MAYBE

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

Proof:
 RT Transformation Processor:
  strict:
   a(x1) -> x1
   a(b(x1)) -> x1
   b(b(x1)) -> c(x1)
   c(a(x1)) -> a(a(b(c(x1))))
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   interpretation:
    [c](x0) = x0 + 8,
    
    [b](x0) = x0 + 1,
    
    [a](x0) = x0
   orientation:
    a(x1) = x1 >= x1 = x1
    
    a(b(x1)) = x1 + 1 >= x1 = x1
    
    b(b(x1)) = x1 + 2 >= x1 + 8 = c(x1)
    
    c(a(x1)) = x1 + 8 >= x1 + 9 = a(a(b(c(x1))))
   problem:
    strict:
     a(x1) -> x1
     b(b(x1)) -> c(x1)
     c(a(x1)) -> a(a(b(c(x1))))
    weak:
     a(b(x1)) -> x1
   Matrix Interpretation Processor:
    dimension: 1
    interpretation:
     [c](x0) = x0 + 5,
     
     [b](x0) = x0 + 16,
     
     [a](x0) = x0
    orientation:
     a(x1) = x1 >= x1 = x1
     
     b(b(x1)) = x1 + 32 >= x1 + 5 = c(x1)
     
     c(a(x1)) = x1 + 5 >= x1 + 21 = a(a(b(c(x1))))
     
     a(b(x1)) = x1 + 16 >= x1 = x1
    problem:
     strict:
      a(x1) -> x1
      c(a(x1)) -> a(a(b(c(x1))))
     weak:
      b(b(x1)) -> c(x1)
      a(b(x1)) -> x1
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [c](x0) = x0,
      
      [b](x0) = x0 + 2,
      
      [a](x0) = x0 + 2
     orientation:
      a(x1) = x1 + 2 >= x1 = x1
      
      c(a(x1)) = x1 + 2 >= x1 + 6 = a(a(b(c(x1))))
      
      b(b(x1)) = x1 + 4 >= x1 = c(x1)
      
      a(b(x1)) = x1 + 4 >= x1 = x1
     problem:
      strict:
       c(a(x1)) -> a(a(b(c(x1))))
      weak:
       a(x1) -> x1
       b(b(x1)) -> c(x1)
       a(b(x1)) -> x1
     Open