YES(?,ELEMENTARY)

'epo* (timeout of 60.0 seconds)'
--------------------------------
Answer:           YES(?,ELEMENTARY)
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  a__f(f(X)) -> a__c(f(g(f(X))))
     , a__c(X) -> d(X)
     , a__h(X) -> a__c(d(X))
     , mark(f(X)) -> a__f(mark(X))
     , mark(c(X)) -> a__c(X)
     , mark(h(X)) -> a__h(mark(X))
     , mark(g(X)) -> g(X)
     , mark(d(X)) -> d(X)
     , a__f(X) -> f(X)
     , a__c(X) -> c(X)
     , a__h(X) -> h(X)}

Proof Output:    
  Strict Rules in Predicative Notation:
   {  a__f(; f(; X)) -> a__c(; f(; g(; f(; X))))
    , a__c(; X) -> d(; X)
    , a__h(; X) -> a__c(; d(; X))
    , mark(f(; X);) -> a__f(; mark(X;))
    , mark(c(; X);) -> a__c(; X)
    , mark(h(; X);) -> a__h(; mark(X;))
    , mark(g(; X);) -> g(; X)
    , mark(d(; X);) -> d(; X)
    , a__f(; X) -> f(; X)
    , a__c(; X) -> c(; X)
    , a__h(; X) -> h(; X)}
  Safe Mapping:
   safe(a__f) = {1}, safe(f) = {1}, safe(a__c) = {1}, safe(g) = {1},
   safe(d) = {1}, safe(a__h) = {1}, safe(mark) = {}, safe(c) = {1},
   safe(h) = {1}
  Argument Permutation:
   mu(a__f) = [1], mu(a__c) = [1], mu(a__h) = [1], mu(mark) = [1]
  Precedence:
   mark ~ mark, mark > a__h, mark > a__c, mark > a__f, a__h ~ a__h,
   a__h > a__c, a__h ~ a__f, a__c ~ a__c, a__f ~ a__h, a__f > a__c,
   a__f ~ a__f