YES

TRS:

  U11(tt(),V1,V2) -> U12(isNatKind(activate(V1)),activate(V1),activate(V2))
  U12(tt(),V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2))
  U13(tt(),V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2))
  U14(tt(),V1,V2) -> U15(isNat(activate(V1)),activate(V2))
  U15(tt(),V2) -> U16(isNat(activate(V2)))
  U16(tt()) -> tt()
  U21(tt(),V1) -> U22(isNatKind(activate(V1)),activate(V1))
  U22(tt(),V1) -> U23(isNat(activate(V1)))
  U23(tt()) -> tt()
  U31(tt(),V2) -> U32(isNatKind(activate(V2)))
  U32(tt()) -> tt()
  U41(tt()) -> tt()
  U51(tt(),N) -> U52(isNatKind(activate(N)),activate(N))
  U52(tt(),N) -> activate(N)
  U61(tt(),M,N) -> U62(isNatKind(activate(M)),activate(M),activate(N))
  U62(tt(),M,N) -> U63(isNat(activate(N)),activate(M),activate(N))
  U63(tt(),M,N) -> U64(isNatKind(activate(N)),activate(M),activate(N))
  U64(tt(),M,N) -> s(plus(activate(N),activate(M)))
  isNat(n__0()) -> tt()
  isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2))
  isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1))
  isNatKind(n__0()) -> tt()
  isNatKind(n__plus(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V2))
  isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1)))
  plus(N,0()) -> U51(isNat(N),N)
  plus(N,s(M)) -> U61(isNat(M),M,N)
  0() -> n__0()
  plus(X1,X2) -> n__plus(X1,X2)
  s(X) -> n__s(X)
  activate(n__0()) -> 0()
  activate(n__plus(X1,X2)) -> plus(X1,X2)
  activate(n__s(X)) -> s(X)
  activate(X) -> X

linear polynomial interpretations on N:

  U11_A(x1,x2,x3) = 1
  U11#_A(x1,x2,x3) = x2 + x3 + 9
  tt_A = 1
  tt#_A = 3
  U12_A(x1,x2,x3) = 1
  U12#_A(x1,x2,x3) = x2 + x3 + 8
  isNatKind_A(x1) = 1
  isNatKind#_A(x1) = x1 + 2
  activate_A(x1) = x1
  activate#_A(x1) = x1
  U13_A(x1,x2,x3) = x1
  U13#_A(x1,x2,x3) = x2 + x3 + 7
  U14_A(x1,x2,x3) = 1
  U14#_A(x1,x2,x3) = x2 + x3 + 6
  U15_A(x1,x2) = 1
  U15#_A(x1,x2) = x2 + 5
  isNat_A(x1) = 1
  isNat#_A(x1) = x1 + 4
  U16_A(x1) = 1
  U16#_A(x1) = 4
  U21_A(x1,x2) = 1
  U21#_A(x1,x2) = x2 + 6
  U22_A(x1,x2) = 1
  U22#_A(x1,x2) = x2 + 5
  U23_A(x1) = 1
  U23#_A(x1) = 4
  U31_A(x1,x2) = 1
  U31#_A(x1,x2) = x2 + 11
  U32_A(x1) = x1
  U32#_A(x1) = 4
  U41_A(x1) = 1
  U41#_A(x1) = 2
  U51_A(x1,x2) = x2
  U51#_A(x1,x2) = x2 + 3
  U52_A(x1,x2) = x2
  U52#_A(x1,x2) = x2 + 1
  U61_A(x1,x2,x3) = x2 + x3 + 24
  U61#_A(x1,x2,x3) = x2 + x3 + 15
  U62_A(x1,x2,x3) = x2 + x3 + 24
  U62#_A(x1,x2,x3) = x2 + x3 + 14
  U63_A(x1,x2,x3) = x2 + x3 + 24
  U63#_A(x1,x2,x3) = x2 + x3 + 13
  U64_A(x1,x2,x3) = x2 + x3 + 24
  U64#_A(x1,x2,x3) = x2 + x3 + 12
  s_A(x1) = x1 + 12
  s#_A(x1) = 11
  plus_A(x1,x2) = x1 + x2 + 12
  plus#_A(x1,x2) = x1 + x2 + 11
  n__0_A = 6
  n__0#_A = 4
  n__plus_A(x1,x2) = x1 + x2 + 12
  n__plus#_A(x1,x2) = x1 + x2 + 10
  n__s_A(x1) = x1 + 12
  n__s#_A(x1) = 1
  0_A = 6
  0#_A = 5

precedence:

  U12 > U13 = U62 > U14 = U63 > U15 = U22 = U52 = U64 = n__plus > activate = U16 = U23 = n__0 > plus = 0 > U11 = isNat = U51 = U61 > s > n__s > U21 > isNatKind > U31 > U32 > tt > U41