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, [ arg1==arg1P_1 ], cost: 1
      1: f2 -> f3 : arg1'=arg1P_2, arg2'=arg2P_2, [ arg2==arg2P_2 ], cost: 1
     14: f3 -> f4 : arg1'=arg1P_15, arg2'=arg2P_15, [ arg2>0 && arg1>0 && arg1<arg2 && arg1==arg1P_15 && arg2==arg2P_15 ], cost: 1
     15: f3 -> f4 : arg1'=arg1P_16, arg2'=arg2P_16, [ arg2>0 && arg1>0 && arg1>arg2 && arg1==arg1P_16 && arg2==arg2P_16 ], cost: 1
     17: f3 -> f15 : arg1'=arg1P_18, arg2'=arg2P_18, [ arg1==arg2 && arg1==arg1P_18 && arg2==arg2P_18 ], cost: 1
     18: f3 -> f15 : arg1'=arg1P_19, arg2'=arg2P_19, [ arg2<=0 && arg1==arg1P_19 && arg2==arg2P_19 ], cost: 1
     19: f3 -> f15 : arg1'=arg1P_20, arg2'=arg2P_20, [ arg1<=0 && arg1==arg1P_20 && arg2==arg2P_20 ], cost: 1
      2: f5 -> f8 : arg1'=arg1P_3, arg2'=arg2P_3, [ arg2P_3==-1+arg2 && arg1==arg1P_3 ], cost: 1
      3: f8 -> f9 : arg1'=arg1P_4, arg2'=arg2P_4, [ arg2==arg2P_4 ], cost: 1
     12: f9 -> f7 : arg1'=arg1P_13, arg2'=arg2P_13, [ arg1==arg1P_13 && arg2==arg2P_13 ], cost: 1
      4: f10 -> f13 : arg1'=arg1P_5, arg2'=arg2P_5, [ arg1P_5==-1+arg1 && arg2==arg2P_5 ], cost: 1
      5: f13 -> f14 : arg1'=arg1P_6, arg2'=arg2P_6, [ arg1==arg1P_6 ], cost: 1
      8: f14 -> f12 : arg1'=arg1P_9, arg2'=arg2P_9, [ arg1==arg1P_9 && arg2==arg2P_9 ], cost: 1
      6: f6 -> f10 : arg1'=arg1P_7, arg2'=arg2P_7, [ arg1<arg2 && arg1==arg1P_7 && arg2==arg2P_7 ], cost: 1
      7: f6 -> f11 : arg1'=arg1P_8, arg2'=arg2P_8, [ arg1>=arg2 && arg1==arg1P_8 && arg2==arg2P_8 ], cost: 1
      9: f11 -> f12 : arg1'=arg1P_10, arg2'=arg2P_10, [ arg1==arg1P_10 && arg2==arg2P_10 ], cost: 1
     13: f12 -> f7 : arg1'=arg1P_14, arg2'=arg2P_14, [ arg1==arg1P_14 && arg2==arg2P_14 ], cost: 1
     10: f4 -> f5 : arg1'=arg1P_11, arg2'=arg2P_11, [ arg2<arg1 && arg1==arg1P_11 && arg2==arg2P_11 ], cost: 1
     11: f4 -> f6 : arg1'=arg1P_12, arg2'=arg2P_12, [ arg2>=arg1 && arg1==arg1P_12 && arg2==arg2P_12 ], cost: 1
     16: f7 -> f3 : arg1'=arg1P_17, arg2'=arg2P_17, [ arg1==arg1P_17 && arg2==arg2P_17 ], 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, [ arg1==arg1P_1 ], cost: 1
      1: f2 -> f3 : arg1'=arg1P_2, arg2'=arg2P_2, [ arg2==arg2P_2 ], cost: 1
     14: f3 -> f4 : arg1'=arg1P_15, arg2'=arg2P_15, [ arg2>0 && arg1>0 && arg1<arg2 && arg1==arg1P_15 && arg2==arg2P_15 ], cost: 1
     15: f3 -> f4 : arg1'=arg1P_16, arg2'=arg2P_16, [ arg2>0 && arg1>0 && arg1>arg2 && arg1==arg1P_16 && arg2==arg2P_16 ], cost: 1
      2: f5 -> f8 : arg1'=arg1P_3, arg2'=arg2P_3, [ arg2P_3==-1+arg2 && arg1==arg1P_3 ], cost: 1
      3: f8 -> f9 : arg1'=arg1P_4, arg2'=arg2P_4, [ arg2==arg2P_4 ], cost: 1
     12: f9 -> f7 : arg1'=arg1P_13, arg2'=arg2P_13, [ arg1==arg1P_13 && arg2==arg2P_13 ], cost: 1
      4: f10 -> f13 : arg1'=arg1P_5, arg2'=arg2P_5, [ arg1P_5==-1+arg1 && arg2==arg2P_5 ], cost: 1
      5: f13 -> f14 : arg1'=arg1P_6, arg2'=arg2P_6, [ arg1==arg1P_6 ], cost: 1
      8: f14 -> f12 : arg1'=arg1P_9, arg2'=arg2P_9, [ arg1==arg1P_9 && arg2==arg2P_9 ], cost: 1
      6: f6 -> f10 : arg1'=arg1P_7, arg2'=arg2P_7, [ arg1<arg2 && arg1==arg1P_7 && arg2==arg2P_7 ], cost: 1
      7: f6 -> f11 : arg1'=arg1P_8, arg2'=arg2P_8, [ arg1>=arg2 && arg1==arg1P_8 && arg2==arg2P_8 ], cost: 1
      9: f11 -> f12 : arg1'=arg1P_10, arg2'=arg2P_10, [ arg1==arg1P_10 && arg2==arg2P_10 ], cost: 1
     13: f12 -> f7 : arg1'=arg1P_14, arg2'=arg2P_14, [ arg1==arg1P_14 && arg2==arg2P_14 ], cost: 1
     10: f4 -> f5 : arg1'=arg1P_11, arg2'=arg2P_11, [ arg2<arg1 && arg1==arg1P_11 && arg2==arg2P_11 ], cost: 1
     11: f4 -> f6 : arg1'=arg1P_12, arg2'=arg2P_12, [ arg2>=arg1 && arg1==arg1P_12 && arg2==arg2P_12 ], cost: 1
     16: f7 -> f3 : arg1'=arg1P_17, arg2'=arg2P_17, [ arg1==arg1P_17 && arg2==arg2P_17 ], cost: 1
     20: __init -> f1 : arg1'=arg1P_21, arg2'=arg2P_21, [], cost: 1

Simplified all rules, resulting in:
   Start location: __init
      0: f1 -> f2 : arg2'=arg2P_1, [], cost: 1
      1: f2 -> f3 : arg1'=arg1P_2, [], cost: 1
     14: f3 -> f4 : [ arg1>0 && arg1<arg2 ], cost: 1
     15: f3 -> f4 : [ arg2>0 && arg1>0 && arg1>arg2 ], cost: 1
      2: f5 -> f8 : arg2'=-1+arg2, [], cost: 1
      3: f8 -> f9 : arg1'=arg1P_4, [], cost: 1
     12: f9 -> f7 : [], cost: 1
      4: f10 -> f13 : arg1'=-1+arg1, [], cost: 1
      5: f13 -> f14 : arg2'=arg2P_6, [], cost: 1
      8: f14 -> f12 : [], cost: 1
      6: f6 -> f10 : [ arg1<arg2 ], cost: 1
      7: f6 -> f11 : [ arg1>=arg2 ], cost: 1
      9: f11 -> f12 : [], cost: 1
     13: f12 -> f7 : [], cost: 1
     10: f4 -> f5 : [ arg2<arg1 ], cost: 1
     11: f4 -> f6 : [ arg2>=arg1 ], cost: 1
     16: f7 -> f3 : [], 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
     14: f3 -> f4 : [ arg1>0 && arg1<arg2 ], cost: 1
     15: f3 -> f4 : [ arg2>0 && arg1>0 && arg1>arg2 ], cost: 1
     27: f6 -> f12 : [ arg1>=arg2 ], cost: 2
     29: f6 -> f12 : arg1'=-1+arg1, arg2'=arg2P_6, [ arg1<arg2 ], cost: 4
     13: f12 -> f7 : [], cost: 1
     11: f4 -> f6 : [ arg2>=arg1 ], cost: 1
     25: f4 -> f7 : arg1'=arg1P_4, arg2'=-1+arg2, [ arg2<arg1 ], cost: 4
     16: f7 -> f3 : [], cost: 1
     22: __init -> f3 : arg1'=arg1P_2, arg2'=arg2P_1, [], cost: 3

Eliminated locations (on tree-shaped paths):
   Start location: __init
     30: f3 -> f6 : [ arg1>0 && arg1<arg2 ], cost: 2
     31: f3 -> f7 : arg1'=arg1P_4, arg2'=-1+arg2, [ arg2>0 && arg1>0 && arg1>arg2 ], cost: 5
     32: f6 -> f7 : [ arg1>=arg2 ], cost: 3
     33: f6 -> f7 : arg1'=-1+arg1, arg2'=arg2P_6, [ arg1<arg2 ], cost: 5
     16: f7 -> f3 : [], cost: 1
     22: __init -> f3 : arg1'=arg1P_2, arg2'=arg2P_1, [], cost: 3

Eliminated locations (on tree-shaped paths):
   Start location: __init
     35: f3 -> f3 : arg1'=arg1P_4, arg2'=-1+arg2, [ arg2>0 && arg1>0 && arg1>arg2 ], cost: 6
     36: f3 -> f3 : arg1'=-1+arg1, arg2'=arg2P_6, [ arg1>0 && arg1<arg2 ], cost: 8
     22: __init -> f3 : arg1'=arg1P_2, arg2'=arg2P_1, [], cost: 3

Accelerating simple loops of location 2.
   Accelerating the following rules:
     35: f3 -> f3 : arg1'=arg1P_4, arg2'=-1+arg2, [ arg2>0 && arg1>0 && arg1>arg2 ], cost: 6
     36: f3 -> f3 : arg1'=-1+arg1, arg2'=arg2P_6, [ arg1>0 && arg1<arg2 ], cost: 8

[test] deduced pseudo-invariant arg1-arg1P_4<=0, also trying -arg1+arg1P_4<=-1
[test] deduced pseudo-invariant -arg1+arg1P_4<=0, also trying arg1-arg1P_4<=-1
   Accelerated rule 35 with backward acceleration, yielding the new rule 37.
[test] deduced pseudo-invariant -2-arg2P_6+3*arg1<=0, also trying 2+arg2P_6-3*arg1<=-1
[test] deduced pseudo-invariant -1+arg2-arg2P_6<=0, also trying 1-arg2+arg2P_6<=-1
   Accelerated rule 36 with backward acceleration, yielding the new rule 38.
   Accelerated rule 36 with backward acceleration, yielding the new rule 39.
[accelerate] Nesting with 3 inner and 2 outer candidates

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     35: f3 -> f3 : arg1'=arg1P_4, arg2'=-1+arg2, [ arg2>0 && arg1>0 && arg1>arg2 ], cost: 6
     36: f3 -> f3 : arg1'=-1+arg1, arg2'=arg2P_6, [ arg1>0 && arg1<arg2 ], cost: 8
     37: f3 -> f3 : arg1'=arg1P_4, arg2'=0, [ arg1>0 && arg1>arg2 && arg1-arg1P_4<=0 && -arg1+arg1P_4<=0 && arg2>=1 ], cost: 6*arg2
     38: f3 -> f3 : arg1'=0, arg2'=arg2P_6, [ arg1<arg2 && -2-arg2P_6+3*arg1<=0 && arg1>=1 ], cost: 8*arg1
     39: f3 -> f3 : arg1'=-k_5+arg1, arg2'=arg2P_6, [ arg1>0 && arg1<arg2 && -1+arg2-arg2P_6<=0 && k_5>=1 && -1+arg2P_6+3*k_5-3*arg1<=-1 ], cost: 8*k_5
     22: __init -> f3 : arg1'=arg1P_2, arg2'=arg2P_1, [], cost: 3

Chained accelerated rules (with incoming rules):
   Start location: __init
     22: __init -> f3 : arg1'=arg1P_2, arg2'=arg2P_1, [], cost: 3
     40: __init -> f3 : arg1'=arg1P_4, arg2'=-1+arg2P_1, [ arg2P_1>0 ], cost: 9
     41: __init -> f3 : arg1'=-1+arg1P_2, arg2'=arg2P_6, [ arg1P_2>0 ], cost: 11
     42: __init -> f3 : arg1'=arg1P_2, arg2'=0, [ arg1P_2>0 && arg1P_2>arg2P_1 && arg2P_1>=1 ], cost: 3+6*arg2P_1
     43: __init -> f3 : arg1'=0, arg2'=arg2P_6, [ -2-arg2P_6+3*arg1P_2<=0 && arg1P_2>=1 ], cost: 3+8*arg1P_2
     44: __init -> f3 : arg1'=-k_5+arg1P_2, arg2'=arg2P_6, [ arg1P_2>0 && k_5>=1 && -1+arg2P_6+3*k_5-3*arg1P_2<=-1 && 1+arg1P_2<=1+arg2P_6 ], cost: 3+8*k_5

Removed unreachable locations (and leaf rules with constant cost):
   Start location: __init
     42: __init -> f3 : arg1'=arg1P_2, arg2'=0, [ arg1P_2>0 && arg1P_2>arg2P_1 && arg2P_1>=1 ], cost: 3+6*arg2P_1
     43: __init -> f3 : arg1'=0, arg2'=arg2P_6, [ -2-arg2P_6+3*arg1P_2<=0 && arg1P_2>=1 ], cost: 3+8*arg1P_2
     44: __init -> f3 : arg1'=-k_5+arg1P_2, arg2'=arg2P_6, [ arg1P_2>0 && k_5>=1 && -1+arg2P_6+3*k_5-3*arg1P_2<=-1 && 1+arg1P_2<=1+arg2P_6 ], cost: 3+8*k_5

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: __init
     42: __init -> f3 : arg1'=arg1P_2, arg2'=0, [ arg1P_2>0 && arg1P_2>arg2P_1 && arg2P_1>=1 ], cost: 3+6*arg2P_1
     43: __init -> f3 : arg1'=0, arg2'=arg2P_6, [ -2-arg2P_6+3*arg1P_2<=0 && arg1P_2>=1 ], cost: 3+8*arg1P_2
     44: __init -> f3 : arg1'=-k_5+arg1P_2, arg2'=arg2P_6, [ arg1P_2>0 && k_5>=1 && -1+arg2P_6+3*k_5-3*arg1P_2<=-1 && 1+arg1P_2<=1+arg2P_6 ], cost: 3+8*k_5

Computing asymptotic complexity for rule 43
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 42
   Simplified the guard:
     42: __init -> f3 : arg1'=arg1P_2, arg2'=0, [ arg1P_2>arg2P_1 && arg2P_1>=1 ], cost: 3+6*arg2P_1
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 44
   Simplified the guard:
     44: __init -> f3 : arg1'=-k_5+arg1P_2, arg2'=arg2P_6, [ k_5>=1 && -1+arg2P_6+3*k_5-3*arg1P_2<=-1 && 1+arg1P_2<=1+arg2P_6 ], cost: 3+8*k_5
   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),?)