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

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
     17: __init -> f1 : arg1'=arg1P_18, arg2'=arg2P_18, [], 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
     12: f3 -> f4 : arg1'=arg1P_13, arg2'=arg2P_13, [ arg1>0 && arg2>0 && arg1==arg1P_13 && arg2==arg2P_13 ], cost: 1
      2: f8 -> f11 : arg1'=arg1P_3, arg2'=arg2P_3, [ arg1P_3==-arg2+arg1 && arg2==arg2P_3 ], cost: 1
      6: f11 -> f10 : arg1'=arg1P_7, arg2'=arg2P_7, [ arg1==arg1P_7 && arg2==arg2P_7 ], cost: 1
      3: f9 -> f12 : arg1'=arg1P_4, arg2'=arg2P_4, [ arg2P_4==arg2-arg1 && arg1==arg1P_4 ], cost: 1
      7: f12 -> f10 : arg1'=arg1P_8, arg2'=arg2P_8, [ arg1==arg1P_8 && arg2==arg2P_8 ], cost: 1
      4: f7 -> f8 : arg1'=arg1P_5, arg2'=arg2P_5, [ arg1>arg2 && arg1==arg1P_5 && arg2==arg2P_5 ], cost: 1
      5: f7 -> f9 : arg1'=arg1P_6, arg2'=arg2P_6, [ arg1<=arg2 && arg1==arg1P_6 && arg2==arg2P_6 ], cost: 1
     10: f10 -> f4 : arg1'=arg1P_11, arg2'=arg2P_11, [ arg1==arg1P_11 && arg2==arg2P_11 ], cost: 1
      8: f4 -> f7 : arg1'=arg1P_9, arg2'=arg2P_9, [ arg1<arg2 && arg1==arg1P_9 && arg2==arg2P_9 ], cost: 1
      9: f4 -> f7 : arg1'=arg1P_10, arg2'=arg2P_10, [ arg1>arg2 && arg1==arg1P_10 && arg2==arg2P_10 ], cost: 1
     17: __init -> f1 : arg1'=arg1P_18, arg2'=arg2P_18, [], 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
     12: f3 -> f4 : [ arg1>0 && arg2>0 ], cost: 1
      2: f8 -> f11 : arg1'=-arg2+arg1, [], cost: 1
      6: f11 -> f10 : [], cost: 1
      3: f9 -> f12 : arg2'=arg2-arg1, [], cost: 1
      7: f12 -> f10 : [], cost: 1
      4: f7 -> f8 : [ arg1>arg2 ], cost: 1
      5: f7 -> f9 : [ arg1<=arg2 ], cost: 1
     10: f10 -> f4 : [], cost: 1
      8: f4 -> f7 : [ arg1<arg2 ], cost: 1
      9: f4 -> f7 : [ arg1>arg2 ], cost: 1
     17: __init -> f1 : arg1'=arg1P_18, arg2'=arg2P_18, [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: __init
     23: f7 -> f10 : arg1'=-arg2+arg1, [ arg1>arg2 ], cost: 3
     24: f7 -> f10 : arg2'=arg2-arg1, [ arg1<=arg2 ], cost: 3
     10: f10 -> f4 : [], cost: 1
      8: f4 -> f7 : [ arg1<arg2 ], cost: 1
      9: f4 -> f7 : [ arg1>arg2 ], cost: 1
     20: __init -> f4 : arg1'=arg1P_1, arg2'=arg2P_2, [ arg1P_1>0 && arg2P_2>0 ], cost: 4

Eliminated locations (on tree-shaped paths):
   Start location: __init
     10: f10 -> f4 : [], cost: 1
     25: f4 -> f10 : arg2'=arg2-arg1, [ arg1<arg2 ], cost: 4
     26: f4 -> f10 : arg1'=-arg2+arg1, [ arg1>arg2 ], cost: 4
     20: __init -> f4 : arg1'=arg1P_1, arg2'=arg2P_2, [ arg1P_1>0 && arg2P_2>0 ], cost: 4

Eliminated locations (on tree-shaped paths):
   Start location: __init
     27: f4 -> f4 : arg2'=arg2-arg1, [ arg1<arg2 ], cost: 5
     28: f4 -> f4 : arg1'=-arg2+arg1, [ arg1>arg2 ], cost: 5
     20: __init -> f4 : arg1'=arg1P_1, arg2'=arg2P_2, [ arg1P_1>0 && arg2P_2>0 ], cost: 4

Accelerating simple loops of location 9.
   Accelerating the following rules:
     27: f4 -> f4 : arg2'=arg2-arg1, [ arg1<arg2 ], cost: 5
     28: f4 -> f4 : arg1'=-arg2+arg1, [ arg1>arg2 ], cost: 5

[test] deduced invariant -arg1<=0
   Accelerated rule 27 with non-termination, yielding the new rule 29.
   Accelerated rule 27 with non-termination, yielding the new rule 30.
   Accelerated rule 27 with backward acceleration, yielding the new rule 31.
[test] deduced invariant -arg2<=0
   Accelerated rule 28 with non-termination, yielding the new rule 32.
   Accelerated rule 28 with non-termination, yielding the new rule 33.
   Accelerated rule 28 with backward acceleration, yielding the new rule 34.
[accelerate] Nesting with 2 inner and 2 outer candidates
   Also removing duplicate rules: 29 32.

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     27: f4 -> f4 : arg2'=arg2-arg1, [ arg1<arg2 ], cost: 5
     28: f4 -> f4 : arg1'=-arg2+arg1, [ arg1>arg2 ], cost: 5
     30: f4 -> [14] : [ arg1<arg2 && arg2==1 && arg1==0 ], cost: NONTERM
     31: f4 -> f4 : arg2'=arg2-k*arg1, [ -arg1<=0 && k>=0 && arg1<-(-1+k)*arg1+arg2 ], cost: 5*k
     33: f4 -> [14] : [ arg1>arg2 && arg2==0 && arg1==1 ], cost: NONTERM
     34: f4 -> f4 : arg1'=-k_2*arg2+arg1, [ -arg2<=0 && k_2>=0 && -arg2*(-1+k_2)+arg1>arg2 ], cost: 5*k_2
     20: __init -> f4 : arg1'=arg1P_1, arg2'=arg2P_2, [ arg1P_1>0 && arg2P_2>0 ], cost: 4

Chained accelerated rules (with incoming rules):
   Start location: __init
     20: __init -> f4 : arg1'=arg1P_1, arg2'=arg2P_2, [ arg1P_1>0 && arg2P_2>0 ], cost: 4
     35: __init -> f4 : arg1'=arg1P_1, arg2'=arg2P_2-arg1P_1, [ arg1P_1>0 && arg2P_2>0 && arg1P_1<arg2P_2 ], cost: 9
     36: __init -> f4 : arg1'=-arg2P_2+arg1P_1, arg2'=arg2P_2, [ arg1P_1>0 && arg2P_2>0 && arg1P_1>arg2P_2 ], cost: 9
     37: __init -> f4 : arg1'=arg1P_1, arg2'=arg2P_2-arg1P_1*k, [ arg1P_1>0 && arg2P_2>0 && k>=0 && arg1P_1<arg2P_2-arg1P_1*(-1+k) ], cost: 4+5*k
     38: __init -> f4 : arg1'=arg1P_1-arg2P_2*k_2, arg2'=arg2P_2, [ arg1P_1>0 && arg2P_2>0 && k_2>=0 && -arg2P_2*(-1+k_2)+arg1P_1>arg2P_2 ], cost: 4+5*k_2

Removed unreachable locations (and leaf rules with constant cost):
   Start location: __init
     37: __init -> f4 : arg1'=arg1P_1, arg2'=arg2P_2-arg1P_1*k, [ arg1P_1>0 && arg2P_2>0 && k>=0 && arg1P_1<arg2P_2-arg1P_1*(-1+k) ], cost: 4+5*k
     38: __init -> f4 : arg1'=arg1P_1-arg2P_2*k_2, arg2'=arg2P_2, [ arg1P_1>0 && arg2P_2>0 && k_2>=0 && -arg2P_2*(-1+k_2)+arg1P_1>arg2P_2 ], cost: 4+5*k_2

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: __init
     37: __init -> f4 : arg1'=arg1P_1, arg2'=arg2P_2-arg1P_1*k, [ arg1P_1>0 && arg2P_2>0 && k>=0 && arg1P_1<arg2P_2-arg1P_1*(-1+k) ], cost: 4+5*k
     38: __init -> f4 : arg1'=arg1P_1-arg2P_2*k_2, arg2'=arg2P_2, [ arg1P_1>0 && arg2P_2>0 && k_2>=0 && -arg2P_2*(-1+k_2)+arg1P_1>arg2P_2 ], cost: 4+5*k_2

Computing asymptotic complexity for rule 37
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 38
   Simplified the guard:
     38: __init -> f4 : arg1'=arg1P_1-arg2P_2*k_2, arg2'=arg2P_2, [ arg2P_2>0 && k_2>=0 && -arg2P_2*(-1+k_2)+arg1P_1>arg2P_2 ], cost: 4+5*k_2
   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),?)