YES Consider the TRS R consisting of the following rewrite rules: or(x,x) -> x and(x,x) -> x not(not(x)) -> x not(and(x,y)) -> or(not(x),not(y)) not(or(x,y)) -> and(not(x),not(y)) The TRS R is terminating because R is match-raise-bounded for RFC#'(R) by 0. A raise-compatible and quasi-deterministic tree automaton compatible with match(R) and RFC#'(R) has - 8 states (1,...,8) - 6 final states (1,2,5,6,7,8) - 41 transitions: 4 -> 6 7 -> 6 8 -> 6 not_0(7) -> 6 not_0(1) -> 6 not_0(8) -> 6 or_0(3,4) -> 6 or_0(6,7) -> 6 or_0(8,8) -> 6 or_0(3,8) -> 6 or_0(6,4) -> 6 or_0(7,6) -> 6 or_0(6,8) -> 6 or_0(7,7) -> 6 or_0(7,4) -> 6 or_0(8,6) -> 6 or_0(3,6) -> 6 or_0(7,8) -> 6 or_0(6,6) -> 6 or_0(8,7) -> 6 or_0(3,7) -> 6 or_0(8,4) -> 6 #_0 -> 7 #_0 -> 6 #_0 -> 8 and_0(4,6) -> 6 and_0(6,7) -> 6 and_0(8,8) -> 6 and_0(6,4) -> 6 and_0(7,6) -> 6 and_0(4,7) -> 6 and_0(6,8) -> 6 and_0(4,4) -> 6 and_0(7,7) -> 6 and_0(4,8) -> 6 and_0(7,4) -> 6 and_0(8,6) -> 6 and_0(7,8) -> 6 and_0(6,6) -> 6 and_0(8,7) -> 6 and_0(8,4) -> 6 __________________________________________________________________ TTTbox (0.007 seconds) - April 13, 2007 Source file - /home/ami/mkorp/Testbench/tpdb-3.2/TRS/SK90/2.33.trs