MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            -(x,0()) -> x
            -(s(x),s(y)) -> -(x,y)
            f(s(x),s(y)) -> f(-(max(s(x),s(y)),min(s(x),s(y))),p(twice(min(x,y))))
            max(x,0()) -> x
            max(0(),y) -> y
            max(s(x),s(y)) -> s(max(x,y))
            min(x,0()) -> 0()
            min(0(),y) -> 0()
            min(s(x),s(y)) -> s(min(x,y))
            p(s(x)) -> x
            twice(0()) -> 0()
            twice(s(x)) -> s(s(twice(x)))
        - Signature:
            {-/2,f/2,max/2,min/2,p/1,twice/1} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {-,f,max,min,p,twice} and constructors {0,s}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          -#(x,0()) -> c_1()
          -#(s(x),s(y)) -> c_2(-#(x,y))
          f#(s(x),s(y)) -> c_3(f#(-(max(s(x),s(y)),min(s(x),s(y))),p(twice(min(x,y))))
                              ,-#(max(s(x),s(y)),min(s(x),s(y)))
                              ,max#(s(x),s(y))
                              ,min#(s(x),s(y))
                              ,p#(twice(min(x,y)))
                              ,twice#(min(x,y))
                              ,min#(x,y))
          max#(x,0()) -> c_4()
          max#(0(),y) -> c_5()
          max#(s(x),s(y)) -> c_6(max#(x,y))
          min#(x,0()) -> c_7()
          min#(0(),y) -> c_8()
          min#(s(x),s(y)) -> c_9(min#(x,y))
          p#(s(x)) -> c_10()
          twice#(0()) -> c_11()
          twice#(s(x)) -> c_12(twice#(x))
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            -#(x,0()) -> c_1()
            -#(s(x),s(y)) -> c_2(-#(x,y))
            f#(s(x),s(y)) -> c_3(f#(-(max(s(x),s(y)),min(s(x),s(y))),p(twice(min(x,y))))
                                ,-#(max(s(x),s(y)),min(s(x),s(y)))
                                ,max#(s(x),s(y))
                                ,min#(s(x),s(y))
                                ,p#(twice(min(x,y)))
                                ,twice#(min(x,y))
                                ,min#(x,y))
            max#(x,0()) -> c_4()
            max#(0(),y) -> c_5()
            max#(s(x),s(y)) -> c_6(max#(x,y))
            min#(x,0()) -> c_7()
            min#(0(),y) -> c_8()
            min#(s(x),s(y)) -> c_9(min#(x,y))
            p#(s(x)) -> c_10()
            twice#(0()) -> c_11()
            twice#(s(x)) -> c_12(twice#(x))
        - Weak TRS:
            -(x,0()) -> x
            -(s(x),s(y)) -> -(x,y)
            f(s(x),s(y)) -> f(-(max(s(x),s(y)),min(s(x),s(y))),p(twice(min(x,y))))
            max(x,0()) -> x
            max(0(),y) -> y
            max(s(x),s(y)) -> s(max(x,y))
            min(x,0()) -> 0()
            min(0(),y) -> 0()
            min(s(x),s(y)) -> s(min(x,y))
            p(s(x)) -> x
            twice(0()) -> 0()
            twice(s(x)) -> s(s(twice(x)))
        - Signature:
            {-/2,f/2,max/2,min/2,p/1,twice/1,-#/2,f#/2,max#/2,min#/2,p#/1,twice#/1} / {0/0,s/1,c_1/0,c_2/1,c_3/7,c_4/0
            ,c_5/0,c_6/1,c_7/0,c_8/0,c_9/1,c_10/0,c_11/0,c_12/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {-#,f#,max#,min#,p#,twice#} and constructors {0,s}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          -(x,0()) -> x
          -(s(x),s(y)) -> -(x,y)
          max(x,0()) -> x
          max(0(),y) -> y
          max(s(x),s(y)) -> s(max(x,y))
          min(x,0()) -> 0()
          min(0(),y) -> 0()
          min(s(x),s(y)) -> s(min(x,y))
          p(s(x)) -> x
          twice(0()) -> 0()
          twice(s(x)) -> s(s(twice(x)))
          -#(x,0()) -> c_1()
          -#(s(x),s(y)) -> c_2(-#(x,y))
          f#(s(x),s(y)) -> c_3(f#(-(max(s(x),s(y)),min(s(x),s(y))),p(twice(min(x,y))))
                              ,-#(max(s(x),s(y)),min(s(x),s(y)))
                              ,max#(s(x),s(y))
                              ,min#(s(x),s(y))
                              ,p#(twice(min(x,y)))
                              ,twice#(min(x,y))
                              ,min#(x,y))
          max#(x,0()) -> c_4()
          max#(0(),y) -> c_5()
          max#(s(x),s(y)) -> c_6(max#(x,y))
          min#(x,0()) -> c_7()
          min#(0(),y) -> c_8()
          min#(s(x),s(y)) -> c_9(min#(x,y))
          p#(s(x)) -> c_10()
          twice#(0()) -> c_11()
          twice#(s(x)) -> c_12(twice#(x))
* Step 3: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            -#(x,0()) -> c_1()
            -#(s(x),s(y)) -> c_2(-#(x,y))
            f#(s(x),s(y)) -> c_3(f#(-(max(s(x),s(y)),min(s(x),s(y))),p(twice(min(x,y))))
                                ,-#(max(s(x),s(y)),min(s(x),s(y)))
                                ,max#(s(x),s(y))
                                ,min#(s(x),s(y))
                                ,p#(twice(min(x,y)))
                                ,twice#(min(x,y))
                                ,min#(x,y))
            max#(x,0()) -> c_4()
            max#(0(),y) -> c_5()
            max#(s(x),s(y)) -> c_6(max#(x,y))
            min#(x,0()) -> c_7()
            min#(0(),y) -> c_8()
            min#(s(x),s(y)) -> c_9(min#(x,y))
            p#(s(x)) -> c_10()
            twice#(0()) -> c_11()
            twice#(s(x)) -> c_12(twice#(x))
        - Weak TRS:
            -(x,0()) -> x
            -(s(x),s(y)) -> -(x,y)
            max(x,0()) -> x
            max(0(),y) -> y
            max(s(x),s(y)) -> s(max(x,y))
            min(x,0()) -> 0()
            min(0(),y) -> 0()
            min(s(x),s(y)) -> s(min(x,y))
            p(s(x)) -> x
            twice(0()) -> 0()
            twice(s(x)) -> s(s(twice(x)))
        - Signature:
            {-/2,f/2,max/2,min/2,p/1,twice/1,-#/2,f#/2,max#/2,min#/2,p#/1,twice#/1} / {0/0,s/1,c_1/0,c_2/1,c_3/7,c_4/0
            ,c_5/0,c_6/1,c_7/0,c_8/0,c_9/1,c_10/0,c_11/0,c_12/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {-#,f#,max#,min#,p#,twice#} and constructors {0,s}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,4,5,7,8,10,11}
        by application of
          Pre({1,4,5,7,8,10,11}) = {2,3,6,9,12}.
        Here rules are labelled as follows:
          1: -#(x,0()) -> c_1()
          2: -#(s(x),s(y)) -> c_2(-#(x,y))
          3: f#(s(x),s(y)) -> c_3(f#(-(max(s(x),s(y)),min(s(x),s(y))),p(twice(min(x,y))))
                                 ,-#(max(s(x),s(y)),min(s(x),s(y)))
                                 ,max#(s(x),s(y))
                                 ,min#(s(x),s(y))
                                 ,p#(twice(min(x,y)))
                                 ,twice#(min(x,y))
                                 ,min#(x,y))
          4: max#(x,0()) -> c_4()
          5: max#(0(),y) -> c_5()
          6: max#(s(x),s(y)) -> c_6(max#(x,y))
          7: min#(x,0()) -> c_7()
          8: min#(0(),y) -> c_8()
          9: min#(s(x),s(y)) -> c_9(min#(x,y))
          10: p#(s(x)) -> c_10()
          11: twice#(0()) -> c_11()
          12: twice#(s(x)) -> c_12(twice#(x))
* Step 4: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            -#(s(x),s(y)) -> c_2(-#(x,y))
            f#(s(x),s(y)) -> c_3(f#(-(max(s(x),s(y)),min(s(x),s(y))),p(twice(min(x,y))))
                                ,-#(max(s(x),s(y)),min(s(x),s(y)))
                                ,max#(s(x),s(y))
                                ,min#(s(x),s(y))
                                ,p#(twice(min(x,y)))
                                ,twice#(min(x,y))
                                ,min#(x,y))
            max#(s(x),s(y)) -> c_6(max#(x,y))
            min#(s(x),s(y)) -> c_9(min#(x,y))
            twice#(s(x)) -> c_12(twice#(x))
        - Weak DPs:
            -#(x,0()) -> c_1()
            max#(x,0()) -> c_4()
            max#(0(),y) -> c_5()
            min#(x,0()) -> c_7()
            min#(0(),y) -> c_8()
            p#(s(x)) -> c_10()
            twice#(0()) -> c_11()
        - Weak TRS:
            -(x,0()) -> x
            -(s(x),s(y)) -> -(x,y)
            max(x,0()) -> x
            max(0(),y) -> y
            max(s(x),s(y)) -> s(max(x,y))
            min(x,0()) -> 0()
            min(0(),y) -> 0()
            min(s(x),s(y)) -> s(min(x,y))
            p(s(x)) -> x
            twice(0()) -> 0()
            twice(s(x)) -> s(s(twice(x)))
        - Signature:
            {-/2,f/2,max/2,min/2,p/1,twice/1,-#/2,f#/2,max#/2,min#/2,p#/1,twice#/1} / {0/0,s/1,c_1/0,c_2/1,c_3/7,c_4/0
            ,c_5/0,c_6/1,c_7/0,c_8/0,c_9/1,c_10/0,c_11/0,c_12/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {-#,f#,max#,min#,p#,twice#} and constructors {0,s}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:-#(s(x),s(y)) -> c_2(-#(x,y))
             -->_1 -#(x,0()) -> c_1():6
             -->_1 -#(s(x),s(y)) -> c_2(-#(x,y)):1
          
          2:S:f#(s(x),s(y)) -> c_3(f#(-(max(s(x),s(y)),min(s(x),s(y))),p(twice(min(x,y))))
                                  ,-#(max(s(x),s(y)),min(s(x),s(y)))
                                  ,max#(s(x),s(y))
                                  ,min#(s(x),s(y))
                                  ,p#(twice(min(x,y)))
                                  ,twice#(min(x,y))
                                  ,min#(x,y))
             -->_6 twice#(s(x)) -> c_12(twice#(x)):5
             -->_7 min#(s(x),s(y)) -> c_9(min#(x,y)):4
             -->_4 min#(s(x),s(y)) -> c_9(min#(x,y)):4
             -->_3 max#(s(x),s(y)) -> c_6(max#(x,y)):3
             -->_6 twice#(0()) -> c_11():12
             -->_5 p#(s(x)) -> c_10():11
             -->_7 min#(0(),y) -> c_8():10
             -->_7 min#(x,0()) -> c_7():9
             -->_2 -#(x,0()) -> c_1():6
             -->_1 f#(s(x),s(y)) -> c_3(f#(-(max(s(x),s(y)),min(s(x),s(y))),p(twice(min(x,y))))
                                       ,-#(max(s(x),s(y)),min(s(x),s(y)))
                                       ,max#(s(x),s(y))
                                       ,min#(s(x),s(y))
                                       ,p#(twice(min(x,y)))
                                       ,twice#(min(x,y))
                                       ,min#(x,y)):2
             -->_2 -#(s(x),s(y)) -> c_2(-#(x,y)):1
          
          3:S:max#(s(x),s(y)) -> c_6(max#(x,y))
             -->_1 max#(0(),y) -> c_5():8
             -->_1 max#(x,0()) -> c_4():7
             -->_1 max#(s(x),s(y)) -> c_6(max#(x,y)):3
          
          4:S:min#(s(x),s(y)) -> c_9(min#(x,y))
             -->_1 min#(0(),y) -> c_8():10
             -->_1 min#(x,0()) -> c_7():9
             -->_1 min#(s(x),s(y)) -> c_9(min#(x,y)):4
          
          5:S:twice#(s(x)) -> c_12(twice#(x))
             -->_1 twice#(0()) -> c_11():12
             -->_1 twice#(s(x)) -> c_12(twice#(x)):5
          
          6:W:-#(x,0()) -> c_1()
             
          
          7:W:max#(x,0()) -> c_4()
             
          
          8:W:max#(0(),y) -> c_5()
             
          
          9:W:min#(x,0()) -> c_7()
             
          
          10:W:min#(0(),y) -> c_8()
             
          
          11:W:p#(s(x)) -> c_10()
             
          
          12:W:twice#(0()) -> c_11()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          11: p#(s(x)) -> c_10()
          7: max#(x,0()) -> c_4()
          8: max#(0(),y) -> c_5()
          9: min#(x,0()) -> c_7()
          10: min#(0(),y) -> c_8()
          12: twice#(0()) -> c_11()
          6: -#(x,0()) -> c_1()
* Step 5: SimplifyRHS MAYBE
    + Considered Problem:
        - Strict DPs:
            -#(s(x),s(y)) -> c_2(-#(x,y))
            f#(s(x),s(y)) -> c_3(f#(-(max(s(x),s(y)),min(s(x),s(y))),p(twice(min(x,y))))
                                ,-#(max(s(x),s(y)),min(s(x),s(y)))
                                ,max#(s(x),s(y))
                                ,min#(s(x),s(y))
                                ,p#(twice(min(x,y)))
                                ,twice#(min(x,y))
                                ,min#(x,y))
            max#(s(x),s(y)) -> c_6(max#(x,y))
            min#(s(x),s(y)) -> c_9(min#(x,y))
            twice#(s(x)) -> c_12(twice#(x))
        - Weak TRS:
            -(x,0()) -> x
            -(s(x),s(y)) -> -(x,y)
            max(x,0()) -> x
            max(0(),y) -> y
            max(s(x),s(y)) -> s(max(x,y))
            min(x,0()) -> 0()
            min(0(),y) -> 0()
            min(s(x),s(y)) -> s(min(x,y))
            p(s(x)) -> x
            twice(0()) -> 0()
            twice(s(x)) -> s(s(twice(x)))
        - Signature:
            {-/2,f/2,max/2,min/2,p/1,twice/1,-#/2,f#/2,max#/2,min#/2,p#/1,twice#/1} / {0/0,s/1,c_1/0,c_2/1,c_3/7,c_4/0
            ,c_5/0,c_6/1,c_7/0,c_8/0,c_9/1,c_10/0,c_11/0,c_12/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {-#,f#,max#,min#,p#,twice#} and constructors {0,s}
    + Applied Processor:
        SimplifyRHS
    + Details:
        Consider the dependency graph
          1:S:-#(s(x),s(y)) -> c_2(-#(x,y))
             -->_1 -#(s(x),s(y)) -> c_2(-#(x,y)):1
          
          2:S:f#(s(x),s(y)) -> c_3(f#(-(max(s(x),s(y)),min(s(x),s(y))),p(twice(min(x,y))))
                                  ,-#(max(s(x),s(y)),min(s(x),s(y)))
                                  ,max#(s(x),s(y))
                                  ,min#(s(x),s(y))
                                  ,p#(twice(min(x,y)))
                                  ,twice#(min(x,y))
                                  ,min#(x,y))
             -->_6 twice#(s(x)) -> c_12(twice#(x)):5
             -->_7 min#(s(x),s(y)) -> c_9(min#(x,y)):4
             -->_4 min#(s(x),s(y)) -> c_9(min#(x,y)):4
             -->_3 max#(s(x),s(y)) -> c_6(max#(x,y)):3
             -->_1 f#(s(x),s(y)) -> c_3(f#(-(max(s(x),s(y)),min(s(x),s(y))),p(twice(min(x,y))))
                                       ,-#(max(s(x),s(y)),min(s(x),s(y)))
                                       ,max#(s(x),s(y))
                                       ,min#(s(x),s(y))
                                       ,p#(twice(min(x,y)))
                                       ,twice#(min(x,y))
                                       ,min#(x,y)):2
             -->_2 -#(s(x),s(y)) -> c_2(-#(x,y)):1
          
          3:S:max#(s(x),s(y)) -> c_6(max#(x,y))
             -->_1 max#(s(x),s(y)) -> c_6(max#(x,y)):3
          
          4:S:min#(s(x),s(y)) -> c_9(min#(x,y))
             -->_1 min#(s(x),s(y)) -> c_9(min#(x,y)):4
          
          5:S:twice#(s(x)) -> c_12(twice#(x))
             -->_1 twice#(s(x)) -> c_12(twice#(x)):5
          
        Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
          f#(s(x),s(y)) -> c_3(f#(-(max(s(x),s(y)),min(s(x),s(y))),p(twice(min(x,y))))
                              ,-#(max(s(x),s(y)),min(s(x),s(y)))
                              ,max#(s(x),s(y))
                              ,min#(s(x),s(y))
                              ,twice#(min(x,y))
                              ,min#(x,y))
* Step 6: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          -#(s(x),s(y)) -> c_2(-#(x,y))
          f#(s(x),s(y)) -> c_3(f#(-(max(s(x),s(y)),min(s(x),s(y))),p(twice(min(x,y))))
                              ,-#(max(s(x),s(y)),min(s(x),s(y)))
                              ,max#(s(x),s(y))
                              ,min#(s(x),s(y))
                              ,twice#(min(x,y))
                              ,min#(x,y))
          max#(s(x),s(y)) -> c_6(max#(x,y))
          min#(s(x),s(y)) -> c_9(min#(x,y))
          twice#(s(x)) -> c_12(twice#(x))
      - Weak TRS:
          -(x,0()) -> x
          -(s(x),s(y)) -> -(x,y)
          max(x,0()) -> x
          max(0(),y) -> y
          max(s(x),s(y)) -> s(max(x,y))
          min(x,0()) -> 0()
          min(0(),y) -> 0()
          min(s(x),s(y)) -> s(min(x,y))
          p(s(x)) -> x
          twice(0()) -> 0()
          twice(s(x)) -> s(s(twice(x)))
      - Signature:
          {-/2,f/2,max/2,min/2,p/1,twice/1,-#/2,f#/2,max#/2,min#/2,p#/1,twice#/1} / {0/0,s/1,c_1/0,c_2/1,c_3/6,c_4/0
          ,c_5/0,c_6/1,c_7/0,c_8/0,c_9/1,c_10/0,c_11/0,c_12/1}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {-#,f#,max#,min#,p#,twice#} and constructors {0,s}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE