LMPO
MAYBE
We consider the following Problem:
Strict Trs:
{ minus(x, x) -> 0()
, minus(0(), x) -> 0()
, minus(x, 0()) -> x
, minus(s(x), s(y)) -> minus(x, y)
, le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, quot(x, y) -> if_quot(minus(x, y), y, le(y, 0()), le(y, x))
, if_quot(x, y, true(), z) -> divByZeroError()
, if_quot(x, y, false(), true()) -> s(quot(x, y))
, if_quot(x, y, false(), false()) -> 0()}
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(x, x) -> 0()
, minus(0(), x) -> 0()
, minus(x, 0()) -> x
, minus(s(x), s(y)) -> minus(x, y)
, le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, quot(x, y) -> if_quot(minus(x, y), y, le(y, 0()), le(y, x))
, if_quot(x, y, true(), z) -> divByZeroError()
, if_quot(x, y, false(), true()) -> s(quot(x, y))
, if_quot(x, y, false(), false()) -> 0()}
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(x, x) -> 0()
, minus(0(), x) -> 0()
, minus(x, 0()) -> x
, minus(s(x), s(y)) -> minus(x, y)
, le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, quot(x, y) -> if_quot(minus(x, y), y, le(y, 0()), le(y, x))
, if_quot(x, y, true(), z) -> divByZeroError()
, if_quot(x, y, false(), true()) -> s(quot(x, y))
, if_quot(x, y, false(), false()) -> 0()}
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(x, x) -> 0()
, minus(0(), x) -> 0()
, minus(x, 0()) -> x
, minus(s(x), s(y)) -> minus(x, y)
, le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, quot(x, y) -> if_quot(minus(x, y), y, le(y, 0()), le(y, x))
, if_quot(x, y, true(), z) -> divByZeroError()
, if_quot(x, y, false(), true()) -> s(quot(x, y))
, if_quot(x, y, false(), false()) -> 0()}
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(x, x) -> 0()
, minus(0(), x) -> 0()
, minus(x, 0()) -> x
, minus(s(x), s(y)) -> minus(x, y)
, le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, quot(x, y) -> if_quot(minus(x, y), y, le(y, 0()), le(y, x))
, if_quot(x, y, true(), z) -> divByZeroError()
, if_quot(x, y, false(), true()) -> s(quot(x, y))
, if_quot(x, y, false(), false()) -> 0()}
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(x, x) -> 0()
, minus(0(), x) -> 0()
, minus(x, 0()) -> x
, minus(s(x), s(y)) -> minus(x, y)
, le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, quot(x, y) -> if_quot(minus(x, y), y, le(y, 0()), le(y, x))
, if_quot(x, y, true(), z) -> divByZeroError()
, if_quot(x, y, false(), true()) -> s(quot(x, y))
, if_quot(x, y, false(), false()) -> 0()}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..