MAYBE

Problem:
 a(b(x)) -> b(a(a(x)))
 b(c(x)) -> c(b(b(x)))
 c(a(x)) -> a(c(c(x)))
 u(a(x)) -> x
 v(b(x)) -> x
 w(c(x)) -> x
 a(u(x)) -> x
 b(v(x)) -> x
 c(w(x)) -> x

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