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)
, inc(0()) -> 0()
, inc(s(x)) -> s(inc(x))
, minus(0(), y) -> 0()
, minus(x, 0()) -> x
, minus(s(x), s(y)) -> minus(x, y)
, quot(0(), s(y)) -> 0()
, quot(s(x), s(y)) -> s(quot(minus(x, y), s(y)))
, log(x) -> log2(x, 0())
, log2(x, y) -> if(le(x, 0()), le(x, s(0())), x, inc(y))
, if(true(), b, x, y) -> log_undefined()
, if(false(), b, x, y) -> if2(b, x, y)
, if2(true(), x, s(y)) -> y
, if2(false(), x, y) -> log2(quot(x, s(s(0()))), 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:
{ le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, inc(0()) -> 0()
, inc(s(x)) -> s(inc(x))
, minus(0(), y) -> 0()
, minus(x, 0()) -> x
, minus(s(x), s(y)) -> minus(x, y)
, quot(0(), s(y)) -> 0()
, quot(s(x), s(y)) -> s(quot(minus(x, y), s(y)))
, log(x) -> log2(x, 0())
, log2(x, y) -> if(le(x, 0()), le(x, s(0())), x, inc(y))
, if(true(), b, x, y) -> log_undefined()
, if(false(), b, x, y) -> if2(b, x, y)
, if2(true(), x, s(y)) -> y
, if2(false(), x, y) -> log2(quot(x, s(s(0()))), 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:
{ le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, inc(0()) -> 0()
, inc(s(x)) -> s(inc(x))
, minus(0(), y) -> 0()
, minus(x, 0()) -> x
, minus(s(x), s(y)) -> minus(x, y)
, quot(0(), s(y)) -> 0()
, quot(s(x), s(y)) -> s(quot(minus(x, y), s(y)))
, log(x) -> log2(x, 0())
, log2(x, y) -> if(le(x, 0()), le(x, s(0())), x, inc(y))
, if(true(), b, x, y) -> log_undefined()
, if(false(), b, x, y) -> if2(b, x, y)
, if2(true(), x, s(y)) -> y
, if2(false(), x, y) -> log2(quot(x, s(s(0()))), 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:
{ le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, inc(0()) -> 0()
, inc(s(x)) -> s(inc(x))
, minus(0(), y) -> 0()
, minus(x, 0()) -> x
, minus(s(x), s(y)) -> minus(x, y)
, quot(0(), s(y)) -> 0()
, quot(s(x), s(y)) -> s(quot(minus(x, y), s(y)))
, log(x) -> log2(x, 0())
, log2(x, y) -> if(le(x, 0()), le(x, s(0())), x, inc(y))
, if(true(), b, x, y) -> log_undefined()
, if(false(), b, x, y) -> if2(b, x, y)
, if2(true(), x, s(y)) -> y
, if2(false(), x, y) -> log2(quot(x, s(s(0()))), 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:
{ le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, inc(0()) -> 0()
, inc(s(x)) -> s(inc(x))
, minus(0(), y) -> 0()
, minus(x, 0()) -> x
, minus(s(x), s(y)) -> minus(x, y)
, quot(0(), s(y)) -> 0()
, quot(s(x), s(y)) -> s(quot(minus(x, y), s(y)))
, log(x) -> log2(x, 0())
, log2(x, y) -> if(le(x, 0()), le(x, s(0())), x, inc(y))
, if(true(), b, x, y) -> log_undefined()
, if(false(), b, x, y) -> if2(b, x, y)
, if2(true(), x, s(y)) -> y
, if2(false(), x, y) -> log2(quot(x, s(s(0()))), 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:
{ le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, inc(0()) -> 0()
, inc(s(x)) -> s(inc(x))
, minus(0(), y) -> 0()
, minus(x, 0()) -> x
, minus(s(x), s(y)) -> minus(x, y)
, quot(0(), s(y)) -> 0()
, quot(s(x), s(y)) -> s(quot(minus(x, y), s(y)))
, log(x) -> log2(x, 0())
, log2(x, y) -> if(le(x, 0()), le(x, s(0())), x, inc(y))
, if(true(), b, x, y) -> log_undefined()
, if(false(), b, x, y) -> if2(b, x, y)
, if2(true(), x, s(y)) -> y
, if2(false(), x, y) -> log2(quot(x, s(s(0()))), y)}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..