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, [ arg2==arg2P_1 && arg3==arg3P_1 && arg4==arg4P_1 && arg5==arg5P_1 ], cost: 1
      1: f2 -> f3 : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, arg5'=arg5P_2, [ arg1==arg1P_2 && arg3==arg3P_2 && arg4==arg4P_2 && arg5==arg5P_2 ], cost: 1
      2: f3 -> f4 : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, arg5'=arg5P_3, [ arg1==arg1P_3 && arg2==arg2P_3 && arg4==arg4P_3 && arg5==arg5P_3 ], cost: 1
      3: f4 -> f5 : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, arg5'=arg5P_4, [ arg1==arg1P_4 && arg2==arg2P_4 && arg3==arg3P_4 && arg5==arg5P_4 ], cost: 1
      4: f5 -> f6 : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, arg5'=arg5P_5, [ arg1==arg1P_5 && arg2==arg2P_5 && arg3==arg3P_5 && arg4==arg4P_5 ], cost: 1
     22: f6 -> f7 : arg1'=arg1P_23, arg2'=arg2P_23, arg3'=arg3P_23, arg4'=arg4P_23, arg5'=arg5P_23, [ arg3+arg1>=0 && arg1==arg1P_23 && arg2==arg2P_23 && arg3==arg3P_23 && arg4==arg4P_23 && arg5==arg5P_23 ], cost: 1
     23: f6 -> f8 : arg1'=arg1P_24, arg2'=arg2P_24, arg3'=arg3P_24, arg4'=arg4P_24, arg5'=arg5P_24, [ arg3+arg1<0 && arg1==arg1P_24 && arg2==arg2P_24 && arg3==arg3P_24 && arg4==arg4P_24 && arg5==arg5P_24 ], cost: 1
      5: f11 -> f14 : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, arg4'=arg4P_6, arg5'=arg5P_6, [ arg1==arg1P_6 && arg1==arg2P_6 && arg3==arg3P_6 && arg4==arg4P_6 && arg5==arg5P_6 ], cost: 1
      6: f14 -> f15 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, arg5'=arg5P_7, [ arg1==arg1P_7 && arg2==arg2P_7 && arg3==arg3P_7 && arg3==arg4P_7 && arg5==arg5P_7 ], cost: 1
      7: f15 -> f16 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, arg4'=arg4P_8, arg5'=arg5P_8, [ arg2==arg2P_8 && arg3==arg3P_8 && arg4==arg4P_8 && arg5==arg5P_8 ], cost: 1
      8: f16 -> f17 : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, arg4'=arg4P_9, arg5'=arg5P_9, [ arg1==arg1P_9 && arg2==arg2P_9 && arg4==arg4P_9 && arg5==arg5P_9 ], cost: 1
     14: f17 -> f13 : arg1'=arg1P_15, arg2'=arg2P_15, arg3'=arg3P_15, arg4'=arg4P_15, arg5'=arg5P_15, [ arg1==arg1P_15 && arg2==arg2P_15 && arg3==arg3P_15 && arg4==arg4P_15 && arg5==arg5P_15 ], cost: 1
      9: f12 -> f18 : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, arg4'=arg4P_10, arg5'=arg5P_10, [ arg1==arg1P_10 && arg1==arg2P_10 && arg3==arg3P_10 && arg4==arg4P_10 && arg5==arg5P_10 ], cost: 1
     10: f18 -> f19 : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, arg4'=arg4P_11, arg5'=arg5P_11, [ arg2==arg2P_11 && arg3==arg3P_11 && arg4==arg4P_11 && arg5==arg5P_11 ], cost: 1
     15: f19 -> f13 : arg1'=arg1P_16, arg2'=arg2P_16, arg3'=arg3P_16, arg4'=arg4P_16, arg5'=arg5P_16, [ arg1==arg1P_16 && arg2==arg2P_16 && arg3==arg3P_16 && arg4==arg4P_16 && arg5==arg5P_16 ], cost: 1
     11: f10 -> f11 : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, arg4'=arg4P_12, arg5'=arg5P_12, [ x63_1<0 && arg1==arg1P_12 && arg2==arg2P_12 && arg3==arg3P_12 && arg4==arg4P_12 && arg5==arg5P_12 ], cost: 1
     12: f10 -> f11 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, arg4'=arg4P_13, arg5'=arg5P_13, [ x120_1>0 && arg1==arg1P_13 && arg2==arg2P_13 && arg3==arg3P_13 && arg4==arg4P_13 && arg5==arg5P_13 ], cost: 1
     13: f10 -> f12 : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, arg4'=arg4P_14, arg5'=arg5P_14, [ x69_1==0 && arg1==arg1P_14 && arg2==arg2P_14 && arg3==arg3P_14 && arg4==arg4P_14 && arg5==arg5P_14 ], cost: 1
     17: f13 -> f7 : arg1'=arg1P_18, arg2'=arg2P_18, arg3'=arg3P_18, arg4'=arg4P_18, arg5'=arg5P_18, [ arg1==arg1P_18 && arg2==arg2P_18 && arg3==arg3P_18 && arg4==arg4P_18 && arg5==arg5P_18 ], cost: 1
     16: f7 -> f10 : arg1'=arg1P_17, arg2'=arg2P_17, arg3'=arg3P_17, arg4'=arg4P_17, arg5'=arg5P_17, [ arg1<=arg5 && arg1>=2*arg2+arg3 && arg3>=1+arg4 && arg1>=1+arg2 && arg1==arg1P_17 && arg2==arg2P_17 && arg3==arg3P_17 && arg4==arg4P_17 && arg5==arg5P_17 ], cost: 1
     18: f7 -> f20 : arg1'=arg1P_19, arg2'=arg2P_19, arg3'=arg3P_19, arg4'=arg4P_19, arg5'=arg5P_19, [ arg1<1+arg2 && arg1==arg1P_19 && arg2==arg2P_19 && arg3==arg3P_19 && arg4==arg4P_19 && arg5==arg5P_19 ], cost: 1
     19: f7 -> f20 : arg1'=arg1P_20, arg2'=arg2P_20, arg3'=arg3P_20, arg4'=arg4P_20, arg5'=arg5P_20, [ arg3<1+arg4 && arg1==arg1P_20 && arg2==arg2P_20 && arg3==arg3P_20 && arg4==arg4P_20 && arg5==arg5P_20 ], cost: 1
     20: f7 -> f20 : arg1'=arg1P_21, arg2'=arg2P_21, arg3'=arg3P_21, arg4'=arg4P_21, arg5'=arg5P_21, [ arg1>arg5 && arg1==arg1P_21 && arg2==arg2P_21 && arg3==arg3P_21 && arg4==arg4P_21 && arg5==arg5P_21 ], cost: 1
     21: f7 -> f20 : arg1'=arg1P_22, arg2'=arg2P_22, arg3'=arg3P_22, arg4'=arg4P_22, arg5'=arg5P_22, [ arg1<2*arg2+arg3 && arg1==arg1P_22 && arg2==arg2P_22 && arg3==arg3P_22 && arg4==arg4P_22 && arg5==arg5P_22 ], cost: 1
     24: f20 -> f9 : arg1'=arg1P_25, arg2'=arg2P_25, arg3'=arg3P_25, arg4'=arg4P_25, arg5'=arg5P_25, [ arg1==arg1P_25 && arg2==arg2P_25 && arg3==arg3P_25 && arg4==arg4P_25 && arg5==arg5P_25 ], cost: 1
     25: f8 -> f9 : arg1'=arg1P_26, arg2'=arg2P_26, arg3'=arg3P_26, arg4'=arg4P_26, arg5'=arg5P_26, [ arg1==arg1P_26 && arg2==arg2P_26 && arg3==arg3P_26 && arg4==arg4P_26 && arg5==arg5P_26 ], cost: 1
     26: __init -> f1 : arg1'=arg1P_27, arg2'=arg2P_27, arg3'=arg3P_27, arg4'=arg4P_27, arg5'=arg5P_27, [], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
     26: __init -> f1 : arg1'=arg1P_27, arg2'=arg2P_27, arg3'=arg3P_27, arg4'=arg4P_27, arg5'=arg5P_27, [], 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, [ arg2==arg2P_1 && arg3==arg3P_1 && arg4==arg4P_1 && arg5==arg5P_1 ], cost: 1
      1: f2 -> f3 : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, arg5'=arg5P_2, [ arg1==arg1P_2 && arg3==arg3P_2 && arg4==arg4P_2 && arg5==arg5P_2 ], cost: 1
      2: f3 -> f4 : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, arg5'=arg5P_3, [ arg1==arg1P_3 && arg2==arg2P_3 && arg4==arg4P_3 && arg5==arg5P_3 ], cost: 1
      3: f4 -> f5 : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, arg5'=arg5P_4, [ arg1==arg1P_4 && arg2==arg2P_4 && arg3==arg3P_4 && arg5==arg5P_4 ], cost: 1
      4: f5 -> f6 : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, arg5'=arg5P_5, [ arg1==arg1P_5 && arg2==arg2P_5 && arg3==arg3P_5 && arg4==arg4P_5 ], cost: 1
     22: f6 -> f7 : arg1'=arg1P_23, arg2'=arg2P_23, arg3'=arg3P_23, arg4'=arg4P_23, arg5'=arg5P_23, [ arg3+arg1>=0 && arg1==arg1P_23 && arg2==arg2P_23 && arg3==arg3P_23 && arg4==arg4P_23 && arg5==arg5P_23 ], cost: 1
      5: f11 -> f14 : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, arg4'=arg4P_6, arg5'=arg5P_6, [ arg1==arg1P_6 && arg1==arg2P_6 && arg3==arg3P_6 && arg4==arg4P_6 && arg5==arg5P_6 ], cost: 1
      6: f14 -> f15 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, arg5'=arg5P_7, [ arg1==arg1P_7 && arg2==arg2P_7 && arg3==arg3P_7 && arg3==arg4P_7 && arg5==arg5P_7 ], cost: 1
      7: f15 -> f16 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, arg4'=arg4P_8, arg5'=arg5P_8, [ arg2==arg2P_8 && arg3==arg3P_8 && arg4==arg4P_8 && arg5==arg5P_8 ], cost: 1
      8: f16 -> f17 : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, arg4'=arg4P_9, arg5'=arg5P_9, [ arg1==arg1P_9 && arg2==arg2P_9 && arg4==arg4P_9 && arg5==arg5P_9 ], cost: 1
     14: f17 -> f13 : arg1'=arg1P_15, arg2'=arg2P_15, arg3'=arg3P_15, arg4'=arg4P_15, arg5'=arg5P_15, [ arg1==arg1P_15 && arg2==arg2P_15 && arg3==arg3P_15 && arg4==arg4P_15 && arg5==arg5P_15 ], cost: 1
      9: f12 -> f18 : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, arg4'=arg4P_10, arg5'=arg5P_10, [ arg1==arg1P_10 && arg1==arg2P_10 && arg3==arg3P_10 && arg4==arg4P_10 && arg5==arg5P_10 ], cost: 1
     10: f18 -> f19 : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, arg4'=arg4P_11, arg5'=arg5P_11, [ arg2==arg2P_11 && arg3==arg3P_11 && arg4==arg4P_11 && arg5==arg5P_11 ], cost: 1
     15: f19 -> f13 : arg1'=arg1P_16, arg2'=arg2P_16, arg3'=arg3P_16, arg4'=arg4P_16, arg5'=arg5P_16, [ arg1==arg1P_16 && arg2==arg2P_16 && arg3==arg3P_16 && arg4==arg4P_16 && arg5==arg5P_16 ], cost: 1
     11: f10 -> f11 : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, arg4'=arg4P_12, arg5'=arg5P_12, [ x63_1<0 && arg1==arg1P_12 && arg2==arg2P_12 && arg3==arg3P_12 && arg4==arg4P_12 && arg5==arg5P_12 ], cost: 1
     12: f10 -> f11 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, arg4'=arg4P_13, arg5'=arg5P_13, [ x120_1>0 && arg1==arg1P_13 && arg2==arg2P_13 && arg3==arg3P_13 && arg4==arg4P_13 && arg5==arg5P_13 ], cost: 1
     13: f10 -> f12 : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, arg4'=arg4P_14, arg5'=arg5P_14, [ x69_1==0 && arg1==arg1P_14 && arg2==arg2P_14 && arg3==arg3P_14 && arg4==arg4P_14 && arg5==arg5P_14 ], cost: 1
     17: f13 -> f7 : arg1'=arg1P_18, arg2'=arg2P_18, arg3'=arg3P_18, arg4'=arg4P_18, arg5'=arg5P_18, [ arg1==arg1P_18 && arg2==arg2P_18 && arg3==arg3P_18 && arg4==arg4P_18 && arg5==arg5P_18 ], cost: 1
     16: f7 -> f10 : arg1'=arg1P_17, arg2'=arg2P_17, arg3'=arg3P_17, arg4'=arg4P_17, arg5'=arg5P_17, [ arg1<=arg5 && arg1>=2*arg2+arg3 && arg3>=1+arg4 && arg1>=1+arg2 && arg1==arg1P_17 && arg2==arg2P_17 && arg3==arg3P_17 && arg4==arg4P_17 && arg5==arg5P_17 ], cost: 1
     26: __init -> f1 : arg1'=arg1P_27, arg2'=arg2P_27, arg3'=arg3P_27, arg4'=arg4P_27, arg5'=arg5P_27, [], 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
      2: f3 -> f4 : arg3'=arg3P_3, [], cost: 1
      3: f4 -> f5 : arg4'=arg4P_4, [], cost: 1
      4: f5 -> f6 : arg5'=arg5P_5, [], cost: 1
     22: f6 -> f7 : [ arg3+arg1>=0 ], cost: 1
      5: f11 -> f14 : arg2'=arg1, [], cost: 1
      6: f14 -> f15 : arg4'=arg3, [], cost: 1
      7: f15 -> f16 : arg1'=arg1P_8, [], cost: 1
      8: f16 -> f17 : arg3'=arg3P_9, [], cost: 1
     14: f17 -> f13 : [], cost: 1
      9: f12 -> f18 : arg2'=arg1, [], cost: 1
     10: f18 -> f19 : arg1'=arg1P_11, [], cost: 1
     15: f19 -> f13 : [], cost: 1
     12: f10 -> f11 : [], cost: 1
     13: f10 -> f12 : [], cost: 1
     17: f13 -> f7 : [], cost: 1
     16: f7 -> f10 : [ arg1<=arg5 && arg1>=2*arg2+arg3 && arg3>=1+arg4 && arg1>=1+arg2 ], cost: 1
     26: __init -> f1 : arg1'=arg1P_27, arg2'=arg2P_27, arg3'=arg3P_27, arg4'=arg4P_27, arg5'=arg5P_27, [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: __init
     38: f10 -> f13 : arg1'=arg1P_11, arg2'=arg1, [], cost: 4
     40: f10 -> f13 : arg1'=arg1P_8, arg2'=arg1, arg3'=arg3P_9, arg4'=arg3, [], cost: 6
     17: f13 -> f7 : [], cost: 1
     16: f7 -> f10 : [ arg1<=arg5 && arg1>=2*arg2+arg3 && arg3>=1+arg4 && arg1>=1+arg2 ], cost: 1
     32: __init -> f7 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_3, arg4'=arg4P_4, arg5'=arg5P_5, [ arg3P_3+arg1P_1>=0 ], cost: 7

Eliminated locations (on tree-shaped paths):
   Start location: __init
     17: f13 -> f7 : [], cost: 1
     41: f7 -> f13 : arg1'=arg1P_11, arg2'=arg1, [ arg1<=arg5 && arg1>=2*arg2+arg3 && arg3>=1+arg4 && arg1>=1+arg2 ], cost: 5
     42: f7 -> f13 : arg1'=arg1P_8, arg2'=arg1, arg3'=arg3P_9, arg4'=arg3, [ arg1<=arg5 && arg1>=2*arg2+arg3 && arg3>=1+arg4 && arg1>=1+arg2 ], cost: 7
     32: __init -> f7 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_3, arg4'=arg4P_4, arg5'=arg5P_5, [ arg3P_3+arg1P_1>=0 ], cost: 7

Eliminated locations (on tree-shaped paths):
   Start location: __init
     43: f7 -> f7 : arg1'=arg1P_11, arg2'=arg1, [ arg1<=arg5 && arg1>=2*arg2+arg3 && arg3>=1+arg4 && arg1>=1+arg2 ], cost: 6
     44: f7 -> f7 : arg1'=arg1P_8, arg2'=arg1, arg3'=arg3P_9, arg4'=arg3, [ arg1<=arg5 && arg1>=2*arg2+arg3 && arg3>=1+arg4 && arg1>=1+arg2 ], cost: 8
     32: __init -> f7 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_3, arg4'=arg4P_4, arg5'=arg5P_5, [ arg3P_3+arg1P_1>=0 ], cost: 7

Accelerating simple loops of location 16.
   Accelerating the following rules:
     43: f7 -> f7 : arg1'=arg1P_11, arg2'=arg1, [ arg1<=arg5 && arg1>=2*arg2+arg3 && arg3>=1+arg4 && arg1>=1+arg2 ], cost: 6
     44: f7 -> f7 : arg1'=arg1P_8, arg2'=arg1, arg3'=arg3P_9, arg4'=arg3, [ arg1<=arg5 && arg1>=2*arg2+arg3 && arg3>=1+arg4 && arg1>=1+arg2 ], cost: 8

   Failed to prove monotonicity of the guard of rule 43.
   Failed to prove monotonicity of the guard of rule 44.
[accelerate] Nesting with 2 inner and 2 outer candidates

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     43: f7 -> f7 : arg1'=arg1P_11, arg2'=arg1, [ arg1<=arg5 && arg1>=2*arg2+arg3 && arg3>=1+arg4 && arg1>=1+arg2 ], cost: 6
     44: f7 -> f7 : arg1'=arg1P_8, arg2'=arg1, arg3'=arg3P_9, arg4'=arg3, [ arg1<=arg5 && arg1>=2*arg2+arg3 && arg3>=1+arg4 && arg1>=1+arg2 ], cost: 8
     32: __init -> f7 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_3, arg4'=arg4P_4, arg5'=arg5P_5, [ arg3P_3+arg1P_1>=0 ], cost: 7

Chained accelerated rules (with incoming rules):
   Start location: __init
     32: __init -> f7 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_3, arg4'=arg4P_4, arg5'=arg5P_5, [ arg3P_3+arg1P_1>=0 ], cost: 7
     45: __init -> f7 : arg1'=arg1P_11, arg2'=arg1P_1, arg3'=arg3P_3, arg4'=arg4P_4, arg5'=arg5P_5, [ arg3P_3+arg1P_1>=0 && arg1P_1<=arg5P_5 && arg1P_1>=arg3P_3+2*arg2P_2 && arg3P_3>=1+arg4P_4 && arg1P_1>=1+arg2P_2 ], cost: 13
     46: __init -> f7 : arg1'=arg1P_8, arg2'=arg1P_1, arg3'=arg3P_9, arg4'=arg3P_3, arg5'=arg5P_5, [ arg3P_3+arg1P_1>=0 && arg1P_1<=arg5P_5 && arg1P_1>=arg3P_3+2*arg2P_2 && arg1P_1>=1+arg2P_2 ], cost: 15

Removed unreachable locations (and leaf rules with constant cost):
   Start location: __init
     <empty>

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: __init
     <empty>

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),?)