WORST_CASE(Omega(1),?)

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

Initial linear ITS problem
   Start location: __init
      0: f1_0_main_ConstantStackPush -> f99_0_loop_aux_LE : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, [ arg1>0 && arg2>-1 && 0==arg1P_1 && 0==arg2P_1 && 10*arg2==arg3P_1 ], cost: 1
      1: f99_0_loop_aux_LE -> f128_0_loop_aux_EQ : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ arg3<10 && arg3>1 && arg1==arg1P_2 && arg3==arg2P_2 && arg2==arg3P_2 ], cost: 1
      2: f99_0_loop_aux_LE -> f128_0_loop_aux_EQ : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg3>10 && arg1==arg1P_3 && arg3==arg2P_3 && arg2==arg3P_3 ], cost: 1
      4: f99_0_loop_aux_LE -> f99_0_loop_aux_LE : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ arg1<2 && 1==arg3 && 1==arg1P_5 && 1==arg2P_5 && 2==arg3P_5 ], cost: 1
      5: f99_0_loop_aux_LE -> f99_0_loop_aux_LE : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [ arg1<2 && 10==arg3 && 0==arg1P_6 && 0==arg2P_6 && 9==arg3P_6 ], cost: 1
      3: f128_0_loop_aux_EQ -> f99_0_loop_aux_LE : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ arg1<2 && arg2>1 && 0==arg3 && 0==arg1P_4 && 0==arg2P_4 && -1+arg2==arg3P_4 ], cost: 1
      6: f128_0_loop_aux_EQ -> f99_0_loop_aux_LE : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [ arg1<2 && arg2>1 && 1==arg3 && 1==arg1P_7 && 1==arg2P_7 && 1+arg2==arg3P_7 ], cost: 1
      7: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, [], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
      7: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, [], cost: 1

Simplified all rules, resulting in:
   Start location: __init
      0: f1_0_main_ConstantStackPush -> f99_0_loop_aux_LE : arg1'=0, arg2'=0, arg3'=10*arg2, [ arg1>0 && arg2>-1 ], cost: 1
      1: f99_0_loop_aux_LE -> f128_0_loop_aux_EQ : arg2'=arg3, arg3'=arg2, [ arg3<10 && arg3>1 ], cost: 1
      2: f99_0_loop_aux_LE -> f128_0_loop_aux_EQ : arg2'=arg3, arg3'=arg2, [ arg3>10 ], cost: 1
      4: f99_0_loop_aux_LE -> f99_0_loop_aux_LE : arg1'=1, arg2'=1, arg3'=2, [ arg1<2 && 1==arg3 ], cost: 1
      5: f99_0_loop_aux_LE -> f99_0_loop_aux_LE : arg1'=0, arg2'=0, arg3'=9, [ arg1<2 && 10==arg3 ], cost: 1
      3: f128_0_loop_aux_EQ -> f99_0_loop_aux_LE : arg1'=0, arg2'=0, arg3'=-1+arg2, [ arg1<2 && arg2>1 && 0==arg3 ], cost: 1
      6: f128_0_loop_aux_EQ -> f99_0_loop_aux_LE : arg1'=1, arg2'=1, arg3'=1+arg2, [ arg1<2 && arg2>1 && 1==arg3 ], cost: 1
      7: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, [], cost: 1

### Simplification by acceleration and chaining ###

Accelerating simple loops of location 1.
   Accelerating the following rules:
      4: f99_0_loop_aux_LE -> f99_0_loop_aux_LE : arg1'=1, arg2'=1, arg3'=2, [ arg1<2 && 1==arg3 ], cost: 1
      5: f99_0_loop_aux_LE -> f99_0_loop_aux_LE : arg1'=0, arg2'=0, arg3'=9, [ arg1<2 && 10==arg3 ], cost: 1

   Failed to prove monotonicity of the guard of rule 4.
   Failed to prove monotonicity of the guard of rule 5.
[accelerate] Nesting with 2 inner and 2 outer candidates

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
      0: f1_0_main_ConstantStackPush -> f99_0_loop_aux_LE : arg1'=0, arg2'=0, arg3'=10*arg2, [ arg1>0 && arg2>-1 ], cost: 1
      1: f99_0_loop_aux_LE -> f128_0_loop_aux_EQ : arg2'=arg3, arg3'=arg2, [ arg3<10 && arg3>1 ], cost: 1
      2: f99_0_loop_aux_LE -> f128_0_loop_aux_EQ : arg2'=arg3, arg3'=arg2, [ arg3>10 ], cost: 1
      4: f99_0_loop_aux_LE -> f99_0_loop_aux_LE : arg1'=1, arg2'=1, arg3'=2, [ arg1<2 && 1==arg3 ], cost: 1
      5: f99_0_loop_aux_LE -> f99_0_loop_aux_LE : arg1'=0, arg2'=0, arg3'=9, [ arg1<2 && 10==arg3 ], cost: 1
      3: f128_0_loop_aux_EQ -> f99_0_loop_aux_LE : arg1'=0, arg2'=0, arg3'=-1+arg2, [ arg1<2 && arg2>1 && 0==arg3 ], cost: 1
      6: f128_0_loop_aux_EQ -> f99_0_loop_aux_LE : arg1'=1, arg2'=1, arg3'=1+arg2, [ arg1<2 && arg2>1 && 1==arg3 ], cost: 1
      7: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, [], cost: 1

Chained accelerated rules (with incoming rules):
   Start location: __init
      0: f1_0_main_ConstantStackPush -> f99_0_loop_aux_LE : arg1'=0, arg2'=0, arg3'=10*arg2, [ arg1>0 && arg2>-1 ], cost: 1
      9: f1_0_main_ConstantStackPush -> f99_0_loop_aux_LE : arg1'=0, arg2'=0, arg3'=9, [ arg1>0 && arg2>-1 && 10==10*arg2 ], cost: 2
      1: f99_0_loop_aux_LE -> f128_0_loop_aux_EQ : arg2'=arg3, arg3'=arg2, [ arg3<10 && arg3>1 ], cost: 1
      2: f99_0_loop_aux_LE -> f128_0_loop_aux_EQ : arg2'=arg3, arg3'=arg2, [ arg3>10 ], cost: 1
      3: f128_0_loop_aux_EQ -> f99_0_loop_aux_LE : arg1'=0, arg2'=0, arg3'=-1+arg2, [ arg1<2 && arg2>1 && 0==arg3 ], cost: 1
      6: f128_0_loop_aux_EQ -> f99_0_loop_aux_LE : arg1'=1, arg2'=1, arg3'=1+arg2, [ arg1<2 && arg2>1 && 1==arg3 ], cost: 1
      8: f128_0_loop_aux_EQ -> f99_0_loop_aux_LE : arg1'=1, arg2'=1, arg3'=2, [ arg1<2 && 0==arg3 && 1==-1+arg2 ], cost: 2
     10: f128_0_loop_aux_EQ -> f99_0_loop_aux_LE : arg1'=0, arg2'=0, arg3'=9, [ arg1<2 && 0==arg3 && 10==-1+arg2 ], cost: 2
     11: f128_0_loop_aux_EQ -> f99_0_loop_aux_LE : arg1'=0, arg2'=0, arg3'=9, [ arg1<2 && 1==arg3 && 10==1+arg2 ], cost: 2
      7: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, [], cost: 1

Eliminated locations (on tree-shaped paths):
   Start location: __init
     14: f99_0_loop_aux_LE -> f99_0_loop_aux_LE : arg1'=0, arg2'=0, arg3'=-1+arg3, [ arg3<10 && arg3>1 && arg1<2 && 0==arg2 ], cost: 2
     15: f99_0_loop_aux_LE -> f99_0_loop_aux_LE : arg1'=1, arg2'=1, arg3'=1+arg3, [ arg3<10 && arg3>1 && arg1<2 && 1==arg2 ], cost: 2
     16: f99_0_loop_aux_LE -> f99_0_loop_aux_LE : arg1'=1, arg2'=1, arg3'=2, [ arg1<2 && 0==arg2 && 1==-1+arg3 ], cost: 3
     17: f99_0_loop_aux_LE -> f99_0_loop_aux_LE : arg1'=0, arg2'=0, arg3'=9, [ arg1<2 && 1==arg2 && 10==1+arg3 ], cost: 3
     18: f99_0_loop_aux_LE -> f99_0_loop_aux_LE : arg1'=0, arg2'=0, arg3'=-1+arg3, [ arg3>10 && arg1<2 && 0==arg2 ], cost: 2
     19: f99_0_loop_aux_LE -> f99_0_loop_aux_LE : arg1'=1, arg2'=1, arg3'=1+arg3, [ arg3>10 && arg1<2 && 1==arg2 ], cost: 2
     20: f99_0_loop_aux_LE -> f99_0_loop_aux_LE : arg1'=0, arg2'=0, arg3'=9, [ arg1<2 && 0==arg2 && 10==-1+arg3 ], cost: 3
     12: __init -> f99_0_loop_aux_LE : arg1'=0, arg2'=0, arg3'=10*arg2P_8, [ arg1P_8>0 && arg2P_8>-1 ], cost: 2
     13: __init -> f99_0_loop_aux_LE : arg1'=0, arg2'=0, arg3'=9, [ arg1P_8>0 && arg2P_8>-1 && 10==10*arg2P_8 ], cost: 3

Applied pruning (of leafs and parallel rules):
   Start location: __init
     14: f99_0_loop_aux_LE -> f99_0_loop_aux_LE : arg1'=0, arg2'=0, arg3'=-1+arg3, [ arg3<10 && arg3>1 && arg1<2 && 0==arg2 ], cost: 2
     15: f99_0_loop_aux_LE -> f99_0_loop_aux_LE : arg1'=1, arg2'=1, arg3'=1+arg3, [ arg3<10 && arg3>1 && arg1<2 && 1==arg2 ], cost: 2
     16: f99_0_loop_aux_LE -> f99_0_loop_aux_LE : arg1'=1, arg2'=1, arg3'=2, [ arg1<2 && 0==arg2 && 1==-1+arg3 ], cost: 3
     17: f99_0_loop_aux_LE -> f99_0_loop_aux_LE : arg1'=0, arg2'=0, arg3'=9, [ arg1<2 && 1==arg2 && 10==1+arg3 ], cost: 3
     18: f99_0_loop_aux_LE -> f99_0_loop_aux_LE : arg1'=0, arg2'=0, arg3'=-1+arg3, [ arg3>10 && arg1<2 && 0==arg2 ], cost: 2
     12: __init -> f99_0_loop_aux_LE : arg1'=0, arg2'=0, arg3'=10*arg2P_8, [ arg1P_8>0 && arg2P_8>-1 ], cost: 2
     13: __init -> f99_0_loop_aux_LE : arg1'=0, arg2'=0, arg3'=9, [ arg1P_8>0 && arg2P_8>-1 && 10==10*arg2P_8 ], cost: 3

Accelerating simple loops of location 1.
   Accelerating the following rules:
     14: f99_0_loop_aux_LE -> f99_0_loop_aux_LE : arg1'=0, arg2'=0, arg3'=-1+arg3, [ arg3<10 && arg3>1 && arg1<2 && 0==arg2 ], cost: 2
     15: f99_0_loop_aux_LE -> f99_0_loop_aux_LE : arg1'=1, arg2'=1, arg3'=1+arg3, [ arg3<10 && arg3>1 && arg1<2 && 1==arg2 ], cost: 2
     16: f99_0_loop_aux_LE -> f99_0_loop_aux_LE : arg1'=1, arg2'=1, arg3'=2, [ arg1<2 && 0==arg2 && 1==-1+arg3 ], cost: 3
     17: f99_0_loop_aux_LE -> f99_0_loop_aux_LE : arg1'=0, arg2'=0, arg3'=9, [ arg1<2 && 1==arg2 && 10==1+arg3 ], cost: 3
     18: f99_0_loop_aux_LE -> f99_0_loop_aux_LE : arg1'=0, arg2'=0, arg3'=-1+arg3, [ arg3>10 && arg1<2 && 0==arg2 ], cost: 2

   Accelerated rule 14 with backward acceleration, yielding the new rule 21.
   Accelerated rule 15 with backward acceleration, yielding the new rule 22.
   Failed to prove monotonicity of the guard of rule 16.
   Failed to prove monotonicity of the guard of rule 17.
   Accelerated rule 18 with backward acceleration, yielding the new rule 23.
[accelerate] Nesting with 5 inner and 5 outer candidates
   Removing the simple loops: 14 15 18.

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     16: f99_0_loop_aux_LE -> f99_0_loop_aux_LE : arg1'=1, arg2'=1, arg3'=2, [ arg1<2 && 0==arg2 && 1==-1+arg3 ], cost: 3
     17: f99_0_loop_aux_LE -> f99_0_loop_aux_LE : arg1'=0, arg2'=0, arg3'=9, [ arg1<2 && 1==arg2 && 10==1+arg3 ], cost: 3
     21: f99_0_loop_aux_LE -> f99_0_loop_aux_LE : arg1'=0, arg2'=0, arg3'=1, [ arg3<10 && arg1<2 && 0==arg2 && -1+arg3>=1 ], cost: -2+2*arg3
     22: f99_0_loop_aux_LE -> f99_0_loop_aux_LE : arg1'=1, arg2'=1, arg3'=10, [ arg3>1 && arg1<2 && 1==arg2 && 10-arg3>=1 ], cost: 20-2*arg3
     23: f99_0_loop_aux_LE -> f99_0_loop_aux_LE : arg1'=0, arg2'=0, arg3'=10, [ arg1<2 && 0==arg2 && -10+arg3>=1 ], cost: -20+2*arg3
     12: __init -> f99_0_loop_aux_LE : arg1'=0, arg2'=0, arg3'=10*arg2P_8, [ arg1P_8>0 && arg2P_8>-1 ], cost: 2
     13: __init -> f99_0_loop_aux_LE : arg1'=0, arg2'=0, arg3'=9, [ arg1P_8>0 && arg2P_8>-1 && 10==10*arg2P_8 ], cost: 3

Chained accelerated rules (with incoming rules):
   Start location: __init
     12: __init -> f99_0_loop_aux_LE : arg1'=0, arg2'=0, arg3'=10*arg2P_8, [ arg1P_8>0 && arg2P_8>-1 ], cost: 2
     13: __init -> f99_0_loop_aux_LE : arg1'=0, arg2'=0, arg3'=9, [ arg1P_8>0 && arg2P_8>-1 && 10==10*arg2P_8 ], cost: 3
     24: __init -> f99_0_loop_aux_LE : arg1'=0, arg2'=0, arg3'=1, [], cost: 19
     25: __init -> f99_0_loop_aux_LE : arg1'=0, arg2'=0, arg3'=10, [ arg2P_8>-1 && -10+10*arg2P_8>=1 ], cost: -18+20*arg2P_8

Removed unreachable locations (and leaf rules with constant cost):
   Start location: __init
     25: __init -> f99_0_loop_aux_LE : arg1'=0, arg2'=0, arg3'=10, [ arg2P_8>-1 && -10+10*arg2P_8>=1 ], cost: -18+20*arg2P_8

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: __init
     25: __init -> f99_0_loop_aux_LE : arg1'=0, arg2'=0, arg3'=10, [ arg2P_8>-1 && -10+10*arg2P_8>=1 ], cost: -18+20*arg2P_8

Computing asymptotic complexity for rule 25
   Simplified the guard:
     25: __init -> f99_0_loop_aux_LE : arg1'=0, arg2'=0, arg3'=10, [ -10+10*arg2P_8>=1 ], cost: -18+20*arg2P_8
   Resulting cost 0 has complexity: Unknown

Obtained the following overall complexity (w.r.t. the length of the input n):
   Complexity:  Constant
   Cpx degree:  0
   Solved cost: 1
   Rule cost:   1
   Rule guard:  []

WORST_CASE(Omega(1),?)