Substitutions:

{_1?w = 2$_$_2?x. 2$_$_2?L = :L. 2$_$_2?x = 3$_$_1?x. 2$_$_2?ys = 3$_$_1?L. 3$_$_1?y = :b. 3$_$_1?L = :x. 3$_$_1?x = 5$_$_3?x. 5$_$_3?x = :b. }.{_1?w = 2$_$_1?x. 2$_$_1?L = :L. 2$_$_1?y = :a. 2$_$_1?x = 3$_$_3?x. 3$_$_3?x = :a. }.
N3Trace:

11 [:call {_1?w :element :L. }].
:alternatives = {{2$_$_2?x :element 2$_$_2?ys. 2$_$_2?ys rdf:rest 2$_$_2?L. }
{2$_$_1?y rdf:first 2$_$_1?L. 2$_$_1?x :eq 2$_$_1?y. }
}
:subtitutions = {{_1?w = 2$_$_2?x. 2$_$_2?L = :L. _1?w = 2$_$_1?x. 2$_$_1?L = :L. }.}
:goalList = {{  . }
{_1?w :element :L. }
}
[:call {2$_$_2?x :element 2$_$_2?ys. }].
:alternatives = {{3$_$_2?x :element 3$_$_2?ys. 3$_$_2?ys rdf:rest 3$_$_2?L. }
{3$_$_1?y rdf:first 3$_$_1?L. 3$_$_1?x :eq 3$_$_1?y. }
}
:subtitutions = {{_1?w = 2$_$_2?x. 2$_$_2?L = :L. 2$_$_2?x = 3$_$_2?x. 2$_$_2?ys = 3$_$_2?L. 2$_$_2?x = 3$_$_1?x. 2$_$_2?ys = 3$_$_1?L. }.}
:goalList = {{2$_$_2?x :element 2$_$_2?ys. }
{2$_$_2?ys rdf:rest 2$_$_2?L. }
}
[:call {3$_$_1?y rdf:first 3$_$_1?L. }].
:alternatives = {{:a rdf:first :L. }
{:b rdf:first :x. }
}
:subtitutions = {{_1?w = 2$_$_2?x. 2$_$_2?L = :L. 2$_$_2?x = 3$_$_1?x. 2$_$_2?ys = 3$_$_1?L. 3$_$_1?y = :a. 3$_$_1?L = :L. 3$_$_1?y = :b. 3$_$_1?L = :x. }.}
:goalList = {{3$_$_1?y rdf:first 3$_$_1?L. }
{3$_$_1?x :eq 3$_$_1?y. }
{2$_$_2?ys rdf:rest 2$_$_2?L. }
}
[:call {3$_$_1?x :eq :a. }].
:alternatives = {{:a :eq :a. }
}
:subtitutions = {{_1?w = 2$_$_2?x. 2$_$_2?L = :L. 2$_$_2?x = 3$_$_1?x. 2$_$_2?ys = 3$_$_1?L. 3$_$_1?y = :a. 3$_$_1?L = :L. 3$_$_1?x = 5$_$_3?x. 5$_$_3?x = :a. }.}
:goalList = {{:a rdf:first :L. }
{3$_$_1?x :eq 3$_$_1?y. }
{2$_$_2?ys rdf:rest 2$_$_2?L. }
}
[:failed {:L rdf:rest :L. }].
[:call {3$_$_1?x :eq :b. }].
:alternatives = {{:b :eq :b. }
}
:subtitutions = {{_1?w = 2$_$_2?x. 2$_$_2?L = :L. 2$_$_2?x = 3$_$_1?x. 2$_$_2?ys = 3$_$_1?L. 3$_$_1?y = :b. 3$_$_1?L = :x. 3$_$_1?x = 5$_$_3?x. 5$_$_3?x = :b. }.}
:goalList = {{:b rdf:first :x. }
{3$_$_1?x :eq 3$_$_1?y. }
{2$_$_2?ys rdf:rest 2$_$_2?L. }
}
[:call {:x rdf:rest :L. }].
:alternatives = {{:x rdf:rest :L. }
}
:subtitutions = {{_1?w = 2$_$_2?x. 2$_$_2?L = :L. 2$_$_2?x = 3$_$_1?x. 2$_$_2?ys = 3$_$_1?L. 3$_$_1?y = :b. 3$_$_1?L = :x. 3$_$_1?x = 5$_$_3?x. 5$_$_3?x = :b. }.}
:goalList = {{:b :eq :b. }
{2$_$_2?ys rdf:rest 2$_$_2?L. }
}
{:solution = {_1?w = 2$_$_2?x. 2$_$_2?L = :L. 2$_$_2?x = 3$_$_1?x. 2$_$_2?ys = 3$_$_1?L. 3$_$_1?y = :b. 3$_$_1?L = :x. 3$_$_1?x = 5$_$_3?x. 5$_$_3?x = :b. }.}.
[:call {2$_$_1?y rdf:first :L. }].
:alternatives = {{:a rdf:first :L. }
}
:subtitutions = {{_1?w = 2$_$_1?x. 2$_$_1?L = :L. 2$_$_1?y = :a. }.}
:goalList = {{2$_$_1?y rdf:first 2$_$_1?L. }
{2$_$_1?x :eq 2$_$_1?y. }
}
[:call {2$_$_1?x :eq :a. }].
:alternatives = {{:a :eq :a. }
}
:subtitutions = {{_1?w = 2$_$_1?x. 2$_$_1?L = :L. 2$_$_1?y = :a. 2$_$_1?x = 3$_$_3?x. 3$_$_3?x = :a. }.}
:goalList = {{:a rdf:first :L. }
{2$_$_1?x :eq 2$_$_1?y. }
}
{:solution = {_1?w = 2$_$_1?x. 2$_$_1?L = :L. 2$_$_1?y = :a. 2$_$_1?x = 3$_$_3?x. 3$_$_3?x = :a. }.}.

Query:

{_1?w :element :L. }

Solution:

{:b :element :L. }

Solution:

{:a :element :L. }