NO

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

Initial linear ITS problem
   Start location: [0]
      0: [0] -> [1] : n_number'=nondet, numerator'=1, denominator'=1, nmul'=n_number, dmul'=r_number, nCr'=1, [ n_number>=1 ], cost: 1
      1: [1] -> [2] : [ n_number>=r_number ], cost: 1
      2: [1] -> [3] : [ n_number<r_number ], cost: 1
      3: [2] -> [4] : [ nCr>=1 ], cost: 1
      6: [2] -> [6] : [ numerator<1 ], cost: 1
      4: [4] -> [5] : numerator'=nmul*numerator, denominator'=dmul*denominator, nmul'=-1+nmul, dmul'=-1+dmul, [], cost: 1
      5: [5] -> [2] : [ 1>=1 ], cost: 1
      7: [6] -> [3] : nCr'=numerator*denominator^(-1), [], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
      0: [0] -> [1] : n_number'=nondet, numerator'=1, denominator'=1, nmul'=n_number, dmul'=r_number, nCr'=1, [ n_number>=1 ], cost: 1

Removed unreachable and leaf rules:
   Start location: [0]
      0: [0] -> [1] : n_number'=nondet, numerator'=1, denominator'=1, nmul'=n_number, dmul'=r_number, nCr'=1, [ n_number>=1 ], cost: 1
      1: [1] -> [2] : [ n_number>=r_number ], cost: 1
      3: [2] -> [4] : [ nCr>=1 ], cost: 1
      4: [4] -> [5] : numerator'=nmul*numerator, denominator'=dmul*denominator, nmul'=-1+nmul, dmul'=-1+dmul, [], cost: 1
      5: [5] -> [2] : [ 1>=1 ], cost: 1

Simplified all rules, resulting in:
   Start location: [0]
      0: [0] -> [1] : n_number'=nondet, numerator'=1, denominator'=1, nmul'=n_number, dmul'=r_number, nCr'=1, [ n_number>=1 ], cost: 1
      1: [1] -> [2] : [ n_number>=r_number ], cost: 1
      3: [2] -> [4] : [ nCr>=1 ], cost: 1
      4: [4] -> [5] : numerator'=nmul*numerator, denominator'=dmul*denominator, nmul'=-1+nmul, dmul'=-1+dmul, [], cost: 1
      5: [5] -> [2] : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: [0]
      8: [0] -> [2] : n_number'=nondet, numerator'=1, denominator'=1, nmul'=n_number, dmul'=r_number, nCr'=1, [ n_number>=1 && nondet>=r_number ], cost: 2
     10: [2] -> [2] : numerator'=nmul*numerator, denominator'=dmul*denominator, nmul'=-1+nmul, dmul'=-1+dmul, [ nCr>=1 ], cost: 3

Accelerating simple loops of location 2.
   Accelerating the following rules:
     10: [2] -> [2] : numerator'=nmul*numerator, denominator'=dmul*denominator, nmul'=-1+nmul, dmul'=-1+dmul, [ nCr>=1 ], cost: 3

   Accelerated rule 10 with non-termination, yielding the new rule 11.
[accelerate] Nesting with 0 inner and 0 outer candidates
   Removing the simple loops: 10.

Accelerated all simple loops using metering functions (where possible):
   Start location: [0]
      8: [0] -> [2] : n_number'=nondet, numerator'=1, denominator'=1, nmul'=n_number, dmul'=r_number, nCr'=1, [ n_number>=1 && nondet>=r_number ], cost: 2
     11: [2] -> [7] : [ nCr>=1 ], cost: NONTERM

Chained accelerated rules (with incoming rules):
   Start location: [0]
      8: [0] -> [2] : n_number'=nondet, numerator'=1, denominator'=1, nmul'=n_number, dmul'=r_number, nCr'=1, [ n_number>=1 && nondet>=r_number ], cost: 2
     12: [0] -> [7] : [ n_number>=1 ], cost: NONTERM

Removed unreachable locations (and leaf rules with constant cost):
   Start location: [0]
     12: [0] -> [7] : [ n_number>=1 ], cost: NONTERM

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: [0]
     12: [0] -> [7] : [ n_number>=1 ], cost: NONTERM

Computing asymptotic complexity for rule 12
   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:  [ n_number>=1 ]

NO