LMPO
MAYBE
We consider the following Problem:
Strict Trs:
{ le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, zero(0()) -> true()
, zero(s(x)) -> false()
, id(0()) -> 0()
, id(s(x)) -> s(id(x))
, minus(x, 0()) -> x
, minus(s(x), s(y)) -> minus(x, y)
, mod(x, y) -> if_mod(zero(x), zero(y), le(y, x), id(x), id(y))
, if_mod(true(), b1, b2, x, y) -> 0()
, if_mod(false(), b1, b2, x, y) -> if2(b1, b2, x, y)
, if2(true(), b2, x, y) -> 0()
, if2(false(), b2, x, y) -> if3(b2, x, y)
, if3(true(), x, y) -> mod(minus(x, y), s(y))
, if3(false(), x, y) -> 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:
{ le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, zero(0()) -> true()
, zero(s(x)) -> false()
, id(0()) -> 0()
, id(s(x)) -> s(id(x))
, minus(x, 0()) -> x
, minus(s(x), s(y)) -> minus(x, y)
, mod(x, y) -> if_mod(zero(x), zero(y), le(y, x), id(x), id(y))
, if_mod(true(), b1, b2, x, y) -> 0()
, if_mod(false(), b1, b2, x, y) -> if2(b1, b2, x, y)
, if2(true(), b2, x, y) -> 0()
, if2(false(), b2, x, y) -> if3(b2, x, y)
, if3(true(), x, y) -> mod(minus(x, y), s(y))
, if3(false(), x, y) -> 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:
{ le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, zero(0()) -> true()
, zero(s(x)) -> false()
, id(0()) -> 0()
, id(s(x)) -> s(id(x))
, minus(x, 0()) -> x
, minus(s(x), s(y)) -> minus(x, y)
, mod(x, y) -> if_mod(zero(x), zero(y), le(y, x), id(x), id(y))
, if_mod(true(), b1, b2, x, y) -> 0()
, if_mod(false(), b1, b2, x, y) -> if2(b1, b2, x, y)
, if2(true(), b2, x, y) -> 0()
, if2(false(), b2, x, y) -> if3(b2, x, y)
, if3(true(), x, y) -> mod(minus(x, y), s(y))
, if3(false(), x, y) -> 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:
{ le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, zero(0()) -> true()
, zero(s(x)) -> false()
, id(0()) -> 0()
, id(s(x)) -> s(id(x))
, minus(x, 0()) -> x
, minus(s(x), s(y)) -> minus(x, y)
, mod(x, y) -> if_mod(zero(x), zero(y), le(y, x), id(x), id(y))
, if_mod(true(), b1, b2, x, y) -> 0()
, if_mod(false(), b1, b2, x, y) -> if2(b1, b2, x, y)
, if2(true(), b2, x, y) -> 0()
, if2(false(), b2, x, y) -> if3(b2, x, y)
, if3(true(), x, y) -> mod(minus(x, y), s(y))
, if3(false(), x, y) -> 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:
{ le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, zero(0()) -> true()
, zero(s(x)) -> false()
, id(0()) -> 0()
, id(s(x)) -> s(id(x))
, minus(x, 0()) -> x
, minus(s(x), s(y)) -> minus(x, y)
, mod(x, y) -> if_mod(zero(x), zero(y), le(y, x), id(x), id(y))
, if_mod(true(), b1, b2, x, y) -> 0()
, if_mod(false(), b1, b2, x, y) -> if2(b1, b2, x, y)
, if2(true(), b2, x, y) -> 0()
, if2(false(), b2, x, y) -> if3(b2, x, y)
, if3(true(), x, y) -> mod(minus(x, y), s(y))
, if3(false(), x, y) -> 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:
{ le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, zero(0()) -> true()
, zero(s(x)) -> false()
, id(0()) -> 0()
, id(s(x)) -> s(id(x))
, minus(x, 0()) -> x
, minus(s(x), s(y)) -> minus(x, y)
, mod(x, y) -> if_mod(zero(x), zero(y), le(y, x), id(x), id(y))
, if_mod(true(), b1, b2, x, y) -> 0()
, if_mod(false(), b1, b2, x, y) -> if2(b1, b2, x, y)
, if2(true(), b2, x, y) -> 0()
, if2(false(), b2, x, y) -> if3(b2, x, y)
, if3(true(), x, y) -> mod(minus(x, y), s(y))
, if3(false(), x, y) -> x}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..