LMPO
MAYBE
We consider the following Problem:
Strict Trs:
{ a__incr(nil()) -> nil()
, a__incr(cons(X, L)) -> cons(s(mark(X)), incr(L))
, a__adx(nil()) -> nil()
, a__adx(cons(X, L)) -> a__incr(cons(mark(X), adx(L)))
, a__nats() -> a__adx(a__zeros())
, a__zeros() -> cons(0(), zeros())
, a__head(cons(X, L)) -> mark(X)
, a__tail(cons(X, L)) -> mark(L)
, mark(incr(X)) -> a__incr(mark(X))
, mark(adx(X)) -> a__adx(mark(X))
, mark(nats()) -> a__nats()
, mark(zeros()) -> a__zeros()
, mark(head(X)) -> a__head(mark(X))
, mark(tail(X)) -> a__tail(mark(X))
, mark(nil()) -> nil()
, mark(cons(X1, X2)) -> cons(mark(X1), X2)
, mark(s(X)) -> s(mark(X))
, mark(0()) -> 0()
, a__incr(X) -> incr(X)
, a__adx(X) -> adx(X)
, a__nats() -> nats()
, a__zeros() -> zeros()
, a__head(X) -> head(X)
, a__tail(X) -> tail(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:
{ a__incr(nil()) -> nil()
, a__incr(cons(X, L)) -> cons(s(mark(X)), incr(L))
, a__adx(nil()) -> nil()
, a__adx(cons(X, L)) -> a__incr(cons(mark(X), adx(L)))
, a__nats() -> a__adx(a__zeros())
, a__zeros() -> cons(0(), zeros())
, a__head(cons(X, L)) -> mark(X)
, a__tail(cons(X, L)) -> mark(L)
, mark(incr(X)) -> a__incr(mark(X))
, mark(adx(X)) -> a__adx(mark(X))
, mark(nats()) -> a__nats()
, mark(zeros()) -> a__zeros()
, mark(head(X)) -> a__head(mark(X))
, mark(tail(X)) -> a__tail(mark(X))
, mark(nil()) -> nil()
, mark(cons(X1, X2)) -> cons(mark(X1), X2)
, mark(s(X)) -> s(mark(X))
, mark(0()) -> 0()
, a__incr(X) -> incr(X)
, a__adx(X) -> adx(X)
, a__nats() -> nats()
, a__zeros() -> zeros()
, a__head(X) -> head(X)
, a__tail(X) -> tail(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:
{ a__incr(nil()) -> nil()
, a__incr(cons(X, L)) -> cons(s(mark(X)), incr(L))
, a__adx(nil()) -> nil()
, a__adx(cons(X, L)) -> a__incr(cons(mark(X), adx(L)))
, a__nats() -> a__adx(a__zeros())
, a__zeros() -> cons(0(), zeros())
, a__head(cons(X, L)) -> mark(X)
, a__tail(cons(X, L)) -> mark(L)
, mark(incr(X)) -> a__incr(mark(X))
, mark(adx(X)) -> a__adx(mark(X))
, mark(nats()) -> a__nats()
, mark(zeros()) -> a__zeros()
, mark(head(X)) -> a__head(mark(X))
, mark(tail(X)) -> a__tail(mark(X))
, mark(nil()) -> nil()
, mark(cons(X1, X2)) -> cons(mark(X1), X2)
, mark(s(X)) -> s(mark(X))
, mark(0()) -> 0()
, a__incr(X) -> incr(X)
, a__adx(X) -> adx(X)
, a__nats() -> nats()
, a__zeros() -> zeros()
, a__head(X) -> head(X)
, a__tail(X) -> tail(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:
{ a__incr(nil()) -> nil()
, a__incr(cons(X, L)) -> cons(s(mark(X)), incr(L))
, a__adx(nil()) -> nil()
, a__adx(cons(X, L)) -> a__incr(cons(mark(X), adx(L)))
, a__nats() -> a__adx(a__zeros())
, a__zeros() -> cons(0(), zeros())
, a__head(cons(X, L)) -> mark(X)
, a__tail(cons(X, L)) -> mark(L)
, mark(incr(X)) -> a__incr(mark(X))
, mark(adx(X)) -> a__adx(mark(X))
, mark(nats()) -> a__nats()
, mark(zeros()) -> a__zeros()
, mark(head(X)) -> a__head(mark(X))
, mark(tail(X)) -> a__tail(mark(X))
, mark(nil()) -> nil()
, mark(cons(X1, X2)) -> cons(mark(X1), X2)
, mark(s(X)) -> s(mark(X))
, mark(0()) -> 0()
, a__incr(X) -> incr(X)
, a__adx(X) -> adx(X)
, a__nats() -> nats()
, a__zeros() -> zeros()
, a__head(X) -> head(X)
, a__tail(X) -> tail(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:
{ a__incr(nil()) -> nil()
, a__incr(cons(X, L)) -> cons(s(mark(X)), incr(L))
, a__adx(nil()) -> nil()
, a__adx(cons(X, L)) -> a__incr(cons(mark(X), adx(L)))
, a__nats() -> a__adx(a__zeros())
, a__zeros() -> cons(0(), zeros())
, a__head(cons(X, L)) -> mark(X)
, a__tail(cons(X, L)) -> mark(L)
, mark(incr(X)) -> a__incr(mark(X))
, mark(adx(X)) -> a__adx(mark(X))
, mark(nats()) -> a__nats()
, mark(zeros()) -> a__zeros()
, mark(head(X)) -> a__head(mark(X))
, mark(tail(X)) -> a__tail(mark(X))
, mark(nil()) -> nil()
, mark(cons(X1, X2)) -> cons(mark(X1), X2)
, mark(s(X)) -> s(mark(X))
, mark(0()) -> 0()
, a__incr(X) -> incr(X)
, a__adx(X) -> adx(X)
, a__nats() -> nats()
, a__zeros() -> zeros()
, a__head(X) -> head(X)
, a__tail(X) -> tail(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:
{ a__incr(nil()) -> nil()
, a__incr(cons(X, L)) -> cons(s(mark(X)), incr(L))
, a__adx(nil()) -> nil()
, a__adx(cons(X, L)) -> a__incr(cons(mark(X), adx(L)))
, a__nats() -> a__adx(a__zeros())
, a__zeros() -> cons(0(), zeros())
, a__head(cons(X, L)) -> mark(X)
, a__tail(cons(X, L)) -> mark(L)
, mark(incr(X)) -> a__incr(mark(X))
, mark(adx(X)) -> a__adx(mark(X))
, mark(nats()) -> a__nats()
, mark(zeros()) -> a__zeros()
, mark(head(X)) -> a__head(mark(X))
, mark(tail(X)) -> a__tail(mark(X))
, mark(nil()) -> nil()
, mark(cons(X1, X2)) -> cons(mark(X1), X2)
, mark(s(X)) -> s(mark(X))
, mark(0()) -> 0()
, a__incr(X) -> incr(X)
, a__adx(X) -> adx(X)
, a__nats() -> nats()
, a__zeros() -> zeros()
, a__head(X) -> head(X)
, a__tail(X) -> tail(X)}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..