WORST_CASE(Omega(1),?)

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

Initial linear ITS problem
   Start location: __init
      0: f1_0_main_Load -> f113_0_upAndDown_GT : arg1'=arg1P_1, arg2'=arg2P_1, [ arg1>0 && arg2>-1 && 0==arg1P_1 && arg2==arg2P_1 ], cost: 1
      1: f113_0_upAndDown_GT -> f113_0_upAndDown_GT : arg1'=arg1P_2, arg2'=arg2P_2, [ arg2<10 && arg2<11 && arg2>0 && 1==arg1 && 1==arg1P_2 && 1+arg2==arg2P_2 ], cost: 1
      2: f113_0_upAndDown_GT -> f113_0_upAndDown_GT : arg1'=arg1P_3, arg2'=arg2P_3, [ arg2<10 && arg2>0 && arg2<11 && 0==arg1 && 0==arg1P_3 && -1+arg2==arg2P_3 ], cost: 1
      3: f113_0_upAndDown_GT -> f113_0_upAndDown_GT : arg1'=arg1P_4, arg2'=arg2P_4, [ 10==arg2 && 0==arg1P_4 && 9==arg2P_4 ], cost: 1
      4: f113_0_upAndDown_GT -> f113_0_upAndDown_GT : arg1'=arg1P_5, arg2'=arg2P_5, [ 0==arg2 && 1==arg1P_5 && 1==arg2P_5 ], cost: 1
      5: __init -> f1_0_main_Load : arg1'=arg1P_6, arg2'=arg2P_6, [], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
      5: __init -> f1_0_main_Load : arg1'=arg1P_6, arg2'=arg2P_6, [], cost: 1

Simplified all rules, resulting in:
   Start location: __init
      0: f1_0_main_Load -> f113_0_upAndDown_GT : arg1'=0, [ arg1>0 && arg2>-1 ], cost: 1
      1: f113_0_upAndDown_GT -> f113_0_upAndDown_GT : arg1'=1, arg2'=1+arg2, [ arg2<10 && arg2>0 && 1==arg1 ], cost: 1
      2: f113_0_upAndDown_GT -> f113_0_upAndDown_GT : arg1'=0, arg2'=-1+arg2, [ arg2<10 && arg2>0 && 0==arg1 ], cost: 1
      3: f113_0_upAndDown_GT -> f113_0_upAndDown_GT : arg1'=0, arg2'=9, [ 10==arg2 ], cost: 1
      4: f113_0_upAndDown_GT -> f113_0_upAndDown_GT : arg1'=1, arg2'=1, [ 0==arg2 ], cost: 1
      5: __init -> f1_0_main_Load : arg1'=arg1P_6, arg2'=arg2P_6, [], cost: 1

### Simplification by acceleration and chaining ###

Accelerating simple loops of location 1.
   Accelerating the following rules:
      1: f113_0_upAndDown_GT -> f113_0_upAndDown_GT : arg1'=1, arg2'=1+arg2, [ arg2<10 && arg2>0 && 1==arg1 ], cost: 1
      2: f113_0_upAndDown_GT -> f113_0_upAndDown_GT : arg1'=0, arg2'=-1+arg2, [ arg2<10 && arg2>0 && 0==arg1 ], cost: 1
      3: f113_0_upAndDown_GT -> f113_0_upAndDown_GT : arg1'=0, arg2'=9, [ 10==arg2 ], cost: 1
      4: f113_0_upAndDown_GT -> f113_0_upAndDown_GT : arg1'=1, arg2'=1, [ 0==arg2 ], cost: 1

   Accelerated rule 1 with metering function 10-arg2, yielding the new rule 6.
   Accelerated rule 2 with metering function arg2, yielding the new rule 7.
   Accelerated rule 3 with metering function -9+arg2, yielding the new rule 8.
   Accelerated rule 4 with metering function 1-arg2, yielding the new rule 9.
   Removing the simple loops: 1 2 3 4.

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
      0: f1_0_main_Load -> f113_0_upAndDown_GT : arg1'=0, [ arg1>0 && arg2>-1 ], cost: 1
      6: f113_0_upAndDown_GT -> f113_0_upAndDown_GT : arg1'=1, arg2'=10, [ arg2<10 && arg2>0 && 1==arg1 ], cost: 10-arg2
      7: f113_0_upAndDown_GT -> f113_0_upAndDown_GT : arg1'=0, arg2'=0, [ arg2<10 && arg2>0 && 0==arg1 ], cost: arg2
      8: f113_0_upAndDown_GT -> f113_0_upAndDown_GT : arg1'=0, arg2'=9, [ 10==arg2 ], cost: -9+arg2
      9: f113_0_upAndDown_GT -> f113_0_upAndDown_GT : arg1'=1, arg2'=1, [ 0==arg2 ], cost: 1-arg2
      5: __init -> f1_0_main_Load : arg1'=arg1P_6, arg2'=arg2P_6, [], cost: 1

Chained accelerated rules (with incoming rules):
   Start location: __init
      0: f1_0_main_Load -> f113_0_upAndDown_GT : arg1'=0, [ arg1>0 && arg2>-1 ], cost: 1
     10: f1_0_main_Load -> f113_0_upAndDown_GT : arg1'=0, arg2'=0, [ arg1>0 && arg2<10 && arg2>0 ], cost: 1+arg2
     11: f1_0_main_Load -> f113_0_upAndDown_GT : arg1'=0, arg2'=9, [ arg1>0 && 10==arg2 ], cost: -8+arg2
     12: f1_0_main_Load -> f113_0_upAndDown_GT : arg1'=1, arg2'=1, [ arg1>0 && 0==arg2 ], cost: 2-arg2
      5: __init -> f1_0_main_Load : arg1'=arg1P_6, arg2'=arg2P_6, [], cost: 1

Removed unreachable locations (and leaf rules with constant cost):
   Start location: __init
     10: f1_0_main_Load -> f113_0_upAndDown_GT : arg1'=0, arg2'=0, [ arg1>0 && arg2<10 && arg2>0 ], cost: 1+arg2
     11: f1_0_main_Load -> f113_0_upAndDown_GT : arg1'=0, arg2'=9, [ arg1>0 && 10==arg2 ], cost: -8+arg2
     12: f1_0_main_Load -> f113_0_upAndDown_GT : arg1'=1, arg2'=1, [ arg1>0 && 0==arg2 ], cost: 2-arg2
      5: __init -> f1_0_main_Load : arg1'=arg1P_6, arg2'=arg2P_6, [], cost: 1

Eliminated locations (on tree-shaped paths):
   Start location: __init
     13: __init -> f113_0_upAndDown_GT : arg1'=0, arg2'=0, [ arg1P_6>0 && arg2P_6<10 && arg2P_6>0 ], cost: 2+arg2P_6
     14: __init -> f113_0_upAndDown_GT : arg1'=0, arg2'=9, [ arg1P_6>0 && 10==arg2P_6 ], cost: -7+arg2P_6
     15: __init -> f113_0_upAndDown_GT : arg1'=1, arg2'=1, [ arg1P_6>0 && 0==arg2P_6 ], cost: 3-arg2P_6

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: __init
     13: __init -> f113_0_upAndDown_GT : arg1'=0, arg2'=0, [ arg1P_6>0 && arg2P_6<10 && arg2P_6>0 ], cost: 2+arg2P_6
     14: __init -> f113_0_upAndDown_GT : arg1'=0, arg2'=9, [ arg1P_6>0 && 10==arg2P_6 ], cost: -7+arg2P_6
     15: __init -> f113_0_upAndDown_GT : arg1'=1, arg2'=1, [ arg1P_6>0 && 0==arg2P_6 ], cost: 3-arg2P_6

Computing asymptotic complexity for rule 13
   Could not solve the limit problem.
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 14
   Could not solve the limit problem.
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 15
   Could not solve the limit problem.
   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),?)