YES

Problem:
 a__f(X,g(X),Y) -> a__f(Y,Y,Y)
 a__g(b()) -> c()
 a__b() -> c()
 mark(f(X1,X2,X3)) -> a__f(X1,X2,X3)
 mark(g(X)) -> a__g(mark(X))
 mark(b()) -> a__b()
 mark(c()) -> c()
 a__f(X1,X2,X3) -> f(X1,X2,X3)
 a__g(X) -> g(X)
 a__b() -> b()

Proof:
 DP Processor:
  DPs:
   a__f#(X,g(X),Y) -> a__f#(Y,Y,Y)
   mark#(f(X1,X2,X3)) -> a__f#(X1,X2,X3)
   mark#(g(X)) -> mark#(X)
   mark#(g(X)) -> a__g#(mark(X))
   mark#(b()) -> a__b#()
  TRS:
   a__f(X,g(X),Y) -> a__f(Y,Y,Y)
   a__g(b()) -> c()
   a__b() -> c()
   mark(f(X1,X2,X3)) -> a__f(X1,X2,X3)
   mark(g(X)) -> a__g(mark(X))
   mark(b()) -> a__b()
   mark(c()) -> c()
   a__f(X1,X2,X3) -> f(X1,X2,X3)
   a__g(X) -> g(X)
   a__b() -> b()
  TDG Processor:
   DPs:
    a__f#(X,g(X),Y) -> a__f#(Y,Y,Y)
    mark#(f(X1,X2,X3)) -> a__f#(X1,X2,X3)
    mark#(g(X)) -> mark#(X)
    mark#(g(X)) -> a__g#(mark(X))
    mark#(b()) -> a__b#()
   TRS:
    a__f(X,g(X),Y) -> a__f(Y,Y,Y)
    a__g(b()) -> c()
    a__b() -> c()
    mark(f(X1,X2,X3)) -> a__f(X1,X2,X3)
    mark(g(X)) -> a__g(mark(X))
    mark(b()) -> a__b()
    mark(c()) -> c()
    a__f(X1,X2,X3) -> f(X1,X2,X3)
    a__g(X) -> g(X)
    a__b() -> b()
   graph:
    mark#(f(X1,X2,X3)) -> a__f#(X1,X2,X3) -> a__f#(X,g(X),Y) -> a__f#(Y,Y,Y)
    mark#(g(X)) -> mark#(X) -> mark#(b()) -> a__b#()
    mark#(g(X)) -> mark#(X) -> mark#(g(X)) -> a__g#(mark(X))
    mark#(g(X)) -> mark#(X) -> mark#(g(X)) -> mark#(X)
    mark#(g(X)) -> mark#(X) -> mark#(f(X1,X2,X3)) -> a__f#(X1,X2,X3)
    a__f#(X,g(X),Y) -> a__f#(Y,Y,Y) -> a__f#(X,g(X),Y) -> a__f#(Y,Y,Y)
   EDG Processor:
    DPs:
     a__f#(X,g(X),Y) -> a__f#(Y,Y,Y)
     mark#(f(X1,X2,X3)) -> a__f#(X1,X2,X3)
     mark#(g(X)) -> mark#(X)
     mark#(g(X)) -> a__g#(mark(X))
     mark#(b()) -> a__b#()
    TRS:
     a__f(X,g(X),Y) -> a__f(Y,Y,Y)
     a__g(b()) -> c()
     a__b() -> c()
     mark(f(X1,X2,X3)) -> a__f(X1,X2,X3)
     mark(g(X)) -> a__g(mark(X))
     mark(b()) -> a__b()
     mark(c()) -> c()
     a__f(X1,X2,X3) -> f(X1,X2,X3)
     a__g(X) -> g(X)
     a__b() -> b()
    graph:
     mark#(f(X1,X2,X3)) -> a__f#(X1,X2,X3) ->
     a__f#(X,g(X),Y) -> a__f#(Y,Y,Y)
     mark#(g(X)) -> mark#(X) -> mark#(f(X1,X2,X3)) -> a__f#(X1,X2,X3)
     mark#(g(X)) -> mark#(X) -> mark#(g(X)) -> mark#(X)
     mark#(g(X)) -> mark#(X) -> mark#(g(X)) -> a__g#(mark(X))
     mark#(g(X)) -> mark#(X) -> mark#(b()) -> a__b#()
    SCC Processor:
     #sccs: 1
     #rules: 1
     #arcs: 5/25
     DPs:
      mark#(g(X)) -> mark#(X)
     TRS:
      a__f(X,g(X),Y) -> a__f(Y,Y,Y)
      a__g(b()) -> c()
      a__b() -> c()
      mark(f(X1,X2,X3)) -> a__f(X1,X2,X3)
      mark(g(X)) -> a__g(mark(X))
      mark(b()) -> a__b()
      mark(c()) -> c()
      a__f(X1,X2,X3) -> f(X1,X2,X3)
      a__g(X) -> g(X)
      a__b() -> b()
     Matrix Interpretation Processor:
      dimension: 1
      interpretation:
       [mark#](x0) = x0 + 1,
       
       [mark](x0) = x0 + 1,
       
       [f](x0, x1, x2) = 0,
       
       [a__b] = 1,
       
       [c] = 1,
       
       [a__g](x0) = x0 + 1,
       
       [b] = 0,
       
       [a__f](x0, x1, x2) = 1,
       
       [g](x0) = x0 + 1
      orientation:
       mark#(g(X)) = X + 2 >= X + 1 = mark#(X)
       
       a__f(X,g(X),Y) = 1 >= 1 = a__f(Y,Y,Y)
       
       a__g(b()) = 1 >= 1 = c()
       
       a__b() = 1 >= 1 = c()
       
       mark(f(X1,X2,X3)) = 1 >= 1 = a__f(X1,X2,X3)
       
       mark(g(X)) = X + 2 >= X + 2 = a__g(mark(X))
       
       mark(b()) = 1 >= 1 = a__b()
       
       mark(c()) = 2 >= 1 = c()
       
       a__f(X1,X2,X3) = 1 >= 0 = f(X1,X2,X3)
       
       a__g(X) = X + 1 >= X + 1 = g(X)
       
       a__b() = 1 >= 0 = b()
      problem:
       DPs:
        
       TRS:
        a__f(X,g(X),Y) -> a__f(Y,Y,Y)
        a__g(b()) -> c()
        a__b() -> c()
        mark(f(X1,X2,X3)) -> a__f(X1,X2,X3)
        mark(g(X)) -> a__g(mark(X))
        mark(b()) -> a__b()
        mark(c()) -> c()
        a__f(X1,X2,X3) -> f(X1,X2,X3)
        a__g(X) -> g(X)
        a__b() -> b()
      Qed