MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            add(0(),X) -> X
            add(s(X),Y) -> s(add(X,Y))
            from(X) -> cons(X,from(s(X)))
            fst(0(),Z) -> nil()
            fst(s(X),cons(Y,Z)) -> cons(Y,fst(X,Z))
            len(cons(X,Z)) -> s(len(Z))
            len(nil()) -> 0()
        - Signature:
            {add/2,from/1,fst/2,len/1} / {0/0,cons/2,nil/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add,from,fst,len} and constructors {0,cons,nil,s}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          add#(0(),X) -> c_1()
          add#(s(X),Y) -> c_2(add#(X,Y))
          from#(X) -> c_3(from#(s(X)))
          fst#(0(),Z) -> c_4()
          fst#(s(X),cons(Y,Z)) -> c_5(fst#(X,Z))
          len#(cons(X,Z)) -> c_6(len#(Z))
          len#(nil()) -> c_7()
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            add#(0(),X) -> c_1()
            add#(s(X),Y) -> c_2(add#(X,Y))
            from#(X) -> c_3(from#(s(X)))
            fst#(0(),Z) -> c_4()
            fst#(s(X),cons(Y,Z)) -> c_5(fst#(X,Z))
            len#(cons(X,Z)) -> c_6(len#(Z))
            len#(nil()) -> c_7()
        - Weak TRS:
            add(0(),X) -> X
            add(s(X),Y) -> s(add(X,Y))
            from(X) -> cons(X,from(s(X)))
            fst(0(),Z) -> nil()
            fst(s(X),cons(Y,Z)) -> cons(Y,fst(X,Z))
            len(cons(X,Z)) -> s(len(Z))
            len(nil()) -> 0()
        - Signature:
            {add/2,from/1,fst/2,len/1,add#/2,from#/1,fst#/2,len#/1} / {0/0,cons/2,nil/0,s/1,c_1/0,c_2/1,c_3/1,c_4/0
            ,c_5/1,c_6/1,c_7/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add#,from#,fst#,len#} and constructors {0,cons,nil,s}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          add#(0(),X) -> c_1()
          add#(s(X),Y) -> c_2(add#(X,Y))
          from#(X) -> c_3(from#(s(X)))
          fst#(0(),Z) -> c_4()
          fst#(s(X),cons(Y,Z)) -> c_5(fst#(X,Z))
          len#(cons(X,Z)) -> c_6(len#(Z))
          len#(nil()) -> c_7()
* Step 3: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            add#(0(),X) -> c_1()
            add#(s(X),Y) -> c_2(add#(X,Y))
            from#(X) -> c_3(from#(s(X)))
            fst#(0(),Z) -> c_4()
            fst#(s(X),cons(Y,Z)) -> c_5(fst#(X,Z))
            len#(cons(X,Z)) -> c_6(len#(Z))
            len#(nil()) -> c_7()
        - Signature:
            {add/2,from/1,fst/2,len/1,add#/2,from#/1,fst#/2,len#/1} / {0/0,cons/2,nil/0,s/1,c_1/0,c_2/1,c_3/1,c_4/0
            ,c_5/1,c_6/1,c_7/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add#,from#,fst#,len#} and constructors {0,cons,nil,s}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,4,7}
        by application of
          Pre({1,4,7}) = {2,5,6}.
        Here rules are labelled as follows:
          1: add#(0(),X) -> c_1()
          2: add#(s(X),Y) -> c_2(add#(X,Y))
          3: from#(X) -> c_3(from#(s(X)))
          4: fst#(0(),Z) -> c_4()
          5: fst#(s(X),cons(Y,Z)) -> c_5(fst#(X,Z))
          6: len#(cons(X,Z)) -> c_6(len#(Z))
          7: len#(nil()) -> c_7()
* Step 4: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            add#(s(X),Y) -> c_2(add#(X,Y))
            from#(X) -> c_3(from#(s(X)))
            fst#(s(X),cons(Y,Z)) -> c_5(fst#(X,Z))
            len#(cons(X,Z)) -> c_6(len#(Z))
        - Weak DPs:
            add#(0(),X) -> c_1()
            fst#(0(),Z) -> c_4()
            len#(nil()) -> c_7()
        - Signature:
            {add/2,from/1,fst/2,len/1,add#/2,from#/1,fst#/2,len#/1} / {0/0,cons/2,nil/0,s/1,c_1/0,c_2/1,c_3/1,c_4/0
            ,c_5/1,c_6/1,c_7/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add#,from#,fst#,len#} and constructors {0,cons,nil,s}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:add#(s(X),Y) -> c_2(add#(X,Y))
             -->_1 add#(0(),X) -> c_1():5
             -->_1 add#(s(X),Y) -> c_2(add#(X,Y)):1
          
          2:S:from#(X) -> c_3(from#(s(X)))
             -->_1 from#(X) -> c_3(from#(s(X))):2
          
          3:S:fst#(s(X),cons(Y,Z)) -> c_5(fst#(X,Z))
             -->_1 fst#(0(),Z) -> c_4():6
             -->_1 fst#(s(X),cons(Y,Z)) -> c_5(fst#(X,Z)):3
          
          4:S:len#(cons(X,Z)) -> c_6(len#(Z))
             -->_1 len#(nil()) -> c_7():7
             -->_1 len#(cons(X,Z)) -> c_6(len#(Z)):4
          
          5:W:add#(0(),X) -> c_1()
             
          
          6:W:fst#(0(),Z) -> c_4()
             
          
          7:W:len#(nil()) -> c_7()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          7: len#(nil()) -> c_7()
          6: fst#(0(),Z) -> c_4()
          5: add#(0(),X) -> c_1()
* Step 5: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          add#(s(X),Y) -> c_2(add#(X,Y))
          from#(X) -> c_3(from#(s(X)))
          fst#(s(X),cons(Y,Z)) -> c_5(fst#(X,Z))
          len#(cons(X,Z)) -> c_6(len#(Z))
      - Signature:
          {add/2,from/1,fst/2,len/1,add#/2,from#/1,fst#/2,len#/1} / {0/0,cons/2,nil/0,s/1,c_1/0,c_2/1,c_3/1,c_4/0
          ,c_5/1,c_6/1,c_7/0}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {add#,from#,fst#,len#} and constructors {0,cons,nil,s}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE