NO

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

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

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
     10: l7 -> l6 : i^0'=i^post_11, j^0'=j^post_11, x^0'=x^post_11, y^0'=y^post_11, [ i^0==i^post_11 && j^0==j^post_11 && x^0==x^post_11 && y^0==y^post_11 ], cost: 1

Removed unreachable and leaf rules:
   Start location: l7
      0: l0 -> l1 : i^0'=i^post_1, j^0'=j^post_1, x^0'=x^post_1, y^0'=y^post_1, [ x^post_1==-1+x^0 && y^post_1==-1+y^0 && i^0==i^post_1 && j^0==j^post_1 ], cost: 1
      4: l1 -> l2 : i^0'=i^post_5, j^0'=j^post_5, x^0'=x^post_5, y^0'=y^post_5, [ i^0==i^post_5 && j^0==j^post_5 && x^0==x^post_5 && y^0==y^post_5 ], cost: 1
      2: l2 -> l0 : i^0'=i^post_3, j^0'=j^post_3, x^0'=x^post_3, y^0'=y^post_3, [ 1<=x^0 && i^0==i^post_3 && j^0==j^post_3 && x^0==x^post_3 && y^0==y^post_3 ], cost: 1
      3: l2 -> l0 : i^0'=i^post_4, j^0'=j^post_4, x^0'=x^post_4, y^0'=y^post_4, [ 1+x^0<=0 && i^0==i^post_4 && j^0==j^post_4 && x^0==x^post_4 && y^0==y^post_4 ], cost: 1
      9: l6 -> l1 : i^0'=i^post_10, j^0'=j^post_10, x^0'=x^post_10, y^0'=y^post_10, [ x^post_10==i^0 && y^post_10==j^0 && i^0==i^post_10 && j^0==j^post_10 ], cost: 1
     10: l7 -> l6 : i^0'=i^post_11, j^0'=j^post_11, x^0'=x^post_11, y^0'=y^post_11, [ i^0==i^post_11 && j^0==j^post_11 && x^0==x^post_11 && y^0==y^post_11 ], cost: 1

Simplified all rules, resulting in:
   Start location: l7
      0: l0 -> l1 : x^0'=-1+x^0, y^0'=-1+y^0, [], cost: 1
      4: l1 -> l2 : [], cost: 1
      2: l2 -> l0 : [ 1<=x^0 ], cost: 1
      3: l2 -> l0 : [ 1+x^0<=0 ], cost: 1
      9: l6 -> l1 : x^0'=i^0, y^0'=j^0, [], cost: 1
     10: l7 -> l6 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: l7
      0: l0 -> l1 : x^0'=-1+x^0, y^0'=-1+y^0, [], cost: 1
      4: l1 -> l2 : [], cost: 1
      2: l2 -> l0 : [ 1<=x^0 ], cost: 1
      3: l2 -> l0 : [ 1+x^0<=0 ], cost: 1
     11: l7 -> l1 : x^0'=i^0, y^0'=j^0, [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: l7
      0: l0 -> l1 : x^0'=-1+x^0, y^0'=-1+y^0, [], cost: 1
     12: l1 -> l0 : [ 1<=x^0 ], cost: 2
     13: l1 -> l0 : [ 1+x^0<=0 ], cost: 2
     11: l7 -> l1 : x^0'=i^0, y^0'=j^0, [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: l7
     14: l1 -> l1 : x^0'=-1+x^0, y^0'=-1+y^0, [ 1<=x^0 ], cost: 3
     15: l1 -> l1 : x^0'=-1+x^0, y^0'=-1+y^0, [ 1+x^0<=0 ], cost: 3
     11: l7 -> l1 : x^0'=i^0, y^0'=j^0, [], cost: 2

Accelerating simple loops of location 1.
   Accelerating the following rules:
     14: l1 -> l1 : x^0'=-1+x^0, y^0'=-1+y^0, [ 1<=x^0 ], cost: 3
     15: l1 -> l1 : x^0'=-1+x^0, y^0'=-1+y^0, [ 1+x^0<=0 ], cost: 3

   Accelerated rule 14 with backward acceleration, yielding the new rule 16.
   Accelerated rule 15 with non-termination, yielding the new rule 17.
[accelerate] Nesting with 1 inner and 1 outer candidates
   Removing the simple loops: 14 15.

Accelerated all simple loops using metering functions (where possible):
   Start location: l7
     16: l1 -> l1 : x^0'=0, y^0'=-x^0+y^0, [ x^0>=0 ], cost: 3*x^0
     17: l1 -> [8] : [ 1+x^0<=0 ], cost: NONTERM
     11: l7 -> l1 : x^0'=i^0, y^0'=j^0, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l7
     11: l7 -> l1 : x^0'=i^0, y^0'=j^0, [], cost: 2
     18: l7 -> l1 : x^0'=0, y^0'=j^0-i^0, [ i^0>=0 ], cost: 2+3*i^0
     19: l7 -> [8] : [ 1+i^0<=0 ], cost: NONTERM

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l7
     18: l7 -> l1 : x^0'=0, y^0'=j^0-i^0, [ i^0>=0 ], cost: 2+3*i^0
     19: l7 -> [8] : [ 1+i^0<=0 ], cost: NONTERM

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l7
     18: l7 -> l1 : x^0'=0, y^0'=j^0-i^0, [ i^0>=0 ], cost: 2+3*i^0
     19: l7 -> [8] : [ 1+i^0<=0 ], cost: NONTERM

Computing asymptotic complexity for rule 19
   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+i^0<=0 ]

NO