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, arg3'=arg3P_1, arg4'=arg4P_1, arg5'=arg5P_1, arg6'=arg6P_1, arg7'=arg7P_1, [ arg1==arg1P_1 && arg2==arg2P_1 && arg3==arg3P_1 && arg5==arg5P_1 && arg6==arg6P_1 && arg7==arg7P_1 ], cost: 1
      1: f2 -> f3 : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, arg5'=arg5P_2, arg6'=arg6P_2, arg7'=arg7P_2, [ arg1==arg1P_2 && arg2==arg2P_2 && arg3==arg3P_2 && arg4==arg4P_2 && arg6==arg6P_2 && arg7==arg7P_2 ], cost: 1
      2: f3 -> f4 : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, arg5'=arg5P_3, arg6'=arg6P_3, arg7'=arg7P_3, [ arg1==arg1P_3 && arg2==arg2P_3 && arg3==arg3P_3 && arg4==arg4P_3 && arg5==arg5P_3 && arg7==arg7P_3 ], cost: 1
      3: f4 -> f5 : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, arg5'=arg5P_4, arg6'=arg6P_4, arg7'=arg7P_4, [ arg1==arg1P_4 && arg2==arg2P_4 && arg3==arg3P_4 && arg4==arg4P_4 && arg5==arg5P_4 && arg6==arg6P_4 ], cost: 1
      4: f5 -> f6 : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, arg5'=arg5P_5, arg6'=arg6P_5, arg7'=arg7P_5, [ arg4==arg1P_5 && arg2==arg2P_5 && arg3==arg3P_5 && arg4==arg4P_5 && arg5==arg5P_5 && arg6==arg6P_5 && arg7==arg7P_5 ], cost: 1
      5: f6 -> f7 : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, arg4'=arg4P_6, arg5'=arg5P_6, arg6'=arg6P_6, arg7'=arg7P_6, [ arg1==arg1P_6 && arg5==arg2P_6 && arg3==arg3P_6 && arg4==arg4P_6 && arg5==arg5P_6 && arg6==arg6P_6 && arg7==arg7P_6 ], cost: 1
      6: f7 -> f8 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, arg5'=arg5P_7, arg6'=arg6P_7, arg7'=arg7P_7, [ arg1==arg1P_7 && arg2==arg2P_7 && 0==arg3P_7 && arg4==arg4P_7 && arg5==arg5P_7 && arg6==arg6P_7 && arg7==arg7P_7 ], cost: 1
     10: f8 -> f9 : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, arg4'=arg4P_11, arg5'=arg5P_11, arg6'=arg6P_11, arg7'=arg7P_11, [ arg4<arg6 && arg1==arg1P_11 && arg2==arg2P_11 && arg3==arg3P_11 && arg4==arg4P_11 && arg5==arg5P_11 && arg6==arg6P_11 && arg7==arg7P_11 ], cost: 1
     11: f8 -> f9 : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, arg4'=arg4P_12, arg5'=arg5P_12, arg6'=arg6P_12, arg7'=arg7P_12, [ arg5<arg7 && arg1==arg1P_12 && arg2==arg2P_12 && arg3==arg3P_12 && arg4==arg4P_12 && arg5==arg5P_12 && arg6==arg6P_12 && arg7==arg7P_12 ], cost: 1
     13: f8 -> f13 : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, arg4'=arg4P_14, arg5'=arg5P_14, arg6'=arg6P_14, arg7'=arg7P_14, [ arg4>=arg6 && arg5>=arg7 && arg1==arg1P_14 && arg2==arg2P_14 && arg3==arg3P_14 && arg4==arg4P_14 && arg5==arg5P_14 && arg6==arg6P_14 && arg7==arg7P_14 ], cost: 1
      7: f9 -> f10 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, arg4'=arg4P_8, arg5'=arg5P_8, arg6'=arg6P_8, arg7'=arg7P_8, [ arg4P_8==1+arg4 && arg1==arg1P_8 && arg2==arg2P_8 && arg3==arg3P_8 && arg5==arg5P_8 && arg6==arg6P_8 && arg7==arg7P_8 ], cost: 1
      8: f10 -> f11 : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, arg4'=arg4P_9, arg5'=arg5P_9, arg6'=arg6P_9, arg7'=arg7P_9, [ arg5P_9==1+arg5 && arg1==arg1P_9 && arg2==arg2P_9 && arg3==arg3P_9 && arg4==arg4P_9 && arg6==arg6P_9 && arg7==arg7P_9 ], cost: 1
      9: f11 -> f12 : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, arg4'=arg4P_10, arg5'=arg5P_10, arg6'=arg6P_10, arg7'=arg7P_10, [ arg3P_10==1+arg3 && arg1==arg1P_10 && arg2==arg2P_10 && arg4==arg4P_10 && arg5==arg5P_10 && arg6==arg6P_10 && arg7==arg7P_10 ], cost: 1
     12: f12 -> f8 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, arg4'=arg4P_13, arg5'=arg5P_13, arg6'=arg6P_13, arg7'=arg7P_13, [ arg1==arg1P_13 && arg2==arg2P_13 && arg3==arg3P_13 && arg4==arg4P_13 && arg5==arg5P_13 && arg6==arg6P_13 && arg7==arg7P_13 ], cost: 1
     14: __init -> f1 : arg1'=arg1P_15, arg2'=arg2P_15, arg3'=arg3P_15, arg4'=arg4P_15, arg5'=arg5P_15, arg6'=arg6P_15, arg7'=arg7P_15, [], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
     14: __init -> f1 : arg1'=arg1P_15, arg2'=arg2P_15, arg3'=arg3P_15, arg4'=arg4P_15, arg5'=arg5P_15, arg6'=arg6P_15, arg7'=arg7P_15, [], cost: 1

Removed unreachable and leaf rules:
   Start location: __init
      0: f1 -> f2 : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, arg4'=arg4P_1, arg5'=arg5P_1, arg6'=arg6P_1, arg7'=arg7P_1, [ arg1==arg1P_1 && arg2==arg2P_1 && arg3==arg3P_1 && arg5==arg5P_1 && arg6==arg6P_1 && arg7==arg7P_1 ], cost: 1
      1: f2 -> f3 : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, arg5'=arg5P_2, arg6'=arg6P_2, arg7'=arg7P_2, [ arg1==arg1P_2 && arg2==arg2P_2 && arg3==arg3P_2 && arg4==arg4P_2 && arg6==arg6P_2 && arg7==arg7P_2 ], cost: 1
      2: f3 -> f4 : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, arg5'=arg5P_3, arg6'=arg6P_3, arg7'=arg7P_3, [ arg1==arg1P_3 && arg2==arg2P_3 && arg3==arg3P_3 && arg4==arg4P_3 && arg5==arg5P_3 && arg7==arg7P_3 ], cost: 1
      3: f4 -> f5 : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, arg5'=arg5P_4, arg6'=arg6P_4, arg7'=arg7P_4, [ arg1==arg1P_4 && arg2==arg2P_4 && arg3==arg3P_4 && arg4==arg4P_4 && arg5==arg5P_4 && arg6==arg6P_4 ], cost: 1
      4: f5 -> f6 : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, arg5'=arg5P_5, arg6'=arg6P_5, arg7'=arg7P_5, [ arg4==arg1P_5 && arg2==arg2P_5 && arg3==arg3P_5 && arg4==arg4P_5 && arg5==arg5P_5 && arg6==arg6P_5 && arg7==arg7P_5 ], cost: 1
      5: f6 -> f7 : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, arg4'=arg4P_6, arg5'=arg5P_6, arg6'=arg6P_6, arg7'=arg7P_6, [ arg1==arg1P_6 && arg5==arg2P_6 && arg3==arg3P_6 && arg4==arg4P_6 && arg5==arg5P_6 && arg6==arg6P_6 && arg7==arg7P_6 ], cost: 1
      6: f7 -> f8 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, arg5'=arg5P_7, arg6'=arg6P_7, arg7'=arg7P_7, [ arg1==arg1P_7 && arg2==arg2P_7 && 0==arg3P_7 && arg4==arg4P_7 && arg5==arg5P_7 && arg6==arg6P_7 && arg7==arg7P_7 ], cost: 1
     10: f8 -> f9 : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, arg4'=arg4P_11, arg5'=arg5P_11, arg6'=arg6P_11, arg7'=arg7P_11, [ arg4<arg6 && arg1==arg1P_11 && arg2==arg2P_11 && arg3==arg3P_11 && arg4==arg4P_11 && arg5==arg5P_11 && arg6==arg6P_11 && arg7==arg7P_11 ], cost: 1
     11: f8 -> f9 : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, arg4'=arg4P_12, arg5'=arg5P_12, arg6'=arg6P_12, arg7'=arg7P_12, [ arg5<arg7 && arg1==arg1P_12 && arg2==arg2P_12 && arg3==arg3P_12 && arg4==arg4P_12 && arg5==arg5P_12 && arg6==arg6P_12 && arg7==arg7P_12 ], cost: 1
      7: f9 -> f10 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, arg4'=arg4P_8, arg5'=arg5P_8, arg6'=arg6P_8, arg7'=arg7P_8, [ arg4P_8==1+arg4 && arg1==arg1P_8 && arg2==arg2P_8 && arg3==arg3P_8 && arg5==arg5P_8 && arg6==arg6P_8 && arg7==arg7P_8 ], cost: 1
      8: f10 -> f11 : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, arg4'=arg4P_9, arg5'=arg5P_9, arg6'=arg6P_9, arg7'=arg7P_9, [ arg5P_9==1+arg5 && arg1==arg1P_9 && arg2==arg2P_9 && arg3==arg3P_9 && arg4==arg4P_9 && arg6==arg6P_9 && arg7==arg7P_9 ], cost: 1
      9: f11 -> f12 : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, arg4'=arg4P_10, arg5'=arg5P_10, arg6'=arg6P_10, arg7'=arg7P_10, [ arg3P_10==1+arg3 && arg1==arg1P_10 && arg2==arg2P_10 && arg4==arg4P_10 && arg5==arg5P_10 && arg6==arg6P_10 && arg7==arg7P_10 ], cost: 1
     12: f12 -> f8 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, arg4'=arg4P_13, arg5'=arg5P_13, arg6'=arg6P_13, arg7'=arg7P_13, [ arg1==arg1P_13 && arg2==arg2P_13 && arg3==arg3P_13 && arg4==arg4P_13 && arg5==arg5P_13 && arg6==arg6P_13 && arg7==arg7P_13 ], cost: 1
     14: __init -> f1 : arg1'=arg1P_15, arg2'=arg2P_15, arg3'=arg3P_15, arg4'=arg4P_15, arg5'=arg5P_15, arg6'=arg6P_15, arg7'=arg7P_15, [], cost: 1

Simplified all rules, resulting in:
   Start location: __init
      0: f1 -> f2 : arg4'=arg4P_1, [], cost: 1
      1: f2 -> f3 : arg5'=arg5P_2, [], cost: 1
      2: f3 -> f4 : arg6'=arg6P_3, [], cost: 1
      3: f4 -> f5 : arg7'=arg7P_4, [], cost: 1
      4: f5 -> f6 : arg1'=arg4, [], cost: 1
      5: f6 -> f7 : arg2'=arg5, [], cost: 1
      6: f7 -> f8 : arg3'=0, [], cost: 1
     10: f8 -> f9 : [ arg4<arg6 ], cost: 1
     11: f8 -> f9 : [ arg5<arg7 ], cost: 1
      7: f9 -> f10 : arg4'=1+arg4, [], cost: 1
      8: f10 -> f11 : arg5'=1+arg5, [], cost: 1
      9: f11 -> f12 : arg3'=1+arg3, [], cost: 1
     12: f12 -> f8 : [], cost: 1
     14: __init -> f1 : arg1'=arg1P_15, arg2'=arg2P_15, arg3'=arg3P_15, arg4'=arg4P_15, arg5'=arg5P_15, arg6'=arg6P_15, arg7'=arg7P_15, [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: __init
     10: f8 -> f9 : [ arg4<arg6 ], cost: 1
     11: f8 -> f9 : [ arg5<arg7 ], cost: 1
     24: f9 -> f8 : arg3'=1+arg3, arg4'=1+arg4, arg5'=1+arg5, [], cost: 4
     21: __init -> f8 : arg1'=arg4P_1, arg2'=arg5P_2, arg3'=0, arg4'=arg4P_1, arg5'=arg5P_2, arg6'=arg6P_3, arg7'=arg7P_4, [], cost: 8

Eliminated locations (on tree-shaped paths):
   Start location: __init
     25: f8 -> f8 : arg3'=1+arg3, arg4'=1+arg4, arg5'=1+arg5, [ arg4<arg6 ], cost: 5
     26: f8 -> f8 : arg3'=1+arg3, arg4'=1+arg4, arg5'=1+arg5, [ arg5<arg7 ], cost: 5
     21: __init -> f8 : arg1'=arg4P_1, arg2'=arg5P_2, arg3'=0, arg4'=arg4P_1, arg5'=arg5P_2, arg6'=arg6P_3, arg7'=arg7P_4, [], cost: 8

Accelerating simple loops of location 7.
   Accelerating the following rules:
     25: f8 -> f8 : arg3'=1+arg3, arg4'=1+arg4, arg5'=1+arg5, [ arg4<arg6 ], cost: 5
     26: f8 -> f8 : arg3'=1+arg3, arg4'=1+arg4, arg5'=1+arg5, [ arg5<arg7 ], cost: 5

   Accelerated rule 25 with backward acceleration, yielding the new rule 27.
   Accelerated rule 26 with backward acceleration, yielding the new rule 28.
[accelerate] Nesting with 2 inner and 2 outer candidates
   Removing the simple loops: 25 26.

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     27: f8 -> f8 : arg3'=arg6+arg3-arg4, arg4'=arg6, arg5'=arg5+arg6-arg4, [ arg6-arg4>=0 ], cost: 5*arg6-5*arg4
     28: f8 -> f8 : arg3'=-arg5+arg3+arg7, arg4'=-arg5+arg7+arg4, arg5'=arg7, [ -arg5+arg7>=0 ], cost: -5*arg5+5*arg7
     21: __init -> f8 : arg1'=arg4P_1, arg2'=arg5P_2, arg3'=0, arg4'=arg4P_1, arg5'=arg5P_2, arg6'=arg6P_3, arg7'=arg7P_4, [], cost: 8

Chained accelerated rules (with incoming rules):
   Start location: __init
     21: __init -> f8 : arg1'=arg4P_1, arg2'=arg5P_2, arg3'=0, arg4'=arg4P_1, arg5'=arg5P_2, arg6'=arg6P_3, arg7'=arg7P_4, [], cost: 8
     29: __init -> f8 : arg1'=arg4P_1, arg2'=arg5P_2, arg3'=-arg4P_1+arg6P_3, arg4'=arg6P_3, arg5'=-arg4P_1+arg5P_2+arg6P_3, arg6'=arg6P_3, arg7'=arg7P_4, [ -arg4P_1+arg6P_3>=0 ], cost: 8-5*arg4P_1+5*arg6P_3
     30: __init -> f8 : arg1'=arg4P_1, arg2'=arg5P_2, arg3'=arg7P_4-arg5P_2, arg4'=arg4P_1+arg7P_4-arg5P_2, arg5'=arg7P_4, arg6'=arg6P_3, arg7'=arg7P_4, [ arg7P_4-arg5P_2>=0 ], cost: 8+5*arg7P_4-5*arg5P_2

Removed unreachable locations (and leaf rules with constant cost):
   Start location: __init
     29: __init -> f8 : arg1'=arg4P_1, arg2'=arg5P_2, arg3'=-arg4P_1+arg6P_3, arg4'=arg6P_3, arg5'=-arg4P_1+arg5P_2+arg6P_3, arg6'=arg6P_3, arg7'=arg7P_4, [ -arg4P_1+arg6P_3>=0 ], cost: 8-5*arg4P_1+5*arg6P_3
     30: __init -> f8 : arg1'=arg4P_1, arg2'=arg5P_2, arg3'=arg7P_4-arg5P_2, arg4'=arg4P_1+arg7P_4-arg5P_2, arg5'=arg7P_4, arg6'=arg6P_3, arg7'=arg7P_4, [ arg7P_4-arg5P_2>=0 ], cost: 8+5*arg7P_4-5*arg5P_2

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: __init
     29: __init -> f8 : arg1'=arg4P_1, arg2'=arg5P_2, arg3'=-arg4P_1+arg6P_3, arg4'=arg6P_3, arg5'=-arg4P_1+arg5P_2+arg6P_3, arg6'=arg6P_3, arg7'=arg7P_4, [ -arg4P_1+arg6P_3>=0 ], cost: 8-5*arg4P_1+5*arg6P_3
     30: __init -> f8 : arg1'=arg4P_1, arg2'=arg5P_2, arg3'=arg7P_4-arg5P_2, arg4'=arg4P_1+arg7P_4-arg5P_2, arg5'=arg7P_4, arg6'=arg6P_3, arg7'=arg7P_4, [ arg7P_4-arg5P_2>=0 ], cost: 8+5*arg7P_4-5*arg5P_2

Computing asymptotic complexity for rule 29
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 30
   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),?)