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, [ arg2==arg2P_1 && arg3==arg3P_1 && arg4==arg4P_1 ], cost: 1
      1: f2 -> f3 : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, [ arg1==arg1P_2 && arg3==arg3P_2 && arg4==arg4P_2 ], cost: 1
     17: f3 -> f4 : arg1'=arg1P_18, arg2'=arg2P_18, arg3'=arg3P_18, arg4'=arg4P_18, [ -arg2+arg1>=1 && arg1==arg1P_18 && arg2==arg2P_18 && arg3==arg3P_18 && arg4==arg4P_18 ], cost: 1
     19: f3 -> f18 : arg1'=arg1P_20, arg2'=arg2P_20, arg3'=arg3P_20, arg4'=arg4P_20, [ -arg2+arg1<1 && arg1==arg1P_20 && arg2==arg2P_20 && arg3==arg3P_20 && arg4==arg4P_20 ], cost: 1
      2: f4 -> f5 : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, [ arg1==arg1P_3 && arg2==arg2P_3 && arg4==arg4P_3 ], cost: 1
      4: f5 -> f6 : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, [ arg3<0 && arg1==arg1P_5 && arg2==arg2P_5 && arg3==arg3P_5 && arg4==arg4P_5 ], cost: 1
      5: f5 -> f7 : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, arg4'=arg4P_6, [ arg3>=0 && arg1==arg1P_6 && arg2==arg2P_6 && arg3==arg3P_6 && arg4==arg4P_6 ], cost: 1
      3: f6 -> f9 : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, [ arg3P_4==-arg3 && arg1==arg1P_4 && arg2==arg2P_4 && arg4==arg4P_4 ], cost: 1
      6: f9 -> f8 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, [ arg1==arg1P_7 && arg2==arg2P_7 && arg3==arg3P_7 && arg4==arg4P_7 ], cost: 1
      7: f7 -> f8 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, arg4'=arg4P_8, [ arg1==arg1P_8 && arg2==arg2P_8 && arg3==arg3P_8 && arg4==arg4P_8 ], cost: 1
      8: f8 -> f10 : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, arg4'=arg4P_9, [ arg1P_9==-arg3+arg1 && arg2==arg2P_9 && arg3==arg3P_9 && arg4==arg4P_9 ], cost: 1
      9: f10 -> f11 : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, arg4'=arg4P_10, [ arg1==arg1P_10 && arg2==arg2P_10 && arg3==arg3P_10 ], cost: 1
     11: f11 -> f12 : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, arg4'=arg4P_12, [ arg4<0 && arg1==arg1P_12 && arg2==arg2P_12 && arg3==arg3P_12 && arg4==arg4P_12 ], cost: 1
     12: f11 -> f13 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, arg4'=arg4P_13, [ arg4>=0 && arg1==arg1P_13 && arg2==arg2P_13 && arg3==arg3P_13 && arg4==arg4P_13 ], cost: 1
     10: f12 -> f15 : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, arg4'=arg4P_11, [ arg4P_11==-arg4 && arg1==arg1P_11 && arg2==arg2P_11 && arg3==arg3P_11 ], cost: 1
     13: f15 -> f14 : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, arg4'=arg4P_14, [ arg1==arg1P_14 && arg2==arg2P_14 && arg3==arg3P_14 && arg4==arg4P_14 ], cost: 1
     14: f13 -> f14 : arg1'=arg1P_15, arg2'=arg2P_15, arg3'=arg3P_15, arg4'=arg4P_15, [ arg1==arg1P_15 && arg2==arg2P_15 && arg3==arg3P_15 && arg4==arg4P_15 ], cost: 1
     15: f14 -> f16 : arg1'=arg1P_16, arg2'=arg2P_16, arg3'=arg3P_16, arg4'=arg4P_16, [ arg4P_16==1+arg4 && arg1==arg1P_16 && arg2==arg2P_16 && arg3==arg3P_16 ], cost: 1
     16: f16 -> f17 : arg1'=arg1P_17, arg2'=arg2P_17, arg3'=arg3P_17, arg4'=arg4P_17, [ arg2P_17==arg2+arg4 && arg1==arg1P_17 && arg3==arg3P_17 && arg4==arg4P_17 ], cost: 1
     18: f17 -> f3 : arg1'=arg1P_19, arg2'=arg2P_19, arg3'=arg3P_19, arg4'=arg4P_19, [ arg1==arg1P_19 && arg2==arg2P_19 && arg3==arg3P_19 && arg4==arg4P_19 ], cost: 1
     20: __init -> f1 : arg1'=arg1P_21, arg2'=arg2P_21, arg3'=arg3P_21, arg4'=arg4P_21, [], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
     20: __init -> f1 : arg1'=arg1P_21, arg2'=arg2P_21, arg3'=arg3P_21, arg4'=arg4P_21, [], 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, [ arg2==arg2P_1 && arg3==arg3P_1 && arg4==arg4P_1 ], cost: 1
      1: f2 -> f3 : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, [ arg1==arg1P_2 && arg3==arg3P_2 && arg4==arg4P_2 ], cost: 1
     17: f3 -> f4 : arg1'=arg1P_18, arg2'=arg2P_18, arg3'=arg3P_18, arg4'=arg4P_18, [ -arg2+arg1>=1 && arg1==arg1P_18 && arg2==arg2P_18 && arg3==arg3P_18 && arg4==arg4P_18 ], cost: 1
      2: f4 -> f5 : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, [ arg1==arg1P_3 && arg2==arg2P_3 && arg4==arg4P_3 ], cost: 1
      4: f5 -> f6 : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, [ arg3<0 && arg1==arg1P_5 && arg2==arg2P_5 && arg3==arg3P_5 && arg4==arg4P_5 ], cost: 1
      5: f5 -> f7 : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, arg4'=arg4P_6, [ arg3>=0 && arg1==arg1P_6 && arg2==arg2P_6 && arg3==arg3P_6 && arg4==arg4P_6 ], cost: 1
      3: f6 -> f9 : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, [ arg3P_4==-arg3 && arg1==arg1P_4 && arg2==arg2P_4 && arg4==arg4P_4 ], cost: 1
      6: f9 -> f8 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, [ arg1==arg1P_7 && arg2==arg2P_7 && arg3==arg3P_7 && arg4==arg4P_7 ], cost: 1
      7: f7 -> f8 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, arg4'=arg4P_8, [ arg1==arg1P_8 && arg2==arg2P_8 && arg3==arg3P_8 && arg4==arg4P_8 ], cost: 1
      8: f8 -> f10 : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, arg4'=arg4P_9, [ arg1P_9==-arg3+arg1 && arg2==arg2P_9 && arg3==arg3P_9 && arg4==arg4P_9 ], cost: 1
      9: f10 -> f11 : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, arg4'=arg4P_10, [ arg1==arg1P_10 && arg2==arg2P_10 && arg3==arg3P_10 ], cost: 1
     11: f11 -> f12 : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, arg4'=arg4P_12, [ arg4<0 && arg1==arg1P_12 && arg2==arg2P_12 && arg3==arg3P_12 && arg4==arg4P_12 ], cost: 1
     12: f11 -> f13 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, arg4'=arg4P_13, [ arg4>=0 && arg1==arg1P_13 && arg2==arg2P_13 && arg3==arg3P_13 && arg4==arg4P_13 ], cost: 1
     10: f12 -> f15 : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, arg4'=arg4P_11, [ arg4P_11==-arg4 && arg1==arg1P_11 && arg2==arg2P_11 && arg3==arg3P_11 ], cost: 1
     13: f15 -> f14 : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, arg4'=arg4P_14, [ arg1==arg1P_14 && arg2==arg2P_14 && arg3==arg3P_14 && arg4==arg4P_14 ], cost: 1
     14: f13 -> f14 : arg1'=arg1P_15, arg2'=arg2P_15, arg3'=arg3P_15, arg4'=arg4P_15, [ arg1==arg1P_15 && arg2==arg2P_15 && arg3==arg3P_15 && arg4==arg4P_15 ], cost: 1
     15: f14 -> f16 : arg1'=arg1P_16, arg2'=arg2P_16, arg3'=arg3P_16, arg4'=arg4P_16, [ arg4P_16==1+arg4 && arg1==arg1P_16 && arg2==arg2P_16 && arg3==arg3P_16 ], cost: 1
     16: f16 -> f17 : arg1'=arg1P_17, arg2'=arg2P_17, arg3'=arg3P_17, arg4'=arg4P_17, [ arg2P_17==arg2+arg4 && arg1==arg1P_17 && arg3==arg3P_17 && arg4==arg4P_17 ], cost: 1
     18: f17 -> f3 : arg1'=arg1P_19, arg2'=arg2P_19, arg3'=arg3P_19, arg4'=arg4P_19, [ arg1==arg1P_19 && arg2==arg2P_19 && arg3==arg3P_19 && arg4==arg4P_19 ], cost: 1
     20: __init -> f1 : arg1'=arg1P_21, arg2'=arg2P_21, arg3'=arg3P_21, arg4'=arg4P_21, [], 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
     17: f3 -> f4 : [ -arg2+arg1>=1 ], cost: 1
      2: f4 -> f5 : arg3'=arg3P_3, [], cost: 1
      4: f5 -> f6 : [ arg3<0 ], cost: 1
      5: f5 -> f7 : [ arg3>=0 ], cost: 1
      3: f6 -> f9 : arg3'=-arg3, [], cost: 1
      6: f9 -> f8 : [], cost: 1
      7: f7 -> f8 : [], cost: 1
      8: f8 -> f10 : arg1'=-arg3+arg1, [], cost: 1
      9: f10 -> f11 : arg4'=arg4P_10, [], cost: 1
     11: f11 -> f12 : [ arg4<0 ], cost: 1
     12: f11 -> f13 : [ arg4>=0 ], cost: 1
     10: f12 -> f15 : arg4'=-arg4, [], cost: 1
     13: f15 -> f14 : [], cost: 1
     14: f13 -> f14 : [], cost: 1
     15: f14 -> f16 : arg4'=1+arg4, [], cost: 1
     16: f16 -> f17 : arg2'=arg2+arg4, [], cost: 1
     18: f17 -> f3 : [], cost: 1
     20: __init -> f1 : arg1'=arg1P_21, arg2'=arg2P_21, arg3'=arg3P_21, arg4'=arg4P_21, [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: __init
     23: f3 -> f5 : arg3'=arg3P_3, [ -arg2+arg1>=1 ], cost: 2
     25: f5 -> f8 : [ arg3>=0 ], cost: 2
     26: f5 -> f8 : arg3'=-arg3, [ arg3<0 ], cost: 3
     27: f8 -> f11 : arg1'=-arg3+arg1, arg4'=arg4P_10, [], cost: 2
     29: f11 -> f14 : [ arg4>=0 ], cost: 2
     30: f11 -> f14 : arg4'=-arg4, [ arg4<0 ], cost: 3
     32: f14 -> f3 : arg2'=1+arg2+arg4, arg4'=1+arg4, [], cost: 3
     22: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_21, arg4'=arg4P_21, [], cost: 3

Eliminated locations (on tree-shaped paths):
   Start location: __init
     33: f3 -> f8 : arg3'=arg3P_3, [ -arg2+arg1>=1 && arg3P_3>=0 ], cost: 4
     34: f3 -> f8 : arg3'=-arg3P_3, [ -arg2+arg1>=1 && arg3P_3<0 ], cost: 5
     35: f8 -> f14 : arg1'=-arg3+arg1, arg4'=arg4P_10, [ arg4P_10>=0 ], cost: 4
     36: f8 -> f14 : arg1'=-arg3+arg1, arg4'=-arg4P_10, [ arg4P_10<0 ], cost: 5
     32: f14 -> f3 : arg2'=1+arg2+arg4, arg4'=1+arg4, [], cost: 3
     22: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_21, arg4'=arg4P_21, [], cost: 3

Eliminated locations (on tree-shaped paths):
   Start location: __init
     37: f3 -> f14 : arg1'=-arg3P_3+arg1, arg3'=arg3P_3, arg4'=arg4P_10, [ -arg2+arg1>=1 && arg3P_3>=0 && arg4P_10>=0 ], cost: 8
     38: f3 -> f14 : arg1'=-arg3P_3+arg1, arg3'=arg3P_3, arg4'=-arg4P_10, [ -arg2+arg1>=1 && arg3P_3>=0 && arg4P_10<0 ], cost: 9
     39: f3 -> f14 : arg1'=arg3P_3+arg1, arg3'=-arg3P_3, arg4'=arg4P_10, [ -arg2+arg1>=1 && arg3P_3<0 && arg4P_10>=0 ], cost: 9
     40: f3 -> f14 : arg1'=arg3P_3+arg1, arg3'=-arg3P_3, arg4'=-arg4P_10, [ -arg2+arg1>=1 && arg3P_3<0 && arg4P_10<0 ], cost: 10
     32: f14 -> f3 : arg2'=1+arg2+arg4, arg4'=1+arg4, [], cost: 3
     22: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_21, arg4'=arg4P_21, [], cost: 3

Eliminated locations (on tree-shaped paths):
   Start location: __init
     41: f3 -> f3 : arg1'=-arg3P_3+arg1, arg2'=1+arg2+arg4P_10, arg3'=arg3P_3, arg4'=1+arg4P_10, [ -arg2+arg1>=1 && arg3P_3>=0 && arg4P_10>=0 ], cost: 11
     42: f3 -> f3 : arg1'=-arg3P_3+arg1, arg2'=1+arg2-arg4P_10, arg3'=arg3P_3, arg4'=1-arg4P_10, [ -arg2+arg1>=1 && arg3P_3>=0 && arg4P_10<0 ], cost: 12
     43: f3 -> f3 : arg1'=arg3P_3+arg1, arg2'=1+arg2+arg4P_10, arg3'=-arg3P_3, arg4'=1+arg4P_10, [ -arg2+arg1>=1 && arg3P_3<0 && arg4P_10>=0 ], cost: 12
     44: f3 -> f3 : arg1'=arg3P_3+arg1, arg2'=1+arg2-arg4P_10, arg3'=-arg3P_3, arg4'=1-arg4P_10, [ -arg2+arg1>=1 && arg3P_3<0 && arg4P_10<0 ], cost: 13
     22: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_21, arg4'=arg4P_21, [], cost: 3

Accelerating simple loops of location 2.
   Accelerating the following rules:
     41: f3 -> f3 : arg1'=-arg3P_3+arg1, arg2'=1+arg2+arg4P_10, arg3'=arg3P_3, arg4'=1+arg4P_10, [ -arg2+arg1>=1 && arg3P_3>=0 && arg4P_10>=0 ], cost: 11
     42: f3 -> f3 : arg1'=-arg3P_3+arg1, arg2'=1+arg2-arg4P_10, arg3'=arg3P_3, arg4'=1-arg4P_10, [ -arg2+arg1>=1 && arg3P_3>=0 && arg4P_10<0 ], cost: 12
     43: f3 -> f3 : arg1'=arg3P_3+arg1, arg2'=1+arg2+arg4P_10, arg3'=-arg3P_3, arg4'=1+arg4P_10, [ -arg2+arg1>=1 && arg3P_3<0 && arg4P_10>=0 ], cost: 12
     44: f3 -> f3 : arg1'=arg3P_3+arg1, arg2'=1+arg2-arg4P_10, arg3'=-arg3P_3, arg4'=1-arg4P_10, [ -arg2+arg1>=1 && arg3P_3<0 && arg4P_10<0 ], cost: 13

   Accelerated rule 41 with backward acceleration, yielding the new rule 45.
   Accelerated rule 42 with backward acceleration, yielding the new rule 46.
   Accelerated rule 43 with backward acceleration, yielding the new rule 47.
   Accelerated rule 44 with backward acceleration, yielding the new rule 48.
[accelerate] Nesting with 4 inner and 4 outer candidates
   Removing the simple loops: 41 42 43 44.

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     45: f3 -> f3 : arg1'=-arg3P_3*k+arg1, arg2'=arg2+arg4P_10*k+k, arg3'=arg3P_3, arg4'=1+arg4P_10, [ arg3P_3>=0 && arg4P_10>=0 && k>=1 && 1-arg3P_3*(-1+k)-arg2-k+arg1-arg4P_10*(-1+k)>=1 ], cost: 11*k
     46: f3 -> f3 : arg1'=-arg3P_3*k_1+arg1, arg2'=arg2-arg4P_10*k_1+k_1, arg3'=arg3P_3, arg4'=1-arg4P_10, [ arg3P_3>=0 && arg4P_10<0 && k_1>=1 && 1-arg2-arg3P_3*(-1+k_1)+arg4P_10*(-1+k_1)-k_1+arg1>=1 ], cost: 12*k_1
     47: f3 -> f3 : arg1'=arg1+k_2*arg3P_3, arg2'=k_2*arg4P_10+k_2+arg2, arg3'=-arg3P_3, arg4'=1+arg4P_10, [ arg3P_3<0 && arg4P_10>=0 && k_2>=1 && 1-k_2-arg2-(-1+k_2)*arg4P_10+(-1+k_2)*arg3P_3+arg1>=1 ], cost: 12*k_2
     48: f3 -> f3 : arg1'=arg3P_3*k_3+arg1, arg2'=arg2-arg4P_10*k_3+k_3, arg3'=-arg3P_3, arg4'=1-arg4P_10, [ arg3P_3<0 && arg4P_10<0 && k_3>=1 && 1-arg2+arg3P_3*(-1+k_3)+arg4P_10*(-1+k_3)-k_3+arg1>=1 ], cost: 13*k_3
     22: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_21, arg4'=arg4P_21, [], cost: 3

Chained accelerated rules (with incoming rules):
   Start location: __init
     22: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_21, arg4'=arg4P_21, [], cost: 3
     49: __init -> f3 : arg1'=-arg3P_3*k+arg1P_1, arg2'=arg2P_2+arg4P_10*k+k, arg3'=arg3P_3, arg4'=1+arg4P_10, [ arg3P_3>=0 && arg4P_10>=0 && k>=1 && 1-arg3P_3*(-1+k)-arg2P_2+arg1P_1-k-arg4P_10*(-1+k)>=1 ], cost: 3+11*k
     50: __init -> f3 : arg1'=-arg3P_3*k_1+arg1P_1, arg2'=arg2P_2-arg4P_10*k_1+k_1, arg3'=arg3P_3, arg4'=1-arg4P_10, [ arg3P_3>=0 && arg4P_10<0 && k_1>=1 && 1-arg2P_2-arg3P_3*(-1+k_1)+arg1P_1+arg4P_10*(-1+k_1)-k_1>=1 ], cost: 3+12*k_1
     51: __init -> f3 : arg1'=arg1P_1+k_2*arg3P_3, arg2'=k_2*arg4P_10+k_2+arg2P_2, arg3'=-arg3P_3, arg4'=1+arg4P_10, [ arg3P_3<0 && arg4P_10>=0 && k_2>=1 && 1-k_2-arg2P_2-(-1+k_2)*arg4P_10+(-1+k_2)*arg3P_3+arg1P_1>=1 ], cost: 3+12*k_2
     52: __init -> f3 : arg1'=arg3P_3*k_3+arg1P_1, arg2'=arg2P_2-arg4P_10*k_3+k_3, arg3'=-arg3P_3, arg4'=1-arg4P_10, [ arg3P_3<0 && arg4P_10<0 && k_3>=1 && 1-arg2P_2+arg3P_3*(-1+k_3)+arg4P_10*(-1+k_3)+arg1P_1-k_3>=1 ], cost: 3+13*k_3

Removed unreachable locations (and leaf rules with constant cost):
   Start location: __init
     49: __init -> f3 : arg1'=-arg3P_3*k+arg1P_1, arg2'=arg2P_2+arg4P_10*k+k, arg3'=arg3P_3, arg4'=1+arg4P_10, [ arg3P_3>=0 && arg4P_10>=0 && k>=1 && 1-arg3P_3*(-1+k)-arg2P_2+arg1P_1-k-arg4P_10*(-1+k)>=1 ], cost: 3+11*k
     50: __init -> f3 : arg1'=-arg3P_3*k_1+arg1P_1, arg2'=arg2P_2-arg4P_10*k_1+k_1, arg3'=arg3P_3, arg4'=1-arg4P_10, [ arg3P_3>=0 && arg4P_10<0 && k_1>=1 && 1-arg2P_2-arg3P_3*(-1+k_1)+arg1P_1+arg4P_10*(-1+k_1)-k_1>=1 ], cost: 3+12*k_1
     51: __init -> f3 : arg1'=arg1P_1+k_2*arg3P_3, arg2'=k_2*arg4P_10+k_2+arg2P_2, arg3'=-arg3P_3, arg4'=1+arg4P_10, [ arg3P_3<0 && arg4P_10>=0 && k_2>=1 && 1-k_2-arg2P_2-(-1+k_2)*arg4P_10+(-1+k_2)*arg3P_3+arg1P_1>=1 ], cost: 3+12*k_2
     52: __init -> f3 : arg1'=arg3P_3*k_3+arg1P_1, arg2'=arg2P_2-arg4P_10*k_3+k_3, arg3'=-arg3P_3, arg4'=1-arg4P_10, [ arg3P_3<0 && arg4P_10<0 && k_3>=1 && 1-arg2P_2+arg3P_3*(-1+k_3)+arg4P_10*(-1+k_3)+arg1P_1-k_3>=1 ], cost: 3+13*k_3

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: __init
     49: __init -> f3 : arg1'=-arg3P_3*k+arg1P_1, arg2'=arg2P_2+arg4P_10*k+k, arg3'=arg3P_3, arg4'=1+arg4P_10, [ arg3P_3>=0 && arg4P_10>=0 && k>=1 && 1-arg3P_3*(-1+k)-arg2P_2+arg1P_1-k-arg4P_10*(-1+k)>=1 ], cost: 3+11*k
     50: __init -> f3 : arg1'=-arg3P_3*k_1+arg1P_1, arg2'=arg2P_2-arg4P_10*k_1+k_1, arg3'=arg3P_3, arg4'=1-arg4P_10, [ arg3P_3>=0 && arg4P_10<0 && k_1>=1 && 1-arg2P_2-arg3P_3*(-1+k_1)+arg1P_1+arg4P_10*(-1+k_1)-k_1>=1 ], cost: 3+12*k_1
     51: __init -> f3 : arg1'=arg1P_1+k_2*arg3P_3, arg2'=k_2*arg4P_10+k_2+arg2P_2, arg3'=-arg3P_3, arg4'=1+arg4P_10, [ arg3P_3<0 && arg4P_10>=0 && k_2>=1 && 1-k_2-arg2P_2-(-1+k_2)*arg4P_10+(-1+k_2)*arg3P_3+arg1P_1>=1 ], cost: 3+12*k_2
     52: __init -> f3 : arg1'=arg3P_3*k_3+arg1P_1, arg2'=arg2P_2-arg4P_10*k_3+k_3, arg3'=-arg3P_3, arg4'=1-arg4P_10, [ arg3P_3<0 && arg4P_10<0 && k_3>=1 && 1-arg2P_2+arg3P_3*(-1+k_3)+arg4P_10*(-1+k_3)+arg1P_1-k_3>=1 ], cost: 3+13*k_3

Computing asymptotic complexity for rule 49
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 50
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 51
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 52
   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),?)