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

Simplified all rules, resulting in:
   Start location: l9
      0: l0 -> l1 : A^0'=0, __rho_1_^0'=n^post_1, n^0'=n^post_1, [ dobreak^0<=0 ], cost: 1
      1: l0 -> l2 : [ 1<=dobreak^0 ], cost: 1
      3: l1 -> l4 : [], cost: 1
      5: l2 -> l7 : [], cost: 1
      2: l3 -> l0 : [], cost: 1
      7: l4 -> l1 : n^0'=-1+n^0, [ 1<=n^0 ], cost: 1
      8: l4 -> l3 : R^0'=0, dobreak^0'=dobreak^post_9, [ n^0<=0 ], cost: 1
      6: l7 -> l2 : [], cost: 1
      9: l8 -> l3 : A^0'=0, R^0'=0, dobreak^0'=dobreak^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 : A^0'=0, __rho_1_^0'=n^post_1, n^0'=n^post_1, [ dobreak^0<=0 ], cost: 1
      1: l0 -> l2 : [ 1<=dobreak^0 ], cost: 1
      3: l1 -> l4 : [], cost: 1
     12: l2 -> l2 : [], cost: 2
      2: l3 -> l0 : [], cost: 1
      7: l4 -> l1 : n^0'=-1+n^0, [ 1<=n^0 ], cost: 1
      8: l4 -> l3 : R^0'=0, dobreak^0'=dobreak^post_9, [ n^0<=0 ], cost: 1
     11: l9 -> l3 : A^0'=0, R^0'=0, dobreak^0'=dobreak^post_10, [], cost: 2

Accelerating simple loops of location 2.
   Accelerating the following rules:
     12: l2 -> l2 : [], cost: 2

   Accelerated rule 12 with NONTERM, yielding the new rule 13.
   Removing the simple loops: 12.

Accelerated all simple loops using metering functions (where possible):
   Start location: l9
      0: l0 -> l1 : A^0'=0, __rho_1_^0'=n^post_1, n^0'=n^post_1, [ dobreak^0<=0 ], cost: 1
      1: l0 -> l2 : [ 1<=dobreak^0 ], cost: 1
      3: l1 -> l4 : [], cost: 1
     13: l2 -> [10] : [], cost: NONTERM
      2: l3 -> l0 : [], cost: 1
      7: l4 -> l1 : n^0'=-1+n^0, [ 1<=n^0 ], cost: 1
      8: l4 -> l3 : R^0'=0, dobreak^0'=dobreak^post_9, [ n^0<=0 ], cost: 1
     11: l9 -> l3 : A^0'=0, R^0'=0, dobreak^0'=dobreak^post_10, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l9
      0: l0 -> l1 : A^0'=0, __rho_1_^0'=n^post_1, n^0'=n^post_1, [ dobreak^0<=0 ], cost: 1
      1: l0 -> l2 : [ 1<=dobreak^0 ], cost: 1
     14: l0 -> [10] : [ 1<=dobreak^0 ], cost: NONTERM
      3: l1 -> l4 : [], cost: 1
      2: l3 -> l0 : [], cost: 1
      7: l4 -> l1 : n^0'=-1+n^0, [ 1<=n^0 ], cost: 1
      8: l4 -> l3 : R^0'=0, dobreak^0'=dobreak^post_9, [ n^0<=0 ], cost: 1
     11: l9 -> l3 : A^0'=0, R^0'=0, dobreak^0'=dobreak^post_10, [], cost: 2

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l9
      0: l0 -> l1 : A^0'=0, __rho_1_^0'=n^post_1, n^0'=n^post_1, [ dobreak^0<=0 ], cost: 1
     14: l0 -> [10] : [ 1<=dobreak^0 ], cost: NONTERM
      3: l1 -> l4 : [], cost: 1
      2: l3 -> l0 : [], cost: 1
      7: l4 -> l1 : n^0'=-1+n^0, [ 1<=n^0 ], cost: 1
      8: l4 -> l3 : R^0'=0, dobreak^0'=dobreak^post_9, [ n^0<=0 ], cost: 1
     11: l9 -> l3 : A^0'=0, R^0'=0, dobreak^0'=dobreak^post_10, [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: l9
     17: l1 -> l1 : n^0'=-1+n^0, [ 1<=n^0 ], cost: 2
     18: l1 -> l3 : R^0'=0, dobreak^0'=dobreak^post_9, [ n^0<=0 ], cost: 2
     15: l3 -> l1 : A^0'=0, __rho_1_^0'=n^post_1, n^0'=n^post_1, [ dobreak^0<=0 ], cost: 2
     16: l3 -> [10] : [ 1<=dobreak^0 ], cost: NONTERM
     11: l9 -> l3 : A^0'=0, R^0'=0, dobreak^0'=dobreak^post_10, [], cost: 2

Accelerating simple loops of location 1.
   Accelerating the following rules:
     17: l1 -> l1 : n^0'=-1+n^0, [ 1<=n^0 ], cost: 2

   Accelerated rule 17 with metering function n^0, yielding the new rule 19.
   Removing the simple loops: 17.

Accelerated all simple loops using metering functions (where possible):
   Start location: l9
     18: l1 -> l3 : R^0'=0, dobreak^0'=dobreak^post_9, [ n^0<=0 ], cost: 2
     19: l1 -> l1 : n^0'=0, [ 1<=n^0 ], cost: 2*n^0
     15: l3 -> l1 : A^0'=0, __rho_1_^0'=n^post_1, n^0'=n^post_1, [ dobreak^0<=0 ], cost: 2
     16: l3 -> [10] : [ 1<=dobreak^0 ], cost: NONTERM
     11: l9 -> l3 : A^0'=0, R^0'=0, dobreak^0'=dobreak^post_10, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l9
     18: l1 -> l3 : R^0'=0, dobreak^0'=dobreak^post_9, [ n^0<=0 ], cost: 2
     15: l3 -> l1 : A^0'=0, __rho_1_^0'=n^post_1, n^0'=n^post_1, [ dobreak^0<=0 ], cost: 2
     16: l3 -> [10] : [ 1<=dobreak^0 ], cost: NONTERM
     20: l3 -> l1 : A^0'=0, __rho_1_^0'=n^post_1, n^0'=0, [ dobreak^0<=0 && 1<=n^post_1 ], cost: 2+2*n^post_1
     11: l9 -> l3 : A^0'=0, R^0'=0, dobreak^0'=dobreak^post_10, [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: l9
     16: l3 -> [10] : [ 1<=dobreak^0 ], cost: NONTERM
     21: l3 -> l3 : A^0'=0, R^0'=0, __rho_1_^0'=n^post_1, dobreak^0'=dobreak^post_9, n^0'=n^post_1, [ dobreak^0<=0 && n^post_1<=0 ], cost: 4
     22: l3 -> l3 : A^0'=0, R^0'=0, __rho_1_^0'=n^post_1, dobreak^0'=dobreak^post_9, n^0'=0, [ dobreak^0<=0 && 1<=n^post_1 ], cost: 4+2*n^post_1
     11: l9 -> l3 : A^0'=0, R^0'=0, dobreak^0'=dobreak^post_10, [], cost: 2

Accelerating simple loops of location 3.
   Accelerating the following rules:
     21: l3 -> l3 : A^0'=0, R^0'=0, __rho_1_^0'=n^post_1, dobreak^0'=dobreak^post_9, n^0'=n^post_1, [ dobreak^0<=0 && n^post_1<=0 ], cost: 4
     22: l3 -> l3 : A^0'=0, R^0'=0, __rho_1_^0'=n^post_1, dobreak^0'=dobreak^post_9, n^0'=0, [ dobreak^0<=0 && 1<=n^post_1 ], cost: 4+2*n^post_1

   Accelerated rule 21 with NONTERM (after strengthening guard), yielding the new rule 23.
   Accelerated rule 22 with NONTERM (after strengthening guard), yielding the new rule 24.
   Removing the simple loops:.

Accelerated all simple loops using metering functions (where possible):
   Start location: l9
     16: l3 -> [10] : [ 1<=dobreak^0 ], cost: NONTERM
     21: l3 -> l3 : A^0'=0, R^0'=0, __rho_1_^0'=n^post_1, dobreak^0'=dobreak^post_9, n^0'=n^post_1, [ dobreak^0<=0 && n^post_1<=0 ], cost: 4
     22: l3 -> l3 : A^0'=0, R^0'=0, __rho_1_^0'=n^post_1, dobreak^0'=dobreak^post_9, n^0'=0, [ dobreak^0<=0 && 1<=n^post_1 ], cost: 4+2*n^post_1
     23: l3 -> [12] : [ dobreak^0<=0 && n^post_1<=0 && dobreak^post_9<=0 ], cost: NONTERM
     24: l3 -> [12] : [ dobreak^0<=0 && 1<=n^post_1 && dobreak^post_9<=0 && 4+2*n^post_1>=1 ], cost: NONTERM
     11: l9 -> l3 : A^0'=0, R^0'=0, dobreak^0'=dobreak^post_10, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l9
     16: l3 -> [10] : [ 1<=dobreak^0 ], cost: NONTERM
     11: l9 -> l3 : A^0'=0, R^0'=0, dobreak^0'=dobreak^post_10, [], cost: 2
     25: l9 -> l3 : A^0'=0, R^0'=0, __rho_1_^0'=n^post_1, dobreak^0'=dobreak^post_9, n^0'=n^post_1, [ n^post_1<=0 ], cost: 6
     26: l9 -> l3 : A^0'=0, R^0'=0, __rho_1_^0'=n^post_1, dobreak^0'=dobreak^post_9, n^0'=0, [ 1<=n^post_1 ], cost: 6+2*n^post_1
     27: l9 -> [12] : A^0'=0, R^0'=0, dobreak^0'=dobreak^post_10, [ dobreak^post_10<=0 ], cost: NONTERM
     28: l9 -> [12] : A^0'=0, R^0'=0, dobreak^0'=dobreak^post_10, [ dobreak^post_10<=0 && 1<=n^post_1 && 4+2*n^post_1>=1 ], cost: NONTERM

Eliminated locations (on tree-shaped paths):
   Start location: l9
     27: l9 -> [12] : A^0'=0, R^0'=0, dobreak^0'=dobreak^post_10, [ dobreak^post_10<=0 ], cost: NONTERM
     28: l9 -> [12] : A^0'=0, R^0'=0, dobreak^0'=dobreak^post_10, [ dobreak^post_10<=0 && 1<=n^post_1 && 4+2*n^post_1>=1 ], cost: NONTERM
     29: l9 -> [10] : A^0'=0, R^0'=0, dobreak^0'=dobreak^post_10, [ 1<=dobreak^post_10 ], cost: NONTERM
     30: l9 -> [10] : A^0'=0, R^0'=0, __rho_1_^0'=n^post_1, dobreak^0'=dobreak^post_9, n^0'=n^post_1, [ n^post_1<=0 && 1<=dobreak^post_9 ], cost: NONTERM
     31: l9 -> [10] : A^0'=0, R^0'=0, __rho_1_^0'=n^post_1, dobreak^0'=dobreak^post_9, n^0'=0, [ 1<=n^post_1 && 1<=dobreak^post_9 ], cost: NONTERM

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l9
     27: l9 -> [12] : A^0'=0, R^0'=0, dobreak^0'=dobreak^post_10, [ dobreak^post_10<=0 ], cost: NONTERM
     28: l9 -> [12] : A^0'=0, R^0'=0, dobreak^0'=dobreak^post_10, [ dobreak^post_10<=0 && 1<=n^post_1 && 4+2*n^post_1>=1 ], cost: NONTERM
     29: l9 -> [10] : A^0'=0, R^0'=0, dobreak^0'=dobreak^post_10, [ 1<=dobreak^post_10 ], cost: NONTERM
     30: l9 -> [10] : A^0'=0, R^0'=0, __rho_1_^0'=n^post_1, dobreak^0'=dobreak^post_9, n^0'=n^post_1, [ n^post_1<=0 && 1<=dobreak^post_9 ], cost: NONTERM
     31: l9 -> [10] : A^0'=0, R^0'=0, __rho_1_^0'=n^post_1, dobreak^0'=dobreak^post_9, n^0'=0, [ 1<=n^post_1 && 1<=dobreak^post_9 ], 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:  [ dobreak^post_10<=0 ]

NO