LMPO
MAYBE
We consider the following Problem:
Strict Trs:
{ sum(cons(s(n), x), cons(m, y)) -> sum(cons(n, x), cons(s(m), y))
, sum(cons(0(), x), y) -> sum(x, y)
, sum(nil(), y) -> y
, empty(nil()) -> true()
, empty(cons(n, x)) -> false()
, tail(nil()) -> nil()
, tail(cons(n, x)) -> x
, head(cons(n, x)) -> n
, weight(x) -> if(empty(x), empty(tail(x)), x)
, if(true(), b, x) -> weight_undefined_error()
, if(false(), b, x) -> if2(b, x)
, if2(true(), x) -> head(x)
, if2(false(), x) -> weight(sum(x, cons(0(), tail(tail(x)))))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
MPO
MAYBE
We consider the following Problem:
Strict Trs:
{ sum(cons(s(n), x), cons(m, y)) -> sum(cons(n, x), cons(s(m), y))
, sum(cons(0(), x), y) -> sum(x, y)
, sum(nil(), y) -> y
, empty(nil()) -> true()
, empty(cons(n, x)) -> false()
, tail(nil()) -> nil()
, tail(cons(n, x)) -> x
, head(cons(n, x)) -> n
, weight(x) -> if(empty(x), empty(tail(x)), x)
, if(true(), b, x) -> weight_undefined_error()
, if(false(), b, x) -> if2(b, x)
, if2(true(), x) -> head(x)
, if2(false(), x) -> weight(sum(x, cons(0(), tail(tail(x)))))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
POP*
MAYBE
We consider the following Problem:
Strict Trs:
{ sum(cons(s(n), x), cons(m, y)) -> sum(cons(n, x), cons(s(m), y))
, sum(cons(0(), x), y) -> sum(x, y)
, sum(nil(), y) -> y
, empty(nil()) -> true()
, empty(cons(n, x)) -> false()
, tail(nil()) -> nil()
, tail(cons(n, x)) -> x
, head(cons(n, x)) -> n
, weight(x) -> if(empty(x), empty(tail(x)), x)
, if(true(), b, x) -> weight_undefined_error()
, if(false(), b, x) -> if2(b, x)
, if2(true(), x) -> head(x)
, if2(false(), x) -> weight(sum(x, cons(0(), tail(tail(x)))))}
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:
{ sum(cons(s(n), x), cons(m, y)) -> sum(cons(n, x), cons(s(m), y))
, sum(cons(0(), x), y) -> sum(x, y)
, sum(nil(), y) -> y
, empty(nil()) -> true()
, empty(cons(n, x)) -> false()
, tail(nil()) -> nil()
, tail(cons(n, x)) -> x
, head(cons(n, x)) -> n
, weight(x) -> if(empty(x), empty(tail(x)), x)
, if(true(), b, x) -> weight_undefined_error()
, if(false(), b, x) -> if2(b, x)
, if2(true(), x) -> head(x)
, if2(false(), x) -> weight(sum(x, cons(0(), tail(tail(x)))))}
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:
{ sum(cons(s(n), x), cons(m, y)) -> sum(cons(n, x), cons(s(m), y))
, sum(cons(0(), x), y) -> sum(x, y)
, sum(nil(), y) -> y
, empty(nil()) -> true()
, empty(cons(n, x)) -> false()
, tail(nil()) -> nil()
, tail(cons(n, x)) -> x
, head(cons(n, x)) -> n
, weight(x) -> if(empty(x), empty(tail(x)), x)
, if(true(), b, x) -> weight_undefined_error()
, if(false(), b, x) -> if2(b, x)
, if2(true(), x) -> head(x)
, if2(false(), x) -> weight(sum(x, cons(0(), tail(tail(x)))))}
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:
{ sum(cons(s(n), x), cons(m, y)) -> sum(cons(n, x), cons(s(m), y))
, sum(cons(0(), x), y) -> sum(x, y)
, sum(nil(), y) -> y
, empty(nil()) -> true()
, empty(cons(n, x)) -> false()
, tail(nil()) -> nil()
, tail(cons(n, x)) -> x
, head(cons(n, x)) -> n
, weight(x) -> if(empty(x), empty(tail(x)), x)
, if(true(), b, x) -> weight_undefined_error()
, if(false(), b, x) -> if2(b, x)
, if2(true(), x) -> head(x)
, if2(false(), x) -> weight(sum(x, cons(0(), tail(tail(x)))))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..