Term Rewriting Systems SS 11 Solution -Exam 17.08.2011 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 semi-decidable 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: Collections: Computer Technologies and Information Sciences