WORST_CASE(Omega(1),?)

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

Initial linear ITS problem
   Start location: __init
      0: f2 -> f3 : arg1'=arg1P_1, arg2'=arg2P_1, [ arg2P_1==-1+arg2 && arg1==arg1P_1 ], cost: 1
      3: f3 -> f4 : arg1'=arg1P_4, arg2'=arg2P_4, [ arg2<0 && arg1==arg1P_4 && arg2==arg2P_4 ], cost: 1
      4: f3 -> f5 : arg1'=arg1P_5, arg2'=arg2P_5, [ arg2>=0 && arg1==arg1P_5 && arg2==arg2P_5 ], cost: 1
      1: f4 -> f7 : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1P_2==-1+arg1 && arg2==arg2P_2 ], cost: 1
      2: f7 -> f8 : arg1'=arg1P_3, arg2'=arg2P_3, [ arg1==arg1P_3 ], cost: 1
      5: f8 -> f6 : arg1'=arg1P_6, arg2'=arg2P_6, [ arg1==arg1P_6 && arg2==arg2P_6 ], cost: 1
      6: f5 -> f6 : arg1'=arg1P_7, arg2'=arg2P_7, [ arg1==arg1P_7 && arg2==arg2P_7 ], cost: 1
      8: f6 -> f1 : arg1'=arg1P_9, arg2'=arg2P_9, [ arg1==arg1P_9 && arg2==arg2P_9 ], cost: 1
      7: f1 -> f2 : arg1'=arg1P_8, arg2'=arg2P_8, [ arg1>=0 && arg2>=0 && arg1==arg1P_8 && arg2==arg2P_8 ], cost: 1
      9: f1 -> f9 : arg1'=arg1P_10, arg2'=arg2P_10, [ arg1<0 && arg1==arg1P_10 && arg2==arg2P_10 ], cost: 1
     10: f1 -> f9 : arg1'=arg1P_11, arg2'=arg2P_11, [ arg2<0 && arg1==arg1P_11 && arg2==arg2P_11 ], cost: 1
     11: __init -> f1 : arg1'=arg1P_12, arg2'=arg2P_12, [], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
     11: __init -> f1 : arg1'=arg1P_12, arg2'=arg2P_12, [], cost: 1

Removed unreachable and leaf rules:
   Start location: __init
      0: f2 -> f3 : arg1'=arg1P_1, arg2'=arg2P_1, [ arg2P_1==-1+arg2 && arg1==arg1P_1 ], cost: 1
      3: f3 -> f4 : arg1'=arg1P_4, arg2'=arg2P_4, [ arg2<0 && arg1==arg1P_4 && arg2==arg2P_4 ], cost: 1
      4: f3 -> f5 : arg1'=arg1P_5, arg2'=arg2P_5, [ arg2>=0 && arg1==arg1P_5 && arg2==arg2P_5 ], cost: 1
      1: f4 -> f7 : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1P_2==-1+arg1 && arg2==arg2P_2 ], cost: 1
      2: f7 -> f8 : arg1'=arg1P_3, arg2'=arg2P_3, [ arg1==arg1P_3 ], cost: 1
      5: f8 -> f6 : arg1'=arg1P_6, arg2'=arg2P_6, [ arg1==arg1P_6 && arg2==arg2P_6 ], cost: 1
      6: f5 -> f6 : arg1'=arg1P_7, arg2'=arg2P_7, [ arg1==arg1P_7 && arg2==arg2P_7 ], cost: 1
      8: f6 -> f1 : arg1'=arg1P_9, arg2'=arg2P_9, [ arg1==arg1P_9 && arg2==arg2P_9 ], cost: 1
      7: f1 -> f2 : arg1'=arg1P_8, arg2'=arg2P_8, [ arg1>=0 && arg2>=0 && arg1==arg1P_8 && arg2==arg2P_8 ], cost: 1
     11: __init -> f1 : arg1'=arg1P_12, arg2'=arg2P_12, [], cost: 1

Simplified all rules, resulting in:
   Start location: __init
      0: f2 -> f3 : arg2'=-1+arg2, [], cost: 1
      3: f3 -> f4 : [ arg2<0 ], cost: 1
      4: f3 -> f5 : [ arg2>=0 ], cost: 1
      1: f4 -> f7 : arg1'=-1+arg1, [], cost: 1
      2: f7 -> f8 : arg2'=arg2P_3, [], cost: 1
      5: f8 -> f6 : [], cost: 1
      6: f5 -> f6 : [], cost: 1
      8: f6 -> f1 : [], cost: 1
      7: f1 -> f2 : [ arg1>=0 && arg2>=0 ], cost: 1
     11: __init -> f1 : arg1'=arg1P_12, arg2'=arg2P_12, [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: __init
     14: f3 -> f6 : [ arg2>=0 ], cost: 2
     16: f3 -> f6 : arg1'=-1+arg1, arg2'=arg2P_3, [ arg2<0 ], cost: 4
      8: f6 -> f1 : [], cost: 1
     12: f1 -> f3 : arg2'=-1+arg2, [ arg1>=0 && arg2>=0 ], cost: 2
     11: __init -> f1 : arg1'=arg1P_12, arg2'=arg2P_12, [], cost: 1

Eliminated locations (on tree-shaped paths):
   Start location: __init
      8: f6 -> f1 : [], cost: 1
     17: f1 -> f6 : arg2'=-1+arg2, [ arg1>=0 && -1+arg2>=0 ], cost: 4
     18: f1 -> f6 : arg1'=-1+arg1, arg2'=arg2P_3, [ arg1>=0 && arg2>=0 && -1+arg2<0 ], cost: 6
     11: __init -> f1 : arg1'=arg1P_12, arg2'=arg2P_12, [], cost: 1

Eliminated locations (on tree-shaped paths):
   Start location: __init
     19: f1 -> f1 : arg2'=-1+arg2, [ arg1>=0 && -1+arg2>=0 ], cost: 5
     20: f1 -> f1 : arg1'=-1+arg1, arg2'=arg2P_3, [ arg1>=0 && arg2>=0 && -1+arg2<0 ], cost: 7
     11: __init -> f1 : arg1'=arg1P_12, arg2'=arg2P_12, [], cost: 1

Accelerating simple loops of location 7.
   Simplified some of the simple loops (and removed duplicate rules).
   Accelerating the following rules:
     19: f1 -> f1 : arg2'=-1+arg2, [ arg1>=0 && -1+arg2>=0 ], cost: 5
     20: f1 -> f1 : arg1'=-1+arg1, arg2'=arg2P_3, [ arg1>=0 && -arg2==0 ], cost: 7

   Accelerated rule 19 with backward acceleration, yielding the new rule 21.
[test] deduced pseudo-invariant arg2-arg2P_3<=0, also trying -arg2+arg2P_3<=-1
   Failed to prove monotonicity of the guard of rule 20.
[accelerate] Nesting with 2 inner and 2 outer candidates
   Nested simple loops 20 (outer loop) and 21 (inner loop) with Rule(7 | -arg2==0, arg2P_3>=0, arg1>=1, 0>=0, | 5*arg2P_3*arg1+7*arg1 || 7 | 0=0, 1=0, ), resulting in the new rules: 22, 23.
   Removing the simple loops: 19 20.

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     21: f1 -> f1 : arg2'=0, [ arg1>=0 && arg2>=0 ], cost: 5*arg2
     22: f1 -> f1 : arg1'=0, arg2'=0, [ -arg2==0 && arg2P_3>=0 && arg1>=1 ], cost: 5*arg2P_3*arg1+7*arg1
     23: f1 -> f1 : arg1'=0, arg2'=0, [ arg2>=0 && arg2P_3>=0 && arg1>=1 ], cost: 5*arg2+5*arg2P_3*arg1+7*arg1
     11: __init -> f1 : arg1'=arg1P_12, arg2'=arg2P_12, [], cost: 1

Chained accelerated rules (with incoming rules):
   Start location: __init
     11: __init -> f1 : arg1'=arg1P_12, arg2'=arg2P_12, [], cost: 1
     24: __init -> f1 : arg1'=arg1P_12, arg2'=0, [ arg1P_12>=0 && arg2P_12>=0 ], cost: 1+5*arg2P_12
     25: __init -> f1 : arg1'=0, arg2'=0, [ arg2P_3>=0 && arg1P_12>=1 ], cost: 1+5*arg2P_3*arg1P_12+7*arg1P_12
     26: __init -> f1 : arg1'=0, arg2'=0, [ arg2P_12>=0 && arg2P_3>=0 && arg1P_12>=1 ], cost: 1+5*arg2P_12+5*arg2P_3*arg1P_12+7*arg1P_12

Removed unreachable locations (and leaf rules with constant cost):
   Start location: __init
     24: __init -> f1 : arg1'=arg1P_12, arg2'=0, [ arg1P_12>=0 && arg2P_12>=0 ], cost: 1+5*arg2P_12
     25: __init -> f1 : arg1'=0, arg2'=0, [ arg2P_3>=0 && arg1P_12>=1 ], cost: 1+5*arg2P_3*arg1P_12+7*arg1P_12
     26: __init -> f1 : arg1'=0, arg2'=0, [ arg2P_12>=0 && arg2P_3>=0 && arg1P_12>=1 ], cost: 1+5*arg2P_12+5*arg2P_3*arg1P_12+7*arg1P_12

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: __init
     24: __init -> f1 : arg1'=arg1P_12, arg2'=0, [ arg1P_12>=0 && arg2P_12>=0 ], cost: 1+5*arg2P_12
     25: __init -> f1 : arg1'=0, arg2'=0, [ arg2P_3>=0 && arg1P_12>=1 ], cost: 1+5*arg2P_3*arg1P_12+7*arg1P_12
     26: __init -> f1 : arg1'=0, arg2'=0, [ arg2P_12>=0 && arg2P_3>=0 && arg1P_12>=1 ], cost: 1+5*arg2P_12+5*arg2P_3*arg1P_12+7*arg1P_12

Computing asymptotic complexity for rule 25
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 26
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 24
   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),?)