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, arg4'=arg4P_1, [ arg2==arg2P_1 && arg3==arg3P_1 && arg4==arg4P_1 ], cost: 1
      1: f2 -> f3 : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, [ arg1==arg1P_2 && arg2==arg2P_2 && 0==arg3P_2 && arg4==arg4P_2 ], cost: 1
     11: f3 -> f4 : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, arg4'=arg4P_12, [ arg1>1 && arg1==arg1P_12 && arg2==arg2P_12 && arg3==arg3P_12 && arg4==arg4P_12 ], cost: 1
     13: f3 -> f13 : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, arg4'=arg4P_14, [ arg1<=1 && arg1==arg1P_14 && arg2==arg2P_14 && arg3==arg3P_14 && arg4==arg4P_14 ], cost: 1
      2: f4 -> f5 : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, [ arg2P_3==-2+arg1 && arg1==arg1P_3 && arg3==arg3P_3 && arg4==arg4P_3 ], cost: 1
      3: f5 -> f6 : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, [ arg1==arg1P_4 && arg2==arg2P_4 && arg3==arg3P_4 && 0==arg4P_4 ], cost: 1
      6: f6 -> f7 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, [ arg2>1 && arg1==arg1P_7 && arg2==arg2P_7 && arg3==arg3P_7 && arg4==arg4P_7 ], cost: 1
      8: f6 -> f10 : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, arg4'=arg4P_9, [ arg2<=1 && arg1==arg1P_9 && arg2==arg2P_9 && arg3==arg3P_9 && arg4==arg4P_9 ], cost: 1
      4: f7 -> f8 : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, [ arg2P_5==-2+arg2 && arg1==arg1P_5 && arg3==arg3P_5 && arg4==arg4P_5 ], cost: 1
      5: f8 -> f9 : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, arg4'=arg4P_6, [ arg4P_6==1+arg4 && arg1==arg1P_6 && arg2==arg2P_6 && arg3==arg3P_6 ], cost: 1
      7: f9 -> f6 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, arg4'=arg4P_8, [ arg1==arg1P_8 && arg2==arg2P_8 && arg3==arg3P_8 && arg4==arg4P_8 ], cost: 1
      9: f10 -> f11 : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, arg4'=arg4P_10, [ arg1P_10==1+arg2 && arg2==arg2P_10 && arg3==arg3P_10 && arg4==arg4P_10 ], cost: 1
     10: f11 -> f12 : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, arg4'=arg4P_11, [ arg3P_11==1+arg3 && arg1==arg1P_11 && arg2==arg2P_11 && arg4==arg4P_11 ], cost: 1
     12: f12 -> f3 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, arg4'=arg4P_13, [ arg1==arg1P_13 && arg2==arg2P_13 && arg3==arg3P_13 && arg4==arg4P_13 ], cost: 1
     14: __init -> f1 : arg1'=arg1P_15, arg2'=arg2P_15, arg3'=arg3P_15, arg4'=arg4P_15, [], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
     14: __init -> f1 : arg1'=arg1P_15, arg2'=arg2P_15, arg3'=arg3P_15, arg4'=arg4P_15, [], cost: 1

Removed unreachable and leaf rules:
   Start location: __init
      0: f1 -> f2 : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, arg4'=arg4P_1, [ arg2==arg2P_1 && arg3==arg3P_1 && arg4==arg4P_1 ], cost: 1
      1: f2 -> f3 : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, [ arg1==arg1P_2 && arg2==arg2P_2 && 0==arg3P_2 && arg4==arg4P_2 ], cost: 1
     11: f3 -> f4 : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, arg4'=arg4P_12, [ arg1>1 && arg1==arg1P_12 && arg2==arg2P_12 && arg3==arg3P_12 && arg4==arg4P_12 ], cost: 1
      2: f4 -> f5 : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, [ arg2P_3==-2+arg1 && arg1==arg1P_3 && arg3==arg3P_3 && arg4==arg4P_3 ], cost: 1
      3: f5 -> f6 : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, [ arg1==arg1P_4 && arg2==arg2P_4 && arg3==arg3P_4 && 0==arg4P_4 ], cost: 1
      6: f6 -> f7 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, [ arg2>1 && arg1==arg1P_7 && arg2==arg2P_7 && arg3==arg3P_7 && arg4==arg4P_7 ], cost: 1
      8: f6 -> f10 : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, arg4'=arg4P_9, [ arg2<=1 && arg1==arg1P_9 && arg2==arg2P_9 && arg3==arg3P_9 && arg4==arg4P_9 ], cost: 1
      4: f7 -> f8 : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, [ arg2P_5==-2+arg2 && arg1==arg1P_5 && arg3==arg3P_5 && arg4==arg4P_5 ], cost: 1
      5: f8 -> f9 : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, arg4'=arg4P_6, [ arg4P_6==1+arg4 && arg1==arg1P_6 && arg2==arg2P_6 && arg3==arg3P_6 ], cost: 1
      7: f9 -> f6 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, arg4'=arg4P_8, [ arg1==arg1P_8 && arg2==arg2P_8 && arg3==arg3P_8 && arg4==arg4P_8 ], cost: 1
      9: f10 -> f11 : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, arg4'=arg4P_10, [ arg1P_10==1+arg2 && arg2==arg2P_10 && arg3==arg3P_10 && arg4==arg4P_10 ], cost: 1
     10: f11 -> f12 : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, arg4'=arg4P_11, [ arg3P_11==1+arg3 && arg1==arg1P_11 && arg2==arg2P_11 && arg4==arg4P_11 ], cost: 1
     12: f12 -> f3 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, arg4'=arg4P_13, [ arg1==arg1P_13 && arg2==arg2P_13 && arg3==arg3P_13 && arg4==arg4P_13 ], cost: 1
     14: __init -> f1 : arg1'=arg1P_15, arg2'=arg2P_15, arg3'=arg3P_15, arg4'=arg4P_15, [], cost: 1

Simplified all rules, resulting in:
   Start location: __init
      0: f1 -> f2 : arg1'=arg1P_1, [], cost: 1
      1: f2 -> f3 : arg3'=0, [], cost: 1
     11: f3 -> f4 : [ arg1>1 ], cost: 1
      2: f4 -> f5 : arg2'=-2+arg1, [], cost: 1
      3: f5 -> f6 : arg4'=0, [], cost: 1
      6: f6 -> f7 : [ arg2>1 ], cost: 1
      8: f6 -> f10 : [ arg2<=1 ], cost: 1
      4: f7 -> f8 : arg2'=-2+arg2, [], cost: 1
      5: f8 -> f9 : arg4'=1+arg4, [], cost: 1
      7: f9 -> f6 : [], cost: 1
      9: f10 -> f11 : arg1'=1+arg2, [], cost: 1
     10: f11 -> f12 : arg3'=1+arg3, [], cost: 1
     12: f12 -> f3 : [], cost: 1
     14: __init -> f1 : arg1'=arg1P_15, arg2'=arg2P_15, arg3'=arg3P_15, arg4'=arg4P_15, [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: __init
     18: f3 -> f6 : arg2'=-2+arg1, arg4'=0, [ arg1>1 ], cost: 3
     23: f6 -> f6 : arg2'=-2+arg2, arg4'=1+arg4, [ arg2>1 ], cost: 4
     24: f6 -> f3 : arg1'=1+arg2, arg3'=1+arg3, [ arg2<=1 ], cost: 4
     16: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_15, arg3'=0, arg4'=arg4P_15, [], cost: 3

Accelerating simple loops of location 5.
   Accelerating the following rules:
     23: f6 -> f6 : arg2'=-2+arg2, arg4'=1+arg4, [ arg2>1 ], cost: 4

   Accelerated rule 23 with backward acceleration, yielding the new rule 25.
[accelerate] Nesting with 1 inner and 1 outer candidates
   Removing the simple loops: 23.

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     18: f3 -> f6 : arg2'=-2+arg1, arg4'=0, [ arg1>1 ], cost: 3
     24: f6 -> f3 : arg1'=1+arg2, arg3'=1+arg3, [ arg2<=1 ], cost: 4
     25: f6 -> f6 : arg2'=arg2-2*k, arg4'=k+arg4, [ k>=0 && 2+arg2-2*k>1 ], cost: 4*k
     16: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_15, arg3'=0, arg4'=arg4P_15, [], cost: 3

Chained accelerated rules (with incoming rules):
   Start location: __init
     18: f3 -> f6 : arg2'=-2+arg1, arg4'=0, [ arg1>1 ], cost: 3
     26: f3 -> f6 : arg2'=-2-2*k+arg1, arg4'=k, [ arg1>1 && k>=0 && -2*k+arg1>1 ], cost: 3+4*k
     24: f6 -> f3 : arg1'=1+arg2, arg3'=1+arg3, [ arg2<=1 ], cost: 4
     16: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_15, arg3'=0, arg4'=arg4P_15, [], cost: 3

Eliminated locations (on tree-shaped paths):
   Start location: __init
     27: f3 -> f3 : arg1'=-1+arg1, arg2'=-2+arg1, arg3'=1+arg3, arg4'=0, [ arg1>1 && -2+arg1<=1 ], cost: 7
     28: f3 -> f3 : arg1'=-1-2*k+arg1, arg2'=-2-2*k+arg1, arg3'=1+arg3, arg4'=k, [ arg1>1 && k>=0 && -2*k+arg1>1 && -2-2*k+arg1<=1 ], cost: 7+4*k
     16: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_15, arg3'=0, arg4'=arg4P_15, [], cost: 3

Accelerating simple loops of location 2.
   Accelerating the following rules:
     27: f3 -> f3 : arg1'=-1+arg1, arg2'=-2+arg1, arg3'=1+arg3, arg4'=0, [ arg1>1 && -2+arg1<=1 ], cost: 7
     28: f3 -> f3 : arg1'=-1-2*k+arg1, arg2'=-2-2*k+arg1, arg3'=1+arg3, arg4'=k, [ arg1>1 && k>=0 && -2*k+arg1>1 && -2-2*k+arg1<=1 ], cost: 7+4*k

   Accelerated rule 27 with backward acceleration, yielding the new rule 29.
   Accelerated rule 28 with backward acceleration, yielding the new rule 30.
[accelerate] Nesting with 2 inner and 2 outer candidates
   Removing the simple loops: 27 28.

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     29: f3 -> f3 : arg1'=1, arg2'=0, arg3'=-1+arg3+arg1, arg4'=0, [ -2+arg1<=1 && -1+arg1>=1 ], cost: -7+7*arg1
     30: f3 -> f3 : arg1'=-k_2-2*k*k_2+arg1, arg2'=-1-2*(-1+k_2)*k-2*k-k_2+arg1, arg3'=arg3+k_2, arg4'=k, [ k>=0 && -2-2*k+arg1<=1 && k_2>=1 && 1-2*(-1+k_2)*k-k_2+arg1>1 && 1-2*(-1+k_2)*k-2*k-k_2+arg1>1 ], cost: 7*k_2+4*k*k_2
     16: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_15, arg3'=0, arg4'=arg4P_15, [], cost: 3

Chained accelerated rules (with incoming rules):
   Start location: __init
     16: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_15, arg3'=0, arg4'=arg4P_15, [], cost: 3
     31: __init -> f3 : arg1'=1, arg2'=0, arg3'=-1+arg1P_1, arg4'=0, [ -2+arg1P_1<=1 && -1+arg1P_1>=1 ], cost: -4+7*arg1P_1
     32: __init -> f3 : arg1'=-k_2+arg1P_1-2*k*k_2, arg2'=-1-2*(-1+k_2)*k-2*k-k_2+arg1P_1, arg3'=k_2, arg4'=k, [ k>=0 && -2-2*k+arg1P_1<=1 && k_2>=1 && 1-2*(-1+k_2)*k-k_2+arg1P_1>1 && 1-2*(-1+k_2)*k-2*k-k_2+arg1P_1>1 ], cost: 3+7*k_2+4*k*k_2

Removed unreachable locations (and leaf rules with constant cost):
   Start location: __init
     31: __init -> f3 : arg1'=1, arg2'=0, arg3'=-1+arg1P_1, arg4'=0, [ -2+arg1P_1<=1 && -1+arg1P_1>=1 ], cost: -4+7*arg1P_1
     32: __init -> f3 : arg1'=-k_2+arg1P_1-2*k*k_2, arg2'=-1-2*(-1+k_2)*k-2*k-k_2+arg1P_1, arg3'=k_2, arg4'=k, [ k>=0 && -2-2*k+arg1P_1<=1 && k_2>=1 && 1-2*(-1+k_2)*k-k_2+arg1P_1>1 && 1-2*(-1+k_2)*k-2*k-k_2+arg1P_1>1 ], cost: 3+7*k_2+4*k*k_2

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: __init
     31: __init -> f3 : arg1'=1, arg2'=0, arg3'=-1+arg1P_1, arg4'=0, [ -2+arg1P_1<=1 && -1+arg1P_1>=1 ], cost: -4+7*arg1P_1
     32: __init -> f3 : arg1'=-k_2+arg1P_1-2*k*k_2, arg2'=-1-2*(-1+k_2)*k-2*k-k_2+arg1P_1, arg3'=k_2, arg4'=k, [ k>=0 && -2-2*k+arg1P_1<=1 && k_2>=1 && 1-2*(-1+k_2)*k-k_2+arg1P_1>1 && 1-2*(-1+k_2)*k-2*k-k_2+arg1P_1>1 ], cost: 3+7*k_2+4*k*k_2

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

Computing asymptotic complexity for rule 31
   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),?)