NO

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

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

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
      6: l5 -> l4 : N^0'=N^post_7, p^0'=p^post_7, q^0'=q^post_7, r^0'=r^post_7, [ N^0==N^post_7 && p^0==p^post_7 && q^0==q^post_7 && r^0==r^post_7 ], cost: 1

Removed unreachable and leaf rules:
   Start location: l5
      0: l0 -> l1 : N^0'=N^post_1, p^0'=p^post_1, q^0'=q^post_1, r^0'=r^post_1, [ r^post_1==p^0 && N^0==N^post_1 && p^0==p^post_1 && q^0==q^post_1 ], cost: 1
      1: l0 -> l1 : N^0'=N^post_2, p^0'=p^post_2, q^0'=q^post_2, r^0'=r^post_2, [ q^post_2==p^0 && N^0==N^post_2 && p^0==p^post_2 && r^0==r^post_2 ], cost: 1
      4: l1 -> l2 : N^0'=N^post_5, p^0'=p^post_5, q^0'=q^post_5, r^0'=r^post_5, [ N^0==N^post_5 && p^0==p^post_5 && q^0==q^post_5 && r^0==r^post_5 ], cost: 1
      3: l2 -> l0 : N^0'=N^post_4, p^0'=p^post_4, q^0'=q^post_4, r^0'=r^post_4, [ 2+r^0<=q^0 && p^post_4==p^post_4 && N^0==N^post_4 && q^0==q^post_4 && r^0==r^post_4 ], cost: 1
      5: l4 -> l1 : N^0'=N^post_6, p^0'=p^post_6, q^0'=q^post_6, r^0'=r^post_6, [ r^post_6==1 && q^post_6==N^0 && N^0==N^post_6 && p^0==p^post_6 ], cost: 1
      6: l5 -> l4 : N^0'=N^post_7, p^0'=p^post_7, q^0'=q^post_7, r^0'=r^post_7, [ N^0==N^post_7 && p^0==p^post_7 && q^0==q^post_7 && r^0==r^post_7 ], cost: 1

Simplified all rules, resulting in:
   Start location: l5
      0: l0 -> l1 : r^0'=p^0, [], cost: 1
      1: l0 -> l1 : q^0'=p^0, [], cost: 1
      4: l1 -> l2 : [], cost: 1
      3: l2 -> l0 : p^0'=p^post_4, [ 2+r^0<=q^0 ], cost: 1
      5: l4 -> l1 : q^0'=N^0, r^0'=1, [], cost: 1
      6: l5 -> l4 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: l5
      0: l0 -> l1 : r^0'=p^0, [], cost: 1
      1: l0 -> l1 : q^0'=p^0, [], cost: 1
      8: l1 -> l0 : p^0'=p^post_4, [ 2+r^0<=q^0 ], cost: 2
      7: l5 -> l1 : q^0'=N^0, r^0'=1, [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: l5
      9: l1 -> l1 : p^0'=p^post_4, r^0'=p^post_4, [ 2+r^0<=q^0 ], cost: 3
     10: l1 -> l1 : p^0'=p^post_4, q^0'=p^post_4, [ 2+r^0<=q^0 ], cost: 3
      7: l5 -> l1 : q^0'=N^0, r^0'=1, [], cost: 2

Accelerating simple loops of location 1.
   Accelerating the following rules:
      9: l1 -> l1 : p^0'=p^post_4, r^0'=p^post_4, [ 2+r^0<=q^0 ], cost: 3
     10: l1 -> l1 : p^0'=p^post_4, q^0'=p^post_4, [ 2+r^0<=q^0 ], cost: 3

[test] deduced pseudo-invariant p^post_4-r^0<=0, also trying -p^post_4+r^0<=-1
   Accelerated rule 9 with non-termination, yielding the new rule 11.
   Accelerated rule 9 with non-termination, yielding the new rule 12.
   Accelerated rule 9 with backward acceleration, yielding the new rule 13.
[test] deduced pseudo-invariant q^0-p^post_4<=0, also trying -q^0+p^post_4<=-1
   Accelerated rule 10 with non-termination, yielding the new rule 14.
   Accelerated rule 10 with non-termination, yielding the new rule 15.
   Accelerated rule 10 with backward acceleration, yielding the new rule 16.
[accelerate] Nesting with 0 inner and 2 outer candidates
   Also removing duplicate rules: 12 15.

Accelerated all simple loops using metering functions (where possible):
   Start location: l5
      9: l1 -> l1 : p^0'=p^post_4, r^0'=p^post_4, [ 2+r^0<=q^0 ], cost: 3
     10: l1 -> l1 : p^0'=p^post_4, q^0'=p^post_4, [ 2+r^0<=q^0 ], cost: 3
     11: l1 -> [6] : [ 2+r^0<=q^0 && 2+p^post_4<=q^0 ], cost: NONTERM
     13: l1 -> [6] : [ 2+r^0<=q^0 && p^post_4-r^0<=0 ], cost: NONTERM
     14: l1 -> [6] : [ 2+r^0<=q^0 && 2+r^0<=p^post_4 ], cost: NONTERM
     16: l1 -> [6] : [ 2+r^0<=q^0 && q^0-p^post_4<=0 ], cost: NONTERM
      7: l5 -> l1 : q^0'=N^0, r^0'=1, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l5
      7: l5 -> l1 : q^0'=N^0, r^0'=1, [], cost: 2
     17: l5 -> l1 : p^0'=p^post_4, q^0'=N^0, r^0'=p^post_4, [ 3<=N^0 ], cost: 5
     18: l5 -> l1 : p^0'=p^post_4, q^0'=p^post_4, r^0'=1, [ 3<=N^0 ], cost: 5
     19: l5 -> [6] : [ 3<=N^0 ], cost: NONTERM
     20: l5 -> [6] : [ 3<=N^0 ], cost: NONTERM
     21: l5 -> [6] : [ 3<=N^0 ], cost: NONTERM
     22: l5 -> [6] : [ 3<=N^0 ], cost: NONTERM

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l5
     19: l5 -> [6] : [ 3<=N^0 ], cost: NONTERM
     20: l5 -> [6] : [ 3<=N^0 ], cost: NONTERM
     21: l5 -> [6] : [ 3<=N^0 ], cost: NONTERM
     22: l5 -> [6] : [ 3<=N^0 ], cost: NONTERM

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l5
     22: l5 -> [6] : [ 3<=N^0 ], cost: NONTERM

Computing asymptotic complexity for rule 22
   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:  [ 3<=N^0 ]

NO