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

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
     19: __init -> f1 : arg1'=arg1P_20, arg2'=arg2P_20, arg3'=arg3P_20, [], cost: 1

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

Simplified all rules, resulting in:
   Start location: __init
      0: f1 -> f2 : arg2'=arg2P_1, [], cost: 1
      1: f2 -> f3 : arg3'=arg3P_2, [], cost: 1
      2: f3 -> f4 : arg1'=0, [], cost: 1
     16: f4 -> f5 : [ arg2+arg3>0 ], cost: 1
      3: f6 -> f9 : arg2'=-1+arg2, [], cost: 1
     13: f9 -> f8 : [], cost: 1
      4: f10 -> f13 : arg2'=-1+arg2, [], cost: 1
      9: f13 -> f12 : [], cost: 1
      5: f11 -> f14 : arg3'=-1+arg3, [], cost: 1
     10: f14 -> f12 : [], cost: 1
      6: f7 -> f10 : [ arg2==arg3 ], cost: 1
      7: f7 -> f11 : [ arg2<arg3 ], cost: 1
      8: f7 -> f11 : [ arg2>arg3 ], cost: 1
     14: f12 -> f8 : [], cost: 1
     11: f5 -> f6 : [ arg2>arg3 ], cost: 1
     12: f5 -> f7 : [ arg2<=arg3 ], cost: 1
     15: f8 -> f15 : arg1'=1+arg1, [], cost: 1
     17: f15 -> f4 : [], cost: 1
     19: __init -> f1 : arg1'=arg1P_20, arg2'=arg2P_20, arg3'=arg3P_20, [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: __init
     16: f4 -> f5 : [ arg2+arg3>0 ], cost: 1
     27: f11 -> f12 : arg3'=-1+arg3, [], cost: 2
      7: f7 -> f11 : [ arg2<arg3 ], cost: 1
      8: f7 -> f11 : [ arg2>arg3 ], cost: 1
     26: f7 -> f12 : arg2'=-1+arg2, [ arg2==arg3 ], cost: 3
     14: f12 -> f8 : [], cost: 1
     12: f5 -> f7 : [ arg2<=arg3 ], cost: 1
     24: f5 -> f8 : arg2'=-1+arg2, [ arg2>arg3 ], cost: 3
     28: f8 -> f4 : arg1'=1+arg1, [], cost: 2
     22: __init -> f4 : arg1'=0, arg2'=arg2P_1, arg3'=arg3P_2, [], cost: 4

Eliminated locations (on tree-shaped paths):
   Start location: __init
     29: f4 -> f7 : [ arg2+arg3>0 && arg2<=arg3 ], cost: 2
     30: f4 -> f8 : arg2'=-1+arg2, [ arg2+arg3>0 && arg2>arg3 ], cost: 4
     33: f7 -> f8 : arg2'=-1+arg2, [ arg2==arg3 ], cost: 4
     34: f7 -> f8 : arg3'=-1+arg3, [ arg2<arg3 ], cost: 4
     35: f7 -> f8 : arg3'=-1+arg3, [ arg2>arg3 ], cost: 4
     28: f8 -> f4 : arg1'=1+arg1, [], cost: 2
     22: __init -> f4 : arg1'=0, arg2'=arg2P_1, arg3'=arg3P_2, [], cost: 4

Eliminated locations (on tree-shaped paths):
   Start location: __init
     38: f4 -> f4 : arg1'=1+arg1, arg2'=-1+arg2, [ arg2+arg3>0 && arg2>arg3 ], cost: 6
     39: f4 -> f4 : arg1'=1+arg1, arg2'=-1+arg2, [ arg2+arg3>0 && arg2==arg3 ], cost: 8
     40: f4 -> f4 : arg1'=1+arg1, arg3'=-1+arg3, [ arg2+arg3>0 && arg2<arg3 ], cost: 8
     22: __init -> f4 : arg1'=0, arg2'=arg2P_1, arg3'=arg3P_2, [], cost: 4

Accelerating simple loops of location 3.
   Accelerating the following rules:
     38: f4 -> f4 : arg1'=1+arg1, arg2'=-1+arg2, [ arg2+arg3>0 && arg2>arg3 ], cost: 6
     39: f4 -> f4 : arg1'=1+arg1, arg2'=-1+arg2, [ arg2+arg3>0 && arg2==arg3 ], cost: 8
     40: f4 -> f4 : arg1'=1+arg1, arg3'=-1+arg3, [ arg2+arg3>0 && arg2<arg3 ], cost: 8

   Accelerated rule 38 with backward acceleration, yielding the new rule 41.
   Accelerated rule 38 with backward acceleration, yielding the new rule 42.
   Failed to prove monotonicity of the guard of rule 39.
   Accelerated rule 40 with backward acceleration, yielding the new rule 43.
   Accelerated rule 40 with backward acceleration, yielding the new rule 44.
[accelerate] Nesting with 5 inner and 3 outer candidates
   Nested simple loops 40 (outer loop) and 39 (inner loop) with Rule(3 | arg2==arg3, k_3>=0, 1+arg2+arg3-2*k_3>0, | 16*k_3 || 3 | 0=2*k_3+arg1, 1=arg2-k_3, 2=arg3-k_3, ), resulting in the new rules: 45, 46.
   Removing the simple loops: 38 40.

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     39: f4 -> f4 : arg1'=1+arg1, arg2'=-1+arg2, [ arg2+arg3>0 && arg2==arg3 ], cost: 8
     41: f4 -> f4 : arg1'=arg2+arg3+arg1, arg2'=-arg3, [ arg2+arg3>=0 && 1-arg3>arg3 ], cost: 6*arg2+6*arg3
     42: f4 -> f4 : arg1'=arg2-arg3+arg1, arg2'=arg3, [ arg2-arg3>=0 && 1+2*arg3>0 ], cost: 6*arg2-6*arg3
     43: f4 -> f4 : arg1'=arg2+arg3+arg1, arg3'=-arg2, [ arg2+arg3>=0 && arg2<1-arg2 ], cost: 8*arg2+8*arg3
     44: f4 -> f4 : arg1'=-arg2+arg3+arg1, arg3'=arg2, [ -arg2+arg3>=0 && 1+2*arg2>0 ], cost: -8*arg2+8*arg3
     45: f4 -> f4 : arg1'=2*k_3+arg1, arg2'=arg2-k_3, arg3'=arg3-k_3, [ arg2==arg3 && k_3>=0 && 1+arg2+arg3-2*k_3>0 ], cost: 16*k_3
     46: f4 -> f4 : arg1'=1+2*k_3+arg1, arg2'=arg2-k_3, arg3'=-1+arg3-k_3, [ arg2+arg3>0 && arg2==-1+arg3 && k_3>=0 && arg2+arg3-2*k_3>0 ], cost: 8+16*k_3
     22: __init -> f4 : arg1'=0, arg2'=arg2P_1, arg3'=arg3P_2, [], cost: 4

Chained accelerated rules (with incoming rules):
   Start location: __init
     22: __init -> f4 : arg1'=0, arg2'=arg2P_1, arg3'=arg3P_2, [], cost: 4
     47: __init -> f4 : arg1'=1, arg2'=-1+arg3P_2, arg3'=arg3P_2, [ 2*arg3P_2>0 ], cost: 12
     48: __init -> f4 : arg1'=arg2P_1+arg3P_2, arg2'=-arg3P_2, arg3'=arg3P_2, [ arg2P_1+arg3P_2>=0 && 1-arg3P_2>arg3P_2 ], cost: 4+6*arg2P_1+6*arg3P_2
     49: __init -> f4 : arg1'=arg2P_1-arg3P_2, arg2'=arg3P_2, arg3'=arg3P_2, [ arg2P_1-arg3P_2>=0 && 1+2*arg3P_2>0 ], cost: 4+6*arg2P_1-6*arg3P_2
     50: __init -> f4 : arg1'=arg2P_1+arg3P_2, arg2'=arg2P_1, arg3'=-arg2P_1, [ arg2P_1+arg3P_2>=0 && arg2P_1<1-arg2P_1 ], cost: 4+8*arg2P_1+8*arg3P_2
     51: __init -> f4 : arg1'=-arg2P_1+arg3P_2, arg2'=arg2P_1, arg3'=arg2P_1, [ -arg2P_1+arg3P_2>=0 && 1+2*arg2P_1>0 ], cost: 4-8*arg2P_1+8*arg3P_2
     52: __init -> f4 : arg1'=2*k_3, arg2'=-k_3+arg3P_2, arg3'=-k_3+arg3P_2, [ k_3>=0 && 1-2*k_3+2*arg3P_2>0 ], cost: 4+16*k_3
     53: __init -> f4 : arg1'=1+2*k_3, arg2'=-1-k_3+arg3P_2, arg3'=-1-k_3+arg3P_2, [ -1+2*arg3P_2>0 && k_3>=0 && -1-2*k_3+2*arg3P_2>0 ], cost: 12+16*k_3

Removed unreachable locations (and leaf rules with constant cost):
   Start location: __init
     48: __init -> f4 : arg1'=arg2P_1+arg3P_2, arg2'=-arg3P_2, arg3'=arg3P_2, [ arg2P_1+arg3P_2>=0 && 1-arg3P_2>arg3P_2 ], cost: 4+6*arg2P_1+6*arg3P_2
     49: __init -> f4 : arg1'=arg2P_1-arg3P_2, arg2'=arg3P_2, arg3'=arg3P_2, [ arg2P_1-arg3P_2>=0 && 1+2*arg3P_2>0 ], cost: 4+6*arg2P_1-6*arg3P_2
     50: __init -> f4 : arg1'=arg2P_1+arg3P_2, arg2'=arg2P_1, arg3'=-arg2P_1, [ arg2P_1+arg3P_2>=0 && arg2P_1<1-arg2P_1 ], cost: 4+8*arg2P_1+8*arg3P_2
     51: __init -> f4 : arg1'=-arg2P_1+arg3P_2, arg2'=arg2P_1, arg3'=arg2P_1, [ -arg2P_1+arg3P_2>=0 && 1+2*arg2P_1>0 ], cost: 4-8*arg2P_1+8*arg3P_2
     52: __init -> f4 : arg1'=2*k_3, arg2'=-k_3+arg3P_2, arg3'=-k_3+arg3P_2, [ k_3>=0 && 1-2*k_3+2*arg3P_2>0 ], cost: 4+16*k_3
     53: __init -> f4 : arg1'=1+2*k_3, arg2'=-1-k_3+arg3P_2, arg3'=-1-k_3+arg3P_2, [ -1+2*arg3P_2>0 && k_3>=0 && -1-2*k_3+2*arg3P_2>0 ], cost: 12+16*k_3

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: __init
     48: __init -> f4 : arg1'=arg2P_1+arg3P_2, arg2'=-arg3P_2, arg3'=arg3P_2, [ arg2P_1+arg3P_2>=0 && 1-arg3P_2>arg3P_2 ], cost: 4+6*arg2P_1+6*arg3P_2
     49: __init -> f4 : arg1'=arg2P_1-arg3P_2, arg2'=arg3P_2, arg3'=arg3P_2, [ arg2P_1-arg3P_2>=0 && 1+2*arg3P_2>0 ], cost: 4+6*arg2P_1-6*arg3P_2
     50: __init -> f4 : arg1'=arg2P_1+arg3P_2, arg2'=arg2P_1, arg3'=-arg2P_1, [ arg2P_1+arg3P_2>=0 && arg2P_1<1-arg2P_1 ], cost: 4+8*arg2P_1+8*arg3P_2
     51: __init -> f4 : arg1'=-arg2P_1+arg3P_2, arg2'=arg2P_1, arg3'=arg2P_1, [ -arg2P_1+arg3P_2>=0 && 1+2*arg2P_1>0 ], cost: 4-8*arg2P_1+8*arg3P_2
     52: __init -> f4 : arg1'=2*k_3, arg2'=-k_3+arg3P_2, arg3'=-k_3+arg3P_2, [ k_3>=0 && 1-2*k_3+2*arg3P_2>0 ], cost: 4+16*k_3
     53: __init -> f4 : arg1'=1+2*k_3, arg2'=-1-k_3+arg3P_2, arg3'=-1-k_3+arg3P_2, [ -1+2*arg3P_2>0 && k_3>=0 && -1-2*k_3+2*arg3P_2>0 ], cost: 12+16*k_3

Computing asymptotic complexity for rule 48
   Resulting cost 0 has complexity: Unknown

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

Computing asymptotic complexity for rule 53
   Simplified the guard:
     53: __init -> f4 : arg1'=1+2*k_3, arg2'=-1-k_3+arg3P_2, arg3'=-1-k_3+arg3P_2, [ k_3>=0 && -1-2*k_3+2*arg3P_2>0 ], cost: 12+16*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),?)