MAYBE

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

Proof:
 RT Transformation Processor:
  strict:
   a(x1) -> x1
   a(b(x1)) -> b(a(a(c(b(a(x1))))))
   b(x1) -> x1
   c(c(x1)) -> x1
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   interpretation:
    [c](x0) = x0,
    
    [b](x0) = x0 + 12,
    
    [a](x0) = x0 + 4
   orientation:
    a(x1) = x1 + 4 >= x1 = x1
    
    a(b(x1)) = x1 + 16 >= x1 + 36 = b(a(a(c(b(a(x1))))))
    
    b(x1) = x1 + 12 >= x1 = x1
    
    c(c(x1)) = x1 >= x1 = x1
   problem:
    strict:
     a(b(x1)) -> b(a(a(c(b(a(x1))))))
     c(c(x1)) -> x1
    weak:
     a(x1) -> x1
     b(x1) -> x1
   Matrix Interpretation Processor:
    dimension: 1
    interpretation:
     [c](x0) = x0 + 1,
     
     [b](x0) = x0,
     
     [a](x0) = x0 + 4
    orientation:
     a(b(x1)) = x1 + 4 >= x1 + 13 = b(a(a(c(b(a(x1))))))
     
     c(c(x1)) = x1 + 2 >= x1 = x1
     
     a(x1) = x1 + 4 >= x1 = x1
     
     b(x1) = x1 >= x1 = x1
    problem:
     strict:
      a(b(x1)) -> b(a(a(c(b(a(x1))))))
     weak:
      c(c(x1)) -> x1
      a(x1) -> x1
      b(x1) -> x1
    Open