LMPO
MAYBE
We consider the following Problem:
Strict Trs:
{ p(s(x)) -> x
, p(0()) -> 0()
, le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, average(x, y) ->
if(le(x, 0()), le(y, 0()), le(y, s(0())), le(y, s(s(0()))), x, y)
, if(true(), b1, b2, b3, x, y) -> if2(b1, b2, b3, x, y)
, if(false(), b1, b2, b3, x, y) -> average(p(x), s(y))
, if2(true(), b2, b3, x, y) -> 0()
, if2(false(), b2, b3, x, y) -> if3(b2, b3, x, y)
, if3(true(), b3, x, y) -> 0()
, if3(false(), b3, x, y) -> if4(b3, x, y)
, if4(true(), x, y) -> s(0())
, if4(false(), x, y) -> average(s(x), p(p(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:
{ p(s(x)) -> x
, p(0()) -> 0()
, le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, average(x, y) ->
if(le(x, 0()), le(y, 0()), le(y, s(0())), le(y, s(s(0()))), x, y)
, if(true(), b1, b2, b3, x, y) -> if2(b1, b2, b3, x, y)
, if(false(), b1, b2, b3, x, y) -> average(p(x), s(y))
, if2(true(), b2, b3, x, y) -> 0()
, if2(false(), b2, b3, x, y) -> if3(b2, b3, x, y)
, if3(true(), b3, x, y) -> 0()
, if3(false(), b3, x, y) -> if4(b3, x, y)
, if4(true(), x, y) -> s(0())
, if4(false(), x, y) -> average(s(x), p(p(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:
{ p(s(x)) -> x
, p(0()) -> 0()
, le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, average(x, y) ->
if(le(x, 0()), le(y, 0()), le(y, s(0())), le(y, s(s(0()))), x, y)
, if(true(), b1, b2, b3, x, y) -> if2(b1, b2, b3, x, y)
, if(false(), b1, b2, b3, x, y) -> average(p(x), s(y))
, if2(true(), b2, b3, x, y) -> 0()
, if2(false(), b2, b3, x, y) -> if3(b2, b3, x, y)
, if3(true(), b3, x, y) -> 0()
, if3(false(), b3, x, y) -> if4(b3, x, y)
, if4(true(), x, y) -> s(0())
, if4(false(), x, y) -> average(s(x), p(p(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:
{ p(s(x)) -> x
, p(0()) -> 0()
, le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, average(x, y) ->
if(le(x, 0()), le(y, 0()), le(y, s(0())), le(y, s(s(0()))), x, y)
, if(true(), b1, b2, b3, x, y) -> if2(b1, b2, b3, x, y)
, if(false(), b1, b2, b3, x, y) -> average(p(x), s(y))
, if2(true(), b2, b3, x, y) -> 0()
, if2(false(), b2, b3, x, y) -> if3(b2, b3, x, y)
, if3(true(), b3, x, y) -> 0()
, if3(false(), b3, x, y) -> if4(b3, x, y)
, if4(true(), x, y) -> s(0())
, if4(false(), x, y) -> average(s(x), p(p(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:
{ p(s(x)) -> x
, p(0()) -> 0()
, le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, average(x, y) ->
if(le(x, 0()), le(y, 0()), le(y, s(0())), le(y, s(s(0()))), x, y)
, if(true(), b1, b2, b3, x, y) -> if2(b1, b2, b3, x, y)
, if(false(), b1, b2, b3, x, y) -> average(p(x), s(y))
, if2(true(), b2, b3, x, y) -> 0()
, if2(false(), b2, b3, x, y) -> if3(b2, b3, x, y)
, if3(true(), b3, x, y) -> 0()
, if3(false(), b3, x, y) -> if4(b3, x, y)
, if4(true(), x, y) -> s(0())
, if4(false(), x, y) -> average(s(x), p(p(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:
{ p(s(x)) -> x
, p(0()) -> 0()
, le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, average(x, y) ->
if(le(x, 0()), le(y, 0()), le(y, s(0())), le(y, s(s(0()))), x, y)
, if(true(), b1, b2, b3, x, y) -> if2(b1, b2, b3, x, y)
, if(false(), b1, b2, b3, x, y) -> average(p(x), s(y))
, if2(true(), b2, b3, x, y) -> 0()
, if2(false(), b2, b3, x, y) -> if3(b2, b3, x, y)
, if3(true(), b3, x, y) -> 0()
, if3(false(), b3, x, y) -> if4(b3, x, y)
, if4(true(), x, y) -> s(0())
, if4(false(), x, y) -> average(s(x), p(p(y)))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..