3: 1 {O(1)}

  978: n_evalstartbb3in___1->n_evalstartbb2in___4, Arg_0: Arg_0 {O(n)}

  978: n_evalstartbb3in___1->n_evalstartbb2in___4, Arg_1: Arg_1 {O(n)}

  978: n_evalstartbb3in___1->n_evalstartbb2in___4, Arg_2: -1+Arg_0 {O(n)}

  978: n_evalstartbb3in___1->n_evalstartbb2in___4, Arg_3: Arg_3 {O(n)}

  979: n_evalstartbb3in___2->n_evalstartbb2in___5, Arg_0: Arg_0 {O(n)}

  979: n_evalstartbb3in___2->n_evalstartbb2in___5, Arg_1: Arg_1 {O(n)}

  979: n_evalstartbb3in___2->n_evalstartbb2in___5, Arg_2: -1+Arg_0 {O(n)}

  979: n_evalstartbb3in___2->n_evalstartbb2in___5, Arg_3: 0 {O(1)}

  980: n_evalstartbb3in___3->n_evalstartbb2in___6, Arg_0: Arg_0 {O(n)}

  980: n_evalstartbb3in___3->n_evalstartbb2in___6, Arg_1: Arg_1 {O(n)}

  980: n_evalstartbb3in___3->n_evalstartbb2in___6, Arg_2: 1+Arg_0+max([0, -1+Arg_1]) {O(n)}

  980: n_evalstartbb3in___3->n_evalstartbb2in___6, Arg_3: 1 {O(1)}

  981: n_evalstartbb3in___7->n_evalstartbb2in___4, Arg_0: Arg_0 {O(n)}

  981: n_evalstartbb3in___7->n_evalstartbb2in___4, Arg_1: Arg_1 {O(n)}

  981: n_evalstartbb3in___7->n_evalstartbb2in___4, Arg_2: -1+Arg_0 {O(n)}

  981: n_evalstartbb3in___7->n_evalstartbb2in___4, Arg_3: Arg_3 {O(n)}

  982: n_evalstartbb3in___7->n_evalstartbb2in___5, Arg_0: Arg_0 {O(n)}

  982: n_evalstartbb3in___7->n_evalstartbb2in___5, Arg_1: Arg_1 {O(n)}

  982: n_evalstartbb3in___7->n_evalstartbb2in___5, Arg_2: -1+Arg_0 {O(n)}

  982: n_evalstartbb3in___7->n_evalstartbb2in___5, Arg_3: 0 {O(1)}

  983: n_evalstartbb3in___7->n_evalstartbb2in___6, Arg_0: Arg_0 {O(n)}

  983: n_evalstartbb3in___7->n_evalstartbb2in___6, Arg_1: Arg_1 {O(n)}

  983: n_evalstartbb3in___7->n_evalstartbb2in___6, Arg_2: 1+Arg_0 {O(n)}

  983: n_evalstartbb3in___7->n_evalstartbb2in___6, Arg_3: 1 {O(1)}


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

(2)
BOUNDS(1, nat(1 + Arg_0) + nat(2 * Arg_0) + max(34, 32 + 2 * Arg_0) + nat(Arg_1) + max(8 + Arg_1, 9))

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

(3) Loat Proof (FINISHED)


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



Initial linear ITS problem

   Start location: evalstartstart

      0: evalstartstart -> evalstartbb0in : [], cost: 1

      1: evalstartbb0in -> evalstart0 : [], cost: 1

      2: evalstart0 -> evalstart1 : [], cost: 1

      3: evalstart1 -> evalstart2 : [], cost: 1

      4: evalstart2 -> evalstart3 : [], cost: 1

      5: evalstart3 -> evalstartbb1in : [ A>=1 ], cost: 1

      6: evalstart3 -> evalstartbb6in : [ 0>=A ], cost: 1

      7: evalstartbb1in -> evalstartbb2in : C'=A, [ B>=1+A ], cost: 1

      8: evalstartbb1in -> evalstartbb5in : [ A>=B ], cost: 1

      9: evalstartbb2in -> evalstartbb3in : [ C>=1 && B>=1+C ], cost: 1

     10: evalstartbb2in -> evalstartbb4in : [ 0>=C ], cost: 1

     11: evalstartbb2in -> evalstartbb4in : [ C>=B ], cost: 1

     12: evalstartbb3in -> evalstartbb2in : C'=1+C, [ D==1 ], cost: 1

     13: evalstartbb3in -> evalstartbb2in : C'=-1+C, [ 0>=D ], cost: 1

     14: evalstartbb3in -> evalstartbb2in : C'=-1+C, [ D>=2 ], cost: 1

     15: evalstartbb4in -> evalstartstop : [], cost: 1

     16: evalstartbb5in -> evalstart8 : [], cost: 1

     17: evalstart8 -> evalstart9 : [], cost: 1

     18: evalstart9 -> evalstartstop : [], cost: 1

     19: evalstartbb6in -> evalstart10 : [], cost: 1

     20: evalstart10 -> evalstart11 : [], cost: 1

     21: evalstart11 -> evalstartstop : [], cost: 1



Checking for constant complexity:

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

      0: evalstartstart -> evalstartbb0in : [], cost: 1



Removed unreachable and leaf rules:

   Start location: evalstartstart

      0: evalstartstart -> evalstartbb0in : [], cost: 1

      1: evalstartbb0in -> evalstart0 : [], cost: 1

      2: evalstart0 -> evalstart1 : [], cost: 1

      3: evalstart1 -> evalstart2 : [], cost: 1

      4: evalstart2 -> evalstart3 : [], cost: 1

      5: evalstart3 -> evalstartbb1in : [ A>=1 ], cost: 1

      7: evalstartbb1in -> evalstartbb2in : C'=A, [ B>=1+A ], cost: 1

      9: evalstartbb2in -> evalstartbb3in : [ C>=1 && B>=1+C ], cost: 1

     12: evalstartbb3in -> evalstartbb2in : C'=1+C, [ D==1 ], cost: 1

     13: evalstartbb3in -> evalstartbb2in : C'=-1+C, [ 0>=D ], cost: 1

     14: evalstartbb3in -> evalstartbb2in : C'=-1+C, [ D>=2 ], cost: 1



### Simplification by acceleration and chaining ###



Eliminated locations (on linear paths):

   Start location: evalstartstart

     27: evalstartstart -> evalstartbb2in : C'=A, [ A>=1 && B>=1+A ], cost: 7

      9: evalstartbb2in -> evalstartbb3in : [ C>=1 && B>=1+C ], cost: 1

     12: evalstartbb3in -> evalstartbb2in : C'=1+C, [ D==1 ], cost: 1

     13: evalstartbb3in -> evalstartbb2in : C'=-1+C, [ 0>=D ], cost: 1

     14: evalstartbb3in -> evalstartbb2in : C'=-1+C, [ D>=2 ], cost: 1



Eliminated locations (on tree-shaped paths):

   Start location: evalstartstart

     27: evalstartstart -> evalstartbb2in : C'=A, [ A>=1 && B>=1+A ], cost: 7

     28: evalstartbb2in -> evalstartbb2in : C'=1+C, [ C>=1 && B>=1+C && D==1 ], cost: 2

     29: evalstartbb2in -> evalstartbb2in : C'=-1+C, [ C>=1 && B>=1+C && 0>=D ], cost: 2

     30: evalstartbb2in -> evalstartbb2in : C'=-1+C, [ C>=1 && B>=1+C && D>=2 ], cost: 2



Accelerating simple loops of location 7.

   Accelerating the following rules:

     28: evalstartbb2in -> evalstartbb2in : C'=1+C, [ C>=1 && B>=1+C && D==1 ], cost: 2

     29: evalstartbb2in -> evalstartbb2in : C'=-1+C, [ C>=1 && B>=1+C && 0>=D ], cost: 2

     30: evalstartbb2in -> evalstartbb2in : C'=-1+C, [ C>=1 && B>=1+C && D>=2 ], cost: 2



   Accelerated rule 28 with metering function -C+B, yielding the new rule 31.

   Accelerated rule 29 with metering function C, yielding the new rule 32.

   Accelerated rule 30 with metering function C, yielding the new rule 33.

   Removing the simple loops: 28 29 30.



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

   Start location: evalstartstart

     27: evalstartstart -> evalstartbb2in : C'=A, [ A>=1 && B>=1+A ], cost: 7

     31: evalstartbb2in -> evalstartbb2in : C'=B, [ C>=1 && B>=1+C && D==1 ], cost: -2*C+2*B

     32: evalstartbb2in -> evalstartbb2in : C'=0, [ C>=1 && B>=1+C && 0>=D ], cost: 2*C

     33: evalstartbb2in -> evalstartbb2in : C'=0, [ C>=1 && B>=1+C && D>=2 ], cost: 2*C



Chained accelerated rules (with incoming rules):

   Start location: evalstartstart

     27: evalstartstart -> evalstartbb2in : C'=A, [ A>=1 && B>=1+A ], cost: 7

     34: evalstartstart -> evalstartbb2in : C'=B, [ A>=1 && B>=1+A && D==1 ], cost: 7-2*A+2*B

     35: evalstartstart -> evalstartbb2in : C'=0, [ A>=1 && B>=1+A && 0>=D ], cost: 7+2*A

     36: evalstartstart -> evalstartbb2in : C'=0, [ A>=1 && B>=1+A && D>=2 ], cost: 7+2*A



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

   Start location: evalstartstart

     34: evalstartstart -> evalstartbb2in : C'=B, [ A>=1 && B>=1+A && D==1 ], cost: 7-2*A+2*B

     35: evalstartstart -> evalstartbb2in : C'=0, [ A>=1 && B>=1+A && 0>=D ], cost: 7+2*A

     36: evalstartstart -> evalstartbb2in : C'=0, [ A>=1 && B>=1+A && D>=2 ], cost: 7+2*A



### Computing asymptotic complexity ###



Fully simplified ITS problem

   Start location: evalstartstart

     34: evalstartstart -> evalstartbb2in : C'=B, [ A>=1 && B>=1+A && D==1 ], cost: 7-2*A+2*B

     35: evalstartstart -> evalstartbb2in : C'=0, [ A>=1 && B>=1+A && 0>=D ], cost: 7+2*A

     36: evalstartstart -> evalstartbb2in : C'=0, [ A>=1 && B>=1+A && D>=2 ], cost: 7+2*A



Computing asymptotic complexity for rule 34

   Solved the limit problem by the following transformations:

      Created initial limit problem:

      2-D (+/+!), D (+/+!), A (+/+!), -A+B (+/+!), 7-2*A+2*B (+) [not solved]



      removing all constraints (solved by SMT)

      resulting limit problem: [solved]



      applying transformation rule (C) using substitution {D==1,A==n,B==2*n}

      resulting limit problem:

      [solved]



   Solution:

      D / 1

      A / n

      B / 2*n

   Resulting cost 7+2*n has complexity: Poly(n^1)



Found new complexity Poly(n^1).



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

   Complexity:  Poly(n^1)

   Cpx degree:  1

   Solved cost: 7+2*n

   Rule cost:   7-2*A+2*B

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



WORST_CASE(Omega(n^1),?)


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

(4)
BOUNDS(n^1, INF)