YES

TRS:

  a__U11(tt(),V1,V2) -> a__U12(a__isNatKind(V1),V1,V2)
  a__U12(tt(),V1,V2) -> a__U13(a__isNatKind(V2),V1,V2)
  a__U13(tt(),V1,V2) -> a__U14(a__isNatKind(V2),V1,V2)
  a__U14(tt(),V1,V2) -> a__U15(a__isNat(V1),V2)
  a__U15(tt(),V2) -> a__U16(a__isNat(V2))
  a__U16(tt()) -> tt()
  a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1)
  a__U22(tt(),V1) -> a__U23(a__isNat(V1))
  a__U23(tt()) -> tt()
  a__U31(tt(),V2) -> a__U32(a__isNatKind(V2))
  a__U32(tt()) -> tt()
  a__U41(tt()) -> tt()
  a__U51(tt(),N) -> a__U52(a__isNatKind(N),N)
  a__U52(tt(),N) -> mark(N)
  a__U61(tt(),M,N) -> a__U62(a__isNatKind(M),M,N)
  a__U62(tt(),M,N) -> a__U63(a__isNat(N),M,N)
  a__U63(tt(),M,N) -> a__U64(a__isNatKind(N),M,N)
  a__U64(tt(),M,N) -> s(a__plus(mark(N),mark(M)))
  a__isNat(0()) -> tt()
  a__isNat(plus(V1,V2)) -> a__U11(a__isNatKind(V1),V1,V2)
  a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1)
  a__isNatKind(0()) -> tt()
  a__isNatKind(plus(V1,V2)) -> a__U31(a__isNatKind(V1),V2)
  a__isNatKind(s(V1)) -> a__U41(a__isNatKind(V1))
  a__plus(N,0()) -> a__U51(a__isNat(N),N)
  a__plus(N,s(M)) -> a__U61(a__isNat(M),M,N)
  mark(U11(X1,X2,X3)) -> a__U11(mark(X1),X2,X3)
  mark(U12(X1,X2,X3)) -> a__U12(mark(X1),X2,X3)
  mark(isNatKind(X)) -> a__isNatKind(X)
  mark(U13(X1,X2,X3)) -> a__U13(mark(X1),X2,X3)
  mark(U14(X1,X2,X3)) -> a__U14(mark(X1),X2,X3)
  mark(U15(X1,X2)) -> a__U15(mark(X1),X2)
  mark(isNat(X)) -> a__isNat(X)
  mark(U16(X)) -> a__U16(mark(X))
  mark(U21(X1,X2)) -> a__U21(mark(X1),X2)
  mark(U22(X1,X2)) -> a__U22(mark(X1),X2)
  mark(U23(X)) -> a__U23(mark(X))
  mark(U31(X1,X2)) -> a__U31(mark(X1),X2)
  mark(U32(X)) -> a__U32(mark(X))
  mark(U41(X)) -> a__U41(mark(X))
  mark(U51(X1,X2)) -> a__U51(mark(X1),X2)
  mark(U52(X1,X2)) -> a__U52(mark(X1),X2)
  mark(U61(X1,X2,X3)) -> a__U61(mark(X1),X2,X3)
  mark(U62(X1,X2,X3)) -> a__U62(mark(X1),X2,X3)
  mark(U63(X1,X2,X3)) -> a__U63(mark(X1),X2,X3)
  mark(U64(X1,X2,X3)) -> a__U64(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,X3) -> U11(X1,X2,X3)
  a__U12(X1,X2,X3) -> U12(X1,X2,X3)
  a__isNatKind(X) -> isNatKind(X)
  a__U13(X1,X2,X3) -> U13(X1,X2,X3)
  a__U14(X1,X2,X3) -> U14(X1,X2,X3)
  a__U15(X1,X2) -> U15(X1,X2)
  a__isNat(X) -> isNat(X)
  a__U16(X) -> U16(X)
  a__U21(X1,X2) -> U21(X1,X2)
  a__U22(X1,X2) -> U22(X1,X2)
  a__U23(X) -> U23(X)
  a__U31(X1,X2) -> U31(X1,X2)
  a__U32(X) -> U32(X)
  a__U41(X) -> U41(X)
  a__U51(X1,X2) -> U51(X1,X2)
  a__U52(X1,X2) -> U52(X1,X2)
  a__U61(X1,X2,X3) -> U61(X1,X2,X3)
  a__U62(X1,X2,X3) -> U62(X1,X2,X3)
  a__U63(X1,X2,X3) -> U63(X1,X2,X3)
  a__U64(X1,X2,X3) -> U64(X1,X2,X3)
  a__plus(X1,X2) -> plus(X1,X2)

linear polynomial interpretations on N:

  a__U11_A(x1,x2,x3) = x1
  a__U11#_A(x1,x2,x3) = x1 + 7
  tt_A = 0
  tt#_A = 9
  a__U12_A(x1,x2,x3) = x1
  a__U12#_A(x1,x2,x3) = 6
  a__isNatKind_A(x1) = 0
  a__isNatKind#_A(x1) = 2
  a__U13_A(x1,x2,x3) = x1
  a__U13#_A(x1,x2,x3) = x1 + 5
  a__U14_A(x1,x2,x3) = x1
  a__U14#_A(x1,x2,x3) = 4
  a__U15_A(x1,x2) = x1
  a__U15#_A(x1,x2) = 4
  a__isNat_A(x1) = 0
  a__isNat#_A(x1) = 3
  a__U16_A(x1) = x1
  a__U16#_A(x1) = 1
  a__U21_A(x1,x2) = x1
  a__U21#_A(x1,x2) = 5
  a__U22_A(x1,x2) = x1
  a__U22#_A(x1,x2) = 4
  a__U23_A(x1) = x1
  a__U23#_A(x1) = 1
  a__U31_A(x1,x2) = x1
  a__U31#_A(x1,x2) = 7
  a__U32_A(x1) = x1
  a__U32#_A(x1) = 6
  a__U41_A(x1) = x1
  a__U41#_A(x1) = x1 + 1
  a__U51_A(x1,x2) = x1 + x2 + 4
  a__U51#_A(x1,x2) = x2 + 11
  a__U52_A(x1,x2) = x1 + x2 + 3
  a__U52#_A(x1,x2) = x2 + 10
  mark_A(x1) = x1
  mark#_A(x1) = x1 + 8
  a__U61_A(x1,x2,x3) = x1 + x2 + x3 + 10
  a__U61#_A(x1,x2,x3) = x2 + x3 + 16
  a__U62_A(x1,x2,x3) = x1 + x2 + x3 + 10
  a__U62#_A(x1,x2,x3) = x2 + x3 + 15
  a__U63_A(x1,x2,x3) = x1 + x2 + x3 + 10
  a__U63#_A(x1,x2,x3) = x2 + x3 + 14
  a__U64_A(x1,x2,x3) = x1 + x2 + x3 + 10
  a__U64#_A(x1,x2,x3) = x2 + x3 + 13
  s_A(x1) = x1 + 7
  s#_A(x1) = x1 + 9
  a__plus_A(x1,x2) = x1 + x2 + 3
  a__plus#_A(x1,x2) = x1 + x2 + 10
  0_A = 3
  0#_A = 10
  plus_A(x1,x2) = x1 + x2 + 3
  plus#_A(x1,x2) = x1 + x2 + 9
  U11_A(x1,x2,x3) = x1
  U11#_A(x1,x2,x3) = x1 + 6
  U12_A(x1,x2,x3) = x1
  U12#_A(x1,x2,x3) = 5
  isNatKind_A(x1) = 0
  isNatKind#_A(x1) = 0
  U13_A(x1,x2,x3) = x1
  U13#_A(x1,x2,x3) = x1 + 4
  U14_A(x1,x2,x3) = x1
  U14#_A(x1,x2,x3) = 3
  U15_A(x1,x2) = x1
  U15#_A(x1,x2) = 3
  isNat_A(x1) = 0
  isNat#_A(x1) = 0
  U16_A(x1) = x1
  U16#_A(x1) = 0
  U21_A(x1,x2) = x1
  U21#_A(x1,x2) = 4
  U22_A(x1,x2) = x1
  U22#_A(x1,x2) = 0
  U23_A(x1) = x1
  U23#_A(x1) = 0
  U31_A(x1,x2) = x1
  U31#_A(x1,x2) = 6
  U32_A(x1) = x1
  U32#_A(x1) = 0
  U41_A(x1) = x1
  U41#_A(x1) = x1
  U51_A(x1,x2) = x1 + x2 + 4
  U51#_A(x1,x2) = 10
  U52_A(x1,x2) = x1 + x2 + 3
  U52#_A(x1,x2) = x2 + 9
  U61_A(x1,x2,x3) = x1 + x2 + x3 + 10
  U61#_A(x1,x2,x3) = x2 + x3 + 7
  U62_A(x1,x2,x3) = x1 + x2 + x3 + 10
  U62#_A(x1,x2,x3) = 0
  U63_A(x1,x2,x3) = x1 + x2 + x3 + 10
  U63#_A(x1,x2,x3) = 9
  U64_A(x1,x2,x3) = x1 + x2 + x3 + 10
  U64#_A(x1,x2,x3) = 9

precedence:

  a__U13 = a__U51 = U14 > a__U11 = a__U14 = a__U52 = a__U62 > tt = a__U15 = U11 = U13 = U16 = U31 = U32 = U51 = U52 = U62 = U63 = U64 > mark > a__U12 = a__U16 = a__U63 = 0 > a__U64 = U12 > s = a__plus = U61 > a__U61 = plus > a__isNatKind = isNat > a__isNat = a__U31 = a__U41 = isNatKind = U15 > a__U21 = a__U32 = U41 > a__U22 = U21 > a__U23 = U22 > U23