NO 0.09/0.17 NO 0.09/0.17 0.09/0.17 Problem: 0.09/0.17 uTake2(tt()) -> cons(N) 0.09/0.17 uLength(tt()) -> s(length(L)) 0.09/0.17 and(tt(),T) -> T 0.09/0.17 isNatIList() -> isNatList() 0.09/0.17 isNat() -> tt() 0.09/0.17 isNat() -> isNat() 0.09/0.17 isNat() -> isNatList() 0.09/0.17 isNatIList() -> tt() 0.09/0.17 isNatIList() -> and(isNat(),isNatIList()) 0.09/0.17 isNatList() -> tt() 0.09/0.17 isNatList() -> and(isNat(),isNatList()) 0.09/0.17 isNatList() -> and(isNat(),isNatIList()) 0.09/0.17 zeros() -> cons(0()) 0.09/0.17 take(0(),IL) -> uTake1(isNatIList()) 0.09/0.17 uTake1(tt()) -> nil() 0.09/0.17 take(s(M),cons(N)) -> uTake2(and(isNat(),and(isNat(),isNatIList()))) 0.09/0.17 length(cons(N)) -> uLength(and(isNat(),isNatList())) 0.09/0.17 0.09/0.17 Proof: 0.09/0.17 Fresh Variable Processor: 0.09/0.17 loop length: 1 0.09/0.17 terms: 0.09/0.17 uTake2(tt()) 0.09/0.17 context: cons([]) 0.09/0.17 substitution: 0.09/0.17 N -> uTake2(tt()) 0.09/0.17 Qed 0.09/0.18 EOF