LMPO
MAYBE
We consider the following Problem:
Strict Trs:
{ le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, eq(0(), 0()) -> true()
, eq(0(), s(y)) -> false()
, eq(s(x), 0()) -> false()
, eq(s(x), s(y)) -> eq(x, y)
, minsort(nil()) -> nil()
, minsort(cons(x, xs)) ->
cons(min(cons(x, xs)), minsort(rm(min(cons(x, xs)), cons(x, xs))))
, min(nil()) -> 0()
, min(cons(x, nil())) -> x
, min(cons(x, cons(y, xs))) -> if1(le(x, y), x, y, xs)
, if1(true(), x, y, xs) -> min(cons(x, xs))
, if1(false(), x, y, xs) -> min(cons(y, xs))
, rm(x, nil()) -> nil()
, rm(x, cons(y, xs)) -> if2(eq(x, y), x, y, xs)
, if2(true(), x, y, xs) -> rm(x, xs)
, if2(false(), x, y, xs) -> cons(y, rm(x, xs))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
MPO
MAYBE
We consider the following Problem:
Strict Trs:
{ le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, eq(0(), 0()) -> true()
, eq(0(), s(y)) -> false()
, eq(s(x), 0()) -> false()
, eq(s(x), s(y)) -> eq(x, y)
, minsort(nil()) -> nil()
, minsort(cons(x, xs)) ->
cons(min(cons(x, xs)), minsort(rm(min(cons(x, xs)), cons(x, xs))))
, min(nil()) -> 0()
, min(cons(x, nil())) -> x
, min(cons(x, cons(y, xs))) -> if1(le(x, y), x, y, xs)
, if1(true(), x, y, xs) -> min(cons(x, xs))
, if1(false(), x, y, xs) -> min(cons(y, xs))
, rm(x, nil()) -> nil()
, rm(x, cons(y, xs)) -> if2(eq(x, y), x, y, xs)
, if2(true(), x, y, xs) -> rm(x, xs)
, if2(false(), x, y, xs) -> cons(y, rm(x, xs))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
POP*
MAYBE
We consider the following Problem:
Strict Trs:
{ le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, eq(0(), 0()) -> true()
, eq(0(), s(y)) -> false()
, eq(s(x), 0()) -> false()
, eq(s(x), s(y)) -> eq(x, y)
, minsort(nil()) -> nil()
, minsort(cons(x, xs)) ->
cons(min(cons(x, xs)), minsort(rm(min(cons(x, xs)), cons(x, xs))))
, min(nil()) -> 0()
, min(cons(x, nil())) -> x
, min(cons(x, cons(y, xs))) -> if1(le(x, y), x, y, xs)
, if1(true(), x, y, xs) -> min(cons(x, xs))
, if1(false(), x, y, xs) -> min(cons(y, xs))
, rm(x, nil()) -> nil()
, rm(x, cons(y, xs)) -> if2(eq(x, y), x, y, xs)
, if2(true(), x, y, xs) -> rm(x, xs)
, if2(false(), x, y, xs) -> cons(y, rm(x, xs))}
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:
{ le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, eq(0(), 0()) -> true()
, eq(0(), s(y)) -> false()
, eq(s(x), 0()) -> false()
, eq(s(x), s(y)) -> eq(x, y)
, minsort(nil()) -> nil()
, minsort(cons(x, xs)) ->
cons(min(cons(x, xs)), minsort(rm(min(cons(x, xs)), cons(x, xs))))
, min(nil()) -> 0()
, min(cons(x, nil())) -> x
, min(cons(x, cons(y, xs))) -> if1(le(x, y), x, y, xs)
, if1(true(), x, y, xs) -> min(cons(x, xs))
, if1(false(), x, y, xs) -> min(cons(y, xs))
, rm(x, nil()) -> nil()
, rm(x, cons(y, xs)) -> if2(eq(x, y), x, y, xs)
, if2(true(), x, y, xs) -> rm(x, xs)
, if2(false(), x, y, xs) -> cons(y, rm(x, xs))}
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:
{ le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, eq(0(), 0()) -> true()
, eq(0(), s(y)) -> false()
, eq(s(x), 0()) -> false()
, eq(s(x), s(y)) -> eq(x, y)
, minsort(nil()) -> nil()
, minsort(cons(x, xs)) ->
cons(min(cons(x, xs)), minsort(rm(min(cons(x, xs)), cons(x, xs))))
, min(nil()) -> 0()
, min(cons(x, nil())) -> x
, min(cons(x, cons(y, xs))) -> if1(le(x, y), x, y, xs)
, if1(true(), x, y, xs) -> min(cons(x, xs))
, if1(false(), x, y, xs) -> min(cons(y, xs))
, rm(x, nil()) -> nil()
, rm(x, cons(y, xs)) -> if2(eq(x, y), x, y, xs)
, if2(true(), x, y, xs) -> rm(x, xs)
, if2(false(), x, y, xs) -> cons(y, rm(x, xs))}
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:
{ le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, eq(0(), 0()) -> true()
, eq(0(), s(y)) -> false()
, eq(s(x), 0()) -> false()
, eq(s(x), s(y)) -> eq(x, y)
, minsort(nil()) -> nil()
, minsort(cons(x, xs)) ->
cons(min(cons(x, xs)), minsort(rm(min(cons(x, xs)), cons(x, xs))))
, min(nil()) -> 0()
, min(cons(x, nil())) -> x
, min(cons(x, cons(y, xs))) -> if1(le(x, y), x, y, xs)
, if1(true(), x, y, xs) -> min(cons(x, xs))
, if1(false(), x, y, xs) -> min(cons(y, xs))
, rm(x, nil()) -> nil()
, rm(x, cons(y, xs)) -> if2(eq(x, y), x, y, xs)
, if2(true(), x, y, xs) -> rm(x, xs)
, if2(false(), x, y, xs) -> cons(y, rm(x, xs))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..