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 c -> e d -> e k -> e l -> e s(c) -> t(k) s(c) -> t(l) s(e) -> t(e) g(x, x) -> h(x, x) ?1(t(y), x) -> pair(x, y) f(x) -> ?1(s(x), x) DP Processor: DPs: a#() -> c#() a#() -> d#() b#() -> c#() b#() -> d#() s#(c()) -> k#() s#(c()) -> l#() f#(x) -> s#(x) f#(x) -> ?1#(s(x),x) TRS: a() -> c() a() -> d() b() -> c() b() -> d() c() -> e() d() -> e() k() -> e() l() -> e() s(c()) -> t(k()) s(c()) -> t(l()) s(e()) -> t(e()) g(x,x) -> h(x,x) ?1(t(y),x) -> pair(x,y) f(x) -> ?1(s(x),x) TDG Processor: DPs: a#() -> c#() a#() -> d#() b#() -> c#() b#() -> d#() s#(c()) -> k#() s#(c()) -> l#() f#(x) -> s#(x) f#(x) -> ?1#(s(x),x) TRS: a() -> c() a() -> d() b() -> c() b() -> d() c() -> e() d() -> e() k() -> e() l() -> e() s(c()) -> t(k()) s(c()) -> t(l()) s(e()) -> t(e()) g(x,x) -> h(x,x) ?1(t(y),x) -> pair(x,y) f(x) -> ?1(s(x),x) graph: f#(x) -> s#(x) -> s#(c()) -> l#() f#(x) -> s#(x) -> s#(c()) -> k#() SCC Processor: #sccs: 0 #rules: 0 #arcs: 2/64