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

Eliminated locations (on tree-shaped paths):
   Start location: __init
     25: f3 -> f6 : [ arg2+arg1>0 && arg1<=arg2 ], cost: 2
     26: f3 -> f7 : arg1'=-1+arg1, [ arg2+arg1>0 && arg1>arg2 ], cost: 4
     29: f6 -> f7 : arg1'=-1+arg1, [ arg1==arg2 ], cost: 4
     30: f6 -> f7 : arg2'=-1+arg2, [ arg1<arg2 ], cost: 4
     31: f6 -> f7 : arg2'=-1+arg2, [ arg1>arg2 ], cost: 4
     15: f7 -> f3 : [], cost: 1
     19: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, [], cost: 3

Eliminated locations (on tree-shaped paths):
   Start location: __init
     34: f3 -> f3 : arg1'=-1+arg1, [ arg2+arg1>0 && arg1>arg2 ], cost: 5
     35: f3 -> f3 : arg1'=-1+arg1, [ arg2+arg1>0 && arg1==arg2 ], cost: 7
     36: f3 -> f3 : arg2'=-1+arg2, [ arg2+arg1>0 && arg1<arg2 ], cost: 7
     19: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, [], cost: 3

Accelerating simple loops of location 2.
   Accelerating the following rules:
     34: f3 -> f3 : arg1'=-1+arg1, [ arg2+arg1>0 && arg1>arg2 ], cost: 5
     35: f3 -> f3 : arg1'=-1+arg1, [ arg2+arg1>0 && arg1==arg2 ], cost: 7
     36: f3 -> f3 : arg2'=-1+arg2, [ arg2+arg1>0 && arg1<arg2 ], cost: 7

   Accelerated rule 34 with backward acceleration, yielding the new rule 37.
   Accelerated rule 34 with backward acceleration, yielding the new rule 38.
   Failed to prove monotonicity of the guard of rule 35.
   Accelerated rule 36 with backward acceleration, yielding the new rule 39.
   Accelerated rule 36 with backward acceleration, yielding the new rule 40.
[accelerate] Nesting with 5 inner and 3 outer candidates
   Nested simple loops 36 (outer loop) and 35 (inner loop) with Rule(2 | arg1==arg2, k_3>=0, 1-2*k_3+arg2+arg1>0, | 14*k_3 || 2 | 0=-k_3+arg1, 1=-k_3+arg2, ), resulting in the new rules: 41, 42.
   Removing the simple loops: 34 36.

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     35: f3 -> f3 : arg1'=-1+arg1, [ arg2+arg1>0 && arg1==arg2 ], cost: 7
     37: f3 -> f3 : arg1'=-arg2, [ arg2+arg1>=0 && 1-arg2>arg2 ], cost: 5*arg2+5*arg1
     38: f3 -> f3 : arg1'=arg2, [ -arg2+arg1>=0 && 1+2*arg2>0 ], cost: -5*arg2+5*arg1
     39: f3 -> f3 : arg2'=-arg1, [ arg2+arg1>=0 && arg1<1-arg1 ], cost: 7*arg2+7*arg1
     40: f3 -> f3 : arg2'=arg1, [ arg2-arg1>=0 && 1+2*arg1>0 ], cost: 7*arg2-7*arg1
     41: f3 -> f3 : arg1'=-k_3+arg1, arg2'=-k_3+arg2, [ arg1==arg2 && k_3>=0 && 1-2*k_3+arg2+arg1>0 ], cost: 14*k_3
     42: f3 -> f3 : arg1'=-k_3+arg1, arg2'=-1-k_3+arg2, [ arg2+arg1>0 && arg1==-1+arg2 && k_3>=0 && -2*k_3+arg2+arg1>0 ], cost: 7+14*k_3
     19: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, [], cost: 3

Chained accelerated rules (with incoming rules):
   Start location: __init
     19: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, [], cost: 3
     43: __init -> f3 : arg1'=-1+arg1P_1, arg2'=arg1P_1, [ 2*arg1P_1>0 ], cost: 10
     44: __init -> f3 : arg1'=-arg2P_2, arg2'=arg2P_2, [ arg2P_2+arg1P_1>=0 && 1-arg2P_2>arg2P_2 ], cost: 3+5*arg2P_2+5*arg1P_1
     45: __init -> f3 : arg1'=arg2P_2, arg2'=arg2P_2, [ -arg2P_2+arg1P_1>=0 && 1+2*arg2P_2>0 ], cost: 3-5*arg2P_2+5*arg1P_1
     46: __init -> f3 : arg1'=arg1P_1, arg2'=-arg1P_1, [ arg2P_2+arg1P_1>=0 && arg1P_1<1-arg1P_1 ], cost: 3+7*arg2P_2+7*arg1P_1
     47: __init -> f3 : arg1'=arg1P_1, arg2'=arg1P_1, [ arg2P_2-arg1P_1>=0 && 1+2*arg1P_1>0 ], cost: 3+7*arg2P_2-7*arg1P_1
     48: __init -> f3 : arg1'=-k_3+arg1P_1, arg2'=-k_3+arg1P_1, [ k_3>=0 && 1-2*k_3+2*arg1P_1>0 ], cost: 3+14*k_3
     49: __init -> f3 : arg1'=-k_3+arg1P_1, arg2'=-k_3+arg1P_1, [ 1+2*arg1P_1>0 && k_3>=0 && 1-2*k_3+2*arg1P_1>0 ], cost: 10+14*k_3

Removed unreachable locations (and leaf rules with constant cost):
   Start location: __init
     44: __init -> f3 : arg1'=-arg2P_2, arg2'=arg2P_2, [ arg2P_2+arg1P_1>=0 && 1-arg2P_2>arg2P_2 ], cost: 3+5*arg2P_2+5*arg1P_1
     45: __init -> f3 : arg1'=arg2P_2, arg2'=arg2P_2, [ -arg2P_2+arg1P_1>=0 && 1+2*arg2P_2>0 ], cost: 3-5*arg2P_2+5*arg1P_1
     46: __init -> f3 : arg1'=arg1P_1, arg2'=-arg1P_1, [ arg2P_2+arg1P_1>=0 && arg1P_1<1-arg1P_1 ], cost: 3+7*arg2P_2+7*arg1P_1
     47: __init -> f3 : arg1'=arg1P_1, arg2'=arg1P_1, [ arg2P_2-arg1P_1>=0 && 1+2*arg1P_1>0 ], cost: 3+7*arg2P_2-7*arg1P_1
     48: __init -> f3 : arg1'=-k_3+arg1P_1, arg2'=-k_3+arg1P_1, [ k_3>=0 && 1-2*k_3+2*arg1P_1>0 ], cost: 3+14*k_3
     49: __init -> f3 : arg1'=-k_3+arg1P_1, arg2'=-k_3+arg1P_1, [ 1+2*arg1P_1>0 && k_3>=0 && 1-2*k_3+2*arg1P_1>0 ], cost: 10+14*k_3

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: __init
     44: __init -> f3 : arg1'=-arg2P_2, arg2'=arg2P_2, [ arg2P_2+arg1P_1>=0 && 1-arg2P_2>arg2P_2 ], cost: 3+5*arg2P_2+5*arg1P_1
     45: __init -> f3 : arg1'=arg2P_2, arg2'=arg2P_2, [ -arg2P_2+arg1P_1>=0 && 1+2*arg2P_2>0 ], cost: 3-5*arg2P_2+5*arg1P_1
     46: __init -> f3 : arg1'=arg1P_1, arg2'=-arg1P_1, [ arg2P_2+arg1P_1>=0 && arg1P_1<1-arg1P_1 ], cost: 3+7*arg2P_2+7*arg1P_1
     47: __init -> f3 : arg1'=arg1P_1, arg2'=arg1P_1, [ arg2P_2-arg1P_1>=0 && 1+2*arg1P_1>0 ], cost: 3+7*arg2P_2-7*arg1P_1
     48: __init -> f3 : arg1'=-k_3+arg1P_1, arg2'=-k_3+arg1P_1, [ k_3>=0 && 1-2*k_3+2*arg1P_1>0 ], cost: 3+14*k_3
     49: __init -> f3 : arg1'=-k_3+arg1P_1, arg2'=-k_3+arg1P_1, [ 1+2*arg1P_1>0 && k_3>=0 && 1-2*k_3+2*arg1P_1>0 ], cost: 10+14*k_3

Computing asymptotic complexity for rule 44
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 45
   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

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

Computing asymptotic complexity for rule 49
   Simplified the guard:
     49: __init -> f3 : arg1'=-k_3+arg1P_1, arg2'=-k_3+arg1P_1, [ k_3>=0 && 1-2*k_3+2*arg1P_1>0 ], cost: 10+14*k_3
   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),?)