WORST_CASE(Omega(1),?)

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

Initial linear ITS problem
   Start location: __init
      0: f1 -> f2 : arg1'=arg1P_1, arg2'=arg2P_1, [ arg2==arg2P_1 ], cost: 1
      1: f2 -> f3 : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1==arg1P_2 ], cost: 1
      4: f3 -> f4 : arg1'=arg1P_5, arg2'=arg2P_5, [ arg1>arg2 && arg2>=1 && arg2<=2 && arg1==arg1P_5 && arg2==arg2P_5 ], cost: 1
      6: f3 -> f7 : arg1'=arg1P_7, arg2'=arg2P_7, [ arg2>2 && arg1==arg1P_7 && arg2==arg2P_7 ], cost: 1
      7: f3 -> f7 : arg1'=arg1P_8, arg2'=arg2P_8, [ arg1<=arg2 && arg1==arg1P_8 && arg2==arg2P_8 ], cost: 1
      8: f3 -> f7 : arg1'=arg1P_9, arg2'=arg2P_9, [ arg2<1 && arg1==arg1P_9 && arg2==arg2P_9 ], cost: 1
      2: f4 -> f5 : arg1'=arg1P_3, arg2'=arg2P_3, [ arg1P_3==-arg2+arg1 && arg2==arg2P_3 ], cost: 1
      3: f5 -> f6 : arg1'=arg1P_4, arg2'=arg2P_4, [ arg1==arg1P_4 ], cost: 1
      5: f6 -> f3 : arg1'=arg1P_6, arg2'=arg2P_6, [ arg1==arg1P_6 && arg2==arg2P_6 ], cost: 1
      9: __init -> f1 : arg1'=arg1P_10, arg2'=arg2P_10, [], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
      9: __init -> f1 : arg1'=arg1P_10, arg2'=arg2P_10, [], cost: 1

Removed unreachable and leaf rules:
   Start location: __init
      0: f1 -> f2 : arg1'=arg1P_1, arg2'=arg2P_1, [ arg2==arg2P_1 ], cost: 1
      1: f2 -> f3 : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1==arg1P_2 ], cost: 1
      4: f3 -> f4 : arg1'=arg1P_5, arg2'=arg2P_5, [ arg1>arg2 && arg2>=1 && arg2<=2 && arg1==arg1P_5 && arg2==arg2P_5 ], cost: 1
      2: f4 -> f5 : arg1'=arg1P_3, arg2'=arg2P_3, [ arg1P_3==-arg2+arg1 && arg2==arg2P_3 ], cost: 1
      3: f5 -> f6 : arg1'=arg1P_4, arg2'=arg2P_4, [ arg1==arg1P_4 ], cost: 1
      5: f6 -> f3 : arg1'=arg1P_6, arg2'=arg2P_6, [ arg1==arg1P_6 && arg2==arg2P_6 ], cost: 1
      9: __init -> f1 : arg1'=arg1P_10, arg2'=arg2P_10, [], cost: 1

Simplified all rules, resulting in:
   Start location: __init
      0: f1 -> f2 : arg1'=arg1P_1, [], cost: 1
      1: f2 -> f3 : arg2'=arg2P_2, [], cost: 1
      4: f3 -> f4 : [ arg1>arg2 && arg2>=1 && arg2<=2 ], cost: 1
      2: f4 -> f5 : arg1'=-arg2+arg1, [], cost: 1
      3: f5 -> f6 : arg2'=arg2P_4, [], cost: 1
      5: f6 -> f3 : [], cost: 1
      9: __init -> f1 : arg1'=arg1P_10, arg2'=arg2P_10, [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: __init
     14: f3 -> f3 : arg1'=-arg2+arg1, arg2'=arg2P_4, [ arg1>arg2 && arg2>=1 && arg2<=2 ], cost: 4
     11: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, [], cost: 3

Accelerating simple loops of location 2.
   Accelerating the following rules:
     14: f3 -> f3 : arg1'=-arg2+arg1, arg2'=arg2P_4, [ arg1>arg2 && arg2>=1 && arg2<=2 ], cost: 4

[test] deduced pseudo-invariant -4+2*arg2P_4<=0, also trying 4-2*arg2P_4<=-1
[test] deduced pseudo-invariant 6-3*arg2P_4<=0, also trying -6+3*arg2P_4<=-1
[test] deduced pseudo-invariant -arg2+arg2P_4<=0, also trying arg2-arg2P_4<=-1
   Accelerated rule 14 with backward acceleration, yielding the new rule 15.
   Accelerated rule 14 with backward acceleration, yielding the new rule 16.
[accelerate] Nesting with 2 inner and 1 outer candidates

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     14: f3 -> f3 : arg1'=-arg2+arg1, arg2'=arg2P_4, [ arg1>arg2 && arg2>=1 && arg2<=2 ], cost: 4
     15: f3 -> f3 : arg1'=-arg2P_4*k+arg1, arg2'=arg2P_4, [ arg2>=1 && arg2<=2 && -4+2*arg2P_4<=0 && 6-3*arg2P_4<=0 && k>=1 && -arg2P_4*(-1+k)+arg1>arg2P_4 ], cost: 4*k
     16: f3 -> f3 : arg1'=-arg2P_4*k_2+arg1, arg2'=arg2P_4, [ arg2<=2 && -6+3*arg2P_4<=-1 && -arg2+arg2P_4<=0 && k_2>=1 && -arg2P_4*(-1+k_2)+arg1>arg2P_4 && arg2P_4>=1 ], cost: 4*k_2
     11: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, [], cost: 3

Chained accelerated rules (with incoming rules):
   Start location: __init
     11: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, [], cost: 3
     17: __init -> f3 : arg1'=-arg2P_2+arg1P_1, arg2'=arg2P_4, [ arg1P_1>arg2P_2 && arg2P_2>=1 && arg2P_2<=2 ], cost: 7
     18: __init -> f3 : arg1'=arg1P_1-arg2P_4*k, arg2'=arg2P_4, [ -4+2*arg2P_4<=0 && 6-3*arg2P_4<=0 && k>=1 && arg1P_1-arg2P_4*(-1+k)>arg2P_4 ], cost: 3+4*k
     19: __init -> f3 : arg1'=-arg2P_4*k_2+arg1P_1, arg2'=arg2P_4, [ -6+3*arg2P_4<=-1 && k_2>=1 && arg1P_1-arg2P_4*(-1+k_2)>arg2P_4 && arg2P_4>=1 && arg2P_4<=2 ], cost: 3+4*k_2

Removed unreachable locations (and leaf rules with constant cost):
   Start location: __init
     18: __init -> f3 : arg1'=arg1P_1-arg2P_4*k, arg2'=arg2P_4, [ -4+2*arg2P_4<=0 && 6-3*arg2P_4<=0 && k>=1 && arg1P_1-arg2P_4*(-1+k)>arg2P_4 ], cost: 3+4*k
     19: __init -> f3 : arg1'=-arg2P_4*k_2+arg1P_1, arg2'=arg2P_4, [ -6+3*arg2P_4<=-1 && k_2>=1 && arg1P_1-arg2P_4*(-1+k_2)>arg2P_4 && arg2P_4>=1 && arg2P_4<=2 ], cost: 3+4*k_2

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: __init
     18: __init -> f3 : arg1'=arg1P_1-arg2P_4*k, arg2'=arg2P_4, [ -4+2*arg2P_4<=0 && 6-3*arg2P_4<=0 && k>=1 && arg1P_1-arg2P_4*(-1+k)>arg2P_4 ], cost: 3+4*k
     19: __init -> f3 : arg1'=-arg2P_4*k_2+arg1P_1, arg2'=arg2P_4, [ -6+3*arg2P_4<=-1 && k_2>=1 && arg1P_1-arg2P_4*(-1+k_2)>arg2P_4 && arg2P_4>=1 && arg2P_4<=2 ], cost: 3+4*k_2

Computing asymptotic complexity for rule 18
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 19
   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),?)