 
Summary: Term Rewriting Systems SS 11
Solution  Exam 17.08.2011
aaProf. Dr. Jürgen Giesl Marc Brockschmidt, Carsten Fuhs, Thomas Ströder
Exercise 1 (Theoretical Foundations): (6 × 4 = 24 points)
Give a short proof sketch or a counterexample for each of the following statements:
a) The question whether s E t holds is semidecidable for every set E of equations between terms.
b) For every terminating term rewrite system R, +
R is a simplification order.
c) For every set M and every relation M × M such that every p M has at most one normal form,
we have that is confluent.
d) Let be a signature with c 2, let x, y be variables. If {c(x, y) x, c(x, y) y} E, then for all terms
s, t we have s E t.
e) The embedding order on terms is normalizing.
f) A relation is called strongly confluent iff for all p, s, and t with p s and p t there is a q with
s =
q and t =
q. Here, s =
q means that s q or s = q holds. Then every confluent relation is also
strongly confluent.
Solution:
