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, [ arg1==arg1P_1 && arg3==arg3P_1 ], cost: 1
      1: f2 -> f3 : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ arg1==arg1P_2 && arg2==arg2P_2 ], cost: 1
      4: f3 -> f4 : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ x14_1<0 && arg1==arg1P_5 && arg2==arg2P_5 && arg3==arg3P_5 ], cost: 1
      5: f3 -> f4 : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [ x43_1>0 && arg1==arg1P_6 && arg2==arg2P_6 && arg3==arg3P_6 ], cost: 1
      6: f3 -> f5 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [ x18_1==0 && arg1==arg1P_7 && arg2==arg2P_7 && arg3==arg3P_7 ], cost: 1
      2: f4 -> f7 : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ 1==arg1P_3 && arg2==arg2P_3 && arg3==arg3P_3 ], cost: 1
      7: f7 -> f6 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, [ arg1==arg1P_8 && arg2==arg2P_8 && arg3==arg3P_8 ], cost: 1
      3: f5 -> f8 : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ arg1P_4==-1 && arg2==arg2P_4 && arg3==arg3P_4 ], cost: 1
      8: f8 -> f6 : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, [ arg1==arg1P_9 && arg2==arg2P_9 && arg3==arg3P_9 ], cost: 1
     11: f6 -> f9 : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, [ arg2<100 && arg3<100 && arg1==arg1P_12 && arg2==arg2P_12 && arg3==arg3P_12 ], cost: 1
     13: f6 -> f12 : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, [ arg2>=100 && arg1==arg1P_14 && arg2==arg2P_14 && arg3==arg3P_14 ], cost: 1
     14: f6 -> f12 : arg1'=arg1P_15, arg2'=arg2P_15, arg3'=arg3P_15, [ arg3>=100 && arg1==arg1P_15 && arg2==arg2P_15 && arg3==arg3P_15 ], cost: 1
      9: f9 -> f10 : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, [ arg2P_10==arg2+arg1 && arg1==arg1P_10 && arg3==arg3P_10 ], cost: 1
     10: f10 -> f11 : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, [ arg3P_11==arg3-arg1 && arg1==arg1P_11 && arg2==arg2P_11 ], cost: 1
     12: f11 -> f6 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, [ arg1==arg1P_13 && arg2==arg2P_13 && arg3==arg3P_13 ], 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, [ arg1==arg1P_1 && arg3==arg3P_1 ], cost: 1
      1: f2 -> f3 : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ arg1==arg1P_2 && arg2==arg2P_2 ], cost: 1
      4: f3 -> f4 : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ x14_1<0 && arg1==arg1P_5 && arg2==arg2P_5 && arg3==arg3P_5 ], cost: 1
      5: f3 -> f4 : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [ x43_1>0 && arg1==arg1P_6 && arg2==arg2P_6 && arg3==arg3P_6 ], cost: 1
      6: f3 -> f5 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [ x18_1==0 && arg1==arg1P_7 && arg2==arg2P_7 && arg3==arg3P_7 ], cost: 1
      2: f4 -> f7 : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ 1==arg1P_3 && arg2==arg2P_3 && arg3==arg3P_3 ], cost: 1
      7: f7 -> f6 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, [ arg1==arg1P_8 && arg2==arg2P_8 && arg3==arg3P_8 ], cost: 1
      3: f5 -> f8 : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ arg1P_4==-1 && arg2==arg2P_4 && arg3==arg3P_4 ], cost: 1
      8: f8 -> f6 : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, [ arg1==arg1P_9 && arg2==arg2P_9 && arg3==arg3P_9 ], cost: 1
     11: f6 -> f9 : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, [ arg2<100 && arg3<100 && arg1==arg1P_12 && arg2==arg2P_12 && arg3==arg3P_12 ], cost: 1
      9: f9 -> f10 : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, [ arg2P_10==arg2+arg1 && arg1==arg1P_10 && arg3==arg3P_10 ], cost: 1
     10: f10 -> f11 : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, [ arg3P_11==arg3-arg1 && arg1==arg1P_11 && arg2==arg2P_11 ], cost: 1
     12: f11 -> f6 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, [ arg1==arg1P_13 && arg2==arg2P_13 && arg3==arg3P_13 ], 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 : arg2'=arg2P_1, [], cost: 1
      1: f2 -> f3 : arg3'=arg3P_2, [], cost: 1
      5: f3 -> f4 : [], cost: 1
      6: f3 -> f5 : [], cost: 1
      2: f4 -> f7 : arg1'=1, [], cost: 1
      7: f7 -> f6 : [], cost: 1
      3: f5 -> f8 : arg1'=-1, [], cost: 1
      8: f8 -> f6 : [], cost: 1
     11: f6 -> f9 : [ arg2<100 && arg3<100 ], cost: 1
      9: f9 -> f10 : arg2'=arg2+arg1, [], cost: 1
     10: f10 -> f11 : arg3'=arg3-arg1, [], cost: 1
     12: f11 -> f6 : [], 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
     20: f3 -> f6 : arg1'=1, [], cost: 3
     21: f3 -> f6 : arg1'=-1, [], cost: 3
     24: f6 -> f6 : arg2'=arg2+arg1, arg3'=arg3-arg1, [ arg2<100 && arg3<100 ], cost: 4
     17: __init -> f3 : arg1'=arg1P_16, arg2'=arg2P_1, arg3'=arg3P_2, [], cost: 3

Accelerating simple loops of location 7.
   Accelerating the following rules:
     24: f6 -> f6 : arg2'=arg2+arg1, arg3'=arg3-arg1, [ arg2<100 && arg3<100 ], cost: 4

   Accelerated rule 24 with non-termination, yielding the new rule 25.
[accelerate] Nesting with 0 inner and 1 outer candidates

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     20: f3 -> f6 : arg1'=1, [], cost: 3
     21: f3 -> f6 : arg1'=-1, [], cost: 3
     24: f6 -> f6 : arg2'=arg2+arg1, arg3'=arg3-arg1, [ arg2<100 && arg3<100 ], cost: 4
     25: f6 -> [13] : [ arg2==99 && arg3==99 && arg1==0 ], cost: NONTERM
     17: __init -> f3 : arg1'=arg1P_16, arg2'=arg2P_1, arg3'=arg3P_2, [], cost: 3

Chained accelerated rules (with incoming rules):
   Start location: __init
     20: f3 -> f6 : arg1'=1, [], cost: 3
     21: f3 -> f6 : arg1'=-1, [], cost: 3
     26: f3 -> f6 : arg1'=1, arg2'=1+arg2, arg3'=-1+arg3, [ arg2<100 && arg3<100 ], cost: 7
     27: f3 -> f6 : arg1'=-1, arg2'=-1+arg2, arg3'=1+arg3, [ arg2<100 && arg3<100 ], cost: 7
     17: __init -> f3 : arg1'=arg1P_16, arg2'=arg2P_1, arg3'=arg3P_2, [], cost: 3

Removed unreachable locations (and leaf rules with constant cost):
   Start location: __init
     <empty>

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: __init
     <empty>

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),?)