MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            del(x,cons(y,xs)) -> if(eq(x,y),x,y,xs)
            del(x,nil()) -> nil()
            eq(0(),0()) -> true()
            eq(0(),s(y)) -> false()
            eq(s(x),0()) -> false()
            eq(s(x),s(y)) -> eq(x,y)
            if(false(),x,y,xs) -> cons(y,del(x,xs))
            if(true(),x,y,xs) -> xs
            last(cons(x,cons(y,xs))) -> last(cons(y,xs))
            last(cons(x,nil())) -> x
            last(nil()) -> 0()
            reverse(cons(x,xs)) -> cons(last(cons(x,xs)),reverse(del(last(cons(x,xs)),cons(x,xs))))
            reverse(nil()) -> nil()
        - Signature:
            {del/2,eq/2,if/4,last/1,reverse/1} / {0/0,cons/2,false/0,nil/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {del,eq,if,last,reverse} and constructors {0,cons,false
            ,nil,s,true}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          del#(x,cons(y,xs)) -> c_1(if#(eq(x,y),x,y,xs),eq#(x,y))
          del#(x,nil()) -> c_2()
          eq#(0(),0()) -> c_3()
          eq#(0(),s(y)) -> c_4()
          eq#(s(x),0()) -> c_5()
          eq#(s(x),s(y)) -> c_6(eq#(x,y))
          if#(false(),x,y,xs) -> c_7(del#(x,xs))
          if#(true(),x,y,xs) -> c_8()
          last#(cons(x,cons(y,xs))) -> c_9(last#(cons(y,xs)))
          last#(cons(x,nil())) -> c_10()
          last#(nil()) -> c_11()
          reverse#(cons(x,xs)) -> c_12(last#(cons(x,xs))
                                      ,reverse#(del(last(cons(x,xs)),cons(x,xs)))
                                      ,del#(last(cons(x,xs)),cons(x,xs))
                                      ,last#(cons(x,xs)))
          reverse#(nil()) -> c_13()
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            del#(x,cons(y,xs)) -> c_1(if#(eq(x,y),x,y,xs),eq#(x,y))
            del#(x,nil()) -> c_2()
            eq#(0(),0()) -> c_3()
            eq#(0(),s(y)) -> c_4()
            eq#(s(x),0()) -> c_5()
            eq#(s(x),s(y)) -> c_6(eq#(x,y))
            if#(false(),x,y,xs) -> c_7(del#(x,xs))
            if#(true(),x,y,xs) -> c_8()
            last#(cons(x,cons(y,xs))) -> c_9(last#(cons(y,xs)))
            last#(cons(x,nil())) -> c_10()
            last#(nil()) -> c_11()
            reverse#(cons(x,xs)) -> c_12(last#(cons(x,xs))
                                        ,reverse#(del(last(cons(x,xs)),cons(x,xs)))
                                        ,del#(last(cons(x,xs)),cons(x,xs))
                                        ,last#(cons(x,xs)))
            reverse#(nil()) -> c_13()
        - Weak TRS:
            del(x,cons(y,xs)) -> if(eq(x,y),x,y,xs)
            del(x,nil()) -> nil()
            eq(0(),0()) -> true()
            eq(0(),s(y)) -> false()
            eq(s(x),0()) -> false()
            eq(s(x),s(y)) -> eq(x,y)
            if(false(),x,y,xs) -> cons(y,del(x,xs))
            if(true(),x,y,xs) -> xs
            last(cons(x,cons(y,xs))) -> last(cons(y,xs))
            last(cons(x,nil())) -> x
            last(nil()) -> 0()
            reverse(cons(x,xs)) -> cons(last(cons(x,xs)),reverse(del(last(cons(x,xs)),cons(x,xs))))
            reverse(nil()) -> nil()
        - Signature:
            {del/2,eq/2,if/4,last/1,reverse/1,del#/2,eq#/2,if#/4,last#/1,reverse#/1} / {0/0,cons/2,false/0,nil/0,s/1
            ,true/0,c_1/2,c_2/0,c_3/0,c_4/0,c_5/0,c_6/1,c_7/1,c_8/0,c_9/1,c_10/0,c_11/0,c_12/4,c_13/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {del#,eq#,if#,last#,reverse#} and constructors {0,cons
            ,false,nil,s,true}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          del(x,cons(y,xs)) -> if(eq(x,y),x,y,xs)
          del(x,nil()) -> nil()
          eq(0(),0()) -> true()
          eq(0(),s(y)) -> false()
          eq(s(x),0()) -> false()
          eq(s(x),s(y)) -> eq(x,y)
          if(false(),x,y,xs) -> cons(y,del(x,xs))
          if(true(),x,y,xs) -> xs
          last(cons(x,cons(y,xs))) -> last(cons(y,xs))
          last(cons(x,nil())) -> x
          del#(x,cons(y,xs)) -> c_1(if#(eq(x,y),x,y,xs),eq#(x,y))
          del#(x,nil()) -> c_2()
          eq#(0(),0()) -> c_3()
          eq#(0(),s(y)) -> c_4()
          eq#(s(x),0()) -> c_5()
          eq#(s(x),s(y)) -> c_6(eq#(x,y))
          if#(false(),x,y,xs) -> c_7(del#(x,xs))
          if#(true(),x,y,xs) -> c_8()
          last#(cons(x,cons(y,xs))) -> c_9(last#(cons(y,xs)))
          last#(cons(x,nil())) -> c_10()
          last#(nil()) -> c_11()
          reverse#(cons(x,xs)) -> c_12(last#(cons(x,xs))
                                      ,reverse#(del(last(cons(x,xs)),cons(x,xs)))
                                      ,del#(last(cons(x,xs)),cons(x,xs))
                                      ,last#(cons(x,xs)))
          reverse#(nil()) -> c_13()
* Step 3: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            del#(x,cons(y,xs)) -> c_1(if#(eq(x,y),x,y,xs),eq#(x,y))
            del#(x,nil()) -> c_2()
            eq#(0(),0()) -> c_3()
            eq#(0(),s(y)) -> c_4()
            eq#(s(x),0()) -> c_5()
            eq#(s(x),s(y)) -> c_6(eq#(x,y))
            if#(false(),x,y,xs) -> c_7(del#(x,xs))
            if#(true(),x,y,xs) -> c_8()
            last#(cons(x,cons(y,xs))) -> c_9(last#(cons(y,xs)))
            last#(cons(x,nil())) -> c_10()
            last#(nil()) -> c_11()
            reverse#(cons(x,xs)) -> c_12(last#(cons(x,xs))
                                        ,reverse#(del(last(cons(x,xs)),cons(x,xs)))
                                        ,del#(last(cons(x,xs)),cons(x,xs))
                                        ,last#(cons(x,xs)))
            reverse#(nil()) -> c_13()
        - Weak TRS:
            del(x,cons(y,xs)) -> if(eq(x,y),x,y,xs)
            del(x,nil()) -> nil()
            eq(0(),0()) -> true()
            eq(0(),s(y)) -> false()
            eq(s(x),0()) -> false()
            eq(s(x),s(y)) -> eq(x,y)
            if(false(),x,y,xs) -> cons(y,del(x,xs))
            if(true(),x,y,xs) -> xs
            last(cons(x,cons(y,xs))) -> last(cons(y,xs))
            last(cons(x,nil())) -> x
        - Signature:
            {del/2,eq/2,if/4,last/1,reverse/1,del#/2,eq#/2,if#/4,last#/1,reverse#/1} / {0/0,cons/2,false/0,nil/0,s/1
            ,true/0,c_1/2,c_2/0,c_3/0,c_4/0,c_5/0,c_6/1,c_7/1,c_8/0,c_9/1,c_10/0,c_11/0,c_12/4,c_13/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {del#,eq#,if#,last#,reverse#} 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
          {2,3,4,5,8,10,11,13}
        by application of
          Pre({2,3,4,5,8,10,11,13}) = {1,6,7,9,12}.
        Here rules are labelled as follows:
          1: del#(x,cons(y,xs)) -> c_1(if#(eq(x,y),x,y,xs),eq#(x,y))
          2: del#(x,nil()) -> c_2()
          3: eq#(0(),0()) -> c_3()
          4: eq#(0(),s(y)) -> c_4()
          5: eq#(s(x),0()) -> c_5()
          6: eq#(s(x),s(y)) -> c_6(eq#(x,y))
          7: if#(false(),x,y,xs) -> c_7(del#(x,xs))
          8: if#(true(),x,y,xs) -> c_8()
          9: last#(cons(x,cons(y,xs))) -> c_9(last#(cons(y,xs)))
          10: last#(cons(x,nil())) -> c_10()
          11: last#(nil()) -> c_11()
          12: reverse#(cons(x,xs)) -> c_12(last#(cons(x,xs))
                                          ,reverse#(del(last(cons(x,xs)),cons(x,xs)))
                                          ,del#(last(cons(x,xs)),cons(x,xs))
                                          ,last#(cons(x,xs)))
          13: reverse#(nil()) -> c_13()
* Step 4: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            del#(x,cons(y,xs)) -> c_1(if#(eq(x,y),x,y,xs),eq#(x,y))
            eq#(s(x),s(y)) -> c_6(eq#(x,y))
            if#(false(),x,y,xs) -> c_7(del#(x,xs))
            last#(cons(x,cons(y,xs))) -> c_9(last#(cons(y,xs)))
            reverse#(cons(x,xs)) -> c_12(last#(cons(x,xs))
                                        ,reverse#(del(last(cons(x,xs)),cons(x,xs)))
                                        ,del#(last(cons(x,xs)),cons(x,xs))
                                        ,last#(cons(x,xs)))
        - Weak DPs:
            del#(x,nil()) -> c_2()
            eq#(0(),0()) -> c_3()
            eq#(0(),s(y)) -> c_4()
            eq#(s(x),0()) -> c_5()
            if#(true(),x,y,xs) -> c_8()
            last#(cons(x,nil())) -> c_10()
            last#(nil()) -> c_11()
            reverse#(nil()) -> c_13()
        - Weak TRS:
            del(x,cons(y,xs)) -> if(eq(x,y),x,y,xs)
            del(x,nil()) -> nil()
            eq(0(),0()) -> true()
            eq(0(),s(y)) -> false()
            eq(s(x),0()) -> false()
            eq(s(x),s(y)) -> eq(x,y)
            if(false(),x,y,xs) -> cons(y,del(x,xs))
            if(true(),x,y,xs) -> xs
            last(cons(x,cons(y,xs))) -> last(cons(y,xs))
            last(cons(x,nil())) -> x
        - Signature:
            {del/2,eq/2,if/4,last/1,reverse/1,del#/2,eq#/2,if#/4,last#/1,reverse#/1} / {0/0,cons/2,false/0,nil/0,s/1
            ,true/0,c_1/2,c_2/0,c_3/0,c_4/0,c_5/0,c_6/1,c_7/1,c_8/0,c_9/1,c_10/0,c_11/0,c_12/4,c_13/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {del#,eq#,if#,last#,reverse#} and constructors {0,cons
            ,false,nil,s,true}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:del#(x,cons(y,xs)) -> c_1(if#(eq(x,y),x,y,xs),eq#(x,y))
             -->_1 if#(false(),x,y,xs) -> c_7(del#(x,xs)):3
             -->_2 eq#(s(x),s(y)) -> c_6(eq#(x,y)):2
             -->_1 if#(true(),x,y,xs) -> c_8():10
             -->_2 eq#(s(x),0()) -> c_5():9
             -->_2 eq#(0(),s(y)) -> c_4():8
             -->_2 eq#(0(),0()) -> c_3():7
          
          2:S:eq#(s(x),s(y)) -> c_6(eq#(x,y))
             -->_1 eq#(s(x),0()) -> c_5():9
             -->_1 eq#(0(),s(y)) -> c_4():8
             -->_1 eq#(0(),0()) -> c_3():7
             -->_1 eq#(s(x),s(y)) -> c_6(eq#(x,y)):2
          
          3:S:if#(false(),x,y,xs) -> c_7(del#(x,xs))
             -->_1 del#(x,nil()) -> c_2():6
             -->_1 del#(x,cons(y,xs)) -> c_1(if#(eq(x,y),x,y,xs),eq#(x,y)):1
          
          4:S:last#(cons(x,cons(y,xs))) -> c_9(last#(cons(y,xs)))
             -->_1 last#(cons(x,nil())) -> c_10():11
             -->_1 last#(cons(x,cons(y,xs))) -> c_9(last#(cons(y,xs))):4
          
          5:S:reverse#(cons(x,xs)) -> c_12(last#(cons(x,xs))
                                          ,reverse#(del(last(cons(x,xs)),cons(x,xs)))
                                          ,del#(last(cons(x,xs)),cons(x,xs))
                                          ,last#(cons(x,xs)))
             -->_2 reverse#(nil()) -> c_13():13
             -->_4 last#(cons(x,nil())) -> c_10():11
             -->_1 last#(cons(x,nil())) -> c_10():11
             -->_2 reverse#(cons(x,xs)) -> c_12(last#(cons(x,xs))
                                               ,reverse#(del(last(cons(x,xs)),cons(x,xs)))
                                               ,del#(last(cons(x,xs)),cons(x,xs))
                                               ,last#(cons(x,xs))):5
             -->_4 last#(cons(x,cons(y,xs))) -> c_9(last#(cons(y,xs))):4
             -->_1 last#(cons(x,cons(y,xs))) -> c_9(last#(cons(y,xs))):4
             -->_3 del#(x,cons(y,xs)) -> c_1(if#(eq(x,y),x,y,xs),eq#(x,y)):1
          
          6:W:del#(x,nil()) -> c_2()
             
          
          7:W:eq#(0(),0()) -> c_3()
             
          
          8:W:eq#(0(),s(y)) -> c_4()
             
          
          9:W:eq#(s(x),0()) -> c_5()
             
          
          10:W:if#(true(),x,y,xs) -> c_8()
             
          
          11:W:last#(cons(x,nil())) -> c_10()
             
          
          12:W:last#(nil()) -> c_11()
             
          
          13:W:reverse#(nil()) -> c_13()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          12: last#(nil()) -> c_11()
          13: reverse#(nil()) -> c_13()
          11: last#(cons(x,nil())) -> c_10()
          10: if#(true(),x,y,xs) -> c_8()
          7: eq#(0(),0()) -> c_3()
          8: eq#(0(),s(y)) -> c_4()
          9: eq#(s(x),0()) -> c_5()
          6: del#(x,nil()) -> c_2()
* Step 5: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          del#(x,cons(y,xs)) -> c_1(if#(eq(x,y),x,y,xs),eq#(x,y))
          eq#(s(x),s(y)) -> c_6(eq#(x,y))
          if#(false(),x,y,xs) -> c_7(del#(x,xs))
          last#(cons(x,cons(y,xs))) -> c_9(last#(cons(y,xs)))
          reverse#(cons(x,xs)) -> c_12(last#(cons(x,xs))
                                      ,reverse#(del(last(cons(x,xs)),cons(x,xs)))
                                      ,del#(last(cons(x,xs)),cons(x,xs))
                                      ,last#(cons(x,xs)))
      - Weak TRS:
          del(x,cons(y,xs)) -> if(eq(x,y),x,y,xs)
          del(x,nil()) -> nil()
          eq(0(),0()) -> true()
          eq(0(),s(y)) -> false()
          eq(s(x),0()) -> false()
          eq(s(x),s(y)) -> eq(x,y)
          if(false(),x,y,xs) -> cons(y,del(x,xs))
          if(true(),x,y,xs) -> xs
          last(cons(x,cons(y,xs))) -> last(cons(y,xs))
          last(cons(x,nil())) -> x
      - Signature:
          {del/2,eq/2,if/4,last/1,reverse/1,del#/2,eq#/2,if#/4,last#/1,reverse#/1} / {0/0,cons/2,false/0,nil/0,s/1
          ,true/0,c_1/2,c_2/0,c_3/0,c_4/0,c_5/0,c_6/1,c_7/1,c_8/0,c_9/1,c_10/0,c_11/0,c_12/4,c_13/0}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {del#,eq#,if#,last#,reverse#} and constructors {0,cons
          ,false,nil,s,true}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE