NO
0.08/0.19	NO
0.08/0.19	
0.08/0.19	Problem:
0.08/0.19	 U41(tt()) -> N
0.08/0.19	 U51(tt()) -> s(plus(N,M))
0.08/0.19	 U71(tt()) -> plus(x(N,M),N)
0.08/0.19	 and(tt()) -> X
0.08/0.19	 U11(tt()) -> U12(isNat())
0.08/0.19	 U12(tt()) -> U13(isNat())
0.08/0.19	 U13(tt()) -> tt()
0.08/0.19	 U21(tt()) -> U22(isNat())
0.08/0.19	 U22(tt()) -> tt()
0.08/0.19	 U31(tt()) -> U32(isNat())
0.08/0.19	 U32(tt()) -> U33(isNat())
0.08/0.19	 U33(tt()) -> tt()
0.08/0.19	 U61(tt()) -> 0()
0.08/0.19	 isNat() -> tt()
0.08/0.19	 isNat() -> U11(and(isNatKind()))
0.08/0.19	 isNat() -> U21(isNatKind())
0.08/0.19	 isNat() -> U31(and(isNatKind()))
0.08/0.19	 isNatKind() -> tt()
0.08/0.19	 isNatKind() -> and(isNatKind())
0.08/0.19	 isNatKind() -> isNatKind()
0.08/0.19	 plus(N,0()) -> U41(and(isNat()))
0.08/0.19	 plus(N,s(M)) -> U51(and(and(isNat())))
0.08/0.19	 x(N,0()) -> U61(and(isNat()))
0.08/0.19	 x(N,s(M)) -> U71(and(and(isNat())))
0.08/0.19	
0.08/0.19	Proof:
0.08/0.19	 Fresh Variable Processor: loop length: 1
0.08/0.19	                           terms:
0.08/0.19	                            U41(tt())
0.08/0.19	                           context: []
0.08/0.19	                           substitution:
0.08/0.19	                            N -> U41(tt())
0.08/0.19	  Qed
0.08/0.19	EOF