NO

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

Initial linear ITS problem
   Start location: [0]
      0: [0] -> [1] : z'=1+z, [ z>=4 ], cost: 1
      1: [1] -> [2] : z'=1+z, [ x>=0 && w<=-5 ], cost: 1
      2: [1] -> [2] : z'=-1+z, [ x<0 ], cost: 1
      3: [2] -> [3] : [ 0<=0 ], cost: 1
      4: [3] -> [4] : [ x>=w ], cost: 1
      8: [3] -> [6] : z'=-1+z, [ x<0 ], cost: 1
      5: [4] -> [5] : [ z<=8 ], cost: 1
      6: [4] -> [5] : [ z>8 ], cost: 1
      7: [5] -> [3] : x'=z^2, w'=-1+w, [], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
      0: [0] -> [1] : z'=1+z, [ z>=4 ], cost: 1

Removed unreachable and leaf rules:
   Start location: [0]
      0: [0] -> [1] : z'=1+z, [ z>=4 ], cost: 1
      1: [1] -> [2] : z'=1+z, [ x>=0 && w<=-5 ], cost: 1
      2: [1] -> [2] : z'=-1+z, [ x<0 ], cost: 1
      3: [2] -> [3] : [ 0<=0 ], cost: 1
      4: [3] -> [4] : [ x>=w ], cost: 1
      5: [4] -> [5] : [ z<=8 ], cost: 1
      6: [4] -> [5] : [ z>8 ], cost: 1
      7: [5] -> [3] : x'=z^2, w'=-1+w, [], cost: 1

Simplified all rules, resulting in:
   Start location: [0]
      0: [0] -> [1] : z'=1+z, [ z>=4 ], cost: 1
      1: [1] -> [2] : z'=1+z, [ x>=0 && w<=-5 ], cost: 1
      2: [1] -> [2] : z'=-1+z, [ x<0 ], cost: 1
      3: [2] -> [3] : [], cost: 1
      4: [3] -> [4] : [ x>=w ], cost: 1
      5: [4] -> [5] : [ z<=8 ], cost: 1
      6: [4] -> [5] : [ z>8 ], cost: 1
      7: [5] -> [3] : x'=z^2, w'=-1+w, [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on tree-shaped paths):
   Start location: [0]
      9: [0] -> [2] : z'=2+z, [ z>=4 && x>=0 && w<=-5 ], cost: 2
     10: [0] -> [2] : z'=z, [ z>=4 && x<0 ], cost: 2
      3: [2] -> [3] : [], cost: 1
     11: [3] -> [5] : [ x>=w && z<=8 ], cost: 2
     12: [3] -> [5] : [ x>=w && z>8 ], cost: 2
      7: [5] -> [3] : x'=z^2, w'=-1+w, [], cost: 1

Eliminated locations (on tree-shaped paths):
   Start location: [0]
     13: [0] -> [3] : z'=2+z, [ z>=4 && x>=0 && w<=-5 ], cost: 3
     14: [0] -> [3] : z'=z, [ z>=4 && x<0 ], cost: 3
     15: [3] -> [3] : x'=z^2, w'=-1+w, [ x>=w && z<=8 ], cost: 3
     16: [3] -> [3] : x'=z^2, w'=-1+w, [ x>=w && z>8 ], cost: 3

Accelerating simple loops of location 3.
   Accelerating the following rules:
     15: [3] -> [3] : x'=z^2, w'=-1+w, [ x>=w && z<=8 ], cost: 3
     16: [3] -> [3] : x'=z^2, w'=-1+w, [ x>=w && z>8 ], cost: 3

   Accelerated rule 15 with non-termination, yielding the new rule 17.
   Accelerated rule 16 with non-termination, yielding the new rule 18.
[accelerate] Nesting with 0 inner and 2 outer candidates

Accelerated all simple loops using metering functions (where possible):
   Start location: [0]
     13: [0] -> [3] : z'=2+z, [ z>=4 && x>=0 && w<=-5 ], cost: 3
     14: [0] -> [3] : z'=z, [ z>=4 && x<0 ], cost: 3
     15: [3] -> [3] : x'=z^2, w'=-1+w, [ x>=w && z<=8 ], cost: 3
     16: [3] -> [3] : x'=z^2, w'=-1+w, [ x>=w && z>8 ], cost: 3
     17: [3] -> [7] : [ x>=w && z<=8 && z^2>=-1+w ], cost: NONTERM
     18: [3] -> [7] : [ x>=w && z>8 && z^2>=-1+w ], cost: NONTERM

Chained accelerated rules (with incoming rules):
   Start location: [0]
     13: [0] -> [3] : z'=2+z, [ z>=4 && x>=0 && w<=-5 ], cost: 3
     14: [0] -> [3] : z'=z, [ z>=4 && x<0 ], cost: 3
     19: [0] -> [3] : z'=2+z, x'=(2+z)^2, w'=-1+w, [ z>=4 && x>=0 && w<=-5 && x>=w && 2+z<=8 ], cost: 6
     20: [0] -> [3] : x'=z^2, w'=-1+w, [ z>=4 && x<0 && x>=w && z<=8 ], cost: 6
     21: [0] -> [3] : z'=2+z, x'=(2+z)^2, w'=-1+w, [ z>=4 && x>=0 && w<=-5 && x>=w && 2+z>8 ], cost: 6
     22: [0] -> [3] : x'=z^2, w'=-1+w, [ z>=4 && x<0 && x>=w && z>8 ], cost: 6
     23: [0] -> [7] : [ z>=4 && x>=0 && w<=-5 && x>=w && 2+z<=8 && (2+z)^2>=-1+w ], cost: NONTERM
     24: [0] -> [7] : [ z>=4 && x<0 && x>=w && z<=8 && z^2>=-1+w ], cost: NONTERM
     25: [0] -> [7] : [ z>=4 && x>=0 && w<=-5 && x>=w && 2+z>8 && (2+z)^2>=-1+w ], cost: NONTERM
     26: [0] -> [7] : [ z>=4 && x<0 && x>=w && z>8 && z^2>=-1+w ], cost: NONTERM

Removed unreachable locations (and leaf rules with constant cost):
   Start location: [0]
     23: [0] -> [7] : [ z>=4 && x>=0 && w<=-5 && x>=w && 2+z<=8 && (2+z)^2>=-1+w ], cost: NONTERM
     24: [0] -> [7] : [ z>=4 && x<0 && x>=w && z<=8 && z^2>=-1+w ], cost: NONTERM
     25: [0] -> [7] : [ z>=4 && x>=0 && w<=-5 && x>=w && 2+z>8 && (2+z)^2>=-1+w ], cost: NONTERM
     26: [0] -> [7] : [ z>=4 && x<0 && x>=w && z>8 && z^2>=-1+w ], cost: NONTERM

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: [0]
     23: [0] -> [7] : [ z>=4 && x>=0 && w<=-5 && x>=w && 2+z<=8 && (2+z)^2>=-1+w ], cost: NONTERM
     24: [0] -> [7] : [ z>=4 && x<0 && x>=w && z<=8 && z^2>=-1+w ], cost: NONTERM
     25: [0] -> [7] : [ z>=4 && x>=0 && w<=-5 && x>=w && 2+z>8 && (2+z)^2>=-1+w ], cost: NONTERM
     26: [0] -> [7] : [ z>=4 && x<0 && x>=w && z>8 && z^2>=-1+w ], cost: NONTERM

Computing asymptotic complexity for rule 24
   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:  [ z>=4 && x<0 && x>=w && z<=8 ]

NO