YES Proof: This system is quasi-decreasing. By \cite{O02}, p. 214, Proposition 7.2.50. This system is of type 3 or smaller. This system is deterministic. System R transformed to U(R). Call external tool: ttt2 - trs 30 Input: ?1(a, x) -> b f(x) -> ?1(g(x, x), x) DP Processor: DPs: f#(x) -> ?1#(g(x,x),x) TRS: ?1(a(),x) -> b() f(x) -> ?1(g(x,x),x) TDG Processor: DPs: f#(x) -> ?1#(g(x,x),x) TRS: ?1(a(),x) -> b() f(x) -> ?1(g(x,x),x) graph: Qed