YES
TRS:
 {       f(ok(X)) -> ok(f(X)),
         g(ok(X)) -> ok(g(X)),
  active(f(g(X))) -> mark(g(X)),
      active(c()) -> mark(f(g(c()))),
     proper(f(X)) -> f(proper(X)),
     proper(g(X)) -> g(proper(X)),
      proper(c()) -> ok(c()),
     top(mark(X)) -> top(proper(X)),
       top(ok(X)) -> top(active(X))}
 DP:
  Strict:
   {    f#(ok(X)) -> f#(X),
        g#(ok(X)) -> g#(X),
     active#(c()) -> f#(g(c())),
     active#(c()) -> g#(c()),
    proper#(f(X)) -> f#(proper(X)),
    proper#(f(X)) -> proper#(X),
    proper#(g(X)) -> g#(proper(X)),
    proper#(g(X)) -> proper#(X),
    top#(mark(X)) -> proper#(X),
    top#(mark(X)) -> top#(proper(X)),
      top#(ok(X)) -> active#(X),
      top#(ok(X)) -> top#(active(X))}
  Weak:
  {       f(ok(X)) -> ok(f(X)),
          g(ok(X)) -> ok(g(X)),
   active(f(g(X))) -> mark(g(X)),
       active(c()) -> mark(f(g(c()))),
      proper(f(X)) -> f(proper(X)),
      proper(g(X)) -> g(proper(X)),
       proper(c()) -> ok(c()),
      top(mark(X)) -> top(proper(X)),
        top(ok(X)) -> top(active(X))}
  EDG:
   {(f#(ok(X)) -> f#(X), f#(ok(X)) -> f#(X))
    (proper#(f(X)) -> proper#(X), proper#(g(X)) -> proper#(X))
    (proper#(f(X)) -> proper#(X), proper#(g(X)) -> g#(proper(X)))
    (proper#(f(X)) -> proper#(X), proper#(f(X)) -> proper#(X))
    (proper#(f(X)) -> proper#(X), proper#(f(X)) -> f#(proper(X)))
    (top#(mark(X)) -> proper#(X), proper#(g(X)) -> proper#(X))
    (top#(mark(X)) -> proper#(X), proper#(g(X)) -> g#(proper(X)))
    (top#(mark(X)) -> proper#(X), proper#(f(X)) -> proper#(X))
    (top#(mark(X)) -> proper#(X), proper#(f(X)) -> f#(proper(X)))
    (proper#(g(X)) -> g#(proper(X)), g#(ok(X)) -> g#(X))
    (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#(mark(X)) -> top#(proper(X)), top#(mark(X)) -> proper#(X))
    (top#(mark(X)) -> top#(proper(X)), top#(mark(X)) -> top#(proper(X)))
    (top#(mark(X)) -> top#(proper(X)), top#(ok(X)) -> active#(X))
    (top#(mark(X)) -> top#(proper(X)), top#(ok(X)) -> top#(active(X)))
    (proper#(f(X)) -> f#(proper(X)), f#(ok(X)) -> f#(X))
    (top#(ok(X)) -> active#(X), active#(c()) -> f#(g(c())))
    (top#(ok(X)) -> active#(X), active#(c()) -> g#(c()))
    (proper#(g(X)) -> proper#(X), proper#(f(X)) -> f#(proper(X)))
    (proper#(g(X)) -> proper#(X), proper#(f(X)) -> proper#(X))
    (proper#(g(X)) -> proper#(X), proper#(g(X)) -> g#(proper(X)))
    (proper#(g(X)) -> proper#(X), proper#(g(X)) -> proper#(X))
    (g#(ok(X)) -> g#(X), g#(ok(X)) -> g#(X))}
   SCCS:
    Scc:
     {top#(mark(X)) -> top#(proper(X)),
        top#(ok(X)) -> top#(active(X))}
    Scc:
     {proper#(f(X)) -> proper#(X),
      proper#(g(X)) -> proper#(X)}
    Scc:
     {g#(ok(X)) -> g#(X)}
    Scc:
     {f#(ok(X)) -> f#(X)}
    SCC:
     Strict:
      {top#(mark(X)) -> top#(proper(X)),
         top#(ok(X)) -> top#(active(X))}
     Weak:
     {       f(ok(X)) -> ok(f(X)),
             g(ok(X)) -> ok(g(X)),
      active(f(g(X))) -> mark(g(X)),
          active(c()) -> mark(f(g(c()))),
         proper(f(X)) -> f(proper(X)),
         proper(g(X)) -> g(proper(X)),
          proper(c()) -> ok(c()),
         top(mark(X)) -> top(proper(X)),
           top(ok(X)) -> top(active(X))}
     BOUND:
      Bound: match(-raise)-DP-bounded by 3
      Automaton:
       {  top#_3(138) -> 139*
           top#_2(97) -> 98*
           top#_1(24) -> 25*
           top#_0(21) -> 22*
           top#_0(20) -> 10*
            top_0(20) -> 18*
            top_0(19) -> 18*
            top_0(18) -> 18*
            top_0(17) -> 18*
            top_0(16) -> 18*
            top_0(14) -> 18*
            top_0(13) -> 18*
            top_0(12) -> 18*
        proper_2(132) -> 133*
        proper_2(130) -> 131*
        proper_2(127) -> 128*
        proper_2(123) -> 124*
        proper_2(121) -> 122*
        proper_2(118) -> 119*
        proper_2(112) -> 113*
         proper_1(87) -> 88*
         proper_1(79) -> 80*
         proper_1(77) -> 78*
         proper_1(75) -> 76*
         proper_1(73) -> 74*
         proper_1(71) -> 72*
         proper_1(69) -> 70*
         proper_1(66) -> 67*
         proper_1(63) -> 64*
         proper_1(61) -> 62*
         proper_1(43) -> 44*
         proper_0(20) -> 17*
         proper_0(19) -> 17*
         proper_0(18) -> 17*
         proper_0(17) -> 17*
         proper_0(16) -> 17*
         proper_0(14) -> 17*
         proper_0(13) -> 17*
         proper_0(12) -> 17*
            ok_2(141) -> 142*
            ok_2(135) -> 136*
            ok_2(125) -> 126*
             ok_1(94) -> 95*
             ok_1(91) -> 92*
             ok_1(83) -> 84*
             ok_1(81) -> 82*
             ok_0(20) -> 16*
             ok_0(19) -> 16*
             ok_0(18) -> 16*
             ok_0(17) -> 16*
             ok_0(16) -> 16*
             ok_0(14) -> 16*
             ok_0(13) -> 16*
             ok_0(12) -> 16*
        active_3(137) -> 138*
        active_2(107) -> 108*
         active_2(96) -> 97*
         active_1(38) -> 39*
         active_1(36) -> 37*
         active_1(34) -> 35*
         active_1(32) -> 33*
         active_1(30) -> 31*
         active_1(28) -> 29*
         active_1(26) -> 27*
         active_1(23) -> 24*
         active_0(20) -> 20*
         active_0(19) -> 20*
         active_0(18) -> 20*
         active_0(17) -> 20*
         active_0(16) -> 20*
         active_0(14) -> 20*
         active_0(13) -> 20*
         active_0(12) -> 20*
                c_2() -> 125*
                c_1() -> 57*
                c_0() -> 19*
             g_2(149) -> 150*
             g_2(145) -> 146*
             g_2(134) -> 135*
             g_2(119) -> 120*
             g_2(116) -> 117*
             g_2(114) -> 115*
             g_2(109) -> 110*
             g_1(105) -> 106*
             g_1(103) -> 104*
              g_1(93) -> 94*
              g_1(88) -> 89*
              g_1(67) -> 68*
              g_1(57) -> 58*
              g_1(55) -> 56*
              g_1(53) -> 54*
              g_1(51) -> 52*
              g_1(49) -> 50*
              g_1(47) -> 48*
              g_1(45) -> 46*
              g_1(40) -> 41*
              g_0(20) -> 14*
              g_0(19) -> 14*
              g_0(18) -> 14*
              g_0(17) -> 14*
              g_0(16) -> 14*
              g_0(14) -> 14*
              g_0(13) -> 14*
              g_0(12) -> 14*
             f_2(147) -> 148*
             f_2(143) -> 144*
             f_2(140) -> 141*
             f_2(128) -> 129*
             f_1(101) -> 102*
              f_1(99) -> 100*
              f_1(90) -> 91*
              f_1(85) -> 86*
              f_1(64) -> 65*
              f_1(58) -> 59*
              f_0(20) -> 13*
              f_0(19) -> 13*
              f_0(18) -> 13*
              f_0(17) -> 13*
              f_0(16) -> 13*
              f_0(14) -> 13*
              f_0(13) -> 13*
              f_0(12) -> 13*
          mark_2(110) -> 111*
           mark_1(59) -> 60*
           mark_1(41) -> 42*
           mark_0(20) -> 12*
           mark_0(19) -> 12*
           mark_0(18) -> 12*
           mark_0(17) -> 12*
           mark_0(16) -> 12*
           mark_0(14) -> 12*
           mark_0(13) -> 12*
           mark_0(12) -> 12*
                  150 -> 135*
                  148 -> 141*
                  146 -> 135*
                  144 -> 141*
                  142 -> 129*
                  141 -> 149 | 147
                  139 -> 98*
                  136 -> 120*
                  135 -> 145 | 143 | 137
                  133 -> 128*
                  131 -> 128*
                  129 -> 131 | 122
                  126 -> 128 | 119
                  125 -> 140 | 134
                  124 -> 119*
                  122 -> 119*
                  120 -> 133 | 124 | 113
                  117 -> 110*
                  116 -> 123*
                  115 -> 110*
                  114 -> 121*
                  113 -> 97*
                  111 -> 108*
                  110 -> 112*
                  109 -> 118*
                  108 -> 97*
                  106 -> 94*
                  105 -> 116*
                  104 -> 94*
                  103 -> 114*
                  102 -> 91*
                  101 -> 132*
                  100 -> 91*
                   99 -> 130*
                   98 -> 25*
                   95 -> 89 | 68
                   94 -> 105 | 101 | 96
                   93 -> 109*
                   92 -> 86 | 65
                   91 -> 107 | 103 | 99
                   90 -> 127*
                   89 -> 64*
                   86 -> 74 | 70
                   84 -> 88 | 78
                   83 -> 93 | 90
                   82 -> 50 | 48 | 46
                   80 -> 67*
                   78 -> 67*
                   76 -> 67*
                   74 -> 67*
                   72 -> 67*
                   70 -> 67*
                   68 -> 74 | 72 | 44
                   67 -> 85*
                   65 -> 62*
                   62 -> 24*
                   60 -> 37*
                   59 -> 61*
                   58 -> 63*
                   57 -> 87 | 83
                   56 -> 41*
                   55 -> 79*
                   54 -> 41*
                   53 -> 77*
                   52 -> 41*
                   51 -> 75*
                   50 -> 41*
                   49 -> 73*
                   48 -> 41*
                   47 -> 71*
                   46 -> 41*
                   45 -> 69*
                   44 -> 24*
                   42 -> 33 | 27
                   41 -> 81 | 43
                   40 -> 66*
                   39 -> 24*
                   37 -> 24*
                   35 -> 24*
                   33 -> 24*
                   31 -> 24*
                   29 -> 24*
                   27 -> 24*
                   25 -> 22*
                   22 -> 10*
                   20 -> 55 | 38
                   19 -> 53 | 36
                   18 -> 51 | 34
                   17 -> 49 | 32 | 21
                   16 -> 30 | 17 | 14 | 13
                   14 -> 47 | 28 | 17
                   13 -> 45 | 26 | 17
                   12 -> 40 | 23 | 20}
      Strict:
       {top#(mark(X)) -> top#(proper(X))}
      EDG:
       {(top#(mark(X)) -> top#(proper(X)), top#(mark(X)) -> top#(proper(X)))}
       SCCS:
        Scc:
         {top#(mark(X)) -> top#(proper(X))}
        SCC:
         Strict:
          {top#(mark(X)) -> top#(proper(X))}
         Weak:
         {       f(ok(X)) -> ok(f(X)),
                 g(ok(X)) -> ok(g(X)),
          active(f(g(X))) -> mark(g(X)),
              active(c()) -> mark(f(g(c()))),
             proper(f(X)) -> f(proper(X)),
             proper(g(X)) -> g(proper(X)),
              proper(c()) -> ok(c()),
             top(mark(X)) -> top(proper(X)),
               top(ok(X)) -> top(active(X))}
         POLY:
          Argument Filtering:
           pi(top#) = 0, pi(top) = [], pi(proper) = [], pi(ok) = [], pi(active) = [], pi(c) = [], pi(g) = [], pi(f) = [], pi(mark) = []
          Usable Rules:
           {}
          Interpretation:
           [proper] = 0,
           [mark] = 1
          Strict:
           {}
          Weak:
           {       f(ok(X)) -> ok(f(X)),
                   g(ok(X)) -> ok(g(X)),
            active(f(g(X))) -> mark(g(X)),
                active(c()) -> mark(f(g(c()))),
               proper(f(X)) -> f(proper(X)),
               proper(g(X)) -> g(proper(X)),
                proper(c()) -> ok(c()),
               top(mark(X)) -> top(proper(X)),
                 top(ok(X)) -> top(active(X))}
          Qed
    SCC:
     Strict:
      {proper#(f(X)) -> proper#(X),
       proper#(g(X)) -> proper#(X)}
     Weak:
     {       f(ok(X)) -> ok(f(X)),
             g(ok(X)) -> ok(g(X)),
      active(f(g(X))) -> mark(g(X)),
          active(c()) -> mark(f(g(c()))),
         proper(f(X)) -> f(proper(X)),
         proper(g(X)) -> g(proper(X)),
          proper(c()) -> ok(c()),
         top(mark(X)) -> top(proper(X)),
           top(ok(X)) -> top(active(X))}
     SPSC:
      Simple Projection:
       pi(proper#) = 0
      Strict:
       {proper#(g(X)) -> proper#(X)}
      EDG:
       {(proper#(g(X)) -> proper#(X), proper#(g(X)) -> proper#(X))}
       SCCS:
        Scc:
         {proper#(g(X)) -> proper#(X)}
        SCC:
         Strict:
          {proper#(g(X)) -> proper#(X)}
         Weak:
         {       f(ok(X)) -> ok(f(X)),
                 g(ok(X)) -> ok(g(X)),
          active(f(g(X))) -> mark(g(X)),
              active(c()) -> mark(f(g(c()))),
             proper(f(X)) -> f(proper(X)),
             proper(g(X)) -> g(proper(X)),
              proper(c()) -> ok(c()),
             top(mark(X)) -> top(proper(X)),
               top(ok(X)) -> top(active(X))}
         SPSC:
          Simple Projection:
           pi(proper#) = 0
          Strict:
           {}
          Qed
    SCC:
     Strict:
      {g#(ok(X)) -> g#(X)}
     Weak:
     {       f(ok(X)) -> ok(f(X)),
             g(ok(X)) -> ok(g(X)),
      active(f(g(X))) -> mark(g(X)),
          active(c()) -> mark(f(g(c()))),
         proper(f(X)) -> f(proper(X)),
         proper(g(X)) -> g(proper(X)),
          proper(c()) -> ok(c()),
         top(mark(X)) -> top(proper(X)),
           top(ok(X)) -> top(active(X))}
     SPSC:
      Simple Projection:
       pi(g#) = 0
      Strict:
       {}
      Qed
    SCC:
     Strict:
      {f#(ok(X)) -> f#(X)}
     Weak:
     {       f(ok(X)) -> ok(f(X)),
             g(ok(X)) -> ok(g(X)),
      active(f(g(X))) -> mark(g(X)),
          active(c()) -> mark(f(g(c()))),
         proper(f(X)) -> f(proper(X)),
         proper(g(X)) -> g(proper(X)),
          proper(c()) -> ok(c()),
         top(mark(X)) -> top(proper(X)),
           top(ok(X)) -> top(active(X))}
     SPSC:
      Simple Projection:
       pi(f#) = 0
      Strict:
       {}
      Qed