NO

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

Initial linear ITS problem
   Start location: l10
      0: l0 -> l1 : 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 && 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 : 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 && length4^0==length4^post_2 && s^0==s^post_2 && tmp^0==tmp^post_2 ], cost: 1
      7: l1 -> l7 : i5^0'=i5^post_8, length4^0'=length4^post_8, s^0'=s^post_8, tmp^0'=tmp^post_8, tmp___08^0'=tmp___08^post_8, [ i5^0==i5^post_8 && length4^0==length4^post_8 && s^0==s^post_8 && tmp^0==tmp^post_8 && tmp___08^0==tmp___08^post_8 ], cost: 1
      2: l2 -> l0 : 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, [ 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 -> l4 : 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, [ 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 ], cost: 1
     12: l4 -> l5 : i5^0'=i5^post_13, length4^0'=length4^post_13, s^0'=s^post_13, tmp^0'=tmp^post_13, tmp___08^0'=tmp___08^post_13, [ i5^0==i5^post_13 && length4^0==length4^post_13 && s^0==s^post_13 && tmp^0==tmp^post_13 && tmp___08^0==tmp___08^post_13 ], cost: 1
      4: l5 -> l3 : 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, [ 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
      5: l5 -> l6 : i5^0'=i5^post_6, length4^0'=length4^post_6, s^0'=s^post_6, tmp^0'=tmp^post_6, tmp___08^0'=tmp___08^post_6, [ i5^0==i5^post_6 && length4^0==length4^post_6 && s^0==s^post_6 && tmp^0==tmp^post_6 && tmp___08^0==tmp___08^post_6 ], cost: 1
      6: l5 -> l3 : i5^0'=i5^post_7, length4^0'=length4^post_7, s^0'=s^post_7, tmp^0'=tmp^post_7, tmp___08^0'=tmp___08^post_7, [ i5^0==i5^post_7 && length4^0==length4^post_7 && s^0==s^post_7 && tmp^0==tmp^post_7 && tmp___08^0==tmp___08^post_7 ], cost: 1
      9: l7 -> l8 : i5^0'=i5^post_10, length4^0'=length4^post_10, s^0'=s^post_10, tmp^0'=tmp^post_10, tmp___08^0'=tmp___08^post_10, [ i5^0==i5^post_10 && length4^0==length4^post_10 && s^0==s^post_10 && tmp^0==tmp^post_10 && tmp___08^0==tmp___08^post_10 ], cost: 1
     10: l7 -> l8 : i5^0'=i5^post_11, length4^0'=length4^post_11, s^0'=s^post_11, tmp^0'=tmp^post_11, tmp___08^0'=tmp___08^post_11, [ i5^0==i5^post_11 && length4^0==length4^post_11 && s^0==s^post_11 && tmp^0==tmp^post_11 && tmp___08^0==tmp___08^post_11 ], cost: 1
     11: l7 -> l4 : i5^0'=i5^post_12, length4^0'=length4^post_12, s^0'=s^post_12, tmp^0'=tmp^post_12, tmp___08^0'=tmp___08^post_12, [ i5^0==i5^post_12 && length4^0==length4^post_12 && s^0==s^post_12 && tmp^0==tmp^post_12 && tmp___08^0==tmp___08^post_12 ], cost: 1
      8: l8 -> l1 : i5^0'=i5^post_9, length4^0'=length4^post_9, s^0'=s^post_9, tmp^0'=tmp^post_9, tmp___08^0'=tmp___08^post_9, [ i5^0==i5^post_9 && length4^0==length4^post_9 && s^0==s^post_9 && tmp^0==tmp^post_9 && tmp___08^0==tmp___08^post_9 ], cost: 1
     13: l9 -> l2 : i5^0'=i5^post_14, length4^0'=length4^post_14, s^0'=s^post_14, tmp^0'=tmp^post_14, tmp___08^0'=tmp___08^post_14, [ tmp^post_14==tmp^post_14 && s^post_14==tmp^post_14 && length4^post_14==s^post_14 && i5^post_14==0 && tmp___08^0==tmp___08^post_14 ], cost: 1
     14: l10 -> l9 : i5^0'=i5^post_15, length4^0'=length4^post_15, s^0'=s^post_15, tmp^0'=tmp^post_15, tmp___08^0'=tmp___08^post_15, [ i5^0==i5^post_15 && length4^0==length4^post_15 && s^0==s^post_15 && tmp^0==tmp^post_15 && tmp___08^0==tmp___08^post_15 ], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
     14: l10 -> l9 : i5^0'=i5^post_15, length4^0'=length4^post_15, s^0'=s^post_15, tmp^0'=tmp^post_15, tmp___08^0'=tmp___08^post_15, [ i5^0==i5^post_15 && length4^0==length4^post_15 && s^0==s^post_15 && tmp^0==tmp^post_15 && tmp___08^0==tmp___08^post_15 ], cost: 1

Removed unreachable and leaf rules:
   Start location: l10
      0: l0 -> l1 : 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 && 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 : 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 && length4^0==length4^post_2 && s^0==s^post_2 && tmp^0==tmp^post_2 ], cost: 1
      7: l1 -> l7 : i5^0'=i5^post_8, length4^0'=length4^post_8, s^0'=s^post_8, tmp^0'=tmp^post_8, tmp___08^0'=tmp___08^post_8, [ i5^0==i5^post_8 && length4^0==length4^post_8 && s^0==s^post_8 && tmp^0==tmp^post_8 && tmp___08^0==tmp___08^post_8 ], cost: 1
      2: l2 -> l0 : 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, [ 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 -> l4 : 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, [ 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 ], cost: 1
     12: l4 -> l5 : i5^0'=i5^post_13, length4^0'=length4^post_13, s^0'=s^post_13, tmp^0'=tmp^post_13, tmp___08^0'=tmp___08^post_13, [ i5^0==i5^post_13 && length4^0==length4^post_13 && s^0==s^post_13 && tmp^0==tmp^post_13 && tmp___08^0==tmp___08^post_13 ], cost: 1
      4: l5 -> l3 : 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, [ 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
      6: l5 -> l3 : i5^0'=i5^post_7, length4^0'=length4^post_7, s^0'=s^post_7, tmp^0'=tmp^post_7, tmp___08^0'=tmp___08^post_7, [ i5^0==i5^post_7 && length4^0==length4^post_7 && s^0==s^post_7 && tmp^0==tmp^post_7 && tmp___08^0==tmp___08^post_7 ], cost: 1
      9: l7 -> l8 : i5^0'=i5^post_10, length4^0'=length4^post_10, s^0'=s^post_10, tmp^0'=tmp^post_10, tmp___08^0'=tmp___08^post_10, [ i5^0==i5^post_10 && length4^0==length4^post_10 && s^0==s^post_10 && tmp^0==tmp^post_10 && tmp___08^0==tmp___08^post_10 ], cost: 1
     10: l7 -> l8 : i5^0'=i5^post_11, length4^0'=length4^post_11, s^0'=s^post_11, tmp^0'=tmp^post_11, tmp___08^0'=tmp___08^post_11, [ i5^0==i5^post_11 && length4^0==length4^post_11 && s^0==s^post_11 && tmp^0==tmp^post_11 && tmp___08^0==tmp___08^post_11 ], cost: 1
     11: l7 -> l4 : i5^0'=i5^post_12, length4^0'=length4^post_12, s^0'=s^post_12, tmp^0'=tmp^post_12, tmp___08^0'=tmp___08^post_12, [ i5^0==i5^post_12 && length4^0==length4^post_12 && s^0==s^post_12 && tmp^0==tmp^post_12 && tmp___08^0==tmp___08^post_12 ], cost: 1
      8: l8 -> l1 : i5^0'=i5^post_9, length4^0'=length4^post_9, s^0'=s^post_9, tmp^0'=tmp^post_9, tmp___08^0'=tmp___08^post_9, [ i5^0==i5^post_9 && length4^0==length4^post_9 && s^0==s^post_9 && tmp^0==tmp^post_9 && tmp___08^0==tmp___08^post_9 ], cost: 1
     13: l9 -> l2 : i5^0'=i5^post_14, length4^0'=length4^post_14, s^0'=s^post_14, tmp^0'=tmp^post_14, tmp___08^0'=tmp___08^post_14, [ tmp^post_14==tmp^post_14 && s^post_14==tmp^post_14 && length4^post_14==s^post_14 && i5^post_14==0 && tmp___08^0==tmp___08^post_14 ], cost: 1
     14: l10 -> l9 : i5^0'=i5^post_15, length4^0'=length4^post_15, s^0'=s^post_15, tmp^0'=tmp^post_15, tmp___08^0'=tmp___08^post_15, [ i5^0==i5^post_15 && length4^0==length4^post_15 && s^0==s^post_15 && tmp^0==tmp^post_15 && tmp___08^0==tmp___08^post_15 ], cost: 1

Simplified all rules, resulting in:
   Start location: l10
      0: l0 -> l1 : [ length4^0<=i5^0 ], cost: 1
      1: l0 -> l2 : i5^0'=1+i5^0, tmp___08^0'=tmp___08^post_2, [ 1+i5^0<=length4^0 ], cost: 1
      7: l1 -> l7 : [], cost: 1
      2: l2 -> l0 : [], cost: 1
      3: l3 -> l4 : [], cost: 1
     12: l4 -> l5 : [], cost: 1
      6: l5 -> l3 : [], cost: 1
     10: l7 -> l8 : [], cost: 1
     11: l7 -> l4 : [], cost: 1
      8: l8 -> l1 : [], cost: 1
     13: l9 -> l2 : i5^0'=0, length4^0'=tmp^post_14, s^0'=tmp^post_14, tmp^0'=tmp^post_14, [], cost: 1
     14: l10 -> l9 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: l10
      0: l0 -> l1 : [ length4^0<=i5^0 ], cost: 1
      1: l0 -> l2 : i5^0'=1+i5^0, tmp___08^0'=tmp___08^post_2, [ 1+i5^0<=length4^0 ], cost: 1
      7: l1 -> l7 : [], cost: 1
      2: l2 -> l0 : [], cost: 1
     18: l4 -> l4 : [], cost: 3
     11: l7 -> l4 : [], cost: 1
     16: l7 -> l1 : [], cost: 2
     15: l10 -> l2 : i5^0'=0, length4^0'=tmp^post_14, s^0'=tmp^post_14, tmp^0'=tmp^post_14, [], cost: 2

Accelerating simple loops of location 4.
   Accelerating the following rules:
     18: l4 -> l4 : [], cost: 3

   Accelerated rule 18 with non-termination, yielding the new rule 19.
[accelerate] Nesting with 0 inner and 0 outer candidates
   Removing the simple loops: 18.

Accelerated all simple loops using metering functions (where possible):
   Start location: l10
      0: l0 -> l1 : [ length4^0<=i5^0 ], cost: 1
      1: l0 -> l2 : i5^0'=1+i5^0, tmp___08^0'=tmp___08^post_2, [ 1+i5^0<=length4^0 ], cost: 1
      7: l1 -> l7 : [], cost: 1
      2: l2 -> l0 : [], cost: 1
     19: l4 -> [11] : [], cost: NONTERM
     11: l7 -> l4 : [], cost: 1
     16: l7 -> l1 : [], cost: 2
     15: l10 -> l2 : i5^0'=0, length4^0'=tmp^post_14, s^0'=tmp^post_14, tmp^0'=tmp^post_14, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l10
      0: l0 -> l1 : [ length4^0<=i5^0 ], cost: 1
      1: l0 -> l2 : i5^0'=1+i5^0, tmp___08^0'=tmp___08^post_2, [ 1+i5^0<=length4^0 ], cost: 1
      7: l1 -> l7 : [], cost: 1
      2: l2 -> l0 : [], cost: 1
     11: l7 -> l4 : [], cost: 1
     16: l7 -> l1 : [], cost: 2
     20: l7 -> [11] : [], cost: NONTERM
     15: l10 -> l2 : i5^0'=0, length4^0'=tmp^post_14, s^0'=tmp^post_14, tmp^0'=tmp^post_14, [], cost: 2

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l10
      0: l0 -> l1 : [ length4^0<=i5^0 ], cost: 1
      1: l0 -> l2 : i5^0'=1+i5^0, tmp___08^0'=tmp___08^post_2, [ 1+i5^0<=length4^0 ], cost: 1
      7: l1 -> l7 : [], cost: 1
      2: l2 -> l0 : [], cost: 1
     16: l7 -> l1 : [], cost: 2
     20: l7 -> [11] : [], cost: NONTERM
     15: l10 -> l2 : i5^0'=0, length4^0'=tmp^post_14, s^0'=tmp^post_14, tmp^0'=tmp^post_14, [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: l10
     23: l1 -> l1 : [], cost: 3
     24: l1 -> [11] : [], cost: NONTERM
     21: l2 -> l1 : [ length4^0<=i5^0 ], cost: 2
     22: l2 -> l2 : i5^0'=1+i5^0, tmp___08^0'=tmp___08^post_2, [ 1+i5^0<=length4^0 ], cost: 2
     15: l10 -> l2 : i5^0'=0, length4^0'=tmp^post_14, s^0'=tmp^post_14, tmp^0'=tmp^post_14, [], cost: 2

Accelerating simple loops of location 1.
   Accelerating the following rules:
     23: l1 -> l1 : [], cost: 3

   Accelerated rule 23 with non-termination, yielding the new rule 25.
[accelerate] Nesting with 0 inner and 0 outer candidates
   Removing the simple loops: 23.

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

   Accelerated rule 22 with backward acceleration, yielding the new rule 26.
[accelerate] Nesting with 1 inner and 1 outer candidates
   Removing the simple loops: 22.

Accelerated all simple loops using metering functions (where possible):
   Start location: l10
     24: l1 -> [11] : [], cost: NONTERM
     25: l1 -> [12] : [], cost: NONTERM
     21: l2 -> l1 : [ length4^0<=i5^0 ], cost: 2
     26: l2 -> l2 : i5^0'=length4^0, tmp___08^0'=tmp___08^post_2, [ length4^0-i5^0>=1 ], cost: 2*length4^0-2*i5^0
     15: l10 -> l2 : i5^0'=0, length4^0'=tmp^post_14, s^0'=tmp^post_14, tmp^0'=tmp^post_14, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l10
     24: l1 -> [11] : [], cost: NONTERM
     21: l2 -> l1 : [ length4^0<=i5^0 ], cost: 2
     27: l2 -> [12] : [ length4^0<=i5^0 ], cost: NONTERM
     15: l10 -> l2 : i5^0'=0, length4^0'=tmp^post_14, s^0'=tmp^post_14, tmp^0'=tmp^post_14, [], cost: 2
     28: l10 -> l2 : i5^0'=tmp^post_14, length4^0'=tmp^post_14, s^0'=tmp^post_14, tmp^0'=tmp^post_14, tmp___08^0'=tmp___08^post_2, [ tmp^post_14>=1 ], cost: 2+2*tmp^post_14

Eliminated locations (on linear paths):
   Start location: l10
     27: l2 -> [12] : [ length4^0<=i5^0 ], cost: NONTERM
     29: l2 -> [11] : [ length4^0<=i5^0 ], cost: NONTERM
     15: l10 -> l2 : i5^0'=0, length4^0'=tmp^post_14, s^0'=tmp^post_14, tmp^0'=tmp^post_14, [], cost: 2
     28: l10 -> l2 : i5^0'=tmp^post_14, length4^0'=tmp^post_14, s^0'=tmp^post_14, tmp^0'=tmp^post_14, tmp___08^0'=tmp___08^post_2, [ tmp^post_14>=1 ], cost: 2+2*tmp^post_14

Eliminated locations (on tree-shaped paths):
   Start location: l10
     30: l10 -> [12] : [ tmp^post_14<=0 ], cost: NONTERM
     31: l10 -> [11] : [ tmp^post_14<=0 ], cost: NONTERM
     32: l10 -> [12] : [ tmp^post_14>=1 ], cost: NONTERM
     33: l10 -> [11] : [ tmp^post_14>=1 ], cost: NONTERM

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l10
     31: l10 -> [11] : [ tmp^post_14<=0 ], cost: NONTERM
     33: l10 -> [11] : [ tmp^post_14>=1 ], cost: NONTERM

Computing asymptotic complexity for rule 31
   Guard is satisfiable, yielding nontermination
   Resulting cost NONTERM has complexity: Nonterm

Found new complexity Nonterm.

Obtained the following overall complexity (w.r.t. the length of the input n):
   Complexity:  Nonterm
   Cpx degree:  Nonterm
   Solved cost: NONTERM
   Rule cost:   NONTERM
   Rule guard:  [ tmp^post_14<=0 ]

NO