MAYBE

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

Proof:
 DP Processor:
  DPs:
   b#(b(b(x1))) -> a#(b(x1))
   b#(b(b(x1))) -> b#(a(b(x1)))
   a#(a(x1)) -> b#(x1)
   a#(a(x1)) -> b#(b(x1))
   a#(a(x1)) -> b#(b(b(x1)))
  TRS:
   a(b(a(x1))) -> b(a(x1))
   b(b(b(x1))) -> b(a(b(x1)))
   a(a(x1)) -> b(b(b(x1)))
  TDG Processor:
   DPs:
    b#(b(b(x1))) -> a#(b(x1))
    b#(b(b(x1))) -> b#(a(b(x1)))
    a#(a(x1)) -> b#(x1)
    a#(a(x1)) -> b#(b(x1))
    a#(a(x1)) -> b#(b(b(x1)))
   TRS:
    a(b(a(x1))) -> b(a(x1))
    b(b(b(x1))) -> b(a(b(x1)))
    a(a(x1)) -> b(b(b(x1)))
   graph:
    b#(b(b(x1))) -> b#(a(b(x1))) -> b#(b(b(x1))) -> b#(a(b(x1)))
    b#(b(b(x1))) -> b#(a(b(x1))) -> b#(b(b(x1))) -> a#(b(x1))
    b#(b(b(x1))) -> a#(b(x1)) -> a#(a(x1)) -> b#(b(b(x1)))
    b#(b(b(x1))) -> a#(b(x1)) -> a#(a(x1)) -> b#(b(x1))
    b#(b(b(x1))) -> a#(b(x1)) -> a#(a(x1)) -> b#(x1)
    a#(a(x1)) -> b#(b(b(x1))) -> b#(b(b(x1))) -> b#(a(b(x1)))
    a#(a(x1)) -> b#(b(b(x1))) -> b#(b(b(x1))) -> a#(b(x1))
    a#(a(x1)) -> b#(b(x1)) -> b#(b(b(x1))) -> b#(a(b(x1)))
    a#(a(x1)) -> b#(b(x1)) -> b#(b(b(x1))) -> a#(b(x1))
    a#(a(x1)) -> b#(x1) -> b#(b(b(x1))) -> b#(a(b(x1)))
    a#(a(x1)) -> b#(x1) -> b#(b(b(x1))) -> a#(b(x1))
   Restore Modifier:
    DPs:
     b#(b(b(x1))) -> a#(b(x1))
     b#(b(b(x1))) -> b#(a(b(x1)))
     a#(a(x1)) -> b#(x1)
     a#(a(x1)) -> b#(b(x1))
     a#(a(x1)) -> b#(b(b(x1)))
    TRS:
     a(b(a(x1))) -> b(a(x1))
     b(b(b(x1))) -> b(a(b(x1)))
     a(a(x1)) -> b(b(b(x1)))
    SCC Processor:
     #sccs: 1
     #rules: 5
     #arcs: 11/25
     DPs:
      b#(b(b(x1))) -> b#(a(b(x1)))
      b#(b(b(x1))) -> a#(b(x1))
      a#(a(x1)) -> b#(x1)
      a#(a(x1)) -> b#(b(x1))
      a#(a(x1)) -> b#(b(b(x1)))
     TRS:
      a(b(a(x1))) -> b(a(x1))
      b(b(b(x1))) -> b(a(b(x1)))
      a(a(x1)) -> b(b(b(x1)))
     Matrix Interpretation Processor:
      dimension: 1
      interpretation:
       [b#](x0) = 0,
       
       [a#](x0) = x0,
       
       [b](x0) = 0,
       
       [a](x0) = x0 + 1
      orientation:
       b#(b(b(x1))) = 0 >= 0 = b#(a(b(x1)))
       
       b#(b(b(x1))) = 0 >= 0 = a#(b(x1))
       
       a#(a(x1)) = x1 + 1 >= 0 = b#(x1)
       
       a#(a(x1)) = x1 + 1 >= 0 = b#(b(x1))
       
       a#(a(x1)) = x1 + 1 >= 0 = b#(b(b(x1)))
       
       a(b(a(x1))) = 1 >= 0 = b(a(x1))
       
       b(b(b(x1))) = 0 >= 0 = b(a(b(x1)))
       
       a(a(x1)) = x1 + 2 >= 0 = b(b(b(x1)))
      problem:
       DPs:
        b#(b(b(x1))) -> b#(a(b(x1)))
        b#(b(b(x1))) -> a#(b(x1))
       TRS:
        a(b(a(x1))) -> b(a(x1))
        b(b(b(x1))) -> b(a(b(x1)))
        a(a(x1)) -> b(b(b(x1)))
      Matrix Interpretation Processor:
       dimension: 1
       interpretation:
        [b#](x0) = x0,
        
        [a#](x0) = 0,
        
        [b](x0) = 1,
        
        [a](x0) = 1
       orientation:
        b#(b(b(x1))) = 1 >= 1 = b#(a(b(x1)))
        
        b#(b(b(x1))) = 1 >= 0 = a#(b(x1))
        
        a(b(a(x1))) = 1 >= 1 = b(a(x1))
        
        b(b(b(x1))) = 1 >= 1 = b(a(b(x1)))
        
        a(a(x1)) = 1 >= 1 = b(b(b(x1)))
       problem:
        DPs:
         b#(b(b(x1))) -> b#(a(b(x1)))
        TRS:
         a(b(a(x1))) -> b(a(x1))
         b(b(b(x1))) -> b(a(b(x1)))
         a(a(x1)) -> b(b(b(x1)))
       Open