LMPO
MAYBE
We consider the following Problem:
Strict Trs:
{ le(0(), y, z) -> greater(y, z)
, le(s(x), 0(), z) -> false()
, le(s(x), s(y), 0()) -> false()
, le(s(x), s(y), s(z)) -> le(x, y, z)
, greater(x, 0()) -> first()
, greater(0(), s(y)) -> second()
, greater(s(x), s(y)) -> greater(x, y)
, double(0()) -> 0()
, double(s(x)) -> s(s(double(x)))
, triple(x) -> if(le(x, x, double(x)), x, 0(), 0())
, if(false(), x, y, z) -> true()
, if(first(), x, y, z) -> if(le(s(x), y, s(z)), s(x), y, s(z))
, if(second(), x, y, z) -> if(le(s(x), s(y), z), s(x), s(y), z)}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
MPO
MAYBE
We consider the following Problem:
Strict Trs:
{ le(0(), y, z) -> greater(y, z)
, le(s(x), 0(), z) -> false()
, le(s(x), s(y), 0()) -> false()
, le(s(x), s(y), s(z)) -> le(x, y, z)
, greater(x, 0()) -> first()
, greater(0(), s(y)) -> second()
, greater(s(x), s(y)) -> greater(x, y)
, double(0()) -> 0()
, double(s(x)) -> s(s(double(x)))
, triple(x) -> if(le(x, x, double(x)), x, 0(), 0())
, if(false(), x, y, z) -> true()
, if(first(), x, y, z) -> if(le(s(x), y, s(z)), s(x), y, s(z))
, if(second(), x, y, z) -> if(le(s(x), s(y), z), s(x), s(y), z)}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
POP*
MAYBE
We consider the following Problem:
Strict Trs:
{ le(0(), y, z) -> greater(y, z)
, le(s(x), 0(), z) -> false()
, le(s(x), s(y), 0()) -> false()
, le(s(x), s(y), s(z)) -> le(x, y, z)
, greater(x, 0()) -> first()
, greater(0(), s(y)) -> second()
, greater(s(x), s(y)) -> greater(x, y)
, double(0()) -> 0()
, double(s(x)) -> s(s(double(x)))
, triple(x) -> if(le(x, x, double(x)), x, 0(), 0())
, if(false(), x, y, z) -> true()
, if(first(), x, y, z) -> if(le(s(x), y, s(z)), s(x), y, s(z))
, if(second(), x, y, z) -> if(le(s(x), s(y), z), s(x), s(y), z)}
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:
{ le(0(), y, z) -> greater(y, z)
, le(s(x), 0(), z) -> false()
, le(s(x), s(y), 0()) -> false()
, le(s(x), s(y), s(z)) -> le(x, y, z)
, greater(x, 0()) -> first()
, greater(0(), s(y)) -> second()
, greater(s(x), s(y)) -> greater(x, y)
, double(0()) -> 0()
, double(s(x)) -> s(s(double(x)))
, triple(x) -> if(le(x, x, double(x)), x, 0(), 0())
, if(false(), x, y, z) -> true()
, if(first(), x, y, z) -> if(le(s(x), y, s(z)), s(x), y, s(z))
, if(second(), x, y, z) -> if(le(s(x), s(y), z), s(x), s(y), z)}
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:
{ le(0(), y, z) -> greater(y, z)
, le(s(x), 0(), z) -> false()
, le(s(x), s(y), 0()) -> false()
, le(s(x), s(y), s(z)) -> le(x, y, z)
, greater(x, 0()) -> first()
, greater(0(), s(y)) -> second()
, greater(s(x), s(y)) -> greater(x, y)
, double(0()) -> 0()
, double(s(x)) -> s(s(double(x)))
, triple(x) -> if(le(x, x, double(x)), x, 0(), 0())
, if(false(), x, y, z) -> true()
, if(first(), x, y, z) -> if(le(s(x), y, s(z)), s(x), y, s(z))
, if(second(), x, y, z) -> if(le(s(x), s(y), z), s(x), s(y), z)}
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:
{ le(0(), y, z) -> greater(y, z)
, le(s(x), 0(), z) -> false()
, le(s(x), s(y), 0()) -> false()
, le(s(x), s(y), s(z)) -> le(x, y, z)
, greater(x, 0()) -> first()
, greater(0(), s(y)) -> second()
, greater(s(x), s(y)) -> greater(x, y)
, double(0()) -> 0()
, double(s(x)) -> s(s(double(x)))
, triple(x) -> if(le(x, x, double(x)), x, 0(), 0())
, if(false(), x, y, z) -> true()
, if(first(), x, y, z) -> if(le(s(x), y, s(z)), s(x), y, s(z))
, if(second(), x, y, z) -> if(le(s(x), s(y), z), s(x), s(y), z)}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..