LMPO
MAYBE
We consider the following Problem:
Strict Trs:
{ minus(x, y) -> if(gt(x, y), x, y)
, if(true(), x, y) -> s(minus(p(x), y))
, if(false(), x, y) -> 0()
, p(0()) -> 0()
, p(s(x)) -> x
, ge(x, 0()) -> true()
, ge(0(), s(x)) -> false()
, ge(s(x), s(y)) -> ge(x, y)
, gt(0(), y) -> false()
, gt(s(x), 0()) -> true()
, gt(s(x), s(y)) -> gt(x, y)
, div(x, y) -> if1(ge(x, y), x, y)
, if1(true(), x, y) -> if2(gt(y, 0()), x, y)
, if1(false(), x, y) -> 0()
, if2(true(), x, y) -> s(div(minus(x, y), y))
, if2(false(), x, y) -> 0()}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
MPO
MAYBE
We consider the following Problem:
Strict Trs:
{ minus(x, y) -> if(gt(x, y), x, y)
, if(true(), x, y) -> s(minus(p(x), y))
, if(false(), x, y) -> 0()
, p(0()) -> 0()
, p(s(x)) -> x
, ge(x, 0()) -> true()
, ge(0(), s(x)) -> false()
, ge(s(x), s(y)) -> ge(x, y)
, gt(0(), y) -> false()
, gt(s(x), 0()) -> true()
, gt(s(x), s(y)) -> gt(x, y)
, div(x, y) -> if1(ge(x, y), x, y)
, if1(true(), x, y) -> if2(gt(y, 0()), x, y)
, if1(false(), x, y) -> 0()
, if2(true(), x, y) -> s(div(minus(x, y), y))
, if2(false(), x, y) -> 0()}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
POP*
MAYBE
We consider the following Problem:
Strict Trs:
{ minus(x, y) -> if(gt(x, y), x, y)
, if(true(), x, y) -> s(minus(p(x), y))
, if(false(), x, y) -> 0()
, p(0()) -> 0()
, p(s(x)) -> x
, ge(x, 0()) -> true()
, ge(0(), s(x)) -> false()
, ge(s(x), s(y)) -> ge(x, y)
, gt(0(), y) -> false()
, gt(s(x), 0()) -> true()
, gt(s(x), s(y)) -> gt(x, y)
, div(x, y) -> if1(ge(x, y), x, y)
, if1(true(), x, y) -> if2(gt(y, 0()), x, y)
, if1(false(), x, y) -> 0()
, if2(true(), x, y) -> s(div(minus(x, y), y))
, if2(false(), x, y) -> 0()}
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:
{ minus(x, y) -> if(gt(x, y), x, y)
, if(true(), x, y) -> s(minus(p(x), y))
, if(false(), x, y) -> 0()
, p(0()) -> 0()
, p(s(x)) -> x
, ge(x, 0()) -> true()
, ge(0(), s(x)) -> false()
, ge(s(x), s(y)) -> ge(x, y)
, gt(0(), y) -> false()
, gt(s(x), 0()) -> true()
, gt(s(x), s(y)) -> gt(x, y)
, div(x, y) -> if1(ge(x, y), x, y)
, if1(true(), x, y) -> if2(gt(y, 0()), x, y)
, if1(false(), x, y) -> 0()
, if2(true(), x, y) -> s(div(minus(x, y), y))
, if2(false(), x, y) -> 0()}
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:
{ minus(x, y) -> if(gt(x, y), x, y)
, if(true(), x, y) -> s(minus(p(x), y))
, if(false(), x, y) -> 0()
, p(0()) -> 0()
, p(s(x)) -> x
, ge(x, 0()) -> true()
, ge(0(), s(x)) -> false()
, ge(s(x), s(y)) -> ge(x, y)
, gt(0(), y) -> false()
, gt(s(x), 0()) -> true()
, gt(s(x), s(y)) -> gt(x, y)
, div(x, y) -> if1(ge(x, y), x, y)
, if1(true(), x, y) -> if2(gt(y, 0()), x, y)
, if1(false(), x, y) -> 0()
, if2(true(), x, y) -> s(div(minus(x, y), y))
, if2(false(), x, y) -> 0()}
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:
{ minus(x, y) -> if(gt(x, y), x, y)
, if(true(), x, y) -> s(minus(p(x), y))
, if(false(), x, y) -> 0()
, p(0()) -> 0()
, p(s(x)) -> x
, ge(x, 0()) -> true()
, ge(0(), s(x)) -> false()
, ge(s(x), s(y)) -> ge(x, y)
, gt(0(), y) -> false()
, gt(s(x), 0()) -> true()
, gt(s(x), s(y)) -> gt(x, y)
, div(x, y) -> if1(ge(x, y), x, y)
, if1(true(), x, y) -> if2(gt(y, 0()), x, y)
, if1(false(), x, y) -> 0()
, if2(true(), x, y) -> s(div(minus(x, y), y))
, if2(false(), x, y) -> 0()}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..