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
     17: f2 -> f3 : arg1'=arg1P_18, arg2'=arg2P_18, [ arg1>1 && arg1==arg1P_18 && arg2==arg2P_18 ], cost: 1
     19: f2 -> f16 : arg1'=arg1P_20, arg2'=arg2P_20, [ arg1<=1 && arg1==arg1P_20 && arg2==arg2P_20 ], cost: 1
      1: f3 -> f4 : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1==arg1P_2 && arg1==arg2P_2 ], cost: 1
      3: f4 -> f5 : arg1'=arg1P_4, arg2'=arg2P_4, [ arg2>1 && arg1==arg1P_4 && arg2==arg2P_4 ], cost: 1
      5: f4 -> f7 : arg1'=arg1P_6, arg2'=arg2P_6, [ arg2<=1 && arg1==arg1P_6 && arg2==arg2P_6 ], cost: 1
      2: f5 -> f6 : arg1'=arg1P_3, arg2'=arg2P_3, [ arg2P_3==-2+arg2 && arg1==arg1P_3 ], cost: 1
      4: f6 -> f4 : arg1'=arg1P_5, arg2'=arg2P_5, [ arg1==arg1P_5 && arg2==arg2P_5 ], cost: 1
     12: f7 -> f8 : arg1'=arg1P_13, arg2'=arg2P_13, [ arg2==0 && arg1==arg1P_13 && arg2==arg2P_13 ], cost: 1
     13: f7 -> f9 : arg1'=arg1P_14, arg2'=arg2P_14, [ arg2<0 && arg1==arg1P_14 && arg2==arg2P_14 ], cost: 1
     14: f7 -> f9 : arg1'=arg1P_15, arg2'=arg2P_15, [ arg2>0 && arg1==arg1P_15 && arg2==arg2P_15 ], cost: 1
      6: f11 -> f12 : arg1'=arg1P_7, arg2'=arg2P_7, [ arg2P_7==1+arg2 && arg1==arg1P_7 ], cost: 1
      8: f12 -> f8 : arg1'=arg1P_9, arg2'=arg2P_9, [ arg1==arg1P_9 && arg2==arg2P_9 ], cost: 1
      7: f8 -> f11 : arg1'=arg1P_8, arg2'=arg2P_8, [ 2*arg2<arg1 && arg1==arg1P_8 && arg2==arg2P_8 ], cost: 1
      9: f8 -> f13 : arg1'=arg1P_10, arg2'=arg2P_10, [ 2*arg2>=arg1 && arg1==arg1P_10 && arg2==arg2P_10 ], cost: 1
     10: f13 -> f14 : arg1'=arg1P_11, arg2'=arg2P_11, [ arg2==arg1P_11 && arg2==arg2P_11 ], cost: 1
     15: f14 -> f10 : arg1'=arg1P_16, arg2'=arg2P_16, [ arg1==arg1P_16 && arg2==arg2P_16 ], cost: 1
     11: f9 -> f15 : arg1'=arg1P_12, arg2'=arg2P_12, [ arg1P_12==1+3*arg1 && arg2==arg2P_12 ], cost: 1
     16: f15 -> f10 : arg1'=arg1P_17, arg2'=arg2P_17, [ arg1==arg1P_17 && arg2==arg2P_17 ], cost: 1
     18: f10 -> f2 : arg1'=arg1P_19, arg2'=arg2P_19, [ arg1==arg1P_19 && arg2==arg2P_19 ], cost: 1
     20: __init -> f1 : arg1'=arg1P_21, arg2'=arg2P_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, [], cost: 1

Removed unreachable and leaf rules:
   Start location: __init
      0: f1 -> f2 : arg1'=arg1P_1, arg2'=arg2P_1, [ arg2==arg2P_1 ], cost: 1
     17: f2 -> f3 : arg1'=arg1P_18, arg2'=arg2P_18, [ arg1>1 && arg1==arg1P_18 && arg2==arg2P_18 ], cost: 1
      1: f3 -> f4 : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1==arg1P_2 && arg1==arg2P_2 ], cost: 1
      3: f4 -> f5 : arg1'=arg1P_4, arg2'=arg2P_4, [ arg2>1 && arg1==arg1P_4 && arg2==arg2P_4 ], cost: 1
      5: f4 -> f7 : arg1'=arg1P_6, arg2'=arg2P_6, [ arg2<=1 && arg1==arg1P_6 && arg2==arg2P_6 ], cost: 1
      2: f5 -> f6 : arg1'=arg1P_3, arg2'=arg2P_3, [ arg2P_3==-2+arg2 && arg1==arg1P_3 ], cost: 1
      4: f6 -> f4 : arg1'=arg1P_5, arg2'=arg2P_5, [ arg1==arg1P_5 && arg2==arg2P_5 ], cost: 1
     12: f7 -> f8 : arg1'=arg1P_13, arg2'=arg2P_13, [ arg2==0 && arg1==arg1P_13 && arg2==arg2P_13 ], cost: 1
     13: f7 -> f9 : arg1'=arg1P_14, arg2'=arg2P_14, [ arg2<0 && arg1==arg1P_14 && arg2==arg2P_14 ], cost: 1
     14: f7 -> f9 : arg1'=arg1P_15, arg2'=arg2P_15, [ arg2>0 && arg1==arg1P_15 && arg2==arg2P_15 ], cost: 1
      6: f11 -> f12 : arg1'=arg1P_7, arg2'=arg2P_7, [ arg2P_7==1+arg2 && arg1==arg1P_7 ], cost: 1
      8: f12 -> f8 : arg1'=arg1P_9, arg2'=arg2P_9, [ arg1==arg1P_9 && arg2==arg2P_9 ], cost: 1
      7: f8 -> f11 : arg1'=arg1P_8, arg2'=arg2P_8, [ 2*arg2<arg1 && arg1==arg1P_8 && arg2==arg2P_8 ], cost: 1
      9: f8 -> f13 : arg1'=arg1P_10, arg2'=arg2P_10, [ 2*arg2>=arg1 && arg1==arg1P_10 && arg2==arg2P_10 ], cost: 1
     10: f13 -> f14 : arg1'=arg1P_11, arg2'=arg2P_11, [ arg2==arg1P_11 && arg2==arg2P_11 ], cost: 1
     15: f14 -> f10 : arg1'=arg1P_16, arg2'=arg2P_16, [ arg1==arg1P_16 && arg2==arg2P_16 ], cost: 1
     11: f9 -> f15 : arg1'=arg1P_12, arg2'=arg2P_12, [ arg1P_12==1+3*arg1 && arg2==arg2P_12 ], cost: 1
     16: f15 -> f10 : arg1'=arg1P_17, arg2'=arg2P_17, [ arg1==arg1P_17 && arg2==arg2P_17 ], cost: 1
     18: f10 -> f2 : arg1'=arg1P_19, arg2'=arg2P_19, [ arg1==arg1P_19 && arg2==arg2P_19 ], cost: 1
     20: __init -> f1 : arg1'=arg1P_21, arg2'=arg2P_21, [], cost: 1

Simplified all rules, resulting in:
   Start location: __init
      0: f1 -> f2 : arg1'=arg1P_1, [], cost: 1
     17: f2 -> f3 : [ arg1>1 ], cost: 1
      1: f3 -> f4 : arg2'=arg1, [], cost: 1
      3: f4 -> f5 : [ arg2>1 ], cost: 1
      5: f4 -> f7 : [ arg2<=1 ], cost: 1
      2: f5 -> f6 : arg2'=-2+arg2, [], cost: 1
      4: f6 -> f4 : [], cost: 1
     12: f7 -> f8 : [ arg2==0 ], cost: 1
     13: f7 -> f9 : [ arg2<0 ], cost: 1
     14: f7 -> f9 : [ arg2>0 ], cost: 1
      6: f11 -> f12 : arg2'=1+arg2, [], cost: 1
      8: f12 -> f8 : [], cost: 1
      7: f8 -> f11 : [ 2*arg2<arg1 ], cost: 1
      9: f8 -> f13 : [ 2*arg2>=arg1 ], cost: 1
     10: f13 -> f14 : arg1'=arg2, [], cost: 1
     15: f14 -> f10 : [], cost: 1
     11: f9 -> f15 : arg1'=1+3*arg1, [], cost: 1
     16: f15 -> f10 : [], cost: 1
     18: f10 -> f2 : [], cost: 1
     20: __init -> f1 : arg1'=arg1P_21, arg2'=arg2P_21, [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: __init
     22: f2 -> f4 : arg2'=arg1, [ arg1>1 ], cost: 2
      5: f4 -> f7 : [ arg2<=1 ], cost: 1
     24: f4 -> f4 : arg2'=-2+arg2, [ arg2>1 ], cost: 3
     12: f7 -> f8 : [ arg2==0 ], cost: 1
     13: f7 -> f9 : [ arg2<0 ], cost: 1
     14: f7 -> f9 : [ arg2>0 ], cost: 1
     27: f8 -> f8 : arg2'=1+arg2, [ 2*arg2<arg1 ], cost: 3
     28: f8 -> f10 : arg1'=arg2, [ 2*arg2>=arg1 ], cost: 3
     29: f9 -> f10 : arg1'=1+3*arg1, [], cost: 2
     18: f10 -> f2 : [], cost: 1
     21: __init -> f2 : arg1'=arg1P_1, arg2'=arg2P_21, [], cost: 2

Accelerating simple loops of location 3.
   Accelerating the following rules:
     24: f4 -> f4 : arg2'=-2+arg2, [ arg2>1 ], cost: 3

   Accelerated rule 24 with backward acceleration, yielding the new rule 30.
[accelerate] Nesting with 1 inner and 1 outer candidates
   Removing the simple loops: 24.

Accelerating simple loops of location 9.
   Accelerating the following rules:
     27: f8 -> f8 : arg2'=1+arg2, [ 2*arg2<arg1 ], cost: 3

   Accelerated rule 27 with backward acceleration, yielding the new rule 31.
[accelerate] Nesting with 1 inner and 1 outer candidates
   Removing the simple loops: 27.

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     22: f2 -> f4 : arg2'=arg1, [ arg1>1 ], cost: 2
      5: f4 -> f7 : [ arg2<=1 ], cost: 1
     30: f4 -> f4 : arg2'=arg2-2*k, [ k>=0 && 2+arg2-2*k>1 ], cost: 3*k
     12: f7 -> f8 : [ arg2==0 ], cost: 1
     13: f7 -> f9 : [ arg2<0 ], cost: 1
     14: f7 -> f9 : [ arg2>0 ], cost: 1
     28: f8 -> f10 : arg1'=arg2, [ 2*arg2>=arg1 ], cost: 3
     31: f8 -> f8 : arg2'=arg2+k_1, [ k_1>=0 && -2+2*arg2+2*k_1<arg1 ], cost: 3*k_1
     29: f9 -> f10 : arg1'=1+3*arg1, [], cost: 2
     18: f10 -> f2 : [], cost: 1
     21: __init -> f2 : arg1'=arg1P_1, arg2'=arg2P_21, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: __init
     22: f2 -> f4 : arg2'=arg1, [ arg1>1 ], cost: 2
     32: f2 -> f4 : arg2'=-2*k+arg1, [ arg1>1 && k>=0 && 2-2*k+arg1>1 ], cost: 2+3*k
      5: f4 -> f7 : [ arg2<=1 ], cost: 1
     12: f7 -> f8 : [ arg2==0 ], cost: 1
     13: f7 -> f9 : [ arg2<0 ], cost: 1
     14: f7 -> f9 : [ arg2>0 ], cost: 1
     33: f7 -> f8 : arg2'=arg2+k_1, [ arg2==0 && k_1>=0 && -2+2*arg2+2*k_1<arg1 ], cost: 1+3*k_1
     28: f8 -> f10 : arg1'=arg2, [ 2*arg2>=arg1 ], cost: 3
     29: f9 -> f10 : arg1'=1+3*arg1, [], cost: 2
     18: f10 -> f2 : [], cost: 1
     21: __init -> f2 : arg1'=arg1P_1, arg2'=arg2P_21, [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: __init
     34: f2 -> f7 : arg2'=-2*k+arg1, [ arg1>1 && k>=0 && 2-2*k+arg1>1 && -2*k+arg1<=1 ], cost: 3+3*k
     35: f7 -> f10 : arg1'=arg2, [ arg2==0 && 2*arg2>=arg1 ], cost: 4
     36: f7 -> f10 : arg1'=arg2+k_1, arg2'=arg2+k_1, [ arg2==0 && k_1>=0 && -2+2*arg2+2*k_1<arg1 && 2*arg2+2*k_1>=arg1 ], cost: 4+3*k_1
     37: f7 -> f10 : arg1'=1+3*arg1, [ arg2<0 ], cost: 3
     38: f7 -> f10 : arg1'=1+3*arg1, [ arg2>0 ], cost: 3
     18: f10 -> f2 : [], cost: 1
     21: __init -> f2 : arg1'=arg1P_1, arg2'=arg2P_21, [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: __init
     39: f2 -> f10 : arg1'=-2*k+k_1+arg1, arg2'=-2*k+k_1+arg1, [ arg1>1 && k>=0 && -2*k+arg1==0 && k_1>=0 && -2-4*k+2*k_1+2*arg1<arg1 && -4*k+2*k_1+2*arg1>=arg1 ], cost: 7+3*k+3*k_1
     40: f2 -> f10 : arg1'=1+3*arg1, arg2'=-2*k+arg1, [ arg1>1 && k>=0 && -2*k+arg1<=1 && -2*k+arg1>0 ], cost: 6+3*k
     41: f2 -> [19] : [ arg1>1 && k>=0 && 2-2*k+arg1>1 && -2*k+arg1<=1 ], cost: 3+3*k
     18: f10 -> f2 : [], cost: 1
     21: __init -> f2 : arg1'=arg1P_1, arg2'=arg2P_21, [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: __init
     41: f2 -> [19] : [ arg1>1 && k>=0 && 2-2*k+arg1>1 && -2*k+arg1<=1 ], cost: 3+3*k
     42: f2 -> f2 : arg1'=-2*k+k_1+arg1, arg2'=-2*k+k_1+arg1, [ arg1>1 && k>=0 && -2*k+arg1==0 && k_1>=0 && -2-4*k+2*k_1+2*arg1<arg1 && -4*k+2*k_1+2*arg1>=arg1 ], cost: 8+3*k+3*k_1
     43: f2 -> f2 : arg1'=1+3*arg1, arg2'=-2*k+arg1, [ arg1>1 && k>=0 && -2*k+arg1<=1 && -2*k+arg1>0 ], cost: 7+3*k
     21: __init -> f2 : arg1'=arg1P_1, arg2'=arg2P_21, [], cost: 2

Accelerating simple loops of location 1.
   Simplified some of the simple loops (and removed duplicate rules).
   Accelerating the following rules:
     42: f2 -> f2 : arg1'=-2*k+k_1+arg1, arg2'=-2*k+k_1+arg1, [ arg1>1 && k>=0 && -2*k+arg1==0 && k_1>=0 && -2-4*k+2*k_1+2*arg1<arg1 && -4*k+2*k_1+2*arg1>=arg1 ], cost: 8+3*k+3*k_1
     43: f2 -> f2 : arg1'=1+3*arg1, arg2'=-2*k+arg1, [ arg1>1 && k>=0 && -1-2*k+arg1==0 ], cost: 7+3*k

   Failed to prove monotonicity of the guard of rule 42.
   Failed to prove monotonicity of the guard of rule 43.
[accelerate] Nesting with 2 inner and 2 outer candidates

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     41: f2 -> [19] : [ arg1>1 && k>=0 && 2-2*k+arg1>1 && -2*k+arg1<=1 ], cost: 3+3*k
     42: f2 -> f2 : arg1'=-2*k+k_1+arg1, arg2'=-2*k+k_1+arg1, [ arg1>1 && k>=0 && -2*k+arg1==0 && k_1>=0 && -2-4*k+2*k_1+2*arg1<arg1 && -4*k+2*k_1+2*arg1>=arg1 ], cost: 8+3*k+3*k_1
     43: f2 -> f2 : arg1'=1+3*arg1, arg2'=-2*k+arg1, [ arg1>1 && k>=0 && -1-2*k+arg1==0 ], cost: 7+3*k
     21: __init -> f2 : arg1'=arg1P_1, arg2'=arg2P_21, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: __init
     41: f2 -> [19] : [ arg1>1 && k>=0 && 2-2*k+arg1>1 && -2*k+arg1<=1 ], cost: 3+3*k
     21: __init -> f2 : arg1'=arg1P_1, arg2'=arg2P_21, [], cost: 2
     44: __init -> f2 : arg1'=k_1, arg2'=k_1, [ 2*k>1 && k>=0 && k_1>=0 && -2+2*k_1<2*k && 2*k_1>=2*k ], cost: 10+3*k+3*k_1
     45: __init -> f2 : arg1'=4+6*k, arg2'=1, [ 1+2*k>1 && k>=0 ], cost: 9+3*k

Eliminated locations (on tree-shaped paths):
   Start location: __init
     46: __init -> [19] : arg1'=arg1P_1, arg2'=arg2P_21, [ arg1P_1>1 && k>=0 && 2+arg1P_1-2*k>1 && arg1P_1-2*k<=1 ], cost: 5+3*k
     47: __init -> [21] : [ 2*k>1 && k>=0 && k_1>=0 && -2+2*k_1<2*k && 2*k_1>=2*k ], cost: 10+3*k+3*k_1
     48: __init -> [21] : [ 1+2*k>1 && k>=0 ], cost: 9+3*k

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: __init
     46: __init -> [19] : arg1'=arg1P_1, arg2'=arg2P_21, [ arg1P_1>1 && k>=0 && 2+arg1P_1-2*k>1 && arg1P_1-2*k<=1 ], cost: 5+3*k
     47: __init -> [21] : [ 2*k>1 && k>=0 && k_1>=0 && -2+2*k_1<2*k && 2*k_1>=2*k ], cost: 10+3*k+3*k_1
     48: __init -> [21] : [ 1+2*k>1 && k>=0 ], cost: 9+3*k

Computing asymptotic complexity for rule 48
   Resulting cost 0 has complexity: Unknown

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

Computing asymptotic complexity for rule 47
   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),?)