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: a -> c a -> d b -> c b -> d s(k) -> t(a) s(l) -> t(a) g(x, x) -> h(x, x) ?1(t(y), x, y) -> y f(x, y) -> ?1(s(x), x, y) DP Processor: DPs: s#(k()) -> a#() s#(l()) -> a#() f#(x,y) -> s#(x) f#(x,y) -> ?1#(s(x),x,y) TRS: a() -> c() a() -> d() b() -> c() b() -> d() s(k()) -> t(a()) s(l()) -> t(a()) g(x,x) -> h(x,x) ?1(t(y),x,y) -> y f(x,y) -> ?1(s(x),x,y) TDG Processor: DPs: s#(k()) -> a#() s#(l()) -> a#() f#(x,y) -> s#(x) f#(x,y) -> ?1#(s(x),x,y) TRS: a() -> c() a() -> d() b() -> c() b() -> d() s(k()) -> t(a()) s(l()) -> t(a()) g(x,x) -> h(x,x) ?1(t(y),x,y) -> y f(x,y) -> ?1(s(x),x,y) graph: f#(x,y) -> s#(x) -> s#(l()) -> a#() f#(x,y) -> s#(x) -> s#(k()) -> a#() SCC Processor: #sccs: 0 #rules: 0 #arcs: 2/16