NO

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

Initial linear ITS problem
   Start location: l9
      0: l0 -> l1 : A^0'=A^post_1, R^0'=R^post_1, __rho_1_^0'=__rho_1_^post_1, __rho_2_^0'=__rho_2_^post_1, dobreak^0'=dobreak^post_1, n^0'=n^post_1, [ A^0==A^post_1 && R^0==R^post_1 && __rho_1_^0==__rho_1_^post_1 && __rho_2_^0==__rho_2_^post_1 && dobreak^0==dobreak^post_1 && n^0==n^post_1 ], cost: 1
      7: l1 -> l2 : A^0'=A^post_8, R^0'=R^post_8, __rho_1_^0'=__rho_1_^post_8, __rho_2_^0'=__rho_2_^post_8, dobreak^0'=dobreak^post_8, n^0'=n^post_8, [ dobreak^0<=0 && A^1_1==1 && A^post_8==0 && __rho_2_^post_8==__rho_2_^post_8 && n^post_8==__rho_2_^post_8 && R^0==R^post_8 && __rho_1_^0==__rho_1_^post_8 && dobreak^0==dobreak^post_8 ], cost: 1
      8: l1 -> l6 : A^0'=A^post_9, R^0'=R^post_9, __rho_1_^0'=__rho_1_^post_9, __rho_2_^0'=__rho_2_^post_9, dobreak^0'=dobreak^post_9, n^0'=n^post_9, [ 1<=dobreak^0 && A^0==A^post_9 && R^0==R^post_9 && __rho_1_^0==__rho_1_^post_9 && __rho_2_^0==__rho_2_^post_9 && dobreak^0==dobreak^post_9 && n^0==n^post_9 ], cost: 1
      1: l2 -> l3 : A^0'=A^post_2, R^0'=R^post_2, __rho_1_^0'=__rho_1_^post_2, __rho_2_^0'=__rho_2_^post_2, dobreak^0'=dobreak^post_2, n^0'=n^post_2, [ A^0==A^post_2 && R^0==R^post_2 && __rho_1_^0==__rho_1_^post_2 && __rho_2_^0==__rho_2_^post_2 && dobreak^0==dobreak^post_2 && n^0==n^post_2 ], cost: 1
      5: l3 -> l2 : A^0'=A^post_6, R^0'=R^post_6, __rho_1_^0'=__rho_1_^post_6, __rho_2_^0'=__rho_2_^post_6, dobreak^0'=dobreak^post_6, n^0'=n^post_6, [ 1<=n^0 && A^0==A^post_6 && R^0==R^post_6 && __rho_1_^0==__rho_1_^post_6 && __rho_2_^0==__rho_2_^post_6 && dobreak^0==dobreak^post_6 && n^0==n^post_6 ], cost: 1
      6: l3 -> l0 : A^0'=A^post_7, R^0'=R^post_7, __rho_1_^0'=__rho_1_^post_7, __rho_2_^0'=__rho_2_^post_7, dobreak^0'=dobreak^post_7, n^0'=n^post_7, [ n^0<=0 && R^1_1==1 && R^post_7==0 && __rho_1_^post_7==__rho_1_^post_7 && dobreak^post_7==__rho_1_^post_7 && A^0==A^post_7 && __rho_2_^0==__rho_2_^post_7 && n^0==n^post_7 ], cost: 1
      2: l4 -> l5 : A^0'=A^post_3, R^0'=R^post_3, __rho_1_^0'=__rho_1_^post_3, __rho_2_^0'=__rho_2_^post_3, dobreak^0'=dobreak^post_3, n^0'=n^post_3, [ A^0==A^post_3 && R^0==R^post_3 && __rho_1_^0==__rho_1_^post_3 && __rho_2_^0==__rho_2_^post_3 && dobreak^0==dobreak^post_3 && n^0==n^post_3 ], cost: 1
      3: l6 -> l7 : A^0'=A^post_4, R^0'=R^post_4, __rho_1_^0'=__rho_1_^post_4, __rho_2_^0'=__rho_2_^post_4, dobreak^0'=dobreak^post_4, n^0'=n^post_4, [ A^0==A^post_4 && R^0==R^post_4 && __rho_1_^0==__rho_1_^post_4 && __rho_2_^0==__rho_2_^post_4 && dobreak^0==dobreak^post_4 && n^0==n^post_4 ], cost: 1
      4: l7 -> l6 : A^0'=A^post_5, R^0'=R^post_5, __rho_1_^0'=__rho_1_^post_5, __rho_2_^0'=__rho_2_^post_5, dobreak^0'=dobreak^post_5, n^0'=n^post_5, [ A^0==A^post_5 && R^0==R^post_5 && __rho_1_^0==__rho_1_^post_5 && __rho_2_^0==__rho_2_^post_5 && dobreak^0==dobreak^post_5 && n^0==n^post_5 ], cost: 1
      9: l8 -> l0 : A^0'=A^post_10, R^0'=R^post_10, __rho_1_^0'=__rho_1_^post_10, __rho_2_^0'=__rho_2_^post_10, dobreak^0'=dobreak^post_10, n^0'=n^post_10, [ A^post_10==0 && R^post_10==0 && __rho_1_^post_10==__rho_1_^post_10 && dobreak^post_10==__rho_1_^post_10 && __rho_2_^0==__rho_2_^post_10 && n^0==n^post_10 ], cost: 1
     10: l9 -> l8 : A^0'=A^post_11, R^0'=R^post_11, __rho_1_^0'=__rho_1_^post_11, __rho_2_^0'=__rho_2_^post_11, dobreak^0'=dobreak^post_11, n^0'=n^post_11, [ A^0==A^post_11 && R^0==R^post_11 && __rho_1_^0==__rho_1_^post_11 && __rho_2_^0==__rho_2_^post_11 && dobreak^0==dobreak^post_11 && n^0==n^post_11 ], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
     10: l9 -> l8 : A^0'=A^post_11, R^0'=R^post_11, __rho_1_^0'=__rho_1_^post_11, __rho_2_^0'=__rho_2_^post_11, dobreak^0'=dobreak^post_11, n^0'=n^post_11, [ A^0==A^post_11 && R^0==R^post_11 && __rho_1_^0==__rho_1_^post_11 && __rho_2_^0==__rho_2_^post_11 && dobreak^0==dobreak^post_11 && n^0==n^post_11 ], cost: 1

Removed unreachable and leaf rules:
   Start location: l9
      0: l0 -> l1 : A^0'=A^post_1, R^0'=R^post_1, __rho_1_^0'=__rho_1_^post_1, __rho_2_^0'=__rho_2_^post_1, dobreak^0'=dobreak^post_1, n^0'=n^post_1, [ A^0==A^post_1 && R^0==R^post_1 && __rho_1_^0==__rho_1_^post_1 && __rho_2_^0==__rho_2_^post_1 && dobreak^0==dobreak^post_1 && n^0==n^post_1 ], cost: 1
      7: l1 -> l2 : A^0'=A^post_8, R^0'=R^post_8, __rho_1_^0'=__rho_1_^post_8, __rho_2_^0'=__rho_2_^post_8, dobreak^0'=dobreak^post_8, n^0'=n^post_8, [ dobreak^0<=0 && A^1_1==1 && A^post_8==0 && __rho_2_^post_8==__rho_2_^post_8 && n^post_8==__rho_2_^post_8 && R^0==R^post_8 && __rho_1_^0==__rho_1_^post_8 && dobreak^0==dobreak^post_8 ], cost: 1
      8: l1 -> l6 : A^0'=A^post_9, R^0'=R^post_9, __rho_1_^0'=__rho_1_^post_9, __rho_2_^0'=__rho_2_^post_9, dobreak^0'=dobreak^post_9, n^0'=n^post_9, [ 1<=dobreak^0 && A^0==A^post_9 && R^0==R^post_9 && __rho_1_^0==__rho_1_^post_9 && __rho_2_^0==__rho_2_^post_9 && dobreak^0==dobreak^post_9 && n^0==n^post_9 ], cost: 1
      1: l2 -> l3 : A^0'=A^post_2, R^0'=R^post_2, __rho_1_^0'=__rho_1_^post_2, __rho_2_^0'=__rho_2_^post_2, dobreak^0'=dobreak^post_2, n^0'=n^post_2, [ A^0==A^post_2 && R^0==R^post_2 && __rho_1_^0==__rho_1_^post_2 && __rho_2_^0==__rho_2_^post_2 && dobreak^0==dobreak^post_2 && n^0==n^post_2 ], cost: 1
      5: l3 -> l2 : A^0'=A^post_6, R^0'=R^post_6, __rho_1_^0'=__rho_1_^post_6, __rho_2_^0'=__rho_2_^post_6, dobreak^0'=dobreak^post_6, n^0'=n^post_6, [ 1<=n^0 && A^0==A^post_6 && R^0==R^post_6 && __rho_1_^0==__rho_1_^post_6 && __rho_2_^0==__rho_2_^post_6 && dobreak^0==dobreak^post_6 && n^0==n^post_6 ], cost: 1
      6: l3 -> l0 : A^0'=A^post_7, R^0'=R^post_7, __rho_1_^0'=__rho_1_^post_7, __rho_2_^0'=__rho_2_^post_7, dobreak^0'=dobreak^post_7, n^0'=n^post_7, [ n^0<=0 && R^1_1==1 && R^post_7==0 && __rho_1_^post_7==__rho_1_^post_7 && dobreak^post_7==__rho_1_^post_7 && A^0==A^post_7 && __rho_2_^0==__rho_2_^post_7 && n^0==n^post_7 ], cost: 1
      3: l6 -> l7 : A^0'=A^post_4, R^0'=R^post_4, __rho_1_^0'=__rho_1_^post_4, __rho_2_^0'=__rho_2_^post_4, dobreak^0'=dobreak^post_4, n^0'=n^post_4, [ A^0==A^post_4 && R^0==R^post_4 && __rho_1_^0==__rho_1_^post_4 && __rho_2_^0==__rho_2_^post_4 && dobreak^0==dobreak^post_4 && n^0==n^post_4 ], cost: 1
      4: l7 -> l6 : A^0'=A^post_5, R^0'=R^post_5, __rho_1_^0'=__rho_1_^post_5, __rho_2_^0'=__rho_2_^post_5, dobreak^0'=dobreak^post_5, n^0'=n^post_5, [ A^0==A^post_5 && R^0==R^post_5 && __rho_1_^0==__rho_1_^post_5 && __rho_2_^0==__rho_2_^post_5 && dobreak^0==dobreak^post_5 && n^0==n^post_5 ], cost: 1
      9: l8 -> l0 : A^0'=A^post_10, R^0'=R^post_10, __rho_1_^0'=__rho_1_^post_10, __rho_2_^0'=__rho_2_^post_10, dobreak^0'=dobreak^post_10, n^0'=n^post_10, [ A^post_10==0 && R^post_10==0 && __rho_1_^post_10==__rho_1_^post_10 && dobreak^post_10==__rho_1_^post_10 && __rho_2_^0==__rho_2_^post_10 && n^0==n^post_10 ], cost: 1
     10: l9 -> l8 : A^0'=A^post_11, R^0'=R^post_11, __rho_1_^0'=__rho_1_^post_11, __rho_2_^0'=__rho_2_^post_11, dobreak^0'=dobreak^post_11, n^0'=n^post_11, [ A^0==A^post_11 && R^0==R^post_11 && __rho_1_^0==__rho_1_^post_11 && __rho_2_^0==__rho_2_^post_11 && dobreak^0==dobreak^post_11 && n^0==n^post_11 ], cost: 1

Simplified all rules, resulting in:
   Start location: l9
      0: l0 -> l1 : [], cost: 1
      7: l1 -> l2 : A^0'=0, __rho_2_^0'=__rho_2_^post_8, n^0'=__rho_2_^post_8, [ dobreak^0<=0 ], cost: 1
      8: l1 -> l6 : [ 1<=dobreak^0 ], cost: 1
      1: l2 -> l3 : [], cost: 1
      5: l3 -> l2 : [ 1<=n^0 ], cost: 1
      6: l3 -> l0 : R^0'=0, __rho_1_^0'=__rho_1_^post_7, dobreak^0'=__rho_1_^post_7, [ n^0<=0 ], cost: 1
      3: l6 -> l7 : [], cost: 1
      4: l7 -> l6 : [], cost: 1
      9: l8 -> l0 : A^0'=0, R^0'=0, __rho_1_^0'=__rho_1_^post_10, dobreak^0'=__rho_1_^post_10, [], cost: 1
     10: l9 -> l8 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: l9
      0: l0 -> l1 : [], cost: 1
      7: l1 -> l2 : A^0'=0, __rho_2_^0'=__rho_2_^post_8, n^0'=__rho_2_^post_8, [ dobreak^0<=0 ], cost: 1
      8: l1 -> l6 : [ 1<=dobreak^0 ], cost: 1
      1: l2 -> l3 : [], cost: 1
      5: l3 -> l2 : [ 1<=n^0 ], cost: 1
      6: l3 -> l0 : R^0'=0, __rho_1_^0'=__rho_1_^post_7, dobreak^0'=__rho_1_^post_7, [ n^0<=0 ], cost: 1
     12: l6 -> l6 : [], cost: 2
     11: l9 -> l0 : A^0'=0, R^0'=0, __rho_1_^0'=__rho_1_^post_10, dobreak^0'=__rho_1_^post_10, [], cost: 2

Accelerating simple loops of location 6.
   Accelerating the following rules:
     12: l6 -> l6 : [], cost: 2

   Accelerated rule 12 with non-termination, yielding the new rule 13.
[accelerate] Nesting with 0 inner and 0 outer candidates
   Removing the simple loops: 12.

Accelerated all simple loops using metering functions (where possible):
   Start location: l9
      0: l0 -> l1 : [], cost: 1
      7: l1 -> l2 : A^0'=0, __rho_2_^0'=__rho_2_^post_8, n^0'=__rho_2_^post_8, [ dobreak^0<=0 ], cost: 1
      8: l1 -> l6 : [ 1<=dobreak^0 ], cost: 1
      1: l2 -> l3 : [], cost: 1
      5: l3 -> l2 : [ 1<=n^0 ], cost: 1
      6: l3 -> l0 : R^0'=0, __rho_1_^0'=__rho_1_^post_7, dobreak^0'=__rho_1_^post_7, [ n^0<=0 ], cost: 1
     13: l6 -> [10] : [], cost: NONTERM
     11: l9 -> l0 : A^0'=0, R^0'=0, __rho_1_^0'=__rho_1_^post_10, dobreak^0'=__rho_1_^post_10, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l9
      0: l0 -> l1 : [], cost: 1
      7: l1 -> l2 : A^0'=0, __rho_2_^0'=__rho_2_^post_8, n^0'=__rho_2_^post_8, [ dobreak^0<=0 ], cost: 1
      8: l1 -> l6 : [ 1<=dobreak^0 ], cost: 1
     14: l1 -> [10] : [ 1<=dobreak^0 ], cost: NONTERM
      1: l2 -> l3 : [], cost: 1
      5: l3 -> l2 : [ 1<=n^0 ], cost: 1
      6: l3 -> l0 : R^0'=0, __rho_1_^0'=__rho_1_^post_7, dobreak^0'=__rho_1_^post_7, [ n^0<=0 ], cost: 1
     11: l9 -> l0 : A^0'=0, R^0'=0, __rho_1_^0'=__rho_1_^post_10, dobreak^0'=__rho_1_^post_10, [], cost: 2

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l9
      0: l0 -> l1 : [], cost: 1
      7: l1 -> l2 : A^0'=0, __rho_2_^0'=__rho_2_^post_8, n^0'=__rho_2_^post_8, [ dobreak^0<=0 ], cost: 1
     14: l1 -> [10] : [ 1<=dobreak^0 ], cost: NONTERM
      1: l2 -> l3 : [], cost: 1
      5: l3 -> l2 : [ 1<=n^0 ], cost: 1
      6: l3 -> l0 : R^0'=0, __rho_1_^0'=__rho_1_^post_7, dobreak^0'=__rho_1_^post_7, [ n^0<=0 ], cost: 1
     11: l9 -> l0 : A^0'=0, R^0'=0, __rho_1_^0'=__rho_1_^post_10, dobreak^0'=__rho_1_^post_10, [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: l9
     15: l0 -> l2 : A^0'=0, __rho_2_^0'=__rho_2_^post_8, n^0'=__rho_2_^post_8, [ dobreak^0<=0 ], cost: 2
     16: l0 -> [10] : [ 1<=dobreak^0 ], cost: NONTERM
     17: l2 -> l2 : [ 1<=n^0 ], cost: 2
     18: l2 -> l0 : R^0'=0, __rho_1_^0'=__rho_1_^post_7, dobreak^0'=__rho_1_^post_7, [ n^0<=0 ], cost: 2
     11: l9 -> l0 : A^0'=0, R^0'=0, __rho_1_^0'=__rho_1_^post_10, dobreak^0'=__rho_1_^post_10, [], cost: 2

Accelerating simple loops of location 2.
   Accelerating the following rules:
     17: l2 -> l2 : [ 1<=n^0 ], cost: 2

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

Accelerated all simple loops using metering functions (where possible):
   Start location: l9
     15: l0 -> l2 : A^0'=0, __rho_2_^0'=__rho_2_^post_8, n^0'=__rho_2_^post_8, [ dobreak^0<=0 ], cost: 2
     16: l0 -> [10] : [ 1<=dobreak^0 ], cost: NONTERM
     18: l2 -> l0 : R^0'=0, __rho_1_^0'=__rho_1_^post_7, dobreak^0'=__rho_1_^post_7, [ n^0<=0 ], cost: 2
     19: l2 -> [11] : [ 1<=n^0 ], cost: NONTERM
     11: l9 -> l0 : A^0'=0, R^0'=0, __rho_1_^0'=__rho_1_^post_10, dobreak^0'=__rho_1_^post_10, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l9
     15: l0 -> l2 : A^0'=0, __rho_2_^0'=__rho_2_^post_8, n^0'=__rho_2_^post_8, [ dobreak^0<=0 ], cost: 2
     16: l0 -> [10] : [ 1<=dobreak^0 ], cost: NONTERM
     20: l0 -> [11] : [ dobreak^0<=0 ], cost: NONTERM
     18: l2 -> l0 : R^0'=0, __rho_1_^0'=__rho_1_^post_7, dobreak^0'=__rho_1_^post_7, [ n^0<=0 ], cost: 2
     11: l9 -> l0 : A^0'=0, R^0'=0, __rho_1_^0'=__rho_1_^post_10, dobreak^0'=__rho_1_^post_10, [], cost: 2

Eliminated locations (on linear paths):
   Start location: l9
     16: l0 -> [10] : [ 1<=dobreak^0 ], cost: NONTERM
     20: l0 -> [11] : [ dobreak^0<=0 ], cost: NONTERM
     21: l0 -> l0 : A^0'=0, R^0'=0, __rho_1_^0'=__rho_1_^post_7, __rho_2_^0'=__rho_2_^post_8, dobreak^0'=__rho_1_^post_7, n^0'=__rho_2_^post_8, [ dobreak^0<=0 && __rho_2_^post_8<=0 ], cost: 4
     11: l9 -> l0 : A^0'=0, R^0'=0, __rho_1_^0'=__rho_1_^post_10, dobreak^0'=__rho_1_^post_10, [], cost: 2

Accelerating simple loops of location 0.
   Accelerating the following rules:
     21: l0 -> l0 : A^0'=0, R^0'=0, __rho_1_^0'=__rho_1_^post_7, __rho_2_^0'=__rho_2_^post_8, dobreak^0'=__rho_1_^post_7, n^0'=__rho_2_^post_8, [ dobreak^0<=0 && __rho_2_^post_8<=0 ], cost: 4

[test] deduced pseudo-invariant -dobreak^0+__rho_1_^post_7<=0, also trying dobreak^0-__rho_1_^post_7<=-1
   Accelerated rule 21 with non-termination, yielding the new rule 22.
   Accelerated rule 21 with non-termination, yielding the new rule 23.
   Accelerated rule 21 with backward acceleration, yielding the new rule 24.
[accelerate] Nesting with 0 inner and 1 outer candidates
   Also removing duplicate rules: 23.

Accelerated all simple loops using metering functions (where possible):
   Start location: l9
     16: l0 -> [10] : [ 1<=dobreak^0 ], cost: NONTERM
     20: l0 -> [11] : [ dobreak^0<=0 ], cost: NONTERM
     21: l0 -> l0 : A^0'=0, R^0'=0, __rho_1_^0'=__rho_1_^post_7, __rho_2_^0'=__rho_2_^post_8, dobreak^0'=__rho_1_^post_7, n^0'=__rho_2_^post_8, [ dobreak^0<=0 && __rho_2_^post_8<=0 ], cost: 4
     22: l0 -> [12] : [ dobreak^0<=0 && __rho_2_^post_8<=0 && __rho_1_^post_7<=0 ], cost: NONTERM
     24: l0 -> [12] : [ dobreak^0<=0 && __rho_2_^post_8<=0 && -dobreak^0+__rho_1_^post_7<=0 ], cost: NONTERM
     11: l9 -> l0 : A^0'=0, R^0'=0, __rho_1_^0'=__rho_1_^post_10, dobreak^0'=__rho_1_^post_10, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l9
     16: l0 -> [10] : [ 1<=dobreak^0 ], cost: NONTERM
     20: l0 -> [11] : [ dobreak^0<=0 ], cost: NONTERM
     11: l9 -> l0 : A^0'=0, R^0'=0, __rho_1_^0'=__rho_1_^post_10, dobreak^0'=__rho_1_^post_10, [], cost: 2
     25: l9 -> l0 : A^0'=0, R^0'=0, __rho_1_^0'=__rho_1_^post_7, __rho_2_^0'=__rho_2_^post_8, dobreak^0'=__rho_1_^post_7, n^0'=__rho_2_^post_8, [ __rho_2_^post_8<=0 ], cost: 6
     26: l9 -> [12] : [], cost: NONTERM
     27: l9 -> [12] : [], cost: NONTERM

Eliminated locations (on tree-shaped paths):
   Start location: l9
     26: l9 -> [12] : [], cost: NONTERM
     27: l9 -> [12] : [], cost: NONTERM
     28: l9 -> [10] : [ 1<=__rho_1_^post_10 ], cost: NONTERM
     29: l9 -> [11] : [ __rho_1_^post_10<=0 ], cost: NONTERM
     30: l9 -> [10] : [ __rho_2_^post_8<=0 && 1<=__rho_1_^post_7 ], cost: NONTERM
     31: l9 -> [11] : [ __rho_2_^post_8<=0 && __rho_1_^post_7<=0 ], cost: NONTERM

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l9
     27: l9 -> [12] : [], cost: NONTERM
     28: l9 -> [10] : [ 1<=__rho_1_^post_10 ], cost: NONTERM
     29: l9 -> [11] : [ __rho_1_^post_10<=0 ], cost: NONTERM
     30: l9 -> [10] : [ __rho_2_^post_8<=0 && 1<=__rho_1_^post_7 ], cost: NONTERM
     31: l9 -> [11] : [ __rho_2_^post_8<=0 && __rho_1_^post_7<=0 ], cost: NONTERM

Computing asymptotic complexity for rule 27
   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