MAYBE

Problem:
 f(b(a(),z)) -> z
 b(y,b(a(),z)) -> b(f(c(y,y,a())),b(f(z),a()))
 f(f(f(c(z,x,a())))) -> b(f(x),z)

Proof:
 DP Processor:
  DPs:
   b#(y,b(a(),z)) -> f#(z)
   b#(y,b(a(),z)) -> b#(f(z),a())
   b#(y,b(a(),z)) -> f#(c(y,y,a()))
   b#(y,b(a(),z)) -> b#(f(c(y,y,a())),b(f(z),a()))
   f#(f(f(c(z,x,a())))) -> f#(x)
   f#(f(f(c(z,x,a())))) -> b#(f(x),z)
  TRS:
   f(b(a(),z)) -> z
   b(y,b(a(),z)) -> b(f(c(y,y,a())),b(f(z),a()))
   f(f(f(c(z,x,a())))) -> b(f(x),z)
  EDG Processor:
   DPs:
    b#(y,b(a(),z)) -> f#(z)
    b#(y,b(a(),z)) -> b#(f(z),a())
    b#(y,b(a(),z)) -> f#(c(y,y,a()))
    b#(y,b(a(),z)) -> b#(f(c(y,y,a())),b(f(z),a()))
    f#(f(f(c(z,x,a())))) -> f#(x)
    f#(f(f(c(z,x,a())))) -> b#(f(x),z)
   TRS:
    f(b(a(),z)) -> z
    b(y,b(a(),z)) -> b(f(c(y,y,a())),b(f(z),a()))
    f(f(f(c(z,x,a())))) -> b(f(x),z)
   graph:
    b#(y,b(a(),z)) -> b#(f(c(y,y,a())),b(f(z),a())) ->
    b#(y,b(a(),z)) -> f#(z)
    b#(y,b(a(),z)) -> b#(f(c(y,y,a())),b(f(z),a())) ->
    b#(y,b(a(),z)) -> b#(f(z),a())
    b#(y,b(a(),z)) -> b#(f(c(y,y,a())),b(f(z),a())) ->
    b#(y,b(a(),z)) -> f#(c(y,y,a()))
    b#(y,b(a(),z)) -> b#(f(c(y,y,a())),b(f(z),a())) ->
    b#(y,b(a(),z)) -> b#(f(c(y,y,a())),b(f(z),a()))
    b#(y,b(a(),z)) -> f#(z) -> f#(f(f(c(z,x,a())))) -> f#(x)
    b#(y,b(a(),z)) -> f#(z) -> f#(f(f(c(z,x,a())))) -> b#(f(x),z)
    f#(f(f(c(z,x,a())))) -> b#(f(x),z) -> b#(y,b(a(),z)) -> f#(z)
    f#(f(f(c(z,x,a())))) -> b#(f(x),z) ->
    b#(y,b(a(),z)) -> b#(f(z),a())
    f#(f(f(c(z,x,a())))) -> b#(f(x),z) ->
    b#(y,b(a(),z)) -> f#(c(y,y,a()))
    f#(f(f(c(z,x,a())))) -> b#(f(x),z) ->
    b#(y,b(a(),z)) -> b#(f(c(y,y,a())),b(f(z),a()))
    f#(f(f(c(z,x,a())))) -> f#(x) -> f#(f(f(c(z,x,a())))) -> f#(x)
    f#(f(f(c(z,x,a())))) -> f#(x) -> f#(f(f(c(z,x,a())))) -> b#(f(x),z)
   SCC Processor:
    #sccs: 1
    #rules: 4
    #arcs: 12/36
    DPs:
     b#(y,b(a(),z)) -> b#(f(c(y,y,a())),b(f(z),a()))
     b#(y,b(a(),z)) -> f#(z)
     f#(f(f(c(z,x,a())))) -> b#(f(x),z)
     f#(f(f(c(z,x,a())))) -> f#(x)
    TRS:
     f(b(a(),z)) -> z
     b(y,b(a(),z)) -> b(f(c(y,y,a())),b(f(z),a()))
     f(f(f(c(z,x,a())))) -> b(f(x),z)
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [b#](x0, x1) = x1 + 1,
      
      [f#](x0) = x0 + 1,
      
      [c](x0, x1, x2) = x0 + x1 + 1,
      
      [f](x0) = x0,
      
      [b](x0, x1) = x1,
      
      [a] = 0
     orientation:
      b#(y,b(a(),z)) = z + 1 >= 1 = b#(f(c(y,y,a())),b(f(z),a()))
      
      b#(y,b(a(),z)) = z + 1 >= z + 1 = f#(z)
      
      f#(f(f(c(z,x,a())))) = x + z + 2 >= z + 1 = b#(f(x),z)
      
      f#(f(f(c(z,x,a())))) = x + z + 2 >= x + 1 = f#(x)
      
      f(b(a(),z)) = z >= z = z
      
      b(y,b(a(),z)) = z >= 0 = b(f(c(y,y,a())),b(f(z),a()))
      
      f(f(f(c(z,x,a())))) = x + z + 1 >= z = b(f(x),z)
     problem:
      DPs:
       b#(y,b(a(),z)) -> b#(f(c(y,y,a())),b(f(z),a()))
       b#(y,b(a(),z)) -> f#(z)
      TRS:
       f(b(a(),z)) -> z
       b(y,b(a(),z)) -> b(f(c(y,y,a())),b(f(z),a()))
       f(f(f(c(z,x,a())))) -> b(f(x),z)
     Matrix Interpretation Processor:
      dimension: 1
      interpretation:
       [b#](x0, x1) = 1,
       
       [f#](x0) = 0,
       
       [c](x0, x1, x2) = x0,
       
       [f](x0) = x0,
       
       [b](x0, x1) = x1,
       
       [a] = 0
      orientation:
       b#(y,b(a(),z)) = 1 >= 1 = b#(f(c(y,y,a())),b(f(z),a()))
       
       b#(y,b(a(),z)) = 1 >= 0 = f#(z)
       
       f(b(a(),z)) = z >= z = z
       
       b(y,b(a(),z)) = z >= 0 = b(f(c(y,y,a())),b(f(z),a()))
       
       f(f(f(c(z,x,a())))) = z >= z = b(f(x),z)
      problem:
       DPs:
        b#(y,b(a(),z)) -> b#(f(c(y,y,a())),b(f(z),a()))
       TRS:
        f(b(a(),z)) -> z
        b(y,b(a(),z)) -> b(f(c(y,y,a())),b(f(z),a()))
        f(f(f(c(z,x,a())))) -> b(f(x),z)
      Open