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, [ arg2==arg2P_1 ], cost: 1
      1: f2 -> f3 : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1==arg1P_2 ], cost: 1
     12: f3 -> f4 : arg1'=arg1P_13, arg2'=arg2P_13, [ arg1>=2 && arg1==arg1P_13 && arg2==arg2P_13 ], cost: 1
     14: f3 -> f12 : arg1'=arg1P_15, arg2'=arg2P_15, [ arg1<2 && arg1==arg1P_15 && arg2==arg2P_15 ], cost: 1
      2: f4 -> f5 : arg1'=arg1P_3, arg2'=arg2P_3, [ arg1P_3==-1+arg1 && arg2==arg2P_3 ], cost: 1
      3: f5 -> f6 : arg1'=arg1P_4, arg2'=arg2P_4, [ arg2P_4==arg2+arg1 && arg1==arg1P_4 ], cost: 1
      5: f6 -> f7 : arg1'=arg1P_6, arg2'=arg2P_6, [ arg2>=arg1 && x12_1<0 && arg1==arg1P_6 && arg2==arg2P_6 ], cost: 1
      6: f6 -> f7 : arg1'=arg1P_7, arg2'=arg2P_7, [ arg2>=arg1 && x36_1>0 && arg1==arg1P_7 && arg2==arg2P_7 ], cost: 1
      8: f6 -> f9 : arg1'=arg1P_9, arg2'=arg2P_9, [ arg2<arg1 && arg1==arg1P_9 && arg2==arg2P_9 ], cost: 1
      9: f6 -> f9 : arg1'=arg1P_10, arg2'=arg2P_10, [ x39_1==0 && arg1==arg1P_10 && arg2==arg2P_10 ], cost: 1
      4: f7 -> f8 : arg1'=arg1P_5, arg2'=arg2P_5, [ arg2P_5==-1+arg2 && arg1==arg1P_5 ], cost: 1
      7: f8 -> f6 : arg1'=arg1P_8, arg2'=arg2P_8, [ arg1==arg1P_8 && arg2==arg2P_8 ], cost: 1
     10: f9 -> f10 : arg1'=arg1P_11, arg2'=arg2P_11, [ arg1P_11==-1+arg1 && arg2==arg2P_11 ], cost: 1
     11: f10 -> f11 : arg1'=arg1P_12, arg2'=arg2P_12, [ arg2P_12==arg2-arg1 && arg1==arg1P_12 ], cost: 1
     13: f11 -> f3 : arg1'=arg1P_14, arg2'=arg2P_14, [ arg1==arg1P_14 && arg2==arg2P_14 ], cost: 1
     15: __init -> f1 : arg1'=arg1P_16, arg2'=arg2P_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, [], cost: 1

Removed unreachable and leaf rules:
   Start location: __init
      0: f1 -> f2 : arg1'=arg1P_1, arg2'=arg2P_1, [ arg2==arg2P_1 ], cost: 1
      1: f2 -> f3 : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1==arg1P_2 ], cost: 1
     12: f3 -> f4 : arg1'=arg1P_13, arg2'=arg2P_13, [ arg1>=2 && arg1==arg1P_13 && arg2==arg2P_13 ], cost: 1
      2: f4 -> f5 : arg1'=arg1P_3, arg2'=arg2P_3, [ arg1P_3==-1+arg1 && arg2==arg2P_3 ], cost: 1
      3: f5 -> f6 : arg1'=arg1P_4, arg2'=arg2P_4, [ arg2P_4==arg2+arg1 && arg1==arg1P_4 ], cost: 1
      5: f6 -> f7 : arg1'=arg1P_6, arg2'=arg2P_6, [ arg2>=arg1 && x12_1<0 && arg1==arg1P_6 && arg2==arg2P_6 ], cost: 1
      6: f6 -> f7 : arg1'=arg1P_7, arg2'=arg2P_7, [ arg2>=arg1 && x36_1>0 && arg1==arg1P_7 && arg2==arg2P_7 ], cost: 1
      8: f6 -> f9 : arg1'=arg1P_9, arg2'=arg2P_9, [ arg2<arg1 && arg1==arg1P_9 && arg2==arg2P_9 ], cost: 1
      9: f6 -> f9 : arg1'=arg1P_10, arg2'=arg2P_10, [ x39_1==0 && arg1==arg1P_10 && arg2==arg2P_10 ], cost: 1
      4: f7 -> f8 : arg1'=arg1P_5, arg2'=arg2P_5, [ arg2P_5==-1+arg2 && arg1==arg1P_5 ], cost: 1
      7: f8 -> f6 : arg1'=arg1P_8, arg2'=arg2P_8, [ arg1==arg1P_8 && arg2==arg2P_8 ], cost: 1
     10: f9 -> f10 : arg1'=arg1P_11, arg2'=arg2P_11, [ arg1P_11==-1+arg1 && arg2==arg2P_11 ], cost: 1
     11: f10 -> f11 : arg1'=arg1P_12, arg2'=arg2P_12, [ arg2P_12==arg2-arg1 && arg1==arg1P_12 ], cost: 1
     13: f11 -> f3 : arg1'=arg1P_14, arg2'=arg2P_14, [ arg1==arg1P_14 && arg2==arg2P_14 ], cost: 1
     15: __init -> f1 : arg1'=arg1P_16, arg2'=arg2P_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
     12: f3 -> f4 : [ arg1>=2 ], cost: 1
      2: f4 -> f5 : arg1'=-1+arg1, [], cost: 1
      3: f5 -> f6 : arg2'=arg2+arg1, [], cost: 1
      6: f6 -> f7 : [ arg2>=arg1 ], cost: 1
      8: f6 -> f9 : [ arg2<arg1 ], cost: 1
      9: f6 -> f9 : [], cost: 1
      4: f7 -> f8 : arg2'=-1+arg2, [], cost: 1
      7: f8 -> f6 : [], cost: 1
     10: f9 -> f10 : arg1'=-1+arg1, [], cost: 1
     11: f10 -> f11 : arg2'=arg2-arg1, [], cost: 1
     13: f11 -> f3 : [], cost: 1
     15: __init -> f1 : arg1'=arg1P_16, arg2'=arg2P_16, [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: __init
     19: f3 -> f6 : arg1'=-1+arg1, arg2'=-1+arg2+arg1, [ arg1>=2 ], cost: 3
      8: f6 -> f9 : [ arg2<arg1 ], cost: 1
      9: f6 -> f9 : [], cost: 1
     21: f6 -> f6 : arg2'=-1+arg2, [ arg2>=arg1 ], cost: 3
     23: f9 -> f3 : arg1'=-1+arg1, arg2'=1+arg2-arg1, [], cost: 3
     17: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, [], cost: 3

Accelerating simple loops of location 5.
   Accelerating the following rules:
     21: f6 -> f6 : arg2'=-1+arg2, [ arg2>=arg1 ], 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 : arg1'=-1+arg1, arg2'=-1+arg2+arg1, [ arg1>=2 ], cost: 3
      8: f6 -> f9 : [ arg2<arg1 ], cost: 1
      9: f6 -> f9 : [], cost: 1
     24: f6 -> f6 : arg2'=-1+arg1, [ 1+arg2-arg1>=0 ], cost: 3+3*arg2-3*arg1
     23: f9 -> f3 : arg1'=-1+arg1, arg2'=1+arg2-arg1, [], cost: 3
     17: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, [], cost: 3

Chained accelerated rules (with incoming rules):
   Start location: __init
     19: f3 -> f6 : arg1'=-1+arg1, arg2'=-1+arg2+arg1, [ arg1>=2 ], cost: 3
     25: f3 -> f6 : arg1'=-1+arg1, arg2'=-2+arg1, [ arg1>=2 && 1+arg2>=0 ], cost: 6+3*arg2
      8: f6 -> f9 : [ arg2<arg1 ], cost: 1
      9: f6 -> f9 : [], cost: 1
     23: f9 -> f3 : arg1'=-1+arg1, arg2'=1+arg2-arg1, [], cost: 3
     17: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, [], cost: 3

Eliminated locations (on tree-shaped paths):
   Start location: __init
     26: f3 -> f9 : arg1'=-1+arg1, arg2'=-1+arg2+arg1, [ arg1>=2 && -1+arg2+arg1<-1+arg1 ], cost: 4
     27: f3 -> f9 : arg1'=-1+arg1, arg2'=-1+arg2+arg1, [ arg1>=2 ], cost: 4
     28: f3 -> f9 : arg1'=-1+arg1, arg2'=-2+arg1, [ arg1>=2 && 1+arg2>=0 ], cost: 7+3*arg2
     29: f3 -> f9 : arg1'=-1+arg1, arg2'=-2+arg1, [ arg1>=2 && 1+arg2>=0 ], cost: 7+3*arg2
     23: f9 -> f3 : arg1'=-1+arg1, arg2'=1+arg2-arg1, [], cost: 3
     17: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, [], cost: 3

Merged rules:
   Start location: __init
     30: f3 -> f9 : arg1'=-1+arg1, arg2'=-1+arg2+arg1, [ arg1>=2 ], cost: 4
     31: f3 -> f9 : arg1'=-1+arg1, arg2'=-2+arg1, [ arg1>=2 && 1+arg2>=0 ], cost: 7+3*arg2
     23: f9 -> f3 : arg1'=-1+arg1, arg2'=1+arg2-arg1, [], cost: 3
     17: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, [], cost: 3

Eliminated locations (on tree-shaped paths):
   Start location: __init
     32: f3 -> f3 : arg1'=-2+arg1, arg2'=1+arg2, [ arg1>=2 ], cost: 7
     33: f3 -> f3 : arg1'=-2+arg1, arg2'=0, [ arg1>=2 && 1+arg2>=0 ], cost: 10+3*arg2
     17: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, [], cost: 3

Accelerating simple loops of location 2.
   Accelerating the following rules:
     32: f3 -> f3 : arg1'=-2+arg1, arg2'=1+arg2, [ arg1>=2 ], cost: 7
     33: f3 -> f3 : arg1'=-2+arg1, arg2'=0, [ arg1>=2 && 1+arg2>=0 ], cost: 10+3*arg2

   Accelerated rule 32 with backward acceleration, yielding the new rule 34.
   Accelerated rule 33 with backward acceleration, yielding the new rule 35.
[accelerate] Nesting with 2 inner and 2 outer candidates
   Removing the simple loops: 32 33.

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     34: f3 -> f3 : arg1'=-2*k_1+arg1, arg2'=k_1+arg2, [ k_1>=0 && 2-2*k_1+arg1>=2 ], cost: 7*k_1
     35: f3 -> f3 : arg1'=-2*k_2+arg1, arg2'=0, [ 1+arg2>=0 && k_2>=1 && 2-2*k_2+arg1>=2 ], cost: 10*k_2
     17: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, [], cost: 3

Chained accelerated rules (with incoming rules):
   Start location: __init
     17: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, [], cost: 3
     36: __init -> f3 : arg1'=arg1P_1-2*k_1, arg2'=arg2P_2+k_1, [ k_1>=0 && 2+arg1P_1-2*k_1>=2 ], cost: 3+7*k_1
     37: __init -> f3 : arg1'=arg1P_1-2*k_2, arg2'=0, [ k_2>=1 && 2+arg1P_1-2*k_2>=2 ], cost: 3+10*k_2

Removed unreachable locations (and leaf rules with constant cost):
   Start location: __init
     36: __init -> f3 : arg1'=arg1P_1-2*k_1, arg2'=arg2P_2+k_1, [ k_1>=0 && 2+arg1P_1-2*k_1>=2 ], cost: 3+7*k_1
     37: __init -> f3 : arg1'=arg1P_1-2*k_2, arg2'=0, [ k_2>=1 && 2+arg1P_1-2*k_2>=2 ], cost: 3+10*k_2

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: __init
     36: __init -> f3 : arg1'=arg1P_1-2*k_1, arg2'=arg2P_2+k_1, [ k_1>=0 && 2+arg1P_1-2*k_1>=2 ], cost: 3+7*k_1
     37: __init -> f3 : arg1'=arg1P_1-2*k_2, arg2'=0, [ k_2>=1 && 2+arg1P_1-2*k_2>=2 ], cost: 3+10*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

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),?)