LMPO
MAYBE
We consider the following Problem:
Strict Trs:
{ minus_active(0(), y) -> 0()
, mark(0()) -> 0()
, minus_active(s(x), s(y)) -> minus_active(x, y)
, mark(s(x)) -> s(mark(x))
, ge_active(x, 0()) -> true()
, mark(minus(x, y)) -> minus_active(x, y)
, ge_active(0(), s(y)) -> false()
, mark(ge(x, y)) -> ge_active(x, y)
, ge_active(s(x), s(y)) -> ge_active(x, y)
, mark(div(x, y)) -> div_active(mark(x), y)
, div_active(0(), s(y)) -> 0()
, mark(if(x, y, z)) -> if_active(mark(x), y, z)
, div_active(s(x), s(y)) ->
if_active(ge_active(x, y), s(div(minus(x, y), s(y))), 0())
, if_active(true(), x, y) -> mark(x)
, minus_active(x, y) -> minus(x, y)
, if_active(false(), x, y) -> mark(y)
, ge_active(x, y) -> ge(x, y)
, if_active(x, y, z) -> if(x, y, z)
, div_active(x, y) -> div(x, y)}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
MPO
MAYBE
We consider the following Problem:
Strict Trs:
{ minus_active(0(), y) -> 0()
, mark(0()) -> 0()
, minus_active(s(x), s(y)) -> minus_active(x, y)
, mark(s(x)) -> s(mark(x))
, ge_active(x, 0()) -> true()
, mark(minus(x, y)) -> minus_active(x, y)
, ge_active(0(), s(y)) -> false()
, mark(ge(x, y)) -> ge_active(x, y)
, ge_active(s(x), s(y)) -> ge_active(x, y)
, mark(div(x, y)) -> div_active(mark(x), y)
, div_active(0(), s(y)) -> 0()
, mark(if(x, y, z)) -> if_active(mark(x), y, z)
, div_active(s(x), s(y)) ->
if_active(ge_active(x, y), s(div(minus(x, y), s(y))), 0())
, if_active(true(), x, y) -> mark(x)
, minus_active(x, y) -> minus(x, y)
, if_active(false(), x, y) -> mark(y)
, ge_active(x, y) -> ge(x, y)
, if_active(x, y, z) -> if(x, y, z)
, div_active(x, y) -> div(x, y)}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
POP*
MAYBE
We consider the following Problem:
Strict Trs:
{ minus_active(0(), y) -> 0()
, mark(0()) -> 0()
, minus_active(s(x), s(y)) -> minus_active(x, y)
, mark(s(x)) -> s(mark(x))
, ge_active(x, 0()) -> true()
, mark(minus(x, y)) -> minus_active(x, y)
, ge_active(0(), s(y)) -> false()
, mark(ge(x, y)) -> ge_active(x, y)
, ge_active(s(x), s(y)) -> ge_active(x, y)
, mark(div(x, y)) -> div_active(mark(x), y)
, div_active(0(), s(y)) -> 0()
, mark(if(x, y, z)) -> if_active(mark(x), y, z)
, div_active(s(x), s(y)) ->
if_active(ge_active(x, y), s(div(minus(x, y), s(y))), 0())
, if_active(true(), x, y) -> mark(x)
, minus_active(x, y) -> minus(x, y)
, if_active(false(), x, y) -> mark(y)
, ge_active(x, y) -> ge(x, y)
, if_active(x, y, z) -> if(x, y, z)
, div_active(x, y) -> div(x, y)}
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:
{ minus_active(0(), y) -> 0()
, mark(0()) -> 0()
, minus_active(s(x), s(y)) -> minus_active(x, y)
, mark(s(x)) -> s(mark(x))
, ge_active(x, 0()) -> true()
, mark(minus(x, y)) -> minus_active(x, y)
, ge_active(0(), s(y)) -> false()
, mark(ge(x, y)) -> ge_active(x, y)
, ge_active(s(x), s(y)) -> ge_active(x, y)
, mark(div(x, y)) -> div_active(mark(x), y)
, div_active(0(), s(y)) -> 0()
, mark(if(x, y, z)) -> if_active(mark(x), y, z)
, div_active(s(x), s(y)) ->
if_active(ge_active(x, y), s(div(minus(x, y), s(y))), 0())
, if_active(true(), x, y) -> mark(x)
, minus_active(x, y) -> minus(x, y)
, if_active(false(), x, y) -> mark(y)
, ge_active(x, y) -> ge(x, y)
, if_active(x, y, z) -> if(x, y, z)
, div_active(x, y) -> div(x, y)}
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:
{ minus_active(0(), y) -> 0()
, mark(0()) -> 0()
, minus_active(s(x), s(y)) -> minus_active(x, y)
, mark(s(x)) -> s(mark(x))
, ge_active(x, 0()) -> true()
, mark(minus(x, y)) -> minus_active(x, y)
, ge_active(0(), s(y)) -> false()
, mark(ge(x, y)) -> ge_active(x, y)
, ge_active(s(x), s(y)) -> ge_active(x, y)
, mark(div(x, y)) -> div_active(mark(x), y)
, div_active(0(), s(y)) -> 0()
, mark(if(x, y, z)) -> if_active(mark(x), y, z)
, div_active(s(x), s(y)) ->
if_active(ge_active(x, y), s(div(minus(x, y), s(y))), 0())
, if_active(true(), x, y) -> mark(x)
, minus_active(x, y) -> minus(x, y)
, if_active(false(), x, y) -> mark(y)
, ge_active(x, y) -> ge(x, y)
, if_active(x, y, z) -> if(x, y, z)
, div_active(x, y) -> div(x, y)}
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:
{ minus_active(0(), y) -> 0()
, mark(0()) -> 0()
, minus_active(s(x), s(y)) -> minus_active(x, y)
, mark(s(x)) -> s(mark(x))
, ge_active(x, 0()) -> true()
, mark(minus(x, y)) -> minus_active(x, y)
, ge_active(0(), s(y)) -> false()
, mark(ge(x, y)) -> ge_active(x, y)
, ge_active(s(x), s(y)) -> ge_active(x, y)
, mark(div(x, y)) -> div_active(mark(x), y)
, div_active(0(), s(y)) -> 0()
, mark(if(x, y, z)) -> if_active(mark(x), y, z)
, div_active(s(x), s(y)) ->
if_active(ge_active(x, y), s(div(minus(x, y), s(y))), 0())
, if_active(true(), x, y) -> mark(x)
, minus_active(x, y) -> minus(x, y)
, if_active(false(), x, y) -> mark(y)
, ge_active(x, y) -> ge(x, y)
, if_active(x, y, z) -> if(x, y, z)
, div_active(x, y) -> div(x, y)}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..