YES Consider the TRS R consisting of the following rewrite rule: f(f(y,z),f(x,f(a,x))) -> f(f(f(a,z),f(x,a)),f(a,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) - 1 final state (1) - 13 transitions: #_0 -> 3 a_0 -> 2 f_0(6,7) -> 1 f_0(2,2) -> 5 f_0(8,5) -> 6 f_0(5,2) -> 5 f_0(6,8) -> 1 f_0(2,3) -> 8 f_0(3,2) -> 5 f_0(2,4) -> 7 f_0(4,5) -> 6 f_0(2,8) -> 7 f_0(2,5) -> 4 __________________________________________________________________________ TTTbox (0.008 seconds) - April 13, 2007 Source file - /home/ami/mkorp/Testbench/tpdb-3.2/TRS/secret05/teparla1.trs