MAYBE

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

Proof:
 RT Transformation Processor:
  strict:
   a(x1) -> b(x1)
   a(b(x1)) -> b(a(c(a(x1))))
   b(x1) -> c(x1)
   c(c(x1)) -> x1
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   interpretation:
    [c](x0) = x0,
    
    [b](x0) = x0 + 5,
    
    [a](x0) = x0 + 16
   orientation:
    a(x1) = x1 + 16 >= x1 + 5 = b(x1)
    
    a(b(x1)) = x1 + 21 >= x1 + 37 = b(a(c(a(x1))))
    
    b(x1) = x1 + 5 >= x1 = c(x1)
    
    c(c(x1)) = x1 >= x1 = x1
   problem:
    strict:
     a(b(x1)) -> b(a(c(a(x1))))
     c(c(x1)) -> x1
    weak:
     a(x1) -> b(x1)
     b(x1) -> c(x1)
   Matrix Interpretation Processor:
    dimension: 1
    interpretation:
     [c](x0) = x0 + 8,
     
     [b](x0) = x0 + 10,
     
     [a](x0) = x0 + 11
    orientation:
     a(b(x1)) = x1 + 21 >= x1 + 40 = b(a(c(a(x1))))
     
     c(c(x1)) = x1 + 16 >= x1 = x1
     
     a(x1) = x1 + 11 >= x1 + 10 = b(x1)
     
     b(x1) = x1 + 10 >= x1 + 8 = c(x1)
    problem:
     strict:
      a(b(x1)) -> b(a(c(a(x1))))
     weak:
      c(c(x1)) -> x1
      a(x1) -> b(x1)
      b(x1) -> c(x1)
    Open