0.00/0.00 NO 0.00/0.00 We consider the system theBenchmark. 0.00/0.00 0.00/0.00 Alphabet: 0.00/0.00 0.00/0.00 f : [d -> d * b] --> c 0.00/0.00 g : [b * a] --> d -> d 0.00/0.00 h : [a -> b -> c] --> b 0.00/0.00 i : [c] --> c 0.00/0.00 0.00/0.00 Rules: 0.00/0.00 0.00/0.00 f(g(h(j), x), y) => i(j x y) 0.00/0.00 0.00/0.00 This AFS is converted to an AFSM simply by replacing all free variables by meta-variables (with arity 0). 0.00/0.00 0.00/0.00 This system is non-terminating, as demonstrated by the following reduction: 0.00/0.00 0.00/0.00 f(g(h(/\x./\y.f(g(y, x), y)), z), h(/\u./\v.f(g(v, u), v))) 0.00/0.00 => i((/\x./\y.f(g(y, x), y)) z h(/\u./\v.f(g(v, u), v))) 0.00/0.00 =>_beta i(f(g(h(/\x./\y.f(g(y, x), y)), z), h(/\u./\v.f(g(v, u), v)))) 0.00/0.00 0.00/0.00 That is, a term s reduces to a term of the form C[s]. 0.00/0.00 0.00/0.00 EOF