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 && arg3==arg3P_2 && arg4==arg4P_2 ], cost: 1
     11: f3 -> f4 : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, arg4'=arg4P_12, [ arg2>0 && arg1>0 && arg1==arg1P_12 && arg2==arg2P_12 && arg3==arg3P_12 && arg4==arg4P_12 ], cost: 1
     13: f3 -> f12 : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, arg4'=arg4P_14, [ arg2<=0 && arg1==arg1P_14 && arg2==arg2P_14 && arg3==arg3P_14 && arg4==arg4P_14 ], cost: 1
     14: f3 -> f12 : arg1'=arg1P_15, arg2'=arg2P_15, arg3'=arg3P_15, arg4'=arg4P_15, [ arg1<=0 && arg1==arg1P_15 && arg2==arg2P_15 && arg3==arg3P_15 && arg4==arg4P_15 ], cost: 1
      2: f4 -> f5 : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, [ arg1==arg1P_3 && arg2==arg2P_3 && arg2==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 && arg1==arg4P_4 ], cost: 1
      5: f6 -> f7 : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, arg4'=arg4P_6, [ arg4>=arg2 && arg2>0 && arg1==arg1P_6 && arg2==arg2P_6 && arg3==arg3P_6 && arg4==arg4P_6 ], cost: 1
      7: f6 -> f9 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, arg4'=arg4P_8, [ arg4<arg2 && arg1==arg1P_8 && arg2==arg2P_8 && arg3==arg3P_8 && arg4==arg4P_8 ], cost: 1
      8: f6 -> f9 : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, arg4'=arg4P_9, [ arg2<=0 && 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, [ arg4P_5==-arg2+arg4 && arg1==arg1P_5 && arg2==arg2P_5 && arg3==arg3P_5 ], cost: 1
      6: f8 -> f6 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, [ arg1==arg1P_7 && arg2==arg2P_7 && arg3==arg3P_7 && arg4==arg4P_7 ], cost: 1
      9: f9 -> f10 : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, arg4'=arg4P_10, [ arg1==arg1P_10 && arg4==arg2P_10 && arg3==arg3P_10 && arg4==arg4P_10 ], cost: 1
     10: f10 -> f11 : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, arg4'=arg4P_11, [ arg3==arg1P_11 && arg2==arg2P_11 && arg3==arg3P_11 && arg4==arg4P_11 ], cost: 1
     12: f11 -> 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
     15: __init -> f1 : arg1'=arg1P_16, arg2'=arg2P_16, arg3'=arg3P_16, arg4'=arg4P_16, [], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
     15: __init -> f1 : arg1'=arg1P_16, arg2'=arg2P_16, arg3'=arg3P_16, arg4'=arg4P_16, [], 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 && arg3==arg3P_2 && arg4==arg4P_2 ], cost: 1
     11: f3 -> f4 : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, arg4'=arg4P_12, [ arg2>0 && arg1>0 && 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, [ arg1==arg1P_3 && arg2==arg2P_3 && arg2==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 && arg1==arg4P_4 ], cost: 1
      5: f6 -> f7 : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, arg4'=arg4P_6, [ arg4>=arg2 && arg2>0 && arg1==arg1P_6 && arg2==arg2P_6 && arg3==arg3P_6 && arg4==arg4P_6 ], cost: 1
      7: f6 -> f9 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, arg4'=arg4P_8, [ arg4<arg2 && arg1==arg1P_8 && arg2==arg2P_8 && arg3==arg3P_8 && arg4==arg4P_8 ], cost: 1
      8: f6 -> f9 : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, arg4'=arg4P_9, [ arg2<=0 && 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, [ arg4P_5==-arg2+arg4 && arg1==arg1P_5 && arg2==arg2P_5 && arg3==arg3P_5 ], cost: 1
      6: f8 -> f6 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, [ arg1==arg1P_7 && arg2==arg2P_7 && arg3==arg3P_7 && arg4==arg4P_7 ], cost: 1
      9: f9 -> f10 : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, arg4'=arg4P_10, [ arg1==arg1P_10 && arg4==arg2P_10 && arg3==arg3P_10 && arg4==arg4P_10 ], cost: 1
     10: f10 -> f11 : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, arg4'=arg4P_11, [ arg3==arg1P_11 && arg2==arg2P_11 && arg3==arg3P_11 && arg4==arg4P_11 ], cost: 1
     12: f11 -> 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
     15: __init -> f1 : arg1'=arg1P_16, arg2'=arg2P_16, arg3'=arg3P_16, arg4'=arg4P_16, [], cost: 1

Simplified all rules, resulting in:
   Start location: __init
      0: f1 -> f2 : arg1'=arg1P_1, [], cost: 1
      1: f2 -> f3 : arg2'=arg2P_2, [], cost: 1
     11: f3 -> f4 : [ arg2>0 && arg1>0 ], cost: 1
      2: f4 -> f5 : arg3'=arg2, [], cost: 1
      3: f5 -> f6 : arg4'=arg1, [], cost: 1
      5: f6 -> f7 : [ arg4>=arg2 && arg2>0 ], cost: 1
      7: f6 -> f9 : [ arg4<arg2 ], cost: 1
      8: f6 -> f9 : [ arg2<=0 ], cost: 1
      4: f7 -> f8 : arg4'=-arg2+arg4, [], cost: 1
      6: f8 -> f6 : [], cost: 1
      9: f9 -> f10 : arg2'=arg4, [], cost: 1
     10: f10 -> f11 : arg1'=arg3, [], cost: 1
     12: f11 -> f3 : [], cost: 1
     15: __init -> f1 : arg1'=arg1P_16, arg2'=arg2P_16, arg3'=arg3P_16, arg4'=arg4P_16, [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: __init
     19: f3 -> f6 : arg3'=arg2, arg4'=arg1, [ arg2>0 && arg1>0 ], cost: 3
      7: f6 -> f9 : [ arg4<arg2 ], cost: 1
      8: f6 -> f9 : [ arg2<=0 ], cost: 1
     21: f6 -> f6 : arg4'=-arg2+arg4, [ arg4>=arg2 && arg2>0 ], cost: 3
     23: f9 -> f3 : arg1'=arg3, arg2'=arg4, [], cost: 3
     17: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_16, arg4'=arg4P_16, [], cost: 3

Accelerating simple loops of location 5.
   Accelerating the following rules:
     21: f6 -> f6 : arg4'=-arg2+arg4, [ arg4>=arg2 && arg2>0 ], cost: 3

   Accelerated rule 21 with backward acceleration, yielding the new rule 24.
[accelerate] Nesting with 1 inner and 1 outer candidates
   Removing the simple loops: 21.

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     19: f3 -> f6 : arg3'=arg2, arg4'=arg1, [ arg2>0 && arg1>0 ], cost: 3
      7: f6 -> f9 : [ arg4<arg2 ], cost: 1
      8: f6 -> f9 : [ arg2<=0 ], cost: 1
     24: f6 -> f6 : arg4'=-arg2*k+arg4, [ arg2>0 && k>=0 && -arg2*(-1+k)+arg4>=arg2 ], cost: 3*k
     23: f9 -> f3 : arg1'=arg3, arg2'=arg4, [], cost: 3
     17: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_16, arg4'=arg4P_16, [], cost: 3

Chained accelerated rules (with incoming rules):
   Start location: __init
     19: f3 -> f6 : arg3'=arg2, arg4'=arg1, [ arg2>0 && arg1>0 ], cost: 3
     25: f3 -> f6 : arg3'=arg2, arg4'=-arg2*k+arg1, [ arg2>0 && arg1>0 && k>=0 && -arg2*(-1+k)+arg1>=arg2 ], cost: 3+3*k
      7: f6 -> f9 : [ arg4<arg2 ], cost: 1
      8: f6 -> f9 : [ arg2<=0 ], cost: 1
     23: f9 -> f3 : arg1'=arg3, arg2'=arg4, [], cost: 3
     17: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_16, arg4'=arg4P_16, [], cost: 3

Eliminated locations (on tree-shaped paths):
   Start location: __init
     26: f3 -> f9 : arg3'=arg2, arg4'=arg1, [ arg2>0 && arg1>0 && arg1<arg2 ], cost: 4
     27: f3 -> f9 : arg3'=arg2, arg4'=-arg2*k+arg1, [ arg2>0 && arg1>0 && k>=0 && -arg2*(-1+k)+arg1>=arg2 && -arg2*k+arg1<arg2 ], cost: 4+3*k
     28: f3 -> [14] : [ arg2>0 && arg1>0 && k>=0 && -arg2*(-1+k)+arg1>=arg2 ], cost: 3+3*k
     23: f9 -> f3 : arg1'=arg3, arg2'=arg4, [], cost: 3
     17: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_16, arg4'=arg4P_16, [], cost: 3

Eliminated locations (on tree-shaped paths):
   Start location: __init
     28: f3 -> [14] : [ arg2>0 && arg1>0 && k>=0 && -arg2*(-1+k)+arg1>=arg2 ], cost: 3+3*k
     29: f3 -> f3 : arg1'=arg2, arg2'=arg1, arg3'=arg2, arg4'=arg1, [ arg2>0 && arg1>0 && arg1<arg2 ], cost: 7
     30: f3 -> f3 : arg1'=arg2, arg2'=-arg2*k+arg1, arg3'=arg2, arg4'=-arg2*k+arg1, [ arg2>0 && arg1>0 && k>=0 && -arg2*(-1+k)+arg1>=arg2 && -arg2*k+arg1<arg2 ], cost: 7+3*k
     17: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_16, arg4'=arg4P_16, [], cost: 3

Accelerating simple loops of location 2.
   Accelerating the following rules:
     29: f3 -> f3 : arg1'=arg2, arg2'=arg1, arg3'=arg2, arg4'=arg1, [ arg2>0 && arg1>0 && arg1<arg2 ], cost: 7
     30: f3 -> f3 : arg1'=arg2, arg2'=-arg2*k+arg1, arg3'=arg2, arg4'=-arg2*k+arg1, [ arg2>0 && arg1>0 && k>=0 && -arg2*(-1+k)+arg1>=arg2 && -arg2*k+arg1<arg2 ], cost: 7+3*k

   Failed to prove monotonicity of the guard of rule 29.
   Found no closed form for 30.
[accelerate] Nesting with 1 inner and 2 outer candidates

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     28: f3 -> [14] : [ arg2>0 && arg1>0 && k>=0 && -arg2*(-1+k)+arg1>=arg2 ], cost: 3+3*k
     29: f3 -> f3 : arg1'=arg2, arg2'=arg1, arg3'=arg2, arg4'=arg1, [ arg2>0 && arg1>0 && arg1<arg2 ], cost: 7
     30: f3 -> f3 : arg1'=arg2, arg2'=-arg2*k+arg1, arg3'=arg2, arg4'=-arg2*k+arg1, [ arg2>0 && arg1>0 && k>=0 && -arg2*(-1+k)+arg1>=arg2 && -arg2*k+arg1<arg2 ], cost: 7+3*k
     17: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_16, arg4'=arg4P_16, [], cost: 3

Chained accelerated rules (with incoming rules):
   Start location: __init
     28: f3 -> [14] : [ arg2>0 && arg1>0 && k>=0 && -arg2*(-1+k)+arg1>=arg2 ], cost: 3+3*k
     17: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_16, arg4'=arg4P_16, [], cost: 3
     31: __init -> f3 : arg1'=arg2P_2, arg2'=arg1P_1, arg3'=arg2P_2, arg4'=arg1P_1, [ arg2P_2>0 && arg1P_1>0 && arg1P_1<arg2P_2 ], cost: 10
     32: __init -> f3 : arg1'=arg2P_2, arg2'=-arg2P_2*k+arg1P_1, arg3'=arg2P_2, arg4'=-arg2P_2*k+arg1P_1, [ arg2P_2>0 && arg1P_1>0 && k>=0 && -arg2P_2*(-1+k)+arg1P_1>=arg2P_2 && -arg2P_2*k+arg1P_1<arg2P_2 ], cost: 10+3*k

Eliminated locations (on tree-shaped paths):
   Start location: __init
     33: __init -> [14] : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_16, arg4'=arg4P_16, [ arg2P_2>0 && arg1P_1>0 && k>=0 && -arg2P_2*(-1+k)+arg1P_1>=arg2P_2 ], cost: 6+3*k
     34: __init -> [14] : arg1'=arg2P_2, arg2'=arg1P_1, arg3'=arg2P_2, arg4'=arg1P_1, [ arg2P_2>0 && arg1P_1>0 && arg1P_1<arg2P_2 && k>=0 && arg2P_2-(-1+k)*arg1P_1>=arg1P_1 ], cost: 13+3*k
     35: __init -> [14] : arg1'=arg2P_2, arg2'=-arg2P_2*k+arg1P_1, arg3'=arg2P_2, arg4'=-arg2P_2*k+arg1P_1, [ arg2P_2>0 && arg1P_1>0 && k>=0 && -arg2P_2*k+arg1P_1<arg2P_2 && -arg2P_2*k+arg1P_1>0 && arg2P_2+(arg2P_2*k-arg1P_1)*(-1+k)>=-arg2P_2*k+arg1P_1 ], cost: 13+6*k

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: __init
     33: __init -> [14] : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_16, arg4'=arg4P_16, [ arg2P_2>0 && arg1P_1>0 && k>=0 && -arg2P_2*(-1+k)+arg1P_1>=arg2P_2 ], cost: 6+3*k
     34: __init -> [14] : arg1'=arg2P_2, arg2'=arg1P_1, arg3'=arg2P_2, arg4'=arg1P_1, [ arg2P_2>0 && arg1P_1>0 && arg1P_1<arg2P_2 && k>=0 && arg2P_2-(-1+k)*arg1P_1>=arg1P_1 ], cost: 13+3*k
     35: __init -> [14] : arg1'=arg2P_2, arg2'=-arg2P_2*k+arg1P_1, arg3'=arg2P_2, arg4'=-arg2P_2*k+arg1P_1, [ arg2P_2>0 && arg1P_1>0 && k>=0 && -arg2P_2*k+arg1P_1<arg2P_2 && -arg2P_2*k+arg1P_1>0 && arg2P_2+(arg2P_2*k-arg1P_1)*(-1+k)>=-arg2P_2*k+arg1P_1 ], cost: 13+6*k

Computing asymptotic complexity for rule 33
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 34
   Simplified the guard:
     34: __init -> [14] : arg1'=arg2P_2, arg2'=arg1P_1, arg3'=arg2P_2, arg4'=arg1P_1, [ arg1P_1>0 && arg1P_1<arg2P_2 && k>=0 && arg2P_2-(-1+k)*arg1P_1>=arg1P_1 ], cost: 13+3*k
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 35
   Simplified the guard:
     35: __init -> [14] : arg1'=arg2P_2, arg2'=-arg2P_2*k+arg1P_1, arg3'=arg2P_2, arg4'=-arg2P_2*k+arg1P_1, [ k>=0 && -arg2P_2*k+arg1P_1<arg2P_2 && -arg2P_2*k+arg1P_1>0 && arg2P_2+(arg2P_2*k-arg1P_1)*(-1+k)>=-arg2P_2*k+arg1P_1 ], cost: 13+6*k
   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),?)