Problem:
U11(tt()) -> N
U21(tt()) -> s(plus(N,M))
U41(tt()) -> plus(x(N,M),N)
and(tt()) -> X
U31(tt()) -> 0()
isNat() -> tt()
isNat() -> and(isNat())
isNat() -> isNat()
plus(N,0()) -> U11(isNat())
plus(N,s(M)) -> U21(and(isNat()))
x(N,0()) -> U31(isNat())
x(N,s(M)) -> U41(and(isNat()))
Proof:
Fresh Variable Processor: loop length: 1
terms:
U11(tt())
context: []
substitution:
N -> U11(tt())
Qed