NO

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

Initial linear ITS problem
   Start location: l8
      0: l0 -> l1 : p^0'=p^post_1, x^0'=x^post_1, y^0'=y^post_1, [ x^post_1==1 && p^0==p^post_1 && y^0==y^post_1 ], cost: 1
      1: l1 -> l0 : p^0'=p^post_2, x^0'=x^post_2, y^0'=y^post_2, [ p^0==p^post_2 && x^0==x^post_2 && y^0==y^post_2 ], cost: 1
      2: l2 -> l0 : p^0'=p^post_3, x^0'=x^post_3, y^0'=y^post_3, [ y^0<=0 && p^post_3==0 && x^0==x^post_3 && y^0==y^post_3 ], cost: 1
      3: l2 -> l3 : p^0'=p^post_4, x^0'=x^post_4, y^0'=y^post_4, [ 1<=y^0 && y^post_4==-1+y^0 && p^0==p^post_4 && x^0==x^post_4 ], cost: 1
      4: l3 -> l2 : p^0'=p^post_5, x^0'=x^post_5, y^0'=y^post_5, [ p^0==p^post_5 && x^0==x^post_5 && y^0==y^post_5 ], cost: 1
      5: l4 -> l0 : p^0'=p^post_6, x^0'=x^post_6, y^0'=y^post_6, [ 2<=0 && p^0==p^post_6 && x^0==x^post_6 && y^0==y^post_6 ], cost: 1
      6: l4 -> l5 : p^0'=p^post_7, x^0'=x^post_7, y^0'=y^post_7, [ p^post_7==1+p^0 && x^0==x^post_7 && y^0==y^post_7 ], cost: 1
      7: l5 -> l4 : p^0'=p^post_8, x^0'=x^post_8, y^0'=y^post_8, [ p^0==p^post_8 && x^0==x^post_8 && y^0==y^post_8 ], cost: 1
      8: l6 -> l2 : p^0'=p^post_9, x^0'=x^post_9, y^0'=y^post_9, [ x^0<=0 && p^0==p^post_9 && x^0==x^post_9 && y^0==y^post_9 ], cost: 1
      9: l6 -> l4 : p^0'=p^post_10, x^0'=x^post_10, y^0'=y^post_10, [ 1<=x^0 && p^0==p^post_10 && x^0==x^post_10 && y^0==y^post_10 ], cost: 1
     10: l7 -> l6 : p^0'=p^post_11, x^0'=x^post_11, y^0'=y^post_11, [ p^post_11==0 && x^0==x^post_11 && y^0==y^post_11 ], cost: 1
     11: l8 -> l7 : p^0'=p^post_12, x^0'=x^post_12, y^0'=y^post_12, [ p^0==p^post_12 && x^0==x^post_12 && y^0==y^post_12 ], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
     11: l8 -> l7 : p^0'=p^post_12, x^0'=x^post_12, y^0'=y^post_12, [ p^0==p^post_12 && x^0==x^post_12 && y^0==y^post_12 ], cost: 1

Removed rules with unsatisfiable guard:
   Start location: l8
      0: l0 -> l1 : p^0'=p^post_1, x^0'=x^post_1, y^0'=y^post_1, [ x^post_1==1 && p^0==p^post_1 && y^0==y^post_1 ], cost: 1
      1: l1 -> l0 : p^0'=p^post_2, x^0'=x^post_2, y^0'=y^post_2, [ p^0==p^post_2 && x^0==x^post_2 && y^0==y^post_2 ], cost: 1
      2: l2 -> l0 : p^0'=p^post_3, x^0'=x^post_3, y^0'=y^post_3, [ y^0<=0 && p^post_3==0 && x^0==x^post_3 && y^0==y^post_3 ], cost: 1
      3: l2 -> l3 : p^0'=p^post_4, x^0'=x^post_4, y^0'=y^post_4, [ 1<=y^0 && y^post_4==-1+y^0 && p^0==p^post_4 && x^0==x^post_4 ], cost: 1
      4: l3 -> l2 : p^0'=p^post_5, x^0'=x^post_5, y^0'=y^post_5, [ p^0==p^post_5 && x^0==x^post_5 && y^0==y^post_5 ], cost: 1
      6: l4 -> l5 : p^0'=p^post_7, x^0'=x^post_7, y^0'=y^post_7, [ p^post_7==1+p^0 && x^0==x^post_7 && y^0==y^post_7 ], cost: 1
      7: l5 -> l4 : p^0'=p^post_8, x^0'=x^post_8, y^0'=y^post_8, [ p^0==p^post_8 && x^0==x^post_8 && y^0==y^post_8 ], cost: 1
      8: l6 -> l2 : p^0'=p^post_9, x^0'=x^post_9, y^0'=y^post_9, [ x^0<=0 && p^0==p^post_9 && x^0==x^post_9 && y^0==y^post_9 ], cost: 1
      9: l6 -> l4 : p^0'=p^post_10, x^0'=x^post_10, y^0'=y^post_10, [ 1<=x^0 && p^0==p^post_10 && x^0==x^post_10 && y^0==y^post_10 ], cost: 1
     10: l7 -> l6 : p^0'=p^post_11, x^0'=x^post_11, y^0'=y^post_11, [ p^post_11==0 && x^0==x^post_11 && y^0==y^post_11 ], cost: 1
     11: l8 -> l7 : p^0'=p^post_12, x^0'=x^post_12, y^0'=y^post_12, [ p^0==p^post_12 && x^0==x^post_12 && y^0==y^post_12 ], cost: 1

Simplified all rules, resulting in:
   Start location: l8
      0: l0 -> l1 : x^0'=1, [], cost: 1
      1: l1 -> l0 : [], cost: 1
      2: l2 -> l0 : p^0'=0, [ y^0<=0 ], cost: 1
      3: l2 -> l3 : y^0'=-1+y^0, [ 1<=y^0 ], cost: 1
      4: l3 -> l2 : [], cost: 1
      6: l4 -> l5 : p^0'=1+p^0, [], cost: 1
      7: l5 -> l4 : [], cost: 1
      8: l6 -> l2 : [ x^0<=0 ], cost: 1
      9: l6 -> l4 : [ 1<=x^0 ], cost: 1
     10: l7 -> l6 : p^0'=0, [], cost: 1
     11: l8 -> l7 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: l8
     14: l0 -> l0 : x^0'=1, [], cost: 2
      2: l2 -> l0 : p^0'=0, [ y^0<=0 ], cost: 1
     13: l2 -> l2 : y^0'=-1+y^0, [ 1<=y^0 ], cost: 2
     15: l4 -> l4 : p^0'=1+p^0, [], cost: 2
      8: l6 -> l2 : [ x^0<=0 ], cost: 1
      9: l6 -> l4 : [ 1<=x^0 ], cost: 1
     12: l8 -> l6 : p^0'=0, [], cost: 2

Accelerating simple loops of location 0.
   Accelerating the following rules:
     14: l0 -> l0 : x^0'=1, [], cost: 2

   Accelerated rule 14 with non-termination, yielding the new rule 16.
[accelerate] Nesting with 0 inner and 0 outer candidates
   Removing the simple loops: 14.

Accelerating simple loops of location 2.
   Accelerating the following rules:
     13: l2 -> l2 : y^0'=-1+y^0, [ 1<=y^0 ], cost: 2

   Accelerated rule 13 with backward acceleration, yielding the new rule 17.
[accelerate] Nesting with 1 inner and 1 outer candidates
   Removing the simple loops: 13.

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

   Accelerated rule 15 with non-termination, yielding the new rule 18.
[accelerate] Nesting with 0 inner and 0 outer candidates
   Removing the simple loops: 15.

Accelerated all simple loops using metering functions (where possible):
   Start location: l8
     16: l0 -> [9] : [], cost: NONTERM
      2: l2 -> l0 : p^0'=0, [ y^0<=0 ], cost: 1
     17: l2 -> l2 : y^0'=0, [ y^0>=0 ], cost: 2*y^0
     18: l4 -> [11] : [], cost: NONTERM
      8: l6 -> l2 : [ x^0<=0 ], cost: 1
      9: l6 -> l4 : [ 1<=x^0 ], cost: 1
     12: l8 -> l6 : p^0'=0, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l8
      2: l2 -> l0 : p^0'=0, [ y^0<=0 ], cost: 1
     19: l2 -> [9] : [ y^0<=0 ], cost: NONTERM
      8: l6 -> l2 : [ x^0<=0 ], cost: 1
      9: l6 -> l4 : [ 1<=x^0 ], cost: 1
     20: l6 -> l2 : y^0'=0, [ x^0<=0 && y^0>=0 ], cost: 1+2*y^0
     21: l6 -> [11] : [ 1<=x^0 ], cost: NONTERM
     12: l8 -> l6 : p^0'=0, [], cost: 2

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l8
     19: l2 -> [9] : [ y^0<=0 ], cost: NONTERM
      8: l6 -> l2 : [ x^0<=0 ], cost: 1
     20: l6 -> l2 : y^0'=0, [ x^0<=0 && y^0>=0 ], cost: 1+2*y^0
     21: l6 -> [11] : [ 1<=x^0 ], cost: NONTERM
     12: l8 -> l6 : p^0'=0, [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: l8
     19: l2 -> [9] : [ y^0<=0 ], cost: NONTERM
     22: l8 -> l2 : p^0'=0, [ x^0<=0 ], cost: 3
     23: l8 -> l2 : p^0'=0, y^0'=0, [ x^0<=0 && y^0>=0 ], cost: 3+2*y^0
     24: l8 -> [11] : [ 1<=x^0 ], cost: NONTERM

Eliminated locations (on tree-shaped paths):
   Start location: l8
     24: l8 -> [11] : [ 1<=x^0 ], cost: NONTERM
     25: l8 -> [9] : [ x^0<=0 && y^0<=0 ], cost: NONTERM
     26: l8 -> [9] : [ x^0<=0 && y^0>=0 ], cost: NONTERM

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l8
     24: l8 -> [11] : [ 1<=x^0 ], cost: NONTERM
     25: l8 -> [9] : [ x^0<=0 && y^0<=0 ], cost: NONTERM
     26: l8 -> [9] : [ x^0<=0 && y^0>=0 ], 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:  [ 1<=x^0 ]

NO