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 && arg2==arg2P_1 ], cost: 1
      1: f2 -> f3 : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ arg2==arg2P_2 && arg3==arg3P_2 ], cost: 1
      2: f3 -> f4 : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg1==arg1P_3 && arg3==arg3P_3 ], cost: 1
     16: f4 -> f5 : arg1'=arg1P_17, arg2'=arg2P_17, arg3'=arg3P_17, [ arg1>=0 && arg1==arg1P_17 && arg2==arg2P_17 && arg3==arg3P_17 ], cost: 1
     18: f4 -> f13 : arg1'=arg1P_19, arg2'=arg2P_19, arg3'=arg3P_19, [ arg1<0 && arg1==arg1P_19 && arg2==arg2P_19 && arg3==arg3P_19 ], cost: 1
      3: f6 -> f7 : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ arg2P_4==-1+arg2 && arg1==arg1P_4 && arg3==arg3P_4 ], cost: 1
      6: f7 -> f5 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [ arg1==arg1P_7 && arg2==arg2P_7 && arg3==arg3P_7 ], cost: 1
      4: f5 -> f6 : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ arg2>=0 && x15_1<0 && arg1==arg1P_5 && arg2==arg2P_5 && arg3==arg3P_5 ], cost: 1
      5: f5 -> f6 : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [ arg2>=0 && x52_1>0 && arg1==arg1P_6 && arg2==arg2P_6 && arg3==arg3P_6 ], cost: 1
      7: f5 -> f8 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, [ arg2<0 && arg1==arg1P_8 && arg2==arg2P_8 && arg3==arg3P_8 ], cost: 1
      8: f5 -> f8 : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, [ x56_1==0 && arg1==arg1P_9 && arg2==arg2P_9 && arg3==arg3P_9 ], cost: 1
      9: f8 -> f9 : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, [ arg1P_10==-1+arg1 && arg2==arg2P_10 && arg3==arg3P_10 ], cost: 1
     11: f9 -> f10 : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, [ arg2<=arg3 && x32_1<0 && arg1==arg1P_12 && arg2==arg2P_12 && arg3==arg3P_12 ], cost: 1
     12: f9 -> f10 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, [ arg2<=arg3 && x68_1>0 && arg1==arg1P_13 && arg2==arg2P_13 && arg3==arg3P_13 ], cost: 1
     14: f9 -> f12 : arg1'=arg1P_15, arg2'=arg2P_15, arg3'=arg3P_15, [ arg2>arg3 && arg1==arg1P_15 && arg2==arg2P_15 && arg3==arg3P_15 ], cost: 1
     15: f9 -> f12 : arg1'=arg1P_16, arg2'=arg2P_16, arg3'=arg3P_16, [ x72_1==0 && arg1==arg1P_16 && arg2==arg2P_16 && arg3==arg3P_16 ], cost: 1
     10: f10 -> f11 : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, [ arg2P_11==1+arg2 && arg1==arg1P_11 && arg3==arg3P_11 ], cost: 1
     13: f11 -> f9 : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, [ arg1==arg1P_14 && arg2==arg2P_14 && arg3==arg3P_14 ], cost: 1
     17: f12 -> f4 : arg1'=arg1P_18, arg2'=arg2P_18, arg3'=arg3P_18, [ arg1==arg1P_18 && arg2==arg2P_18 && arg3==arg3P_18 ], cost: 1
     19: __init -> f1 : arg1'=arg1P_20, arg2'=arg2P_20, arg3'=arg3P_20, [], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
     19: __init -> f1 : arg1'=arg1P_20, arg2'=arg2P_20, arg3'=arg3P_20, [], 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 && arg2==arg2P_1 ], cost: 1
      1: f2 -> f3 : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ arg2==arg2P_2 && arg3==arg3P_2 ], cost: 1
      2: f3 -> f4 : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg1==arg1P_3 && arg3==arg3P_3 ], cost: 1
     16: f4 -> f5 : arg1'=arg1P_17, arg2'=arg2P_17, arg3'=arg3P_17, [ arg1>=0 && arg1==arg1P_17 && arg2==arg2P_17 && arg3==arg3P_17 ], cost: 1
      3: f6 -> f7 : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ arg2P_4==-1+arg2 && arg1==arg1P_4 && arg3==arg3P_4 ], cost: 1
      6: f7 -> f5 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [ arg1==arg1P_7 && arg2==arg2P_7 && arg3==arg3P_7 ], cost: 1
      4: f5 -> f6 : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ arg2>=0 && x15_1<0 && arg1==arg1P_5 && arg2==arg2P_5 && arg3==arg3P_5 ], cost: 1
      5: f5 -> f6 : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [ arg2>=0 && x52_1>0 && arg1==arg1P_6 && arg2==arg2P_6 && arg3==arg3P_6 ], cost: 1
      7: f5 -> f8 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, [ arg2<0 && arg1==arg1P_8 && arg2==arg2P_8 && arg3==arg3P_8 ], cost: 1
      8: f5 -> f8 : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, [ x56_1==0 && arg1==arg1P_9 && arg2==arg2P_9 && arg3==arg3P_9 ], cost: 1
      9: f8 -> f9 : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, [ arg1P_10==-1+arg1 && arg2==arg2P_10 && arg3==arg3P_10 ], cost: 1
     11: f9 -> f10 : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, [ arg2<=arg3 && x32_1<0 && arg1==arg1P_12 && arg2==arg2P_12 && arg3==arg3P_12 ], cost: 1
     12: f9 -> f10 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, [ arg2<=arg3 && x68_1>0 && arg1==arg1P_13 && arg2==arg2P_13 && arg3==arg3P_13 ], cost: 1
     14: f9 -> f12 : arg1'=arg1P_15, arg2'=arg2P_15, arg3'=arg3P_15, [ arg2>arg3 && arg1==arg1P_15 && arg2==arg2P_15 && arg3==arg3P_15 ], cost: 1
     15: f9 -> f12 : arg1'=arg1P_16, arg2'=arg2P_16, arg3'=arg3P_16, [ x72_1==0 && arg1==arg1P_16 && arg2==arg2P_16 && arg3==arg3P_16 ], cost: 1
     10: f10 -> f11 : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, [ arg2P_11==1+arg2 && arg1==arg1P_11 && arg3==arg3P_11 ], cost: 1
     13: f11 -> f9 : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, [ arg1==arg1P_14 && arg2==arg2P_14 && arg3==arg3P_14 ], cost: 1
     17: f12 -> f4 : arg1'=arg1P_18, arg2'=arg2P_18, arg3'=arg3P_18, [ arg1==arg1P_18 && arg2==arg2P_18 && arg3==arg3P_18 ], cost: 1
     19: __init -> f1 : arg1'=arg1P_20, arg2'=arg2P_20, arg3'=arg3P_20, [], cost: 1

Simplified all rules, resulting in:
   Start location: __init
      0: f1 -> f2 : arg3'=arg3P_1, [], cost: 1
      1: f2 -> f3 : arg1'=arg1P_2, [], cost: 1
      2: f3 -> f4 : arg2'=arg2P_3, [], cost: 1
     16: f4 -> f5 : [ arg1>=0 ], cost: 1
      3: f6 -> f7 : arg2'=-1+arg2, [], cost: 1
      6: f7 -> f5 : [], cost: 1
      5: f5 -> f6 : [ arg2>=0 ], cost: 1
      7: f5 -> f8 : [ arg2<0 ], cost: 1
      8: f5 -> f8 : [], cost: 1
      9: f8 -> f9 : arg1'=-1+arg1, [], cost: 1
     12: f9 -> f10 : [ arg2<=arg3 ], cost: 1
     14: f9 -> f12 : [ arg2>arg3 ], cost: 1
     15: f9 -> f12 : [], cost: 1
     10: f10 -> f11 : arg2'=1+arg2, [], cost: 1
     13: f11 -> f9 : [], cost: 1
     17: f12 -> f4 : [], cost: 1
     19: __init -> f1 : arg1'=arg1P_20, arg2'=arg2P_20, arg3'=arg3P_20, [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: __init
     16: f4 -> f5 : [ arg1>=0 ], cost: 1
      7: f5 -> f8 : [ arg2<0 ], cost: 1
      8: f5 -> f8 : [], cost: 1
     24: f5 -> f5 : arg2'=-1+arg2, [ arg2>=0 ], cost: 3
      9: f8 -> f9 : arg1'=-1+arg1, [], cost: 1
     14: f9 -> f12 : [ arg2>arg3 ], cost: 1
     15: f9 -> f12 : [], cost: 1
     26: f9 -> f9 : arg2'=1+arg2, [ arg2<=arg3 ], cost: 3
     17: f12 -> f4 : [], cost: 1
     22: __init -> f4 : arg1'=arg1P_2, arg2'=arg2P_3, arg3'=arg3P_1, [], cost: 4

Accelerating simple loops of location 6.
   Accelerating the following rules:
     24: f5 -> f5 : arg2'=-1+arg2, [ arg2>=0 ], cost: 3

   Accelerated rule 24 with backward acceleration, yielding the new rule 27.
[accelerate] Nesting with 1 inner and 1 outer candidates
   Removing the simple loops: 24.

Accelerating simple loops of location 8.
   Accelerating the following rules:
     26: f9 -> f9 : arg2'=1+arg2, [ arg2<=arg3 ], cost: 3

   Accelerated rule 26 with backward acceleration, yielding the new rule 28.
[accelerate] Nesting with 1 inner and 1 outer candidates
   Removing the simple loops: 26.

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     16: f4 -> f5 : [ arg1>=0 ], cost: 1
      7: f5 -> f8 : [ arg2<0 ], cost: 1
      8: f5 -> f8 : [], cost: 1
     27: f5 -> f5 : arg2'=-1, [ 1+arg2>=0 ], cost: 3+3*arg2
      9: f8 -> f9 : arg1'=-1+arg1, [], cost: 1
     14: f9 -> f12 : [ arg2>arg3 ], cost: 1
     15: f9 -> f12 : [], cost: 1
     28: f9 -> f9 : arg2'=1+arg3, [ 1-arg2+arg3>=0 ], cost: 3-3*arg2+3*arg3
     17: f12 -> f4 : [], cost: 1
     22: __init -> f4 : arg1'=arg1P_2, arg2'=arg2P_3, arg3'=arg3P_1, [], cost: 4

Chained accelerated rules (with incoming rules):
   Start location: __init
     16: f4 -> f5 : [ arg1>=0 ], cost: 1
     29: f4 -> f5 : arg2'=-1, [ arg1>=0 && 1+arg2>=0 ], cost: 4+3*arg2
      7: f5 -> f8 : [ arg2<0 ], cost: 1
      8: f5 -> f8 : [], cost: 1
      9: f8 -> f9 : arg1'=-1+arg1, [], cost: 1
     30: f8 -> f9 : arg1'=-1+arg1, arg2'=1+arg3, [ 1-arg2+arg3>=0 ], cost: 4-3*arg2+3*arg3
     14: f9 -> f12 : [ arg2>arg3 ], cost: 1
     15: f9 -> f12 : [], cost: 1
     17: f12 -> f4 : [], cost: 1
     22: __init -> f4 : arg1'=arg1P_2, arg2'=arg2P_3, arg3'=arg3P_1, [], cost: 4

Eliminated locations (on tree-shaped paths):
   Start location: __init
     31: f4 -> f8 : [ arg1>=0 && arg2<0 ], cost: 2
     32: f4 -> f8 : [ arg1>=0 ], cost: 2
     33: f4 -> f8 : arg2'=-1, [ arg1>=0 && 1+arg2>=0 ], cost: 5+3*arg2
     34: f4 -> f8 : arg2'=-1, [ arg1>=0 && 1+arg2>=0 ], cost: 5+3*arg2
     35: f8 -> f12 : arg1'=-1+arg1, [ arg2>arg3 ], cost: 2
     36: f8 -> f12 : arg1'=-1+arg1, [], cost: 2
     37: f8 -> f12 : arg1'=-1+arg1, arg2'=1+arg3, [ 1-arg2+arg3>=0 ], cost: 5-3*arg2+3*arg3
     38: f8 -> f12 : arg1'=-1+arg1, arg2'=1+arg3, [ 1-arg2+arg3>=0 ], cost: 5-3*arg2+3*arg3
     17: f12 -> f4 : [], cost: 1
     22: __init -> f4 : arg1'=arg1P_2, arg2'=arg2P_3, arg3'=arg3P_1, [], cost: 4

Merged rules:
   Start location: __init
     39: f4 -> f8 : [ arg1>=0 ], cost: 2
     40: f4 -> f8 : arg2'=-1, [ arg1>=0 && 1+arg2>=0 ], cost: 5+3*arg2
     41: f8 -> f12 : arg1'=-1+arg1, [], cost: 2
     42: f8 -> f12 : arg1'=-1+arg1, arg2'=1+arg3, [ 1-arg2+arg3>=0 ], cost: 5-3*arg2+3*arg3
     17: f12 -> f4 : [], cost: 1
     22: __init -> f4 : arg1'=arg1P_2, arg2'=arg2P_3, arg3'=arg3P_1, [], cost: 4

Eliminated locations (on tree-shaped paths):
   Start location: __init
     43: f4 -> f12 : arg1'=-1+arg1, [ arg1>=0 ], cost: 4
     44: f4 -> f12 : arg1'=-1+arg1, arg2'=1+arg3, [ arg1>=0 && 1-arg2+arg3>=0 ], cost: 7-3*arg2+3*arg3
     45: f4 -> f12 : arg1'=-1+arg1, arg2'=-1, [ arg1>=0 && 1+arg2>=0 ], cost: 7+3*arg2
     46: f4 -> f12 : arg1'=-1+arg1, arg2'=1+arg3, [ arg1>=0 && 1+arg2>=0 && 2+arg3>=0 ], cost: 13+3*arg2+3*arg3
     17: f12 -> f4 : [], cost: 1
     22: __init -> f4 : arg1'=arg1P_2, arg2'=arg2P_3, arg3'=arg3P_1, [], cost: 4

Eliminated locations (on tree-shaped paths):
   Start location: __init
     47: f4 -> f4 : arg1'=-1+arg1, [ arg1>=0 ], cost: 5
     48: f4 -> f4 : arg1'=-1+arg1, arg2'=1+arg3, [ arg1>=0 && 1-arg2+arg3>=0 ], cost: 8-3*arg2+3*arg3
     49: f4 -> f4 : arg1'=-1+arg1, arg2'=-1, [ arg1>=0 && 1+arg2>=0 ], cost: 8+3*arg2
     50: f4 -> f4 : arg1'=-1+arg1, arg2'=1+arg3, [ arg1>=0 && 1+arg2>=0 && 2+arg3>=0 ], cost: 14+3*arg2+3*arg3
     22: __init -> f4 : arg1'=arg1P_2, arg2'=arg2P_3, arg3'=arg3P_1, [], cost: 4

Accelerating simple loops of location 3.
   Accelerating the following rules:
     47: f4 -> f4 : arg1'=-1+arg1, [ arg1>=0 ], cost: 5
     48: f4 -> f4 : arg1'=-1+arg1, arg2'=1+arg3, [ arg1>=0 && 1-arg2+arg3>=0 ], cost: 8-3*arg2+3*arg3
     49: f4 -> f4 : arg1'=-1+arg1, arg2'=-1, [ arg1>=0 && 1+arg2>=0 ], cost: 8+3*arg2
     50: f4 -> f4 : arg1'=-1+arg1, arg2'=1+arg3, [ arg1>=0 && 1+arg2>=0 && 2+arg3>=0 ], cost: 14+3*arg2+3*arg3

   Accelerated rule 47 with backward acceleration, yielding the new rule 51.
   Accelerated rule 48 with backward acceleration, yielding the new rule 52.
   Accelerated rule 49 with backward acceleration, yielding the new rule 53.
   Accelerated rule 50 with backward acceleration, yielding the new rule 54.
[accelerate] Nesting with 4 inner and 4 outer candidates
   Removing the simple loops: 47 48 49 50.

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     51: f4 -> f4 : arg1'=-1, [ 1+arg1>=0 ], cost: 5+5*arg1
     52: f4 -> f4 : arg1'=-1, arg2'=1+arg3, [ 1-arg2+arg3>=0 && 1+arg1>=1 ], cost: 5+5*arg1
     53: f4 -> f4 : arg1'=-1, arg2'=-1, [ 1+arg2>=0 && 1+arg1>=1 ], cost: 5+5*arg1
     54: f4 -> f4 : arg1'=-1, arg2'=1+arg3, [ 1+arg2>=0 && 2+arg3>=0 && 1+arg1>=1 ], cost: 17+6*(1+arg1)*arg3+17*arg1
     22: __init -> f4 : arg1'=arg1P_2, arg2'=arg2P_3, arg3'=arg3P_1, [], cost: 4

Chained accelerated rules (with incoming rules):
   Start location: __init
     22: __init -> f4 : arg1'=arg1P_2, arg2'=arg2P_3, arg3'=arg3P_1, [], cost: 4
     55: __init -> f4 : arg1'=-1, arg2'=arg2P_3, arg3'=arg3P_1, [ 1+arg1P_2>=0 ], cost: 9+5*arg1P_2
     56: __init -> f4 : arg1'=-1, arg2'=1+arg3P_1, arg3'=arg3P_1, [ 1+arg1P_2>=1 ], cost: 9+5*arg1P_2
     57: __init -> f4 : arg1'=-1, arg2'=-1, arg3'=arg3P_1, [ 1+arg1P_2>=1 ], cost: 9+5*arg1P_2
     58: __init -> f4 : arg1'=-1, arg2'=1+arg3P_1, arg3'=arg3P_1, [ 2+arg3P_1>=0 && 1+arg1P_2>=1 ], cost: 21+17*arg1P_2+6*arg3P_1*(1+arg1P_2)

Removed unreachable locations (and leaf rules with constant cost):
   Start location: __init
     55: __init -> f4 : arg1'=-1, arg2'=arg2P_3, arg3'=arg3P_1, [ 1+arg1P_2>=0 ], cost: 9+5*arg1P_2
     56: __init -> f4 : arg1'=-1, arg2'=1+arg3P_1, arg3'=arg3P_1, [ 1+arg1P_2>=1 ], cost: 9+5*arg1P_2
     57: __init -> f4 : arg1'=-1, arg2'=-1, arg3'=arg3P_1, [ 1+arg1P_2>=1 ], cost: 9+5*arg1P_2
     58: __init -> f4 : arg1'=-1, arg2'=1+arg3P_1, arg3'=arg3P_1, [ 2+arg3P_1>=0 && 1+arg1P_2>=1 ], cost: 21+17*arg1P_2+6*arg3P_1*(1+arg1P_2)

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: __init
     55: __init -> f4 : arg1'=-1, arg2'=arg2P_3, arg3'=arg3P_1, [ 1+arg1P_2>=0 ], cost: 9+5*arg1P_2
     57: __init -> f4 : arg1'=-1, arg2'=-1, arg3'=arg3P_1, [ 1+arg1P_2>=1 ], cost: 9+5*arg1P_2
     58: __init -> f4 : arg1'=-1, arg2'=1+arg3P_1, arg3'=arg3P_1, [ 2+arg3P_1>=0 && 1+arg1P_2>=1 ], cost: 21+17*arg1P_2+6*arg3P_1*(1+arg1P_2)

Computing asymptotic complexity for rule 58
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 55
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 57
   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),?)