MAYBE

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

Proof:
 DP Processor:
  DPs:
   g#(c(),g(a(x),y)) -> a#(y)
   g#(c(),g(a(x),y)) -> g#(a(y),x)
   g#(c(),g(a(x),y)) -> a#(b())
   g#(c(),g(a(x),y)) -> f#(a(b()))
   g#(c(),g(a(x),y)) -> g#(f(a(b())),g(a(y),x))
  TRS:
   g(c(),g(a(x),y)) -> g(f(a(b())),g(a(y),x))
   f(a(x)) -> c()
   a(b()) -> d()
  TDG Processor:
   DPs:
    g#(c(),g(a(x),y)) -> a#(y)
    g#(c(),g(a(x),y)) -> g#(a(y),x)
    g#(c(),g(a(x),y)) -> a#(b())
    g#(c(),g(a(x),y)) -> f#(a(b()))
    g#(c(),g(a(x),y)) -> g#(f(a(b())),g(a(y),x))
   TRS:
    g(c(),g(a(x),y)) -> g(f(a(b())),g(a(y),x))
    f(a(x)) -> c()
    a(b()) -> d()
   graph:
    g#(c(),g(a(x),y)) -> g#(f(a(b())),g(a(y),x)) ->
    g#(c(),g(a(x),y)) -> g#(f(a(b())),g(a(y),x))
    g#(c(),g(a(x),y)) -> g#(f(a(b())),g(a(y),x)) ->
    g#(c(),g(a(x),y)) -> f#(a(b()))
    g#(c(),g(a(x),y)) -> g#(f(a(b())),g(a(y),x)) ->
    g#(c(),g(a(x),y)) -> a#(b())
    g#(c(),g(a(x),y)) -> g#(f(a(b())),g(a(y),x)) ->
    g#(c(),g(a(x),y)) -> g#(a(y),x)
    g#(c(),g(a(x),y)) -> g#(f(a(b())),g(a(y),x)) ->
    g#(c(),g(a(x),y)) -> a#(y)
    g#(c(),g(a(x),y)) -> g#(a(y),x) ->
    g#(c(),g(a(x),y)) -> g#(f(a(b())),g(a(y),x))
    g#(c(),g(a(x),y)) -> g#(a(y),x) ->
    g#(c(),g(a(x),y)) -> f#(a(b()))
    g#(c(),g(a(x),y)) -> g#(a(y),x) -> g#(c(),g(a(x),y)) -> a#(b())
    g#(c(),g(a(x),y)) -> g#(a(y),x) ->
    g#(c(),g(a(x),y)) -> g#(a(y),x)
    g#(c(),g(a(x),y)) -> g#(a(y),x) -> g#(c(),g(a(x),y)) -> a#(y)
   SCC Processor:
    #sccs: 1
    #rules: 2
    #arcs: 10/25
    DPs:
     g#(c(),g(a(x),y)) -> g#(f(a(b())),g(a(y),x))
     g#(c(),g(a(x),y)) -> g#(a(y),x)
    TRS:
     g(c(),g(a(x),y)) -> g(f(a(b())),g(a(y),x))
     f(a(x)) -> c()
     a(b()) -> d()
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [g#](x0, x1) = x0,
      
      [d] = 0,
      
      [f](x0) = 1,
      
      [b] = 0,
      
      [g](x0, x1) = 1,
      
      [a](x0) = 0,
      
      [c] = 1
     orientation:
      g#(c(),g(a(x),y)) = 1 >= 1 = g#(f(a(b())),g(a(y),x))
      
      g#(c(),g(a(x),y)) = 1 >= 0 = g#(a(y),x)
      
      g(c(),g(a(x),y)) = 1 >= 1 = g(f(a(b())),g(a(y),x))
      
      f(a(x)) = 1 >= 1 = c()
      
      a(b()) = 0 >= 0 = d()
     problem:
      DPs:
       g#(c(),g(a(x),y)) -> g#(f(a(b())),g(a(y),x))
      TRS:
       g(c(),g(a(x),y)) -> g(f(a(b())),g(a(y),x))
       f(a(x)) -> c()
       a(b()) -> d()
     Open