NO

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

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

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
      7: l5 -> l4 : x^0'=x^post_8, y^0'=y^post_8, [ x^0==x^post_8 && y^0==y^post_8 ], cost: 1

Simplified all rules, resulting in:
   Start location: l5
      0: l0 -> l1 : y^0'=x^0, [ 1<=x^0 ], cost: 1
      1: l1 -> l2 : y^0'=-1+y^0, [ 1<=y^0 ], cost: 1
      3: l1 -> l3 : [], cost: 1
      2: l2 -> l1 : [], cost: 1
      4: l3 -> l0 : y^0'=1+y^0, [], cost: 1
      5: l3 -> l0 : x^0'=-1+x^0, y^0'=1+y^0, [], cost: 1
      6: l4 -> l0 : [], cost: 1
      7: l5 -> l4 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: l5
      0: l0 -> l1 : y^0'=x^0, [ 1<=x^0 ], cost: 1
      3: l1 -> l3 : [], cost: 1
      9: l1 -> l1 : y^0'=-1+y^0, [ 1<=y^0 ], cost: 2
      4: l3 -> l0 : y^0'=1+y^0, [], cost: 1
      5: l3 -> l0 : x^0'=-1+x^0, y^0'=1+y^0, [], cost: 1
      8: l5 -> l0 : [], cost: 2

Accelerating simple loops of location 1.
   Accelerating the following rules:
      9: l1 -> l1 : y^0'=-1+y^0, [ 1<=y^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: l5
      0: l0 -> l1 : y^0'=x^0, [ 1<=x^0 ], cost: 1
      3: l1 -> l3 : [], cost: 1
     10: l1 -> l1 : y^0'=0, [ y^0>=0 ], cost: 2*y^0
      4: l3 -> l0 : y^0'=1+y^0, [], cost: 1
      5: l3 -> l0 : x^0'=-1+x^0, y^0'=1+y^0, [], cost: 1
      8: l5 -> l0 : [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l5
      0: l0 -> l1 : y^0'=x^0, [ 1<=x^0 ], cost: 1
     11: l0 -> l1 : y^0'=0, [ 1<=x^0 ], cost: 1+2*x^0
      3: l1 -> l3 : [], cost: 1
      4: l3 -> l0 : y^0'=1+y^0, [], cost: 1
      5: l3 -> l0 : x^0'=-1+x^0, y^0'=1+y^0, [], cost: 1
      8: l5 -> l0 : [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: l5
     12: l0 -> l3 : y^0'=x^0, [ 1<=x^0 ], cost: 2
     13: l0 -> l3 : y^0'=0, [ 1<=x^0 ], cost: 2+2*x^0
      4: l3 -> l0 : y^0'=1+y^0, [], cost: 1
      5: l3 -> l0 : x^0'=-1+x^0, y^0'=1+y^0, [], cost: 1
      8: l5 -> l0 : [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: l5
     14: l0 -> l0 : y^0'=1+x^0, [ 1<=x^0 ], cost: 3
     15: l0 -> l0 : x^0'=-1+x^0, y^0'=1+x^0, [ 1<=x^0 ], cost: 3
     16: l0 -> l0 : y^0'=1, [ 1<=x^0 ], cost: 3+2*x^0
     17: l0 -> l0 : x^0'=-1+x^0, y^0'=1, [ 1<=x^0 ], cost: 3+2*x^0
      8: l5 -> l0 : [], cost: 2

Accelerating simple loops of location 0.
   Accelerating the following rules:
     14: l0 -> l0 : y^0'=1+x^0, [ 1<=x^0 ], cost: 3
     15: l0 -> l0 : x^0'=-1+x^0, y^0'=1+x^0, [ 1<=x^0 ], cost: 3
     16: l0 -> l0 : y^0'=1, [ 1<=x^0 ], cost: 3+2*x^0
     17: l0 -> l0 : x^0'=-1+x^0, y^0'=1, [ 1<=x^0 ], cost: 3+2*x^0

   Accelerated rule 14 with non-termination, yielding the new rule 18.
   Accelerated rule 15 with backward acceleration, yielding the new rule 19.
   Accelerated rule 16 with non-termination, yielding the new rule 20.
   Accelerated rule 17 with backward acceleration, yielding the new rule 21.
[accelerate] Nesting with 2 inner and 2 outer candidates
   Removing the simple loops: 14 15 16 17.
   Also removing duplicate rules: 18.

Accelerated all simple loops using metering functions (where possible):
   Start location: l5
     19: l0 -> l0 : x^0'=0, y^0'=2, [ x^0>=1 ], cost: 3*x^0
     20: l0 -> [7] : [ 1<=x^0 ], cost: NONTERM
     21: l0 -> l0 : x^0'=0, y^0'=1, [ x^0>=1 ], cost: x^0^2+4*x^0
      8: l5 -> l0 : [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l5
      8: l5 -> l0 : [], cost: 2
     22: l5 -> l0 : x^0'=0, y^0'=2, [ x^0>=1 ], cost: 2+3*x^0
     23: l5 -> [7] : [ 1<=x^0 ], cost: NONTERM
     24: l5 -> l0 : x^0'=0, y^0'=1, [ x^0>=1 ], cost: 2+x^0^2+4*x^0

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l5
     22: l5 -> l0 : x^0'=0, y^0'=2, [ x^0>=1 ], cost: 2+3*x^0
     23: l5 -> [7] : [ 1<=x^0 ], cost: NONTERM
     24: l5 -> l0 : x^0'=0, y^0'=1, [ x^0>=1 ], cost: 2+x^0^2+4*x^0

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l5
     22: l5 -> l0 : x^0'=0, y^0'=2, [ x^0>=1 ], cost: 2+3*x^0
     23: l5 -> [7] : [ 1<=x^0 ], cost: NONTERM
     24: l5 -> l0 : x^0'=0, y^0'=1, [ x^0>=1 ], cost: 2+x^0^2+4*x^0

Computing asymptotic complexity for rule 23
   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:  [ 1<=x^0 ]

NO