LMPO
MAYBE
We consider the following Problem:
Strict Trs:
{ a__and(true(), X) -> mark(X)
, a__and(false(), Y) -> false()
, a__if(true(), X, Y) -> mark(X)
, a__if(false(), X, Y) -> mark(Y)
, 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(Y, first(X, Z))
, a__from(X) -> cons(X, from(s(X)))
, mark(and(X1, X2)) -> a__and(mark(X1), X2)
, mark(if(X1, X2, X3)) -> a__if(mark(X1), X2, X3)
, mark(add(X1, X2)) -> a__add(mark(X1), X2)
, mark(first(X1, X2)) -> a__first(mark(X1), mark(X2))
, mark(from(X)) -> a__from(X)
, mark(true()) -> true()
, mark(false()) -> false()
, mark(0()) -> 0()
, mark(s(X)) -> s(X)
, mark(nil()) -> nil()
, mark(cons(X1, X2)) -> cons(X1, X2)
, a__and(X1, X2) -> and(X1, X2)
, a__if(X1, X2, X3) -> if(X1, X2, X3)
, a__add(X1, X2) -> add(X1, X2)
, a__first(X1, X2) -> first(X1, X2)
, a__from(X) -> from(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__and(true(), X) -> mark(X)
, a__and(false(), Y) -> false()
, a__if(true(), X, Y) -> mark(X)
, a__if(false(), X, Y) -> mark(Y)
, 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(Y, first(X, Z))
, a__from(X) -> cons(X, from(s(X)))
, mark(and(X1, X2)) -> a__and(mark(X1), X2)
, mark(if(X1, X2, X3)) -> a__if(mark(X1), X2, X3)
, mark(add(X1, X2)) -> a__add(mark(X1), X2)
, mark(first(X1, X2)) -> a__first(mark(X1), mark(X2))
, mark(from(X)) -> a__from(X)
, mark(true()) -> true()
, mark(false()) -> false()
, mark(0()) -> 0()
, mark(s(X)) -> s(X)
, mark(nil()) -> nil()
, mark(cons(X1, X2)) -> cons(X1, X2)
, a__and(X1, X2) -> and(X1, X2)
, a__if(X1, X2, X3) -> if(X1, X2, X3)
, a__add(X1, X2) -> add(X1, X2)
, a__first(X1, X2) -> first(X1, X2)
, a__from(X) -> from(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__and(true(), X) -> mark(X)
, a__and(false(), Y) -> false()
, a__if(true(), X, Y) -> mark(X)
, a__if(false(), X, Y) -> mark(Y)
, 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(Y, first(X, Z))
, a__from(X) -> cons(X, from(s(X)))
, mark(and(X1, X2)) -> a__and(mark(X1), X2)
, mark(if(X1, X2, X3)) -> a__if(mark(X1), X2, X3)
, mark(add(X1, X2)) -> a__add(mark(X1), X2)
, mark(first(X1, X2)) -> a__first(mark(X1), mark(X2))
, mark(from(X)) -> a__from(X)
, mark(true()) -> true()
, mark(false()) -> false()
, mark(0()) -> 0()
, mark(s(X)) -> s(X)
, mark(nil()) -> nil()
, mark(cons(X1, X2)) -> cons(X1, X2)
, a__and(X1, X2) -> and(X1, X2)
, a__if(X1, X2, X3) -> if(X1, X2, X3)
, a__add(X1, X2) -> add(X1, X2)
, a__first(X1, X2) -> first(X1, X2)
, a__from(X) -> from(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__and(true(), X) -> mark(X)
, a__and(false(), Y) -> false()
, a__if(true(), X, Y) -> mark(X)
, a__if(false(), X, Y) -> mark(Y)
, 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(Y, first(X, Z))
, a__from(X) -> cons(X, from(s(X)))
, mark(and(X1, X2)) -> a__and(mark(X1), X2)
, mark(if(X1, X2, X3)) -> a__if(mark(X1), X2, X3)
, mark(add(X1, X2)) -> a__add(mark(X1), X2)
, mark(first(X1, X2)) -> a__first(mark(X1), mark(X2))
, mark(from(X)) -> a__from(X)
, mark(true()) -> true()
, mark(false()) -> false()
, mark(0()) -> 0()
, mark(s(X)) -> s(X)
, mark(nil()) -> nil()
, mark(cons(X1, X2)) -> cons(X1, X2)
, a__and(X1, X2) -> and(X1, X2)
, a__if(X1, X2, X3) -> if(X1, X2, X3)
, a__add(X1, X2) -> add(X1, X2)
, a__first(X1, X2) -> first(X1, X2)
, a__from(X) -> from(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__and(true(), X) -> mark(X)
, a__and(false(), Y) -> false()
, a__if(true(), X, Y) -> mark(X)
, a__if(false(), X, Y) -> mark(Y)
, 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(Y, first(X, Z))
, a__from(X) -> cons(X, from(s(X)))
, mark(and(X1, X2)) -> a__and(mark(X1), X2)
, mark(if(X1, X2, X3)) -> a__if(mark(X1), X2, X3)
, mark(add(X1, X2)) -> a__add(mark(X1), X2)
, mark(first(X1, X2)) -> a__first(mark(X1), mark(X2))
, mark(from(X)) -> a__from(X)
, mark(true()) -> true()
, mark(false()) -> false()
, mark(0()) -> 0()
, mark(s(X)) -> s(X)
, mark(nil()) -> nil()
, mark(cons(X1, X2)) -> cons(X1, X2)
, a__and(X1, X2) -> and(X1, X2)
, a__if(X1, X2, X3) -> if(X1, X2, X3)
, a__add(X1, X2) -> add(X1, X2)
, a__first(X1, X2) -> first(X1, X2)
, a__from(X) -> from(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__and(true(), X) -> mark(X)
, a__and(false(), Y) -> false()
, a__if(true(), X, Y) -> mark(X)
, a__if(false(), X, Y) -> mark(Y)
, 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(Y, first(X, Z))
, a__from(X) -> cons(X, from(s(X)))
, mark(and(X1, X2)) -> a__and(mark(X1), X2)
, mark(if(X1, X2, X3)) -> a__if(mark(X1), X2, X3)
, mark(add(X1, X2)) -> a__add(mark(X1), X2)
, mark(first(X1, X2)) -> a__first(mark(X1), mark(X2))
, mark(from(X)) -> a__from(X)
, mark(true()) -> true()
, mark(false()) -> false()
, mark(0()) -> 0()
, mark(s(X)) -> s(X)
, mark(nil()) -> nil()
, mark(cons(X1, X2)) -> cons(X1, X2)
, a__and(X1, X2) -> and(X1, X2)
, a__if(X1, X2, X3) -> if(X1, X2, X3)
, a__add(X1, X2) -> add(X1, X2)
, a__first(X1, X2) -> first(X1, X2)
, a__from(X) -> from(X)}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..