YES

Problem:
 strict:
  b(b(x1)) -> c(d(x1))
  c(c(x1)) -> d(d(d(x1)))
  d(d(d(x1))) -> a(c(x1))
 weak:
  a(a(x1)) -> b(c(x1))
  b(c(x1)) -> a(a(x1))

Proof:
 Arctic Interpretation Processor:
  dimension: 1
  interpretation:
   [d](x0) = 2x0,
   
   [a](x0) = 3x0,
   
   [b](x0) = 3x0,
   
   [c](x0) = 3x0
  orientation:
   b(b(x1)) = 6x1 >= 5x1 = c(d(x1))
   
   c(c(x1)) = 6x1 >= 6x1 = d(d(d(x1)))
   
   d(d(d(x1))) = 6x1 >= 6x1 = a(c(x1))
   
   a(a(x1)) = 6x1 >= 6x1 = b(c(x1))
   
   b(c(x1)) = 6x1 >= 6x1 = a(a(x1))
  problem:
   strict:
    c(c(x1)) -> d(d(d(x1)))
    d(d(d(x1))) -> a(c(x1))
   weak:
    a(a(x1)) -> b(c(x1))
    b(c(x1)) -> a(a(x1))
  String Reversal Processor:
   strict:
    c(c(x1)) -> d(d(d(x1)))
    d(d(d(x1))) -> c(a(x1))
   weak:
    a(a(x1)) -> c(b(x1))
    c(b(x1)) -> a(a(x1))
   Arctic Interpretation Processor:
    dimension: 1
    interpretation:
     [d](x0) = 4x0,
     
     [a](x0) = 4x0,
     
     [b](x0) = x0,
     
     [c](x0) = 8x0
    orientation:
     c(c(x1)) = 16x1 >= 12x1 = d(d(d(x1)))
     
     d(d(d(x1))) = 12x1 >= 12x1 = c(a(x1))
     
     a(a(x1)) = 8x1 >= 8x1 = c(b(x1))
     
     c(b(x1)) = 8x1 >= 8x1 = a(a(x1))
    problem:
     strict:
      d(d(d(x1))) -> c(a(x1))
     weak:
      a(a(x1)) -> c(b(x1))
      c(b(x1)) -> a(a(x1))
    Arctic Interpretation Processor:
     dimension: 1
     interpretation:
      [d](x0) = 1x0,
      
      [a](x0) = x0,
      
      [b](x0) = x0,
      
      [c](x0) = x0
     orientation:
      d(d(d(x1))) = 3x1 >= x1 = c(a(x1))
      
      a(a(x1)) = x1 >= x1 = c(b(x1))
      
      c(b(x1)) = x1 >= x1 = a(a(x1))
     problem:
      strict:
       
      weak:
       a(a(x1)) -> c(b(x1))
       c(b(x1)) -> a(a(x1))
     Qed