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, [ 0==arg1P_3 && arg2==arg2P_3 && arg3==arg3P_3 ], cost: 1
     14: f4 -> f5 : arg1'=arg1P_15, arg2'=arg2P_15, arg3'=arg3P_15, [ arg2+arg3>0 && arg1==arg1P_15 && arg2==arg2P_15 && arg3==arg3P_15 ], cost: 1
     16: f4 -> f15 : arg1'=arg1P_17, arg2'=arg2P_17, arg3'=arg3P_17, [ arg2+arg3<=0 && arg1==arg1P_17 && arg2==arg2P_17 && arg3==arg3P_17 ], 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
     11: f9 -> f8 : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, [ arg1==arg1P_12 && arg2==arg2P_12 && arg3==arg3P_12 ], cost: 1
      4: f10 -> f13 : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ arg3P_5==-1+arg3 && arg1==arg1P_5 && arg2==arg2P_5 ], cost: 1
      7: f13 -> f12 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, [ arg1==arg1P_8 && arg2==arg2P_8 && arg3==arg3P_8 ], cost: 1
      5: f7 -> f10 : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [ arg3>0 && arg1==arg1P_6 && arg2==arg2P_6 && arg3==arg3P_6 ], cost: 1
      6: f7 -> f11 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [ arg3<=0 && arg1==arg1P_7 && arg2==arg2P_7 && arg3==arg3P_7 ], cost: 1
      8: f11 -> f12 : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, [ arg1==arg1P_9 && arg2==arg2P_9 && arg3==arg3P_9 ], cost: 1
     12: f12 -> f8 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, [ arg1==arg1P_13 && arg2==arg2P_13 && arg3==arg3P_13 ], cost: 1
      9: f5 -> f6 : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, [ arg2>0 && arg1==arg1P_10 && arg2==arg2P_10 && arg3==arg3P_10 ], cost: 1
     10: f5 -> f7 : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, [ arg2<=0 && arg1==arg1P_11 && arg2==arg2P_11 && arg3==arg3P_11 ], cost: 1
     13: f8 -> f14 : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, [ arg1P_14==1+arg1 && arg2==arg2P_14 && arg3==arg3P_14 ], cost: 1
     15: f14 -> f4 : arg1'=arg1P_16, arg2'=arg2P_16, arg3'=arg3P_16, [ arg1==arg1P_16 && arg2==arg2P_16 && arg3==arg3P_16 ], cost: 1
     17: __init -> f1 : arg1'=arg1P_18, arg2'=arg2P_18, arg3'=arg3P_18, [], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
     17: __init -> f1 : arg1'=arg1P_18, arg2'=arg2P_18, arg3'=arg3P_18, [], 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, [ 0==arg1P_3 && arg2==arg2P_3 && arg3==arg3P_3 ], cost: 1
     14: f4 -> f5 : arg1'=arg1P_15, arg2'=arg2P_15, arg3'=arg3P_15, [ arg2+arg3>0 && arg1==arg1P_15 && arg2==arg2P_15 && arg3==arg3P_15 ], 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
     11: f9 -> f8 : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, [ arg1==arg1P_12 && arg2==arg2P_12 && arg3==arg3P_12 ], cost: 1
      4: f10 -> f13 : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ arg3P_5==-1+arg3 && arg1==arg1P_5 && arg2==arg2P_5 ], cost: 1
      7: f13 -> f12 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, [ arg1==arg1P_8 && arg2==arg2P_8 && arg3==arg3P_8 ], cost: 1
      5: f7 -> f10 : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [ arg3>0 && arg1==arg1P_6 && arg2==arg2P_6 && arg3==arg3P_6 ], cost: 1
      6: f7 -> f11 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [ arg3<=0 && arg1==arg1P_7 && arg2==arg2P_7 && arg3==arg3P_7 ], cost: 1
      8: f11 -> f12 : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, [ arg1==arg1P_9 && arg2==arg2P_9 && arg3==arg3P_9 ], cost: 1
     12: f12 -> f8 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, [ arg1==arg1P_13 && arg2==arg2P_13 && arg3==arg3P_13 ], cost: 1
      9: f5 -> f6 : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, [ arg2>0 && arg1==arg1P_10 && arg2==arg2P_10 && arg3==arg3P_10 ], cost: 1
     10: f5 -> f7 : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, [ arg2<=0 && arg1==arg1P_11 && arg2==arg2P_11 && arg3==arg3P_11 ], cost: 1
     13: f8 -> f14 : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, [ arg1P_14==1+arg1 && arg2==arg2P_14 && arg3==arg3P_14 ], cost: 1
     15: f14 -> f4 : arg1'=arg1P_16, arg2'=arg2P_16, arg3'=arg3P_16, [ arg1==arg1P_16 && arg2==arg2P_16 && arg3==arg3P_16 ], cost: 1
     17: __init -> f1 : arg1'=arg1P_18, arg2'=arg2P_18, arg3'=arg3P_18, [], 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'=0, [], cost: 1
     14: f4 -> f5 : [ arg2+arg3>0 ], cost: 1
      3: f6 -> f9 : arg2'=-1+arg2, [], cost: 1
     11: f9 -> f8 : [], cost: 1
      4: f10 -> f13 : arg3'=-1+arg3, [], cost: 1
      7: f13 -> f12 : [], cost: 1
      5: f7 -> f10 : [ arg3>0 ], cost: 1
      6: f7 -> f11 : [ arg3<=0 ], cost: 1
      8: f11 -> f12 : [], cost: 1
     12: f12 -> f8 : [], cost: 1
      9: f5 -> f6 : [ arg2>0 ], cost: 1
     10: f5 -> f7 : [ arg2<=0 ], cost: 1
     13: f8 -> f14 : arg1'=1+arg1, [], cost: 1
     15: f14 -> f4 : [], cost: 1
     17: __init -> f1 : arg1'=arg1P_18, arg2'=arg2P_18, arg3'=arg3P_18, [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: __init
     14: f4 -> f5 : [ arg2+arg3>0 ], cost: 1
     24: f7 -> f12 : [ arg3<=0 ], cost: 2
     25: f7 -> f12 : arg3'=-1+arg3, [ arg3>0 ], cost: 3
     12: f12 -> f8 : [], cost: 1
     10: f5 -> f7 : [ arg2<=0 ], cost: 1
     22: f5 -> f8 : arg2'=-1+arg2, [ arg2>0 ], cost: 3
     26: f8 -> f4 : arg1'=1+arg1, [], cost: 2
     20: __init -> f4 : arg1'=0, arg2'=arg2P_1, arg3'=arg3P_2, [], cost: 4

Eliminated locations (on tree-shaped paths):
   Start location: __init
     27: f4 -> f7 : [ arg2+arg3>0 && arg2<=0 ], cost: 2
     28: f4 -> f8 : arg2'=-1+arg2, [ arg2+arg3>0 && arg2>0 ], cost: 4
     29: f7 -> f8 : [ arg3<=0 ], cost: 3
     30: f7 -> f8 : arg3'=-1+arg3, [ arg3>0 ], cost: 4
     26: f8 -> f4 : arg1'=1+arg1, [], cost: 2
     20: __init -> f4 : arg1'=0, arg2'=arg2P_1, arg3'=arg3P_2, [], cost: 4

Eliminated locations (on tree-shaped paths):
   Start location: __init
     32: f4 -> f4 : arg1'=1+arg1, arg2'=-1+arg2, [ arg2+arg3>0 && arg2>0 ], cost: 6
     33: f4 -> f4 : arg1'=1+arg1, arg3'=-1+arg3, [ arg2+arg3>0 && arg2<=0 && arg3>0 ], cost: 8
     20: __init -> f4 : arg1'=0, arg2'=arg2P_1, arg3'=arg3P_2, [], cost: 4

Accelerating simple loops of location 3.
   Accelerating the following rules:
     32: f4 -> f4 : arg1'=1+arg1, arg2'=-1+arg2, [ arg2+arg3>0 && arg2>0 ], cost: 6
     33: f4 -> f4 : arg1'=1+arg1, arg3'=-1+arg3, [ arg2+arg3>0 && arg2<=0 && arg3>0 ], cost: 8

   Accelerated rule 32 with backward acceleration, yielding the new rule 34.
   Accelerated rule 32 with backward acceleration, yielding the new rule 35.
   Accelerated rule 33 with backward acceleration, yielding the new rule 36.
   Accelerated rule 33 with backward acceleration, yielding the new rule 37.
[accelerate] Nesting with 4 inner and 2 outer candidates
   Removing the simple loops: 32 33.

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     34: f4 -> f4 : arg1'=arg2+arg3+arg1, arg2'=-arg3, [ arg2+arg3>=0 && 1-arg3>0 ], cost: 6*arg2+6*arg3
     35: f4 -> f4 : arg1'=arg2+arg1, arg2'=0, [ arg2>=0 && 1+arg3>0 ], cost: 6*arg2
     36: f4 -> f4 : arg1'=arg2+arg3+arg1, arg3'=-arg2, [ arg2<=0 && arg2+arg3>=0 ], cost: 8*arg2+8*arg3
     37: f4 -> f4 : arg1'=arg3+arg1, arg3'=0, [ arg2<=0 && arg3>=0 && 1+arg2>0 ], cost: 8*arg3
     20: __init -> f4 : arg1'=0, arg2'=arg2P_1, arg3'=arg3P_2, [], cost: 4

Chained accelerated rules (with incoming rules):
   Start location: __init
     20: __init -> f4 : arg1'=0, arg2'=arg2P_1, arg3'=arg3P_2, [], cost: 4
     38: __init -> f4 : arg1'=arg2P_1+arg3P_2, arg2'=-arg3P_2, arg3'=arg3P_2, [ arg2P_1+arg3P_2>=0 && 1-arg3P_2>0 ], cost: 4+6*arg2P_1+6*arg3P_2
     39: __init -> f4 : arg1'=arg2P_1, arg2'=0, arg3'=arg3P_2, [ arg2P_1>=0 && 1+arg3P_2>0 ], cost: 4+6*arg2P_1
     40: __init -> f4 : arg1'=arg2P_1+arg3P_2, arg2'=arg2P_1, arg3'=-arg2P_1, [ arg2P_1<=0 && arg2P_1+arg3P_2>=0 ], cost: 4+8*arg2P_1+8*arg3P_2
     41: __init -> f4 : arg1'=arg3P_2, arg2'=0, arg3'=0, [ arg3P_2>=0 ], cost: 4+8*arg3P_2

Removed unreachable locations (and leaf rules with constant cost):
   Start location: __init
     38: __init -> f4 : arg1'=arg2P_1+arg3P_2, arg2'=-arg3P_2, arg3'=arg3P_2, [ arg2P_1+arg3P_2>=0 && 1-arg3P_2>0 ], cost: 4+6*arg2P_1+6*arg3P_2
     39: __init -> f4 : arg1'=arg2P_1, arg2'=0, arg3'=arg3P_2, [ arg2P_1>=0 && 1+arg3P_2>0 ], cost: 4+6*arg2P_1
     40: __init -> f4 : arg1'=arg2P_1+arg3P_2, arg2'=arg2P_1, arg3'=-arg2P_1, [ arg2P_1<=0 && arg2P_1+arg3P_2>=0 ], cost: 4+8*arg2P_1+8*arg3P_2
     41: __init -> f4 : arg1'=arg3P_2, arg2'=0, arg3'=0, [ arg3P_2>=0 ], cost: 4+8*arg3P_2

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: __init
     38: __init -> f4 : arg1'=arg2P_1+arg3P_2, arg2'=-arg3P_2, arg3'=arg3P_2, [ arg2P_1+arg3P_2>=0 && 1-arg3P_2>0 ], cost: 4+6*arg2P_1+6*arg3P_2
     39: __init -> f4 : arg1'=arg2P_1, arg2'=0, arg3'=arg3P_2, [ arg2P_1>=0 && 1+arg3P_2>0 ], cost: 4+6*arg2P_1
     40: __init -> f4 : arg1'=arg2P_1+arg3P_2, arg2'=arg2P_1, arg3'=-arg2P_1, [ arg2P_1<=0 && arg2P_1+arg3P_2>=0 ], cost: 4+8*arg2P_1+8*arg3P_2
     41: __init -> f4 : arg1'=arg3P_2, arg2'=0, arg3'=0, [ arg3P_2>=0 ], cost: 4+8*arg3P_2

Computing asymptotic complexity for rule 41
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 38
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 39
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 40
   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),?)