WORST_CASE(Omega(1),?)

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

Initial linear ITS problem
   Start location: l6
      0: l0 -> l1 : i10^0'=i10^post_1, i13^0'=i13^post_1, n12^0'=n12^post_1, n9^0'=n9^post_1, n^0'=n^post_1, tmp^0'=tmp^post_1, tmp___0^0'=tmp___0^post_1, [ i10^0==i10^post_1 && i13^0==i13^post_1 && n^0==n^post_1 && n12^0==n12^post_1 && n9^0==n9^post_1 && tmp^0==tmp^post_1 && tmp___0^0==tmp___0^post_1 ], cost: 1
      4: l1 -> l4 : i10^0'=i10^post_5, i13^0'=i13^post_5, n12^0'=n12^post_5, n9^0'=n9^post_5, n^0'=n^post_5, tmp^0'=tmp^post_5, tmp___0^0'=tmp___0^post_5, [ n9^0<=i10^0 && tmp___0^post_5==tmp___0^post_5 && n12^post_5==n^0 && i13^post_5==0 && i10^0==i10^post_5 && n^0==n^post_5 && n9^0==n9^post_5 && tmp^0==tmp^post_5 ], cost: 1
      5: l1 -> l0 : i10^0'=i10^post_6, i13^0'=i13^post_6, n12^0'=n12^post_6, n9^0'=n9^post_6, n^0'=n^post_6, tmp^0'=tmp^post_6, tmp___0^0'=tmp___0^post_6, [ 1+i10^0<=n9^0 && i10^post_6==1+i10^0 && i13^0==i13^post_6 && n^0==n^post_6 && n12^0==n12^post_6 && n9^0==n9^post_6 && tmp^0==tmp^post_6 && tmp___0^0==tmp___0^post_6 ], cost: 1
      1: l2 -> l3 : i10^0'=i10^post_2, i13^0'=i13^post_2, n12^0'=n12^post_2, n9^0'=n9^post_2, n^0'=n^post_2, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, [ n12^0<=i13^0 && i10^0==i10^post_2 && i13^0==i13^post_2 && n^0==n^post_2 && n12^0==n12^post_2 && n9^0==n9^post_2 && tmp^0==tmp^post_2 && tmp___0^0==tmp___0^post_2 ], cost: 1
      2: l2 -> l4 : i10^0'=i10^post_3, i13^0'=i13^post_3, n12^0'=n12^post_3, n9^0'=n9^post_3, n^0'=n^post_3, tmp^0'=tmp^post_3, tmp___0^0'=tmp___0^post_3, [ 1+i13^0<=n12^0 && i13^post_3==1+i13^0 && i10^0==i10^post_3 && n^0==n^post_3 && n12^0==n12^post_3 && n9^0==n9^post_3 && tmp^0==tmp^post_3 && tmp___0^0==tmp___0^post_3 ], cost: 1
      3: l4 -> l2 : i10^0'=i10^post_4, i13^0'=i13^post_4, n12^0'=n12^post_4, n9^0'=n9^post_4, n^0'=n^post_4, tmp^0'=tmp^post_4, tmp___0^0'=tmp___0^post_4, [ i10^0==i10^post_4 && i13^0==i13^post_4 && n^0==n^post_4 && n12^0==n12^post_4 && n9^0==n9^post_4 && tmp^0==tmp^post_4 && tmp___0^0==tmp___0^post_4 ], cost: 1
      6: l5 -> l0 : i10^0'=i10^post_7, i13^0'=i13^post_7, n12^0'=n12^post_7, n9^0'=n9^post_7, n^0'=n^post_7, tmp^0'=tmp^post_7, tmp___0^0'=tmp___0^post_7, [ n^post_7==n^post_7 && tmp^post_7==tmp^post_7 && n9^post_7==n9^post_7 && i10^post_7==0 && i13^0==i13^post_7 && n12^0==n12^post_7 && tmp___0^0==tmp___0^post_7 ], cost: 1
      7: l6 -> l5 : i10^0'=i10^post_8, i13^0'=i13^post_8, n12^0'=n12^post_8, n9^0'=n9^post_8, n^0'=n^post_8, tmp^0'=tmp^post_8, tmp___0^0'=tmp___0^post_8, [ i10^0==i10^post_8 && i13^0==i13^post_8 && n^0==n^post_8 && n12^0==n12^post_8 && n9^0==n9^post_8 && tmp^0==tmp^post_8 && tmp___0^0==tmp___0^post_8 ], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
      7: l6 -> l5 : i10^0'=i10^post_8, i13^0'=i13^post_8, n12^0'=n12^post_8, n9^0'=n9^post_8, n^0'=n^post_8, tmp^0'=tmp^post_8, tmp___0^0'=tmp___0^post_8, [ i10^0==i10^post_8 && i13^0==i13^post_8 && n^0==n^post_8 && n12^0==n12^post_8 && n9^0==n9^post_8 && tmp^0==tmp^post_8 && tmp___0^0==tmp___0^post_8 ], cost: 1

Removed unreachable and leaf rules:
   Start location: l6
      0: l0 -> l1 : i10^0'=i10^post_1, i13^0'=i13^post_1, n12^0'=n12^post_1, n9^0'=n9^post_1, n^0'=n^post_1, tmp^0'=tmp^post_1, tmp___0^0'=tmp___0^post_1, [ i10^0==i10^post_1 && i13^0==i13^post_1 && n^0==n^post_1 && n12^0==n12^post_1 && n9^0==n9^post_1 && tmp^0==tmp^post_1 && tmp___0^0==tmp___0^post_1 ], cost: 1
      4: l1 -> l4 : i10^0'=i10^post_5, i13^0'=i13^post_5, n12^0'=n12^post_5, n9^0'=n9^post_5, n^0'=n^post_5, tmp^0'=tmp^post_5, tmp___0^0'=tmp___0^post_5, [ n9^0<=i10^0 && tmp___0^post_5==tmp___0^post_5 && n12^post_5==n^0 && i13^post_5==0 && i10^0==i10^post_5 && n^0==n^post_5 && n9^0==n9^post_5 && tmp^0==tmp^post_5 ], cost: 1
      5: l1 -> l0 : i10^0'=i10^post_6, i13^0'=i13^post_6, n12^0'=n12^post_6, n9^0'=n9^post_6, n^0'=n^post_6, tmp^0'=tmp^post_6, tmp___0^0'=tmp___0^post_6, [ 1+i10^0<=n9^0 && i10^post_6==1+i10^0 && i13^0==i13^post_6 && n^0==n^post_6 && n12^0==n12^post_6 && n9^0==n9^post_6 && tmp^0==tmp^post_6 && tmp___0^0==tmp___0^post_6 ], cost: 1
      2: l2 -> l4 : i10^0'=i10^post_3, i13^0'=i13^post_3, n12^0'=n12^post_3, n9^0'=n9^post_3, n^0'=n^post_3, tmp^0'=tmp^post_3, tmp___0^0'=tmp___0^post_3, [ 1+i13^0<=n12^0 && i13^post_3==1+i13^0 && i10^0==i10^post_3 && n^0==n^post_3 && n12^0==n12^post_3 && n9^0==n9^post_3 && tmp^0==tmp^post_3 && tmp___0^0==tmp___0^post_3 ], cost: 1
      3: l4 -> l2 : i10^0'=i10^post_4, i13^0'=i13^post_4, n12^0'=n12^post_4, n9^0'=n9^post_4, n^0'=n^post_4, tmp^0'=tmp^post_4, tmp___0^0'=tmp___0^post_4, [ i10^0==i10^post_4 && i13^0==i13^post_4 && n^0==n^post_4 && n12^0==n12^post_4 && n9^0==n9^post_4 && tmp^0==tmp^post_4 && tmp___0^0==tmp___0^post_4 ], cost: 1
      6: l5 -> l0 : i10^0'=i10^post_7, i13^0'=i13^post_7, n12^0'=n12^post_7, n9^0'=n9^post_7, n^0'=n^post_7, tmp^0'=tmp^post_7, tmp___0^0'=tmp___0^post_7, [ n^post_7==n^post_7 && tmp^post_7==tmp^post_7 && n9^post_7==n9^post_7 && i10^post_7==0 && i13^0==i13^post_7 && n12^0==n12^post_7 && tmp___0^0==tmp___0^post_7 ], cost: 1
      7: l6 -> l5 : i10^0'=i10^post_8, i13^0'=i13^post_8, n12^0'=n12^post_8, n9^0'=n9^post_8, n^0'=n^post_8, tmp^0'=tmp^post_8, tmp___0^0'=tmp___0^post_8, [ i10^0==i10^post_8 && i13^0==i13^post_8 && n^0==n^post_8 && n12^0==n12^post_8 && n9^0==n9^post_8 && tmp^0==tmp^post_8 && tmp___0^0==tmp___0^post_8 ], cost: 1

Simplified all rules, resulting in:
   Start location: l6
      0: l0 -> l1 : [], cost: 1
      4: l1 -> l4 : i13^0'=0, n12^0'=n^0, tmp___0^0'=tmp___0^post_5, [ n9^0<=i10^0 ], cost: 1
      5: l1 -> l0 : i10^0'=1+i10^0, [ 1+i10^0<=n9^0 ], cost: 1
      2: l2 -> l4 : i13^0'=1+i13^0, [ 1+i13^0<=n12^0 ], cost: 1
      3: l4 -> l2 : [], cost: 1
      6: l5 -> l0 : i10^0'=0, n9^0'=n9^post_7, n^0'=n^post_7, tmp^0'=tmp^post_7, [], cost: 1
      7: l6 -> l5 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: l6
      0: l0 -> l1 : [], cost: 1
      4: l1 -> l4 : i13^0'=0, n12^0'=n^0, tmp___0^0'=tmp___0^post_5, [ n9^0<=i10^0 ], cost: 1
      5: l1 -> l0 : i10^0'=1+i10^0, [ 1+i10^0<=n9^0 ], cost: 1
      9: l4 -> l4 : i13^0'=1+i13^0, [ 1+i13^0<=n12^0 ], cost: 2
      8: l6 -> l0 : i10^0'=0, n9^0'=n9^post_7, n^0'=n^post_7, tmp^0'=tmp^post_7, [], cost: 2

Accelerating simple loops of location 4.
   Accelerating the following rules:
      9: l4 -> l4 : i13^0'=1+i13^0, [ 1+i13^0<=n12^0 ], cost: 2

   Accelerated rule 9 with backward acceleration, yielding the new rule 10.
[accelerate] Nesting with 1 inner and 1 outer candidates
   Removing the simple loops: 9.

Accelerated all simple loops using metering functions (where possible):
   Start location: l6
      0: l0 -> l1 : [], cost: 1
      4: l1 -> l4 : i13^0'=0, n12^0'=n^0, tmp___0^0'=tmp___0^post_5, [ n9^0<=i10^0 ], cost: 1
      5: l1 -> l0 : i10^0'=1+i10^0, [ 1+i10^0<=n9^0 ], cost: 1
     10: l4 -> l4 : i13^0'=n12^0, [ -i13^0+n12^0>=0 ], cost: -2*i13^0+2*n12^0
      8: l6 -> l0 : i10^0'=0, n9^0'=n9^post_7, n^0'=n^post_7, tmp^0'=tmp^post_7, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l6
      0: l0 -> l1 : [], cost: 1
      4: l1 -> l4 : i13^0'=0, n12^0'=n^0, tmp___0^0'=tmp___0^post_5, [ n9^0<=i10^0 ], cost: 1
      5: l1 -> l0 : i10^0'=1+i10^0, [ 1+i10^0<=n9^0 ], cost: 1
     11: l1 -> l4 : i13^0'=n^0, n12^0'=n^0, tmp___0^0'=tmp___0^post_5, [ n9^0<=i10^0 && n^0>=0 ], cost: 1+2*n^0
      8: l6 -> l0 : i10^0'=0, n9^0'=n9^post_7, n^0'=n^post_7, tmp^0'=tmp^post_7, [], cost: 2

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l6
      0: l0 -> l1 : [], cost: 1
      5: l1 -> l0 : i10^0'=1+i10^0, [ 1+i10^0<=n9^0 ], cost: 1
     11: l1 -> l4 : i13^0'=n^0, n12^0'=n^0, tmp___0^0'=tmp___0^post_5, [ n9^0<=i10^0 && n^0>=0 ], cost: 1+2*n^0
      8: l6 -> l0 : i10^0'=0, n9^0'=n9^post_7, n^0'=n^post_7, tmp^0'=tmp^post_7, [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: l6
     12: l0 -> l0 : i10^0'=1+i10^0, [ 1+i10^0<=n9^0 ], cost: 2
     13: l0 -> l4 : i13^0'=n^0, n12^0'=n^0, tmp___0^0'=tmp___0^post_5, [ n9^0<=i10^0 && n^0>=0 ], cost: 2+2*n^0
      8: l6 -> l0 : i10^0'=0, n9^0'=n9^post_7, n^0'=n^post_7, tmp^0'=tmp^post_7, [], cost: 2

Accelerating simple loops of location 0.
   Accelerating the following rules:
     12: l0 -> l0 : i10^0'=1+i10^0, [ 1+i10^0<=n9^0 ], cost: 2

   Accelerated rule 12 with backward acceleration, yielding the new rule 14.
[accelerate] Nesting with 1 inner and 1 outer candidates
   Removing the simple loops: 12.

Accelerated all simple loops using metering functions (where possible):
   Start location: l6
     13: l0 -> l4 : i13^0'=n^0, n12^0'=n^0, tmp___0^0'=tmp___0^post_5, [ n9^0<=i10^0 && n^0>=0 ], cost: 2+2*n^0
     14: l0 -> l0 : i10^0'=n9^0, [ n9^0-i10^0>=0 ], cost: 2*n9^0-2*i10^0
      8: l6 -> l0 : i10^0'=0, n9^0'=n9^post_7, n^0'=n^post_7, tmp^0'=tmp^post_7, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l6
     13: l0 -> l4 : i13^0'=n^0, n12^0'=n^0, tmp___0^0'=tmp___0^post_5, [ n9^0<=i10^0 && n^0>=0 ], cost: 2+2*n^0
      8: l6 -> l0 : i10^0'=0, n9^0'=n9^post_7, n^0'=n^post_7, tmp^0'=tmp^post_7, [], cost: 2
     15: l6 -> l0 : i10^0'=n9^post_7, n9^0'=n9^post_7, n^0'=n^post_7, tmp^0'=tmp^post_7, [ n9^post_7>=0 ], cost: 2+2*n9^post_7

Eliminated locations (on tree-shaped paths):
   Start location: l6
     16: l6 -> l4 : i10^0'=0, i13^0'=n^post_7, n12^0'=n^post_7, n9^0'=n9^post_7, n^0'=n^post_7, tmp^0'=tmp^post_7, tmp___0^0'=tmp___0^post_5, [ n9^post_7<=0 && n^post_7>=0 ], cost: 4+2*n^post_7
     17: l6 -> l4 : i10^0'=n9^post_7, i13^0'=n^post_7, n12^0'=n^post_7, n9^0'=n9^post_7, n^0'=n^post_7, tmp^0'=tmp^post_7, tmp___0^0'=tmp___0^post_5, [ n9^post_7>=0 && n^post_7>=0 ], cost: 4+2*n9^post_7+2*n^post_7

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l6
     16: l6 -> l4 : i10^0'=0, i13^0'=n^post_7, n12^0'=n^post_7, n9^0'=n9^post_7, n^0'=n^post_7, tmp^0'=tmp^post_7, tmp___0^0'=tmp___0^post_5, [ n9^post_7<=0 && n^post_7>=0 ], cost: 4+2*n^post_7
     17: l6 -> l4 : i10^0'=n9^post_7, i13^0'=n^post_7, n12^0'=n^post_7, n9^0'=n9^post_7, n^0'=n^post_7, tmp^0'=tmp^post_7, tmp___0^0'=tmp___0^post_5, [ n9^post_7>=0 && n^post_7>=0 ], cost: 4+2*n9^post_7+2*n^post_7

Computing asymptotic complexity for rule 16
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 17
   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:  [ i10^0==i10^post_8 && i13^0==i13^post_8 && n^0==n^post_8 && n12^0==n12^post_8 && n9^0==n9^post_8 && tmp^0==tmp^post_8 && tmp___0^0==tmp___0^post_8 ]

WORST_CASE(Omega(1),?)