We consider the following Problem:

  Strict Trs:
    {  a__fst(0(), Z) -> nil()
     , a__fst(s(X), cons(Y, Z)) -> cons(mark(Y), fst(X, Z))
     , a__from(X) -> cons(mark(X), from(s(X)))
     , a__add(0(), X) -> mark(X)
     , a__add(s(X), Y) -> s(add(X, Y))
     , a__len(nil()) -> 0()
     , a__len(cons(X, Z)) -> s(len(Z))
     , mark(fst(X1, X2)) -> a__fst(mark(X1), mark(X2))
     , mark(from(X)) -> a__from(mark(X))
     , mark(add(X1, X2)) -> a__add(mark(X1), mark(X2))
     , mark(len(X)) -> a__len(mark(X))
     , mark(0()) -> 0()
     , mark(s(X)) -> s(X)
     , mark(nil()) -> nil()
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , a__fst(X1, X2) -> fst(X1, X2)
     , a__from(X) -> from(X)
     , a__add(X1, X2) -> add(X1, X2)
     , a__len(X) -> len(X)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: YES(?,O(n^2))

Proof:
  We consider the following Problem:
  
    Strict Trs:
      {  a__fst(0(), Z) -> nil()
       , a__fst(s(X), cons(Y, Z)) -> cons(mark(Y), fst(X, Z))
       , a__from(X) -> cons(mark(X), from(s(X)))
       , a__add(0(), X) -> mark(X)
       , a__add(s(X), Y) -> s(add(X, Y))
       , a__len(nil()) -> 0()
       , a__len(cons(X, Z)) -> s(len(Z))
       , mark(fst(X1, X2)) -> a__fst(mark(X1), mark(X2))
       , mark(from(X)) -> a__from(mark(X))
       , mark(add(X1, X2)) -> a__add(mark(X1), mark(X2))
       , mark(len(X)) -> a__len(mark(X))
       , mark(0()) -> 0()
       , mark(s(X)) -> s(X)
       , mark(nil()) -> nil()
       , mark(cons(X1, X2)) -> cons(mark(X1), X2)
       , a__fst(X1, X2) -> fst(X1, X2)
       , a__from(X) -> from(X)
       , a__add(X1, X2) -> add(X1, X2)
       , a__len(X) -> len(X)}
    StartTerms: basic terms
    Strategy: innermost
  
  Certificate: YES(?,O(n^2))
  
  Proof:
    The weightgap principle applies, where following rules are oriented strictly:
    
    TRS Component:
      {  a__fst(0(), Z) -> nil()
       , a__fst(s(X), cons(Y, Z)) -> cons(mark(Y), fst(X, Z))
       , a__from(X) -> cons(mark(X), from(s(X)))
       , a__add(0(), X) -> mark(X)
       , a__add(s(X), Y) -> s(add(X, Y))
       , a__len(nil()) -> 0()
       , a__len(cons(X, Z)) -> s(len(Z))
       , a__fst(X1, X2) -> fst(X1, X2)
       , a__from(X) -> from(X)
       , a__add(X1, X2) -> add(X1, X2)
       , a__len(X) -> len(X)}
    
    Interpretation of nonconstant growth:
    -------------------------------------
      The following argument positions are usable:
        Uargs(a__fst) = {1, 2}, Uargs(s) = {}, Uargs(cons) = {1},
        Uargs(mark) = {}, Uargs(fst) = {}, Uargs(a__from) = {1},
        Uargs(from) = {}, Uargs(a__add) = {1, 2}, Uargs(add) = {},
        Uargs(a__len) = {1}, Uargs(len) = {}
      We have the following EDA-non-satisfying and IDA(1)-non-satisfying matrix interpretation:
      Interpretation Functions:
       a__fst(x1, x2) = [1 0] x1 + [1 0] x2 + [1]
                        [0 0]      [0 0]      [1]
       0() = [0]
             [0]
       nil() = [0]
               [0]
       s(x1) = [0 0] x1 + [0]
               [0 0]      [1]
       cons(x1, x2) = [1 0] x1 + [0 0] x2 + [0]
                      [0 0]      [0 0]      [1]
       mark(x1) = [0 0] x1 + [0]
                  [0 0]      [1]
       fst(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                     [0 0]      [0 0]      [0]
       a__from(x1) = [1 0] x1 + [1]
                     [0 0]      [1]
       from(x1) = [0 0] x1 + [0]
                  [0 0]      [0]
       a__add(x1, x2) = [1 0] x1 + [1 0] x2 + [1]
                        [0 0]      [0 0]      [1]
       add(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                     [0 0]      [0 0]      [0]
       a__len(x1) = [1 0] x1 + [1]
                    [0 0]      [1]
       len(x1) = [0 0] x1 + [0]
                 [0 0]      [0]
    
    The strictly oriented rules are moved into the weak component.
    
    We consider the following Problem:
    
      Strict Trs:
        {  mark(fst(X1, X2)) -> a__fst(mark(X1), mark(X2))
         , mark(from(X)) -> a__from(mark(X))
         , mark(add(X1, X2)) -> a__add(mark(X1), mark(X2))
         , mark(le