YES

TRS:

  a__U11(tt(),V2) -> a__U12(a__isNat(V2))
  a__U12(tt()) -> tt()
  a__U21(tt()) -> tt()
  a__U31(tt(),N) -> mark(N)
  a__U41(tt(),M,N) -> a__U42(a__isNat(N),M,N)
  a__U42(tt(),M,N) -> s(a__plus(mark(N),mark(M)))
  a__isNat(0()) -> tt()
  a__isNat(plus(V1,V2)) -> a__U11(a__isNat(V1),V2)
  a__isNat(s(V1)) -> a__U21(a__isNat(V1))
  a__plus(N,0()) -> a__U31(a__isNat(N),N)
  a__plus(N,s(M)) -> a__U41(a__isNat(M),M,N)
  mark(U11(X1,X2)) -> a__U11(mark(X1),X2)
  mark(U12(X)) -> a__U12(mark(X))
  mark(isNat(X)) -> a__isNat(X)
  mark(U21(X)) -> a__U21(mark(X))
  mark(U31(X1,X2)) -> a__U31(mark(X1),X2)
  mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3)
  mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3)
  mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2))
  mark(tt()) -> tt()
  mark(s(X)) -> s(mark(X))
  mark(0()) -> 0()
  a__U11(X1,X2) -> U11(X1,X2)
  a__U12(X) -> U12(X)
  a__isNat(X) -> isNat(X)
  a__U21(X) -> U21(X)
  a__U31(X1,X2) -> U31(X1,X2)
  a__U41(X1,X2,X3) -> U41(X1,X2,X3)
  a__U42(X1,X2,X3) -> U42(X1,X2,X3)
  a__plus(X1,X2) -> plus(X1,X2)

linear polynomial interpretations on N:

  a__U11_A(x1,x2) = x1
  a__U11#_A(x1,x2) = 3
  tt_A = 1
  tt#_A = 6
  a__U12_A(x1) = x1
  a__U12#_A(x1) = 2
  a__isNat_A(x1) = 1
  a__isNat#_A(x1) = 2
  a__U21_A(x1) = x1
  a__U21#_A(x1) = 1
  a__U31_A(x1,x2) = x1 + x2 + 2
  a__U31#_A(x1,x2) = x2 + 5
  mark_A(x1) = x1
  mark#_A(x1) = x1 + 4
  a__U41_A(x1,x2,x3) = x1 + x2 + x3 + 5
  a__U41#_A(x1,x2,x3) = x2 + x3 + 8
  a__U42_A(x1,x2,x3) = x1 + x2 + x3 + 5
  a__U42#_A(x1,x2,x3) = x2 + x3 + 7
  s_A(x1) = x1 + 3
  s#_A(x1) = 2
  a__plus_A(x1,x2) = x1 + x2 + 3
  a__plus#_A(x1,x2) = x1 + x2 + 6
  0_A = 4
  0#_A = 7
  plus_A(x1,x2) = x1 + x2 + 3
  plus#_A(x1,x2) = 5
  U11_A(x1,x2) = x1
  U11#_A(x1,x2) = 2
  U12_A(x1) = x1
  U12#_A(x1) = 1
  isNat_A(x1) = 1
  isNat#_A(x1) = 0
  U21_A(x1) = x1
  U21#_A(x1) = 0
  U31_A(x1,x2) = x1 + x2 + 2
  U31#_A(x1,x2) = 3
  U41_A(x1,x2,x3) = x1 + x2 + x3 + 5
  U41#_A(x1,x2,x3) = x2 + x3 + 3
  U42_A(x1,x2,x3) = x1 + x2 + x3 + 5
  U42#_A(x1,x2,x3) = 3

precedence:

  a__plus = U41 > a__U41 > a__U42 > tt = plus = U11 = isNat = U42 > a__isNat = mark = s > a__U11 = a__U21 = a__U31 = 0 > a__U12 = U21 = U31 > U12