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, arg3'=arg3P_1, [ arg1==arg1P_1 && arg3==arg3P_1 ], cost: 1
      1: f2 -> f3 : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ arg1==arg1P_2 && arg2==arg2P_2 ], cost: 1
      2: f3 -> f4 : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg3==arg1P_3 && arg2==arg2P_3 && arg3==arg3P_3 ], cost: 1
     10: f4 -> f5 : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, [ arg1>0 && arg1==arg1P_11 && arg2==arg2P_11 && arg3==arg3P_11 ], cost: 1
     12: f4 -> f12 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, [ arg1<=0 && arg1==arg1P_13 && arg2==arg2P_13 && arg3==arg3P_13 ], cost: 1
      3: f6 -> f9 : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ arg2P_4==-1+arg2 && arg1==arg1P_4 && arg3==arg3P_4 ], cost: 1
      8: f9 -> f8 : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, [ arg1==arg1P_9 && arg2==arg2P_9 && arg3==arg3P_9 ], cost: 1
      4: f7 -> f10 : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ arg1==arg1P_5 && arg3==arg2P_5 && arg3==arg3P_5 ], cost: 1
      5: f10 -> f11 : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [ arg1P_6==-1+arg1 && arg2==arg2P_6 && arg3==arg3P_6 ], cost: 1
      9: f11 -> f8 : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, [ arg1==arg1P_10 && arg2==arg2P_10 && arg3==arg3P_10 ], cost: 1
      6: f5 -> f6 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [ arg2>0 && arg1==arg1P_7 && arg2==arg2P_7 && arg3==arg3P_7 ], cost: 1
      7: f5 -> f7 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, [ arg2<=0 && arg1==arg1P_8 && arg2==arg2P_8 && arg3==arg3P_8 ], cost: 1
     11: f8 -> f4 : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, [ arg1==arg1P_12 && arg2==arg2P_12 && arg3==arg3P_12 ], cost: 1
     13: __init -> f1 : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, [], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
     13: __init -> f1 : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, [], cost: 1

Removed unreachable and leaf rules:
   Start location: __init
      0: f1 -> f2 : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, [ arg1==arg1P_1 && arg3==arg3P_1 ], cost: 1
      1: f2 -> f3 : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ arg1==arg1P_2 && arg2==arg2P_2 ], cost: 1
      2: f3 -> f4 : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg3==arg1P_3 && arg2==arg2P_3 && arg3==arg3P_3 ], cost: 1
     10: f4 -> f5 : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, [ arg1>0 && arg1==arg1P_11 && arg2==arg2P_11 && arg3==arg3P_11 ], cost: 1
      3: f6 -> f9 : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ arg2P_4==-1+arg2 && arg1==arg1P_4 && arg3==arg3P_4 ], cost: 1
      8: f9 -> f8 : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, [ arg1==arg1P_9 && arg2==arg2P_9 && arg3==arg3P_9 ], cost: 1
      4: f7 -> f10 : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ arg1==arg1P_5 && arg3==arg2P_5 && arg3==arg3P_5 ], cost: 1
      5: f10 -> f11 : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [ arg1P_6==-1+arg1 && arg2==arg2P_6 && arg3==arg3P_6 ], cost: 1
      9: f11 -> f8 : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, [ arg1==arg1P_10 && arg2==arg2P_10 && arg3==arg3P_10 ], cost: 1
      6: f5 -> f6 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [ arg2>0 && arg1==arg1P_7 && arg2==arg2P_7 && arg3==arg3P_7 ], cost: 1
      7: f5 -> f7 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, [ arg2<=0 && arg1==arg1P_8 && arg2==arg2P_8 && arg3==arg3P_8 ], cost: 1
     11: f8 -> f4 : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, [ arg1==arg1P_12 && arg2==arg2P_12 && arg3==arg3P_12 ], cost: 1
     13: __init -> f1 : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, [], cost: 1

Simplified all rules, resulting in:
   Start location: __init
      0: f1 -> f2 : arg2'=arg2P_1, [], cost: 1
      1: f2 -> f3 : arg3'=arg3P_2, [], cost: 1
      2: f3 -> f4 : arg1'=arg3, [], cost: 1
     10: f4 -> f5 : [ arg1>0 ], cost: 1
      3: f6 -> f9 : arg2'=-1+arg2, [], cost: 1
      8: f9 -> f8 : [], cost: 1
      4: f7 -> f10 : arg2'=arg3, [], cost: 1
      5: f10 -> f11 : arg1'=-1+arg1, [], cost: 1
      9: f11 -> f8 : [], cost: 1
      6: f5 -> f6 : [ arg2>0 ], cost: 1
      7: f5 -> f7 : [ arg2<=0 ], cost: 1
     11: f8 -> f4 : [], cost: 1
     13: __init -> f1 : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: __init
     10: f4 -> f5 : [ arg1>0 ], cost: 1
     19: f5 -> f8 : arg2'=-1+arg2, [ arg2>0 ], cost: 3
     21: f5 -> f8 : arg1'=-1+arg1, arg2'=arg3, [ arg2<=0 ], cost: 4
     11: f8 -> f4 : [], cost: 1
     16: __init -> f4 : arg1'=arg3P_2, arg2'=arg2P_1, arg3'=arg3P_2, [], cost: 4

Eliminated locations (on tree-shaped paths):
   Start location: __init
     22: f4 -> f8 : arg2'=-1+arg2, [ arg1>0 && arg2>0 ], cost: 4
     23: f4 -> f8 : arg1'=-1+arg1, arg2'=arg3, [ arg1>0 && arg2<=0 ], cost: 5
     11: f8 -> f4 : [], cost: 1
     16: __init -> f4 : arg1'=arg3P_2, arg2'=arg2P_1, arg3'=arg3P_2, [], cost: 4

Eliminated locations (on tree-shaped paths):
   Start location: __init
     24: f4 -> f4 : arg2'=-1+arg2, [ arg1>0 && arg2>0 ], cost: 5
     25: f4 -> f4 : arg1'=-1+arg1, arg2'=arg3, [ arg1>0 && arg2<=0 ], cost: 6
     16: __init -> f4 : arg1'=arg3P_2, arg2'=arg2P_1, arg3'=arg3P_2, [], cost: 4

Accelerating simple loops of location 3.
   Accelerating the following rules:
     24: f4 -> f4 : arg2'=-1+arg2, [ arg1>0 && arg2>0 ], cost: 5
     25: f4 -> f4 : arg1'=-1+arg1, arg2'=arg3, [ arg1>0 && arg2<=0 ], cost: 6

   Accelerated rule 24 with backward acceleration, yielding the new rule 26.
[test] deduced pseudo-invariant arg2-arg3<=0, also trying -arg2+arg3<=-1
   Accelerated rule 25 with backward acceleration, yielding the new rule 27.
[accelerate] Nesting with 2 inner and 2 outer candidates
   Nested simple loops 25 (outer loop) and 26 (inner loop) with Rule(3 | arg2<=0, arg3>=0, -1+arg1>=1, 1>0, | -6+5*arg3*(-1+arg1)+6*arg1 || 3 | 0=1, 1=0, ), resulting in the new rules: 28, 29.
   Removing the simple loops: 24 25.

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     26: f4 -> f4 : arg2'=0, [ arg1>0 && arg2>=0 ], cost: 5*arg2
     27: f4 -> f4 : arg1'=0, arg2'=arg3, [ arg2-arg3<=0 && arg1>=1 && arg3<=0 ], cost: 6*arg1
     28: f4 -> f4 : arg1'=1, arg2'=0, [ arg2<=0 && arg3>=0 && -1+arg1>=1 ], cost: -6+5*arg3*(-1+arg1)+6*arg1
     29: f4 -> f4 : arg1'=1, arg2'=0, [ arg2>=0 && arg3>=0 && -1+arg1>=1 ], cost: -6+5*arg2+5*arg3*(-1+arg1)+6*arg1
     16: __init -> f4 : arg1'=arg3P_2, arg2'=arg2P_1, arg3'=arg3P_2, [], cost: 4

Chained accelerated rules (with incoming rules):
   Start location: __init
     16: __init -> f4 : arg1'=arg3P_2, arg2'=arg2P_1, arg3'=arg3P_2, [], cost: 4
     30: __init -> f4 : arg1'=arg3P_2, arg2'=0, arg3'=arg3P_2, [ arg3P_2>0 && arg2P_1>=0 ], cost: 4+5*arg2P_1
     31: __init -> f4 : arg1'=1, arg2'=0, arg3'=arg3P_2, [ -1+arg3P_2>=1 ], cost: -2+5*(-1+arg3P_2)*arg3P_2+6*arg3P_2
     32: __init -> f4 : arg1'=1, arg2'=0, arg3'=arg3P_2, [ arg2P_1>=0 && -1+arg3P_2>=1 ], cost: -2+5*(-1+arg3P_2)*arg3P_2+5*arg2P_1+6*arg3P_2

Removed unreachable locations (and leaf rules with constant cost):
   Start location: __init
     30: __init -> f4 : arg1'=arg3P_2, arg2'=0, arg3'=arg3P_2, [ arg3P_2>0 && arg2P_1>=0 ], cost: 4+5*arg2P_1
     31: __init -> f4 : arg1'=1, arg2'=0, arg3'=arg3P_2, [ -1+arg3P_2>=1 ], cost: -2+5*(-1+arg3P_2)*arg3P_2+6*arg3P_2
     32: __init -> f4 : arg1'=1, arg2'=0, arg3'=arg3P_2, [ arg2P_1>=0 && -1+arg3P_2>=1 ], cost: -2+5*(-1+arg3P_2)*arg3P_2+5*arg2P_1+6*arg3P_2

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: __init
     30: __init -> f4 : arg1'=arg3P_2, arg2'=0, arg3'=arg3P_2, [ arg3P_2>0 && arg2P_1>=0 ], cost: 4+5*arg2P_1
     31: __init -> f4 : arg1'=1, arg2'=0, arg3'=arg3P_2, [ -1+arg3P_2>=1 ], cost: -2+5*(-1+arg3P_2)*arg3P_2+6*arg3P_2
     32: __init -> f4 : arg1'=1, arg2'=0, arg3'=arg3P_2, [ arg2P_1>=0 && -1+arg3P_2>=1 ], cost: -2+5*(-1+arg3P_2)*arg3P_2+5*arg2P_1+6*arg3P_2

Computing asymptotic complexity for rule 31
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 32
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 30
   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),?)