YES

Problem:
 s(a()) -> a()
 s(s(x)) -> x
 s(f(x,y)) -> f(s(y),s(x))
 s(g(x,y)) -> g(s(x),s(y))
 f(x,a()) -> x
 f(a(),y) -> y
 f(g(x,y),g(u,v)) -> g(f(x,u),f(y,v))
 g(a(),a()) -> a()

Proof:
 DP Processor:
  DPs:
   s#(f(x,y)) -> s#(x)
   s#(f(x,y)) -> s#(y)
   s#(f(x,y)) -> f#(s(y),s(x))
   s#(g(x,y)) -> s#(y)
   s#(g(x,y)) -> s#(x)
   s#(g(x,y)) -> g#(s(x),s(y))
   f#(g(x,y),g(u,v)) -> f#(y,v)
   f#(g(x,y),g(u,v)) -> f#(x,u)
   f#(g(x,y),g(u,v)) -> g#(f(x,u),f(y,v))
  TRS:
   s(a()) -> a()
   s(s(x)) -> x
   s(f(x,y)) -> f(s(y),s(x))
   s(g(x,y)) -> g(s(x),s(y))
   f(x,a()) -> x
   f(a(),y) -> y
   f(g(x,y),g(u,v)) -> g(f(x,u),f(y,v))
   g(a(),a()) -> a()
  TDG Processor:
   DPs:
    s#(f(x,y)) -> s#(x)
    s#(f(x,y)) -> s#(y)
    s#(f(x,y)) -> f#(s(y),s(x))
    s#(g(x,y)) -> s#(y)
    s#(g(x,y)) -> s#(x)
    s#(g(x,y)) -> g#(s(x),s(y))
    f#(g(x,y),g(u,v)) -> f#(y,v)
    f#(g(x,y),g(u,v)) -> f#(x,u)
    f#(g(x,y),g(u,v)) -> g#(f(x,u),f(y,v))
   TRS:
    s(a()) -> a()
    s(s(x)) -> x
    s(f(x,y)) -> f(s(y),s(x))
    s(g(x,y)) -> g(s(x),s(y))
    f(x,a()) -> x
    f(a(),y) -> y
    f(g(x,y),g(u,v)) -> g(f(x,u),f(y,v))
    g(a(),a()) -> a()
   graph:
    f#(g(x,y),g(u,v)) -> f#(y,v) ->
    f#(g(x,y),g(u,v)) -> g#(f(x,u),f(y,v))
    f#(g(x,y),g(u,v)) -> f#(y,v) -> f#(g(x,y),g(u,v)) -> f#(x,u)
    f#(g(x,y),g(u,v)) -> f#(y,v) -> f#(g(x,y),g(u,v)) -> f#(y,v)
    f#(g(x,y),g(u,v)) -> f#(x,u) ->
    f#(g(x,y),g(u,v)) -> g#(f(x,u),f(y,v))
    f#(g(x,y),g(u,v)) -> f#(x,u) -> f#(g(x,y),g(u,v)) -> f#(x,u)
    f#(g(x,y),g(u,v)) -> f#(x,u) -> f#(g(x,y),g(u,v)) -> f#(y,v)
    s#(g(x,y)) -> s#(y) -> s#(g(x,y)) -> g#(s(x),s(y))
    s#(g(x,y)) -> s#(y) -> s#(g(x,y)) -> s#(x)
    s#(g(x,y)) -> s#(y) -> s#(g(x,y)) -> s#(y)
    s#(g(x,y)) -> s#(y) -> s#(f(x,y)) -> f#(s(y),s(x))
    s#(g(x,y)) -> s#(y) -> s#(f(x,y)) -> s#(y)
    s#(g(x,y)) -> s#(y) -> s#(f(x,y)) -> s#(x)
    s#(g(x,y)) -> s#(x) -> s#(g(x,y)) -> g#(s(x),s(y))
    s#(g(x,y)) -> s#(x) -> s#(g(x,y)) -> s#(x)
    s#(g(x,y)) -> s#(x) -> s#(g(x,y)) -> s#(y)
    s#(g(x,y)) -> s#(x) -> s#(f(x,y)) -> f#(s(y),s(x))
    s#(g(x,y)) -> s#(x) -> s#(f(x,y)) -> s#(y)
    s#(g(x,y)) -> s#(x) -> s#(f(x,y)) -> s#(x)
    s#(f(x,y)) -> f#(s(y),s(x)) ->
    f#(g(x,y),g(u,v)) -> g#(f(x,u),f(y,v))
    s#(f(x,y)) -> f#(s(y),s(x)) -> f#(g(x,y),g(u,v)) -> f#(x,u)
    s#(f(x,y)) -> f#(s(y),s(x)) -> f#(g(x,y),g(u,v)) -> f#(y,v)
    s#(f(x,y)) -> s#(y) -> s#(g(x,y)) -> g#(s(x),s(y))
    s#(f(x,y)) -> s#(y) -> s#(g(x,y)) -> s#(x)
    s#(f(x,y)) -> s#(y) -> s#(g(x,y)) -> s#(y)
    s#(f(x,y)) -> s#(y) -> s#(f(x,y)) -> f#(s(y),s(x))
    s#(f(x,y)) -> s#(y) -> s#(f(x,y)) -> s#(y)
    s#(f(x,y)) -> s#(y) -> s#(f(x,y)) -> s#(x)
    s#(f(x,y)) -> s#(x) -> s#(g(x,y)) -> g#(s(x),s(y))
    s#(f(x,y)) -> s#(x) -> s#(g(x,y)) -> s#(x)
    s#(f(x,y)) -> s#(x) -> s#(g(x,y)) -> s#(y)
    s#(f(x,y)) -> s#(x) -> s#(f(x,y)) -> f#(s(y),s(x))
    s#(f(x,y)) -> s#(x) -> s#(f(x,y)) -> s#(y)
    s#(f(x,y)) -> s#(x) -> s#(f(x,y)) -> s#(x)
   CDG Processor:
    DPs:
     s#(f(x,y)) -> s#(x)
     s#(f(x,y)) -> s#(y)
     s#(f(x,y)) -> f#(s(y),s(x))
     s#(g(x,y)) -> s#(y)
     s#(g(x,y)) -> s#(x)
     s#(g(x,y)) -> g#(s(x),s(y))
     f#(g(x,y),g(u,v)) -> f#(y,v)
     f#(g(x,y),g(u,v)) -> f#(x,u)
     f#(g(x,y),g(u,v)) -> g#(f(x,u),f(y,v))
    TRS:
     s(a()) -> a()
     s(s(x)) -> x
     s(f(x,y)) -> f(s(y),s(x))
     s(g(x,y)) -> g(s(x),s(y))
     f(x,a()) -> x
     f(a(),y) -> y
     f(g(x,y),g(u,v)) -> g(f(x,u),f(y,v))
     g(a(),a()) -> a()
    graph:
     s#(f(x,y)) -> f#(s(y),s(x)) -> f#(g(x,y),g(u,v)) -> f#(y,v)
     s#(f(x,y)) -> f#(s(y),s(x)) -> f#(g(x,y),g(u,v)) -> f#(x,u)
     s#(f(x,y)) -> f#(s(y),s(x)) -> f#(g(x,y),g(u,v)) -> g#(f(x,u),f(y,v))
    SCC Processor:
     #sccs: 0
     #rules: 0
     #arcs: 3/81