MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            cond(false(),x,y) -> double(log(x,square(s(s(y)))))
            cond(true(),x,y) -> s(0())
            double(0()) -> 0()
            double(s(x)) -> s(s(double(x)))
            le(0(),v) -> true()
            le(s(u),0()) -> false()
            le(s(u),s(v)) -> le(u,v)
            log(x,s(s(y))) -> cond(le(x,s(s(y))),x,y)
            plus(n,0()) -> n
            plus(n,s(m)) -> s(plus(n,m))
            square(0()) -> 0()
            square(s(x)) -> s(plus(square(x),double(x)))
        - Signature:
            {cond/3,double/1,le/2,log/2,plus/2,square/1} / {0/0,false/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {cond,double,le,log,plus,square} and constructors {0,false
            ,s,true}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          cond#(false(),x,y) -> c_1(double#(log(x,square(s(s(y))))),log#(x,square(s(s(y)))),square#(s(s(y))))
          cond#(true(),x,y) -> c_2()
          double#(0()) -> c_3()
          double#(s(x)) -> c_4(double#(x))
          le#(0(),v) -> c_5()
          le#(s(u),0()) -> c_6()
          le#(s(u),s(v)) -> c_7(le#(u,v))
          log#(x,s(s(y))) -> c_8(cond#(le(x,s(s(y))),x,y),le#(x,s(s(y))))
          plus#(n,0()) -> c_9()
          plus#(n,s(m)) -> c_10(plus#(n,m))
          square#(0()) -> c_11()
          square#(s(x)) -> c_12(plus#(square(x),double(x)),square#(x),double#(x))
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            cond#(false(),x,y) -> c_1(double#(log(x,square(s(s(y))))),log#(x,square(s(s(y)))),square#(s(s(y))))
            cond#(true(),x,y) -> c_2()
            double#(0()) -> c_3()
            double#(s(x)) -> c_4(double#(x))
            le#(0(),v) -> c_5()
            le#(s(u),0()) -> c_6()
            le#(s(u),s(v)) -> c_7(le#(u,v))
            log#(x,s(s(y))) -> c_8(cond#(le(x,s(s(y))),x,y),le#(x,s(s(y))))
            plus#(n,0()) -> c_9()
            plus#(n,s(m)) -> c_10(plus#(n,m))
            square#(0()) -> c_11()
            square#(s(x)) -> c_12(plus#(square(x),double(x)),square#(x),double#(x))
        - Weak TRS:
            cond(false(),x,y) -> double(log(x,square(s(s(y)))))
            cond(true(),x,y) -> s(0())
            double(0()) -> 0()
            double(s(x)) -> s(s(double(x)))
            le(0(),v) -> true()
            le(s(u),0()) -> false()
            le(s(u),s(v)) -> le(u,v)
            log(x,s(s(y))) -> cond(le(x,s(s(y))),x,y)
            plus(n,0()) -> n
            plus(n,s(m)) -> s(plus(n,m))
            square(0()) -> 0()
            square(s(x)) -> s(plus(square(x),double(x)))
        - Signature:
            {cond/3,double/1,le/2,log/2,plus/2,square/1,cond#/3,double#/1,le#/2,log#/2,plus#/2,square#/1} / {0/0,false/0
            ,s/1,true/0,c_1/3,c_2/0,c_3/0,c_4/1,c_5/0,c_6/0,c_7/1,c_8/2,c_9/0,c_10/1,c_11/0,c_12/3}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {cond#,double#,le#,log#,plus#,square#} and constructors {0
            ,false,s,true}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {2,3,5,6,9,11}
        by application of
          Pre({2,3,5,6,9,11}) = {1,4,7,8,10,12}.
        Here rules are labelled as follows:
          1: cond#(false(),x,y) -> c_1(double#(log(x,square(s(s(y))))),log#(x,square(s(s(y)))),square#(s(s(y))))
          2: cond#(true(),x,y) -> c_2()
          3: double#(0()) -> c_3()
          4: double#(s(x)) -> c_4(double#(x))
          5: le#(0(),v) -> c_5()
          6: le#(s(u),0()) -> c_6()
          7: le#(s(u),s(v)) -> c_7(le#(u,v))
          8: log#(x,s(s(y))) -> c_8(cond#(le(x,s(s(y))),x,y),le#(x,s(s(y))))
          9: plus#(n,0()) -> c_9()
          10: plus#(n,s(m)) -> c_10(plus#(n,m))
          11: square#(0()) -> c_11()
          12: square#(s(x)) -> c_12(plus#(square(x),double(x)),square#(x),double#(x))
* Step 3: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            cond#(false(),x,y) -> c_1(double#(log(x,square(s(s(y))))),log#(x,square(s(s(y)))),square#(s(s(y))))
            double#(s(x)) -> c_4(double#(x))
            le#(s(u),s(v)) -> c_7(le#(u,v))
            log#(x,s(s(y))) -> c_8(cond#(le(x,s(s(y))),x,y),le#(x,s(s(y))))
            plus#(n,s(m)) -> c_10(plus#(n,m))
            square#(s(x)) -> c_12(plus#(square(x),double(x)),square#(x),double#(x))
        - Weak DPs:
            cond#(true(),x,y) -> c_2()
            double#(0()) -> c_3()
            le#(0(),v) -> c_5()
            le#(s(u),0()) -> c_6()
            plus#(n,0()) -> c_9()
            square#(0()) -> c_11()
        - Weak TRS:
            cond(false(),x,y) -> double(log(x,square(s(s(y)))))
            cond(true(),x,y) -> s(0())
            double(0()) -> 0()
            double(s(x)) -> s(s(double(x)))
            le(0(),v) -> true()
            le(s(u),0()) -> false()
            le(s(u),s(v)) -> le(u,v)
            log(x,s(s(y))) -> cond(le(x,s(s(y))),x,y)
            plus(n,0()) -> n
            plus(n,s(m)) -> s(plus(n,m))
            square(0()) -> 0()
            square(s(x)) -> s(plus(square(x),double(x)))
        - Signature:
            {cond/3,double/1,le/2,log/2,plus/2,square/1,cond#/3,double#/1,le#/2,log#/2,plus#/2,square#/1} / {0/0,false/0
            ,s/1,true/0,c_1/3,c_2/0,c_3/0,c_4/1,c_5/0,c_6/0,c_7/1,c_8/2,c_9/0,c_10/1,c_11/0,c_12/3}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {cond#,double#,le#,log#,plus#,square#} and constructors {0
            ,false,s,true}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:cond#(false(),x,y) -> c_1(double#(log(x,square(s(s(y))))),log#(x,square(s(s(y)))),square#(s(s(y))))
             -->_3 square#(s(x)) -> c_12(plus#(square(x),double(x)),square#(x),double#(x)):6
             -->_2 log#(x,s(s(y))) -> c_8(cond#(le(x,s(s(y))),x,y),le#(x,s(s(y)))):4
             -->_1 double#(s(x)) -> c_4(double#(x)):2
             -->_1 double#(0()) -> c_3():8
          
          2:S:double#(s(x)) -> c_4(double#(x))
             -->_1 double#(0()) -> c_3():8
             -->_1 double#(s(x)) -> c_4(double#(x)):2
          
          3:S:le#(s(u),s(v)) -> c_7(le#(u,v))
             -->_1 le#(s(u),0()) -> c_6():10
             -->_1 le#(0(),v) -> c_5():9
             -->_1 le#(s(u),s(v)) -> c_7(le#(u,v)):3
          
          4:S:log#(x,s(s(y))) -> c_8(cond#(le(x,s(s(y))),x,y),le#(x,s(s(y))))
             -->_2 le#(0(),v) -> c_5():9
             -->_1 cond#(true(),x,y) -> c_2():7
             -->_2 le#(s(u),s(v)) -> c_7(le#(u,v)):3
             -->_1 cond#(false(),x,y) -> c_1(double#(log(x,square(s(s(y))))),log#(x,square(s(s(y)))),square#(s(s(y)))):1
          
          5:S:plus#(n,s(m)) -> c_10(plus#(n,m))
             -->_1 plus#(n,0()) -> c_9():11
             -->_1 plus#(n,s(m)) -> c_10(plus#(n,m)):5
          
          6:S:square#(s(x)) -> c_12(plus#(square(x),double(x)),square#(x),double#(x))
             -->_2 square#(0()) -> c_11():12
             -->_1 plus#(n,0()) -> c_9():11
             -->_3 double#(0()) -> c_3():8
             -->_2 square#(s(x)) -> c_12(plus#(square(x),double(x)),square#(x),double#(x)):6
             -->_1 plus#(n,s(m)) -> c_10(plus#(n,m)):5
             -->_3 double#(s(x)) -> c_4(double#(x)):2
          
          7:W:cond#(true(),x,y) -> c_2()
             
          
          8:W:double#(0()) -> c_3()
             
          
          9:W:le#(0(),v) -> c_5()
             
          
          10:W:le#(s(u),0()) -> c_6()
             
          
          11:W:plus#(n,0()) -> c_9()
             
          
          12:W:square#(0()) -> c_11()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          10: le#(s(u),0()) -> c_6()
          7: cond#(true(),x,y) -> c_2()
          9: le#(0(),v) -> c_5()
          8: double#(0()) -> c_3()
          11: plus#(n,0()) -> c_9()
          12: square#(0()) -> c_11()
* Step 4: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          cond#(false(),x,y) -> c_1(double#(log(x,square(s(s(y))))),log#(x,square(s(s(y)))),square#(s(s(y))))
          double#(s(x)) -> c_4(double#(x))
          le#(s(u),s(v)) -> c_7(le#(u,v))
          log#(x,s(s(y))) -> c_8(cond#(le(x,s(s(y))),x,y),le#(x,s(s(y))))
          plus#(n,s(m)) -> c_10(plus#(n,m))
          square#(s(x)) -> c_12(plus#(square(x),double(x)),square#(x),double#(x))
      - Weak TRS:
          cond(false(),x,y) -> double(log(x,square(s(s(y)))))
          cond(true(),x,y) -> s(0())
          double(0()) -> 0()
          double(s(x)) -> s(s(double(x)))
          le(0(),v) -> true()
          le(s(u),0()) -> false()
          le(s(u),s(v)) -> le(u,v)
          log(x,s(s(y))) -> cond(le(x,s(s(y))),x,y)
          plus(n,0()) -> n
          plus(n,s(m)) -> s(plus(n,m))
          square(0()) -> 0()
          square(s(x)) -> s(plus(square(x),double(x)))
      - Signature:
          {cond/3,double/1,le/2,log/2,plus/2,square/1,cond#/3,double#/1,le#/2,log#/2,plus#/2,square#/1} / {0/0,false/0
          ,s/1,true/0,c_1/3,c_2/0,c_3/0,c_4/1,c_5/0,c_6/0,c_7/1,c_8/2,c_9/0,c_10/1,c_11/0,c_12/3}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {cond#,double#,le#,log#,plus#,square#} and constructors {0
          ,false,s,true}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE