LMPO
MAYBE
We consider the following Problem:
Strict Trs:
{ eq(0(), 0()) -> true()
, eq(0(), s(x)) -> false()
, eq(s(x), 0()) -> false()
, eq(s(x), s(y)) -> eq(x, y)
, or(true(), y) -> true()
, or(false(), y) -> y
, and(true(), y) -> y
, and(false(), y) -> false()
, size(empty()) -> 0()
, size(edge(x, y, i)) -> s(size(i))
, le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, reachable(x, y, i) -> reach(x, y, 0(), i, i)
, reach(x, y, c, i, j) -> if1(eq(x, y), x, y, c, i, j)
, if1(true(), x, y, c, i, j) -> true()
, if1(false(), x, y, c, i, j) -> if2(le(c, size(j)), x, y, c, i, j)
, if2(false(), x, y, c, i, j) -> false()
, if2(true(), x, y, c, empty(), j) -> false()
, if2(true(), x, y, c, edge(u, v, i), j) ->
or(if2(true(), x, y, c, i, j),
and(eq(x, u), reach(v, y, s(c), j, j)))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
MPO
MAYBE
We consider the following Problem:
Strict Trs:
{ eq(0(), 0()) -> true()
, eq(0(), s(x)) -> false()
, eq(s(x), 0()) -> false()
, eq(s(x), s(y)) -> eq(x, y)
, or(true(), y) -> true()
, or(false(), y) -> y
, and(true(), y) -> y
, and(false(), y) -> false()
, size(empty()) -> 0()
, size(edge(x, y, i)) -> s(size(i))
, le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, reachable(x, y, i) -> reach(x, y, 0(), i, i)
, reach(x, y, c, i, j) -> if1(eq(x, y), x, y, c, i, j)
, if1(true(), x, y, c, i, j) -> true()
, if1(false(), x, y, c, i, j) -> if2(le(c, size(j)), x, y, c, i, j)
, if2(false(), x, y, c, i, j) -> false()
, if2(true(), x, y, c, empty(), j) -> false()
, if2(true(), x, y, c, edge(u, v, i), j) ->
or(if2(true(), x, y, c, i, j),
and(eq(x, u), reach(v, y, s(c), j, j)))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
POP*
MAYBE
We consider the following Problem:
Strict Trs:
{ eq(0(), 0()) -> true()
, eq(0(), s(x)) -> false()
, eq(s(x), 0()) -> false()
, eq(s(x), s(y)) -> eq(x, y)
, or(true(), y) -> true()
, or(false(), y) -> y
, and(true(), y) -> y
, and(false(), y) -> false()
, size(empty()) -> 0()
, size(edge(x, y, i)) -> s(size(i))
, le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, reachable(x, y, i) -> reach(x, y, 0(), i, i)
, reach(x, y, c, i, j) -> if1(eq(x, y), x, y, c, i, j)
, if1(true(), x, y, c, i, j) -> true()
, if1(false(), x, y, c, i, j) -> if2(le(c, size(j)), x, y, c, i, j)
, if2(false(), x, y, c, i, j) -> false()
, if2(true(), x, y, c, empty(), j) -> false()
, if2(true(), x, y, c, edge(u, v, i), j) ->
or(if2(true(), x, y, c, i, j),
and(eq(x, u), reach(v, y, s(c), j, j)))}
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:
{ eq(0(), 0()) -> true()
, eq(0(), s(x)) -> false()
, eq(s(x), 0()) -> false()
, eq(s(x), s(y)) -> eq(x, y)
, or(true(), y) -> true()
, or(false(), y) -> y
, and(true(), y) -> y
, and(false(), y) -> false()
, size(empty()) -> 0()
, size(edge(x, y, i)) -> s(size(i))
, le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, reachable(x, y, i) -> reach(x, y, 0(), i, i)
, reach(x, y, c, i, j) -> if1(eq(x, y), x, y, c, i, j)
, if1(true(), x, y, c, i, j) -> true()
, if1(false(), x, y, c, i, j) -> if2(le(c, size(j)), x, y, c, i, j)
, if2(false(), x, y, c, i, j) -> false()
, if2(true(), x, y, c, empty(), j) -> false()
, if2(true(), x, y, c, edge(u, v, i), j) ->
or(if2(true(), x, y, c, i, j),
and(eq(x, u), reach(v, y, s(c), j, j)))}
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:
{ eq(0(), 0()) -> true()
, eq(0(), s(x)) -> false()
, eq(s(x), 0()) -> false()
, eq(s(x), s(y)) -> eq(x, y)
, or(true(), y) -> true()
, or(false(), y) -> y
, and(true(), y) -> y
, and(false(), y) -> false()
, size(empty()) -> 0()
, size(edge(x, y, i)) -> s(size(i))
, le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, reachable(x, y, i) -> reach(x, y, 0(), i, i)
, reach(x, y, c, i, j) -> if1(eq(x, y), x, y, c, i, j)
, if1(true(), x, y, c, i, j) -> true()
, if1(false(), x, y, c, i, j) -> if2(le(c, size(j)), x, y, c, i, j)
, if2(false(), x, y, c, i, j) -> false()
, if2(true(), x, y, c, empty(), j) -> false()
, if2(true(), x, y, c, edge(u, v, i), j) ->
or(if2(true(), x, y, c, i, j),
and(eq(x, u), reach(v, y, s(c), j, j)))}
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:
{ eq(0(), 0()) -> true()
, eq(0(), s(x)) -> false()
, eq(s(x), 0()) -> false()
, eq(s(x), s(y)) -> eq(x, y)
, or(true(), y) -> true()
, or(false(), y) -> y
, and(true(), y) -> y
, and(false(), y) -> false()
, size(empty()) -> 0()
, size(edge(x, y, i)) -> s(size(i))
, le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, reachable(x, y, i) -> reach(x, y, 0(), i, i)
, reach(x, y, c, i, j) -> if1(eq(x, y), x, y, c, i, j)
, if1(true(), x, y, c, i, j) -> true()
, if1(false(), x, y, c, i, j) -> if2(le(c, size(j)), x, y, c, i, j)
, if2(false(), x, y, c, i, j) -> false()
, if2(true(), x, y, c, empty(), j) -> false()
, if2(true(), x, y, c, edge(u, v, i), j) ->
or(if2(true(), x, y, c, i, j),
and(eq(x, u), reach(v, y, s(c), j, j)))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..