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
     22: f3 -> f4 : arg1'=arg1P_23, arg2'=arg2P_23, [ arg1<0 && arg2>0 && arg1==arg1P_23 && arg2==arg2P_23 ], cost: 1
     23: f3 -> f4 : arg1'=arg1P_24, arg2'=arg2P_24, [ arg1>0 && arg2>0 && arg1==arg1P_24 && arg2==arg2P_24 ], cost: 1
     25: f3 -> f20 : arg1'=arg1P_26, arg2'=arg2P_26, [ arg1==0 && arg1==arg1P_26 && arg2==arg2P_26 ], cost: 1
     26: f3 -> f20 : arg1'=arg1P_27, arg2'=arg2P_27, [ arg2<=0 && arg1==arg1P_27 && arg2==arg2P_27 ], cost: 1
      2: f8 -> f11 : arg1'=arg1P_3, arg2'=arg2P_3, [ arg1P_3==-1+arg1 && arg2==arg2P_3 ], cost: 1
      3: f11 -> f12 : arg1'=arg1P_4, arg2'=arg2P_4, [ arg1==arg1P_4 ], cost: 1
      8: f12 -> f10 : arg1'=arg1P_9, arg2'=arg2P_9, [ arg1==arg1P_9 && arg2==arg2P_9 ], cost: 1
      4: f9 -> f13 : arg1'=arg1P_5, arg2'=arg2P_5, [ arg2P_5==-1+arg2 && arg1==arg1P_5 ], cost: 1
      9: f13 -> f10 : arg1'=arg1P_10, arg2'=arg2P_10, [ arg1==arg1P_10 && arg2==arg2P_10 ], cost: 1
      5: f5 -> f8 : arg1'=arg1P_6, arg2'=arg2P_6, [ x13_1<0 && arg1==arg1P_6 && arg2==arg2P_6 ], cost: 1
      6: f5 -> f8 : arg1'=arg1P_7, arg2'=arg2P_7, [ x57_1>0 && arg1==arg1P_7 && arg2==arg2P_7 ], cost: 1
      7: f5 -> f9 : arg1'=arg1P_8, arg2'=arg2P_8, [ x16_1==0 && arg1==arg1P_8 && arg2==arg2P_8 ], cost: 1
     20: f10 -> f7 : arg1'=arg1P_21, arg2'=arg2P_21, [ arg1==arg1P_21 && arg2==arg2P_21 ], cost: 1
     10: f14 -> f17 : arg1'=arg1P_11, arg2'=arg2P_11, [ arg1P_11==1+arg1 && arg2==arg2P_11 ], cost: 1
     16: f17 -> f16 : arg1'=arg1P_17, arg2'=arg2P_17, [ arg1==arg1P_17 && arg2==arg2P_17 ], cost: 1
     11: f15 -> f18 : arg1'=arg1P_12, arg2'=arg2P_12, [ arg2P_12==-1+arg2 && arg1==arg1P_12 ], cost: 1
     12: f18 -> f19 : arg1'=arg1P_13, arg2'=arg2P_13, [ arg2==arg2P_13 ], cost: 1
     17: f19 -> f16 : arg1'=arg1P_18, arg2'=arg2P_18, [ arg1==arg1P_18 && arg2==arg2P_18 ], cost: 1
     13: f6 -> f14 : arg1'=arg1P_14, arg2'=arg2P_14, [ x30_1<0 && arg1==arg1P_14 && arg2==arg2P_14 ], cost: 1
     14: f6 -> f14 : arg1'=arg1P_15, arg2'=arg2P_15, [ x66_1>0 && arg1==arg1P_15 && arg2==arg2P_15 ], cost: 1
     15: f6 -> f15 : arg1'=arg1P_16, arg2'=arg2P_16, [ x33_1==0 && arg1==arg1P_16 && arg2==arg2P_16 ], cost: 1
     21: f16 -> f7 : arg1'=arg1P_22, arg2'=arg2P_22, [ arg1==arg1P_22 && arg2==arg2P_22 ], cost: 1
     18: f4 -> f5 : arg1'=arg1P_19, arg2'=arg2P_19, [ arg1>0 && arg1==arg1P_19 && arg2==arg2P_19 ], cost: 1
     19: f4 -> f6 : arg1'=arg1P_20, arg2'=arg2P_20, [ arg1<=0 && arg1==arg1P_20 && arg2==arg2P_20 ], cost: 1
     24: f7 -> f3 : arg1'=arg1P_25, arg2'=arg2P_25, [ arg1==arg1P_25 && arg2==arg2P_25 ], cost: 1
     27: __init -> f1 : arg1'=arg1P_28, arg2'=arg2P_28, [], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
     27: __init -> f1 : arg1'=arg1P_28, arg2'=arg2P_28, [], 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
     22: f3 -> f4 : arg1'=arg1P_23, arg2'=arg2P_23, [ arg1<0 && arg2>0 && arg1==arg1P_23 && arg2==arg2P_23 ], cost: 1
     23: f3 -> f4 : arg1'=arg1P_24, arg2'=arg2P_24, [ arg1>0 && arg2>0 && arg1==arg1P_24 && arg2==arg2P_24 ], cost: 1
      2: f8 -> f11 : arg1'=arg1P_3, arg2'=arg2P_3, [ arg1P_3==-1+arg1 && arg2==arg2P_3 ], cost: 1
      3: f11 -> f12 : arg1'=arg1P_4, arg2'=arg2P_4, [ arg1==arg1P_4 ], cost: 1
      8: f12 -> f10 : arg1'=arg1P_9, arg2'=arg2P_9, [ arg1==arg1P_9 && arg2==arg2P_9 ], cost: 1
      4: f9 -> f13 : arg1'=arg1P_5, arg2'=arg2P_5, [ arg2P_5==-1+arg2 && arg1==arg1P_5 ], cost: 1
      9: f13 -> f10 : arg1'=arg1P_10, arg2'=arg2P_10, [ arg1==arg1P_10 && arg2==arg2P_10 ], cost: 1
      5: f5 -> f8 : arg1'=arg1P_6, arg2'=arg2P_6, [ x13_1<0 && arg1==arg1P_6 && arg2==arg2P_6 ], cost: 1
      6: f5 -> f8 : arg1'=arg1P_7, arg2'=arg2P_7, [ x57_1>0 && arg1==arg1P_7 && arg2==arg2P_7 ], cost: 1
      7: f5 -> f9 : arg1'=arg1P_8, arg2'=arg2P_8, [ x16_1==0 && arg1==arg1P_8 && arg2==arg2P_8 ], cost: 1
     20: f10 -> f7 : arg1'=arg1P_21, arg2'=arg2P_21, [ arg1==arg1P_21 && arg2==arg2P_21 ], cost: 1
     10: f14 -> f17 : arg1'=arg1P_11, arg2'=arg2P_11, [ arg1P_11==1+arg1 && arg2==arg2P_11 ], cost: 1
     16: f17 -> f16 : arg1'=arg1P_17, arg2'=arg2P_17, [ arg1==arg1P_17 && arg2==arg2P_17 ], cost: 1
     11: f15 -> f18 : arg1'=arg1P_12, arg2'=arg2P_12, [ arg2P_12==-1+arg2 && arg1==arg1P_12 ], cost: 1
     12: f18 -> f19 : arg1'=arg1P_13, arg2'=arg2P_13, [ arg2==arg2P_13 ], cost: 1
     17: f19 -> f16 : arg1'=arg1P_18, arg2'=arg2P_18, [ arg1==arg1P_18 && arg2==arg2P_18 ], cost: 1
     13: f6 -> f14 : arg1'=arg1P_14, arg2'=arg2P_14, [ x30_1<0 && arg1==arg1P_14 && arg2==arg2P_14 ], cost: 1
     14: f6 -> f14 : arg1'=arg1P_15, arg2'=arg2P_15, [ x66_1>0 && arg1==arg1P_15 && arg2==arg2P_15 ], cost: 1
     15: f6 -> f15 : arg1'=arg1P_16, arg2'=arg2P_16, [ x33_1==0 && arg1==arg1P_16 && arg2==arg2P_16 ], cost: 1
     21: f16 -> f7 : arg1'=arg1P_22, arg2'=arg2P_22, [ arg1==arg1P_22 && arg2==arg2P_22 ], cost: 1
     18: f4 -> f5 : arg1'=arg1P_19, arg2'=arg2P_19, [ arg1>0 && arg1==arg1P_19 && arg2==arg2P_19 ], cost: 1
     19: f4 -> f6 : arg1'=arg1P_20, arg2'=arg2P_20, [ arg1<=0 && arg1==arg1P_20 && arg2==arg2P_20 ], cost: 1
     24: f7 -> f3 : arg1'=arg1P_25, arg2'=arg2P_25, [ arg1==arg1P_25 && arg2==arg2P_25 ], cost: 1
     27: __init -> f1 : arg1'=arg1P_28, arg2'=arg2P_28, [], 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
     22: f3 -> f4 : [ arg1<0 && arg2>0 ], cost: 1
     23: f3 -> f4 : [ arg1>0 && arg2>0 ], cost: 1
      2: f8 -> f11 : arg1'=-1+arg1, [], cost: 1
      3: f11 -> f12 : arg2'=arg2P_4, [], cost: 1
      8: f12 -> f10 : [], cost: 1
      4: f9 -> f13 : arg2'=-1+arg2, [], cost: 1
      9: f13 -> f10 : [], cost: 1
      6: f5 -> f8 : [], cost: 1
      7: f5 -> f9 : [], cost: 1
     20: f10 -> f7 : [], cost: 1
     10: f14 -> f17 : arg1'=1+arg1, [], cost: 1
     16: f17 -> f16 : [], cost: 1
     11: f15 -> f18 : arg2'=-1+arg2, [], cost: 1
     12: f18 -> f19 : arg1'=arg1P_13, [], cost: 1
     17: f19 -> f16 : [], cost: 1
     14: f6 -> f14 : [], cost: 1
     15: f6 -> f15 : [], cost: 1
     21: f16 -> f7 : [], cost: 1
     18: f4 -> f5 : [ arg1>0 ], cost: 1
     19: f4 -> f6 : [ arg1<=0 ], cost: 1
     24: f7 -> f3 : [], cost: 1
     27: __init -> f1 : arg1'=arg1P_28, arg2'=arg2P_28, [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: __init
     22: f3 -> f4 : [ arg1<0 && arg2>0 ], cost: 1
     23: f3 -> f4 : [ arg1>0 && arg2>0 ], cost: 1
     33: f5 -> f10 : arg2'=-1+arg2, [], cost: 3
     34: f5 -> f10 : arg1'=-1+arg1, arg2'=arg2P_4, [], cost: 4
     20: f10 -> f7 : [], cost: 1
     37: f6 -> f16 : arg1'=1+arg1, [], cost: 3
     39: f6 -> f16 : arg1'=arg1P_13, arg2'=-1+arg2, [], cost: 4
     21: f16 -> f7 : [], cost: 1
     18: f4 -> f5 : [ arg1>0 ], cost: 1
     19: f4 -> f6 : [ arg1<=0 ], cost: 1
     24: f7 -> f3 : [], cost: 1
     29: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, [], cost: 3

Eliminated locations (on tree-shaped paths):
   Start location: __init
     40: f3 -> f6 : [ arg1<0 && arg2>0 ], cost: 2
     41: f3 -> f5 : [ arg1>0 && arg2>0 ], cost: 2
     42: f5 -> f7 : arg2'=-1+arg2, [], cost: 4
     43: f5 -> f7 : arg1'=-1+arg1, arg2'=arg2P_4, [], cost: 5
     44: f6 -> f7 : arg1'=1+arg1, [], cost: 4
     45: f6 -> f7 : arg1'=arg1P_13, arg2'=-1+arg2, [], cost: 5
     24: f7 -> f3 : [], cost: 1
     29: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, [], cost: 3

Eliminated locations (on tree-shaped paths):
   Start location: __init
     46: f3 -> f7 : arg2'=-1+arg2, [ arg1>0 && arg2>0 ], cost: 6
     47: f3 -> f7 : arg1'=-1+arg1, arg2'=arg2P_4, [ arg1>0 && arg2>0 ], cost: 7
     48: f3 -> f7 : arg1'=1+arg1, [ arg1<0 && arg2>0 ], cost: 6
     49: f3 -> f7 : arg1'=arg1P_13, arg2'=-1+arg2, [ arg1<0 && arg2>0 ], cost: 7
     24: f7 -> f3 : [], cost: 1
     29: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, [], cost: 3

Eliminated locations (on tree-shaped paths):
   Start location: __init
     50: f3 -> f3 : arg2'=-1+arg2, [ arg1>0 && arg2>0 ], cost: 7
     51: f3 -> f3 : arg1'=-1+arg1, arg2'=arg2P_4, [ arg1>0 && arg2>0 ], cost: 8
     52: f3 -> f3 : arg1'=1+arg1, [ arg1<0 && arg2>0 ], cost: 7
     53: f3 -> f3 : arg1'=arg1P_13, arg2'=-1+arg2, [ arg1<0 && arg2>0 ], cost: 8
     29: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, [], cost: 3

Accelerating simple loops of location 2.
   Accelerating the following rules:
     50: f3 -> f3 : arg2'=-1+arg2, [ arg1>0 && arg2>0 ], cost: 7
     51: f3 -> f3 : arg1'=-1+arg1, arg2'=arg2P_4, [ arg1>0 && arg2>0 ], cost: 8
     52: f3 -> f3 : arg1'=1+arg1, [ arg1<0 && arg2>0 ], cost: 7
     53: f3 -> f3 : arg1'=arg1P_13, arg2'=-1+arg2, [ arg1<0 && arg2>0 ], cost: 8

   Accelerated rule 50 with backward acceleration, yielding the new rule 54.
[test] deduced pseudo-invariant -arg2+arg2P_4<=0, also trying arg2-arg2P_4<=-1
   Accelerated rule 51 with backward acceleration, yielding the new rule 55.
   Accelerated rule 52 with backward acceleration, yielding the new rule 56.
[test] deduced pseudo-invariant -arg1P_13+arg1<=0, also trying arg1P_13-arg1<=-1
   Accelerated rule 53 with backward acceleration, yielding the new rule 57.
[accelerate] Nesting with 4 inner and 4 outer candidates
   Removing the simple loops: 50 52.

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     51: f3 -> f3 : arg1'=-1+arg1, arg2'=arg2P_4, [ arg1>0 && arg2>0 ], cost: 8
     53: f3 -> f3 : arg1'=arg1P_13, arg2'=-1+arg2, [ arg1<0 && arg2>0 ], cost: 8
     54: f3 -> f3 : arg2'=0, [ arg1>0 && arg2>=0 ], cost: 7*arg2
     55: f3 -> f3 : arg1'=0, arg2'=arg2P_4, [ -arg2+arg2P_4<=0 && arg1>=1 && arg2P_4>0 ], cost: 8*arg1
     56: f3 -> f3 : arg1'=0, [ arg2>0 && -arg1>=0 ], cost: -7*arg1
     57: f3 -> f3 : arg1'=arg1P_13, arg2'=0, [ -arg1P_13+arg1<=0 && arg2>=1 && arg1P_13<0 ], cost: 8*arg2
     29: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, [], cost: 3

Chained accelerated rules (with incoming rules):
   Start location: __init
     29: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, [], cost: 3
     58: __init -> f3 : arg1'=-1+arg1P_1, arg2'=arg2P_4, [ arg1P_1>0 ], cost: 11
     59: __init -> f3 : arg1'=arg1P_13, arg2'=-1+arg2P_2, [ arg2P_2>0 ], cost: 11
     60: __init -> f3 : arg1'=arg1P_1, arg2'=0, [ arg1P_1>0 && arg2P_2>=0 ], cost: 3+7*arg2P_2
     61: __init -> f3 : arg1'=0, arg2'=arg2P_4, [ arg1P_1>=1 && arg2P_4>0 ], cost: 3+8*arg1P_1
     62: __init -> f3 : arg1'=0, arg2'=arg2P_2, [ arg2P_2>0 && -arg1P_1>=0 ], cost: 3-7*arg1P_1
     63: __init -> f3 : arg1'=arg1P_13, arg2'=0, [ arg2P_2>=1 && arg1P_13<0 ], cost: 3+8*arg2P_2

Removed unreachable locations (and leaf rules with constant cost):
   Start location: __init
     60: __init -> f3 : arg1'=arg1P_1, arg2'=0, [ arg1P_1>0 && arg2P_2>=0 ], cost: 3+7*arg2P_2
     61: __init -> f3 : arg1'=0, arg2'=arg2P_4, [ arg1P_1>=1 && arg2P_4>0 ], cost: 3+8*arg1P_1
     62: __init -> f3 : arg1'=0, arg2'=arg2P_2, [ arg2P_2>0 && -arg1P_1>=0 ], cost: 3-7*arg1P_1
     63: __init -> f3 : arg1'=arg1P_13, arg2'=0, [ arg2P_2>=1 && arg1P_13<0 ], cost: 3+8*arg2P_2

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: __init
     60: __init -> f3 : arg1'=arg1P_1, arg2'=0, [ arg1P_1>0 && arg2P_2>=0 ], cost: 3+7*arg2P_2
     61: __init -> f3 : arg1'=0, arg2'=arg2P_4, [ arg1P_1>=1 && arg2P_4>0 ], cost: 3+8*arg1P_1
     62: __init -> f3 : arg1'=0, arg2'=arg2P_2, [ arg2P_2>0 && -arg1P_1>=0 ], cost: 3-7*arg1P_1
     63: __init -> f3 : arg1'=arg1P_13, arg2'=0, [ arg2P_2>=1 && arg1P_13<0 ], cost: 3+8*arg2P_2

Computing asymptotic complexity for rule 60
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 61
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 62
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 63
   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),?)