MAYBE

Problem:
 active(f(a(),b(),X)) -> mark(f(X,X,X))
 active(c()) -> mark(a())
 active(c()) -> mark(b())
 active(f(X1,X2,X3)) -> f(X1,X2,active(X3))
 f(X1,X2,mark(X3)) -> mark(f(X1,X2,X3))
 proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3))
 proper(a()) -> ok(a())
 proper(b()) -> ok(b())
 proper(c()) -> ok(c())
 f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3))
 top(mark(X)) -> top(proper(X))
 top(ok(X)) -> top(active(X))

Proof:
 DP Processor:
  DPs:
   active#(f(a(),b(),X)) -> f#(X,X,X)
   active#(f(X1,X2,X3)) -> active#(X3)
   active#(f(X1,X2,X3)) -> f#(X1,X2,active(X3))
   f#(X1,X2,mark(X3)) -> f#(X1,X2,X3)
   proper#(f(X1,X2,X3)) -> proper#(X3)
   proper#(f(X1,X2,X3)) -> proper#(X2)
   proper#(f(X1,X2,X3)) -> proper#(X1)
   proper#(f(X1,X2,X3)) -> f#(proper(X1),proper(X2),proper(X3))
   f#(ok(X1),ok(X2),ok(X3)) -> f#(X1,X2,X3)
   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(a(),b(),X)) -> mark(f(X,X,X))
   active(c()) -> mark(a())
   active(c()) -> mark(b())
   active(f(X1,X2,X3)) -> f(X1,X2,active(X3))
   f(X1,X2,mark(X3)) -> mark(f(X1,X2,X3))
   proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3))
   proper(a()) -> ok(a())
   proper(b()) -> ok(b())
   proper(c()) -> ok(c())
   f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3))
   top(mark(X)) -> top(proper(X))
   top(ok(X)) -> top(active(X))
  TDG Processor:
   DPs:
    active#(f(a(),b(),X)) -> f#(X,X,X)
    active#(f(X1,X2,X3)) -> active#(X3)
    active#(f(X1,X2,X3)) -> f#(X1,X2,active(X3))
    f#(X1,X2,mark(X3)) -> f#(X1,X2,X3)
    proper#(f(X1,X2,X3)) -> proper#(X3)
    proper#(f(X1,X2,X3)) -> proper#(X2)
    proper#(f(X1,X2,X3)) -> proper#(X1)
    proper#(f(X1,X2,X3)) -> f#(proper(X1),proper(X2),proper(X3))
    f#(ok(X1),ok(X2),ok(X3)) -> f#(X1,X2,X3)
    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(a(),b(),X)) -> mark(f(X,X,X))
    active(c()) -> mark(a())
    active(c()) -> mark(b())
    active(f(X1,X2,X3)) -> f(X1,X2,active(X3))
    f(X1,X2,mark(X3)) -> mark(f(X1,X2,X3))
    proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3))
    proper(a()) -> ok(a())
    proper(b()) -> ok(b())
    proper(c()) -> ok(c())
    f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3))
    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,X3)) -> f#(X1,X2,active(X3))
    top#(ok(X)) -> active#(X) -> active#(f(X1,X2,X3)) -> active#(X3)
    top#(ok(X)) -> active#(X) -> active#(f(a(),b(),X)) -> f#(X,X,X)
    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,X3)) -> f#(proper(X1),proper(X2),proper(X3))
    top#(mark(X)) -> proper#(X) -> proper#(f(X1,X2,X3)) -> proper#(X1)
    top#(mark(X)) -> proper#(X) -> proper#(f(X1,X2,X3)) -> proper#(X2)
    top#(mark(X)) -> proper#(X) ->
    proper#(f(X1,X2,X3)) -> proper#(X3)
    proper#(f(X1,X2,X3)) -> proper#(X3) ->
    proper#(f(X1,X2,X3)) -> f#(proper(X1),proper(X2),proper(X3))
    proper#(f(X1,X2,X3)) -> proper#(X3) ->
    proper#(f(X1,X2,X3)) -> proper#(X1)
    proper#(f(X1,X2,X3)) -> proper#(X3) ->
    proper#(f(X1,X2,X3)) -> proper#(X2)
    proper#(f(X1,X2,X3)) -> proper#(X3) ->
    proper#(f(X1,X2,X3)) -> proper#(X3)
    proper#(f(X1,X2,X3)) -> proper#(X2) ->
    proper#(f(X1,X2,X3)) -> f#(proper(X1),proper(X2),proper(X3))
    proper#(f(X1,X2,X3)) -> proper#(X2) ->
    proper#(f(X1,X2,X3)) -> proper#(X1)
    proper#(f(X1,X2,X3)) -> proper#(X2) ->
    proper#(f(X1,X2,X3)) -> proper#(X2)
    proper#(f(X1,X2,X3)) -> proper#(X2) ->
    proper#(f(X1,X2,X3)) -> proper#(X3)
    proper#(f(X1,X2,X3)) -> proper#(X1) ->
    proper#(f(X1,X2,X3)) -> f#(proper(X1),proper(X2),proper(X3))
    proper#(f(X1,X2,X3)) -> proper#(X1) ->
    proper#(f(X1,X2,X3)) -> proper#(X1)
    proper#(f(X1,X2,X3)) -> proper#(X1) ->
    proper#(f(X1,X2,X3)) -> proper#(X2)
    proper#(f(X1,X2,X3)) -> proper#(X1) ->
    proper#(f(X1,X2,X3)) -> proper#(X3)
    proper#(f(X1,X2,X3)) -> f#(proper(X1),proper(X2),proper(X3)) ->
    f#(ok(X1),ok(X2),ok(X3)) -> f#(X1,X2,X3)
    proper#(f(X1,X2,X3)) -> f#(proper(X1),proper(X2),proper(X3)) ->
    f#(X1,X2,mark(X3)) -> f#(X1,X2,X3)
    f#(ok(X1),ok(X2),ok(X3)) -> f#(X1,X2,X3) ->
    f#(ok(X1),ok(X2),ok(X3)) -> f#(X1,X2,X3)
    f#(ok(X1),ok(X2),ok(X3)) -> f#(X1,X2,X3) ->
    f#(X1,X2,mark(X3)) -> f#(X1,X2,X3)
    f#(X1,X2,mark(X3)) -> f#(X1,X2,X3) ->
    f#(ok(X1),ok(X2),ok(X3)) -> f#(X1,X2,X3)
    f#(X1,X2,mark(X3)) -> f#(X1,X2,X3) ->
    f#(X1,X2,mark(X3)) -> f#(X1,X2,X3)
    active#(f(a(),b(),X)) -> f#(X,X,X) ->
    f#(ok(X1),ok(X2),ok(X3)) -> f#(X1,X2,X3)
    active#(f(a(),b(),X)) -> f#(X,X,X) ->
    f#(X1,X2,mark(X3)) -> f#(X1,X2,X3)
    active#(f(X1,X2,X3)) -> f#(X1,X2,active(X3)) ->
    f#(ok(X1),ok(X2),ok(X3)) -> f#(X1,X2,X3)
    active#(f(X1,X2,X3)) -> f#(X1,X2,active(X3)) ->
    f#(X1,X2,mark(X3)) -> f#(X1,X2,X3)
    active#(f(X1,X2,X3)) -> active#(X3) ->
    active#(f(X1,X2,X3)) -> f#(X1,X2,active(X3))
    active#(f(X1,X2,X3)) -> active#(X3) ->
    active#(f(X1,X2,X3)) -> active#(X3)
    active#(f(X1,X2,X3)) -> active#(X3) -> active#(f(a(),b(),X)) -> f#(X,X,X)
   SCC Processor:
    #sccs: 4
    #rules: 8
    #arcs: 40/169
    DPs:
     top#(ok(X)) -> top#(active(X))
     top#(mark(X)) -> top#(proper(X))
    TRS:
     active(f(a(),b(),X)) -> mark(f(X,X,X))
     active(c()) -> mark(a())
     active(c()) -> mark(b())
     active(f(X1,X2,X3)) -> f(X1,X2,active(X3))
     f(X1,X2,mark(X3)) -> mark(f(X1,X2,X3))
     proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3))
     proper(a()) -> ok(a())
     proper(b()) -> ok(b())
     proper(c()) -> ok(c())
     f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Open
    
    DPs:
     active#(f(X1,X2,X3)) -> active#(X3)
    TRS:
     active(f(a(),b(),X)) -> mark(f(X,X,X))
     active(c()) -> mark(a())
     active(c()) -> mark(b())
     active(f(X1,X2,X3)) -> f(X1,X2,active(X3))
     f(X1,X2,mark(X3)) -> mark(f(X1,X2,X3))
     proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3))
     proper(a()) -> ok(a())
     proper(b()) -> ok(b())
     proper(c()) -> ok(c())
     f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3))
     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(a(),b(),X)) -> mark(f(X,X,X))
       active(c()) -> mark(a())
       active(c()) -> mark(b())
       active(f(X1,X2,X3)) -> f(X1,X2,active(X3))
       f(X1,X2,mark(X3)) -> mark(f(X1,X2,X3))
       proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3))
       proper(a()) -> ok(a())
       proper(b()) -> ok(b())
       proper(c()) -> ok(c())
       f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
     Qed
    
    DPs:
     proper#(f(X1,X2,X3)) -> proper#(X3)
     proper#(f(X1,X2,X3)) -> proper#(X2)
     proper#(f(X1,X2,X3)) -> proper#(X1)
    TRS:
     active(f(a(),b(),X)) -> mark(f(X,X,X))
     active(c()) -> mark(a())
     active(c()) -> mark(b())
     active(f(X1,X2,X3)) -> f(X1,X2,active(X3))
     f(X1,X2,mark(X3)) -> mark(f(X1,X2,X3))
     proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3))
     proper(a()) -> ok(a())
     proper(b()) -> ok(b())
     proper(c()) -> ok(c())
     f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3))
     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(a(),b(),X)) -> mark(f(X,X,X))
       active(c()) -> mark(a())
       active(c()) -> mark(b())
       active(f(X1,X2,X3)) -> f(X1,X2,active(X3))
       f(X1,X2,mark(X3)) -> mark(f(X1,X2,X3))
       proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3))
       proper(a()) -> ok(a())
       proper(b()) -> ok(b())
       proper(c()) -> ok(c())
       f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
     Qed
    
    DPs:
     f#(X1,X2,mark(X3)) -> f#(X1,X2,X3)
     f#(ok(X1),ok(X2),ok(X3)) -> f#(X1,X2,X3)
    TRS:
     active(f(a(),b(),X)) -> mark(f(X,X,X))
     active(c()) -> mark(a())
     active(c()) -> mark(b())
     active(f(X1,X2,X3)) -> f(X1,X2,active(X3))
     f(X1,X2,mark(X3)) -> mark(f(X1,X2,X3))
     proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3))
     proper(a()) -> ok(a())
     proper(b()) -> ok(b())
     proper(c()) -> ok(c())
     f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Subterm Criterion Processor:
     simple projection:
      pi(f#) = 2
     problem:
      DPs:
       
      TRS:
       active(f(a(),b(),X)) -> mark(f(X,X,X))
       active(c()) -> mark(a())
       active(c()) -> mark(b())
       active(f(X1,X2,X3)) -> f(X1,X2,active(X3))
       f(X1,X2,mark(X3)) -> mark(f(X1,X2,X3))
       proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3))
       proper(a()) -> ok(a())
       proper(b()) -> ok(b())
       proper(c()) -> ok(c())
       f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
     Qed