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, [ arg2==arg2P_1 && arg3==arg3P_1 ], cost: 1
      1: f2 -> f3 : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ arg1==arg1P_2 && arg3==arg3P_2 ], cost: 1
      2: f3 -> f4 : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg1==arg1P_3 && arg2==arg2P_3 ], cost: 1
     12: f4 -> f5 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, [ arg1>=0 && arg1==arg1P_13 && arg2==arg2P_13 && arg3==arg3P_13 ], cost: 1
     14: f4 -> f13 : arg1'=arg1P_15, arg2'=arg2P_15, arg3'=arg3P_15, [ arg1<0 && arg1==arg1P_15 && arg2==arg2P_15 && arg3==arg3P_15 ], cost: 1
      3: f6 -> f9 : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ arg1P_4==arg2+arg1 && arg2==arg2P_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, [ arg1P_5==arg3+arg1 && arg2==arg2P_5 && arg3==arg3P_5 ], cost: 1
      9: f10 -> f8 : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, [ arg1==arg1P_10 && arg2==arg2P_10 && arg3==arg3P_10 ], cost: 1
      5: f5 -> f6 : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [ x18_1<0 && arg1==arg1P_6 && arg2==arg2P_6 && arg3==arg3P_6 ], cost: 1
      6: f5 -> f6 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [ x51_1>0 && arg1==arg1P_7 && arg2==arg2P_7 && arg3==arg3P_7 ], cost: 1
      7: f5 -> f7 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, [ x22_1==0 && arg1==arg1P_8 && arg2==arg2P_8 && arg3==arg3P_8 ], cost: 1
     10: f8 -> f11 : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, [ arg2P_11==arg2+arg3 && arg1==arg1P_11 && arg3==arg3P_11 ], cost: 1
     11: f11 -> f12 : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, [ arg3P_12==-1+arg3 && arg1==arg1P_12 && arg2==arg2P_12 ], cost: 1
     13: f12 -> f4 : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, [ arg1==arg1P_14 && arg2==arg2P_14 && arg3==arg3P_14 ], cost: 1
     15: __init -> f1 : arg1'=arg1P_16, arg2'=arg2P_16, arg3'=arg3P_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, [], cost: 1

Removed unreachable and leaf rules:
   Start location: __init
      0: f1 -> f2 : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, [ arg2==arg2P_1 && arg3==arg3P_1 ], cost: 1
      1: f2 -> f3 : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ arg1==arg1P_2 && arg3==arg3P_2 ], cost: 1
      2: f3 -> f4 : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg1==arg1P_3 && arg2==arg2P_3 ], cost: 1
     12: f4 -> f5 : 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, [ arg1P_4==arg2+arg1 && arg2==arg2P_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, [ arg1P_5==arg3+arg1 && arg2==arg2P_5 && arg3==arg3P_5 ], cost: 1
      9: f10 -> f8 : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, [ arg1==arg1P_10 && arg2==arg2P_10 && arg3==arg3P_10 ], cost: 1
      5: f5 -> f6 : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [ x18_1<0 && arg1==arg1P_6 && arg2==arg2P_6 && arg3==arg3P_6 ], cost: 1
      6: f5 -> f6 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [ x51_1>0 && arg1==arg1P_7 && arg2==arg2P_7 && arg3==arg3P_7 ], cost: 1
      7: f5 -> f7 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, [ x22_1==0 && arg1==arg1P_8 && arg2==arg2P_8 && arg3==arg3P_8 ], cost: 1
     10: f8 -> f11 : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, [ arg2P_11==arg2+arg3 && arg1==arg1P_11 && arg3==arg3P_11 ], cost: 1
     11: f11 -> f12 : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, [ arg3P_12==-1+arg3 && arg1==arg1P_12 && arg2==arg2P_12 ], cost: 1
     13: f12 -> f4 : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, [ arg1==arg1P_14 && arg2==arg2P_14 && arg3==arg3P_14 ], cost: 1
     15: __init -> f1 : arg1'=arg1P_16, arg2'=arg2P_16, arg3'=arg3P_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
      2: f3 -> f4 : arg3'=arg3P_3, [], cost: 1
     12: f4 -> f5 : [ arg1>=0 ], cost: 1
      3: f6 -> f9 : arg1'=arg2+arg1, [], cost: 1
      8: f9 -> f8 : [], cost: 1
      4: f7 -> f10 : arg1'=arg3+arg1, [], cost: 1
      9: f10 -> f8 : [], cost: 1
      6: f5 -> f6 : [], cost: 1
      7: f5 -> f7 : [], cost: 1
     10: f8 -> f11 : arg2'=arg2+arg3, [], cost: 1
     11: f11 -> f12 : arg3'=-1+arg3, [], cost: 1
     13: f12 -> f4 : [], cost: 1
     15: __init -> f1 : arg1'=arg1P_16, arg2'=arg2P_16, arg3'=arg3P_16, [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: __init
     12: f4 -> f5 : [ arg1>=0 ], cost: 1
     21: f5 -> f8 : arg1'=arg2+arg1, [], cost: 3
     22: f5 -> f8 : arg1'=arg3+arg1, [], cost: 3
     24: f8 -> f4 : arg2'=arg2+arg3, arg3'=-1+arg3, [], cost: 3
     18: __init -> f4 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_3, [], cost: 4

Eliminated locations (on tree-shaped paths):
   Start location: __init
     25: f4 -> f8 : arg1'=arg2+arg1, [ arg1>=0 ], cost: 4
     26: f4 -> f8 : arg1'=arg3+arg1, [ arg1>=0 ], cost: 4
     24: f8 -> f4 : arg2'=arg2+arg3, arg3'=-1+arg3, [], cost: 3
     18: __init -> f4 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_3, [], cost: 4

Eliminated locations (on tree-shaped paths):
   Start location: __init
     27: f4 -> f4 : arg1'=arg2+arg1, arg2'=arg2+arg3, arg3'=-1+arg3, [ arg1>=0 ], cost: 7
     28: f4 -> f4 : arg1'=arg3+arg1, arg2'=arg2+arg3, arg3'=-1+arg3, [ arg1>=0 ], cost: 7
     18: __init -> f4 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_3, [], cost: 4

Accelerating simple loops of location 3.
   Accelerating the following rules:
     27: f4 -> f4 : arg1'=arg2+arg1, arg2'=arg2+arg3, arg3'=-1+arg3, [ arg1>=0 ], cost: 7
     28: f4 -> f4 : arg1'=arg3+arg1, arg2'=arg2+arg3, arg3'=-1+arg3, [ arg1>=0 ], cost: 7

   Failed to prove monotonicity of the guard of rule 27.
[test] deduced pseudo-invariant 1+arg3<=0, also trying -1-arg3<=-1
   Accelerated rule 28 with backward acceleration, yielding the new rule 29.
   Accelerated rule 28 with backward acceleration, yielding the new rule 30.
[accelerate] Nesting with 3 inner and 2 outer candidates

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     27: f4 -> f4 : arg1'=arg2+arg1, arg2'=arg2+arg3, arg3'=-1+arg3, [ arg1>=0 ], cost: 7
     28: f4 -> f4 : arg1'=arg3+arg1, arg2'=arg2+arg3, arg3'=-1+arg3, [ arg1>=0 ], cost: 7
     29: f4 -> f4 : arg1'=-1/2*k^2+1/2*k+arg3*k+arg1, arg2'=arg2-1/2*k^2+1/2*k+arg3*k, arg3'=arg3-k, [ 1+arg3<=0 && k>=0 && -1/2+1/2*k+(-1+k)*arg3-1/2*(-1+k)^2+arg1>=0 ], cost: 7*k
     30: f4 -> f4 : arg1'=1/2-1/2*(1+arg3)^2+1/2*arg3+arg3*(1+arg3)+arg1, arg2'=1/2+arg2-1/2*(1+arg3)^2+1/2*arg3+arg3*(1+arg3), arg3'=-1, [ arg1>=0 && 1+arg3>=0 ], cost: 7+7*arg3
     18: __init -> f4 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_3, [], cost: 4

Chained accelerated rules (with incoming rules):
   Start location: __init
     18: __init -> f4 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_3, [], cost: 4
     31: __init -> f4 : arg1'=arg1P_1+arg2P_2, arg2'=arg2P_2+arg3P_3, arg3'=-1+arg3P_3, [ arg1P_1>=0 ], cost: 11
     32: __init -> f4 : arg1'=arg1P_1+arg3P_3, arg2'=arg2P_2+arg3P_3, arg3'=-1+arg3P_3, [ arg1P_1>=0 ], cost: 11
     33: __init -> f4 : arg1'=-1/2*k^2+arg1P_1+k*arg3P_3+1/2*k, arg2'=-1/2*k^2+k*arg3P_3+1/2*k+arg2P_2, arg3'=-k+arg3P_3, [ 1+arg3P_3<=0 && k>=0 && -1/2+arg1P_1+(-1+k)*arg3P_3+1/2*k-1/2*(-1+k)^2>=0 ], cost: 4+7*k
     34: __init -> f4 : arg1'=1/2+arg1P_1+(1+arg3P_3)*arg3P_3-1/2*(1+arg3P_3)^2+1/2*arg3P_3, arg2'=1/2+arg2P_2+(1+arg3P_3)*arg3P_3-1/2*(1+arg3P_3)^2+1/2*arg3P_3, arg3'=-1, [ arg1P_1>=0 && 1+arg3P_3>=0 ], cost: 11+7*arg3P_3

Removed unreachable locations (and leaf rules with constant cost):
   Start location: __init
     33: __init -> f4 : arg1'=-1/2*k^2+arg1P_1+k*arg3P_3+1/2*k, arg2'=-1/2*k^2+k*arg3P_3+1/2*k+arg2P_2, arg3'=-k+arg3P_3, [ 1+arg3P_3<=0 && k>=0 && -1/2+arg1P_1+(-1+k)*arg3P_3+1/2*k-1/2*(-1+k)^2>=0 ], cost: 4+7*k
     34: __init -> f4 : arg1'=1/2+arg1P_1+(1+arg3P_3)*arg3P_3-1/2*(1+arg3P_3)^2+1/2*arg3P_3, arg2'=1/2+arg2P_2+(1+arg3P_3)*arg3P_3-1/2*(1+arg3P_3)^2+1/2*arg3P_3, arg3'=-1, [ arg1P_1>=0 && 1+arg3P_3>=0 ], cost: 11+7*arg3P_3

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: __init
     33: __init -> f4 : arg1'=-1/2*k^2+arg1P_1+k*arg3P_3+1/2*k, arg2'=-1/2*k^2+k*arg3P_3+1/2*k+arg2P_2, arg3'=-k+arg3P_3, [ 1+arg3P_3<=0 && k>=0 && -1/2+arg1P_1+(-1+k)*arg3P_3+1/2*k-1/2*(-1+k)^2>=0 ], cost: 4+7*k
     34: __init -> f4 : arg1'=1/2+arg1P_1+(1+arg3P_3)*arg3P_3-1/2*(1+arg3P_3)^2+1/2*arg3P_3, arg2'=1/2+arg2P_2+(1+arg3P_3)*arg3P_3-1/2*(1+arg3P_3)^2+1/2*arg3P_3, arg3'=-1, [ arg1P_1>=0 && 1+arg3P_3>=0 ], cost: 11+7*arg3P_3

Computing asymptotic complexity for rule 34
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 33
   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),?)