NO

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

Initial linear ITS problem
   Start location: l8
      0: l0 -> l1 : tmp2^0'=tmp2^post_1, x^0'=x^post_1, [ tmp2^0==tmp2^post_1 && x^0==x^post_1 ], cost: 1
      4: l1 -> l2 : tmp2^0'=tmp2^post_5, x^0'=x^post_5, [ tmp2^post_5==tmp2^post_5 && x^0==x^post_5 ], cost: 1
      1: l2 -> l3 : tmp2^0'=tmp2^post_2, x^0'=x^post_2, [ tmp2^0<=0 && 0<=tmp2^0 && x^1_1==0 && x^post_2==1 && tmp2^0==tmp2^post_2 ], cost: 1
      2: l2 -> l0 : tmp2^0'=tmp2^post_3, x^0'=x^post_3, [ 1<=tmp2^0 && tmp2^0==tmp2^post_3 && x^0==x^post_3 ], cost: 1
      3: l2 -> l0 : tmp2^0'=tmp2^post_4, x^0'=x^post_4, [ 1+tmp2^0<=0 && tmp2^0==tmp2^post_4 && x^0==x^post_4 ], cost: 1
      5: l3 -> l4 : tmp2^0'=tmp2^post_6, x^0'=x^post_6, [ tmp2^0==tmp2^post_6 && x^0==x^post_6 ], cost: 1
      6: l4 -> l3 : tmp2^0'=tmp2^post_7, x^0'=x^post_7, [ tmp2^0==tmp2^post_7 && x^0==x^post_7 ], cost: 1
      7: l5 -> l6 : tmp2^0'=tmp2^post_8, x^0'=x^post_8, [ tmp2^0==tmp2^post_8 && x^0==x^post_8 ], cost: 1
      8: l7 -> l1 : tmp2^0'=tmp2^post_9, x^0'=x^post_9, [ x^post_9==1 && tmp2^0==tmp2^post_9 ], cost: 1
      9: l8 -> l7 : tmp2^0'=tmp2^post_10, x^0'=x^post_10, [ tmp2^0==tmp2^post_10 && x^0==x^post_10 ], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
      9: l8 -> l7 : tmp2^0'=tmp2^post_10, x^0'=x^post_10, [ tmp2^0==tmp2^post_10 && x^0==x^post_10 ], cost: 1

Removed unreachable and leaf rules:
   Start location: l8
      0: l0 -> l1 : tmp2^0'=tmp2^post_1, x^0'=x^post_1, [ tmp2^0==tmp2^post_1 && x^0==x^post_1 ], cost: 1
      4: l1 -> l2 : tmp2^0'=tmp2^post_5, x^0'=x^post_5, [ tmp2^post_5==tmp2^post_5 && x^0==x^post_5 ], cost: 1
      1: l2 -> l3 : tmp2^0'=tmp2^post_2, x^0'=x^post_2, [ tmp2^0<=0 && 0<=tmp2^0 && x^1_1==0 && x^post_2==1 && tmp2^0==tmp2^post_2 ], cost: 1
      2: l2 -> l0 : tmp2^0'=tmp2^post_3, x^0'=x^post_3, [ 1<=tmp2^0 && tmp2^0==tmp2^post_3 && x^0==x^post_3 ], cost: 1
      3: l2 -> l0 : tmp2^0'=tmp2^post_4, x^0'=x^post_4, [ 1+tmp2^0<=0 && tmp2^0==tmp2^post_4 && x^0==x^post_4 ], cost: 1
      5: l3 -> l4 : tmp2^0'=tmp2^post_6, x^0'=x^post_6, [ tmp2^0==tmp2^post_6 && x^0==x^post_6 ], cost: 1
      6: l4 -> l3 : tmp2^0'=tmp2^post_7, x^0'=x^post_7, [ tmp2^0==tmp2^post_7 && x^0==x^post_7 ], cost: 1
      8: l7 -> l1 : tmp2^0'=tmp2^post_9, x^0'=x^post_9, [ x^post_9==1 && tmp2^0==tmp2^post_9 ], cost: 1
      9: l8 -> l7 : tmp2^0'=tmp2^post_10, x^0'=x^post_10, [ tmp2^0==tmp2^post_10 && x^0==x^post_10 ], cost: 1

Simplified all rules, resulting in:
   Start location: l8
      0: l0 -> l1 : [], cost: 1
      4: l1 -> l2 : tmp2^0'=tmp2^post_5, [], cost: 1
      1: l2 -> l3 : x^0'=1, [ tmp2^0==0 ], cost: 1
      2: l2 -> l0 : [ 1<=tmp2^0 ], cost: 1
      3: l2 -> l0 : [ 1+tmp2^0<=0 ], cost: 1
      5: l3 -> l4 : [], cost: 1
      6: l4 -> l3 : [], cost: 1
      8: l7 -> l1 : x^0'=1, [], cost: 1
      9: l8 -> l7 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: l8
      0: l0 -> l1 : [], cost: 1
      4: l1 -> l2 : tmp2^0'=tmp2^post_5, [], cost: 1
      1: l2 -> l3 : x^0'=1, [ tmp2^0==0 ], cost: 1
      2: l2 -> l0 : [ 1<=tmp2^0 ], cost: 1
      3: l2 -> l0 : [ 1+tmp2^0<=0 ], cost: 1
     11: l3 -> l3 : [], cost: 2
     10: l8 -> l1 : x^0'=1, [], cost: 2

Accelerating simple loops of location 3.
   Accelerating the following rules:
     11: l3 -> l3 : [], cost: 2

   Accelerated rule 11 with non-termination, yielding the new rule 12.
[accelerate] Nesting with 0 inner and 0 outer candidates
   Removing the simple loops: 11.

Accelerated all simple loops using metering functions (where possible):
   Start location: l8
      0: l0 -> l1 : [], cost: 1
      4: l1 -> l2 : tmp2^0'=tmp2^post_5, [], cost: 1
      1: l2 -> l3 : x^0'=1, [ tmp2^0==0 ], cost: 1
      2: l2 -> l0 : [ 1<=tmp2^0 ], cost: 1
      3: l2 -> l0 : [ 1+tmp2^0<=0 ], cost: 1
     12: l3 -> [9] : [], cost: NONTERM
     10: l8 -> l1 : x^0'=1, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l8
      0: l0 -> l1 : [], cost: 1
      4: l1 -> l2 : tmp2^0'=tmp2^post_5, [], cost: 1
      1: l2 -> l3 : x^0'=1, [ tmp2^0==0 ], cost: 1
      2: l2 -> l0 : [ 1<=tmp2^0 ], cost: 1
      3: l2 -> l0 : [ 1+tmp2^0<=0 ], cost: 1
     13: l2 -> [9] : [ tmp2^0==0 ], cost: NONTERM
     10: l8 -> l1 : x^0'=1, [], cost: 2

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l8
      0: l0 -> l1 : [], cost: 1
      4: l1 -> l2 : tmp2^0'=tmp2^post_5, [], cost: 1
      2: l2 -> l0 : [ 1<=tmp2^0 ], cost: 1
      3: l2 -> l0 : [ 1+tmp2^0<=0 ], cost: 1
     13: l2 -> [9] : [ tmp2^0==0 ], cost: NONTERM
     10: l8 -> l1 : x^0'=1, [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: l8
      0: l0 -> l1 : [], cost: 1
     14: l1 -> l0 : tmp2^0'=tmp2^post_5, [ 1<=tmp2^post_5 ], cost: 2
     15: l1 -> l0 : tmp2^0'=tmp2^post_5, [ 1+tmp2^post_5<=0 ], cost: 2
     16: l1 -> [9] : [ tmp2^post_5==0 ], cost: NONTERM
     10: l8 -> l1 : x^0'=1, [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: l8
     16: l1 -> [9] : [ tmp2^post_5==0 ], cost: NONTERM
     17: l1 -> l1 : tmp2^0'=tmp2^post_5, [ 1<=tmp2^post_5 ], cost: 3
     18: l1 -> l1 : tmp2^0'=tmp2^post_5, [ 1+tmp2^post_5<=0 ], cost: 3
     10: l8 -> l1 : x^0'=1, [], cost: 2

Accelerating simple loops of location 1.
   Accelerating the following rules:
     17: l1 -> l1 : tmp2^0'=tmp2^post_5, [ 1<=tmp2^post_5 ], cost: 3
     18: l1 -> l1 : tmp2^0'=tmp2^post_5, [ 1+tmp2^post_5<=0 ], cost: 3

   Accelerated rule 17 with non-termination, yielding the new rule 19.
   Accelerated rule 18 with non-termination, yielding the new rule 20.
[accelerate] Nesting with 0 inner and 0 outer candidates
   Removing the simple loops: 17 18.

Accelerated all simple loops using metering functions (where possible):
   Start location: l8
     16: l1 -> [9] : [ tmp2^post_5==0 ], cost: NONTERM
     19: l1 -> [10] : [ 1<=tmp2^post_5 ], cost: NONTERM
     20: l1 -> [10] : [ 1+tmp2^post_5<=0 ], cost: NONTERM
     10: l8 -> l1 : x^0'=1, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l8
     16: l1 -> [9] : [ tmp2^post_5==0 ], cost: NONTERM
     10: l8 -> l1 : x^0'=1, [], cost: 2
     21: l8 -> [10] : [], cost: NONTERM
     22: l8 -> [10] : [], cost: NONTERM

Eliminated locations (on linear paths):
   Start location: l8
     21: l8 -> [10] : [], cost: NONTERM
     22: l8 -> [10] : [], cost: NONTERM
     23: l8 -> [9] : [ tmp2^post_5==0 ], cost: NONTERM

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l8
     22: l8 -> [10] : [], cost: NONTERM
     23: l8 -> [9] : [ tmp2^post_5==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:  []

NO