LMPO
MAYBE
We consider the following Problem:
Strict Trs:
{ cond1(true(), x, y) -> cond2(gr(x, y), x, y)
, cond2(true(), x, y) -> cond3(gr(x, 0()), x, y)
, cond2(false(), x, y) -> cond4(gr(y, 0()), x, y)
, cond3(true(), x, y) -> cond3(gr(x, 0()), p(x), y)
, cond3(false(), x, y) -> cond1(and(gr(x, 0()), gr(y, 0())), x, y)
, cond4(true(), x, y) -> cond4(gr(y, 0()), x, p(y))
, cond4(false(), x, y) -> cond1(and(gr(x, 0()), gr(y, 0())), x, y)
, gr(0(), x) -> false()
, gr(s(x), 0()) -> true()
, gr(s(x), s(y)) -> gr(x, y)
, and(true(), true()) -> true()
, and(false(), x) -> false()
, and(x, false()) -> false()
, p(0()) -> 0()
, p(s(x)) -> 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:
{ cond1(true(), x, y) -> cond2(gr(x, y), x, y)
, cond2(true(), x, y) -> cond3(gr(x, 0()), x, y)
, cond2(false(), x, y) -> cond4(gr(y, 0()), x, y)
, cond3(true(), x, y) -> cond3(gr(x, 0()), p(x), y)
, cond3(false(), x, y) -> cond1(and(gr(x, 0()), gr(y, 0())), x, y)
, cond4(true(), x, y) -> cond4(gr(y, 0()), x, p(y))
, cond4(false(), x, y) -> cond1(and(gr(x, 0()), gr(y, 0())), x, y)
, gr(0(), x) -> false()
, gr(s(x), 0()) -> true()
, gr(s(x), s(y)) -> gr(x, y)
, and(true(), true()) -> true()
, and(false(), x) -> false()
, and(x, false()) -> false()
, p(0()) -> 0()
, p(s(x)) -> 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:
{ cond1(true(), x, y) -> cond2(gr(x, y), x, y)
, cond2(true(), x, y) -> cond3(gr(x, 0()), x, y)
, cond2(false(), x, y) -> cond4(gr(y, 0()), x, y)
, cond3(true(), x, y) -> cond3(gr(x, 0()), p(x), y)
, cond3(false(), x, y) -> cond1(and(gr(x, 0()), gr(y, 0())), x, y)
, cond4(true(), x, y) -> cond4(gr(y, 0()), x, p(y))
, cond4(false(), x, y) -> cond1(and(gr(x, 0()), gr(y, 0())), x, y)
, gr(0(), x) -> false()
, gr(s(x), 0()) -> true()
, gr(s(x), s(y)) -> gr(x, y)
, and(true(), true()) -> true()
, and(false(), x) -> false()
, and(x, false()) -> false()
, p(0()) -> 0()
, p(s(x)) -> 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:
{ cond1(true(), x, y) -> cond2(gr(x, y), x, y)
, cond2(true(), x, y) -> cond3(gr(x, 0()), x, y)
, cond2(false(), x, y) -> cond4(gr(y, 0()), x, y)
, cond3(true(), x, y) -> cond3(gr(x, 0()), p(x), y)
, cond3(false(), x, y) -> cond1(and(gr(x, 0()), gr(y, 0())), x, y)
, cond4(true(), x, y) -> cond4(gr(y, 0()), x, p(y))
, cond4(false(), x, y) -> cond1(and(gr(x, 0()), gr(y, 0())), x, y)
, gr(0(), x) -> false()
, gr(s(x), 0()) -> true()
, gr(s(x), s(y)) -> gr(x, y)
, and(true(), true()) -> true()
, and(false(), x) -> false()
, and(x, false()) -> false()
, p(0()) -> 0()
, p(s(x)) -> 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:
{ cond1(true(), x, y) -> cond2(gr(x, y), x, y)
, cond2(true(), x, y) -> cond3(gr(x, 0()), x, y)
, cond2(false(), x, y) -> cond4(gr(y, 0()), x, y)
, cond3(true(), x, y) -> cond3(gr(x, 0()), p(x), y)
, cond3(false(), x, y) -> cond1(and(gr(x, 0()), gr(y, 0())), x, y)
, cond4(true(), x, y) -> cond4(gr(y, 0()), x, p(y))
, cond4(false(), x, y) -> cond1(and(gr(x, 0()), gr(y, 0())), x, y)
, gr(0(), x) -> false()
, gr(s(x), 0()) -> true()
, gr(s(x), s(y)) -> gr(x, y)
, and(true(), true()) -> true()
, and(false(), x) -> false()
, and(x, false()) -> false()
, p(0()) -> 0()
, p(s(x)) -> 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:
{ cond1(true(), x, y) -> cond2(gr(x, y), x, y)
, cond2(true(), x, y) -> cond3(gr(x, 0()), x, y)
, cond2(false(), x, y) -> cond4(gr(y, 0()), x, y)
, cond3(true(), x, y) -> cond3(gr(x, 0()), p(x), y)
, cond3(false(), x, y) -> cond1(and(gr(x, 0()), gr(y, 0())), x, y)
, cond4(true(), x, y) -> cond4(gr(y, 0()), x, p(y))
, cond4(false(), x, y) -> cond1(and(gr(x, 0()), gr(y, 0())), x, y)
, gr(0(), x) -> false()
, gr(s(x), 0()) -> true()
, gr(s(x), s(y)) -> gr(x, y)
, and(true(), true()) -> true()
, and(false(), x) -> false()
, and(x, false()) -> false()
, p(0()) -> 0()
, p(s(x)) -> x}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..