YES(?,O(1))

We are left with following problem, upon which TcT provides the
certificate YES(?,O(1)).

Strict Trs:
  { main(Nil()) -> ParseFail(0())
  , main(Cons(A(), Nil())) -> ParseFail(S(0()))
  , main(Cons(A(), Cons(A(), x112))) -> ParseFail(S(S(0())))
  , main(Cons(A(), Cons(B(), Nil()))) -> ParseSuccess()
  , main(Cons(A(), Cons(B(), Cons(x120, x88)))) ->
    ParseFail(S(S(0())))
  , main(Cons(A(), Cons(C(), x112))) -> ParseFail(S(S(0())))
  , main(Cons(B(), x14)) -> ParseFail(S(0()))
  , main(Cons(C(), x14)) -> ParseFail(S(0())) }
Obligation:
  innermost runtime complexity
Answer:
  YES(?,O(1))

The input was oriented with the instance of 'Small Polynomial Path
Order (PS)' as induced by the safe mapping

 safe(Nil) = {}, safe(main) = {1}, safe(0) = {},
 safe(ParseFail) = {1}, safe(A) = {}, safe(Cons) = {1, 2},
 safe(S) = {1}, safe(B) = {}, safe(ParseSuccess) = {}, safe(C) = {}

and precedence

 empty .

Following symbols are considered recursive:

 {}

The recursion depth is 0.

For your convenience, here are the satisfied ordering constraints:

                                           main(; Nil()) > ParseFail(; 0())          
                                                                                     
                             main(; Cons(; A(),  Nil())) > ParseFail(; S(; 0()))     
                                                                                     
                main(; Cons(; A(),  Cons(; A(),  x112))) > ParseFail(; S(; S(; 0())))
                                                                                     
               main(; Cons(; A(),  Cons(; B(),  Nil()))) > ParseSuccess()            
                                                                                     
  main(; Cons(; A(),  Cons(; B(),  Cons(; x120,  x88)))) > ParseFail(; S(; S(; 0())))
                                                                                     
                main(; Cons(; A(),  Cons(; C(),  x112))) > ParseFail(; S(; S(; 0())))
                                                                                     
                               main(; Cons(; B(),  x14)) > ParseFail(; S(; 0()))     
                                                                                     
                               main(; Cons(; C(),  x14)) > ParseFail(; S(; 0()))     
                                                                                     

Hurray, we answered YES(?,O(1))