MAYBE

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

Proof:
 Complexity Transformation Processor:
  strict:
   a(a(x1)) -> d(c(x1))
   a(b(x1)) -> c(c(c(x1)))
   b(b(x1)) -> a(c(c(x1)))
   c(c(x1)) -> b(x1)
   c(d(x1)) -> a(a(x1))
   d(d(x1)) -> b(a(c(x1)))
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   max_matrix:
    1
    interpretation:
     [b](x0) = x0 + 1,
     
     [d](x0) = x0,
     
     [c](x0) = x0 + 1,
     
     [a](x0) = x0
    orientation:
     a(a(x1)) = x1 >= x1 + 1 = d(c(x1))
     
     a(b(x1)) = x1 + 1 >= x1 + 3 = c(c(c(x1)))
     
     b(b(x1)) = x1 + 2 >= x1 + 2 = a(c(c(x1)))
     
     c(c(x1)) = x1 + 2 >= x1 + 1 = b(x1)
     
     c(d(x1)) = x1 + 1 >= x1 = a(a(x1))
     
     d(d(x1)) = x1 >= x1 + 2 = b(a(c(x1)))
    problem:
     strict:
      a(a(x1)) -> d(c(x1))
      a(b(x1)) -> c(c(c(x1)))
      b(b(x1)) -> a(c(c(x1)))
      d(d(x1)) -> b(a(c(x1)))
     weak:
      c(c(x1)) -> b(x1)
      c(d(x1)) -> a(a(x1))
    Matrix Interpretation Processor:
     dimension: 1
     max_matrix:
      1
      interpretation:
       [b](x0) = x0,
       
       [d](x0) = x0 + 1,
       
       [c](x0) = x0,
       
       [a](x0) = x0
      orientation:
       a(a(x1)) = x1 >= x1 + 1 = d(c(x1))
       
       a(b(x1)) = x1 >= x1 = c(c(c(x1)))
       
       b(b(x1)) = x1 >= x1 = a(c(c(x1)))
       
       d(d(x1)) = x1 + 2 >= x1 = b(a(c(x1)))
       
       c(c(x1)) = x1 >= x1 = b(x1)
       
       c(d(x1)) = x1 + 1 >= x1 = a(a(x1))
      problem:
       strict:
        a(a(x1)) -> d(c(x1))
        a(b(x1)) -> c(c(c(x1)))
        b(b(x1)) -> a(c(c(x1)))
       weak:
        d(d(x1)) -> b(a(c(x1)))
        c(c(x1)) -> b(x1)
        c(d(x1)) -> a(a(x1))
      Open