WORST_CASE(Omega(1),?)

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

Initial linear ITS problem
   Start location: __init
      0: f1_0_main_Load -> f54_0_loop_LE : arg1'=arg1P_1, arg2'=arg2P_1, [ arg1>0 && arg2>-1 && arg2==arg1P_1 && arg2==arg2P_1 ], cost: 1
      1: f54_0_loop_LE -> f54_0_loop_LE : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1>4 && arg2>0 && arg2>=arg1 && -1+arg1==arg1P_2 && -1+arg2==arg2P_2 ], cost: 1
      2: f54_0_loop_LE -> f54_0_loop_LE : arg1'=arg1P_3, arg2'=arg2P_3, [ arg2>0 && arg2>=arg1 && arg1<5 && -2+arg2-arg1<=2 && arg1>-1 && 2+arg1==arg1P_3 && -1+arg2==arg2P_3 ], cost: 1
      3: f54_0_loop_LE -> f54_0_loop_LE : arg1'=arg1P_4, arg2'=arg2P_4, [ arg2>0 && arg2>=arg1 && arg1<5 && -2+arg2-arg1>2 && arg1>-1 && 1+arg1==arg1P_4 && arg2==arg2P_4 ], cost: 1
      4: f54_0_loop_LE -> f54_0_loop_LE : arg1'=arg1P_5, arg2'=arg2P_5, [ arg2<arg1 && arg1>1 && 1+arg2>=2*arg1 && arg2>0 && 1+arg1==arg1P_5 && 1+arg2==arg2P_5 ], cost: 1
      5: f54_0_loop_LE -> f54_0_loop_LE : arg1'=arg1P_6, arg2'=arg2P_6, [ arg2<arg1 && arg1>1 && 1+arg2<2*arg1 && arg2>0 && -1+arg1==arg1P_6 && 1+arg2==arg2P_6 ], cost: 1
      6: __init -> f1_0_main_Load : arg1'=arg1P_7, arg2'=arg2P_7, [], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
      6: __init -> f1_0_main_Load : arg1'=arg1P_7, arg2'=arg2P_7, [], cost: 1

Removed rules with unsatisfiable guard:
   Start location: __init
      0: f1_0_main_Load -> f54_0_loop_LE : arg1'=arg1P_1, arg2'=arg2P_1, [ arg1>0 && arg2>-1 && arg2==arg1P_1 && arg2==arg2P_1 ], cost: 1
      1: f54_0_loop_LE -> f54_0_loop_LE : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1>4 && arg2>0 && arg2>=arg1 && -1+arg1==arg1P_2 && -1+arg2==arg2P_2 ], cost: 1
      2: f54_0_loop_LE -> f54_0_loop_LE : arg1'=arg1P_3, arg2'=arg2P_3, [ arg2>0 && arg2>=arg1 && arg1<5 && -2+arg2-arg1<=2 && arg1>-1 && 2+arg1==arg1P_3 && -1+arg2==arg2P_3 ], cost: 1
      3: f54_0_loop_LE -> f54_0_loop_LE : arg1'=arg1P_4, arg2'=arg2P_4, [ arg2>0 && arg2>=arg1 && arg1<5 && -2+arg2-arg1>2 && arg1>-1 && 1+arg1==arg1P_4 && arg2==arg2P_4 ], cost: 1
      5: f54_0_loop_LE -> f54_0_loop_LE : arg1'=arg1P_6, arg2'=arg2P_6, [ arg2<arg1 && arg1>1 && 1+arg2<2*arg1 && arg2>0 && -1+arg1==arg1P_6 && 1+arg2==arg2P_6 ], cost: 1
      6: __init -> f1_0_main_Load : arg1'=arg1P_7, arg2'=arg2P_7, [], cost: 1

Simplified all rules, resulting in:
   Start location: __init
      0: f1_0_main_Load -> f54_0_loop_LE : arg1'=arg2, [ arg1>0 && arg2>-1 ], cost: 1
      1: f54_0_loop_LE -> f54_0_loop_LE : arg1'=-1+arg1, arg2'=-1+arg2, [ arg1>4 && arg2>0 && arg2>=arg1 ], cost: 1
      2: f54_0_loop_LE -> f54_0_loop_LE : arg1'=2+arg1, arg2'=-1+arg2, [ arg2>0 && arg2>=arg1 && arg1<5 && -2+arg2-arg1<=2 && arg1>-1 ], cost: 1
      3: f54_0_loop_LE -> f54_0_loop_LE : arg1'=1+arg1, [ arg1<5 && -2+arg2-arg1>2 && arg1>-1 ], cost: 1
      5: f54_0_loop_LE -> f54_0_loop_LE : arg1'=-1+arg1, arg2'=1+arg2, [ arg2<arg1 && arg1>1 && arg2>0 ], cost: 1
      6: __init -> f1_0_main_Load : arg1'=arg1P_7, arg2'=arg2P_7, [], cost: 1

### Simplification by acceleration and chaining ###

Accelerating simple loops of location 1.
   Accelerating the following rules:
      1: f54_0_loop_LE -> f54_0_loop_LE : arg1'=-1+arg1, arg2'=-1+arg2, [ arg1>4 && arg2>0 && arg2>=arg1 ], cost: 1
      2: f54_0_loop_LE -> f54_0_loop_LE : arg1'=2+arg1, arg2'=-1+arg2, [ arg2>0 && arg2>=arg1 && arg1<5 && -2+arg2-arg1<=2 && arg1>-1 ], cost: 1
      3: f54_0_loop_LE -> f54_0_loop_LE : arg1'=1+arg1, [ arg1<5 && -2+arg2-arg1>2 && arg1>-1 ], cost: 1
      5: f54_0_loop_LE -> f54_0_loop_LE : arg1'=-1+arg1, arg2'=1+arg2, [ arg2<arg1 && arg1>1 && arg2>0 ], cost: 1

   Accelerated rule 1 with backward acceleration, yielding the new rule 7.
   Accelerated rule 2 with backward acceleration, yielding the new rule 8.
   Accelerated rule 3 with backward acceleration, yielding the new rule 9.
   Accelerated rule 3 with backward acceleration, yielding the new rule 10.
   Accelerated rule 5 with backward acceleration, yielding the new rule 11.
[accelerate] Nesting with 5 inner and 4 outer candidates
   Nested simple loops 1 (outer loop) and 9 (inner loop) with Rule(1 | arg1>-1, 5-arg1>=0, -8+arg2>=1, 3>2, | -16+2*arg2 || 1 | 0=4, 1=8, ), resulting in the new rules: 12, 13.
   Removing the simple loops: 1 2 3 5.

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
      0: f1_0_main_Load -> f54_0_loop_LE : arg1'=arg2, [ arg1>0 && arg2>-1 ], cost: 1
      7: f54_0_loop_LE -> f54_0_loop_LE : arg1'=4, arg2'=4+arg2-arg1, [ arg2>0 && arg2>=arg1 && -4+arg1>=0 ], cost: -4+arg1
      8: f54_0_loop_LE -> f54_0_loop_LE : arg1'=2*k_1+arg1, arg2'=arg2-k_1, [ -2+arg2-arg1<=2 && arg1>-1 && k_1>=0 && 1+arg2-k_1>0 && 1+arg2-k_1>=-2+2*k_1+arg1 && -2+2*k_1+arg1<5 ], cost: k_1
      9: f54_0_loop_LE -> f54_0_loop_LE : arg1'=5, [ arg1>-1 && 5-arg1>=0 && -6+arg2>2 ], cost: 5-arg1
     10: f54_0_loop_LE -> f54_0_loop_LE : arg1'=-4+arg2, [ arg1>-1 && -4+arg2-arg1>=0 && -5+arg2<5 ], cost: -4+arg2-arg1
     11: f54_0_loop_LE -> f54_0_loop_LE : arg1'=-k_3+arg1, arg2'=arg2+k_3, [ arg2>0 && k_3>=0 && -1+arg2+k_3<1-k_3+arg1 && 1-k_3+arg1>1 ], cost: k_3
     12: f54_0_loop_LE -> f54_0_loop_LE : arg1'=4, arg2'=8, [ arg1>-1 && 5-arg1>=0 && -8+arg2>=1 ], cost: -16+2*arg2
     13: f54_0_loop_LE -> f54_0_loop_LE : arg1'=4, arg2'=8, [ arg1>4 && arg2>=arg1 && 6-arg1>=0 && -9+arg2>=1 ], cost: -17+2*arg2
      6: __init -> f1_0_main_Load : arg1'=arg1P_7, arg2'=arg2P_7, [], cost: 1

Chained accelerated rules (with incoming rules):
   Start location: __init
      0: f1_0_main_Load -> f54_0_loop_LE : arg1'=arg2, [ arg1>0 && arg2>-1 ], cost: 1
     14: f1_0_main_Load -> f54_0_loop_LE : arg1'=4, arg2'=4, [ arg1>0 && -4+arg2>=0 ], cost: -3+arg2
     15: f1_0_main_Load -> f54_0_loop_LE : arg1'=arg2+2*k_1, arg2'=arg2-k_1, [ arg1>0 && arg2>-1 && k_1>=0 && 1+arg2-k_1>0 && 1+arg2-k_1>=-2+arg2+2*k_1 && -2+arg2+2*k_1<5 ], cost: 1+k_1
     16: f1_0_main_Load -> f54_0_loop_LE : arg1'=arg2-k_3, arg2'=arg2+k_3, [ arg1>0 && arg2>0 && k_3>=0 && -1+arg2+k_3<1+arg2-k_3 && 1+arg2-k_3>1 ], cost: 1+k_3
      6: __init -> f1_0_main_Load : arg1'=arg1P_7, arg2'=arg2P_7, [], cost: 1

Removed unreachable locations (and leaf rules with constant cost):
   Start location: __init
     14: f1_0_main_Load -> f54_0_loop_LE : arg1'=4, arg2'=4, [ arg1>0 && -4+arg2>=0 ], cost: -3+arg2
     15: f1_0_main_Load -> f54_0_loop_LE : arg1'=arg2+2*k_1, arg2'=arg2-k_1, [ arg1>0 && arg2>-1 && k_1>=0 && 1+arg2-k_1>0 && 1+arg2-k_1>=-2+arg2+2*k_1 && -2+arg2+2*k_1<5 ], cost: 1+k_1
     16: f1_0_main_Load -> f54_0_loop_LE : arg1'=arg2-k_3, arg2'=arg2+k_3, [ arg1>0 && arg2>0 && k_3>=0 && -1+arg2+k_3<1+arg2-k_3 && 1+arg2-k_3>1 ], cost: 1+k_3
      6: __init -> f1_0_main_Load : arg1'=arg1P_7, arg2'=arg2P_7, [], cost: 1

Eliminated locations (on tree-shaped paths):
   Start location: __init
     17: __init -> f54_0_loop_LE : arg1'=4, arg2'=4, [ arg1P_7>0 && -4+arg2P_7>=0 ], cost: -2+arg2P_7
     18: __init -> f54_0_loop_LE : arg1'=arg2P_7+2*k_1, arg2'=arg2P_7-k_1, [ arg1P_7>0 && arg2P_7>-1 && k_1>=0 && 1+arg2P_7-k_1>0 && 1+arg2P_7-k_1>=-2+arg2P_7+2*k_1 && -2+arg2P_7+2*k_1<5 ], cost: 2+k_1
     19: __init -> f54_0_loop_LE : arg1'=arg2P_7-k_3, arg2'=arg2P_7+k_3, [ arg1P_7>0 && arg2P_7>0 && k_3>=0 && -1+arg2P_7+k_3<1+arg2P_7-k_3 && 1+arg2P_7-k_3>1 ], cost: 2+k_3

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: __init
     17: __init -> f54_0_loop_LE : arg1'=4, arg2'=4, [ arg1P_7>0 && -4+arg2P_7>=0 ], cost: -2+arg2P_7
     18: __init -> f54_0_loop_LE : arg1'=arg2P_7+2*k_1, arg2'=arg2P_7-k_1, [ arg1P_7>0 && arg2P_7>-1 && k_1>=0 && 1+arg2P_7-k_1>0 && 1+arg2P_7-k_1>=-2+arg2P_7+2*k_1 && -2+arg2P_7+2*k_1<5 ], cost: 2+k_1
     19: __init -> f54_0_loop_LE : arg1'=arg2P_7-k_3, arg2'=arg2P_7+k_3, [ arg1P_7>0 && arg2P_7>0 && k_3>=0 && -1+arg2P_7+k_3<1+arg2P_7-k_3 && 1+arg2P_7-k_3>1 ], cost: 2+k_3

Computing asymptotic complexity for rule 17
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 19
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 18
   Simplified the guard:
     18: __init -> f54_0_loop_LE : arg1'=arg2P_7+2*k_1, arg2'=arg2P_7-k_1, [ arg1P_7>0 && k_1>=0 && 1+arg2P_7-k_1>0 && 1+arg2P_7-k_1>=-2+arg2P_7+2*k_1 && -2+arg2P_7+2*k_1<5 ], cost: 2+k_1
   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),?)