WORST_CASE(Omega(1),?)

### Pre-processing the ITS problem ###

Initial linear ITS problem
   Start location: __init
      0: f1_0_main_Load -> f587_0_main_LT : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, arg4'=arg4P_1, [ arg1P_1>-1 && arg2>-1 && arg2P_1>-1 && arg1>0 && arg1P_1-arg2P_1==arg3P_1 && 2==arg4P_1 ], cost: 1
      1: f587_0_main_LT -> f587_0_main_LT : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, [ arg4>-1 && arg3>0 && x8_1>-1 && x9_1>-1 && arg2>-1 && 1+x9_1+arg2>=0 && -x8_1+arg1==arg1P_2 && 1+x9_1+arg2==arg2P_2 && -1-x9_1-arg2-x8_1+arg1==arg3P_2 && 2+arg4==arg4P_2 ], cost: 1
      2: __init -> f1_0_main_Load : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, [], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
      2: __init -> f1_0_main_Load : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, [], cost: 1

Simplified all rules, resulting in:
   Start location: __init
      0: f1_0_main_Load -> f587_0_main_LT : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg1P_1-arg2P_1, arg4'=2, [ arg1P_1>-1 && arg2>-1 && arg2P_1>-1 && arg1>0 ], cost: 1
      1: f587_0_main_LT -> f587_0_main_LT : arg1'=-x8_1+arg1, arg2'=1+x9_1+arg2, arg3'=-1-x9_1-arg2-x8_1+arg1, arg4'=2+arg4, [ arg4>-1 && arg3>0 && x8_1>-1 && x9_1>-1 && arg2>-1 ], cost: 1
      2: __init -> f1_0_main_Load : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, [], cost: 1

### Simplification by acceleration and chaining ###

Accelerating simple loops of location 1.
   Accelerating the following rules:
      1: f587_0_main_LT -> f587_0_main_LT : arg1'=-x8_1+arg1, arg2'=1+x9_1+arg2, arg3'=-1-x9_1-arg2-x8_1+arg1, arg4'=2+arg4, [ arg4>-1 && arg3>0 && x8_1>-1 && x9_1>-1 && arg2>-1 ], cost: 1

[test] deduced invariant -arg2-arg3+arg1<=0
   Accelerated rule 1 with backward acceleration, yielding the new rule 3.
[accelerate] Nesting with 1 inner and 1 outer candidates

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
      0: f1_0_main_Load -> f587_0_main_LT : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg1P_1-arg2P_1, arg4'=2, [ arg1P_1>-1 && arg2>-1 && arg2P_1>-1 && arg1>0 ], cost: 1
      1: f587_0_main_LT -> f587_0_main_LT : arg1'=-x8_1+arg1, arg2'=1+x9_1+arg2, arg3'=-1-x9_1-arg2-x8_1+arg1, arg4'=2+arg4, [ arg4>-1 && arg3>0 && x8_1>-1 && x9_1>-1 && arg2>-1 ], cost: 1
      3: f587_0_main_LT -> f587_0_main_LT : arg1'=arg1-k*x8_1, arg2'=k+k*x9_1+arg2, arg3'=-k-x9_1-x9_1*(-1+k)-arg2-(-1+k)*x8_1-x8_1+arg1, arg4'=2*k+arg4, [ arg4>-1 && x8_1>-1 && x9_1>-1 && arg2>-1 && -arg2-arg3+arg1<=0 && k>=1 && 1-k-x9_1-arg2-x8_1*(-2+k)-x8_1-x9_1*(-2+k)+arg1>0 ], cost: k
      2: __init -> f1_0_main_Load : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, [], cost: 1

Chained accelerated rules (with incoming rules):
   Start location: __init
      0: f1_0_main_Load -> f587_0_main_LT : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg1P_1-arg2P_1, arg4'=2, [ arg1P_1>-1 && arg2>-1 && arg2P_1>-1 && arg1>0 ], cost: 1
      4: f1_0_main_Load -> f587_0_main_LT : arg1'=arg1P_1-x8_1, arg2'=1+x9_1+arg2P_1, arg3'=-1-x9_1+arg1P_1-x8_1-arg2P_1, arg4'=4, [ arg1P_1>-1 && arg2>-1 && arg2P_1>-1 && arg1>0 && arg1P_1-arg2P_1>0 && x8_1>-1 && x9_1>-1 ], cost: 2
      5: f1_0_main_Load -> f587_0_main_LT : arg1'=arg1P_1-k*x8_1, arg2'=k+k*x9_1+arg2P_1, arg3'=-k-x9_1-x9_1*(-1+k)-(-1+k)*x8_1+arg1P_1-x8_1-arg2P_1, arg4'=2+2*k, [ arg1P_1>-1 && arg2>-1 && arg2P_1>-1 && arg1>0 && x8_1>-1 && x9_1>-1 && k>=1 && 1-k-x9_1-x8_1*(-2+k)+arg1P_1-x8_1-x9_1*(-2+k)-arg2P_1>0 ], cost: 1+k
      2: __init -> f1_0_main_Load : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, [], cost: 1

Removed unreachable locations (and leaf rules with constant cost):
   Start location: __init
      5: f1_0_main_Load -> f587_0_main_LT : arg1'=arg1P_1-k*x8_1, arg2'=k+k*x9_1+arg2P_1, arg3'=-k-x9_1-x9_1*(-1+k)-(-1+k)*x8_1+arg1P_1-x8_1-arg2P_1, arg4'=2+2*k, [ arg1P_1>-1 && arg2>-1 && arg2P_1>-1 && arg1>0 && x8_1>-1 && x9_1>-1 && k>=1 && 1-k-x9_1-x8_1*(-2+k)+arg1P_1-x8_1-x9_1*(-2+k)-arg2P_1>0 ], cost: 1+k
      2: __init -> f1_0_main_Load : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, [], cost: 1

Eliminated locations (on linear paths):
   Start location: __init
      6: __init -> f587_0_main_LT : arg1'=arg1P_1-k*x8_1, arg2'=k+k*x9_1+arg2P_1, arg3'=-k-x9_1-x9_1*(-1+k)-(-1+k)*x8_1+arg1P_1-x8_1-arg2P_1, arg4'=2+2*k, [ arg1P_1>-1 && arg2P_3>-1 && arg2P_1>-1 && arg1P_3>0 && x8_1>-1 && x9_1>-1 && k>=1 && 1-k-x9_1-x8_1*(-2+k)+arg1P_1-x8_1-x9_1*(-2+k)-arg2P_1>0 ], cost: 2+k

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: __init
      6: __init -> f587_0_main_LT : arg1'=arg1P_1-k*x8_1, arg2'=k+k*x9_1+arg2P_1, arg3'=-k-x9_1-x9_1*(-1+k)-(-1+k)*x8_1+arg1P_1-x8_1-arg2P_1, arg4'=2+2*k, [ arg1P_1>-1 && arg2P_3>-1 && arg2P_1>-1 && arg1P_3>0 && x8_1>-1 && x9_1>-1 && k>=1 && 1-k-x9_1-x8_1*(-2+k)+arg1P_1-x8_1-x9_1*(-2+k)-arg2P_1>0 ], cost: 2+k

Computing asymptotic complexity for rule 6
   Simplified the guard:
      6: __init -> f587_0_main_LT : arg1'=arg1P_1-k*x8_1, arg2'=k+k*x9_1+arg2P_1, arg3'=-k-x9_1-x9_1*(-1+k)-(-1+k)*x8_1+arg1P_1-x8_1-arg2P_1, arg4'=2+2*k, [ arg2P_3>-1 && arg2P_1>-1 && arg1P_3>0 && x8_1>-1 && x9_1>-1 && k>=1 && 1-k-x9_1-x8_1*(-2+k)+arg1P_1-x8_1-x9_1*(-2+k)-arg2P_1>0 ], cost: 2+k
   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),?)