MAYBE

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)
   SCC Processor:
    #sccs: 2
    #rules: 2
    #arcs: 6/25
    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()
    Subterm Criterion Processor:
     simple projection:
      pi(mark#) = 0
     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
    
    DPs:
     a__f#(X,g(X),Y) -> a__f#(Y,Y,Y)
    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()
    Open