LMPO
MAYBE
We consider the following Problem:
Strict Trs:
{ a__primes() -> a__sieve(a__from(s(s(0()))))
, a__from(X) -> cons(mark(X), from(s(X)))
, a__head(cons(X, Y)) -> mark(X)
, a__tail(cons(X, Y)) -> mark(Y)
, a__if(true(), X, Y) -> mark(X)
, a__if(false(), X, Y) -> mark(Y)
, a__filter(s(s(X)), cons(Y, Z)) ->
a__if(divides(s(s(mark(X))), mark(Y)),
filter(s(s(X)), Z),
cons(Y, filter(X, sieve(Y))))
, a__sieve(cons(X, Y)) -> cons(mark(X), filter(X, sieve(Y)))
, mark(primes()) -> a__primes()
, mark(sieve(X)) -> a__sieve(mark(X))
, mark(from(X)) -> a__from(mark(X))
, mark(head(X)) -> a__head(mark(X))
, mark(tail(X)) -> a__tail(mark(X))
, mark(if(X1, X2, X3)) -> a__if(mark(X1), X2, X3)
, mark(filter(X1, X2)) -> a__filter(mark(X1), mark(X2))
, mark(s(X)) -> s(mark(X))
, mark(0()) -> 0()
, mark(cons(X1, X2)) -> cons(mark(X1), X2)
, mark(true()) -> true()
, mark(false()) -> false()
, mark(divides(X1, X2)) -> divides(mark(X1), mark(X2))
, a__primes() -> primes()
, a__sieve(X) -> sieve(X)
, a__from(X) -> from(X)
, a__head(X) -> head(X)
, a__tail(X) -> tail(X)
, a__if(X1, X2, X3) -> if(X1, X2, X3)
, a__filter(X1, X2) -> filter(X1, X2)}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
MPO
MAYBE
We consider the following Problem:
Strict Trs:
{ a__primes() -> a__sieve(a__from(s(s(0()))))
, a__from(X) -> cons(mark(X), from(s(X)))
, a__head(cons(X, Y)) -> mark(X)
, a__tail(cons(X, Y)) -> mark(Y)
, a__if(true(), X, Y) -> mark(X)
, a__if(false(), X, Y) -> mark(Y)
, a__filter(s(s(X)), cons(Y, Z)) ->
a__if(divides(s(s(mark(X))), mark(Y)),
filter(s(s(X)), Z),
cons(Y, filter(X, sieve(Y))))
, a__sieve(cons(X, Y)) -> cons(mark(X), filter(X, sieve(Y)))
, mark(primes()) -> a__primes()
, mark(sieve(X)) -> a__sieve(mark(X))
, mark(from(X)) -> a__from(mark(X))
, mark(head(X)) -> a__head(mark(X))
, mark(tail(X)) -> a__tail(mark(X))
, mark(if(X1, X2, X3)) -> a__if(mark(X1), X2, X3)
, mark(filter(X1, X2)) -> a__filter(mark(X1), mark(X2))
, mark(s(X)) -> s(mark(X))
, mark(0()) -> 0()
, mark(cons(X1, X2)) -> cons(mark(X1), X2)
, mark(true()) -> true()
, mark(false()) -> false()
, mark(divides(X1, X2)) -> divides(mark(X1), mark(X2))
, a__primes() -> primes()
, a__sieve(X) -> sieve(X)
, a__from(X) -> from(X)
, a__head(X) -> head(X)
, a__tail(X) -> tail(X)
, a__if(X1, X2, X3) -> if(X1, X2, X3)
, a__filter(X1, X2) -> filter(X1, X2)}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
POP*
MAYBE
We consider the following Problem:
Strict Trs:
{ a__primes() -> a__sieve(a__from(s(s(0()))))
, a__from(X) -> cons(mark(X), from(s(X)))
, a__head(cons(X, Y)) -> mark(X)
, a__tail(cons(X, Y)) -> mark(Y)
, a__if(true(), X, Y) -> mark(X)
, a__if(false(), X, Y) -> mark(Y)
, a__filter(s(s(X)), cons(Y, Z)) ->
a__if(divides(s(s(mark(X))), mark(Y)),
filter(s(s(X)), Z),
cons(Y, filter(X, sieve(Y))))
, a__sieve(cons(X, Y)) -> cons(mark(X), filter(X, sieve(Y)))
, mark(primes()) -> a__primes()
, mark(sieve(X)) -> a__sieve(mark(X))
, mark(from(X)) -> a__from(mark(X))
, mark(head(X)) -> a__head(mark(X))
, mark(tail(X)) -> a__tail(mark(X))
, mark(if(X1, X2, X3)) -> a__if(mark(X1), X2, X3)
, mark(filter(X1, X2)) -> a__filter(mark(X1), mark(X2))
, mark(s(X)) -> s(mark(X))
, mark(0()) -> 0()
, mark(cons(X1, X2)) -> cons(mark(X1), X2)
, mark(true()) -> true()
, mark(false()) -> false()
, mark(divides(X1, X2)) -> divides(mark(X1), mark(X2))
, a__primes() -> primes()
, a__sieve(X) -> sieve(X)
, a__from(X) -> from(X)
, a__head(X) -> head(X)
, a__tail(X) -> tail(X)
, a__if(X1, X2, X3) -> if(X1, X2, X3)
, a__filter(X1, X2) -> filter(X1, X2)}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
POP* (PS)
MAYBE
We consider the following Problem:
Strict Trs:
{ a__primes() -> a__sieve(a__from(s(s(0()))))
, a__from(X) -> cons(mark(X), from(s(X)))
, a__head(cons(X, Y)) -> mark(X)
, a__tail(cons(X, Y)) -> mark(Y)
, a__if(true(), X, Y) -> mark(X)
, a__if(false(), X, Y) -> mark(Y)
, a__filter(s(s(X)), cons(Y, Z)) ->
a__if(divides(s(s(mark(X))), mark(Y)),
filter(s(s(X)), Z),
cons(Y, filter(X, sieve(Y))))
, a__sieve(cons(X, Y)) -> cons(mark(X), filter(X, sieve(Y)))
, mark(primes()) -> a__primes()
, mark(sieve(X)) -> a__sieve(mark(X))
, mark(from(X)) -> a__from(mark(X))
, mark(head(X)) -> a__head(mark(X))
, mark(tail(X)) -> a__tail(mark(X))
, mark(if(X1, X2, X3)) -> a__if(mark(X1), X2, X3)
, mark(filter(X1, X2)) -> a__filter(mark(X1), mark(X2))
, mark(s(X)) -> s(mark(X))
, mark(0()) -> 0()
, mark(cons(X1, X2)) -> cons(mark(X1), X2)
, mark(true()) -> true()
, mark(false()) -> false()
, mark(divides(X1, X2)) -> divides(mark(X1), mark(X2))
, a__primes() -> primes()
, a__sieve(X) -> sieve(X)
, a__from(X) -> from(X)
, a__head(X) -> head(X)
, a__tail(X) -> tail(X)
, a__if(X1, X2, X3) -> if(X1, X2, X3)
, a__filter(X1, X2) -> filter(X1, X2)}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
Small POP*
MAYBE
We consider the following Problem:
Strict Trs:
{ a__primes() -> a__sieve(a__from(s(s(0()))))
, a__from(X) -> cons(mark(X), from(s(X)))
, a__head(cons(X, Y)) -> mark(X)
, a__tail(cons(X, Y)) -> mark(Y)
, a__if(true(), X, Y) -> mark(X)
, a__if(false(), X, Y) -> mark(Y)
, a__filter(s(s(X)), cons(Y, Z)) ->
a__if(divides(s(s(mark(X))), mark(Y)),
filter(s(s(X)), Z),
cons(Y, filter(X, sieve(Y))))
, a__sieve(cons(X, Y)) -> cons(mark(X), filter(X, sieve(Y)))
, mark(primes()) -> a__primes()
, mark(sieve(X)) -> a__sieve(mark(X))
, mark(from(X)) -> a__from(mark(X))
, mark(head(X)) -> a__head(mark(X))
, mark(tail(X)) -> a__tail(mark(X))
, mark(if(X1, X2, X3)) -> a__if(mark(X1), X2, X3)
, mark(filter(X1, X2)) -> a__filter(mark(X1), mark(X2))
, mark(s(X)) -> s(mark(X))
, mark(0()) -> 0()
, mark(cons(X1, X2)) -> cons(mark(X1), X2)
, mark(true()) -> true()
, mark(false()) -> false()
, mark(divides(X1, X2)) -> divides(mark(X1), mark(X2))
, a__primes() -> primes()
, a__sieve(X) -> sieve(X)
, a__from(X) -> from(X)
, a__head(X) -> head(X)
, a__tail(X) -> tail(X)
, a__if(X1, X2, X3) -> if(X1, X2, X3)
, a__filter(X1, X2) -> filter(X1, X2)}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
Small POP* (PS)
MAYBE
We consider the following Problem:
Strict Trs:
{ a__primes() -> a__sieve(a__from(s(s(0()))))
, a__from(X) -> cons(mark(X), from(s(X)))
, a__head(cons(X, Y)) -> mark(X)
, a__tail(cons(X, Y)) -> mark(Y)
, a__if(true(), X, Y) -> mark(X)
, a__if(false(), X, Y) -> mark(Y)
, a__filter(s(s(X)), cons(Y, Z)) ->
a__if(divides(s(s(mark(X))), mark(Y)),
filter(s(s(X)), Z),
cons(Y, filter(X, sieve(Y))))
, a__sieve(cons(X, Y)) -> cons(mark(X), filter(X, sieve(Y)))
, mark(primes()) -> a__primes()
, mark(sieve(X)) -> a__sieve(mark(X))
, mark(from(X)) -> a__from(mark(X))
, mark(head(X)) -> a__head(mark(X))
, mark(tail(X)) -> a__tail(mark(X))
, mark(if(X1, X2, X3)) -> a__if(mark(X1), X2, X3)
, mark(filter(X1, X2)) -> a__filter(mark(X1), mark(X2))
, mark(s(X)) -> s(mark(X))
, mark(0()) -> 0()
, mark(cons(X1, X2)) -> cons(mark(X1), X2)
, mark(true()) -> true()
, mark(false()) -> false()
, mark(divides(X1, X2)) -> divides(mark(X1), mark(X2))
, a__primes() -> primes()
, a__sieve(X) -> sieve(X)
, a__from(X) -> from(X)
, a__head(X) -> head(X)
, a__tail(X) -> tail(X)
, a__if(X1, X2, X3) -> if(X1, X2, X3)
, a__filter(X1, X2) -> filter(X1, X2)}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..