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, [ arg2==arg2P_1 && arg3==arg3P_1 ], cost: 1
      1: f2 -> f3 : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ arg1==arg1P_2 && arg3==arg3P_2 ], cost: 1
     19: f3 -> f4 : arg1'=arg1P_20, arg2'=arg2P_20, arg3'=arg3P_20, [ arg2>0 && arg1>0 && arg1==arg1P_20 && arg2==arg2P_20 && arg3==arg3P_20 ], cost: 1
     21: f3 -> f19 : arg1'=arg1P_22, arg2'=arg2P_22, arg3'=arg3P_22, [ arg2<=0 && arg1==arg1P_22 && arg2==arg2P_22 && arg3==arg3P_22 ], cost: 1
     22: f3 -> f19 : arg1'=arg1P_23, arg2'=arg2P_23, arg3'=arg3P_23, [ arg1<=0 && arg1==arg1P_23 && arg2==arg2P_23 && arg3==arg3P_23 ], cost: 1
      2: f5 -> f8 : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg1==arg1P_3 && arg2==arg2P_3 && arg2==arg3P_3 ], cost: 1
      6: f8 -> f7 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [ arg1==arg1P_7 && arg2==arg2P_7 && arg3==arg3P_7 ], cost: 1
      3: f6 -> f9 : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ arg1==arg1P_4 && arg2==arg2P_4 && arg1==arg3P_4 ], cost: 1
      7: f9 -> f7 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, [ arg1==arg1P_8 && arg2==arg2P_8 && arg3==arg3P_8 ], cost: 1
      4: f4 -> f5 : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ arg1>arg2 && arg1==arg1P_5 && arg2==arg2P_5 && arg3==arg3P_5 ], cost: 1
      5: f4 -> f6 : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [ arg1<=arg2 && arg1==arg1P_6 && arg2==arg2P_6 && arg3==arg3P_6 ], cost: 1
     14: f7 -> f10 : arg1'=arg1P_15, arg2'=arg2P_15, arg3'=arg3P_15, [ x44_1<0 && arg1==arg1P_15 && arg2==arg2P_15 && arg3==arg3P_15 ], cost: 1
     15: f7 -> f10 : arg1'=arg1P_16, arg2'=arg2P_16, arg3'=arg3P_16, [ x87_1>0 && arg1==arg1P_16 && arg2==arg2P_16 && arg3==arg3P_16 ], cost: 1
     16: f7 -> f11 : arg1'=arg1P_17, arg2'=arg2P_17, arg3'=arg3P_17, [ x48_1==0 && arg1==arg1P_17 && arg2==arg2P_17 && arg3==arg3P_17 ], cost: 1
      8: f10 -> f13 : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, [ arg2P_9==arg2+arg1 && arg1==arg1P_9 && arg3==arg3P_9 ], cost: 1
      9: f13 -> f14 : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, [ arg1P_10==-1+arg3 && arg2==arg2P_10 && arg3==arg3P_10 ], cost: 1
     10: f14 -> f15 : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, [ arg3P_11==arg2+arg3 && arg1==arg1P_11 && arg2==arg2P_11 ], cost: 1
     17: f15 -> f12 : arg1'=arg1P_18, arg2'=arg2P_18, arg3'=arg3P_18, [ arg1==arg1P_18 && arg2==arg2P_18 && arg3==arg3P_18 ], cost: 1
     11: f11 -> f16 : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, [ arg1P_12==arg2+arg1 && arg2==arg2P_12 && arg3==arg3P_12 ], cost: 1
     12: f16 -> f17 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, [ arg2P_13==-1+arg3 && arg1==arg1P_13 && arg3==arg3P_13 ], cost: 1
     13: f17 -> f18 : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, [ arg3P_14==arg3+arg1 && arg1==arg1P_14 && arg2==arg2P_14 ], cost: 1
     18: f18 -> f12 : arg1'=arg1P_19, arg2'=arg2P_19, arg3'=arg3P_19, [ arg1==arg1P_19 && arg2==arg2P_19 && arg3==arg3P_19 ], cost: 1
     20: f12 -> f3 : arg1'=arg1P_21, arg2'=arg2P_21, arg3'=arg3P_21, [ arg1==arg1P_21 && arg2==arg2P_21 && arg3==arg3P_21 ], cost: 1
     23: __init -> f1 : arg1'=arg1P_24, arg2'=arg2P_24, arg3'=arg3P_24, [], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
     23: __init -> f1 : arg1'=arg1P_24, arg2'=arg2P_24, arg3'=arg3P_24, [], cost: 1

Removed unreachable and leaf rules:
   Start location: __init
      0: f1 -> f2 : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, [ arg2==arg2P_1 && arg3==arg3P_1 ], cost: 1
      1: f2 -> f3 : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ arg1==arg1P_2 && arg3==arg3P_2 ], cost: 1
     19: f3 -> f4 : arg1'=arg1P_20, arg2'=arg2P_20, arg3'=arg3P_20, [ arg2>0 && arg1>0 && arg1==arg1P_20 && arg2==arg2P_20 && arg3==arg3P_20 ], cost: 1
      2: f5 -> f8 : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg1==arg1P_3 && arg2==arg2P_3 && arg2==arg3P_3 ], cost: 1
      6: f8 -> f7 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [ arg1==arg1P_7 && arg2==arg2P_7 && arg3==arg3P_7 ], cost: 1
      3: f6 -> f9 : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ arg1==arg1P_4 && arg2==arg2P_4 && arg1==arg3P_4 ], cost: 1
      7: f9 -> f7 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, [ arg1==arg1P_8 && arg2==arg2P_8 && arg3==arg3P_8 ], cost: 1
      4: f4 -> f5 : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ arg1>arg2 && arg1==arg1P_5 && arg2==arg2P_5 && arg3==arg3P_5 ], cost: 1
      5: f4 -> f6 : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [ arg1<=arg2 && arg1==arg1P_6 && arg2==arg2P_6 && arg3==arg3P_6 ], cost: 1
     14: f7 -> f10 : arg1'=arg1P_15, arg2'=arg2P_15, arg3'=arg3P_15, [ x44_1<0 && arg1==arg1P_15 && arg2==arg2P_15 && arg3==arg3P_15 ], cost: 1
     15: f7 -> f10 : arg1'=arg1P_16, arg2'=arg2P_16, arg3'=arg3P_16, [ x87_1>0 && arg1==arg1P_16 && arg2==arg2P_16 && arg3==arg3P_16 ], cost: 1
     16: f7 -> f11 : arg1'=arg1P_17, arg2'=arg2P_17, arg3'=arg3P_17, [ x48_1==0 && arg1==arg1P_17 && arg2==arg2P_17 && arg3==arg3P_17 ], cost: 1
      8: f10 -> f13 : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, [ arg2P_9==arg2+arg1 && arg1==arg1P_9 && arg3==arg3P_9 ], cost: 1
      9: f13 -> f14 : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, [ arg1P_10==-1+arg3 && arg2==arg2P_10 && arg3==arg3P_10 ], cost: 1
     10: f14 -> f15 : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, [ arg3P_11==arg2+arg3 && arg1==arg1P_11 && arg2==arg2P_11 ], cost: 1
     17: f15 -> f12 : arg1'=arg1P_18, arg2'=arg2P_18, arg3'=arg3P_18, [ arg1==arg1P_18 && arg2==arg2P_18 && arg3==arg3P_18 ], cost: 1
     11: f11 -> f16 : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, [ arg1P_12==arg2+arg1 && arg2==arg2P_12 && arg3==arg3P_12 ], cost: 1
     12: f16 -> f17 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, [ arg2P_13==-1+arg3 && arg1==arg1P_13 && arg3==arg3P_13 ], cost: 1
     13: f17 -> f18 : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, [ arg3P_14==arg3+arg1 && arg1==arg1P_14 && arg2==arg2P_14 ], cost: 1
     18: f18 -> f12 : arg1'=arg1P_19, arg2'=arg2P_19, arg3'=arg3P_19, [ arg1==arg1P_19 && arg2==arg2P_19 && arg3==arg3P_19 ], cost: 1
     20: f12 -> f3 : arg1'=arg1P_21, arg2'=arg2P_21, arg3'=arg3P_21, [ arg1==arg1P_21 && arg2==arg2P_21 && arg3==arg3P_21 ], cost: 1
     23: __init -> f1 : arg1'=arg1P_24, arg2'=arg2P_24, arg3'=arg3P_24, [], 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
     19: f3 -> f4 : [ arg2>0 && arg1>0 ], cost: 1
      2: f5 -> f8 : arg3'=arg2, [], cost: 1
      6: f8 -> f7 : [], cost: 1
      3: f6 -> f9 : arg3'=arg1, [], cost: 1
      7: f9 -> f7 : [], cost: 1
      4: f4 -> f5 : [ arg1>arg2 ], cost: 1
      5: f4 -> f6 : [ arg1<=arg2 ], cost: 1
     15: f7 -> f10 : [], cost: 1
     16: f7 -> f11 : [], cost: 1
      8: f10 -> f13 : arg2'=arg2+arg1, [], cost: 1
      9: f13 -> f14 : arg1'=-1+arg3, [], cost: 1
     10: f14 -> f15 : arg3'=arg2+arg3, [], cost: 1
     17: f15 -> f12 : [], cost: 1
     11: f11 -> f16 : arg1'=arg2+arg1, [], cost: 1
     12: f16 -> f17 : arg2'=-1+arg3, [], cost: 1
     13: f17 -> f18 : arg3'=arg3+arg1, [], cost: 1
     18: f18 -> f12 : [], cost: 1
     20: f12 -> f3 : [], cost: 1
     23: __init -> f1 : arg1'=arg1P_24, arg2'=arg2P_24, arg3'=arg3P_24, [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: __init
     19: f3 -> f4 : [ arg2>0 && arg1>0 ], cost: 1
     28: f4 -> f7 : arg3'=arg2, [ arg1>arg2 ], cost: 3
     29: f4 -> f7 : arg3'=arg1, [ arg1<=arg2 ], cost: 3
     36: f7 -> f12 : arg1'=-1+arg3, arg2'=arg2+arg1, arg3'=arg2+arg3+arg1, [], cost: 5
     37: f7 -> f12 : arg1'=arg2+arg1, arg2'=-1+arg3, arg3'=arg2+arg3+arg1, [], cost: 5
     20: f12 -> f3 : [], cost: 1
     25: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_24, [], cost: 3

Eliminated locations (on tree-shaped paths):
   Start location: __init
     38: f3 -> f7 : arg3'=arg2, [ arg2>0 && arg1>0 && arg1>arg2 ], cost: 4
     39: f3 -> f7 : arg3'=arg1, [ arg2>0 && arg1>0 && arg1<=arg2 ], cost: 4
     40: f7 -> f3 : arg1'=-1+arg3, arg2'=arg2+arg1, arg3'=arg2+arg3+arg1, [], cost: 6
     41: f7 -> f3 : arg1'=arg2+arg1, arg2'=-1+arg3, arg3'=arg2+arg3+arg1, [], cost: 6
     25: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_24, [], cost: 3

Eliminated locations (on tree-shaped paths):
   Start location: __init
     42: f3 -> f3 : arg1'=-1+arg2, arg2'=arg2+arg1, arg3'=2*arg2+arg1, [ arg2>0 && arg1>0 && arg1>arg2 ], cost: 10
     43: f3 -> f3 : arg1'=arg2+arg1, arg2'=-1+arg2, arg3'=2*arg2+arg1, [ arg2>0 && arg1>0 && arg1>arg2 ], cost: 10
     44: f3 -> f3 : arg1'=-1+arg1, arg2'=arg2+arg1, arg3'=arg2+2*arg1, [ arg2>0 && arg1>0 && arg1<=arg2 ], cost: 10
     45: f3 -> f3 : arg1'=arg2+arg1, arg2'=-1+arg1, arg3'=arg2+2*arg1, [ arg2>0 && arg1>0 && arg1<=arg2 ], cost: 10
     25: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_24, [], cost: 3

Accelerating simple loops of location 2.
   Accelerating the following rules:
     42: f3 -> f3 : arg1'=-1+arg2, arg2'=arg2+arg1, arg3'=2*arg2+arg1, [ arg2>0 && arg1>0 && arg1>arg2 ], cost: 10
     43: f3 -> f3 : arg1'=arg2+arg1, arg2'=-1+arg2, arg3'=2*arg2+arg1, [ arg2>0 && arg1>0 && arg1>arg2 ], cost: 10
     44: f3 -> f3 : arg1'=-1+arg1, arg2'=arg2+arg1, arg3'=arg2+2*arg1, [ arg2>0 && arg1>0 && arg1<=arg2 ], cost: 10
     45: f3 -> f3 : arg1'=arg2+arg1, arg2'=-1+arg1, arg3'=arg2+2*arg1, [ arg2>0 && arg1>0 && arg1<=arg2 ], cost: 10

   Failed to prove monotonicity of the guard of rule 42.
   Accelerated rule 43 with backward acceleration, yielding the new rule 46.
   Accelerated rule 44 with backward acceleration, yielding the new rule 47.
   Failed to prove monotonicity of the guard of rule 45.
[accelerate] Nesting with 4 inner and 4 outer candidates
   Nested simple loops 45 (outer loop) and 42 (inner loop) with Rule(2 | arg1>0, arg1>arg2, arg2+arg1>0, k_2>=1, 1+arg2-2*k_2>0, | 20*k_2 || 2 | 0=-2*k_2^2+arg1+k_2+2*arg2*k_2, 1=arg2-2*k_2, 2=3+3*arg2-2*(-1+k_2)^2+2*arg2*(-1+k_2)+arg1-5*k_2, ), resulting in the new rules: 48, 49.
   Nested simple loops 42 (outer loop) and 45 (inner loop) with Rule(2 | arg2>0, arg1<=arg2, arg2+arg1>0, k_3>=1, 1-2*k_3+arg1>0, | 20*k_3 || 2 | 0=-2*k_3+arg1, 1=arg2-2*k_3^2+k_3+2*k_3*arg1, 2=3-2*(-1+k_3)^2+2*(-1+k_3)*arg1+arg2-5*k_3+3*arg1, ), resulting in the new rules: 50, 51.
   Removing the simple loops: 42 43 44 45.

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     46: f3 -> f3 : arg1'=1/2*arg2+1/2*arg2^2+arg1, arg2'=0, arg3'=3/2+1/2*arg2-1/2*(-1+arg2)^2+(-1+arg2)*arg2+arg1, [ arg1>0 && arg1>arg2 && arg2>=1 ], cost: 10*arg2
     47: f3 -> f3 : arg1'=0, arg2'=arg2+1/2*arg1^2+1/2*arg1, arg3'=3/2+arg2-1/2*(-1+arg1)^2+1/2*arg1+(-1+arg1)*arg1, [ arg2>0 && arg1<=arg2 && arg1>=1 ], cost: 10*arg1
     48: f3 -> f3 : arg1'=-2*k_2^2+arg1+k_2+2*arg2*k_2, arg2'=arg2-2*k_2, arg3'=3+3*arg2-2*(-1+k_2)^2+2*arg2*(-1+k_2)+arg1-5*k_2, [ arg1>0 && arg1>arg2 && arg2+arg1>0 && k_2>=1 && 1+arg2-2*k_2>0 ], cost: 20*k_2
     49: f3 -> f3 : arg1'=arg2-2*k_2^2+arg1+k_2+2*(-1+arg1)*k_2, arg2'=-1+arg1-2*k_2, arg3'=2*(-1+k_2)*(-1+arg1)+arg2-2*(-1+k_2)^2+4*arg1-5*k_2, [ arg2>0 && arg1>0 && arg1<=arg2 && arg2+arg1>0 && -1+arg2+2*arg1>0 && k_2>=1 && arg1-2*k_2>0 ], cost: 10+20*k_2
     50: f3 -> f3 : arg1'=-2*k_3+arg1, arg2'=arg2-2*k_3^2+k_3+2*k_3*arg1, arg3'=3-2*(-1+k_3)^2+2*(-1+k_3)*arg1+arg2-5*k_3+3*arg1, [ arg2>0 && arg1<=arg2 && arg2+arg1>0 && k_3>=1 && 1-2*k_3+arg1>0 ], cost: 20*k_3
     51: f3 -> f3 : arg1'=-1+arg2-2*k_3, arg2'=arg2-2*k_3^2+k_3+2*(-1+arg2)*k_3+arg1, arg3'=-2*(-1+k_3)^2+4*arg2-5*k_3+2*(-1+k_3)*(-1+arg2)+arg1, [ arg2>0 && arg1>0 && arg1>arg2 && arg2+arg1>0 && -1+2*arg2+arg1>0 && k_3>=1 && arg2-2*k_3>0 ], cost: 10+20*k_3
     25: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_24, [], cost: 3

Chained accelerated rules (with incoming rules):
   Start location: __init
     25: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_24, [], cost: 3
     52: __init -> f3 : arg1'=1/2*arg2P_2^2+arg1P_1+1/2*arg2P_2, arg2'=0, arg3'=3/2+(-1+arg2P_2)*arg2P_2-1/2*(-1+arg2P_2)^2+arg1P_1+1/2*arg2P_2, [ arg1P_1>0 && arg1P_1>arg2P_2 && arg2P_2>=1 ], cost: 3+10*arg2P_2
     53: __init -> f3 : arg1'=0, arg2'=1/2*arg1P_1+arg2P_2+1/2*arg1P_1^2, arg3'=3/2+arg1P_1*(-1+arg1P_1)+1/2*arg1P_1-1/2*(-1+arg1P_1)^2+arg2P_2, [ arg2P_2>0 && arg1P_1<=arg2P_2 && arg1P_1>=1 ], cost: 3+10*arg1P_1
     54: __init -> f3 : arg1'=arg1P_1+2*arg2P_2*k_2-2*k_2^2+k_2, arg2'=arg2P_2-2*k_2, arg3'=3+2*(-1+k_2)*arg2P_2-2*(-1+k_2)^2+arg1P_1+3*arg2P_2-5*k_2, [ arg1P_1>0 && arg1P_1>arg2P_2 && arg1P_1+arg2P_2>0 && k_2>=1 && 1+arg2P_2-2*k_2>0 ], cost: 3+20*k_2
     55: __init -> f3 : arg1'=arg1P_1+arg2P_2-2*k_2^2+2*(-1+arg1P_1)*k_2+k_2, arg2'=-1+arg1P_1-2*k_2, arg3'=2*(-1+k_2)*(-1+arg1P_1)-2*(-1+k_2)^2+4*arg1P_1+arg2P_2-5*k_2, [ arg2P_2>0 && arg1P_1>0 && arg1P_1<=arg2P_2 && arg1P_1+arg2P_2>0 && -1+2*arg1P_1+arg2P_2>0 && k_2>=1 && arg1P_1-2*k_2>0 ], cost: 13+20*k_2
     56: __init -> f3 : arg1'=arg1P_1-2*k_3, arg2'=2*arg1P_1*k_3-2*k_3^2+arg2P_2+k_3, arg3'=3-2*(-1+k_3)^2+2*(-1+k_3)*arg1P_1+3*arg1P_1+arg2P_2-5*k_3, [ arg2P_2>0 && arg1P_1<=arg2P_2 && arg1P_1+arg2P_2>0 && k_3>=1 && 1+arg1P_1-2*k_3>0 ], cost: 3+20*k_3
     57: __init -> f3 : arg1'=-1+arg2P_2-2*k_3, arg2'=2*(-1+arg2P_2)*k_3+arg1P_1-2*k_3^2+arg2P_2+k_3, arg3'=-2*(-1+k_3)^2+arg1P_1+2*(-1+k_3)*(-1+arg2P_2)+4*arg2P_2-5*k_3, [ arg2P_2>0 && arg1P_1>0 && arg1P_1>arg2P_2 && arg1P_1+arg2P_2>0 && -1+arg1P_1+2*arg2P_2>0 && k_3>=1 && arg2P_2-2*k_3>0 ], cost: 13+20*k_3

Removed unreachable locations (and leaf rules with constant cost):
   Start location: __init
     52: __init -> f3 : arg1'=1/2*arg2P_2^2+arg1P_1+1/2*arg2P_2, arg2'=0, arg3'=3/2+(-1+arg2P_2)*arg2P_2-1/2*(-1+arg2P_2)^2+arg1P_1+1/2*arg2P_2, [ arg1P_1>0 && arg1P_1>arg2P_2 && arg2P_2>=1 ], cost: 3+10*arg2P_2
     53: __init -> f3 : arg1'=0, arg2'=1/2*arg1P_1+arg2P_2+1/2*arg1P_1^2, arg3'=3/2+arg1P_1*(-1+arg1P_1)+1/2*arg1P_1-1/2*(-1+arg1P_1)^2+arg2P_2, [ arg2P_2>0 && arg1P_1<=arg2P_2 && arg1P_1>=1 ], cost: 3+10*arg1P_1
     54: __init -> f3 : arg1'=arg1P_1+2*arg2P_2*k_2-2*k_2^2+k_2, arg2'=arg2P_2-2*k_2, arg3'=3+2*(-1+k_2)*arg2P_2-2*(-1+k_2)^2+arg1P_1+3*arg2P_2-5*k_2, [ arg1P_1>0 && arg1P_1>arg2P_2 && arg1P_1+arg2P_2>0 && k_2>=1 && 1+arg2P_2-2*k_2>0 ], cost: 3+20*k_2
     55: __init -> f3 : arg1'=arg1P_1+arg2P_2-2*k_2^2+2*(-1+arg1P_1)*k_2+k_2, arg2'=-1+arg1P_1-2*k_2, arg3'=2*(-1+k_2)*(-1+arg1P_1)-2*(-1+k_2)^2+4*arg1P_1+arg2P_2-5*k_2, [ arg2P_2>0 && arg1P_1>0 && arg1P_1<=arg2P_2 && arg1P_1+arg2P_2>0 && -1+2*arg1P_1+arg2P_2>0 && k_2>=1 && arg1P_1-2*k_2>0 ], cost: 13+20*k_2
     56: __init -> f3 : arg1'=arg1P_1-2*k_3, arg2'=2*arg1P_1*k_3-2*k_3^2+arg2P_2+k_3, arg3'=3-2*(-1+k_3)^2+2*(-1+k_3)*arg1P_1+3*arg1P_1+arg2P_2-5*k_3, [ arg2P_2>0 && arg1P_1<=arg2P_2 && arg1P_1+arg2P_2>0 && k_3>=1 && 1+arg1P_1-2*k_3>0 ], cost: 3+20*k_3
     57: __init -> f3 : arg1'=-1+arg2P_2-2*k_3, arg2'=2*(-1+arg2P_2)*k_3+arg1P_1-2*k_3^2+arg2P_2+k_3, arg3'=-2*(-1+k_3)^2+arg1P_1+2*(-1+k_3)*(-1+arg2P_2)+4*arg2P_2-5*k_3, [ arg2P_2>0 && arg1P_1>0 && arg1P_1>arg2P_2 && arg1P_1+arg2P_2>0 && -1+arg1P_1+2*arg2P_2>0 && k_3>=1 && arg2P_2-2*k_3>0 ], cost: 13+20*k_3

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: __init
     52: __init -> f3 : arg1'=1/2*arg2P_2^2+arg1P_1+1/2*arg2P_2, arg2'=0, arg3'=3/2+(-1+arg2P_2)*arg2P_2-1/2*(-1+arg2P_2)^2+arg1P_1+1/2*arg2P_2, [ arg1P_1>0 && arg1P_1>arg2P_2 && arg2P_2>=1 ], cost: 3+10*arg2P_2
     53: __init -> f3 : arg1'=0, arg2'=1/2*arg1P_1+arg2P_2+1/2*arg1P_1^2, arg3'=3/2+arg1P_1*(-1+arg1P_1)+1/2*arg1P_1-1/2*(-1+arg1P_1)^2+arg2P_2, [ arg2P_2>0 && arg1P_1<=arg2P_2 && arg1P_1>=1 ], cost: 3+10*arg1P_1
     54: __init -> f3 : arg1'=arg1P_1+2*arg2P_2*k_2-2*k_2^2+k_2, arg2'=arg2P_2-2*k_2, arg3'=3+2*(-1+k_2)*arg2P_2-2*(-1+k_2)^2+arg1P_1+3*arg2P_2-5*k_2, [ arg1P_1>0 && arg1P_1>arg2P_2 && arg1P_1+arg2P_2>0 && k_2>=1 && 1+arg2P_2-2*k_2>0 ], cost: 3+20*k_2
     55: __init -> f3 : arg1'=arg1P_1+arg2P_2-2*k_2^2+2*(-1+arg1P_1)*k_2+k_2, arg2'=-1+arg1P_1-2*k_2, arg3'=2*(-1+k_2)*(-1+arg1P_1)-2*(-1+k_2)^2+4*arg1P_1+arg2P_2-5*k_2, [ arg2P_2>0 && arg1P_1>0 && arg1P_1<=arg2P_2 && arg1P_1+arg2P_2>0 && -1+2*arg1P_1+arg2P_2>0 && k_2>=1 && arg1P_1-2*k_2>0 ], cost: 13+20*k_2
     56: __init -> f3 : arg1'=arg1P_1-2*k_3, arg2'=2*arg1P_1*k_3-2*k_3^2+arg2P_2+k_3, arg3'=3-2*(-1+k_3)^2+2*(-1+k_3)*arg1P_1+3*arg1P_1+arg2P_2-5*k_3, [ arg2P_2>0 && arg1P_1<=arg2P_2 && arg1P_1+arg2P_2>0 && k_3>=1 && 1+arg1P_1-2*k_3>0 ], cost: 3+20*k_3
     57: __init -> f3 : arg1'=-1+arg2P_2-2*k_3, arg2'=2*(-1+arg2P_2)*k_3+arg1P_1-2*k_3^2+arg2P_2+k_3, arg3'=-2*(-1+k_3)^2+arg1P_1+2*(-1+k_3)*(-1+arg2P_2)+4*arg2P_2-5*k_3, [ arg2P_2>0 && arg1P_1>0 && arg1P_1>arg2P_2 && arg1P_1+arg2P_2>0 && -1+arg1P_1+2*arg2P_2>0 && k_3>=1 && arg2P_2-2*k_3>0 ], cost: 13+20*k_3

Computing asymptotic complexity for rule 52
   Simplified the guard:
     52: __init -> f3 : arg1'=1/2*arg2P_2^2+arg1P_1+1/2*arg2P_2, arg2'=0, arg3'=3/2+(-1+arg2P_2)*arg2P_2-1/2*(-1+arg2P_2)^2+arg1P_1+1/2*arg2P_2, [ arg1P_1>arg2P_2 && arg2P_2>=1 ], cost: 3+10*arg2P_2
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 53
   Simplified the guard:
     53: __init -> f3 : arg1'=0, arg2'=1/2*arg1P_1+arg2P_2+1/2*arg1P_1^2, arg3'=3/2+arg1P_1*(-1+arg1P_1)+1/2*arg1P_1-1/2*(-1+arg1P_1)^2+arg2P_2, [ arg1P_1<=arg2P_2 && arg1P_1>=1 ], cost: 3+10*arg1P_1
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 54
   Simplified the guard:
     54: __init -> f3 : arg1'=arg1P_1+2*arg2P_2*k_2-2*k_2^2+k_2, arg2'=arg2P_2-2*k_2, arg3'=3+2*(-1+k_2)*arg2P_2-2*(-1+k_2)^2+arg1P_1+3*arg2P_2-5*k_2, [ arg1P_1>arg2P_2 && arg1P_1+arg2P_2>0 && k_2>=1 && 1+arg2P_2-2*k_2>0 ], cost: 3+20*k_2
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 56
   Simplified the guard:
     56: __init -> f3 : arg1'=arg1P_1-2*k_3, arg2'=2*arg1P_1*k_3-2*k_3^2+arg2P_2+k_3, arg3'=3-2*(-1+k_3)^2+2*(-1+k_3)*arg1P_1+3*arg1P_1+arg2P_2-5*k_3, [ arg1P_1<=arg2P_2 && arg1P_1+arg2P_2>0 && k_3>=1 && 1+arg1P_1-2*k_3>0 ], cost: 3+20*k_3
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 55
   Simplified the guard:
     55: __init -> f3 : arg1'=arg1P_1+arg2P_2-2*k_2^2+2*(-1+arg1P_1)*k_2+k_2, arg2'=-1+arg1P_1-2*k_2, arg3'=2*(-1+k_2)*(-1+arg1P_1)-2*(-1+k_2)^2+4*arg1P_1+arg2P_2-5*k_2, [ arg1P_1<=arg2P_2 && k_2>=1 && arg1P_1-2*k_2>0 ], cost: 13+20*k_2
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 57
   Simplified the guard:
     57: __init -> f3 : arg1'=-1+arg2P_2-2*k_3, arg2'=2*(-1+arg2P_2)*k_3+arg1P_1-2*k_3^2+arg2P_2+k_3, arg3'=-2*(-1+k_3)^2+arg1P_1+2*(-1+k_3)*(-1+arg2P_2)+4*arg2P_2-5*k_3, [ arg1P_1>arg2P_2 && k_3>=1 && arg2P_2-2*k_3>0 ], cost: 13+20*k_3
   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),?)