WORST_CASE(Omega(1),?)

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

Initial linear ITS problem
   Start location: l4
      0: l0 -> l1 : __const_10^0'=__const_10^post_1, i5^0'=i5^post_1, length4^0'=length4^post_1, s^0'=s^post_1, tmp^0'=tmp^post_1, tmp___08^0'=tmp___08^post_1, [ length4^0<=i5^0 && __const_10^0==__const_10^post_1 && i5^0==i5^post_1 && length4^0==length4^post_1 && s^0==s^post_1 && tmp^0==tmp^post_1 && tmp___08^0==tmp___08^post_1 ], cost: 1
      1: l0 -> l2 : __const_10^0'=__const_10^post_2, i5^0'=i5^post_2, length4^0'=length4^post_2, s^0'=s^post_2, tmp^0'=tmp^post_2, tmp___08^0'=tmp___08^post_2, [ 1+i5^0<=length4^0 && tmp___08^post_2==tmp___08^post_2 && i5^post_2==1+i5^0 && __const_10^0==__const_10^post_2 && length4^0==length4^post_2 && s^0==s^post_2 && tmp^0==tmp^post_2 ], cost: 1
      2: l2 -> l0 : __const_10^0'=__const_10^post_3, i5^0'=i5^post_3, length4^0'=length4^post_3, s^0'=s^post_3, tmp^0'=tmp^post_3, tmp___08^0'=tmp___08^post_3, [ __const_10^0==__const_10^post_3 && i5^0==i5^post_3 && length4^0==length4^post_3 && s^0==s^post_3 && tmp^0==tmp^post_3 && tmp___08^0==tmp___08^post_3 ], cost: 1
      3: l3 -> l2 : __const_10^0'=__const_10^post_4, i5^0'=i5^post_4, length4^0'=length4^post_4, s^0'=s^post_4, tmp^0'=tmp^post_4, tmp___08^0'=tmp___08^post_4, [ tmp^post_4==tmp^post_4 && s^post_4==tmp^post_4 && length4^post_4==__const_10^0 && i5^post_4==0 && __const_10^0==__const_10^post_4 && tmp___08^0==tmp___08^post_4 ], cost: 1
      4: l4 -> l3 : __const_10^0'=__const_10^post_5, i5^0'=i5^post_5, length4^0'=length4^post_5, s^0'=s^post_5, tmp^0'=tmp^post_5, tmp___08^0'=tmp___08^post_5, [ __const_10^0==__const_10^post_5 && i5^0==i5^post_5 && length4^0==length4^post_5 && s^0==s^post_5 && tmp^0==tmp^post_5 && tmp___08^0==tmp___08^post_5 ], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
      4: l4 -> l3 : __const_10^0'=__const_10^post_5, i5^0'=i5^post_5, length4^0'=length4^post_5, s^0'=s^post_5, tmp^0'=tmp^post_5, tmp___08^0'=tmp___08^post_5, [ __const_10^0==__const_10^post_5 && i5^0==i5^post_5 && length4^0==length4^post_5 && s^0==s^post_5 && tmp^0==tmp^post_5 && tmp___08^0==tmp___08^post_5 ], cost: 1

Removed unreachable and leaf rules:
   Start location: l4
      1: l0 -> l2 : __const_10^0'=__const_10^post_2, i5^0'=i5^post_2, length4^0'=length4^post_2, s^0'=s^post_2, tmp^0'=tmp^post_2, tmp___08^0'=tmp___08^post_2, [ 1+i5^0<=length4^0 && tmp___08^post_2==tmp___08^post_2 && i5^post_2==1+i5^0 && __const_10^0==__const_10^post_2 && length4^0==length4^post_2 && s^0==s^post_2 && tmp^0==tmp^post_2 ], cost: 1
      2: l2 -> l0 : __const_10^0'=__const_10^post_3, i5^0'=i5^post_3, length4^0'=length4^post_3, s^0'=s^post_3, tmp^0'=tmp^post_3, tmp___08^0'=tmp___08^post_3, [ __const_10^0==__const_10^post_3 && i5^0==i5^post_3 && length4^0==length4^post_3 && s^0==s^post_3 && tmp^0==tmp^post_3 && tmp___08^0==tmp___08^post_3 ], cost: 1
      3: l3 -> l2 : __const_10^0'=__const_10^post_4, i5^0'=i5^post_4, length4^0'=length4^post_4, s^0'=s^post_4, tmp^0'=tmp^post_4, tmp___08^0'=tmp___08^post_4, [ tmp^post_4==tmp^post_4 && s^post_4==tmp^post_4 && length4^post_4==__const_10^0 && i5^post_4==0 && __const_10^0==__const_10^post_4 && tmp___08^0==tmp___08^post_4 ], cost: 1
      4: l4 -> l3 : __const_10^0'=__const_10^post_5, i5^0'=i5^post_5, length4^0'=length4^post_5, s^0'=s^post_5, tmp^0'=tmp^post_5, tmp___08^0'=tmp___08^post_5, [ __const_10^0==__const_10^post_5 && i5^0==i5^post_5 && length4^0==length4^post_5 && s^0==s^post_5 && tmp^0==tmp^post_5 && tmp___08^0==tmp___08^post_5 ], cost: 1

Simplified all rules, resulting in:
   Start location: l4
      1: l0 -> l2 : i5^0'=1+i5^0, tmp___08^0'=tmp___08^post_2, [ 1+i5^0<=length4^0 ], cost: 1
      2: l2 -> l0 : [], cost: 1
      3: l3 -> l2 : i5^0'=0, length4^0'=__const_10^0, s^0'=tmp^post_4, tmp^0'=tmp^post_4, [], cost: 1
      4: l4 -> l3 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: l4
      6: l2 -> l2 : i5^0'=1+i5^0, tmp___08^0'=tmp___08^post_2, [ 1+i5^0<=length4^0 ], cost: 2
      5: l4 -> l2 : i5^0'=0, length4^0'=__const_10^0, s^0'=tmp^post_4, tmp^0'=tmp^post_4, [], cost: 2

Accelerating simple loops of location 2.
   Accelerating the following rules:
      6: l2 -> l2 : i5^0'=1+i5^0, tmp___08^0'=tmp___08^post_2, [ 1+i5^0<=length4^0 ], cost: 2

   Accelerated rule 6 with backward acceleration, yielding the new rule 7.
[accelerate] Nesting with 1 inner and 1 outer candidates
   Removing the simple loops: 6.

Accelerated all simple loops using metering functions (where possible):
   Start location: l4
      7: l2 -> l2 : i5^0'=length4^0, tmp___08^0'=tmp___08^post_2, [ -i5^0+length4^0>=1 ], cost: -2*i5^0+2*length4^0
      5: l4 -> l2 : i5^0'=0, length4^0'=__const_10^0, s^0'=tmp^post_4, tmp^0'=tmp^post_4, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l4
      5: l4 -> l2 : i5^0'=0, length4^0'=__const_10^0, s^0'=tmp^post_4, tmp^0'=tmp^post_4, [], cost: 2
      8: l4 -> l2 : i5^0'=__const_10^0, length4^0'=__const_10^0, s^0'=tmp^post_4, tmp^0'=tmp^post_4, tmp___08^0'=tmp___08^post_2, [ __const_10^0>=1 ], cost: 2+2*__const_10^0

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l4
      8: l4 -> l2 : i5^0'=__const_10^0, length4^0'=__const_10^0, s^0'=tmp^post_4, tmp^0'=tmp^post_4, tmp___08^0'=tmp___08^post_2, [ __const_10^0>=1 ], cost: 2+2*__const_10^0

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l4
      8: l4 -> l2 : i5^0'=__const_10^0, length4^0'=__const_10^0, s^0'=tmp^post_4, tmp^0'=tmp^post_4, tmp___08^0'=tmp___08^post_2, [ __const_10^0>=1 ], cost: 2+2*__const_10^0

Computing asymptotic complexity for rule 8
   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:  [ __const_10^0==__const_10^post_5 && i5^0==i5^post_5 && length4^0==length4^post_5 && s^0==s^post_5 && tmp^0==tmp^post_5 && tmp___08^0==tmp___08^post_5 ]

WORST_CASE(Omega(1),?)