LMPO
MAYBE
We consider the following Problem:
Strict Trs:
{ gcd(x, y) -> gcd2(x, y, 0())
, gcd2(x, y, i) ->
if1(le(x, 0()), le(y, 0()), le(x, y), le(y, x), x, y, inc(i))
, if1(true(), b1, b2, b3, x, y, i) ->
pair(result(y), neededIterations(i))
, if1(false(), b1, b2, b3, x, y, i) -> if2(b1, b2, b3, x, y, i)
, if2(true(), b2, b3, x, y, i) ->
pair(result(x), neededIterations(i))
, if2(false(), b2, b3, x, y, i) -> if3(b2, b3, x, y, i)
, if3(false(), b3, x, y, i) -> gcd2(minus(x, y), y, i)
, if3(true(), b3, x, y, i) -> if4(b3, x, y, i)
, if4(false(), x, y, i) -> gcd2(x, minus(y, x), i)
, if4(true(), x, y, i) -> pair(result(x), neededIterations(i))
, inc(0()) -> 0()
, inc(s(i)) -> s(inc(i))
, le(s(x), 0()) -> false()
, le(0(), y) -> true()
, le(s(x), s(y)) -> le(x, y)
, minus(x, 0()) -> x
, minus(0(), y) -> 0()
, minus(s(x), s(y)) -> minus(x, y)
, a() -> b()
, a() -> c()}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
MPO
MAYBE
We consider the following Problem:
Strict Trs:
{ gcd(x, y) -> gcd2(x, y, 0())
, gcd2(x, y, i) ->
if1(le(x, 0()), le(y, 0()), le(x, y), le(y, x), x, y, inc(i))
, if1(true(), b1, b2, b3, x, y, i) ->
pair(result(y), neededIterations(i))
, if1(false(), b1, b2, b3, x, y, i) -> if2(b1, b2, b3, x, y, i)
, if2(true(), b2, b3, x, y, i) ->
pair(result(x), neededIterations(i))
, if2(false(), b2, b3, x, y, i) -> if3(b2, b3, x, y, i)
, if3(false(), b3, x, y, i) -> gcd2(minus(x, y), y, i)
, if3(true(), b3, x, y, i) -> if4(b3, x, y, i)
, if4(false(), x, y, i) -> gcd2(x, minus(y, x), i)
, if4(true(), x, y, i) -> pair(result(x), neededIterations(i))
, inc(0()) -> 0()
, inc(s(i)) -> s(inc(i))
, le(s(x), 0()) -> false()
, le(0(), y) -> true()
, le(s(x), s(y)) -> le(x, y)
, minus(x, 0()) -> x
, minus(0(), y) -> 0()
, minus(s(x), s(y)) -> minus(x, y)
, a() -> b()
, a() -> c()}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
POP*
MAYBE
We consider the following Problem:
Strict Trs:
{ gcd(x, y) -> gcd2(x, y, 0())
, gcd2(x, y, i) ->
if1(le(x, 0()), le(y, 0()), le(x, y), le(y, x), x, y, inc(i))
, if1(true(), b1, b2, b3, x, y, i) ->
pair(result(y), neededIterations(i))
, if1(false(), b1, b2, b3, x, y, i) -> if2(b1, b2, b3, x, y, i)
, if2(true(), b2, b3, x, y, i) ->
pair(result(x), neededIterations(i))
, if2(false(), b2, b3, x, y, i) -> if3(b2, b3, x, y, i)
, if3(false(), b3, x, y, i) -> gcd2(minus(x, y), y, i)
, if3(true(), b3, x, y, i) -> if4(b3, x, y, i)
, if4(false(), x, y, i) -> gcd2(x, minus(y, x), i)
, if4(true(), x, y, i) -> pair(result(x), neededIterations(i))
, inc(0()) -> 0()
, inc(s(i)) -> s(inc(i))
, le(s(x), 0()) -> false()
, le(0(), y) -> true()
, le(s(x), s(y)) -> le(x, y)
, minus(x, 0()) -> x
, minus(0(), y) -> 0()
, minus(s(x), s(y)) -> minus(x, y)
, a() -> b()
, a() -> c()}
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:
{ gcd(x, y) -> gcd2(x, y, 0())
, gcd2(x, y, i) ->
if1(le(x, 0()), le(y, 0()), le(x, y), le(y, x), x, y, inc(i))
, if1(true(), b1, b2, b3, x, y, i) ->
pair(result(y), neededIterations(i))
, if1(false(), b1, b2, b3, x, y, i) -> if2(b1, b2, b3, x, y, i)
, if2(true(), b2, b3, x, y, i) ->
pair(result(x), neededIterations(i))
, if2(false(), b2, b3, x, y, i) -> if3(b2, b3, x, y, i)
, if3(false(), b3, x, y, i) -> gcd2(minus(x, y), y, i)
, if3(true(), b3, x, y, i) -> if4(b3, x, y, i)
, if4(false(), x, y, i) -> gcd2(x, minus(y, x), i)
, if4(true(), x, y, i) -> pair(result(x), neededIterations(i))
, inc(0()) -> 0()
, inc(s(i)) -> s(inc(i))
, le(s(x), 0()) -> false()
, le(0(), y) -> true()
, le(s(x), s(y)) -> le(x, y)
, minus(x, 0()) -> x
, minus(0(), y) -> 0()
, minus(s(x), s(y)) -> minus(x, y)
, a() -> b()
, a() -> c()}
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:
{ gcd(x, y) -> gcd2(x, y, 0())
, gcd2(x, y, i) ->
if1(le(x, 0()), le(y, 0()), le(x, y), le(y, x), x, y, inc(i))
, if1(true(), b1, b2, b3, x, y, i) ->
pair(result(y), neededIterations(i))
, if1(false(), b1, b2, b3, x, y, i) -> if2(b1, b2, b3, x, y, i)
, if2(true(), b2, b3, x, y, i) ->
pair(result(x), neededIterations(i))
, if2(false(), b2, b3, x, y, i) -> if3(b2, b3, x, y, i)
, if3(false(), b3, x, y, i) -> gcd2(minus(x, y), y, i)
, if3(true(), b3, x, y, i) -> if4(b3, x, y, i)
, if4(false(), x, y, i) -> gcd2(x, minus(y, x), i)
, if4(true(), x, y, i) -> pair(result(x), neededIterations(i))
, inc(0()) -> 0()
, inc(s(i)) -> s(inc(i))
, le(s(x), 0()) -> false()
, le(0(), y) -> true()
, le(s(x), s(y)) -> le(x, y)
, minus(x, 0()) -> x
, minus(0(), y) -> 0()
, minus(s(x), s(y)) -> minus(x, y)
, a() -> b()
, a() -> c()}
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:
{ gcd(x, y) -> gcd2(x, y, 0())
, gcd2(x, y, i) ->
if1(le(x, 0()), le(y, 0()), le(x, y), le(y, x), x, y, inc(i))
, if1(true(), b1, b2, b3, x, y, i) ->
pair(result(y), neededIterations(i))
, if1(false(), b1, b2, b3, x, y, i) -> if2(b1, b2, b3, x, y, i)
, if2(true(), b2, b3, x, y, i) ->
pair(result(x), neededIterations(i))
, if2(false(), b2, b3, x, y, i) -> if3(b2, b3, x, y, i)
, if3(false(), b3, x, y, i) -> gcd2(minus(x, y), y, i)
, if3(true(), b3, x, y, i) -> if4(b3, x, y, i)
, if4(false(), x, y, i) -> gcd2(x, minus(y, x), i)
, if4(true(), x, y, i) -> pair(result(x), neededIterations(i))
, inc(0()) -> 0()
, inc(s(i)) -> s(inc(i))
, le(s(x), 0()) -> false()
, le(0(), y) -> true()
, le(s(x), s(y)) -> le(x, y)
, minus(x, 0()) -> x
, minus(0(), y) -> 0()
, minus(s(x), s(y)) -> minus(x, y)
, a() -> b()
, a() -> c()}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..