LMPO
MAYBE
We consider the following Problem:
Strict Trs:
{ nats() -> adx(zeros())
, zeros() -> cons(n__0(), n__zeros())
, incr(cons(X, Y)) -> cons(n__s(activate(X)), n__incr(activate(Y)))
, adx(cons(X, Y)) -> incr(cons(activate(X), n__adx(activate(Y))))
, hd(cons(X, Y)) -> activate(X)
, tl(cons(X, Y)) -> activate(Y)
, 0() -> n__0()
, zeros() -> n__zeros()
, s(X) -> n__s(X)
, incr(X) -> n__incr(X)
, adx(X) -> n__adx(X)
, activate(n__0()) -> 0()
, activate(n__zeros()) -> zeros()
, activate(n__s(X)) -> s(X)
, activate(n__incr(X)) -> incr(activate(X))
, activate(n__adx(X)) -> adx(activate(X))
, activate(X) -> X}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
MPO
MAYBE
We consider the following Problem:
Strict Trs:
{ nats() -> adx(zeros())
, zeros() -> cons(n__0(), n__zeros())
, incr(cons(X, Y)) -> cons(n__s(activate(X)), n__incr(activate(Y)))
, adx(cons(X, Y)) -> incr(cons(activate(X), n__adx(activate(Y))))
, hd(cons(X, Y)) -> activate(X)
, tl(cons(X, Y)) -> activate(Y)
, 0() -> n__0()
, zeros() -> n__zeros()
, s(X) -> n__s(X)
, incr(X) -> n__incr(X)
, adx(X) -> n__adx(X)
, activate(n__0()) -> 0()
, activate(n__zeros()) -> zeros()
, activate(n__s(X)) -> s(X)
, activate(n__incr(X)) -> incr(activate(X))
, activate(n__adx(X)) -> adx(activate(X))
, activate(X) -> X}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
POP*
MAYBE
We consider the following Problem:
Strict Trs:
{ nats() -> adx(zeros())
, zeros() -> cons(n__0(), n__zeros())
, incr(cons(X, Y)) -> cons(n__s(activate(X)), n__incr(activate(Y)))
, adx(cons(X, Y)) -> incr(cons(activate(X), n__adx(activate(Y))))
, hd(cons(X, Y)) -> activate(X)
, tl(cons(X, Y)) -> activate(Y)
, 0() -> n__0()
, zeros() -> n__zeros()
, s(X) -> n__s(X)
, incr(X) -> n__incr(X)
, adx(X) -> n__adx(X)
, activate(n__0()) -> 0()
, activate(n__zeros()) -> zeros()
, activate(n__s(X)) -> s(X)
, activate(n__incr(X)) -> incr(activate(X))
, activate(n__adx(X)) -> adx(activate(X))
, activate(X) -> X}
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:
{ nats() -> adx(zeros())
, zeros() -> cons(n__0(), n__zeros())
, incr(cons(X, Y)) -> cons(n__s(activate(X)), n__incr(activate(Y)))
, adx(cons(X, Y)) -> incr(cons(activate(X), n__adx(activate(Y))))
, hd(cons(X, Y)) -> activate(X)
, tl(cons(X, Y)) -> activate(Y)
, 0() -> n__0()
, zeros() -> n__zeros()
, s(X) -> n__s(X)
, incr(X) -> n__incr(X)
, adx(X) -> n__adx(X)
, activate(n__0()) -> 0()
, activate(n__zeros()) -> zeros()
, activate(n__s(X)) -> s(X)
, activate(n__incr(X)) -> incr(activate(X))
, activate(n__adx(X)) -> adx(activate(X))
, activate(X) -> X}
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:
{ nats() -> adx(zeros())
, zeros() -> cons(n__0(), n__zeros())
, incr(cons(X, Y)) -> cons(n__s(activate(X)), n__incr(activate(Y)))
, adx(cons(X, Y)) -> incr(cons(activate(X), n__adx(activate(Y))))
, hd(cons(X, Y)) -> activate(X)
, tl(cons(X, Y)) -> activate(Y)
, 0() -> n__0()
, zeros() -> n__zeros()
, s(X) -> n__s(X)
, incr(X) -> n__incr(X)
, adx(X) -> n__adx(X)
, activate(n__0()) -> 0()
, activate(n__zeros()) -> zeros()
, activate(n__s(X)) -> s(X)
, activate(n__incr(X)) -> incr(activate(X))
, activate(n__adx(X)) -> adx(activate(X))
, activate(X) -> X}
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:
{ nats() -> adx(zeros())
, zeros() -> cons(n__0(), n__zeros())
, incr(cons(X, Y)) -> cons(n__s(activate(X)), n__incr(activate(Y)))
, adx(cons(X, Y)) -> incr(cons(activate(X), n__adx(activate(Y))))
, hd(cons(X, Y)) -> activate(X)
, tl(cons(X, Y)) -> activate(Y)
, 0() -> n__0()
, zeros() -> n__zeros()
, s(X) -> n__s(X)
, incr(X) -> n__incr(X)
, adx(X) -> n__adx(X)
, activate(n__0()) -> 0()
, activate(n__zeros()) -> zeros()
, activate(n__s(X)) -> s(X)
, activate(n__incr(X)) -> incr(activate(X))
, activate(n__adx(X)) -> adx(activate(X))
, activate(X) -> X}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..