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
, union(empty(), h) -> h
, union(edge(x, y, i), h) -> edge(x, y, union(i, h))
, isEmpty(empty()) -> true()
, isEmpty(edge(x, y, i)) -> false()
, from(edge(x, y, i)) -> x
, to(edge(x, y, i)) -> y
, rest(edge(x, y, i)) -> i
, rest(empty()) -> empty()
, reach(x, y, i, h) ->
if1(eq(x, y), isEmpty(i), eq(x, from(i)), eq(y, to(i)), x, y, i, h)
, if1(true(), b1, b2, b3, x, y, i, h) -> true()
, if1(false(), b1, b2, b3, x, y, i, h) ->
if2(b1, b2, b3, x, y, i, h)
, if2(true(), b2, b3, x, y, i, h) -> false()
, if2(false(), b2, b3, x, y, i, h) -> if3(b2, b3, x, y, i, h)
, if3(false(), b3, x, y, i, h) ->
reach(x, y, rest(i), edge(from(i), to(i), h))
, if3(true(), b3, x, y, i, h) -> if4(b3, x, y, i, h)
, if4(true(), x, y, i, h) -> true()
, if4(false(), x, y, i, h) ->
or(reach(x, y, rest(i), h),
reach(to(i), y, union(rest(i), h), empty()))}
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
, union(empty(), h) -> h
, union(edge(x, y, i), h) -> edge(x, y, union(i, h))
, isEmpty(empty()) -> true()
, isEmpty(edge(x, y, i)) -> false()
, from(edge(x, y, i)) -> x
, to(edge(x, y, i)) -> y
, rest(edge(x, y, i)) -> i
, rest(empty()) -> empty()
, reach(x, y, i, h) ->
if1(eq(x, y), isEmpty(i), eq(x, from(i)), eq(y, to(i)), x, y, i, h)
, if1(true(), b1, b2, b3, x, y, i, h) -> true()
, if1(false(), b1, b2, b3, x, y, i, h) ->
if2(b1, b2, b3, x, y, i, h)
, if2(true(), b2, b3, x, y, i, h) -> false()
, if2(false(), b2, b3, x, y, i, h) -> if3(b2, b3, x, y, i, h)
, if3(false(), b3, x, y, i, h) ->
reach(x, y, rest(i), edge(from(i), to(i), h))
, if3(true(), b3, x, y, i, h) -> if4(b3, x, y, i, h)
, if4(true(), x, y, i, h) -> true()
, if4(false(), x, y, i, h) ->
or(reach(x, y, rest(i), h),
reach(to(i), y, union(rest(i), h), empty()))}
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
, union(empty(), h) -> h
, union(edge(x, y, i), h) -> edge(x, y, union(i, h))
, isEmpty(empty()) -> true()
, isEmpty(edge(x, y, i)) -> false()
, from(edge(x, y, i)) -> x
, to(edge(x, y, i)) -> y
, rest(edge(x, y, i)) -> i
, rest(empty()) -> empty()
, reach(x, y, i, h) ->
if1(eq(x, y), isEmpty(i), eq(x, from(i)), eq(y, to(i)), x, y, i, h)
, if1(true(), b1, b2, b3, x, y, i, h) -> true()
, if1(false(), b1, b2, b3, x, y, i, h) ->
if2(b1, b2, b3, x, y, i, h)
, if2(true(), b2, b3, x, y, i, h) -> false()
, if2(false(), b2, b3, x, y, i, h) -> if3(b2, b3, x, y, i, h)
, if3(false(), b3, x, y, i, h) ->
reach(x, y, rest(i), edge(from(i), to(i), h))
, if3(true(), b3, x, y, i, h) -> if4(b3, x, y, i, h)
, if4(true(), x, y, i, h) -> true()
, if4(false(), x, y, i, h) ->
or(reach(x, y, rest(i), h),
reach(to(i), y, union(rest(i), h), empty()))}
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
, union(empty(), h) -> h
, union(edge(x, y, i), h) -> edge(x, y, union(i, h))
, isEmpty(empty()) -> true()
, isEmpty(edge(x, y, i)) -> false()
, from(edge(x, y, i)) -> x
, to(edge(x, y, i)) -> y
, rest(edge(x, y, i)) -> i
, rest(empty()) -> empty()
, reach(x, y, i, h) ->
if1(eq(x, y), isEmpty(i), eq(x, from(i)), eq(y, to(i)), x, y, i, h)
, if1(true(), b1, b2, b3, x, y, i, h) -> true()
, if1(false(), b1, b2, b3, x, y, i, h) ->
if2(b1, b2, b3, x, y, i, h)
, if2(true(), b2, b3, x, y, i, h) -> false()
, if2(false(), b2, b3, x, y, i, h) -> if3(b2, b3, x, y, i, h)
, if3(false(), b3, x, y, i, h) ->
reach(x, y, rest(i), edge(from(i), to(i), h))
, if3(true(), b3, x, y, i, h) -> if4(b3, x, y, i, h)
, if4(true(), x, y, i, h) -> true()
, if4(false(), x, y, i, h) ->
or(reach(x, y, rest(i), h),
reach(to(i), y, union(rest(i), h), empty()))}
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
, union(empty(), h) -> h
, union(edge(x, y, i), h) -> edge(x, y, union(i, h))
, isEmpty(empty()) -> true()
, isEmpty(edge(x, y, i)) -> false()
, from(edge(x, y, i)) -> x
, to(edge(x, y, i)) -> y
, rest(edge(x, y, i)) -> i
, rest(empty()) -> empty()
, reach(x, y, i, h) ->
if1(eq(x, y), isEmpty(i), eq(x, from(i)), eq(y, to(i)), x, y, i, h)
, if1(true(), b1, b2, b3, x, y, i, h) -> true()
, if1(false(), b1, b2, b3, x, y, i, h) ->
if2(b1, b2, b3, x, y, i, h)
, if2(true(), b2, b3, x, y, i, h) -> false()
, if2(false(), b2, b3, x, y, i, h) -> if3(b2, b3, x, y, i, h)
, if3(false(), b3, x, y, i, h) ->
reach(x, y, rest(i), edge(from(i), to(i), h))
, if3(true(), b3, x, y, i, h) -> if4(b3, x, y, i, h)
, if4(true(), x, y, i, h) -> true()
, if4(false(), x, y, i, h) ->
or(reach(x, y, rest(i), h),
reach(to(i), y, union(rest(i), h), empty()))}
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
, union(empty(), h) -> h
, union(edge(x, y, i), h) -> edge(x, y, union(i, h))
, isEmpty(empty()) -> true()
, isEmpty(edge(x, y, i)) -> false()
, from(edge(x, y, i)) -> x
, to(edge(x, y, i)) -> y
, rest(edge(x, y, i)) -> i
, rest(empty()) -> empty()
, reach(x, y, i, h) ->
if1(eq(x, y), isEmpty(i), eq(x, from(i)), eq(y, to(i)), x, y, i, h)
, if1(true(), b1, b2, b3, x, y, i, h) -> true()
, if1(false(), b1, b2, b3, x, y, i, h) ->
if2(b1, b2, b3, x, y, i, h)
, if2(true(), b2, b3, x, y, i, h) -> false()
, if2(false(), b2, b3, x, y, i, h) -> if3(b2, b3, x, y, i, h)
, if3(false(), b3, x, y, i, h) ->
reach(x, y, rest(i), edge(from(i), to(i), h))
, if3(true(), b3, x, y, i, h) -> if4(b3, x, y, i, h)
, if4(true(), x, y, i, h) -> true()
, if4(false(), x, y, i, h) ->
or(reach(x, y, rest(i), h),
reach(to(i), y, union(rest(i), h), empty()))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..