WORST_CASE(Omega(1),?)

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

Initial linear ITS problem
   Start location: l10
      0: l0 -> l1 : i^0'=i^post_1, j^0'=j^post_1, tmp5^0'=tmp5^post_1, x3^0'=x3^post_1, y4^0'=y4^post_1, [ i^0==i^post_1 && j^0==j^post_1 && tmp5^0==tmp5^post_1 && x3^0==x3^post_1 && y4^0==y4^post_1 ], cost: 1
     10: l1 -> l4 : i^0'=i^post_11, j^0'=j^post_11, tmp5^0'=tmp5^post_11, x3^0'=x3^post_11, y4^0'=y4^post_11, [ 1+i^0<=0 && i^0==i^post_11 && j^0==j^post_11 && tmp5^0==tmp5^post_11 && x3^0==x3^post_11 && y4^0==y4^post_11 ], cost: 1
     11: l1 -> l6 : i^0'=i^post_12, j^0'=j^post_12, tmp5^0'=tmp5^post_12, x3^0'=x3^post_12, y4^0'=y4^post_12, [ 0<=i^0 && i^0==i^post_12 && j^0==j^post_12 && tmp5^0==tmp5^post_12 && x3^0==x3^post_12 && y4^0==y4^post_12 ], cost: 1
      1: l2 -> l3 : i^0'=i^post_2, j^0'=j^post_2, tmp5^0'=tmp5^post_2, x3^0'=x3^post_2, y4^0'=y4^post_2, [ i^0==i^post_2 && j^0==j^post_2 && tmp5^0==tmp5^post_2 && x3^0==x3^post_2 && y4^0==y4^post_2 ], cost: 1
      2: l4 -> l2 : i^0'=i^post_3, j^0'=j^post_3, tmp5^0'=tmp5^post_3, x3^0'=x3^post_3, y4^0'=y4^post_3, [ i^0==i^post_3 && j^0==j^post_3 && tmp5^0==tmp5^post_3 && x3^0==x3^post_3 && y4^0==y4^post_3 ], cost: 1
      3: l4 -> l2 : i^0'=i^post_4, j^0'=j^post_4, tmp5^0'=tmp5^post_4, x3^0'=x3^post_4, y4^0'=y4^post_4, [ i^0==i^post_4 && j^0==j^post_4 && tmp5^0==tmp5^post_4 && x3^0==x3^post_4 && y4^0==y4^post_4 ], cost: 1
      4: l5 -> l6 : i^0'=i^post_5, j^0'=j^post_5, tmp5^0'=tmp5^post_5, x3^0'=x3^post_5, y4^0'=y4^post_5, [ j^post_5==1+j^0 && i^0==i^post_5 && tmp5^0==tmp5^post_5 && x3^0==x3^post_5 && y4^0==y4^post_5 ], cost: 1
      5: l6 -> l7 : i^0'=i^post_6, j^0'=j^post_6, tmp5^0'=tmp5^post_6, x3^0'=x3^post_6, y4^0'=y4^post_6, [ i^0==i^post_6 && j^0==j^post_6 && tmp5^0==tmp5^post_6 && x3^0==x3^post_6 && y4^0==y4^post_6 ], cost: 1
      8: l7 -> l0 : i^0'=i^post_9, j^0'=j^post_9, tmp5^0'=tmp5^post_9, x3^0'=x3^post_9, y4^0'=y4^post_9, [ i^0<=j^0 && i^post_9==-1+i^0 && j^0==j^post_9 && tmp5^0==tmp5^post_9 && x3^0==x3^post_9 && y4^0==y4^post_9 ], cost: 1
      9: l7 -> l8 : i^0'=i^post_10, j^0'=j^post_10, tmp5^0'=tmp5^post_10, x3^0'=x3^post_10, y4^0'=y4^post_10, [ 1+j^0<=i^0 && i^0==i^post_10 && j^0==j^post_10 && tmp5^0==tmp5^post_10 && x3^0==x3^post_10 && y4^0==y4^post_10 ], cost: 1
      6: l8 -> l5 : i^0'=i^post_7, j^0'=j^post_7, tmp5^0'=tmp5^post_7, x3^0'=x3^post_7, y4^0'=y4^post_7, [ x3^post_7==j^0 && y4^post_7==1+j^0 && tmp5^post_7==tmp5^post_7 && i^0==i^post_7 && j^0==j^post_7 ], cost: 1
      7: l8 -> l5 : i^0'=i^post_8, j^0'=j^post_8, tmp5^0'=tmp5^post_8, x3^0'=x3^post_8, y4^0'=y4^post_8, [ i^0==i^post_8 && j^0==j^post_8 && tmp5^0==tmp5^post_8 && x3^0==x3^post_8 && y4^0==y4^post_8 ], cost: 1
     12: l9 -> l0 : i^0'=i^post_13, j^0'=j^post_13, tmp5^0'=tmp5^post_13, x3^0'=x3^post_13, y4^0'=y4^post_13, [ j^post_13==0 && i^post_13==4 && tmp5^0==tmp5^post_13 && x3^0==x3^post_13 && y4^0==y4^post_13 ], cost: 1
     13: l10 -> l9 : i^0'=i^post_14, j^0'=j^post_14, tmp5^0'=tmp5^post_14, x3^0'=x3^post_14, y4^0'=y4^post_14, [ i^0==i^post_14 && j^0==j^post_14 && tmp5^0==tmp5^post_14 && x3^0==x3^post_14 && y4^0==y4^post_14 ], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
     13: l10 -> l9 : i^0'=i^post_14, j^0'=j^post_14, tmp5^0'=tmp5^post_14, x3^0'=x3^post_14, y4^0'=y4^post_14, [ i^0==i^post_14 && j^0==j^post_14 && tmp5^0==tmp5^post_14 && x3^0==x3^post_14 && y4^0==y4^post_14 ], cost: 1

Removed unreachable and leaf rules:
   Start location: l10
      0: l0 -> l1 : i^0'=i^post_1, j^0'=j^post_1, tmp5^0'=tmp5^post_1, x3^0'=x3^post_1, y4^0'=y4^post_1, [ i^0==i^post_1 && j^0==j^post_1 && tmp5^0==tmp5^post_1 && x3^0==x3^post_1 && y4^0==y4^post_1 ], cost: 1
     11: l1 -> l6 : i^0'=i^post_12, j^0'=j^post_12, tmp5^0'=tmp5^post_12, x3^0'=x3^post_12, y4^0'=y4^post_12, [ 0<=i^0 && i^0==i^post_12 && j^0==j^post_12 && tmp5^0==tmp5^post_12 && x3^0==x3^post_12 && y4^0==y4^post_12 ], cost: 1
      4: l5 -> l6 : i^0'=i^post_5, j^0'=j^post_5, tmp5^0'=tmp5^post_5, x3^0'=x3^post_5, y4^0'=y4^post_5, [ j^post_5==1+j^0 && i^0==i^post_5 && tmp5^0==tmp5^post_5 && x3^0==x3^post_5 && y4^0==y4^post_5 ], cost: 1
      5: l6 -> l7 : i^0'=i^post_6, j^0'=j^post_6, tmp5^0'=tmp5^post_6, x3^0'=x3^post_6, y4^0'=y4^post_6, [ i^0==i^post_6 && j^0==j^post_6 && tmp5^0==tmp5^post_6 && x3^0==x3^post_6 && y4^0==y4^post_6 ], cost: 1
      8: l7 -> l0 : i^0'=i^post_9, j^0'=j^post_9, tmp5^0'=tmp5^post_9, x3^0'=x3^post_9, y4^0'=y4^post_9, [ i^0<=j^0 && i^post_9==-1+i^0 && j^0==j^post_9 && tmp5^0==tmp5^post_9 && x3^0==x3^post_9 && y4^0==y4^post_9 ], cost: 1
      9: l7 -> l8 : i^0'=i^post_10, j^0'=j^post_10, tmp5^0'=tmp5^post_10, x3^0'=x3^post_10, y4^0'=y4^post_10, [ 1+j^0<=i^0 && i^0==i^post_10 && j^0==j^post_10 && tmp5^0==tmp5^post_10 && x3^0==x3^post_10 && y4^0==y4^post_10 ], cost: 1
      6: l8 -> l5 : i^0'=i^post_7, j^0'=j^post_7, tmp5^0'=tmp5^post_7, x3^0'=x3^post_7, y4^0'=y4^post_7, [ x3^post_7==j^0 && y4^post_7==1+j^0 && tmp5^post_7==tmp5^post_7 && i^0==i^post_7 && j^0==j^post_7 ], cost: 1
      7: l8 -> l5 : i^0'=i^post_8, j^0'=j^post_8, tmp5^0'=tmp5^post_8, x3^0'=x3^post_8, y4^0'=y4^post_8, [ i^0==i^post_8 && j^0==j^post_8 && tmp5^0==tmp5^post_8 && x3^0==x3^post_8 && y4^0==y4^post_8 ], cost: 1
     12: l9 -> l0 : i^0'=i^post_13, j^0'=j^post_13, tmp5^0'=tmp5^post_13, x3^0'=x3^post_13, y4^0'=y4^post_13, [ j^post_13==0 && i^post_13==4 && tmp5^0==tmp5^post_13 && x3^0==x3^post_13 && y4^0==y4^post_13 ], cost: 1
     13: l10 -> l9 : i^0'=i^post_14, j^0'=j^post_14, tmp5^0'=tmp5^post_14, x3^0'=x3^post_14, y4^0'=y4^post_14, [ i^0==i^post_14 && j^0==j^post_14 && tmp5^0==tmp5^post_14 && x3^0==x3^post_14 && y4^0==y4^post_14 ], cost: 1

Simplified all rules, resulting in:
   Start location: l10
      0: l0 -> l1 : [], cost: 1
     11: l1 -> l6 : [ 0<=i^0 ], cost: 1
      4: l5 -> l6 : j^0'=1+j^0, [], cost: 1
      5: l6 -> l7 : [], cost: 1
      8: l7 -> l0 : i^0'=-1+i^0, [ i^0<=j^0 ], cost: 1
      9: l7 -> l8 : [ 1+j^0<=i^0 ], cost: 1
      6: l8 -> l5 : tmp5^0'=tmp5^post_7, x3^0'=j^0, y4^0'=1+j^0, [], cost: 1
      7: l8 -> l5 : [], cost: 1
     12: l9 -> l0 : i^0'=4, j^0'=0, [], cost: 1
     13: l10 -> l9 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: l10
     15: l0 -> l6 : [ 0<=i^0 ], cost: 2
      4: l5 -> l6 : j^0'=1+j^0, [], cost: 1
      5: l6 -> l7 : [], cost: 1
      8: l7 -> l0 : i^0'=-1+i^0, [ i^0<=j^0 ], cost: 1
      9: l7 -> l8 : [ 1+j^0<=i^0 ], cost: 1
      6: l8 -> l5 : tmp5^0'=tmp5^post_7, x3^0'=j^0, y4^0'=1+j^0, [], cost: 1
      7: l8 -> l5 : [], cost: 1
     14: l10 -> l0 : i^0'=4, j^0'=0, [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: l10
     15: l0 -> l6 : [ 0<=i^0 ], cost: 2
     16: l6 -> l0 : i^0'=-1+i^0, [ i^0<=j^0 ], cost: 2
     17: l6 -> l8 : [ 1+j^0<=i^0 ], cost: 2
     18: l8 -> l6 : j^0'=1+j^0, tmp5^0'=tmp5^post_7, x3^0'=j^0, y4^0'=1+j^0, [], cost: 2
     19: l8 -> l6 : j^0'=1+j^0, [], cost: 2
     14: l10 -> l0 : i^0'=4, j^0'=0, [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: l10
     15: l0 -> l6 : [ 0<=i^0 ], cost: 2
     16: l6 -> l0 : i^0'=-1+i^0, [ i^0<=j^0 ], cost: 2
     20: l6 -> l6 : j^0'=1+j^0, tmp5^0'=tmp5^post_7, x3^0'=j^0, y4^0'=1+j^0, [ 1+j^0<=i^0 ], cost: 4
     21: l6 -> l6 : j^0'=1+j^0, [ 1+j^0<=i^0 ], cost: 4
     14: l10 -> l0 : i^0'=4, j^0'=0, [], cost: 2

Accelerating simple loops of location 6.
   Accelerating the following rules:
     20: l6 -> l6 : j^0'=1+j^0, tmp5^0'=tmp5^post_7, x3^0'=j^0, y4^0'=1+j^0, [ 1+j^0<=i^0 ], cost: 4
     21: l6 -> l6 : j^0'=1+j^0, [ 1+j^0<=i^0 ], cost: 4

   Accelerated rule 20 with backward acceleration, yielding the new rule 22.
   Accelerated rule 21 with backward acceleration, yielding the new rule 23.
[accelerate] Nesting with 2 inner and 2 outer candidates
   Removing the simple loops: 20 21.

Accelerated all simple loops using metering functions (where possible):
   Start location: l10
     15: l0 -> l6 : [ 0<=i^0 ], cost: 2
     16: l6 -> l0 : i^0'=-1+i^0, [ i^0<=j^0 ], cost: 2
     22: l6 -> l6 : j^0'=i^0, tmp5^0'=tmp5^post_7, x3^0'=-1+i^0, y4^0'=i^0, [ -j^0+i^0>=1 ], cost: -4*j^0+4*i^0
     23: l6 -> l6 : j^0'=i^0, [ -j^0+i^0>=0 ], cost: -4*j^0+4*i^0
     14: l10 -> l0 : i^0'=4, j^0'=0, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l10
     15: l0 -> l6 : [ 0<=i^0 ], cost: 2
     24: l0 -> l6 : j^0'=i^0, tmp5^0'=tmp5^post_7, x3^0'=-1+i^0, y4^0'=i^0, [ 0<=i^0 && -j^0+i^0>=1 ], cost: 2-4*j^0+4*i^0
     25: l0 -> l6 : j^0'=i^0, [ 0<=i^0 && -j^0+i^0>=0 ], cost: 2-4*j^0+4*i^0
     16: l6 -> l0 : i^0'=-1+i^0, [ i^0<=j^0 ], cost: 2
     14: l10 -> l0 : i^0'=4, j^0'=0, [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: l10
     26: l0 -> l0 : i^0'=-1+i^0, [ 0<=i^0 && i^0<=j^0 ], cost: 4
     27: l0 -> l0 : i^0'=-1+i^0, j^0'=i^0, tmp5^0'=tmp5^post_7, x3^0'=-1+i^0, y4^0'=i^0, [ 0<=i^0 && -j^0+i^0>=1 ], cost: 4-4*j^0+4*i^0
     28: l0 -> l0 : i^0'=-1+i^0, j^0'=i^0, [ 0<=i^0 && -j^0+i^0>=0 ], cost: 4-4*j^0+4*i^0
     14: l10 -> l0 : i^0'=4, j^0'=0, [], cost: 2

Accelerating simple loops of location 0.
   Accelerating the following rules:
     26: l0 -> l0 : i^0'=-1+i^0, [ 0<=i^0 && i^0<=j^0 ], cost: 4
     27: l0 -> l0 : i^0'=-1+i^0, j^0'=i^0, tmp5^0'=tmp5^post_7, x3^0'=-1+i^0, y4^0'=i^0, [ 0<=i^0 && -j^0+i^0>=1 ], cost: 4-4*j^0+4*i^0
     28: l0 -> l0 : i^0'=-1+i^0, j^0'=i^0, [ 0<=i^0 && -j^0+i^0>=0 ], cost: 4-4*j^0+4*i^0

   Accelerated rule 26 with backward acceleration, yielding the new rule 29.
   Failed to prove monotonicity of the guard of rule 27.
   Failed to prove monotonicity of the guard of rule 28.
[accelerate] Nesting with 3 inner and 3 outer candidates
   Removing the simple loops: 26.

Accelerated all simple loops using metering functions (where possible):
   Start location: l10
     27: l0 -> l0 : i^0'=-1+i^0, j^0'=i^0, tmp5^0'=tmp5^post_7, x3^0'=-1+i^0, y4^0'=i^0, [ 0<=i^0 && -j^0+i^0>=1 ], cost: 4-4*j^0+4*i^0
     28: l0 -> l0 : i^0'=-1+i^0, j^0'=i^0, [ 0<=i^0 && -j^0+i^0>=0 ], cost: 4-4*j^0+4*i^0
     29: l0 -> l0 : i^0'=-1, [ i^0<=j^0 && 1+i^0>=0 ], cost: 4+4*i^0
     14: l10 -> l0 : i^0'=4, j^0'=0, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l10
     14: l10 -> l0 : i^0'=4, j^0'=0, [], cost: 2
     30: l10 -> l0 : i^0'=3, j^0'=4, tmp5^0'=tmp5^post_7, x3^0'=3, y4^0'=4, [], cost: 22
     31: l10 -> l0 : i^0'=3, j^0'=4, [], cost: 22

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l10
     <empty>

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l10
     <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:  [ i^0==i^post_14 && j^0==j^post_14 && tmp5^0==tmp5^post_14 && x3^0==x3^post_14 && y4^0==y4^post_14 ]

WORST_CASE(Omega(1),?)