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
     13: f4 -> f5 : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, [ arg1>=arg2 && arg1==arg1P_14 && arg2==arg2P_14 && arg3==arg3P_14 ], cost: 1
     15: f4 -> f14 : arg1'=arg1P_16, arg2'=arg2P_16, arg3'=arg3P_16, [ arg1<arg2 && arg1==arg1P_16 && arg2==arg2P_16 && arg3==arg3P_16 ], cost: 1
      3: f6 -> f9 : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ arg1P_4==1+arg1 && arg2==arg2P_4 && arg3==arg3P_4 ], cost: 1
      4: f9 -> f10 : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ arg2P_5==arg2+arg1 && arg1==arg1P_5 && arg3==arg3P_5 ], cost: 1
     11: f10 -> f8 : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, [ arg1==arg1P_12 && arg2==arg2P_12 && arg3==arg3P_12 ], cost: 1
      5: f7 -> f11 : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [ arg1P_6==-arg3+arg1 && arg2==arg2P_6 && arg3==arg3P_6 ], cost: 1
      6: f11 -> f12 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [ arg2P_7==arg3^2+arg2 && arg1==arg1P_7 && arg3==arg3P_7 ], cost: 1
      7: f12 -> f13 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, [ arg3P_8==-1+arg3 && arg1==arg1P_8 && arg2==arg2P_8 ], cost: 1
     12: f13 -> f8 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, [ arg1==arg1P_13 && arg2==arg2P_13 && arg3==arg3P_13 ], cost: 1
      8: f5 -> f6 : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, [ x27_1<0 && arg1==arg1P_9 && arg2==arg2P_9 && arg3==arg3P_9 ], cost: 1
      9: f5 -> f6 : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, [ x66_1>0 && arg1==arg1P_10 && arg2==arg2P_10 && arg3==arg3P_10 ], cost: 1
     10: f5 -> f7 : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, [ x31_1==0 && arg1==arg1P_11 && arg2==arg2P_11 && arg3==arg3P_11 ], cost: 1
     14: f8 -> f4 : arg1'=arg1P_15, arg2'=arg2P_15, arg3'=arg3P_15, [ arg1==arg1P_15 && arg2==arg2P_15 && arg3==arg3P_15 ], cost: 1
     16: __init -> f1 : arg1'=arg1P_17, arg2'=arg2P_17, arg3'=arg3P_17, [], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
     16: __init -> f1 : arg1'=arg1P_17, arg2'=arg2P_17, arg3'=arg3P_17, [], 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
     13: f4 -> f5 : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, [ arg1>=arg2 && arg1==arg1P_14 && arg2==arg2P_14 && arg3==arg3P_14 ], cost: 1
      3: f6 -> f9 : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ arg1P_4==1+arg1 && arg2==arg2P_4 && arg3==arg3P_4 ], cost: 1
      4: f9 -> f10 : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ arg2P_5==arg2+arg1 && arg1==arg1P_5 && arg3==arg3P_5 ], cost: 1
     11: f10 -> f8 : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, [ arg1==arg1P_12 && arg2==arg2P_12 && arg3==arg3P_12 ], cost: 1
      5: f7 -> f11 : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [ arg1P_6==-arg3+arg1 && arg2==arg2P_6 && arg3==arg3P_6 ], cost: 1
      6: f11 -> f12 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [ arg2P_7==arg3^2+arg2 && arg1==arg1P_7 && arg3==arg3P_7 ], cost: 1
      7: f12 -> f13 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, [ arg3P_8==-1+arg3 && arg1==arg1P_8 && arg2==arg2P_8 ], cost: 1
     12: f13 -> f8 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, [ arg1==arg1P_13 && arg2==arg2P_13 && arg3==arg3P_13 ], cost: 1
      8: f5 -> f6 : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, [ x27_1<0 && arg1==arg1P_9 && arg2==arg2P_9 && arg3==arg3P_9 ], cost: 1
      9: f5 -> f6 : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, [ x66_1>0 && arg1==arg1P_10 && arg2==arg2P_10 && arg3==arg3P_10 ], cost: 1
     10: f5 -> f7 : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, [ x31_1==0 && arg1==arg1P_11 && arg2==arg2P_11 && arg3==arg3P_11 ], cost: 1
     14: f8 -> f4 : arg1'=arg1P_15, arg2'=arg2P_15, arg3'=arg3P_15, [ arg1==arg1P_15 && arg2==arg2P_15 && arg3==arg3P_15 ], cost: 1
     16: __init -> f1 : arg1'=arg1P_17, arg2'=arg2P_17, arg3'=arg3P_17, [], 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
     13: f4 -> f5 : [ arg1>=arg2 ], cost: 1
      3: f6 -> f9 : arg1'=1+arg1, [], cost: 1
      4: f9 -> f10 : arg2'=arg2+arg1, [], cost: 1
     11: f10 -> f8 : [], cost: 1
      5: f7 -> f11 : arg1'=-arg3+arg1, [], cost: 1
      6: f11 -> f12 : arg2'=arg3^2+arg2, [], cost: 1
      7: f12 -> f13 : arg3'=-1+arg3, [], cost: 1
     12: f13 -> f8 : [], cost: 1
      9: f5 -> f6 : [], cost: 1
     10: f5 -> f7 : [], cost: 1
     14: f8 -> f4 : [], cost: 1
     16: __init -> f1 : arg1'=arg1P_17, arg2'=arg2P_17, arg3'=arg3P_17, [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: __init
     13: f4 -> f5 : [ arg1>=arg2 ], cost: 1
     24: f5 -> f8 : arg1'=1+arg1, arg2'=1+arg2+arg1, [], cost: 4
     26: f5 -> f8 : arg1'=-arg3+arg1, arg2'=arg3^2+arg2, arg3'=-1+arg3, [], cost: 5
     14: f8 -> f4 : [], cost: 1
     19: __init -> f4 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_3, [], cost: 4

Eliminated locations (on tree-shaped paths):
   Start location: __init
     27: f4 -> f8 : arg1'=1+arg1, arg2'=1+arg2+arg1, [ arg1>=arg2 ], cost: 5
     28: f4 -> f8 : arg1'=-arg3+arg1, arg2'=arg3^2+arg2, arg3'=-1+arg3, [ arg1>=arg2 ], cost: 6
     14: f8 -> f4 : [], cost: 1
     19: __init -> f4 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_3, [], cost: 4

Eliminated locations (on tree-shaped paths):
   Start location: __init
     29: f4 -> f4 : arg1'=1+arg1, arg2'=1+arg2+arg1, [ arg1>=arg2 ], cost: 6
     30: f4 -> f4 : arg1'=-arg3+arg1, arg2'=arg3^2+arg2, arg3'=-1+arg3, [ arg1>=arg2 ], cost: 7
     19: __init -> f4 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_3, [], cost: 4

Accelerating simple loops of location 3.
   Accelerating the following rules:
     29: f4 -> f4 : arg1'=1+arg1, arg2'=1+arg2+arg1, [ arg1>=arg2 ], cost: 6
     30: f4 -> f4 : arg1'=-arg3+arg1, arg2'=arg3^2+arg2, arg3'=-1+arg3, [ arg1>=arg2 ], cost: 7

[test] deduced pseudo-invariant -arg1<=0, also trying arg1<=-1
   Accelerated rule 29 with backward acceleration, yielding the new rule 31.
   Accelerated rule 29 with backward acceleration, yielding the new rule 32.
   Accelerated rule 30 with backward acceleration, yielding the new rule 33.
[accelerate] Nesting with 3 inner and 2 outer candidates
   Removing the simple loops: 30.

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     29: f4 -> f4 : arg1'=1+arg1, arg2'=1+arg2+arg1, [ arg1>=arg2 ], cost: 6
     31: f4 -> f4 : arg1'=k+arg1, arg2'=k*arg1+arg2+1/2*k+1/2*k^2, [ -arg1<=0 && k>=0 && -1+k+arg1>=-1/2+arg2+1/2*k+arg1*(-1+k)+1/2*(-1+k)^2 ], cost: 6*k
     32: f4 -> f4 : arg1'=0, arg2'=arg2-1/2*arg1^2-1/2*arg1, [ arg1>=arg2 && -arg1>=0 ], cost: -6*arg1
     33: f4 -> f4 : arg1'=-arg3*k_2+1/2*k_2^2-1/2*k_2+arg1, arg2'=-arg3*k_2^2+arg2+arg3*k_2+arg3^2*k_2-1/2*k_2^2+1/3*k_2^3+1/6*k_2, arg3'=arg3-k_2, [ k_2>=0 && 1/2-arg3*(-1+k_2)-1/2*k_2+1/2*(-1+k_2)^2+arg1>=-1/6+arg2+arg3*(-1+k_2)-arg3*(-1+k_2)^2+1/6*k_2+arg3^2*(-1+k_2)-1/2*(-1+k_2)^2+1/3*(-1+k_2)^3 ], cost: 7*k_2
     19: __init -> f4 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_3, [], cost: 4

Chained accelerated rules (with incoming rules):
   Start location: __init
     19: __init -> f4 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_3, [], cost: 4
     34: __init -> f4 : arg1'=1+arg1P_1, arg2'=1+arg1P_1+arg2P_2, arg3'=arg3P_3, [ arg1P_1>=arg2P_2 ], cost: 10
     35: __init -> f4 : arg1'=k+arg1P_1, arg2'=k*arg1P_1+1/2*k+1/2*k^2+arg2P_2, arg3'=arg3P_3, [ -arg1P_1<=0 && k>=0 && -1+k+arg1P_1>=-1/2+1/2*k+arg2P_2+arg1P_1*(-1+k)+1/2*(-1+k)^2 ], cost: 4+6*k
     36: __init -> f4 : arg1'=0, arg2'=-1/2*arg1P_1+arg2P_2-1/2*arg1P_1^2, arg3'=arg3P_3, [ arg1P_1>=arg2P_2 && -arg1P_1>=0 ], cost: 4-6*arg1P_1
     37: __init -> f4 : arg1'=-k_2*arg3P_3+arg1P_1+1/2*k_2^2-1/2*k_2, arg2'=k_2*arg3P_3+k_2*arg3P_3^2-1/2*k_2^2+1/3*k_2^3+arg2P_2+1/6*k_2-k_2^2*arg3P_3, arg3'=-k_2+arg3P_3, [ k_2>=0 && 1/2+arg1P_1-(-1+k_2)*arg3P_3-1/2*k_2+1/2*(-1+k_2)^2>=-1/6-(-1+k_2)^2*arg3P_3+(-1+k_2)*arg3P_3+arg2P_2+1/6*k_2+(-1+k_2)*arg3P_3^2-1/2*(-1+k_2)^2+1/3*(-1+k_2)^3 ], cost: 4+7*k_2

Removed unreachable locations (and leaf rules with constant cost):
   Start location: __init
     35: __init -> f4 : arg1'=k+arg1P_1, arg2'=k*arg1P_1+1/2*k+1/2*k^2+arg2P_2, arg3'=arg3P_3, [ -arg1P_1<=0 && k>=0 && -1+k+arg1P_1>=-1/2+1/2*k+arg2P_2+arg1P_1*(-1+k)+1/2*(-1+k)^2 ], cost: 4+6*k
     36: __init -> f4 : arg1'=0, arg2'=-1/2*arg1P_1+arg2P_2-1/2*arg1P_1^2, arg3'=arg3P_3, [ arg1P_1>=arg2P_2 && -arg1P_1>=0 ], cost: 4-6*arg1P_1
     37: __init -> f4 : arg1'=-k_2*arg3P_3+arg1P_1+1/2*k_2^2-1/2*k_2, arg2'=k_2*arg3P_3+k_2*arg3P_3^2-1/2*k_2^2+1/3*k_2^3+arg2P_2+1/6*k_2-k_2^2*arg3P_3, arg3'=-k_2+arg3P_3, [ k_2>=0 && 1/2+arg1P_1-(-1+k_2)*arg3P_3-1/2*k_2+1/2*(-1+k_2)^2>=-1/6-(-1+k_2)^2*arg3P_3+(-1+k_2)*arg3P_3+arg2P_2+1/6*k_2+(-1+k_2)*arg3P_3^2-1/2*(-1+k_2)^2+1/3*(-1+k_2)^3 ], cost: 4+7*k_2

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: __init
     35: __init -> f4 : arg1'=k+arg1P_1, arg2'=k*arg1P_1+1/2*k+1/2*k^2+arg2P_2, arg3'=arg3P_3, [ -arg1P_1<=0 && k>=0 && -1+k+arg1P_1>=-1/2+1/2*k+arg2P_2+arg1P_1*(-1+k)+1/2*(-1+k)^2 ], cost: 4+6*k
     36: __init -> f4 : arg1'=0, arg2'=-1/2*arg1P_1+arg2P_2-1/2*arg1P_1^2, arg3'=arg3P_3, [ arg1P_1>=arg2P_2 && -arg1P_1>=0 ], cost: 4-6*arg1P_1
     37: __init -> f4 : arg1'=-k_2*arg3P_3+arg1P_1+1/2*k_2^2-1/2*k_2, arg2'=k_2*arg3P_3+k_2*arg3P_3^2-1/2*k_2^2+1/3*k_2^3+arg2P_2+1/6*k_2-k_2^2*arg3P_3, arg3'=-k_2+arg3P_3, [ k_2>=0 && 1/2+arg1P_1-(-1+k_2)*arg3P_3-1/2*k_2+1/2*(-1+k_2)^2>=-1/6-(-1+k_2)^2*arg3P_3+(-1+k_2)*arg3P_3+arg2P_2+1/6*k_2+(-1+k_2)*arg3P_3^2-1/2*(-1+k_2)^2+1/3*(-1+k_2)^3 ], cost: 4+7*k_2

Computing asymptotic complexity for rule 36
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 37
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 35
   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),?)