Rewrite rules have the form t1 ⇒ t2 and the basic idea is to look for terms t occurring in expressions e such that t unifies with t1 with unifier θ so that the occurrence t1θ in eθ can be replaced by t2θ.
Jake, the broken, disabled ex-Marine eventually becomes his alien Na'vi avatar, melds with his true love Naytiri, and unifies with nature after defeating the Satanic human forces of corporate evil.
Or GUT-scale baryogenesis, where new physics (and new particles) are found to exist at the grand unification scale, where the electroweak force unifies with the strong force.
We have that (pi ) unifies with the head of constraint axiom (forall a,b., C, a, b), Rightarrow, C, (T^2, a), b), giving substitution (S= [a mapsto T^2,a_1,, b_1 mapsto T^3,a_1]).
Satisfiability is then finally tested for (pi _3 = C,(T^6,mathtt{I}) mathtt{I}), that unifies with (pi _0 = C, T,a),mathtt{I}), which returns (mathbb S _3 = { [a_3mapsto T^5,mathtt{I}]|_emptyset } = { { id}}).
Consider a recursive step in a test of satisfiability where a constraint (pi ) unifies with a constraint head (pi _0 = C,tau _1,ldots,tau _n), with (S={ mgu}(pi _0,pi )).
