YES

Problem:
 active(f(b(),X,c())) -> mark(f(X,c(),X))
 active(c()) -> mark(b())
 active(f(X1,X2,X3)) -> f(X1,active(X2),X3)
 f(X1,mark(X2),X3) -> mark(f(X1,X2,X3))
 proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3))
 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(b(),X,c())) -> f#(X,c(),X)
   active#(f(X1,X2,X3)) -> active#(X2)
   active#(f(X1,X2,X3)) -> f#(X1,active(X2),X3)
   f#(X1,mark(X2),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(b(),X,c())) -> mark(f(X,c(),X))
   active(c()) -> mark(b())
   active(f(X1,X2,X3)) -> f(X1,active(X2),X3)
   f(X1,mark(X2),X3) -> mark(f(X1,X2,X3))
   proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3))
   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(b(),X,c())) -> f#(X,c(),X)
    active#(f(X1,X2,X3)) -> active#(X2)
    active#(f(X1,X2,X3)) -> f#(X1,active(X2),X3)
    f#(X1,mark(X2),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(b(),X,c())) -> mark(f(X,c(),X))
    active(c()) -> mark(b())
    active(f(X1,X2,X3)) -> f(X1,active(X2),X3)
    f(X1,mark(X2),X3) -> mark(f(X1,X2,X3))
    proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3))
    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,active(X2),X3)
    top#(ok(X)) -> active#(X) -> active#(f(X1,X2,X3)) -> active#(X2)
    top#(ok(X)) -> active#(X) ->
    active#(f(b(),X,c())) -> f#(X,c(),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,mark(X2),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,mark(X2),X3) -> f#(X1,X2,X3)
    f#(X1,mark(X2),X3) -> f#(X1,X2,X3) ->
    f#(ok(X1),ok(X2),ok(X3)) -> f#(X1,X2,X3)
    f#(X1,mark(X2),X3) -> f#(X1,X2,X3) ->
    f#(X1,mark(X2),X3) -> f#(X1,X2,X3)
    active#(f(b(),X,c())) -> f#(X,c(),X) ->
    f#(ok(X1),ok(X2),ok(X3)) -> f#(X1,X2,X3)
    active#(f(b(),X,c())) -> f#(X,c(),X) ->
    f#(X1,mark(X2),X3) -> f#(X1,X2,X3)
    active#(f(X1,X2,X3)) -> f#(X1,active(X2),X3) ->
    f#(ok(X1),ok(X2),ok(X3)) -> f#(X1,X2,X3)
    active#(f(X1,X2,X3)) -> f#(X1,active(X2),X3) ->
    f#(X1,mark(X2),X3) -> f#(X1,X2,X3)
    active#(f(X1,X2,X3)) -> active#(X2) ->
    active#(f(X1,X2,X3)) -> f#(X1,active(X2),X3)
    active#(f(X1,X2,X3)) -> active#(X2) ->
    active#(f(X1,X2,X3)) -> active#(X2)
    active#(f(X1,X2,X3)) -> active#(X2) -> active#(f(b(),X,c())) -> f#(X,c(),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(b(),X,c())) -> mark(f(X,c(),X))
     active(c()) -> mark(b())
     active(f(X1,X2,X3)) -> f(X1,active(X2),X3)
     f(X1,mark(X2),X3) -> mark(f(X1,X2,X3))
     proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3))
     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))
    Usable Rule Processor:
     DPs:
      top#(ok(X)) -> top#(active(X))
      top#(mark(X)) -> top#(proper(X))
     TRS:
      active(f(b(),X,c())) -> mark(f(X,c(),X))
      active(c()) -> mark(b())
      active(f(X1,X2,X3)) -> f(X1,active(X2),X3)
      f(X1,mark(X2),X3) -> mark(f(X1,X2,X3))
      f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3))
      proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3))
      proper(b()) -> ok(b())
      proper(c()) -> ok(c())
     Matrix Interpretation Processor: dim=3
      
      usable rules:
       active(f(b(),X,c())) -> mark(f(X,c(),X))
       active(c()) -> mark(b())
       active(f(X1,X2,X3)) -> f(X1,active(X2),X3)
       f(X1,mark(X2),X3) -> mark(f(X1,X2,X3))
       f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3))
       proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3))
       proper(b()) -> ok(b())
       proper(c()) -> ok(c())
      interpretation:
       [top#](x0) = [1 0 0]x0,
       
                    
       [ok](x0) = x0
                    ,
       
                      [0 0 1]  
       [proper](x0) = [0 1 0]x0
                      [1 0 0]  ,
       
                    [0 0 1]     [1]
       [mark](x0) = [0 0 0]x0 + [0]
                    [1 1 0]     [0],
       
                      [1 0 0]  
       [active](x0) = [0 0 0]x0
                      [0 0 1]  ,
       
                         [0 1 0]     [1 1 1]     [1 0 1]  
       [f](x0, x1, x2) = [0 0 0]x0 + [0 0 0]x1 + [0 0 0]x2
                         [0 1 0]     [1 1 1]     [1 0 1]  ,
       
             [1]
       [c] = [0]
             [1],
       
             [0]
       [b] = [1]
             [0]
      orientation:
       top#(ok(X)) = [1 0 0]X >= [1 0 0]X = top#(active(X))
       
       top#(mark(X)) = [0 0 1]X + [1] >= [0 0 1]X = top#(proper(X))
       
                              [1 1 1]    [3]    [1 1 1]    [3]                   
       active(f(b(),X,c())) = [0 0 0]X + [0] >= [0 0 0]X + [0] = mark(f(X,c(),X))
                              [1 1 1]    [3]    [1 1 1]    [2]                   
       
                     [1]    [1]            
       active(c()) = [0] >= [0] = mark(b())
                     [1]    [1]            
       
                             [0 1 0]     [1 1 1]     [1 0 1]      [0 1 0]     [1 0 1]     [1 0 1]                        
       active(f(X1,X2,X3)) = [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 >= [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 = f(X1,active(X2),X3)
                             [0 1 0]     [1 1 1]     [1 0 1]      [0 1 0]     [1 0 1]     [1 0 1]                        
       
                           [0 1 0]     [1 1 1]     [1 0 1]     [1]    [0 1 0]     [1 1 1]     [1 0 1]     [1]                    
       f(X1,mark(X2),X3) = [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 + [0] = mark(f(X1,X2,X3))
                           [0 1 0]     [1 1 1]     [1 0 1]     [1]    [0 1 0]     [1 1 1]     [1 0 1]     [0]                    
       
                                 [0 1 0]     [1 1 1]     [1 0 1]      [0 1 0]     [1 1 1]     [1 0 1]                    
       f(ok(X1),ok(X2),ok(X3)) = [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 >= [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 = ok(f(X1,X2,X3))
                                 [0 1 0]     [1 1 1]     [1 0 1]      [0 1 0]     [1 1 1]     [1 0 1]                    
       
                             [0 1 0]     [1 1 1]     [1 0 1]      [0 1 0]     [1 1 1]     [1 0 1]                                        
       proper(f(X1,X2,X3)) = [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 >= [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 = f(proper(X1),proper(X2),proper(X3))
                             [0 1 0]     [1 1 1]     [1 0 1]      [0 1 0]     [1 1 1]     [1 0 1]                                        
       
                     [0]    [0]          
       proper(b()) = [1] >= [1] = ok(b())
                     [0]    [0]          
       
                     [1]    [1]          
       proper(c()) = [0] >= [0] = ok(c())
                     [1]    [1]          
      problem:
       DPs:
        top#(ok(X)) -> top#(active(X))
       TRS:
        active(f(b(),X,c())) -> mark(f(X,c(),X))
        active(c()) -> mark(b())
        active(f(X1,X2,X3)) -> f(X1,active(X2),X3)
        f(X1,mark(X2),X3) -> mark(f(X1,X2,X3))
        f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3))
        proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3))
        proper(b()) -> ok(b())
        proper(c()) -> ok(c())
      Restore Modifier:
       DPs:
        top#(ok(X)) -> top#(active(X))
       TRS:
        active(f(b(),X,c())) -> mark(f(X,c(),X))
        active(c()) -> mark(b())
        active(f(X1,X2,X3)) -> f(X1,active(X2),X3)
        f(X1,mark(X2),X3) -> mark(f(X1,X2,X3))
        proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3))
        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))
       Bounds Processor:
        bound: 1
        enrichment: top-dp
        automaton:
         final states: {11}
         transitions:
          mark0(10) -> 10*
          proper0(10) -> 10*
          top0(10) -> 10*
          top{#,1}(16) -> 17*
          active1(15) -> 16*
          f1(10,19,10) -> 19*
          f1(10,16,10) -> 16*
          f1(10,18,10) -> 19*
          mark1(19) -> 16*
          b1() -> 19*
          c1() -> 18*
          top{#,0}(10) -> 11*
          ok0(10) -> 10*
          active0(10) -> 10*
          f0(10,10,10) -> 10*
          b0() -> 10*
          c0() -> 10*
          10 -> 15*
          17 -> 11*
        problem:
         DPs:
          
         TRS:
          active(f(b(),X,c())) -> mark(f(X,c(),X))
          active(c()) -> mark(b())
          active(f(X1,X2,X3)) -> f(X1,active(X2),X3)
          f(X1,mark(X2),X3) -> mark(f(X1,X2,X3))
          proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3))
          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:
     active#(f(X1,X2,X3)) -> active#(X2)
    TRS:
     active(f(b(),X,c())) -> mark(f(X,c(),X))
     active(c()) -> mark(b())
     active(f(X1,X2,X3)) -> f(X1,active(X2),X3)
     f(X1,mark(X2),X3) -> mark(f(X1,X2,X3))
     proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3))
     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(b(),X,c())) -> mark(f(X,c(),X))
       active(c()) -> mark(b())
       active(f(X1,X2,X3)) -> f(X1,active(X2),X3)
       f(X1,mark(X2),X3) -> mark(f(X1,X2,X3))
       proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3))
       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(b(),X,c())) -> mark(f(X,c(),X))
     active(c()) -> mark(b())
     active(f(X1,X2,X3)) -> f(X1,active(X2),X3)
     f(X1,mark(X2),X3) -> mark(f(X1,X2,X3))
     proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3))
     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(b(),X,c())) -> mark(f(X,c(),X))
       active(c()) -> mark(b())
       active(f(X1,X2,X3)) -> f(X1,active(X2),X3)
       f(X1,mark(X2),X3) -> mark(f(X1,X2,X3))
       proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3))
       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,mark(X2),X3) -> f#(X1,X2,X3)
     f#(ok(X1),ok(X2),ok(X3)) -> f#(X1,X2,X3)
    TRS:
     active(f(b(),X,c())) -> mark(f(X,c(),X))
     active(c()) -> mark(b())
     active(f(X1,X2,X3)) -> f(X1,active(X2),X3)
     f(X1,mark(X2),X3) -> mark(f(X1,X2,X3))
     proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3))
     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:
       f#(X1,mark(X2),X3) -> f#(X1,X2,X3)
      TRS:
       active(f(b(),X,c())) -> mark(f(X,c(),X))
       active(c()) -> mark(b())
       active(f(X1,X2,X3)) -> f(X1,active(X2),X3)
       f(X1,mark(X2),X3) -> mark(f(X1,X2,X3))
       proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3))
       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#) = 1
      problem:
       DPs:
        
       TRS:
        active(f(b(),X,c())) -> mark(f(X,c(),X))
        active(c()) -> mark(b())
        active(f(X1,X2,X3)) -> f(X1,active(X2),X3)
        f(X1,mark(X2),X3) -> mark(f(X1,X2,X3))
        proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3))
        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