LMPO
MAYBE
We consider the following Problem:
Strict Trs:
{ a__from(X) -> cons(mark(X), from(s(X)))
, a__2ndspos(0(), Z) -> rnil()
, a__2ndspos(s(N), cons(X, Z)) ->
a__2ndspos(s(mark(N)), cons2(X, mark(Z)))
, a__2ndspos(s(N), cons2(X, cons(Y, Z))) ->
rcons(posrecip(mark(Y)), a__2ndsneg(mark(N), mark(Z)))
, a__2ndsneg(0(), Z) -> rnil()
, a__2ndsneg(s(N), cons(X, Z)) ->
a__2ndsneg(s(mark(N)), cons2(X, mark(Z)))
, a__2ndsneg(s(N), cons2(X, cons(Y, Z))) ->
rcons(negrecip(mark(Y)), a__2ndspos(mark(N), mark(Z)))
, a__pi(X) -> a__2ndspos(mark(X), a__from(0()))
, a__plus(0(), Y) -> mark(Y)
, a__plus(s(X), Y) -> s(a__plus(mark(X), mark(Y)))
, a__times(0(), Y) -> 0()
, a__times(s(X), Y) -> a__plus(mark(Y), a__times(mark(X), mark(Y)))
, a__square(X) -> a__times(mark(X), mark(X))
, mark(from(X)) -> a__from(mark(X))
, mark(2ndspos(X1, X2)) -> a__2ndspos(mark(X1), mark(X2))
, mark(2ndsneg(X1, X2)) -> a__2ndsneg(mark(X1), mark(X2))
, mark(pi(X)) -> a__pi(mark(X))
, mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
, mark(times(X1, X2)) -> a__times(mark(X1), mark(X2))
, mark(square(X)) -> a__square(mark(X))
, mark(0()) -> 0()
, mark(s(X)) -> s(mark(X))
, mark(posrecip(X)) -> posrecip(mark(X))
, mark(negrecip(X)) -> negrecip(mark(X))
, mark(nil()) -> nil()
, mark(cons(X1, X2)) -> cons(mark(X1), X2)
, mark(cons2(X1, X2)) -> cons2(X1, mark(X2))
, mark(rnil()) -> rnil()
, mark(rcons(X1, X2)) -> rcons(mark(X1), mark(X2))
, a__from(X) -> from(X)
, a__2ndspos(X1, X2) -> 2ndspos(X1, X2)
, a__2ndsneg(X1, X2) -> 2ndsneg(X1, X2)
, a__pi(X) -> pi(X)
, a__plus(X1, X2) -> plus(X1, X2)
, a__times(X1, X2) -> times(X1, X2)
, a__square(X) -> square(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__from(X) -> cons(mark(X), from(s(X)))
, a__2ndspos(0(), Z) -> rnil()
, a__2ndspos(s(N), cons(X, Z)) ->
a__2ndspos(s(mark(N)), cons2(X, mark(Z)))
, a__2ndspos(s(N), cons2(X, cons(Y, Z))) ->
rcons(posrecip(mark(Y)), a__2ndsneg(mark(N), mark(Z)))
, a__2ndsneg(0(), Z) -> rnil()
, a__2ndsneg(s(N), cons(X, Z)) ->
a__2ndsneg(s(mark(N)), cons2(X, mark(Z)))
, a__2ndsneg(s(N), cons2(X, cons(Y, Z))) ->
rcons(negrecip(mark(Y)), a__2ndspos(mark(N), mark(Z)))
, a__pi(X) -> a__2ndspos(mark(X), a__from(0()))
, a__plus(0(), Y) -> mark(Y)
, a__plus(s(X), Y) -> s(a__plus(mark(X), mark(Y)))
, a__times(0(), Y) -> 0()
, a__times(s(X), Y) -> a__plus(mark(Y), a__times(mark(X), mark(Y)))
, a__square(X) -> a__times(mark(X), mark(X))
, mark(from(X)) -> a__from(mark(X))
, mark(2ndspos(X1, X2)) -> a__2ndspos(mark(X1), mark(X2))
, mark(2ndsneg(X1, X2)) -> a__2ndsneg(mark(X1), mark(X2))
, mark(pi(X)) -> a__pi(mark(X))
, mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
, mark(times(X1, X2)) -> a__times(mark(X1), mark(X2))
, mark(square(X)) -> a__square(mark(X))
, mark(0()) -> 0()
, mark(s(X)) -> s(mark(X))
, mark(posrecip(X)) -> posrecip(mark(X))
, mark(negrecip(X)) -> negrecip(mark(X))
, mark(nil()) -> nil()
, mark(cons(X1, X2)) -> cons(mark(X1), X2)
, mark(cons2(X1, X2)) -> cons2(X1, mark(X2))
, mark(rnil()) -> rnil()
, mark(rcons(X1, X2)) -> rcons(mark(X1), mark(X2))
, a__from(X) -> from(X)
, a__2ndspos(X1, X2) -> 2ndspos(X1, X2)
, a__2ndsneg(X1, X2) -> 2ndsneg(X1, X2)
, a__pi(X) -> pi(X)
, a__plus(X1, X2) -> plus(X1, X2)
, a__times(X1, X2) -> times(X1, X2)
, a__square(X) -> square(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__from(X) -> cons(mark(X), from(s(X)))
, a__2ndspos(0(), Z) -> rnil()
, a__2ndspos(s(N), cons(X, Z)) ->
a__2ndspos(s(mark(N)), cons2(X, mark(Z)))
, a__2ndspos(s(N), cons2(X, cons(Y, Z))) ->
rcons(posrecip(mark(Y)), a__2ndsneg(mark(N), mark(Z)))
, a__2ndsneg(0(), Z) -> rnil()
, a__2ndsneg(s(N), cons(X, Z)) ->
a__2ndsneg(s(mark(N)), cons2(X, mark(Z)))
, a__2ndsneg(s(N), cons2(X, cons(Y, Z))) ->
rcons(negrecip(mark(Y)), a__2ndspos(mark(N), mark(Z)))
, a__pi(X) -> a__2ndspos(mark(X), a__from(0()))
, a__plus(0(), Y) -> mark(Y)
, a__plus(s(X), Y) -> s(a__plus(mark(X), mark(Y)))
, a__times(0(), Y) -> 0()
, a__times(s(X), Y) -> a__plus(mark(Y), a__times(mark(X), mark(Y)))
, a__square(X) -> a__times(mark(X), mark(X))
, mark(from(X)) -> a__from(mark(X))
, mark(2ndspos(X1, X2)) -> a__2ndspos(mark(X1), mark(X2))
, mark(2ndsneg(X1, X2)) -> a__2ndsneg(mark(X1), mark(X2))
, mark(pi(X)) -> a__pi(mark(X))
, mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
, mark(times(X1, X2)) -> a__times(mark(X1), mark(X2))
, mark(square(X)) -> a__square(mark(X))
, mark(0()) -> 0()
, mark(s(X)) -> s(mark(X))
, mark(posrecip(X)) -> posrecip(mark(X))
, mark(negrecip(X)) -> negrecip(mark(X))
, mark(nil()) -> nil()
, mark(cons(X1, X2)) -> cons(mark(X1), X2)
, mark(cons2(X1, X2)) -> cons2(X1, mark(X2))
, mark(rnil()) -> rnil()
, mark(rcons(X1, X2)) -> rcons(mark(X1), mark(X2))
, a__from(X) -> from(X)
, a__2ndspos(X1, X2) -> 2ndspos(X1, X2)
, a__2ndsneg(X1, X2) -> 2ndsneg(X1, X2)
, a__pi(X) -> pi(X)
, a__plus(X1, X2) -> plus(X1, X2)
, a__times(X1, X2) -> times(X1, X2)
, a__square(X) -> square(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__from(X) -> cons(mark(X), from(s(X)))
, a__2ndspos(0(), Z) -> rnil()
, a__2ndspos(s(N), cons(X, Z)) ->
a__2ndspos(s(mark(N)), cons2(X, mark(Z)))
, a__2ndspos(s(N), cons2(X, cons(Y, Z))) ->
rcons(posrecip(mark(Y)), a__2ndsneg(mark(N), mark(Z)))
, a__2ndsneg(0(), Z) -> rnil()
, a__2ndsneg(s(N), cons(X, Z)) ->
a__2ndsneg(s(mark(N)), cons2(X, mark(Z)))
, a__2ndsneg(s(N), cons2(X, cons(Y, Z))) ->
rcons(negrecip(mark(Y)), a__2ndspos(mark(N), mark(Z)))
, a__pi(X) -> a__2ndspos(mark(X), a__from(0()))
, a__plus(0(), Y) -> mark(Y)
, a__plus(s(X), Y) -> s(a__plus(mark(X), mark(Y)))
, a__times(0(), Y) -> 0()
, a__times(s(X), Y) -> a__plus(mark(Y), a__times(mark(X), mark(Y)))
, a__square(X) -> a__times(mark(X), mark(X))
, mark(from(X)) -> a__from(mark(X))
, mark(2ndspos(X1, X2)) -> a__2ndspos(mark(X1), mark(X2))
, mark(2ndsneg(X1, X2)) -> a__2ndsneg(mark(X1), mark(X2))
, mark(pi(X)) -> a__pi(mark(X))
, mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
, mark(times(X1, X2)) -> a__times(mark(X1), mark(X2))
, mark(square(X)) -> a__square(mark(X))
, mark(0()) -> 0()
, mark(s(X)) -> s(mark(X))
, mark(posrecip(X)) -> posrecip(mark(X))
, mark(negrecip(X)) -> negrecip(mark(X))
, mark(nil()) -> nil()
, mark(cons(X1, X2)) -> cons(mark(X1), X2)
, mark(cons2(X1, X2)) -> cons2(X1, mark(X2))
, mark(rnil()) -> rnil()
, mark(rcons(X1, X2)) -> rcons(mark(X1), mark(X2))
, a__from(X) -> from(X)
, a__2ndspos(X1, X2) -> 2ndspos(X1, X2)
, a__2ndsneg(X1, X2) -> 2ndsneg(X1, X2)
, a__pi(X) -> pi(X)
, a__plus(X1, X2) -> plus(X1, X2)
, a__times(X1, X2) -> times(X1, X2)
, a__square(X) -> square(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__from(X) -> cons(mark(X), from(s(X)))
, a__2ndspos(0(), Z) -> rnil()
, a__2ndspos(s(N), cons(X, Z)) ->
a__2ndspos(s(mark(N)), cons2(X, mark(Z)))
, a__2ndspos(s(N), cons2(X, cons(Y, Z))) ->
rcons(posrecip(mark(Y)), a__2ndsneg(mark(N), mark(Z)))
, a__2ndsneg(0(), Z) -> rnil()
, a__2ndsneg(s(N), cons(X, Z)) ->
a__2ndsneg(s(mark(N)), cons2(X, mark(Z)))
, a__2ndsneg(s(N), cons2(X, cons(Y, Z))) ->
rcons(negrecip(mark(Y)), a__2ndspos(mark(N), mark(Z)))
, a__pi(X) -> a__2ndspos(mark(X), a__from(0()))
, a__plus(0(), Y) -> mark(Y)
, a__plus(s(X), Y) -> s(a__plus(mark(X), mark(Y)))
, a__times(0(), Y) -> 0()
, a__times(s(X), Y) -> a__plus(mark(Y), a__times(mark(X), mark(Y)))
, a__square(X) -> a__times(mark(X), mark(X))
, mark(from(X)) -> a__from(mark(X))
, mark(2ndspos(X1, X2)) -> a__2ndspos(mark(X1), mark(X2))
, mark(2ndsneg(X1, X2)) -> a__2ndsneg(mark(X1), mark(X2))
, mark(pi(X)) -> a__pi(mark(X))
, mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
, mark(times(X1, X2)) -> a__times(mark(X1), mark(X2))
, mark(square(X)) -> a__square(mark(X))
, mark(0()) -> 0()
, mark(s(X)) -> s(mark(X))
, mark(posrecip(X)) -> posrecip(mark(X))
, mark(negrecip(X)) -> negrecip(mark(X))
, mark(nil()) -> nil()
, mark(cons(X1, X2)) -> cons(mark(X1), X2)
, mark(cons2(X1, X2)) -> cons2(X1, mark(X2))
, mark(rnil()) -> rnil()
, mark(rcons(X1, X2)) -> rcons(mark(X1), mark(X2))
, a__from(X) -> from(X)
, a__2ndspos(X1, X2) -> 2ndspos(X1, X2)
, a__2ndsneg(X1, X2) -> 2ndsneg(X1, X2)
, a__pi(X) -> pi(X)
, a__plus(X1, X2) -> plus(X1, X2)
, a__times(X1, X2) -> times(X1, X2)
, a__square(X) -> square(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__from(X) -> cons(mark(X), from(s(X)))
, a__2ndspos(0(), Z) -> rnil()
, a__2ndspos(s(N), cons(X, Z)) ->
a__2ndspos(s(mark(N)), cons2(X, mark(Z)))
, a__2ndspos(s(N), cons2(X, cons(Y, Z))) ->
rcons(posrecip(mark(Y)), a__2ndsneg(mark(N), mark(Z)))
, a__2ndsneg(0(), Z) -> rnil()
, a__2ndsneg(s(N), cons(X, Z)) ->
a__2ndsneg(s(mark(N)), cons2(X, mark(Z)))
, a__2ndsneg(s(N), cons2(X, cons(Y, Z))) ->
rcons(negrecip(mark(Y)), a__2ndspos(mark(N), mark(Z)))
, a__pi(X) -> a__2ndspos(mark(X), a__from(0()))
, a__plus(0(), Y) -> mark(Y)
, a__plus(s(X), Y) -> s(a__plus(mark(X), mark(Y)))
, a__times(0(), Y) -> 0()
, a__times(s(X), Y) -> a__plus(mark(Y), a__times(mark(X), mark(Y)))
, a__square(X) -> a__times(mark(X), mark(X))
, mark(from(X)) -> a__from(mark(X))
, mark(2ndspos(X1, X2)) -> a__2ndspos(mark(X1), mark(X2))
, mark(2ndsneg(X1, X2)) -> a__2ndsneg(mark(X1), mark(X2))
, mark(pi(X)) -> a__pi(mark(X))
, mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
, mark(times(X1, X2)) -> a__times(mark(X1), mark(X2))
, mark(square(X)) -> a__square(mark(X))
, mark(0()) -> 0()
, mark(s(X)) -> s(mark(X))
, mark(posrecip(X)) -> posrecip(mark(X))
, mark(negrecip(X)) -> negrecip(mark(X))
, mark(nil()) -> nil()
, mark(cons(X1, X2)) -> cons(mark(X1), X2)
, mark(cons2(X1, X2)) -> cons2(X1, mark(X2))
, mark(rnil()) -> rnil()
, mark(rcons(X1, X2)) -> rcons(mark(X1), mark(X2))
, a__from(X) -> from(X)
, a__2ndspos(X1, X2) -> 2ndspos(X1, X2)
, a__2ndsneg(X1, X2) -> 2ndsneg(X1, X2)
, a__pi(X) -> pi(X)
, a__plus(X1, X2) -> plus(X1, X2)
, a__times(X1, X2) -> times(X1, X2)
, a__square(X) -> square(X)}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..