YES(?,O(n^1))

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

Proof:
 RT Transformation Processor:
  strict:
   b(b(x1)) -> c(c(c(c(x1))))
   c(x1) -> x1
   b(c(b(x1))) -> b(b(b(x1)))
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   interpretation:
    [c](x0) = x0 + 1,
    
    [b](x0) = x0
   orientation:
    b(b(x1)) = x1 >= x1 + 4 = c(c(c(c(x1))))
    
    c(x1) = x1 + 1 >= x1 = x1
    
    b(c(b(x1))) = x1 + 1 >= x1 = b(b(b(x1)))
   problem:
    strict:
     b(b(x1)) -> c(c(c(c(x1))))
    weak:
     c(x1) -> x1
     b(c(b(x1))) -> b(b(b(x1)))
   Arctic Interpretation Processor:
    dimension: 2
    interpretation:
               [0 0]  
     [c](x0) = [0 0]x0,
     
               [1 0]  
     [b](x0) = [2 1]x0
    orientation:
                [2 1]      [0 0]                   
     b(b(x1)) = [3 2]x1 >= [0 0]x1 = c(c(c(c(x1))))
     
             [0 0]             
     c(x1) = [0 0]x1 >= x1 = x1
     
                   [3 2]      [3 2]                
     b(c(b(x1))) = [4 3]x1 >= [4 3]x1 = b(b(b(x1)))
    problem:
     strict:
      
     weak:
      b(b(x1)) -> c(c(c(c(x1))))
      c(x1) -> x1
      b(c(b(x1))) -> b(b(b(x1)))
    Qed