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 && 0==arg2P_2 ], cost: 1
     18: f3 -> f4 : arg1'=arg1P_19, arg2'=arg2P_19, [ 0<=arg1 && arg1<=10 && arg1==arg1P_19 && arg2==arg2P_19 ], cost: 1
     20: f3 -> f18 : arg1'=arg1P_21, arg2'=arg2P_21, [ 0>arg1 && arg1==arg1P_21 && arg2==arg2P_21 ], cost: 1
     21: f3 -> f18 : arg1'=arg1P_22, arg2'=arg2P_22, [ arg1>10 && arg1==arg1P_22 && arg2==arg2P_22 ], cost: 1
      2: f5 -> f8 : arg1'=arg1P_3, arg2'=arg2P_3, [ arg1==arg1P_3 && 0==arg2P_3 ], cost: 1
      5: f8 -> f7 : arg1'=arg1P_6, arg2'=arg2P_6, [ arg1==arg1P_6 && arg2==arg2P_6 ], cost: 1
      3: f4 -> f5 : arg1'=arg1P_4, arg2'=arg2P_4, [ arg1>=10 && arg1==arg1P_4 && arg2==arg2P_4 ], cost: 1
      4: f4 -> f6 : arg1'=arg1P_5, arg2'=arg2P_5, [ arg1<10 && arg1==arg1P_5 && arg2==arg2P_5 ], cost: 1
      6: f6 -> f7 : arg1'=arg1P_7, arg2'=arg2P_7, [ arg1==arg1P_7 && arg2==arg2P_7 ], cost: 1
      8: f7 -> f9 : arg1'=arg1P_9, arg2'=arg2P_9, [ arg1<=0 && arg1==arg1P_9 && arg2==arg2P_9 ], cost: 1
      9: f7 -> f10 : arg1'=arg1P_10, arg2'=arg2P_10, [ arg1>0 && arg1==arg1P_10 && arg2==arg2P_10 ], cost: 1
      7: f9 -> f12 : arg1'=arg1P_8, arg2'=arg2P_8, [ arg1==arg1P_8 && 1==arg2P_8 ], cost: 1
     10: f12 -> f11 : arg1'=arg1P_11, arg2'=arg2P_11, [ arg1==arg1P_11 && arg2==arg2P_11 ], cost: 1
     11: f10 -> f11 : arg1'=arg1P_12, arg2'=arg2P_12, [ arg1==arg1P_12 && arg2==arg2P_12 ], cost: 1
     14: f11 -> f13 : arg1'=arg1P_15, arg2'=arg2P_15, [ arg2>=1 && arg1==arg1P_15 && arg2==arg2P_15 ], cost: 1
     15: f11 -> f14 : arg1'=arg1P_16, arg2'=arg2P_16, [ arg2<1 && arg1==arg1P_16 && arg2==arg2P_16 ], cost: 1
     12: f13 -> f16 : arg1'=arg1P_13, arg2'=arg2P_13, [ arg1P_13==1+arg1 && arg2==arg2P_13 ], cost: 1
     16: f16 -> f15 : arg1'=arg1P_17, arg2'=arg2P_17, [ arg1==arg1P_17 && arg2==arg2P_17 ], cost: 1
     13: f14 -> f17 : arg1'=arg1P_14, arg2'=arg2P_14, [ arg1P_14==-1+arg1 && arg2==arg2P_14 ], cost: 1
     17: f17 -> f15 : arg1'=arg1P_18, arg2'=arg2P_18, [ arg1==arg1P_18 && arg2==arg2P_18 ], cost: 1
     19: f15 -> f3 : arg1'=arg1P_20, arg2'=arg2P_20, [ arg1==arg1P_20 && arg2==arg2P_20 ], cost: 1
     22: __init -> f1 : arg1'=arg1P_23, arg2'=arg2P_23, [], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
     22: __init -> f1 : arg1'=arg1P_23, arg2'=arg2P_23, [], 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 && 0==arg2P_2 ], cost: 1
     18: f3 -> f4 : arg1'=arg1P_19, arg2'=arg2P_19, [ 0<=arg1 && arg1<=10 && arg1==arg1P_19 && arg2==arg2P_19 ], cost: 1
      2: f5 -> f8 : arg1'=arg1P_3, arg2'=arg2P_3, [ arg1==arg1P_3 && 0==arg2P_3 ], cost: 1
      5: f8 -> f7 : arg1'=arg1P_6, arg2'=arg2P_6, [ arg1==arg1P_6 && arg2==arg2P_6 ], cost: 1
      3: f4 -> f5 : arg1'=arg1P_4, arg2'=arg2P_4, [ arg1>=10 && arg1==arg1P_4 && arg2==arg2P_4 ], cost: 1
      4: f4 -> f6 : arg1'=arg1P_5, arg2'=arg2P_5, [ arg1<10 && arg1==arg1P_5 && arg2==arg2P_5 ], cost: 1
      6: f6 -> f7 : arg1'=arg1P_7, arg2'=arg2P_7, [ arg1==arg1P_7 && arg2==arg2P_7 ], cost: 1
      8: f7 -> f9 : arg1'=arg1P_9, arg2'=arg2P_9, [ arg1<=0 && arg1==arg1P_9 && arg2==arg2P_9 ], cost: 1
      9: f7 -> f10 : arg1'=arg1P_10, arg2'=arg2P_10, [ arg1>0 && arg1==arg1P_10 && arg2==arg2P_10 ], cost: 1
      7: f9 -> f12 : arg1'=arg1P_8, arg2'=arg2P_8, [ arg1==arg1P_8 && 1==arg2P_8 ], cost: 1
     10: f12 -> f11 : arg1'=arg1P_11, arg2'=arg2P_11, [ arg1==arg1P_11 && arg2==arg2P_11 ], cost: 1
     11: f10 -> f11 : arg1'=arg1P_12, arg2'=arg2P_12, [ arg1==arg1P_12 && arg2==arg2P_12 ], cost: 1
     14: f11 -> f13 : arg1'=arg1P_15, arg2'=arg2P_15, [ arg2>=1 && arg1==arg1P_15 && arg2==arg2P_15 ], cost: 1
     15: f11 -> f14 : arg1'=arg1P_16, arg2'=arg2P_16, [ arg2<1 && arg1==arg1P_16 && arg2==arg2P_16 ], cost: 1
     12: f13 -> f16 : arg1'=arg1P_13, arg2'=arg2P_13, [ arg1P_13==1+arg1 && arg2==arg2P_13 ], cost: 1
     16: f16 -> f15 : arg1'=arg1P_17, arg2'=arg2P_17, [ arg1==arg1P_17 && arg2==arg2P_17 ], cost: 1
     13: f14 -> f17 : arg1'=arg1P_14, arg2'=arg2P_14, [ arg1P_14==-1+arg1 && arg2==arg2P_14 ], cost: 1
     17: f17 -> f15 : arg1'=arg1P_18, arg2'=arg2P_18, [ arg1==arg1P_18 && arg2==arg2P_18 ], cost: 1
     19: f15 -> f3 : arg1'=arg1P_20, arg2'=arg2P_20, [ arg1==arg1P_20 && arg2==arg2P_20 ], cost: 1
     22: __init -> f1 : arg1'=arg1P_23, arg2'=arg2P_23, [], cost: 1

Simplified all rules, resulting in:
   Start location: __init
      0: f1 -> f2 : arg1'=arg1P_1, [], cost: 1
      1: f2 -> f3 : arg2'=0, [], cost: 1
     18: f3 -> f4 : [ 0<=arg1 && arg1<=10 ], cost: 1
      2: f5 -> f8 : arg2'=0, [], cost: 1
      5: f8 -> f7 : [], cost: 1
      3: f4 -> f5 : [ arg1>=10 ], cost: 1
      4: f4 -> f6 : [ arg1<10 ], cost: 1
      6: f6 -> f7 : [], cost: 1
      8: f7 -> f9 : [ arg1<=0 ], cost: 1
      9: f7 -> f10 : [ arg1>0 ], cost: 1
      7: f9 -> f12 : arg2'=1, [], cost: 1
     10: f12 -> f11 : [], cost: 1
     11: f10 -> f11 : [], cost: 1
     14: f11 -> f13 : [ arg2>=1 ], cost: 1
     15: f11 -> f14 : [ arg2<1 ], cost: 1
     12: f13 -> f16 : arg1'=1+arg1, [], cost: 1
     16: f16 -> f15 : [], cost: 1
     13: f14 -> f17 : arg1'=-1+arg1, [], cost: 1
     17: f17 -> f15 : [], cost: 1
     19: f15 -> f3 : [], cost: 1
     22: __init -> f1 : arg1'=arg1P_23, arg2'=arg2P_23, [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: __init
     18: f3 -> f4 : [ 0<=arg1 && arg1<=10 ], cost: 1
     26: f4 -> f7 : [ arg1<10 ], cost: 2
     27: f4 -> f7 : arg2'=0, [ arg1>=10 ], cost: 3
     29: f7 -> f11 : [ arg1>0 ], cost: 2
     30: f7 -> f11 : arg2'=1, [ arg1<=0 ], cost: 3
     33: f11 -> f15 : arg1'=1+arg1, [ arg2>=1 ], cost: 3
     34: f11 -> f15 : arg1'=-1+arg1, [ arg2<1 ], cost: 3
     19: f15 -> f3 : [], cost: 1
     24: __init -> f3 : arg1'=arg1P_1, arg2'=0, [], cost: 3

Eliminated locations (on tree-shaped paths):
   Start location: __init
     35: f3 -> f7 : [ 0<=arg1 && arg1<10 ], cost: 3
     36: f3 -> f7 : arg2'=0, [ arg1<=10 && arg1>=10 ], cost: 4
     37: f7 -> f15 : arg1'=1+arg1, [ arg1>0 && arg2>=1 ], cost: 5
     38: f7 -> f15 : arg1'=-1+arg1, [ arg1>0 && arg2<1 ], cost: 5
     39: f7 -> f15 : arg1'=1+arg1, arg2'=1, [ arg1<=0 ], cost: 6
     19: f15 -> f3 : [], cost: 1
     24: __init -> f3 : arg1'=arg1P_1, arg2'=0, [], cost: 3

Eliminated locations (on tree-shaped paths):
   Start location: __init
     40: f3 -> f15 : arg1'=1+arg1, [ arg1<10 && arg1>0 && arg2>=1 ], cost: 8
     41: f3 -> f15 : arg1'=-1+arg1, [ arg1<10 && arg1>0 && arg2<1 ], cost: 8
     42: f3 -> f15 : arg1'=1+arg1, arg2'=1, [ 0<=arg1 && arg1<=0 ], cost: 9
     43: f3 -> f15 : arg1'=-1+arg1, arg2'=0, [ arg1<=10 && arg1>=10 ], cost: 9
     19: f15 -> f3 : [], cost: 1
     24: __init -> f3 : arg1'=arg1P_1, arg2'=0, [], cost: 3

Eliminated locations (on tree-shaped paths):
   Start location: __init
     44: f3 -> f3 : arg1'=1+arg1, [ arg1<10 && arg1>0 && arg2>=1 ], cost: 9
     45: f3 -> f3 : arg1'=-1+arg1, [ arg1<10 && arg1>0 && arg2<1 ], cost: 9
     46: f3 -> f3 : arg1'=1+arg1, arg2'=1, [ 0<=arg1 && arg1<=0 ], cost: 10
     47: f3 -> f3 : arg1'=-1+arg1, arg2'=0, [ arg1<=10 && arg1>=10 ], cost: 10
     24: __init -> f3 : arg1'=arg1P_1, arg2'=0, [], cost: 3

Accelerating simple loops of location 2.
   Simplified some of the simple loops (and removed duplicate rules).
   Accelerating the following rules:
     44: f3 -> f3 : arg1'=1+arg1, [ arg1<10 && arg1>0 && arg2>=1 ], cost: 9
     45: f3 -> f3 : arg1'=-1+arg1, [ arg1<10 && arg1>0 && arg2<1 ], cost: 9
     46: f3 -> f3 : arg1'=1+arg1, arg2'=1, [ -arg1==0 ], cost: 10
     47: f3 -> f3 : arg1'=-1+arg1, arg2'=0, [ -10+arg1==0 ], cost: 10

   Accelerated rule 44 with backward acceleration, yielding the new rule 48.
   Accelerated rule 45 with backward acceleration, yielding the new rule 49.
   Failed to prove monotonicity of the guard of rule 46.
   Failed to prove monotonicity of the guard of rule 47.
[accelerate] Nesting with 4 inner and 4 outer candidates
   Removing the simple loops: 44 45.

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     46: f3 -> f3 : arg1'=1+arg1, arg2'=1, [ -arg1==0 ], cost: 10
     47: f3 -> f3 : arg1'=-1+arg1, arg2'=0, [ -10+arg1==0 ], cost: 10
     48: f3 -> f3 : arg1'=10, [ arg1>0 && arg2>=1 && 10-arg1>=0 ], cost: 90-9*arg1
     49: f3 -> f3 : arg1'=0, [ arg1<10 && arg2<1 && arg1>=0 ], cost: 9*arg1
     24: __init -> f3 : arg1'=arg1P_1, arg2'=0, [], cost: 3

Chained accelerated rules (with incoming rules):
   Start location: __init
     24: __init -> f3 : arg1'=arg1P_1, arg2'=0, [], cost: 3
     50: __init -> f3 : arg1'=1, arg2'=1, [], cost: 13
     51: __init -> f3 : arg1'=9, arg2'=0, [], cost: 13
     52: __init -> f3 : arg1'=0, arg2'=0, [ arg1P_1<10 && arg1P_1>=0 ], cost: 3+9*arg1P_1

Removed unreachable locations (and leaf rules with constant cost):
   Start location: __init
     52: __init -> f3 : arg1'=0, arg2'=0, [ arg1P_1<10 && arg1P_1>=0 ], cost: 3+9*arg1P_1

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: __init
     52: __init -> f3 : arg1'=0, arg2'=0, [ arg1P_1<10 && arg1P_1>=0 ], cost: 3+9*arg1P_1

Computing asymptotic complexity for rule 52
   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),?)