LMPO
MAYBE
We consider the following Problem:
Strict Trs:
{ a__minus(0(), Y) -> 0()
, a__minus(s(X), s(Y)) -> a__minus(X, Y)
, a__geq(X, 0()) -> true()
, a__geq(0(), s(Y)) -> false()
, a__geq(s(X), s(Y)) -> a__geq(X, Y)
, a__div(0(), s(Y)) -> 0()
, a__div(s(X), s(Y)) ->
a__if(a__geq(X, Y), s(div(minus(X, Y), s(Y))), 0())
, a__if(true(), X, Y) -> mark(X)
, a__if(false(), X, Y) -> mark(Y)
, mark(minus(X1, X2)) -> a__minus(X1, X2)
, mark(geq(X1, X2)) -> a__geq(X1, X2)
, mark(div(X1, X2)) -> a__div(mark(X1), X2)
, mark(if(X1, X2, X3)) -> a__if(mark(X1), X2, X3)
, mark(0()) -> 0()
, mark(s(X)) -> s(mark(X))
, mark(true()) -> true()
, mark(false()) -> false()
, a__minus(X1, X2) -> minus(X1, X2)
, a__geq(X1, X2) -> geq(X1, X2)
, a__div(X1, X2) -> div(X1, X2)
, a__if(X1, X2, X3) -> if(X1, X2, X3)}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
MPO
MAYBE
We consider the following Problem:
Strict Trs:
{ a__minus(0(), Y) -> 0()
, a__minus(s(X), s(Y)) -> a__minus(X, Y)
, a__geq(X, 0()) -> true()
, a__geq(0(), s(Y)) -> false()
, a__geq(s(X), s(Y)) -> a__geq(X, Y)
, a__div(0(), s(Y)) -> 0()
, a__div(s(X), s(Y)) ->
a__if(a__geq(X, Y), s(div(minus(X, Y), s(Y))), 0())
, a__if(true(), X, Y) -> mark(X)
, a__if(false(), X, Y) -> mark(Y)
, mark(minus(X1, X2)) -> a__minus(X1, X2)
, mark(geq(X1, X2)) -> a__geq(X1, X2)
, mark(div(X1, X2)) -> a__div(mark(X1), X2)
, mark(if(X1, X2, X3)) -> a__if(mark(X1), X2, X3)
, mark(0()) -> 0()
, mark(s(X)) -> s(mark(X))
, mark(true()) -> true()
, mark(false()) -> false()
, a__minus(X1, X2) -> minus(X1, X2)
, a__geq(X1, X2) -> geq(X1, X2)
, a__div(X1, X2) -> div(X1, X2)
, a__if(X1, X2, X3) -> if(X1, X2, X3)}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
POP*
MAYBE
We consider the following Problem:
Strict Trs:
{ a__minus(0(), Y) -> 0()
, a__minus(s(X), s(Y)) -> a__minus(X, Y)
, a__geq(X, 0()) -> true()
, a__geq(0(), s(Y)) -> false()
, a__geq(s(X), s(Y)) -> a__geq(X, Y)
, a__div(0(), s(Y)) -> 0()
, a__div(s(X), s(Y)) ->
a__if(a__geq(X, Y), s(div(minus(X, Y), s(Y))), 0())
, a__if(true(), X, Y) -> mark(X)
, a__if(false(), X, Y) -> mark(Y)
, mark(minus(X1, X2)) -> a__minus(X1, X2)
, mark(geq(X1, X2)) -> a__geq(X1, X2)
, mark(div(X1, X2)) -> a__div(mark(X1), X2)
, mark(if(X1, X2, X3)) -> a__if(mark(X1), X2, X3)
, mark(0()) -> 0()
, mark(s(X)) -> s(mark(X))
, mark(true()) -> true()
, mark(false()) -> false()
, a__minus(X1, X2) -> minus(X1, X2)
, a__geq(X1, X2) -> geq(X1, X2)
, a__div(X1, X2) -> div(X1, X2)
, a__if(X1, X2, X3) -> if(X1, X2, X3)}
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:
{ a__minus(0(), Y) -> 0()
, a__minus(s(X), s(Y)) -> a__minus(X, Y)
, a__geq(X, 0()) -> true()
, a__geq(0(), s(Y)) -> false()
, a__geq(s(X), s(Y)) -> a__geq(X, Y)
, a__div(0(), s(Y)) -> 0()
, a__div(s(X), s(Y)) ->
a__if(a__geq(X, Y), s(div(minus(X, Y), s(Y))), 0())
, a__if(true(), X, Y) -> mark(X)
, a__if(false(), X, Y) -> mark(Y)
, mark(minus(X1, X2)) -> a__minus(X1, X2)
, mark(geq(X1, X2)) -> a__geq(X1, X2)
, mark(div(X1, X2)) -> a__div(mark(X1), X2)
, mark(if(X1, X2, X3)) -> a__if(mark(X1), X2, X3)
, mark(0()) -> 0()
, mark(s(X)) -> s(mark(X))
, mark(true()) -> true()
, mark(false()) -> false()
, a__minus(X1, X2) -> minus(X1, X2)
, a__geq(X1, X2) -> geq(X1, X2)
, a__div(X1, X2) -> div(X1, X2)
, a__if(X1, X2, X3) -> if(X1, X2, X3)}
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:
{ a__minus(0(), Y) -> 0()
, a__minus(s(X), s(Y)) -> a__minus(X, Y)
, a__geq(X, 0()) -> true()
, a__geq(0(), s(Y)) -> false()
, a__geq(s(X), s(Y)) -> a__geq(X, Y)
, a__div(0(), s(Y)) -> 0()
, a__div(s(X), s(Y)) ->
a__if(a__geq(X, Y), s(div(minus(X, Y), s(Y))), 0())
, a__if(true(), X, Y) -> mark(X)
, a__if(false(), X, Y) -> mark(Y)
, mark(minus(X1, X2)) -> a__minus(X1, X2)
, mark(geq(X1, X2)) -> a__geq(X1, X2)
, mark(div(X1, X2)) -> a__div(mark(X1), X2)
, mark(if(X1, X2, X3)) -> a__if(mark(X1), X2, X3)
, mark(0()) -> 0()
, mark(s(X)) -> s(mark(X))
, mark(true()) -> true()
, mark(false()) -> false()
, a__minus(X1, X2) -> minus(X1, X2)
, a__geq(X1, X2) -> geq(X1, X2)
, a__div(X1, X2) -> div(X1, X2)
, a__if(X1, X2, X3) -> if(X1, X2, X3)}
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:
{ a__minus(0(), Y) -> 0()
, a__minus(s(X), s(Y)) -> a__minus(X, Y)
, a__geq(X, 0()) -> true()
, a__geq(0(), s(Y)) -> false()
, a__geq(s(X), s(Y)) -> a__geq(X, Y)
, a__div(0(), s(Y)) -> 0()
, a__div(s(X), s(Y)) ->
a__if(a__geq(X, Y), s(div(minus(X, Y), s(Y))), 0())
, a__if(true(), X, Y) -> mark(X)
, a__if(false(), X, Y) -> mark(Y)
, mark(minus(X1, X2)) -> a__minus(X1, X2)
, mark(geq(X1, X2)) -> a__geq(X1, X2)
, mark(div(X1, X2)) -> a__div(mark(X1), X2)
, mark(if(X1, X2, X3)) -> a__if(mark(X1), X2, X3)
, mark(0()) -> 0()
, mark(s(X)) -> s(mark(X))
, mark(true()) -> true()
, mark(false()) -> false()
, a__minus(X1, X2) -> minus(X1, X2)
, a__geq(X1, X2) -> geq(X1, X2)
, a__div(X1, X2) -> div(X1, X2)
, a__if(X1, X2, X3) -> if(X1, X2, X3)}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..