MAYBE

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

Proof:
 RT Transformation Processor:
  strict:
   a(x1) -> x1
   a(x1) -> b(x1)
   b(b(c(x1))) -> c(c(a(a(a(x1)))))
   c(x1) -> x1
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   interpretation:
    [c](x0) = x0,
    
    [b](x0) = x0,
    
    [a](x0) = x0 + 4
   orientation:
    a(x1) = x1 + 4 >= x1 = x1
    
    a(x1) = x1 + 4 >= x1 = b(x1)
    
    b(b(c(x1))) = x1 >= x1 + 12 = c(c(a(a(a(x1)))))
    
    c(x1) = x1 >= x1 = x1
   problem:
    strict:
     b(b(c(x1))) -> c(c(a(a(a(x1)))))
     c(x1) -> x1
    weak:
     a(x1) -> x1
     a(x1) -> b(x1)
   Matrix Interpretation Processor:
    dimension: 1
    interpretation:
     [c](x0) = x0 + 27,
     
     [b](x0) = x0,
     
     [a](x0) = x0
    orientation:
     b(b(c(x1))) = x1 + 27 >= x1 + 54 = c(c(a(a(a(x1)))))
     
     c(x1) = x1 + 27 >= x1 = x1
     
     a(x1) = x1 >= x1 = x1
     
     a(x1) = x1 >= x1 = b(x1)
    problem:
     strict:
      b(b(c(x1))) -> c(c(a(a(a(x1)))))
     weak:
      c(x1) -> x1
      a(x1) -> x1
      a(x1) -> b(x1)
    Open