MAYBE

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

Proof:
 DP Processor:
  DPs:
   b#(a(x1)) -> b#(x1)
   b#(a(x1)) -> b#(b(x1))
   b#(a(b(x1))) -> a#(x1)
   b#(a(b(x1))) -> a#(a(x1))
   b#(a(b(x1))) -> b#(a(a(x1)))
   a#(a(a(x1))) -> b#(x1)
   a#(a(a(x1))) -> b#(b(x1))
   a#(a(a(x1))) -> a#(b(b(x1)))
  TRS:
   b(a(x1)) -> b(b(x1))
   b(a(b(x1))) -> b(a(a(x1)))
   a(a(a(x1))) -> a(b(b(x1)))
  EDG Processor:
   DPs:
    b#(a(x1)) -> b#(x1)
    b#(a(x1)) -> b#(b(x1))
    b#(a(b(x1))) -> a#(x1)
    b#(a(b(x1))) -> a#(a(x1))
    b#(a(b(x1))) -> b#(a(a(x1)))
    a#(a(a(x1))) -> b#(x1)
    a#(a(a(x1))) -> b#(b(x1))
    a#(a(a(x1))) -> a#(b(b(x1)))
   TRS:
    b(a(x1)) -> b(b(x1))
    b(a(b(x1))) -> b(a(a(x1)))
    a(a(a(x1))) -> a(b(b(x1)))
   graph:
    a#(a(a(x1))) -> a#(b(b(x1))) -> a#(a(a(x1))) -> b#(x1)
    a#(a(a(x1))) -> a#(b(b(x1))) -> a#(a(a(x1))) -> b#(b(x1))
    a#(a(a(x1))) -> a#(b(b(x1))) -> a#(a(a(x1))) -> a#(b(b(x1)))
    a#(a(a(x1))) -> b#(b(x1)) -> b#(a(x1)) -> b#(x1)
    a#(a(a(x1))) -> b#(b(x1)) -> b#(a(x1)) -> b#(b(x1))
    a#(a(a(x1))) -> b#(b(x1)) -> b#(a(b(x1))) -> a#(x1)
    a#(a(a(x1))) -> b#(b(x1)) -> b#(a(b(x1))) -> a#(a(x1))
    a#(a(a(x1))) -> b#(b(x1)) -> b#(a(b(x1))) -> b#(a(a(x1)))
    a#(a(a(x1))) -> b#(x1) -> b#(a(x1)) -> b#(x1)
    a#(a(a(x1))) -> b#(x1) -> b#(a(x1)) -> b#(b(x1))
    a#(a(a(x1))) -> b#(x1) -> b#(a(b(x1))) -> a#(x1)
    a#(a(a(x1))) -> b#(x1) -> b#(a(b(x1))) -> a#(a(x1))
    a#(a(a(x1))) -> b#(x1) -> b#(a(b(x1))) -> b#(a(a(x1)))
    b#(a(b(x1))) -> a#(a(x1)) -> a#(a(a(x1))) -> b#(x1)
    b#(a(b(x1))) -> a#(a(x1)) -> a#(a(a(x1))) -> b#(b(x1))
    b#(a(b(x1))) -> a#(a(x1)) -> a#(a(a(x1))) -> a#(b(b(x1)))
    b#(a(b(x1))) -> a#(x1) -> a#(a(a(x1))) -> b#(x1)
    b#(a(b(x1))) -> a#(x1) -> a#(a(a(x1))) -> b#(b(x1))
    b#(a(b(x1))) -> a#(x1) -> a#(a(a(x1))) -> a#(b(b(x1)))
    b#(a(b(x1))) -> b#(a(a(x1))) -> b#(a(x1)) -> b#(x1)
    b#(a(b(x1))) -> b#(a(a(x1))) -> b#(a(x1)) -> b#(b(x1))
    b#(a(b(x1))) -> b#(a(a(x1))) -> b#(a(b(x1))) -> a#(x1)
    b#(a(b(x1))) -> b#(a(a(x1))) -> b#(a(b(x1))) -> a#(a(x1))
    b#(a(b(x1))) -> b#(a(a(x1))) -> b#(a(b(x1))) -> b#(a(a(x1)))
    b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> b#(x1)
    b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> b#(b(x1))
    b#(a(x1)) -> b#(b(x1)) -> b#(a(b(x1))) -> a#(x1)
    b#(a(x1)) -> b#(b(x1)) -> b#(a(b(x1))) -> a#(a(x1))
    b#(a(x1)) -> b#(b(x1)) -> b#(a(b(x1))) -> b#(a(a(x1)))
    b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1)
    b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(b(x1))
    b#(a(x1)) -> b#(x1) -> b#(a(b(x1))) -> a#(x1)
    b#(a(x1)) -> b#(x1) -> b#(a(b(x1))) -> a#(a(x1))
    b#(a(x1)) -> b#(x1) -> b#(a(b(x1))) -> b#(a(a(x1)))
   Matrix Interpretation Processor:
    dimension: 1
    interpretation:
     [a#](x0) = x0,
     
     [b#](x0) = x0 + 1,
     
     [b](x0) = x0 + 1,
     
     [a](x0) = x0 + 1
    orientation:
     b#(a(x1)) = x1 + 2 >= x1 + 1 = b#(x1)
     
     b#(a(x1)) = x1 + 2 >= x1 + 2 = b#(b(x1))
     
     b#(a(b(x1))) = x1 + 3 >= x1 = a#(x1)
     
     b#(a(b(x1))) = x1 + 3 >= x1 + 1 = a#(a(x1))
     
     b#(a(b(x1))) = x1 + 3 >= x1 + 3 = b#(a(a(x1)))
     
     a#(a(a(x1))) = x1 + 2 >= x1 + 1 = b#(x1)
     
     a#(a(a(x1))) = x1 + 2 >= x1 + 2 = b#(b(x1))
     
     a#(a(a(x1))) = x1 + 2 >= x1 + 2 = a#(b(b(x1)))
     
     b(a(x1)) = x1 + 2 >= x1 + 2 = b(b(x1))
     
     b(a(b(x1))) = x1 + 3 >= x1 + 3 = b(a(a(x1)))
     
     a(a(a(x1))) = x1 + 3 >= x1 + 3 = a(b(b(x1)))
    problem:
     DPs:
      b#(a(x1)) -> b#(b(x1))
      b#(a(b(x1))) -> b#(a(a(x1)))
      a#(a(a(x1))) -> b#(b(x1))
      a#(a(a(x1))) -> a#(b(b(x1)))
     TRS:
      b(a(x1)) -> b(b(x1))
      b(a(b(x1))) -> b(a(a(x1)))
      a(a(a(x1))) -> a(b(b(x1)))
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [a#](x0) = 1,
      
      [b#](x0) = 0,
      
      [b](x0) = 0,
      
      [a](x0) = 0
     orientation:
      b#(a(x1)) = 0 >= 0 = b#(b(x1))
      
      b#(a(b(x1))) = 0 >= 0 = b#(a(a(x1)))
      
      a#(a(a(x1))) = 1 >= 0 = b#(b(x1))
      
      a#(a(a(x1))) = 1 >= 1 = a#(b(b(x1)))
      
      b(a(x1)) = 0 >= 0 = b(b(x1))
      
      b(a(b(x1))) = 0 >= 0 = b(a(a(x1)))
      
      a(a(a(x1))) = 0 >= 0 = a(b(b(x1)))
     problem:
      DPs:
       b#(a(x1)) -> b#(b(x1))
       b#(a(b(x1))) -> b#(a(a(x1)))
       a#(a(a(x1))) -> a#(b(b(x1)))
      TRS:
       b(a(x1)) -> b(b(x1))
       b(a(b(x1))) -> b(a(a(x1)))
       a(a(a(x1))) -> a(b(b(x1)))
     Matrix Interpretation Processor:
      dimension: 1
      interpretation:
       [a#](x0) = x0 + 1,
       
       [b#](x0) = 0,
       
       [b](x0) = 1,
       
       [a](x0) = x0 + 1
      orientation:
       b#(a(x1)) = 0 >= 0 = b#(b(x1))
       
       b#(a(b(x1))) = 0 >= 0 = b#(a(a(x1)))
       
       a#(a(a(x1))) = x1 + 3 >= 2 = a#(b(b(x1)))
       
       b(a(x1)) = 1 >= 1 = b(b(x1))
       
       b(a(b(x1))) = 1 >= 1 = b(a(a(x1)))
       
       a(a(a(x1))) = x1 + 3 >= 2 = a(b(b(x1)))
      problem:
       DPs:
        b#(a(x1)) -> b#(b(x1))
        b#(a(b(x1))) -> b#(a(a(x1)))
       TRS:
        b(a(x1)) -> b(b(x1))
        b(a(b(x1))) -> b(a(a(x1)))
        a(a(a(x1))) -> a(b(b(x1)))
      Matrix Interpretation Processor:
       dimension: 1
       interpretation:
        [b#](x0) = x0,
        
        [b](x0) = 0,
        
        [a](x0) = 1
       orientation:
        b#(a(x1)) = 1 >= 0 = b#(b(x1))
        
        b#(a(b(x1))) = 1 >= 1 = b#(a(a(x1)))
        
        b(a(x1)) = 0 >= 0 = b(b(x1))
        
        b(a(b(x1))) = 0 >= 0 = b(a(a(x1)))
        
        a(a(a(x1))) = 1 >= 1 = a(b(b(x1)))
       problem:
        DPs:
         b#(a(b(x1))) -> b#(a(a(x1)))
        TRS:
         b(a(x1)) -> b(b(x1))
         b(a(b(x1))) -> b(a(a(x1)))
         a(a(a(x1))) -> a(b(b(x1)))
       Open