Problem:
 U41(tt()) -> N
 U51(tt()) -> s(plus(N,M))
 U71(tt()) -> plus(x(N,M),N)
 and(tt()) -> X
 U11(tt()) -> U12(isNat())
 U12(tt()) -> U13(isNat())
 U13(tt()) -> tt()
 U21(tt()) -> U22(isNat())
 U22(tt()) -> tt()
 U31(tt()) -> U32(isNat())
 U32(tt()) -> U33(isNat())
 U33(tt()) -> tt()
 U61(tt()) -> 0()
 isNat() -> tt()
 isNat() -> U11(and(isNatKind()))
 isNat() -> U21(isNatKind())
 isNat() -> U31(and(isNatKind()))
 isNatKind() -> tt()
 isNatKind() -> and(isNatKind())
 isNatKind() -> isNatKind()
 plus(N,0()) -> U41(and(isNat()))
 plus(N,s(M)) -> U51(and(and(isNat())))
 x(N,0()) -> U61(and(isNat()))
 x(N,s(M)) -> U71(and(and(isNat())))

Proof:
 Fresh Variable Processor: loop length: 1
                           terms:
                            U41(tt())
                           context: []
                           substitution:
                            N -> U41(tt())
  Qed