MAYBE

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

Proof:
 RT Transformation Processor:
  strict:
   a(x1) -> x1
   a(b(x1)) -> b(b(a(x1)))
   b(x1) -> c(a(c(x1)))
   c(c(x1)) -> x1
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   interpretation:
    [c](x0) = x0,
    
    [b](x0) = x0 + 4,
    
    [a](x0) = x0 + 10
   orientation:
    a(x1) = x1 + 10 >= x1 = x1
    
    a(b(x1)) = x1 + 14 >= x1 + 18 = b(b(a(x1)))
    
    b(x1) = x1 + 4 >= x1 + 10 = c(a(c(x1)))
    
    c(c(x1)) = x1 >= x1 = x1
   problem:
    strict:
     a(b(x1)) -> b(b(a(x1)))
     b(x1) -> c(a(c(x1)))
     c(c(x1)) -> x1
    weak:
     a(x1) -> x1
   Matrix Interpretation Processor:
    dimension: 1
    interpretation:
     [c](x0) = x0 + 11,
     
     [b](x0) = x0 + 11,
     
     [a](x0) = x0 + 13
    orientation:
     a(b(x1)) = x1 + 24 >= x1 + 35 = b(b(a(x1)))
     
     b(x1) = x1 + 11 >= x1 + 35 = c(a(c(x1)))
     
     c(c(x1)) = x1 + 22 >= x1 = x1
     
     a(x1) = x1 + 13 >= x1 = x1
    problem:
     strict:
      a(b(x1)) -> b(b(a(x1)))
      b(x1) -> c(a(c(x1)))
     weak:
      c(c(x1)) -> x1
      a(x1) -> x1
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [c](x0) = x0,
      
      [b](x0) = x0 + 25,
      
      [a](x0) = x0 + 8
     orientation:
      a(b(x1)) = x1 + 33 >= x1 + 58 = b(b(a(x1)))
      
      b(x1) = x1 + 25 >= x1 + 8 = c(a(c(x1)))
      
      c(c(x1)) = x1 >= x1 = x1
      
      a(x1) = x1 + 8 >= x1 = x1
     problem:
      strict:
       a(b(x1)) -> b(b(a(x1)))
      weak:
       b(x1) -> c(a(c(x1)))
       c(c(x1)) -> x1
       a(x1) -> x1
     Open