YES(?,O(n^1))

Problem:
 a(a(x1)) -> b(b(b(x1)))
 b(b(x1)) -> c(c(c(x1)))
 c(c(c(c(x1)))) -> a(b(x1))

Proof:
 RT Transformation Processor:
  strict:
   a(a(x1)) -> b(b(b(x1)))
   b(b(x1)) -> c(c(c(x1)))
   c(c(c(c(x1)))) -> a(b(x1))
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   interpretation:
    [c](x0) = x0,
    
    [b](x0) = x0 + 20,
    
    [a](x0) = x0 + 5
   orientation:
    a(a(x1)) = x1 + 10 >= x1 + 60 = b(b(b(x1)))
    
    b(b(x1)) = x1 + 40 >= x1 = c(c(c(x1)))
    
    c(c(c(c(x1)))) = x1 >= x1 + 25 = a(b(x1))
   problem:
    strict:
     a(a(x1)) -> b(b(b(x1)))
     c(c(c(c(x1)))) -> a(b(x1))
    weak:
     b(b(x1)) -> c(c(c(x1)))
   Matrix Interpretation Processor:
    dimension: 1
    interpretation:
     [c](x0) = x0 + 2,
     
     [b](x0) = x0 + 4,
     
     [a](x0) = x0 + 15
    orientation:
     a(a(x1)) = x1 + 30 >= x1 + 12 = b(b(b(x1)))
     
     c(c(c(c(x1)))) = x1 + 8 >= x1 + 19 = a(b(x1))
     
     b(b(x1)) = x1 + 8 >= x1 + 6 = c(c(c(x1)))
    problem:
     strict:
      c(c(c(c(x1)))) -> a(b(x1))
     weak:
      a(a(x1)) -> b(b(b(x1)))
      b(b(x1)) -> c(c(c(x1)))
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [c](x0) = x0 + 4,
      
      [b](x0) = x0 + 6,
      
      [a](x0) = x0 + 9
     orientation:
      c(c(c(c(x1)))) = x1 + 16 >= x1 + 15 = a(b(x1))
      
      a(a(x1)) = x1 + 18 >= x1 + 18 = b(b(b(x1)))
      
      b(b(x1)) = x1 + 12 >= x1 + 12 = c(c(c(x1)))
     problem:
      strict:
       
      weak:
       c(c(c(c(x1)))) -> a(b(x1))
       a(a(x1)) -> b(b(b(x1)))
       b(b(x1)) -> c(c(c(x1)))
     Qed