LMPO
MAYBE
We consider the following Problem:
Strict Trs:
{ lt(0(), s(x)) -> true()
, lt(x, 0()) -> false()
, lt(s(x), s(y)) -> lt(x, y)
, logarithm(x) -> ifa(lt(0(), x), x)
, ifa(true(), x) -> help(x, 1())
, ifa(false(), x) -> logZeroError()
, help(x, y) -> ifb(lt(y, x), x, y)
, ifb(true(), x, y) -> help(half(x), s(y))
, ifb(false(), x, y) -> y
, half(0()) -> 0()
, half(s(0())) -> 0()
, half(s(s(x))) -> s(half(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:
{ lt(0(), s(x)) -> true()
, lt(x, 0()) -> false()
, lt(s(x), s(y)) -> lt(x, y)
, logarithm(x) -> ifa(lt(0(), x), x)
, ifa(true(), x) -> help(x, 1())
, ifa(false(), x) -> logZeroError()
, help(x, y) -> ifb(lt(y, x), x, y)
, ifb(true(), x, y) -> help(half(x), s(y))
, ifb(false(), x, y) -> y
, half(0()) -> 0()
, half(s(0())) -> 0()
, half(s(s(x))) -> s(half(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:
{ lt(0(), s(x)) -> true()
, lt(x, 0()) -> false()
, lt(s(x), s(y)) -> lt(x, y)
, logarithm(x) -> ifa(lt(0(), x), x)
, ifa(true(), x) -> help(x, 1())
, ifa(false(), x) -> logZeroError()
, help(x, y) -> ifb(lt(y, x), x, y)
, ifb(true(), x, y) -> help(half(x), s(y))
, ifb(false(), x, y) -> y
, half(0()) -> 0()
, half(s(0())) -> 0()
, half(s(s(x))) -> s(half(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:
{ lt(0(), s(x)) -> true()
, lt(x, 0()) -> false()
, lt(s(x), s(y)) -> lt(x, y)
, logarithm(x) -> ifa(lt(0(), x), x)
, ifa(true(), x) -> help(x, 1())
, ifa(false(), x) -> logZeroError()
, help(x, y) -> ifb(lt(y, x), x, y)
, ifb(true(), x, y) -> help(half(x), s(y))
, ifb(false(), x, y) -> y
, half(0()) -> 0()
, half(s(0())) -> 0()
, half(s(s(x))) -> s(half(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:
{ lt(0(), s(x)) -> true()
, lt(x, 0()) -> false()
, lt(s(x), s(y)) -> lt(x, y)
, logarithm(x) -> ifa(lt(0(), x), x)
, ifa(true(), x) -> help(x, 1())
, ifa(false(), x) -> logZeroError()
, help(x, y) -> ifb(lt(y, x), x, y)
, ifb(true(), x, y) -> help(half(x), s(y))
, ifb(false(), x, y) -> y
, half(0()) -> 0()
, half(s(0())) -> 0()
, half(s(s(x))) -> s(half(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:
{ lt(0(), s(x)) -> true()
, lt(x, 0()) -> false()
, lt(s(x), s(y)) -> lt(x, y)
, logarithm(x) -> ifa(lt(0(), x), x)
, ifa(true(), x) -> help(x, 1())
, ifa(false(), x) -> logZeroError()
, help(x, y) -> ifb(lt(y, x), x, y)
, ifb(true(), x, y) -> help(half(x), s(y))
, ifb(false(), x, y) -> y
, half(0()) -> 0()
, half(s(0())) -> 0()
, half(s(s(x))) -> s(half(x))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..