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 && 0==arg2P_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
      2: f3 -> f4 : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg3==arg1P_3 && arg2==arg2P_3 && arg3==arg3P_3 ], cost: 1
     16: f4 -> f5 : arg1'=arg1P_17, arg2'=arg2P_17, arg3'=arg3P_17, [ arg1>=0 && arg2>=0 && arg1==arg1P_17 && arg2==arg2P_17 && arg3==arg3P_17 ], cost: 1
     18: f4 -> f14 : arg1'=arg1P_19, arg2'=arg2P_19, arg3'=arg3P_19, [ arg1<0 && arg1==arg1P_19 && arg2==arg2P_19 && arg3==arg3P_19 ], cost: 1
     19: f4 -> f14 : arg1'=arg1P_20, arg2'=arg2P_20, arg3'=arg3P_20, [ arg2<0 && arg1==arg1P_20 && arg2==arg2P_20 && arg3==arg3P_20 ], cost: 1
      3: f9 -> f10 : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ arg2P_4==1+arg2 && arg1==arg1P_4 && arg3==arg3P_4 ], cost: 1
      6: f10 -> f6 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [ arg1==arg1P_7 && arg2==arg2P_7 && arg3==arg3P_7 ], cost: 1
      4: f6 -> f9 : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ arg2<=arg3 && x14_1<0 && arg1==arg1P_5 && arg2==arg2P_5 && arg3==arg3P_5 ], cost: 1
      5: f6 -> f9 : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [ arg2<=arg3 && x54_1>0 && arg1==arg1P_6 && arg2==arg2P_6 && arg3==arg3P_6 ], cost: 1
      7: f6 -> f11 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, [ arg2>arg3 && arg1==arg1P_8 && arg2==arg2P_8 && arg3==arg3P_8 ], cost: 1
      8: f6 -> f11 : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, [ x58_1==0 && arg1==arg1P_9 && arg2==arg2P_9 && arg3==arg3P_9 ], cost: 1
      9: f11 -> f12 : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, [ arg1P_10==-1+arg1 && arg2==arg2P_10 && arg3==arg3P_10 ], cost: 1
     13: f12 -> f8 : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, [ arg1==arg1P_14 && arg2==arg2P_14 && arg3==arg3P_14 ], cost: 1
     10: f5 -> f6 : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, [ x28_1<0 && arg1==arg1P_11 && arg2==arg2P_11 && arg3==arg3P_11 ], cost: 1
     11: f5 -> f6 : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, [ x66_1>0 && arg1==arg1P_12 && arg2==arg2P_12 && arg3==arg3P_12 ], cost: 1
     12: f5 -> f7 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, [ x32_1==0 && arg1==arg1P_13 && arg2==arg2P_13 && arg3==arg3P_13 ], cost: 1
     14: f7 -> f8 : arg1'=arg1P_15, arg2'=arg2P_15, arg3'=arg3P_15, [ arg1==arg1P_15 && arg2==arg2P_15 && arg3==arg3P_15 ], cost: 1
     15: f8 -> f13 : arg1'=arg1P_16, arg2'=arg2P_16, arg3'=arg3P_16, [ arg2P_16==-1+arg2 && arg1==arg1P_16 && arg3==arg3P_16 ], cost: 1
     17: f13 -> f4 : arg1'=arg1P_18, arg2'=arg2P_18, arg3'=arg3P_18, [ arg1==arg1P_18 && arg2==arg2P_18 && arg3==arg3P_18 ], cost: 1
     20: __init -> f1 : arg1'=arg1P_21, arg2'=arg2P_21, arg3'=arg3P_21, [], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
     20: __init -> f1 : arg1'=arg1P_21, arg2'=arg2P_21, arg3'=arg3P_21, [], 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 && 0==arg2P_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
      2: f3 -> f4 : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg3==arg1P_3 && arg2==arg2P_3 && arg3==arg3P_3 ], cost: 1
     16: f4 -> f5 : arg1'=arg1P_17, arg2'=arg2P_17, arg3'=arg3P_17, [ arg1>=0 && arg2>=0 && arg1==arg1P_17 && arg2==arg2P_17 && arg3==arg3P_17 ], cost: 1
      3: f9 -> f10 : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ arg2P_4==1+arg2 && arg1==arg1P_4 && arg3==arg3P_4 ], cost: 1
      6: f10 -> f6 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [ arg1==arg1P_7 && arg2==arg2P_7 && arg3==arg3P_7 ], cost: 1
      4: f6 -> f9 : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ arg2<=arg3 && x14_1<0 && arg1==arg1P_5 && arg2==arg2P_5 && arg3==arg3P_5 ], cost: 1
      5: f6 -> f9 : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [ arg2<=arg3 && x54_1>0 && arg1==arg1P_6 && arg2==arg2P_6 && arg3==arg3P_6 ], cost: 1
      7: f6 -> f11 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, [ arg2>arg3 && arg1==arg1P_8 && arg2==arg2P_8 && arg3==arg3P_8 ], cost: 1
      8: f6 -> f11 : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, [ x58_1==0 && arg1==arg1P_9 && arg2==arg2P_9 && arg3==arg3P_9 ], cost: 1
      9: f11 -> f12 : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, [ arg1P_10==-1+arg1 && arg2==arg2P_10 && arg3==arg3P_10 ], cost: 1
     13: f12 -> f8 : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, [ arg1==arg1P_14 && arg2==arg2P_14 && arg3==arg3P_14 ], cost: 1
     10: f5 -> f6 : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, [ x28_1<0 && arg1==arg1P_11 && arg2==arg2P_11 && arg3==arg3P_11 ], cost: 1
     11: f5 -> f6 : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, [ x66_1>0 && arg1==arg1P_12 && arg2==arg2P_12 && arg3==arg3P_12 ], cost: 1
     12: f5 -> f7 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, [ x32_1==0 && arg1==arg1P_13 && arg2==arg2P_13 && arg3==arg3P_13 ], cost: 1
     14: f7 -> f8 : arg1'=arg1P_15, arg2'=arg2P_15, arg3'=arg3P_15, [ arg1==arg1P_15 && arg2==arg2P_15 && arg3==arg3P_15 ], cost: 1
     15: f8 -> f13 : arg1'=arg1P_16, arg2'=arg2P_16, arg3'=arg3P_16, [ arg2P_16==-1+arg2 && arg1==arg1P_16 && arg3==arg3P_16 ], cost: 1
     17: f13 -> f4 : arg1'=arg1P_18, arg2'=arg2P_18, arg3'=arg3P_18, [ arg1==arg1P_18 && arg2==arg2P_18 && arg3==arg3P_18 ], cost: 1
     20: __init -> f1 : arg1'=arg1P_21, arg2'=arg2P_21, arg3'=arg3P_21, [], cost: 1

Simplified all rules, resulting in:
   Start location: __init
      0: f1 -> f2 : arg2'=0, [], cost: 1
      1: f2 -> f3 : arg3'=arg3P_2, [], cost: 1
      2: f3 -> f4 : arg1'=arg3, [], cost: 1
     16: f4 -> f5 : [ arg1>=0 && arg2>=0 ], cost: 1
      3: f9 -> f10 : arg2'=1+arg2, [], cost: 1
      6: f10 -> f6 : [], cost: 1
      5: f6 -> f9 : [ arg2<=arg3 ], cost: 1
      7: f6 -> f11 : [ arg2>arg3 ], cost: 1
      8: f6 -> f11 : [], cost: 1
      9: f11 -> f12 : arg1'=-1+arg1, [], cost: 1
     13: f12 -> f8 : [], cost: 1
     11: f5 -> f6 : [], cost: 1
     12: f5 -> f7 : [], cost: 1
     14: f7 -> f8 : [], cost: 1
     15: f8 -> f13 : arg2'=-1+arg2, [], cost: 1
     17: f13 -> f4 : [], cost: 1
     20: __init -> f1 : arg1'=arg1P_21, arg2'=arg2P_21, arg3'=arg3P_21, [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: __init
     16: f4 -> f5 : [ arg1>=0 && arg2>=0 ], cost: 1
      7: f6 -> f11 : [ arg2>arg3 ], cost: 1
      8: f6 -> f11 : [], cost: 1
     26: f6 -> f6 : arg2'=1+arg2, [ arg2<=arg3 ], cost: 3
     27: f11 -> f8 : arg1'=-1+arg1, [], cost: 2
     11: f5 -> f6 : [], cost: 1
     24: f5 -> f8 : [], cost: 2
     28: f8 -> f4 : arg2'=-1+arg2, [], cost: 2
     23: __init -> f4 : arg1'=arg3P_2, arg2'=0, arg3'=arg3P_2, [], cost: 4

Accelerating simple loops of location 6.
   Accelerating the following rules:
     26: f6 -> f6 : arg2'=1+arg2, [ arg2<=arg3 ], cost: 3

   Accelerated rule 26 with backward acceleration, yielding the new rule 29.
[accelerate] Nesting with 1 inner and 1 outer candidates
   Removing the simple loops: 26.

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     16: f4 -> f5 : [ arg1>=0 && arg2>=0 ], cost: 1
      7: f6 -> f11 : [ arg2>arg3 ], cost: 1
      8: f6 -> f11 : [], cost: 1
     29: f6 -> f6 : arg2'=1+arg3, [ 1-arg2+arg3>=0 ], cost: 3-3*arg2+3*arg3
     27: f11 -> f8 : arg1'=-1+arg1, [], cost: 2
     11: f5 -> f6 : [], cost: 1
     24: f5 -> f8 : [], cost: 2
     28: f8 -> f4 : arg2'=-1+arg2, [], cost: 2
     23: __init -> f4 : arg1'=arg3P_2, arg2'=0, arg3'=arg3P_2, [], cost: 4

Chained accelerated rules (with incoming rules):
   Start location: __init
     16: f4 -> f5 : [ arg1>=0 && arg2>=0 ], cost: 1
      7: f6 -> f11 : [ arg2>arg3 ], cost: 1
      8: f6 -> f11 : [], cost: 1
     27: f11 -> f8 : arg1'=-1+arg1, [], cost: 2
     11: f5 -> f6 : [], cost: 1
     24: f5 -> f8 : [], cost: 2
     30: f5 -> f6 : arg2'=1+arg3, [ 1-arg2+arg3>=0 ], cost: 4-3*arg2+3*arg3
     28: f8 -> f4 : arg2'=-1+arg2, [], cost: 2
     23: __init -> f4 : arg1'=arg3P_2, arg2'=0, arg3'=arg3P_2, [], cost: 4

Eliminated locations (on tree-shaped paths):
   Start location: __init
     31: f4 -> f6 : [ arg1>=0 && arg2>=0 ], cost: 2
     32: f4 -> f8 : [ arg1>=0 && arg2>=0 ], cost: 3
     33: f4 -> f6 : arg2'=1+arg3, [ arg1>=0 && arg2>=0 && 1-arg2+arg3>=0 ], cost: 5-3*arg2+3*arg3
     34: f6 -> f8 : arg1'=-1+arg1, [ arg2>arg3 ], cost: 3
     35: f6 -> f8 : arg1'=-1+arg1, [], cost: 3
     28: f8 -> f4 : arg2'=-1+arg2, [], cost: 2
     23: __init -> f4 : arg1'=arg3P_2, arg2'=0, arg3'=arg3P_2, [], cost: 4

Merged rules:
   Start location: __init
     31: f4 -> f6 : [ arg1>=0 && arg2>=0 ], cost: 2
     32: f4 -> f8 : [ arg1>=0 && arg2>=0 ], cost: 3
     33: f4 -> f6 : arg2'=1+arg3, [ arg1>=0 && arg2>=0 && 1-arg2+arg3>=0 ], cost: 5-3*arg2+3*arg3
     36: f6 -> f8 : arg1'=-1+arg1, [], cost: 3
     28: f8 -> f4 : arg2'=-1+arg2, [], cost: 2
     23: __init -> f4 : arg1'=arg3P_2, arg2'=0, arg3'=arg3P_2, [], cost: 4

Eliminated locations (on tree-shaped paths):
   Start location: __init
     39: f4 -> f4 : arg2'=-1+arg2, [ arg1>=0 && arg2>=0 ], cost: 5
     40: f4 -> f4 : arg1'=-1+arg1, arg2'=-1+arg2, [ arg1>=0 && arg2>=0 ], cost: 7
     41: f4 -> f4 : arg1'=-1+arg1, arg2'=arg3, [ arg1>=0 && arg2>=0 && 1-arg2+arg3>=0 ], cost: 10-3*arg2+3*arg3
     23: __init -> f4 : arg1'=arg3P_2, arg2'=0, arg3'=arg3P_2, [], cost: 4

Accelerating simple loops of location 3.
   Accelerating the following rules:
     39: f4 -> f4 : arg2'=-1+arg2, [ arg1>=0 && arg2>=0 ], cost: 5
     40: f4 -> f4 : arg1'=-1+arg1, arg2'=-1+arg2, [ arg1>=0 && arg2>=0 ], cost: 7
     41: f4 -> f4 : arg1'=-1+arg1, arg2'=arg3, [ arg1>=0 && arg2>=0 && 1-arg2+arg3>=0 ], cost: 10-3*arg2+3*arg3

   Accelerated rule 39 with backward acceleration, yielding the new rule 42.
   Accelerated rule 40 with backward acceleration, yielding the new rule 43.
   Accelerated rule 40 with backward acceleration, yielding the new rule 44.
[test] deduced pseudo-invariant -arg2+arg3<=0, also trying arg2-arg3<=-1
   Accelerated rule 41 with backward acceleration, yielding the new rule 45.
[accelerate] Nesting with 4 inner and 3 outer candidates
   Removing the simple loops: 39 40.

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     41: f4 -> f4 : arg1'=-1+arg1, arg2'=arg3, [ arg1>=0 && arg2>=0 && 1-arg2+arg3>=0 ], cost: 10-3*arg2+3*arg3
     42: f4 -> f4 : arg2'=-1, [ arg1>=0 && 1+arg2>=0 ], cost: 5+5*arg2
     43: f4 -> f4 : arg1'=-1, arg2'=-1+arg2-arg1, [ 1+arg1>=0 && arg2-arg1>=0 ], cost: 7+7*arg1
     44: f4 -> f4 : arg1'=-1-arg2+arg1, arg2'=-1, [ 1+arg2>=0 && -arg2+arg1>=0 ], cost: 7+7*arg2
     45: f4 -> f4 : arg1'=-1, arg2'=arg3, [ 1-arg2+arg3>=0 && -arg2+arg3<=0 && 1+arg1>=1 && arg3>=0 ], cost: 10+10*arg1
     23: __init -> f4 : arg1'=arg3P_2, arg2'=0, arg3'=arg3P_2, [], cost: 4

Chained accelerated rules (with incoming rules):
   Start location: __init
     23: __init -> f4 : arg1'=arg3P_2, arg2'=0, arg3'=arg3P_2, [], cost: 4
     46: __init -> f4 : arg1'=-1+arg3P_2, arg2'=arg3P_2, arg3'=arg3P_2, [ arg3P_2>=0 ], cost: 14+3*arg3P_2
     47: __init -> f4 : arg1'=arg3P_2, arg2'=-1, arg3'=arg3P_2, [ arg3P_2>=0 ], cost: 9
     48: __init -> f4 : arg1'=-1, arg2'=-1-arg3P_2, arg3'=arg3P_2, [ 1+arg3P_2>=0 && -arg3P_2>=0 ], cost: 11+7*arg3P_2
     49: __init -> f4 : arg1'=-1+arg3P_2, arg2'=-1, arg3'=arg3P_2, [ arg3P_2>=0 ], cost: 11
     50: __init -> f4 : arg1'=-1, arg2'=0, arg3'=0, [], cost: 14

Removed unreachable locations (and leaf rules with constant cost):
   Start location: __init
     46: __init -> f4 : arg1'=-1+arg3P_2, arg2'=arg3P_2, arg3'=arg3P_2, [ arg3P_2>=0 ], cost: 14+3*arg3P_2
     48: __init -> f4 : arg1'=-1, arg2'=-1-arg3P_2, arg3'=arg3P_2, [ 1+arg3P_2>=0 && -arg3P_2>=0 ], cost: 11+7*arg3P_2

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: __init
     46: __init -> f4 : arg1'=-1+arg3P_2, arg2'=arg3P_2, arg3'=arg3P_2, [ arg3P_2>=0 ], cost: 14+3*arg3P_2
     48: __init -> f4 : arg1'=-1, arg2'=-1-arg3P_2, arg3'=arg3P_2, [ 1+arg3P_2>=0 && -arg3P_2>=0 ], cost: 11+7*arg3P_2

Computing asymptotic complexity for rule 46
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 48
   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),?)