LMPO
MAYBE
We consider the following Problem:
Strict Trs:
{ a__terms(N) -> cons(recip(a__sqr(mark(N))), terms(s(N)))
, a__sqr(0()) -> 0()
, a__sqr(s(X)) -> s(add(sqr(X), dbl(X)))
, a__dbl(0()) -> 0()
, a__dbl(s(X)) -> s(s(dbl(X)))
, a__add(0(), X) -> mark(X)
, a__add(s(X), Y) -> s(add(X, Y))
, a__first(0(), X) -> nil()
, a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z))
, mark(terms(X)) -> a__terms(mark(X))
, mark(sqr(X)) -> a__sqr(mark(X))
, mark(add(X1, X2)) -> a__add(mark(X1), mark(X2))
, mark(dbl(X)) -> a__dbl(mark(X))
, mark(first(X1, X2)) -> a__first(mark(X1), mark(X2))
, mark(cons(X1, X2)) -> cons(mark(X1), X2)
, mark(recip(X)) -> recip(mark(X))
, mark(s(X)) -> s(X)
, mark(0()) -> 0()
, mark(nil()) -> nil()
, a__terms(X) -> terms(X)
, a__sqr(X) -> sqr(X)
, a__add(X1, X2) -> add(X1, X2)
, a__dbl(X) -> dbl(X)
, a__first(X1, X2) -> first(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__terms(N) -> cons(recip(a__sqr(mark(N))), terms(s(N)))
, a__sqr(0()) -> 0()
, a__sqr(s(X)) -> s(add(sqr(X), dbl(X)))
, a__dbl(0()) -> 0()
, a__dbl(s(X)) -> s(s(dbl(X)))
, a__add(0(), X) -> mark(X)
, a__add(s(X), Y) -> s(add(X, Y))
, a__first(0(), X) -> nil()
, a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z))
, mark(terms(X)) -> a__terms(mark(X))
, mark(sqr(X)) -> a__sqr(mark(X))
, mark(add(X1, X2)) -> a__add(mark(X1), mark(X2))
, mark(dbl(X)) -> a__dbl(mark(X))
, mark(first(X1, X2)) -> a__first(mark(X1), mark(X2))
, mark(cons(X1, X2)) -> cons(mark(X1), X2)
, mark(recip(X)) -> recip(mark(X))
, mark(s(X)) -> s(X)
, mark(0()) -> 0()
, mark(nil()) -> nil()
, a__terms(X) -> terms(X)
, a__sqr(X) -> sqr(X)
, a__add(X1, X2) -> add(X1, X2)
, a__dbl(X) -> dbl(X)
, a__first(X1, X2) -> first(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__terms(N) -> cons(recip(a__sqr(mark(N))), terms(s(N)))
, a__sqr(0()) -> 0()
, a__sqr(s(X)) -> s(add(sqr(X), dbl(X)))
, a__dbl(0()) -> 0()
, a__dbl(s(X)) -> s(s(dbl(X)))
, a__add(0(), X) -> mark(X)
, a__add(s(X), Y) -> s(add(X, Y))
, a__first(0(), X) -> nil()
, a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z))
, mark(terms(X)) -> a__terms(mark(X))
, mark(sqr(X)) -> a__sqr(mark(X))
, mark(add(X1, X2)) -> a__add(mark(X1), mark(X2))
, mark(dbl(X)) -> a__dbl(mark(X))
, mark(first(X1, X2)) -> a__first(mark(X1), mark(X2))
, mark(cons(X1, X2)) -> cons(mark(X1), X2)
, mark(recip(X)) -> recip(mark(X))
, mark(s(X)) -> s(X)
, mark(0()) -> 0()
, mark(nil()) -> nil()
, a__terms(X) -> terms(X)
, a__sqr(X) -> sqr(X)
, a__add(X1, X2) -> add(X1, X2)
, a__dbl(X) -> dbl(X)
, a__first(X1, X2) -> first(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__terms(N) -> cons(recip(a__sqr(mark(N))), terms(s(N)))
, a__sqr(0()) -> 0()
, a__sqr(s(X)) -> s(add(sqr(X), dbl(X)))
, a__dbl(0()) -> 0()
, a__dbl(s(X)) -> s(s(dbl(X)))
, a__add(0(), X) -> mark(X)
, a__add(s(X), Y) -> s(add(X, Y))
, a__first(0(), X) -> nil()
, a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z))
, mark(terms(X)) -> a__terms(mark(X))
, mark(sqr(X)) -> a__sqr(mark(X))
, mark(add(X1, X2)) -> a__add(mark(X1), mark(X2))
, mark(dbl(X)) -> a__dbl(mark(X))
, mark(first(X1, X2)) -> a__first(mark(X1), mark(X2))
, mark(cons(X1, X2)) -> cons(mark(X1), X2)
, mark(recip(X)) -> recip(mark(X))
, mark(s(X)) -> s(X)
, mark(0()) -> 0()
, mark(nil()) -> nil()
, a__terms(X) -> terms(X)
, a__sqr(X) -> sqr(X)
, a__add(X1, X2) -> add(X1, X2)
, a__dbl(X) -> dbl(X)
, a__first(X1, X2) -> first(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__terms(N) -> cons(recip(a__sqr(mark(N))), terms(s(N)))
, a__sqr(0()) -> 0()
, a__sqr(s(X)) -> s(add(sqr(X), dbl(X)))
, a__dbl(0()) -> 0()
, a__dbl(s(X)) -> s(s(dbl(X)))
, a__add(0(), X) -> mark(X)
, a__add(s(X), Y) -> s(add(X, Y))
, a__first(0(), X) -> nil()
, a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z))
, mark(terms(X)) -> a__terms(mark(X))
, mark(sqr(X)) -> a__sqr(mark(X))
, mark(add(X1, X2)) -> a__add(mark(X1), mark(X2))
, mark(dbl(X)) -> a__dbl(mark(X))
, mark(first(X1, X2)) -> a__first(mark(X1), mark(X2))
, mark(cons(X1, X2)) -> cons(mark(X1), X2)
, mark(recip(X)) -> recip(mark(X))
, mark(s(X)) -> s(X)
, mark(0()) -> 0()
, mark(nil()) -> nil()
, a__terms(X) -> terms(X)
, a__sqr(X) -> sqr(X)
, a__add(X1, X2) -> add(X1, X2)
, a__dbl(X) -> dbl(X)
, a__first(X1, X2) -> first(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__terms(N) -> cons(recip(a__sqr(mark(N))), terms(s(N)))
, a__sqr(0()) -> 0()
, a__sqr(s(X)) -> s(add(sqr(X), dbl(X)))
, a__dbl(0()) -> 0()
, a__dbl(s(X)) -> s(s(dbl(X)))
, a__add(0(), X) -> mark(X)
, a__add(s(X), Y) -> s(add(X, Y))
, a__first(0(), X) -> nil()
, a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z))
, mark(terms(X)) -> a__terms(mark(X))
, mark(sqr(X)) -> a__sqr(mark(X))
, mark(add(X1, X2)) -> a__add(mark(X1), mark(X2))
, mark(dbl(X)) -> a__dbl(mark(X))
, mark(first(X1, X2)) -> a__first(mark(X1), mark(X2))
, mark(cons(X1, X2)) -> cons(mark(X1), X2)
, mark(recip(X)) -> recip(mark(X))
, mark(s(X)) -> s(X)
, mark(0()) -> 0()
, mark(nil()) -> nil()
, a__terms(X) -> terms(X)
, a__sqr(X) -> sqr(X)
, a__add(X1, X2) -> add(X1, X2)
, a__dbl(X) -> dbl(X)
, a__first(X1, X2) -> first(X1, X2)}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..