MAYBE

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

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