YES
Input TRS:
      1: a__and(tt(),X) -> mark(X)
      2: a__plus(N,0()) -> mark(N)
      3: a__plus(N,s(M)) -> s(a__plus(mark(N),mark(M)))
      4: a__x(N,0()) -> 0()
      5: a__x(N,s(M)) -> a__plus(a__x(mark(N),mark(M)),mark(N))
      6: mark(and(X1,X2)) -> a__and(mark(X1),X2)
      7: mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2))
      8: mark(x(X1,X2)) -> a__x(mark(X1),mark(X2))
      9: mark(tt()) -> tt()
      10: mark(0()) -> 0()
      11: mark(s(X)) -> s(mark(X))
      12: a__and(X1,X2) -> and(X1,X2)
      13: a__plus(X1,X2) -> plus(X1,X2)
      14: a__x(X1,X2) -> x(X1,X2)
Number of strict rules: 14
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #a__plus(N,0()) -> #mark(N)
     #2: #mark(and(X1,X2)) -> #a__and(mark(X1),X2)
     #3: #mark(and(X1,X2)) -> #mark(X1)
     #4: #mark(s(X)) -> #mark(X)
     #5: #mark(plus(X1,X2)) -> #a__plus(mark(X1),mark(X2))
     #6: #mark(plus(X1,X2)) -> #mark(X1)
     #7: #mark(plus(X1,X2)) -> #mark(X2)
     #8: #a__x(N,s(M)) -> #a__plus(a__x(mark(N),mark(M)),mark(N))
     #9: #a__x(N,s(M)) -> #a__x(mark(N),mark(M))
     #10: #a__x(N,s(M)) -> #mark(N)
     #11: #a__x(N,s(M)) -> #mark(M)
     #12: #a__x(N,s(M)) -> #mark(N)
     #13: #a__plus(N,s(M)) -> #a__plus(mark(N),mark(M))
     #14: #a__plus(N,s(M)) -> #mark(N)
     #15: #a__plus(N,s(M)) -> #mark(M)
     #16: #a__and(tt(),X) -> #mark(X)
     #17: #mark(x(X1,X2)) -> #a__x(mark(X1),mark(X2))
     #18: #mark(x(X1,X2)) -> #mark(X1)
     #19: #mark(x(X1,X2)) -> #mark(X2)
Number of SCCs: 1, DPs: 19
  SCC { #1..19 }
POLO(Sum)... POLO(max)... succeeded.
      a__plus	w: max(x1, x2 + 591)
      s 	w: x1
      and	w: max(x1 + 16911, x2 + 2)
      #a__x	w: max(x1 + 15655, x2 + 15064)
      a__x	w: max(x1 + 591, x2)
      x 	w: max(x1 + 591, x2)
      #a__plus	w: max(x1 + 15064, x2 + 15655)
      #mark	w: x1 + 15064
      0 	w: 553
      #a__and	w: max(x1 + 15067, x2 + 15065)
      mark	w: x1
      plus	w: max(x1, x2 + 591)
      tt	w: 42199
      a__and	w: max(x1 + 16911, x2 + 2)
    USABLE RULES: { 1..14 }
    Removed DPs: #2 #3 #7 #10 #12 #15 #16 #18
Number of SCCs: 1, DPs: 11
  SCC { #1 #4..6 #8 #9 #11 #13 #14 #17 #19 }
POLO(Sum)... succeeded.
      a__plus	w: x1
      s 	w: x1
      and	w: x2 + 1
      #a__x	w: x2 + 3
      a__x	w: x2 + 1
      x 	w: x2 + 1
      #a__plus	w: x1 + 2
      #mark	w: x1 + 2
      0 	w: 1
      #a__and	w: 2
      mark	w: x1
      plus	w: x1
      tt	w: 25074
      a__and	w: x2 + 1
    USABLE RULES: { 1..14 }
    Removed DPs: #11 #19
Number of SCCs: 1, DPs: 9
  SCC { #1 #4..6 #8 #9 #13 #14 #17 }
POLO(Sum)... POLO(max)... QLPOS... succeeded.
      a__plus	s: [1,2]	p: 1
      s 	s: [1]	p: 0
      and	s: 2
      #a__x	s: [1,2]	p: 2
      a__x	s: [1,2]	p: 2
      x 	s: [1,2]	p: 2
      #a__plus	s: [1,2]	p: 1
      #mark	s: [1]	p: 1
      0 	s: []	p: 3
      #a__and	s: [1,2]	p: 0
      mark	s: 1
      plus	s: [1,2]	p: 1
      tt	s: []	p: 4
      a__and	s: 2
    USABLE RULES: { 1..14 }
    Removed DPs: #1 #4..6 #8 #9 #13 #14 #17
Number of SCCs: 0, DPs: 0