MAYBE

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

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