LMPO
MAYBE
We consider the following Problem:
Strict Trs:
{ app(x, y) -> helpa(0(), plus(length(x), length(y)), x, y)
, plus(x, 0()) -> x
, plus(x, s(y)) -> s(plus(x, y))
, length(nil()) -> 0()
, length(cons(x, y)) -> s(length(y))
, helpa(c, l, ys, zs) -> if(ge(c, l), c, l, ys, zs)
, ge(x, 0()) -> true()
, ge(0(), s(x)) -> false()
, ge(s(x), s(y)) -> ge(x, y)
, if(true(), c, l, ys, zs) -> nil()
, if(false(), c, l, ys, zs) -> helpb(c, l, ys, zs)
, take(0(), cons(x, xs()), ys) -> x
, take(0(), nil(), cons(y, ys)) -> y
, take(s(c), cons(x, xs()), ys) -> take(c, xs(), ys)
, take(s(c), nil(), cons(y, ys)) -> take(c, nil(), ys)
, helpb(c, l, ys, zs) ->
cons(take(c, ys, zs), helpa(s(c), l, ys, zs))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
MPO
MAYBE
We consider the following Problem:
Strict Trs:
{ app(x, y) -> helpa(0(), plus(length(x), length(y)), x, y)
, plus(x, 0()) -> x
, plus(x, s(y)) -> s(plus(x, y))
, length(nil()) -> 0()
, length(cons(x, y)) -> s(length(y))
, helpa(c, l, ys, zs) -> if(ge(c, l), c, l, ys, zs)
, ge(x, 0()) -> true()
, ge(0(), s(x)) -> false()
, ge(s(x), s(y)) -> ge(x, y)
, if(true(), c, l, ys, zs) -> nil()
, if(false(), c, l, ys, zs) -> helpb(c, l, ys, zs)
, take(0(), cons(x, xs()), ys) -> x
, take(0(), nil(), cons(y, ys)) -> y
, take(s(c), cons(x, xs()), ys) -> take(c, xs(), ys)
, take(s(c), nil(), cons(y, ys)) -> take(c, nil(), ys)
, helpb(c, l, ys, zs) ->
cons(take(c, ys, zs), helpa(s(c), l, ys, zs))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
POP*
MAYBE
We consider the following Problem:
Strict Trs:
{ app(x, y) -> helpa(0(), plus(length(x), length(y)), x, y)
, plus(x, 0()) -> x
, plus(x, s(y)) -> s(plus(x, y))
, length(nil()) -> 0()
, length(cons(x, y)) -> s(length(y))
, helpa(c, l, ys, zs) -> if(ge(c, l), c, l, ys, zs)
, ge(x, 0()) -> true()
, ge(0(), s(x)) -> false()
, ge(s(x), s(y)) -> ge(x, y)
, if(true(), c, l, ys, zs) -> nil()
, if(false(), c, l, ys, zs) -> helpb(c, l, ys, zs)
, take(0(), cons(x, xs()), ys) -> x
, take(0(), nil(), cons(y, ys)) -> y
, take(s(c), cons(x, xs()), ys) -> take(c, xs(), ys)
, take(s(c), nil(), cons(y, ys)) -> take(c, nil(), ys)
, helpb(c, l, ys, zs) ->
cons(take(c, ys, zs), helpa(s(c), l, ys, zs))}
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:
{ app(x, y) -> helpa(0(), plus(length(x), length(y)), x, y)
, plus(x, 0()) -> x
, plus(x, s(y)) -> s(plus(x, y))
, length(nil()) -> 0()
, length(cons(x, y)) -> s(length(y))
, helpa(c, l, ys, zs) -> if(ge(c, l), c, l, ys, zs)
, ge(x, 0()) -> true()
, ge(0(), s(x)) -> false()
, ge(s(x), s(y)) -> ge(x, y)
, if(true(), c, l, ys, zs) -> nil()
, if(false(), c, l, ys, zs) -> helpb(c, l, ys, zs)
, take(0(), cons(x, xs()), ys) -> x
, take(0(), nil(), cons(y, ys)) -> y
, take(s(c), cons(x, xs()), ys) -> take(c, xs(), ys)
, take(s(c), nil(), cons(y, ys)) -> take(c, nil(), ys)
, helpb(c, l, ys, zs) ->
cons(take(c, ys, zs), helpa(s(c), l, ys, zs))}
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:
{ app(x, y) -> helpa(0(), plus(length(x), length(y)), x, y)
, plus(x, 0()) -> x
, plus(x, s(y)) -> s(plus(x, y))
, length(nil()) -> 0()
, length(cons(x, y)) -> s(length(y))
, helpa(c, l, ys, zs) -> if(ge(c, l), c, l, ys, zs)
, ge(x, 0()) -> true()
, ge(0(), s(x)) -> false()
, ge(s(x), s(y)) -> ge(x, y)
, if(true(), c, l, ys, zs) -> nil()
, if(false(), c, l, ys, zs) -> helpb(c, l, ys, zs)
, take(0(), cons(x, xs()), ys) -> x
, take(0(), nil(), cons(y, ys)) -> y
, take(s(c), cons(x, xs()), ys) -> take(c, xs(), ys)
, take(s(c), nil(), cons(y, ys)) -> take(c, nil(), ys)
, helpb(c, l, ys, zs) ->
cons(take(c, ys, zs), helpa(s(c), l, ys, zs))}
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:
{ app(x, y) -> helpa(0(), plus(length(x), length(y)), x, y)
, plus(x, 0()) -> x
, plus(x, s(y)) -> s(plus(x, y))
, length(nil()) -> 0()
, length(cons(x, y)) -> s(length(y))
, helpa(c, l, ys, zs) -> if(ge(c, l), c, l, ys, zs)
, ge(x, 0()) -> true()
, ge(0(), s(x)) -> false()
, ge(s(x), s(y)) -> ge(x, y)
, if(true(), c, l, ys, zs) -> nil()
, if(false(), c, l, ys, zs) -> helpb(c, l, ys, zs)
, take(0(), cons(x, xs()), ys) -> x
, take(0(), nil(), cons(y, ys)) -> y
, take(s(c), cons(x, xs()), ys) -> take(c, xs(), ys)
, take(s(c), nil(), cons(y, ys)) -> take(c, nil(), ys)
, helpb(c, l, ys, zs) ->
cons(take(c, ys, zs), helpa(s(c), l, ys, zs))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..