WORST_CASE(Omega(1),?)

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

Initial linear ITS problem
   Start location: __init
      0: f1_0_main_ConstantStackPush -> f138_0_ack_GT : arg1'=arg1P_1, arg2'=arg2P_1, [ 12==arg1P_1 && 10==arg2P_1 ], cost: 1
      1: f138_0_ack_GT -> f138_0_ack_GT : arg1'=arg1P_2, arg2'=arg2P_2, [ arg2>0 && arg1<1 && 1==arg1P_2 && -1+arg2==arg2P_2 ], cost: 1
      2: f138_0_ack_GT -> f138_0_ack_GT : arg1'=arg1P_3, arg2'=arg2P_3, [ arg1>0 && -1+arg2<arg2 && arg2>0 && -1+arg1==arg1P_3 && arg2==arg2P_3 ], cost: 1
      3: f138_0_ack_GT -> f138_0_ack_GT : arg1'=arg1P_4, arg2'=arg2P_4, [ arg1>0 && -1+arg2<arg2 && arg2>0 && -1+arg2==arg2P_4 ], cost: 1
      4: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P_5, arg2'=arg2P_5, [], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
      4: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P_5, arg2'=arg2P_5, [], cost: 1

Simplified all rules, resulting in:
   Start location: __init
      0: f1_0_main_ConstantStackPush -> f138_0_ack_GT : arg1'=12, arg2'=10, [], cost: 1
      1: f138_0_ack_GT -> f138_0_ack_GT : arg1'=1, arg2'=-1+arg2, [ arg2>0 && arg1<1 ], cost: 1
      2: f138_0_ack_GT -> f138_0_ack_GT : arg1'=-1+arg1, [ arg1>0 && arg2>0 ], cost: 1
      3: f138_0_ack_GT -> f138_0_ack_GT : arg1'=arg1P_4, arg2'=-1+arg2, [ arg1>0 && arg2>0 ], cost: 1
      4: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P_5, arg2'=arg2P_5, [], cost: 1

### Simplification by acceleration and chaining ###

Accelerating simple loops of location 1.
   Accelerating the following rules:
      1: f138_0_ack_GT -> f138_0_ack_GT : arg1'=1, arg2'=-1+arg2, [ arg2>0 && arg1<1 ], cost: 1
      2: f138_0_ack_GT -> f138_0_ack_GT : arg1'=-1+arg1, [ arg1>0 && arg2>0 ], cost: 1
      3: f138_0_ack_GT -> f138_0_ack_GT : arg1'=arg1P_4, arg2'=-1+arg2, [ arg1>0 && arg2>0 ], cost: 1

   Failed to prove monotonicity of the guard of rule 1.
   Accelerated rule 2 with backward acceleration, yielding the new rule 5.
[test] deduced pseudo-invariant -arg1+arg1P_4<=0, also trying arg1-arg1P_4<=-1
   Accelerated rule 3 with backward acceleration, yielding the new rule 6.
[accelerate] Nesting with 3 inner and 3 outer candidates
   Nested simple loops 2 (outer loop) and 1 (inner loop) with Rule(1 | arg1<1, -1+arg2>=1, 1>0, | -2+2*arg2 || 1 | 0=0, 1=1, ), resulting in the new rules: 7, 8.
   Nested simple loops 3 (outer loop) and 1 (inner loop) with Rule(1 | arg1>0, k_5>=1, 1+arg2-2*k_5>0, | 2*k_5 || 1 | 0=1, 1=arg2-2*k_5, ), resulting in the new rules: 9, 10.
   Removing the simple loops: 2 3.

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
      0: f1_0_main_ConstantStackPush -> f138_0_ack_GT : arg1'=12, arg2'=10, [], cost: 1
      1: f138_0_ack_GT -> f138_0_ack_GT : arg1'=1, arg2'=-1+arg2, [ arg2>0 && arg1<1 ], cost: 1
      5: f138_0_ack_GT -> f138_0_ack_GT : arg1'=0, [ arg2>0 && arg1>=0 ], cost: arg1
      6: f138_0_ack_GT -> f138_0_ack_GT : arg1'=arg1P_4, arg2'=0, [ -arg1+arg1P_4<=0 && arg2>=1 && arg1P_4>0 ], cost: arg2
      7: f138_0_ack_GT -> f138_0_ack_GT : arg1'=0, arg2'=1, [ arg1<1 && -1+arg2>=1 ], cost: -2+2*arg2
      8: f138_0_ack_GT -> f138_0_ack_GT : arg1'=0, arg2'=1, [ arg1>0 && -1+arg1<1 && -1+arg2>=1 ], cost: -1+2*arg2
      9: f138_0_ack_GT -> f138_0_ack_GT : arg1'=1, arg2'=arg2-2*k_5, [ arg1>0 && k_5>=1 && 1+arg2-2*k_5>0 ], cost: 2*k_5
     10: f138_0_ack_GT -> f138_0_ack_GT : arg1'=1, arg2'=-1+arg2-2*k_5, [ arg2>0 && arg1<1 && k_5>=1 && arg2-2*k_5>0 ], cost: 1+2*k_5
      4: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P_5, arg2'=arg2P_5, [], cost: 1

Chained accelerated rules (with incoming rules):
   Start location: __init
      0: f1_0_main_ConstantStackPush -> f138_0_ack_GT : arg1'=12, arg2'=10, [], cost: 1
     11: f1_0_main_ConstantStackPush -> f138_0_ack_GT : arg1'=0, arg2'=10, [], cost: 13
     12: f1_0_main_ConstantStackPush -> f138_0_ack_GT : arg1'=arg1P_4, arg2'=0, [ -12+arg1P_4<=0 && arg1P_4>0 ], cost: 11
     13: f1_0_main_ConstantStackPush -> f138_0_ack_GT : arg1'=1, arg2'=10-2*k_5, [ k_5>=1 && 11-2*k_5>0 ], cost: 1+2*k_5
      4: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P_5, arg2'=arg2P_5, [], cost: 1

Removed unreachable locations (and leaf rules with constant cost):
   Start location: __init
     13: f1_0_main_ConstantStackPush -> f138_0_ack_GT : arg1'=1, arg2'=10-2*k_5, [ k_5>=1 && 11-2*k_5>0 ], cost: 1+2*k_5
      4: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P_5, arg2'=arg2P_5, [], cost: 1

Eliminated locations (on linear paths):
   Start location: __init
     14: __init -> f138_0_ack_GT : arg1'=1, arg2'=10-2*k_5, [ k_5>=1 && 11-2*k_5>0 ], cost: 2+2*k_5

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: __init
     14: __init -> f138_0_ack_GT : arg1'=1, arg2'=10-2*k_5, [ k_5>=1 && 11-2*k_5>0 ], cost: 2+2*k_5

Computing asymptotic complexity for rule 14
   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),?)