MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            add(0(),X) -> X
            add(s(X),Y) -> s(add(X,Y))
            and(false(),Y) -> false()
            and(true(),X) -> X
            first(0(),X) -> nil()
            first(s(X),cons(Y,Z)) -> cons(Y,first(X,Z))
            from(X) -> cons(X,from(s(X)))
            if(false(),X,Y) -> Y
            if(true(),X,Y) -> X
        - Signature:
            {add/2,and/2,first/2,from/1,if/3} / {0/0,cons/2,false/0,nil/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add,and,first,from,if} and constructors {0,cons,false,nil
            ,s,true}
    + 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))
          and#(false(),Y) -> c_3()
          and#(true(),X) -> c_4()
          first#(0(),X) -> c_5()
          first#(s(X),cons(Y,Z)) -> c_6(first#(X,Z))
          from#(X) -> c_7(from#(s(X)))
          if#(false(),X,Y) -> c_8()
          if#(true(),X,Y) -> c_9()
        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))
            and#(false(),Y) -> c_3()
            and#(true(),X) -> c_4()
            first#(0(),X) -> c_5()
            first#(s(X),cons(Y,Z)) -> c_6(first#(X,Z))
            from#(X) -> c_7(from#(s(X)))
            if#(false(),X,Y) -> c_8()
            if#(true(),X,Y) -> c_9()
        - Weak TRS:
            add(0(),X) -> X
            add(s(X),Y) -> s(add(X,Y))
            and(false(),Y) -> false()
            and(true(),X) -> X
            first(0(),X) -> nil()
            first(s(X),cons(Y,Z)) -> cons(Y,first(X,Z))
            from(X) -> cons(X,from(s(X)))
            if(false(),X,Y) -> Y
            if(true(),X,Y) -> X
        - Signature:
            {add/2,and/2,first/2,from/1,if/3,add#/2,and#/2,first#/2,from#/1,if#/3} / {0/0,cons/2,false/0,nil/0,s/1
            ,true/0,c_1/0,c_2/1,c_3/0,c_4/0,c_5/0,c_6/1,c_7/1,c_8/0,c_9/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add#,and#,first#,from#,if#} and constructors {0,cons
            ,false,nil,s,true}
    + 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))
          and#(false(),Y) -> c_3()
          and#(true(),X) -> c_4()
          first#(0(),X) -> c_5()
          first#(s(X),cons(Y,Z)) -> c_6(first#(X,Z))
          from#(X) -> c_7(from#(s(X)))
          if#(false(),X,Y) -> c_8()
          if#(true(),X,Y) -> c_9()
* Step 3: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            add#(0(),X) -> c_1()
            add#(s(X),Y) -> c_2(add#(X,Y))
            and#(false(),Y) -> c_3()
            and#(true(),X) -> c_4()
            first#(0(),X) -> c_5()
            first#(s(X),cons(Y,Z)) -> c_6(first#(X,Z))
            from#(X) -> c_7(from#(s(X)))
            if#(false(),X,Y) -> c_8()
            if#(true(),X,Y) -> c_9()
        - Signature:
            {add/2,and/2,first/2,from/1,if/3,add#/2,and#/2,first#/2,from#/1,if#/3} / {0/0,cons/2,false/0,nil/0,s/1
            ,true/0,c_1/0,c_2/1,c_3/0,c_4/0,c_5/0,c_6/1,c_7/1,c_8/0,c_9/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add#,and#,first#,from#,if#} and constructors {0,cons
            ,false,nil,s,true}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,3,4,5,8,9}
        by application of
          Pre({1,3,4,5,8,9}) = {2,6}.
        Here rules are labelled as follows:
          1: add#(0(),X) -> c_1()
          2: add#(s(X),Y) -> c_2(add#(X,Y))
          3: and#(false(),Y) -> c_3()
          4: and#(true(),X) -> c_4()
          5: first#(0(),X) -> c_5()
          6: first#(s(X),cons(Y,Z)) -> c_6(first#(X,Z))
          7: from#(X) -> c_7(from#(s(X)))
          8: if#(false(),X,Y) -> c_8()
          9: if#(true(),X,Y) -> c_9()
* Step 4: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            add#(s(X),Y) -> c_2(add#(X,Y))
            first#(s(X),cons(Y,Z)) -> c_6(first#(X,Z))
            from#(X) -> c_7(from#(s(X)))
        - Weak DPs:
            add#(0(),X) -> c_1()
            and#(false(),Y) -> c_3()
            and#(true(),X) -> c_4()
            first#(0(),X) -> c_5()
            if#(false(),X,Y) -> c_8()
            if#(true(),X,Y) -> c_9()
        - Signature:
            {add/2,and/2,first/2,from/1,if/3,add#/2,and#/2,first#/2,from#/1,if#/3} / {0/0,cons/2,false/0,nil/0,s/1
            ,true/0,c_1/0,c_2/1,c_3/0,c_4/0,c_5/0,c_6/1,c_7/1,c_8/0,c_9/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add#,and#,first#,from#,if#} and constructors {0,cons
            ,false,nil,s,true}
    + 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():4
             -->_1 add#(s(X),Y) -> c_2(add#(X,Y)):1
          
          2:S:first#(s(X),cons(Y,Z)) -> c_6(first#(X,Z))
             -->_1 first#(0(),X) -> c_5():7
             -->_1 first#(s(X),cons(Y,Z)) -> c_6(first#(X,Z)):2
          
          3:S:from#(X) -> c_7(from#(s(X)))
             -->_1 from#(X) -> c_7(from#(s(X))):3
          
          4:W:add#(0(),X) -> c_1()
             
          
          5:W:and#(false(),Y) -> c_3()
             
          
          6:W:and#(true(),X) -> c_4()
             
          
          7:W:first#(0(),X) -> c_5()
             
          
          8:W:if#(false(),X,Y) -> c_8()
             
          
          9:W:if#(true(),X,Y) -> c_9()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          9: if#(true(),X,Y) -> c_9()
          8: if#(false(),X,Y) -> c_8()
          6: and#(true(),X) -> c_4()
          5: and#(false(),Y) -> c_3()
          7: first#(0(),X) -> c_5()
          4: add#(0(),X) -> c_1()
* Step 5: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          add#(s(X),Y) -> c_2(add#(X,Y))
          first#(s(X),cons(Y,Z)) -> c_6(first#(X,Z))
          from#(X) -> c_7(from#(s(X)))
      - Signature:
          {add/2,and/2,first/2,from/1,if/3,add#/2,and#/2,first#/2,from#/1,if#/3} / {0/0,cons/2,false/0,nil/0,s/1
          ,true/0,c_1/0,c_2/1,c_3/0,c_4/0,c_5/0,c_6/1,c_7/1,c_8/0,c_9/0}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {add#,and#,first#,from#,if#} and constructors {0,cons
          ,false,nil,s,true}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE