MAYBE

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

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