MAYBE

Problem:
 active(f(X,X)) -> mark(f(a(),b()))
 active(b()) -> mark(a())
 active(f(X1,X2)) -> f(active(X1),X2)
 f(mark(X1),X2) -> mark(f(X1,X2))
 proper(f(X1,X2)) -> f(proper(X1),proper(X2))
 proper(a()) -> ok(a())
 proper(b()) -> ok(b())
 f(ok(X1),ok(X2)) -> ok(f(X1,X2))
 top(mark(X)) -> top(proper(X))
 top(ok(X)) -> top(active(X))

Proof:
 DP Processor:
  DPs:
   active#(f(X,X)) -> f#(a(),b())
   active#(f(X1,X2)) -> active#(X1)
   active#(f(X1,X2)) -> f#(active(X1),X2)
   f#(mark(X1),X2) -> f#(X1,X2)
   proper#(f(X1,X2)) -> proper#(X2)
   proper#(f(X1,X2)) -> proper#(X1)
   proper#(f(X1,X2)) -> f#(proper(X1),proper(X2))
   f#(ok(X1),ok(X2)) -> f#(X1,X2)
   top#(mark(X)) -> proper#(X)
   top#(mark(X)) -> top#(proper(X))
   top#(ok(X)) -> active#(X)
   top#(ok(X)) -> top#(active(X))
  TRS:
   active(f(X,X)) -> mark(f(a(),b()))
   active(b()) -> mark(a())
   active(f(X1,X2)) -> f(active(X1),X2)
   f(mark(X1),X2) -> mark(f(X1,X2))
   proper(f(X1,X2)) -> f(proper(X1),proper(X2))
   proper(a()) -> ok(a())
   proper(b()) -> ok(b())
   f(ok(X1),ok(X2)) -> ok(f(X1,X2))
   top(mark(X)) -> top(proper(X))
   top(ok(X)) -> top(active(X))
  TDG Processor:
   DPs:
    active#(f(X,X)) -> f#(a(),b())
    active#(f(X1,X2)) -> active#(X1)
    active#(f(X1,X2)) -> f#(active(X1),X2)
    f#(mark(X1),X2) -> f#(X1,X2)
    proper#(f(X1,X2)) -> proper#(X2)
    proper#(f(X1,X2)) -> proper#(X1)
    proper#(f(X1,X2)) -> f#(proper(X1),proper(X2))
    f#(ok(X1),ok(X2)) -> f#(X1,X2)
    top#(mark(X)) -> proper#(X)
    top#(mark(X)) -> top#(proper(X))
    top#(ok(X)) -> active#(X)
    top#(ok(X)) -> top#(active(X))
   TRS:
    active(f(X,X)) -> mark(f(a(),b()))
    active(b()) -> mark(a())
    active(f(X1,X2)) -> f(active(X1),X2)
    f(mark(X1),X2) -> mark(f(X1,X2))
    proper(f(X1,X2)) -> f(proper(X1),proper(X2))
    proper(a()) -> ok(a())
    proper(b()) -> ok(b())
    f(ok(X1),ok(X2)) -> ok(f(X1,X2))
    top(mark(X)) -> top(proper(X))
    top(ok(X)) -> top(active(X))
   graph:
    top#(ok(X)) -> top#(active(X)) -> top#(ok(X)) -> top#(active(X))
    top#(ok(X)) -> top#(active(X)) -> top#(ok(X)) -> active#(X)
    top#(ok(X)) -> top#(active(X)) ->
    top#(mark(X)) -> top#(proper(X))
    top#(ok(X)) -> top#(active(X)) -> top#(mark(X)) -> proper#(X)
    top#(ok(X)) -> active#(X) -> active#(f(X1,X2)) -> f#(active(X1),X2)
    top#(ok(X)) -> active#(X) -> active#(f(X1,X2)) -> active#(X1)
    top#(ok(X)) -> active#(X) -> active#(f(X,X)) -> f#(a(),b())
    top#(mark(X)) -> top#(proper(X)) ->
    top#(ok(X)) -> top#(active(X))
    top#(mark(X)) -> top#(proper(X)) -> top#(ok(X)) -> active#(X)
    top#(mark(X)) -> top#(proper(X)) ->
    top#(mark(X)) -> top#(proper(X))
    top#(mark(X)) -> top#(proper(X)) -> top#(mark(X)) -> proper#(X)
    top#(mark(X)) -> proper#(X) ->
    proper#(f(X1,X2)) -> f#(proper(X1),proper(X2))
    top#(mark(X)) -> proper#(X) -> proper#(f(X1,X2)) -> proper#(X1)
    top#(mark(X)) -> proper#(X) -> proper#(f(X1,X2)) -> proper#(X2)
    proper#(f(X1,X2)) -> proper#(X2) ->
    proper#(f(X1,X2)) -> f#(proper(X1),proper(X2))
    proper#(f(X1,X2)) -> proper#(X2) ->
    proper#(f(X1,X2)) -> proper#(X1)
    proper#(f(X1,X2)) -> proper#(X2) ->
    proper#(f(X1,X2)) -> proper#(X2)
    proper#(f(X1,X2)) -> proper#(X1) ->
    proper#(f(X1,X2)) -> f#(proper(X1),proper(X2))
    proper#(f(X1,X2)) -> proper#(X1) ->
    proper#(f(X1,X2)) -> proper#(X1)
    proper#(f(X1,X2)) -> proper#(X1) ->
    proper#(f(X1,X2)) -> proper#(X2)
    proper#(f(X1,X2)) -> f#(proper(X1),proper(X2)) ->
    f#(ok(X1),ok(X2)) -> f#(X1,X2)
    proper#(f(X1,X2)) -> f#(proper(X1),proper(X2)) ->
    f#(mark(X1),X2) -> f#(X1,X2)
    f#(ok(X1),ok(X2)) -> f#(X1,X2) -> f#(ok(X1),ok(X2)) -> f#(X1,X2)
    f#(ok(X1),ok(X2)) -> f#(X1,X2) -> f#(mark(X1),X2) -> f#(X1,X2)
    f#(mark(X1),X2) -> f#(X1,X2) -> f#(ok(X1),ok(X2)) -> f#(X1,X2)
    f#(mark(X1),X2) -> f#(X1,X2) ->
    f#(mark(X1),X2) -> f#(X1,X2)
    active#(f(X1,X2)) -> f#(active(X1),X2) ->
    f#(ok(X1),ok(X2)) -> f#(X1,X2)
    active#(f(X1,X2)) -> f#(active(X1),X2) ->
    f#(mark(X1),X2) -> f#(X1,X2)
    active#(f(X1,X2)) -> active#(X1) ->
    active#(f(X1,X2)) -> f#(active(X1),X2)
    active#(f(X1,X2)) -> active#(X1) ->
    active#(f(X1,X2)) -> active#(X1)
    active#(f(X1,X2)) -> active#(X1) ->
    active#(f(X,X)) -> f#(a(),b())
    active#(f(X,X)) -> f#(a(),b()) -> f#(ok(X1),ok(X2)) -> f#(X1,X2)
    active#(f(X,X)) -> f#(a(),b()) -> f#(mark(X1),X2) -> f#(X1,X2)
   SCC Processor:
    #sccs: 4
    #rules: 7
    #arcs: 33/144
    DPs:
     top#(ok(X)) -> top#(active(X))
     top#(mark(X)) -> top#(proper(X))
    TRS:
     active(f(X,X)) -> mark(f(a(),b()))
     active(b()) -> mark(a())
     active(f(X1,X2)) -> f(active(X1),X2)
     f(mark(X1),X2) -> mark(f(X1,X2))
     proper(f(X1,X2)) -> f(proper(X1),proper(X2))
     proper(a()) -> ok(a())
     proper(b()) -> ok(b())
     f(ok(X1),ok(X2)) -> ok(f(X1,X2))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Open
    
    DPs:
     active#(f(X1,X2)) -> active#(X1)
    TRS:
     active(f(X,X)) -> mark(f(a(),b()))
     active(b()) -> mark(a())
     active(f(X1,X2)) -> f(active(X1),X2)
     f(mark(X1),X2) -> mark(f(X1,X2))
     proper(f(X1,X2)) -> f(proper(X1),proper(X2))
     proper(a()) -> ok(a())
     proper(b()) -> ok(b())
     f(ok(X1),ok(X2)) -> ok(f(X1,X2))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Subterm Criterion Processor:
     simple projection:
      pi(active#) = 0
     problem:
      DPs:
       
      TRS:
       active(f(X,X)) -> mark(f(a(),b()))
       active(b()) -> mark(a())
       active(f(X1,X2)) -> f(active(X1),X2)
       f(mark(X1),X2) -> mark(f(X1,X2))
       proper(f(X1,X2)) -> f(proper(X1),proper(X2))
       proper(a()) -> ok(a())
       proper(b()) -> ok(b())
       f(ok(X1),ok(X2)) -> ok(f(X1,X2))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
     Qed
    
    DPs:
     proper#(f(X1,X2)) -> proper#(X2)
     proper#(f(X1,X2)) -> proper#(X1)
    TRS:
     active(f(X,X)) -> mark(f(a(),b()))
     active(b()) -> mark(a())
     active(f(X1,X2)) -> f(active(X1),X2)
     f(mark(X1),X2) -> mark(f(X1,X2))
     proper(f(X1,X2)) -> f(proper(X1),proper(X2))
     proper(a()) -> ok(a())
     proper(b()) -> ok(b())
     f(ok(X1),ok(X2)) -> ok(f(X1,X2))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Subterm Criterion Processor:
     simple projection:
      pi(proper#) = 0
     problem:
      DPs:
       
      TRS:
       active(f(X,X)) -> mark(f(a(),b()))
       active(b()) -> mark(a())
       active(f(X1,X2)) -> f(active(X1),X2)
       f(mark(X1),X2) -> mark(f(X1,X2))
       proper(f(X1,X2)) -> f(proper(X1),proper(X2))
       proper(a()) -> ok(a())
       proper(b()) -> ok(b())
       f(ok(X1),ok(X2)) -> ok(f(X1,X2))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
     Qed
    
    DPs:
     f#(mark(X1),X2) -> f#(X1,X2)
     f#(ok(X1),ok(X2)) -> f#(X1,X2)
    TRS:
     active(f(X,X)) -> mark(f(a(),b()))
     active(b()) -> mark(a())
     active(f(X1,X2)) -> f(active(X1),X2)
     f(mark(X1),X2) -> mark(f(X1,X2))
     proper(f(X1,X2)) -> f(proper(X1),proper(X2))
     proper(a()) -> ok(a())
     proper(b()) -> ok(b())
     f(ok(X1),ok(X2)) -> ok(f(X1,X2))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Subterm Criterion Processor:
     simple projection:
      pi(f#) = 1
     problem:
      DPs:
       f#(mark(X1),X2) -> f#(X1,X2)
      TRS:
       active(f(X,X)) -> mark(f(a(),b()))
       active(b()) -> mark(a())
       active(f(X1,X2)) -> f(active(X1),X2)
       f(mark(X1),X2) -> mark(f(X1,X2))
       proper(f(X1,X2)) -> f(proper(X1),proper(X2))
       proper(a()) -> ok(a())
       proper(b()) -> ok(b())
       f(ok(X1),ok(X2)) -> ok(f(X1,X2))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
     Subterm Criterion Processor:
      simple projection:
       pi(f#) = 0
      problem:
       DPs:
        
       TRS:
        active(f(X,X)) -> mark(f(a(),b()))
        active(b()) -> mark(a())
        active(f(X1,X2)) -> f(active(X1),X2)
        f(mark(X1),X2) -> mark(f(X1,X2))
        proper(f(X1,X2)) -> f(proper(X1),proper(X2))
        proper(a()) -> ok(a())
        proper(b()) -> ok(b())
        f(ok(X1),ok(X2)) -> ok(f(X1,X2))
        top(mark(X)) -> top(proper(X))
        top(ok(X)) -> top(active(X))
      Qed