MAYBE

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

Proof:
 DP Processor:
  DPs:
   a#(b(a(x1))) -> b#(x1)
   a#(b(a(x1))) -> b#(b(x1))
   a#(b(a(x1))) -> b#(b(b(x1)))
   b#(a(b(x1))) -> a#(x1)
   b#(a(b(x1))) -> b#(a(x1))
   b#(a(b(x1))) -> a#(b(a(x1)))
  TRS:
   a(b(a(x1))) -> b(b(b(x1)))
   b(a(b(x1))) -> a(b(a(x1)))
  CDG Processor:
   DPs:
    a#(b(a(x1))) -> b#(x1)
    a#(b(a(x1))) -> b#(b(x1))
    a#(b(a(x1))) -> b#(b(b(x1)))
    b#(a(b(x1))) -> a#(x1)
    b#(a(b(x1))) -> b#(a(x1))
    b#(a(b(x1))) -> a#(b(a(x1)))
   TRS:
    a(b(a(x1))) -> b(b(b(x1)))
    b(a(b(x1))) -> a(b(a(x1)))
   graph:
    b#(a(b(x1))) -> b#(a(x1)) -> b#(a(b(x1))) -> a#(x1)
    b#(a(b(x1))) -> b#(a(x1)) -> b#(a(b(x1))) -> b#(a(x1))
    b#(a(b(x1))) -> b#(a(x1)) -> b#(a(b(x1))) -> a#(b(a(x1)))
    b#(a(b(x1))) -> a#(b(a(x1))) -> a#(b(a(x1))) -> b#(x1)
    b#(a(b(x1))) -> a#(b(a(x1))) -> a#(b(a(x1))) -> b#(b(x1))
    b#(a(b(x1))) -> a#(b(a(x1))) -> a#(b(a(x1))) -> b#(b(b(x1)))
    b#(a(b(x1))) -> a#(x1) -> a#(b(a(x1))) -> b#(x1)
    b#(a(b(x1))) -> a#(x1) -> a#(b(a(x1))) -> b#(b(x1))
    b#(a(b(x1))) -> a#(x1) -> a#(b(a(x1))) -> b#(b(b(x1)))
    a#(b(a(x1))) -> b#(b(b(x1))) -> b#(a(b(x1))) -> a#(x1)
    a#(b(a(x1))) -> b#(b(b(x1))) -> b#(a(b(x1))) -> b#(a(x1))
    a#(b(a(x1))) -> b#(b(b(x1))) -> b#(a(b(x1))) -> a#(b(a(x1)))
    a#(b(a(x1))) -> b#(b(x1)) -> b#(a(b(x1))) -> a#(x1)
    a#(b(a(x1))) -> b#(b(x1)) -> b#(a(b(x1))) -> b#(a(x1))
    a#(b(a(x1))) -> b#(b(x1)) -> b#(a(b(x1))) -> a#(b(a(x1)))
    a#(b(a(x1))) -> b#(x1) -> b#(a(b(x1))) -> a#(x1)
    a#(b(a(x1))) -> b#(x1) -> b#(a(b(x1))) -> b#(a(x1))
    a#(b(a(x1))) -> b#(x1) -> b#(a(b(x1))) -> a#(b(a(x1)))
   Restore Modifier:
    DPs:
     a#(b(a(x1))) -> b#(x1)
     a#(b(a(x1))) -> b#(b(x1))
     a#(b(a(x1))) -> b#(b(b(x1)))
     b#(a(b(x1))) -> a#(x1)
     b#(a(b(x1))) -> b#(a(x1))
     b#(a(b(x1))) -> a#(b(a(x1)))
    TRS:
     a(b(a(x1))) -> b(b(b(x1)))
     b(a(b(x1))) -> a(b(a(x1)))
    SCC Processor:
     #sccs: 1
     #rules: 6
     #arcs: 18/36
     DPs:
      b#(a(b(x1))) -> b#(a(x1))
      b#(a(b(x1))) -> a#(b(a(x1)))
      a#(b(a(x1))) -> b#(b(b(x1)))
      b#(a(b(x1))) -> a#(x1)
      a#(b(a(x1))) -> b#(b(x1))
      a#(b(a(x1))) -> b#(x1)
     TRS:
      a(b(a(x1))) -> b(b(b(x1)))
      b(a(b(x1))) -> a(b(a(x1)))
     Matrix Interpretation Processor:
      dimension: 1
      interpretation:
       [b#](x0) = x0,
       
       [a#](x0) = x0,
       
       [b](x0) = x0 + 1,
       
       [a](x0) = x0 + 1
      orientation:
       b#(a(b(x1))) = x1 + 2 >= x1 + 1 = b#(a(x1))
       
       b#(a(b(x1))) = x1 + 2 >= x1 + 2 = a#(b(a(x1)))
       
       a#(b(a(x1))) = x1 + 2 >= x1 + 2 = b#(b(b(x1)))
       
       b#(a(b(x1))) = x1 + 2 >= x1 = a#(x1)
       
       a#(b(a(x1))) = x1 + 2 >= x1 + 1 = b#(b(x1))
       
       a#(b(a(x1))) = x1 + 2 >= x1 = b#(x1)
       
       a(b(a(x1))) = x1 + 3 >= x1 + 3 = b(b(b(x1)))
       
       b(a(b(x1))) = x1 + 3 >= x1 + 3 = a(b(a(x1)))
      problem:
       DPs:
        b#(a(b(x1))) -> a#(b(a(x1)))
        a#(b(a(x1))) -> b#(b(b(x1)))
       TRS:
        a(b(a(x1))) -> b(b(b(x1)))
        b(a(b(x1))) -> a(b(a(x1)))
      Open