YES
Input TRS:
      1: active(and(tt(),X)) -> mark(X)
      2: active(plus(N,0())) -> mark(N)
      3: active(plus(N,s(M))) -> mark(s(plus(N,M)))
      4: active(and(X1,X2)) -> and(active(X1),X2)
      5: active(plus(X1,X2)) -> plus(active(X1),X2)
      6: active(plus(X1,X2)) -> plus(X1,active(X2))
      7: active(s(X)) -> s(active(X))
      8: and(mark(X1),X2) -> mark(and(X1,X2))
      9: plus(mark(X1),X2) -> mark(plus(X1,X2))
      10: plus(X1,mark(X2)) -> mark(plus(X1,X2))
      11: s(mark(X)) -> mark(s(X))
      12: proper(and(X1,X2)) -> and(proper(X1),proper(X2))
      13: proper(tt()) -> ok(tt())
      14: proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
      15: proper(0()) -> ok(0())
      16: proper(s(X)) -> s(proper(X))
      17: and(ok(X1),ok(X2)) -> ok(and(X1,X2))
      18: plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
      19: s(ok(X)) -> ok(s(X))
      20: top(mark(X)) -> top(proper(X))
      21: top(ok(X)) -> top(active(X))
Number of strict rules: 21
Direct POLO(bPol) ... removes: 1 2
      s 	w: x1 + 29273
      top	w: x1
      and	w: 2 * x1 + x2 + 4
      proper	w: x1
      ok	w: x1
      0 	w: 25532
      mark	w: x1
      plus	w: x1 + x2 + 14459
      active	w: x1
      tt	w: 1
Number of strict rules: 19
Direct POLO(bPol) ... removes: 3
      s 	w: x1 + 1
      top	w: x1 + 32156
      and	w: x1 + x2 + 30249
      proper	w: x1
      ok	w: x1
      0 	w: 11453
      mark	w: x1
      plus	w: x1 + 2 * x2
      active	w: x1
      tt	w: 0
Number of strict rules: 18
Direct POLO(bPol) ... removes: 10 20 9
      s 	w: x1 + 1
      top	w: 2 * x1 + 32154
      and	w: x1 + x2 + 1
      proper	w: x1
      ok	w: x1
      0 	w: 28776
      mark	w: x1 + 1
      plus	w: 2 * x1 + 2 * x2 + 8941
      active	w: x1
      tt	w: 22142
Number of strict rules: 15
Direct POLO(bPol) ... removes: 8
      s 	w: x1 + 3
      top	w: 2 * x1 + 36743
      and	w: 2 * x1 + x2 + 1
      proper	w: x1
      ok	w: x1
      0 	w: 28776
      mark	w: x1 + 3
      plus	w: 2 * x1 + 2 * x2 + 1
      active	w: x1
      tt	w: 22142
Number of strict rules: 14
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #active(plus(X1,X2)) -> #plus(X1,active(X2))
     #2: #active(plus(X1,X2)) -> #active(X2)
     #3: #s(mark(X)) -> #s(X)
     #4: #proper(and(X1,X2)) -> #and(proper(X1),proper(X2))
     #5: #proper(and(X1,X2)) -> #proper(X1)
     #6: #proper(and(X1,X2)) -> #proper(X2)
     #7: #proper(plus(X1,X2)) -> #plus(proper(X1),proper(X2))
     #8: #proper(plus(X1,X2)) -> #proper(X1)
     #9: #proper(plus(X1,X2)) -> #proper(X2)
     #10: #active(s(X)) -> #s(active(X))
     #11: #active(s(X)) -> #active(X)
     #12: #active(plus(X1,X2)) -> #plus(active(X1),X2)
     #13: #active(plus(X1,X2)) -> #active(X1)
     #14: #and(ok(X1),ok(X2)) -> #and(X1,X2)
     #15: #s(ok(X)) -> #s(X)
     #16: #top(ok(X)) -> #top(active(X))
     #17: #top(ok(X)) -> #active(X)
     #18: #proper(s(X)) -> #s(proper(X))
     #19: #proper(s(X)) -> #proper(X)
     #20: #active(and(X1,X2)) -> #and(active(X1),X2)
     #21: #active(and(X1,X2)) -> #active(X1)
     #22: #plus(ok(X1),ok(X2)) -> #plus(X1,X2)
Number of SCCs: 6, DPs: 14
  SCC { #16 }
POLO(Sum)... succeeded.
      s 	w: x1 + 1
      top	w: 0
      and	w: x1 + x2 + 33428
      #plus	w: 0
      #top	w: x1
      proper	w: 0
      ok	w: x1 + 26392
      0 	w: 0
      #s 	w: 0
      mark	w: x1 + 10732
      #proper	w: 0
      plus	w: x1 + x2 + 58713
      active	w: x1 + 26391
      #active	w: 0
      tt	w: 0
      #and	w: 0
    USABLE RULES: { 4..7 11 17..19 }
    Removed DPs: #16
Number of SCCs: 5, DPs: 13
  SCC { #22 }
POLO(Sum)... succeeded.
      s 	w: x1 + 1
      top	w: 0
      and	w: x1 + x2 + 33428
      #plus	w: x1 + x2
      #top	w: x1
      proper	w: 0
      ok	w: x1 + 1
      0 	w: 0
      #s 	w: 0
      mark	w: x1 + 10732
      #proper	w: 0
      plus	w: x1 + x2 + 47562
      active	w: x1 + 1
      #active	w: 0
      tt	w: 0
      #and	w: 0
    USABLE RULES: { 4..7 11 17..19 }
    Removed DPs: #22
Number of SCCs: 4, DPs: 12
  SCC { #14 }
POLO(Sum)... succeeded.
      s 	w: x1 + 1
      top	w: 0
      and	w: x1 + x2 + 22078
      #plus	w: 0
      #top	w: x1
      proper	w: 0
      ok	w: x1 + 1
      0 	w: 0
      #s 	w: 0
      mark	w: x1 + 1
      #proper	w: 0
      plus	w: x1 + x2 + 35495
      active	w: x1 + 1
      #active	w: 0
      tt	w: 0
      #and	w: x1 + x2
    USABLE RULES: { 4..7 11 17..19 }
    Removed DPs: #14
Number of SCCs: 3, DPs: 11
  SCC { #3 #15 }
POLO(Sum)... succeeded.
      s 	w: x1 + 1
      top	w: 0
      and	w: x1 + x2 + 22078
      #plus	w: 0
      #top	w: x1
      proper	w: 0
      ok	w: x1 + 1
      0 	w: 0
      #s 	w: x1
      mark	w: x1 + 1
      #proper	w: 0
      plus	w: x1 + x2 + 57757
      active	w: x1 + 24766
      #active	w: 0
      tt	w: 0
      #and	w: 0
    USABLE RULES: { 4..7 11 17..19 }
    Removed DPs: #3 #15
Number of SCCs: 2, DPs: 9
  SCC { #2 #11 #13 #21 }
POLO(Sum)... succeeded.
      s 	w: x1 + 1
      top	w: 0
      and	w: x1 + x2 + 1
      #plus	w: 0
      #top	w: x1
      proper	w: 0
      ok	w: x1 + 1
      0 	w: 0
      #s 	w: 0
      mark	w: x1 + 32797
      #proper	w: 0
      plus	w: x1 + x2 + 57757
      active	w: x1 + 1
      #active	w: x1
      tt	w: 0
      #and	w: 0
    USABLE RULES: { 4..7 11 17..19 }
    Removed DPs: #2 #11 #13 #21
Number of SCCs: 1, DPs: 5
  SCC { #5 #6 #8 #9 #19 }
POLO(Sum)... succeeded.
      s 	w: x1 + 1
      top	w: 0
      and	w: x1 + x2 + 1
      #plus	w: 0
      #top	w: x1
      proper	w: 0
      ok	w: x1 + 1
      0 	w: 0
      #s 	w: 0
      mark	w: x1 + 32797
      #proper	w: x1
      plus	w: x1 + x2 + 57757
      active	w: x1 + 1
      #active	w: 0
      tt	w: 0
      #and	w: 0
    USABLE RULES: { 4..7 11 17..19 }
    Removed DPs: #5 #6 #8 #9 #19
Number of SCCs: 0, DPs: 0