WORST_CASE(Omega(1),?)

### Pre-processing the ITS problem ###

Initial linear ITS problem
   Start location: l9
      0: l0 -> l1 : i1^0'=i1^post_1, i2^0'=i2^post_1, i3^0'=i3^post_1, i4^0'=i4^post_1, n^0'=n^post_1, [ 1<=i4^0 && i4^post_1==-1+i4^0 && i1^0==i1^post_1 && i2^0==i2^post_1 && i3^0==i3^post_1 && n^0==n^post_1 ], cost: 1
      1: l1 -> l0 : i1^0'=i1^post_2, i2^0'=i2^post_2, i3^0'=i3^post_2, i4^0'=i4^post_2, n^0'=n^post_2, [ i1^0==i1^post_2 && i2^0==i2^post_2 && i3^0==i3^post_2 && i4^0==i4^post_2 && n^0==n^post_2 ], cost: 1
      2: l2 -> l0 : i1^0'=i1^post_3, i2^0'=i2^post_3, i3^0'=i3^post_3, i4^0'=i4^post_3, n^0'=n^post_3, [ n^0<=i3^0 && i4^post_3==i3^0 && i1^0==i1^post_3 && i2^0==i2^post_3 && i3^0==i3^post_3 && n^0==n^post_3 ], cost: 1
      3: l2 -> l3 : i1^0'=i1^post_4, i2^0'=i2^post_4, i3^0'=i3^post_4, i4^0'=i4^post_4, n^0'=n^post_4, [ 1+i3^0<=n^0 && i3^post_4==1+i3^0 && i1^0==i1^post_4 && i2^0==i2^post_4 && i4^0==i4^post_4 && n^0==n^post_4 ], cost: 1
      4: l3 -> l2 : i1^0'=i1^post_5, i2^0'=i2^post_5, i3^0'=i3^post_5, i4^0'=i4^post_5, n^0'=n^post_5, [ i1^0==i1^post_5 && i2^0==i2^post_5 && i3^0==i3^post_5 && i4^0==i4^post_5 && n^0==n^post_5 ], cost: 1
      5: l4 -> l2 : i1^0'=i1^post_6, i2^0'=i2^post_6, i3^0'=i3^post_6, i4^0'=i4^post_6, n^0'=n^post_6, [ i2^0<=0 && i3^post_6==i2^0 && i1^0==i1^post_6 && i2^0==i2^post_6 && i4^0==i4^post_6 && n^0==n^post_6 ], cost: 1
      6: l4 -> l5 : i1^0'=i1^post_7, i2^0'=i2^post_7, i3^0'=i3^post_7, i4^0'=i4^post_7, n^0'=n^post_7, [ 1<=i2^0 && i2^post_7==-1+i2^0 && i1^0==i1^post_7 && i3^0==i3^post_7 && i4^0==i4^post_7 && n^0==n^post_7 ], cost: 1
      7: l5 -> l4 : i1^0'=i1^post_8, i2^0'=i2^post_8, i3^0'=i3^post_8, i4^0'=i4^post_8, n^0'=n^post_8, [ i1^0==i1^post_8 && i2^0==i2^post_8 && i3^0==i3^post_8 && i4^0==i4^post_8 && n^0==n^post_8 ], cost: 1
      8: l6 -> l4 : i1^0'=i1^post_9, i2^0'=i2^post_9, i3^0'=i3^post_9, i4^0'=i4^post_9, n^0'=n^post_9, [ n^0<=i1^0 && i2^post_9==i1^0 && i1^0==i1^post_9 && i3^0==i3^post_9 && i4^0==i4^post_9 && n^0==n^post_9 ], cost: 1
      9: l6 -> l7 : i1^0'=i1^post_10, i2^0'=i2^post_10, i3^0'=i3^post_10, i4^0'=i4^post_10, n^0'=n^post_10, [ 1+i1^0<=n^0 && i1^post_10==1+i1^0 && i2^0==i2^post_10 && i3^0==i3^post_10 && i4^0==i4^post_10 && n^0==n^post_10 ], cost: 1
     10: l7 -> l6 : i1^0'=i1^post_11, i2^0'=i2^post_11, i3^0'=i3^post_11, i4^0'=i4^post_11, n^0'=n^post_11, [ i1^0==i1^post_11 && i2^0==i2^post_11 && i3^0==i3^post_11 && i4^0==i4^post_11 && n^0==n^post_11 ], cost: 1
     11: l8 -> l6 : i1^0'=i1^post_12, i2^0'=i2^post_12, i3^0'=i3^post_12, i4^0'=i4^post_12, n^0'=n^post_12, [ i1^0==i1^post_12 && i2^0==i2^post_12 && i3^0==i3^post_12 && i4^0==i4^post_12 && n^0==n^post_12 ], cost: 1
     12: l9 -> l8 : i1^0'=i1^post_13, i2^0'=i2^post_13, i3^0'=i3^post_13, i4^0'=i4^post_13, n^0'=n^post_13, [ i1^0==i1^post_13 && i2^0==i2^post_13 && i3^0==i3^post_13 && i4^0==i4^post_13 && n^0==n^post_13 ], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
     12: l9 -> l8 : i1^0'=i1^post_13, i2^0'=i2^post_13, i3^0'=i3^post_13, i4^0'=i4^post_13, n^0'=n^post_13, [ i1^0==i1^post_13 && i2^0==i2^post_13 && i3^0==i3^post_13 && i4^0==i4^post_13 && n^0==n^post_13 ], cost: 1

Simplified all rules, resulting in:
   Start location: l9
      0: l0 -> l1 : i4^0'=-1+i4^0, [ 1<=i4^0 ], cost: 1
      1: l1 -> l0 : [], cost: 1
      2: l2 -> l0 : i4^0'=i3^0, [ n^0<=i3^0 ], cost: 1
      3: l2 -> l3 : i3^0'=1+i3^0, [ 1+i3^0<=n^0 ], cost: 1
      4: l3 -> l2 : [], cost: 1
      5: l4 -> l2 : i3^0'=i2^0, [ i2^0<=0 ], cost: 1
      6: l4 -> l5 : i2^0'=-1+i2^0, [ 1<=i2^0 ], cost: 1
      7: l5 -> l4 : [], cost: 1
      8: l6 -> l4 : i2^0'=i1^0, [ n^0<=i1^0 ], cost: 1
      9: l6 -> l7 : i1^0'=1+i1^0, [ 1+i1^0<=n^0 ], cost: 1
     10: l7 -> l6 : [], cost: 1
     11: l8 -> l6 : [], cost: 1
     12: l9 -> l8 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: l9
     17: l0 -> l0 : i4^0'=-1+i4^0, [ 1<=i4^0 ], cost: 2
      2: l2 -> l0 : i4^0'=i3^0, [ n^0<=i3^0 ], cost: 1
     16: l2 -> l2 : i3^0'=1+i3^0, [ 1+i3^0<=n^0 ], cost: 2
      5: l4 -> l2 : i3^0'=i2^0, [ i2^0<=0 ], cost: 1
     15: l4 -> l4 : i2^0'=-1+i2^0, [ 1<=i2^0 ], cost: 2
      8: l6 -> l4 : i2^0'=i1^0, [ n^0<=i1^0 ], cost: 1
     14: l6 -> l6 : i1^0'=1+i1^0, [ 1+i1^0<=n^0 ], cost: 2
     13: l9 -> l6 : [], cost: 2

Accelerating simple loops of location 0.
   Accelerating the following rules:
     17: l0 -> l0 : i4^0'=-1+i4^0, [ 1<=i4^0 ], cost: 2

   Accelerated rule 17 with backward acceleration, yielding the new rule 18.
[accelerate] Nesting with 1 inner and 1 outer candidates
   Removing the simple loops: 17.

Accelerating simple loops of location 2.
   Accelerating the following rules:
     16: l2 -> l2 : i3^0'=1+i3^0, [ 1+i3^0<=n^0 ], cost: 2

   Accelerated rule 16 with backward acceleration, yielding the new rule 19.
[accelerate] Nesting with 1 inner and 1 outer candidates
   Removing the simple loops: 16.

Accelerating simple loops of location 4.
   Accelerating the following rules:
     15: l4 -> l4 : i2^0'=-1+i2^0, [ 1<=i2^0 ], cost: 2

   Accelerated rule 15 with backward acceleration, yielding the new rule 20.
[accelerate] Nesting with 1 inner and 1 outer candidates
   Removing the simple loops: 15.

Accelerating simple loops of location 6.
   Accelerating the following rules:
     14: l6 -> l6 : i1^0'=1+i1^0, [ 1+i1^0<=n^0 ], cost: 2

   Accelerated rule 14 with backward acceleration, yielding the new rule 21.
[accelerate] Nesting with 1 inner and 1 outer candidates
   Removing the simple loops: 14.

Accelerated all simple loops using metering functions (where possible):
   Start location: l9
     18: l0 -> l0 : i4^0'=0, [ i4^0>=0 ], cost: 2*i4^0
      2: l2 -> l0 : i4^0'=i3^0, [ n^0<=i3^0 ], cost: 1
     19: l2 -> l2 : i3^0'=n^0, [ n^0-i3^0>=0 ], cost: 2*n^0-2*i3^0
      5: l4 -> l2 : i3^0'=i2^0, [ i2^0<=0 ], cost: 1
     20: l4 -> l4 : i2^0'=0, [ i2^0>=0 ], cost: 2*i2^0
      8: l6 -> l4 : i2^0'=i1^0, [ n^0<=i1^0 ], cost: 1
     21: l6 -> l6 : i1^0'=n^0, [ n^0-i1^0>=0 ], cost: 2*n^0-2*i1^0
     13: l9 -> l6 : [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l9
      2: l2 -> l0 : i4^0'=i3^0, [ n^0<=i3^0 ], cost: 1
     22: l2 -> l0 : i4^0'=0, [ n^0<=i3^0 && i3^0>=0 ], cost: 1+2*i3^0
      5: l4 -> l2 : i3^0'=i2^0, [ i2^0<=0 ], cost: 1
     23: l4 -> l2 : i3^0'=n^0, [ i2^0<=0 && n^0-i2^0>=0 ], cost: 1+2*n^0-2*i2^0
      8: l6 -> l4 : i2^0'=i1^0, [ n^0<=i1^0 ], cost: 1
     24: l6 -> l4 : i2^0'=0, [ n^0<=i1^0 && i1^0>=0 ], cost: 1+2*i1^0
     13: l9 -> l6 : [], cost: 2
     25: l9 -> l6 : i1^0'=n^0, [ n^0-i1^0>=0 ], cost: 2+2*n^0-2*i1^0

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l9
     22: l2 -> l0 : i4^0'=0, [ n^0<=i3^0 && i3^0>=0 ], cost: 1+2*i3^0
      5: l4 -> l2 : i3^0'=i2^0, [ i2^0<=0 ], cost: 1
     23: l4 -> l2 : i3^0'=n^0, [ i2^0<=0 && n^0-i2^0>=0 ], cost: 1+2*n^0-2*i2^0
      8: l6 -> l4 : i2^0'=i1^0, [ n^0<=i1^0 ], cost: 1
     24: l6 -> l4 : i2^0'=0, [ n^0<=i1^0 && i1^0>=0 ], cost: 1+2*i1^0
     13: l9 -> l6 : [], cost: 2
     25: l9 -> l6 : i1^0'=n^0, [ n^0-i1^0>=0 ], cost: 2+2*n^0-2*i1^0

Eliminated locations (on tree-shaped paths):
   Start location: l9
     30: l4 -> l0 : i3^0'=i2^0, i4^0'=0, [ i2^0<=0 && n^0<=i2^0 && i2^0>=0 ], cost: 2+2*i2^0
     31: l4 -> l0 : i3^0'=n^0, i4^0'=0, [ i2^0<=0 && n^0-i2^0>=0 && n^0>=0 ], cost: 2+4*n^0-2*i2^0
     26: l9 -> l4 : i2^0'=i1^0, [ n^0<=i1^0 ], cost: 3
     27: l9 -> l4 : i2^0'=0, [ n^0<=i1^0 && i1^0>=0 ], cost: 3+2*i1^0
     28: l9 -> l4 : i1^0'=n^0, i2^0'=n^0, [ n^0-i1^0>=0 ], cost: 3+2*n^0-2*i1^0
     29: l9 -> l4 : i1^0'=n^0, i2^0'=0, [ n^0-i1^0>=0 && n^0>=0 ], cost: 3+4*n^0-2*i1^0

Eliminated locations (on tree-shaped paths):
   Start location: l9
     32: l9 -> l0 : i2^0'=i1^0, i3^0'=i1^0, i4^0'=0, [ n^0<=i1^0 && i1^0<=0 && i1^0>=0 ], cost: 5+2*i1^0
     33: l9 -> l0 : i2^0'=i1^0, i3^0'=n^0, i4^0'=0, [ n^0<=i1^0 && i1^0<=0 && n^0-i1^0>=0 && n^0>=0 ], cost: 5+4*n^0-2*i1^0
     34: l9 -> l0 : i2^0'=0, i3^0'=0, i4^0'=0, [ n^0<=i1^0 && i1^0>=0 && n^0<=0 ], cost: 5+2*i1^0
     35: l9 -> l0 : i2^0'=0, i3^0'=n^0, i4^0'=0, [ n^0<=i1^0 && i1^0>=0 && n^0>=0 ], cost: 5+4*n^0+2*i1^0
     36: l9 -> l0 : i1^0'=n^0, i2^0'=n^0, i3^0'=n^0, i4^0'=0, [ n^0-i1^0>=0 && n^0<=0 && n^0>=0 ], cost: 5+4*n^0-2*i1^0
     37: l9 -> l0 : i1^0'=n^0, i2^0'=n^0, i3^0'=n^0, i4^0'=0, [ n^0-i1^0>=0 && n^0<=0 && n^0>=0 ], cost: 5+4*n^0-2*i1^0
     38: l9 -> l0 : i1^0'=n^0, i2^0'=0, i3^0'=0, i4^0'=0, [ n^0-i1^0>=0 && n^0>=0 && n^0<=0 ], cost: 5+4*n^0-2*i1^0
     39: l9 -> l0 : i1^0'=n^0, i2^0'=0, i3^0'=n^0, i4^0'=0, [ n^0-i1^0>=0 && n^0>=0 ], cost: 5+8*n^0-2*i1^0

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l9
     32: l9 -> l0 : i2^0'=i1^0, i3^0'=i1^0, i4^0'=0, [ n^0<=i1^0 && i1^0<=0 && i1^0>=0 ], cost: 5+2*i1^0
     33: l9 -> l0 : i2^0'=i1^0, i3^0'=n^0, i4^0'=0, [ n^0<=i1^0 && i1^0<=0 && n^0-i1^0>=0 && n^0>=0 ], cost: 5+4*n^0-2*i1^0
     34: l9 -> l0 : i2^0'=0, i3^0'=0, i4^0'=0, [ n^0<=i1^0 && i1^0>=0 && n^0<=0 ], cost: 5+2*i1^0
     35: l9 -> l0 : i2^0'=0, i3^0'=n^0, i4^0'=0, [ n^0<=i1^0 && i1^0>=0 && n^0>=0 ], cost: 5+4*n^0+2*i1^0
     37: l9 -> l0 : i1^0'=n^0, i2^0'=n^0, i3^0'=n^0, i4^0'=0, [ n^0-i1^0>=0 && n^0<=0 && n^0>=0 ], cost: 5+4*n^0-2*i1^0
     38: l9 -> l0 : i1^0'=n^0, i2^0'=0, i3^0'=0, i4^0'=0, [ n^0-i1^0>=0 && n^0>=0 && n^0<=0 ], cost: 5+4*n^0-2*i1^0
     39: l9 -> l0 : i1^0'=n^0, i2^0'=0, i3^0'=n^0, i4^0'=0, [ n^0-i1^0>=0 && n^0>=0 ], cost: 5+8*n^0-2*i1^0

Computing asymptotic complexity for rule 39
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 32
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 34
   Simplified the guard:
     34: l9 -> l0 : i2^0'=0, i3^0'=0, i4^0'=0, [ i1^0>=0 && n^0<=0 ], cost: 5+2*i1^0
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 35
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 37
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 38
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 33
   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:  [ i1^0==i1^post_13 && i2^0==i2^post_13 && i3^0==i3^post_13 && i4^0==i4^post_13 && n^0==n^post_13 ]

WORST_CASE(Omega(1),?)