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)
   Restore Modifier:
    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()
    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