YES(?,ELEMENTARY)

'epo* (timeout of 60.0 seconds)'
--------------------------------
Answer:           YES(?,ELEMENTARY)
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  or(true(), y) -> true()
     , or(x, true()) -> true()
     , or(false(), false()) -> false()
     , mem(x, nil()) -> false()
     , mem(x, set(y)) -> =(x, y)
     , mem(x, union(y, z)) -> or(mem(x, y), mem(x, z))}

Proof Output:    
  Strict Rules in Predicative Notation:
   {  or(; true(), y) -> true()
    , or(; x, true()) -> true()
    , or(; false(), false()) -> false()
    , mem(x, nil();) -> false()
    , mem(x, set(; y);) -> =(; x, y)
    , mem(x, union(; y, z);) -> or(; mem(x, y;), mem(x, z;))}
  Safe Mapping:
   safe(or) = {1, 2}, safe(true) = {}, safe(false) = {},
   safe(mem) = {}, safe(nil) = {}, safe(set) = {1}, safe(=) = {1, 2},
   safe(union) = {1, 2}
  Argument Permutation:
   mu(or) = [2, 1], mu(mem) = [2, 1]
  Precedence:
   mem ~ mem, mem > or, or ~ or