MAYBE
* Step 1: InnermostRuleRemoval MAYBE
    + Considered Problem:
        - Strict TRS:
            double(0()) -> 0()
            double(s(x)) -> s(s(double(x)))
            gt(s(x),s(y)) -> gt(x,y)
            gt(s(x),zero()) -> true()
            gt(zero(),y) -> false()
            id(x) -> x
            if(false(),x,y) -> y
            if(true(),x,y) -> x
            minus(x,0()) -> x
            minus(s(x),s(y)) -> minus(x,y)
            not(x) -> if(x,false(),true())
            plus(id(x),s(y)) -> s(plus(x,if(gt(s(y),y),y,s(y))))
            plus(s(x),x) -> plus(if(gt(x,x),id(x),id(x)),s(x))
            plus(s(x),s(y)) -> s(s(plus(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y)))))
            plus(zero(),y) -> y
        - Signature:
            {double/1,gt/2,id/1,if/3,minus/2,not/1,plus/2} / {0/0,false/0,s/1,true/0,zero/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {double,gt,id,if,minus,not,plus} and constructors {0,false
            ,s,true,zero}
    + Applied Processor:
        InnermostRuleRemoval
    + Details:
        Arguments of following rules are not normal-forms.
          plus(id(x),s(y)) -> s(plus(x,if(gt(s(y),y),y,s(y))))
        All above mentioned rules can be savely removed.
* Step 2: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            double(0()) -> 0()
            double(s(x)) -> s(s(double(x)))
            gt(s(x),s(y)) -> gt(x,y)
            gt(s(x),zero()) -> true()
            gt(zero(),y) -> false()
            id(x) -> x
            if(false(),x,y) -> y
            if(true(),x,y) -> x
            minus(x,0()) -> x
            minus(s(x),s(y)) -> minus(x,y)
            not(x) -> if(x,false(),true())
            plus(s(x),x) -> plus(if(gt(x,x),id(x),id(x)),s(x))
            plus(s(x),s(y)) -> s(s(plus(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y)))))
            plus(zero(),y) -> y
        - Signature:
            {double/1,gt/2,id/1,if/3,minus/2,not/1,plus/2} / {0/0,false/0,s/1,true/0,zero/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {double,gt,id,if,minus,not,plus} and constructors {0,false
            ,s,true,zero}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          double#(0()) -> c_1()
          double#(s(x)) -> c_2(double#(x))
          gt#(s(x),s(y)) -> c_3(gt#(x,y))
          gt#(s(x),zero()) -> c_4()
          gt#(zero(),y) -> c_5()
          id#(x) -> c_6()
          if#(false(),x,y) -> c_7()
          if#(true(),x,y) -> c_8()
          minus#(x,0()) -> c_9()
          minus#(s(x),s(y)) -> c_10(minus#(x,y))
          not#(x) -> c_11(if#(x,false(),true()))
          plus#(s(x),x) -> c_12(plus#(if(gt(x,x),id(x),id(x)),s(x)),if#(gt(x,x),id(x),id(x)),gt#(x,x),id#(x),id#(x))
          plus#(s(x),s(y)) -> c_13(plus#(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y)))
                                  ,if#(gt(x,y),x,y)
                                  ,gt#(x,y)
                                  ,if#(not(gt(x,y)),id(x),id(y))
                                  ,not#(gt(x,y))
                                  ,gt#(x,y)
                                  ,id#(x)
                                  ,id#(y))
          plus#(zero(),y) -> c_14()
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 3: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            double#(0()) -> c_1()
            double#(s(x)) -> c_2(double#(x))
            gt#(s(x),s(y)) -> c_3(gt#(x,y))
            gt#(s(x),zero()) -> c_4()
            gt#(zero(),y) -> c_5()
            id#(x) -> c_6()
            if#(false(),x,y) -> c_7()
            if#(true(),x,y) -> c_8()
            minus#(x,0()) -> c_9()
            minus#(s(x),s(y)) -> c_10(minus#(x,y))
            not#(x) -> c_11(if#(x,false(),true()))
            plus#(s(x),x) -> c_12(plus#(if(gt(x,x),id(x),id(x)),s(x)),if#(gt(x,x),id(x),id(x)),gt#(x,x),id#(x),id#(x))
            plus#(s(x),s(y)) -> c_13(plus#(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y)))
                                    ,if#(gt(x,y),x,y)
                                    ,gt#(x,y)
                                    ,if#(not(gt(x,y)),id(x),id(y))
                                    ,not#(gt(x,y))
                                    ,gt#(x,y)
                                    ,id#(x)
                                    ,id#(y))
            plus#(zero(),y) -> c_14()
        - Weak TRS:
            double(0()) -> 0()
            double(s(x)) -> s(s(double(x)))
            gt(s(x),s(y)) -> gt(x,y)
            gt(s(x),zero()) -> true()
            gt(zero(),y) -> false()
            id(x) -> x
            if(false(),x,y) -> y
            if(true(),x,y) -> x
            minus(x,0()) -> x
            minus(s(x),s(y)) -> minus(x,y)
            not(x) -> if(x,false(),true())
            plus(s(x),x) -> plus(if(gt(x,x),id(x),id(x)),s(x))
            plus(s(x),s(y)) -> s(s(plus(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y)))))
            plus(zero(),y) -> y
        - Signature:
            {double/1,gt/2,id/1,if/3,minus/2,not/1,plus/2,double#/1,gt#/2,id#/1,if#/3,minus#/2,not#/1,plus#/2} / {0/0
            ,false/0,s/1,true/0,zero/0,c_1/0,c_2/1,c_3/1,c_4/0,c_5/0,c_6/0,c_7/0,c_8/0,c_9/0,c_10/1,c_11/1,c_12/5,c_13/8
            ,c_14/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {double#,gt#,id#,if#,minus#,not#
            ,plus#} and constructors {0,false,s,true,zero}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          gt(s(x),s(y)) -> gt(x,y)
          gt(s(x),zero()) -> true()
          gt(zero(),y) -> false()
          id(x) -> x
          if(false(),x,y) -> y
          if(true(),x,y) -> x
          not(x) -> if(x,false(),true())
          double#(0()) -> c_1()
          double#(s(x)) -> c_2(double#(x))
          gt#(s(x),s(y)) -> c_3(gt#(x,y))
          gt#(s(x),zero()) -> c_4()
          gt#(zero(),y) -> c_5()
          id#(x) -> c_6()
          if#(false(),x,y) -> c_7()
          if#(true(),x,y) -> c_8()
          minus#(x,0()) -> c_9()
          minus#(s(x),s(y)) -> c_10(minus#(x,y))
          not#(x) -> c_11(if#(x,false(),true()))
          plus#(s(x),x) -> c_12(plus#(if(gt(x,x),id(x),id(x)),s(x)),if#(gt(x,x),id(x),id(x)),gt#(x,x),id#(x),id#(x))
          plus#(s(x),s(y)) -> c_13(plus#(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y)))
                                  ,if#(gt(x,y),x,y)
                                  ,gt#(x,y)
                                  ,if#(not(gt(x,y)),id(x),id(y))
                                  ,not#(gt(x,y))
                                  ,gt#(x,y)
                                  ,id#(x)
                                  ,id#(y))
          plus#(zero(),y) -> c_14()
* Step 4: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            double#(0()) -> c_1()
            double#(s(x)) -> c_2(double#(x))
            gt#(s(x),s(y)) -> c_3(gt#(x,y))
            gt#(s(x),zero()) -> c_4()
            gt#(zero(),y) -> c_5()
            id#(x) -> c_6()
            if#(false(),x,y) -> c_7()
            if#(true(),x,y) -> c_8()
            minus#(x,0()) -> c_9()
            minus#(s(x),s(y)) -> c_10(minus#(x,y))
            not#(x) -> c_11(if#(x,false(),true()))
            plus#(s(x),x) -> c_12(plus#(if(gt(x,x),id(x),id(x)),s(x)),if#(gt(x,x),id(x),id(x)),gt#(x,x),id#(x),id#(x))
            plus#(s(x),s(y)) -> c_13(plus#(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y)))
                                    ,if#(gt(x,y),x,y)
                                    ,gt#(x,y)
                                    ,if#(not(gt(x,y)),id(x),id(y))
                                    ,not#(gt(x,y))
                                    ,gt#(x,y)
                                    ,id#(x)
                                    ,id#(y))
            plus#(zero(),y) -> c_14()
        - Weak TRS:
            gt(s(x),s(y)) -> gt(x,y)
            gt(s(x),zero()) -> true()
            gt(zero(),y) -> false()
            id(x) -> x
            if(false(),x,y) -> y
            if(true(),x,y) -> x
            not(x) -> if(x,false(),true())
        - Signature:
            {double/1,gt/2,id/1,if/3,minus/2,not/1,plus/2,double#/1,gt#/2,id#/1,if#/3,minus#/2,not#/1,plus#/2} / {0/0
            ,false/0,s/1,true/0,zero/0,c_1/0,c_2/1,c_3/1,c_4/0,c_5/0,c_6/0,c_7/0,c_8/0,c_9/0,c_10/1,c_11/1,c_12/5,c_13/8
            ,c_14/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {double#,gt#,id#,if#,minus#,not#
            ,plus#} and constructors {0,false,s,true,zero}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,4,5,6,7,8,9,14}
        by application of
          Pre({1,4,5,6,7,8,9,14}) = {2,3,10,11,12,13}.
        Here rules are labelled as follows:
          1: double#(0()) -> c_1()
          2: double#(s(x)) -> c_2(double#(x))
          3: gt#(s(x),s(y)) -> c_3(gt#(x,y))
          4: gt#(s(x),zero()) -> c_4()
          5: gt#(zero(),y) -> c_5()
          6: id#(x) -> c_6()
          7: if#(false(),x,y) -> c_7()
          8: if#(true(),x,y) -> c_8()
          9: minus#(x,0()) -> c_9()
          10: minus#(s(x),s(y)) -> c_10(minus#(x,y))
          11: not#(x) -> c_11(if#(x,false(),true()))
          12: plus#(s(x),x) -> c_12(plus#(if(gt(x,x),id(x),id(x)),s(x))
                                   ,if#(gt(x,x),id(x),id(x))
                                   ,gt#(x,x)
                                   ,id#(x)
                                   ,id#(x))
          13: plus#(s(x),s(y)) -> c_13(plus#(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y)))
                                      ,if#(gt(x,y),x,y)
                                      ,gt#(x,y)
                                      ,if#(not(gt(x,y)),id(x),id(y))
                                      ,not#(gt(x,y))
                                      ,gt#(x,y)
                                      ,id#(x)
                                      ,id#(y))
          14: plus#(zero(),y) -> c_14()
* Step 5: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            double#(s(x)) -> c_2(double#(x))
            gt#(s(x),s(y)) -> c_3(gt#(x,y))
            minus#(s(x),s(y)) -> c_10(minus#(x,y))
            not#(x) -> c_11(if#(x,false(),true()))
            plus#(s(x),x) -> c_12(plus#(if(gt(x,x),id(x),id(x)),s(x)),if#(gt(x,x),id(x),id(x)),gt#(x,x),id#(x),id#(x))
            plus#(s(x),s(y)) -> c_13(plus#(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y)))
                                    ,if#(gt(x,y),x,y)
                                    ,gt#(x,y)
                                    ,if#(not(gt(x,y)),id(x),id(y))
                                    ,not#(gt(x,y))
                                    ,gt#(x,y)
                                    ,id#(x)
                                    ,id#(y))
        - Weak DPs:
            double#(0()) -> c_1()
            gt#(s(x),zero()) -> c_4()
            gt#(zero(),y) -> c_5()
            id#(x) -> c_6()
            if#(false(),x,y) -> c_7()
            if#(true(),x,y) -> c_8()
            minus#(x,0()) -> c_9()
            plus#(zero(),y) -> c_14()
        - Weak TRS:
            gt(s(x),s(y)) -> gt(x,y)
            gt(s(x),zero()) -> true()
            gt(zero(),y) -> false()
            id(x) -> x
            if(false(),x,y) -> y
            if(true(),x,y) -> x
            not(x) -> if(x,false(),true())
        - Signature:
            {double/1,gt/2,id/1,if/3,minus/2,not/1,plus/2,double#/1,gt#/2,id#/1,if#/3,minus#/2,not#/1,plus#/2} / {0/0
            ,false/0,s/1,true/0,zero/0,c_1/0,c_2/1,c_3/1,c_4/0,c_5/0,c_6/0,c_7/0,c_8/0,c_9/0,c_10/1,c_11/1,c_12/5,c_13/8
            ,c_14/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {double#,gt#,id#,if#,minus#,not#
            ,plus#} and constructors {0,false,s,true,zero}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {4}
        by application of
          Pre({4}) = {6}.
        Here rules are labelled as follows:
          1: double#(s(x)) -> c_2(double#(x))
          2: gt#(s(x),s(y)) -> c_3(gt#(x,y))
          3: minus#(s(x),s(y)) -> c_10(minus#(x,y))
          4: not#(x) -> c_11(if#(x,false(),true()))
          5: plus#(s(x),x) -> c_12(plus#(if(gt(x,x),id(x),id(x)),s(x))
                                  ,if#(gt(x,x),id(x),id(x))
                                  ,gt#(x,x)
                                  ,id#(x)
                                  ,id#(x))
          6: plus#(s(x),s(y)) -> c_13(plus#(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y)))
                                     ,if#(gt(x,y),x,y)
                                     ,gt#(x,y)
                                     ,if#(not(gt(x,y)),id(x),id(y))
                                     ,not#(gt(x,y))
                                     ,gt#(x,y)
                                     ,id#(x)
                                     ,id#(y))
          7: double#(0()) -> c_1()
          8: gt#(s(x),zero()) -> c_4()
          9: gt#(zero(),y) -> c_5()
          10: id#(x) -> c_6()
          11: if#(false(),x,y) -> c_7()
          12: if#(true(),x,y) -> c_8()
          13: minus#(x,0()) -> c_9()
          14: plus#(zero(),y) -> c_14()
* Step 6: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            double#(s(x)) -> c_2(double#(x))
            gt#(s(x),s(y)) -> c_3(gt#(x,y))
            minus#(s(x),s(y)) -> c_10(minus#(x,y))
            plus#(s(x),x) -> c_12(plus#(if(gt(x,x),id(x),id(x)),s(x)),if#(gt(x,x),id(x),id(x)),gt#(x,x),id#(x),id#(x))
            plus#(s(x),s(y)) -> c_13(plus#(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y)))
                                    ,if#(gt(x,y),x,y)
                                    ,gt#(x,y)
                                    ,if#(not(gt(x,y)),id(x),id(y))
                                    ,not#(gt(x,y))
                                    ,gt#(x,y)
                                    ,id#(x)
                                    ,id#(y))
        - Weak DPs:
            double#(0()) -> c_1()
            gt#(s(x),zero()) -> c_4()
            gt#(zero(),y) -> c_5()
            id#(x) -> c_6()
            if#(false(),x,y) -> c_7()
            if#(true(),x,y) -> c_8()
            minus#(x,0()) -> c_9()
            not#(x) -> c_11(if#(x,false(),true()))
            plus#(zero(),y) -> c_14()
        - Weak TRS:
            gt(s(x),s(y)) -> gt(x,y)
            gt(s(x),zero()) -> true()
            gt(zero(),y) -> false()
            id(x) -> x
            if(false(),x,y) -> y
            if(true(),x,y) -> x
            not(x) -> if(x,false(),true())
        - Signature:
            {double/1,gt/2,id/1,if/3,minus/2,not/1,plus/2,double#/1,gt#/2,id#/1,if#/3,minus#/2,not#/1,plus#/2} / {0/0
            ,false/0,s/1,true/0,zero/0,c_1/0,c_2/1,c_3/1,c_4/0,c_5/0,c_6/0,c_7/0,c_8/0,c_9/0,c_10/1,c_11/1,c_12/5,c_13/8
            ,c_14/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {double#,gt#,id#,if#,minus#,not#
            ,plus#} and constructors {0,false,s,true,zero}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:double#(s(x)) -> c_2(double#(x))
             -->_1 double#(0()) -> c_1():6
             -->_1 double#(s(x)) -> c_2(double#(x)):1
          
          2:S:gt#(s(x),s(y)) -> c_3(gt#(x,y))
             -->_1 gt#(zero(),y) -> c_5():8
             -->_1 gt#(s(x),zero()) -> c_4():7
             -->_1 gt#(s(x),s(y)) -> c_3(gt#(x,y)):2
          
          3:S:minus#(s(x),s(y)) -> c_10(minus#(x,y))
             -->_1 minus#(x,0()) -> c_9():12
             -->_1 minus#(s(x),s(y)) -> c_10(minus#(x,y)):3
          
          4:S:plus#(s(x),x) -> c_12(plus#(if(gt(x,x),id(x),id(x)),s(x))
                                   ,if#(gt(x,x),id(x),id(x))
                                   ,gt#(x,x)
                                   ,id#(x)
                                   ,id#(x))
             -->_1 plus#(s(x),s(y)) -> c_13(plus#(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y)))
                                           ,if#(gt(x,y),x,y)
                                           ,gt#(x,y)
                                           ,if#(not(gt(x,y)),id(x),id(y))
                                           ,not#(gt(x,y))
                                           ,gt#(x,y)
                                           ,id#(x)
                                           ,id#(y)):5
             -->_1 plus#(zero(),y) -> c_14():14
             -->_2 if#(true(),x,y) -> c_8():11
             -->_2 if#(false(),x,y) -> c_7():10
             -->_5 id#(x) -> c_6():9
             -->_4 id#(x) -> c_6():9
             -->_3 gt#(zero(),y) -> c_5():8
             -->_1 plus#(s(x),x) -> c_12(plus#(if(gt(x,x),id(x),id(x)),s(x))
                                        ,if#(gt(x,x),id(x),id(x))
                                        ,gt#(x,x)
                                        ,id#(x)
                                        ,id#(x)):4
             -->_3 gt#(s(x),s(y)) -> c_3(gt#(x,y)):2
          
          5:S:plus#(s(x),s(y)) -> c_13(plus#(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y)))
                                      ,if#(gt(x,y),x,y)
                                      ,gt#(x,y)
                                      ,if#(not(gt(x,y)),id(x),id(y))
                                      ,not#(gt(x,y))
                                      ,gt#(x,y)
                                      ,id#(x)
                                      ,id#(y))
             -->_5 not#(x) -> c_11(if#(x,false(),true())):13
             -->_1 plus#(zero(),y) -> c_14():14
             -->_4 if#(true(),x,y) -> c_8():11
             -->_2 if#(true(),x,y) -> c_8():11
             -->_4 if#(false(),x,y) -> c_7():10
             -->_2 if#(false(),x,y) -> c_7():10
             -->_8 id#(x) -> c_6():9
             -->_7 id#(x) -> c_6():9
             -->_6 gt#(zero(),y) -> c_5():8
             -->_3 gt#(zero(),y) -> c_5():8
             -->_6 gt#(s(x),zero()) -> c_4():7
             -->_3 gt#(s(x),zero()) -> c_4():7
             -->_1 plus#(s(x),s(y)) -> c_13(plus#(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y)))
                                           ,if#(gt(x,y),x,y)
                                           ,gt#(x,y)
                                           ,if#(not(gt(x,y)),id(x),id(y))
                                           ,not#(gt(x,y))
                                           ,gt#(x,y)
                                           ,id#(x)
                                           ,id#(y)):5
             -->_1 plus#(s(x),x) -> c_12(plus#(if(gt(x,x),id(x),id(x)),s(x))
                                        ,if#(gt(x,x),id(x),id(x))
                                        ,gt#(x,x)
                                        ,id#(x)
                                        ,id#(x)):4
             -->_6 gt#(s(x),s(y)) -> c_3(gt#(x,y)):2
             -->_3 gt#(s(x),s(y)) -> c_3(gt#(x,y)):2
          
          6:W:double#(0()) -> c_1()
             
          
          7:W:gt#(s(x),zero()) -> c_4()
             
          
          8:W:gt#(zero(),y) -> c_5()
             
          
          9:W:id#(x) -> c_6()
             
          
          10:W:if#(false(),x,y) -> c_7()
             
          
          11:W:if#(true(),x,y) -> c_8()
             
          
          12:W:minus#(x,0()) -> c_9()
             
          
          13:W:not#(x) -> c_11(if#(x,false(),true()))
             -->_1 if#(true(),x,y) -> c_8():11
             -->_1 if#(false(),x,y) -> c_7():10
          
          14:W:plus#(zero(),y) -> c_14()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          9: id#(x) -> c_6()
          14: plus#(zero(),y) -> c_14()
          13: not#(x) -> c_11(if#(x,false(),true()))
          10: if#(false(),x,y) -> c_7()
          11: if#(true(),x,y) -> c_8()
          12: minus#(x,0()) -> c_9()
          7: gt#(s(x),zero()) -> c_4()
          8: gt#(zero(),y) -> c_5()
          6: double#(0()) -> c_1()
* Step 7: SimplifyRHS MAYBE
    + Considered Problem:
        - Strict DPs:
            double#(s(x)) -> c_2(double#(x))
            gt#(s(x),s(y)) -> c_3(gt#(x,y))
            minus#(s(x),s(y)) -> c_10(minus#(x,y))
            plus#(s(x),x) -> c_12(plus#(if(gt(x,x),id(x),id(x)),s(x)),if#(gt(x,x),id(x),id(x)),gt#(x,x),id#(x),id#(x))
            plus#(s(x),s(y)) -> c_13(plus#(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y)))
                                    ,if#(gt(x,y),x,y)
                                    ,gt#(x,y)
                                    ,if#(not(gt(x,y)),id(x),id(y))
                                    ,not#(gt(x,y))
                                    ,gt#(x,y)
                                    ,id#(x)
                                    ,id#(y))
        - Weak TRS:
            gt(s(x),s(y)) -> gt(x,y)
            gt(s(x),zero()) -> true()
            gt(zero(),y) -> false()
            id(x) -> x
            if(false(),x,y) -> y
            if(true(),x,y) -> x
            not(x) -> if(x,false(),true())
        - Signature:
            {double/1,gt/2,id/1,if/3,minus/2,not/1,plus/2,double#/1,gt#/2,id#/1,if#/3,minus#/2,not#/1,plus#/2} / {0/0
            ,false/0,s/1,true/0,zero/0,c_1/0,c_2/1,c_3/1,c_4/0,c_5/0,c_6/0,c_7/0,c_8/0,c_9/0,c_10/1,c_11/1,c_12/5,c_13/8
            ,c_14/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {double#,gt#,id#,if#,minus#,not#
            ,plus#} and constructors {0,false,s,true,zero}
    + Applied Processor:
        SimplifyRHS
    + Details:
        Consider the dependency graph
          1:S:double#(s(x)) -> c_2(double#(x))
             -->_1 double#(s(x)) -> c_2(double#(x)):1
          
          2:S:gt#(s(x),s(y)) -> c_3(gt#(x,y))
             -->_1 gt#(s(x),s(y)) -> c_3(gt#(x,y)):2
          
          3:S:minus#(s(x),s(y)) -> c_10(minus#(x,y))
             -->_1 minus#(s(x),s(y)) -> c_10(minus#(x,y)):3
          
          4:S:plus#(s(x),x) -> c_12(plus#(if(gt(x,x),id(x),id(x)),s(x))
                                   ,if#(gt(x,x),id(x),id(x))
                                   ,gt#(x,x)
                                   ,id#(x)
                                   ,id#(x))
             -->_1 plus#(s(x),s(y)) -> c_13(plus#(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y)))
                                           ,if#(gt(x,y),x,y)
                                           ,gt#(x,y)
                                           ,if#(not(gt(x,y)),id(x),id(y))
                                           ,not#(gt(x,y))
                                           ,gt#(x,y)
                                           ,id#(x)
                                           ,id#(y)):5
             -->_1 plus#(s(x),x) -> c_12(plus#(if(gt(x,x),id(x),id(x)),s(x))
                                        ,if#(gt(x,x),id(x),id(x))
                                        ,gt#(x,x)
                                        ,id#(x)
                                        ,id#(x)):4
             -->_3 gt#(s(x),s(y)) -> c_3(gt#(x,y)):2
          
          5:S:plus#(s(x),s(y)) -> c_13(plus#(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y)))
                                      ,if#(gt(x,y),x,y)
                                      ,gt#(x,y)
                                      ,if#(not(gt(x,y)),id(x),id(y))
                                      ,not#(gt(x,y))
                                      ,gt#(x,y)
                                      ,id#(x)
                                      ,id#(y))
             -->_1 plus#(s(x),s(y)) -> c_13(plus#(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y)))
                                           ,if#(gt(x,y),x,y)
                                           ,gt#(x,y)
                                           ,if#(not(gt(x,y)),id(x),id(y))
                                           ,not#(gt(x,y))
                                           ,gt#(x,y)
                                           ,id#(x)
                                           ,id#(y)):5
             -->_1 plus#(s(x),x) -> c_12(plus#(if(gt(x,x),id(x),id(x)),s(x))
                                        ,if#(gt(x,x),id(x),id(x))
                                        ,gt#(x,x)
                                        ,id#(x)
                                        ,id#(x)):4
             -->_6 gt#(s(x),s(y)) -> c_3(gt#(x,y)):2
             -->_3 gt#(s(x),s(y)) -> c_3(gt#(x,y)):2
          
        Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
          plus#(s(x),x) -> c_12(plus#(if(gt(x,x),id(x),id(x)),s(x)),gt#(x,x))
          plus#(s(x),s(y)) -> c_13(plus#(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y))),gt#(x,y),gt#(x,y))
* Step 8: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          double#(s(x)) -> c_2(double#(x))
          gt#(s(x),s(y)) -> c_3(gt#(x,y))
          minus#(s(x),s(y)) -> c_10(minus#(x,y))
          plus#(s(x),x) -> c_12(plus#(if(gt(x,x),id(x),id(x)),s(x)),gt#(x,x))
          plus#(s(x),s(y)) -> c_13(plus#(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y))),gt#(x,y),gt#(x,y))
      - Weak TRS:
          gt(s(x),s(y)) -> gt(x,y)
          gt(s(x),zero()) -> true()
          gt(zero(),y) -> false()
          id(x) -> x
          if(false(),x,y) -> y
          if(true(),x,y) -> x
          not(x) -> if(x,false(),true())
      - Signature:
          {double/1,gt/2,id/1,if/3,minus/2,not/1,plus/2,double#/1,gt#/2,id#/1,if#/3,minus#/2,not#/1,plus#/2} / {0/0
          ,false/0,s/1,true/0,zero/0,c_1/0,c_2/1,c_3/1,c_4/0,c_5/0,c_6/0,c_7/0,c_8/0,c_9/0,c_10/1,c_11/1,c_12/2,c_13/3
          ,c_14/0}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {double#,gt#,id#,if#,minus#,not#
          ,plus#} and constructors {0,false,s,true,zero}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE