MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            double(0()) -> 0()
            double(s(x)) -> s(s(double(x)))
            if(false(),x,y,z) -> loop(x,double(y),s(z))
            if(true(),x,y,z) -> z
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            log(0()) -> logError()
            log(s(x)) -> loop(s(x),s(0()),0())
            loop(x,s(y),z) -> if(le(x,s(y)),x,s(y),z)
        - Signature:
            {double/1,if/4,le/2,log/1,loop/3} / {0/0,false/0,logError/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {double,if,le,log,loop} and constructors {0,false,logError
            ,s,true}
    + 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))
          if#(false(),x,y,z) -> c_3(loop#(x,double(y),s(z)),double#(y))
          if#(true(),x,y,z) -> c_4()
          le#(0(),y) -> c_5()
          le#(s(x),0()) -> c_6()
          le#(s(x),s(y)) -> c_7(le#(x,y))
          log#(0()) -> c_8()
          log#(s(x)) -> c_9(loop#(s(x),s(0()),0()))
          loop#(x,s(y),z) -> c_10(if#(le(x,s(y)),x,s(y),z),le#(x,s(y)))
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            double#(0()) -> c_1()
            double#(s(x)) -> c_2(double#(x))
            if#(false(),x,y,z) -> c_3(loop#(x,double(y),s(z)),double#(y))
            if#(true(),x,y,z) -> c_4()
            le#(0(),y) -> c_5()
            le#(s(x),0()) -> c_6()
            le#(s(x),s(y)) -> c_7(le#(x,y))
            log#(0()) -> c_8()
            log#(s(x)) -> c_9(loop#(s(x),s(0()),0()))
            loop#(x,s(y),z) -> c_10(if#(le(x,s(y)),x,s(y),z),le#(x,s(y)))
        - Weak TRS:
            double(0()) -> 0()
            double(s(x)) -> s(s(double(x)))
            if(false(),x,y,z) -> loop(x,double(y),s(z))
            if(true(),x,y,z) -> z
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            log(0()) -> logError()
            log(s(x)) -> loop(s(x),s(0()),0())
            loop(x,s(y),z) -> if(le(x,s(y)),x,s(y),z)
        - Signature:
            {double/1,if/4,le/2,log/1,loop/3,double#/1,if#/4,le#/2,log#/1,loop#/3} / {0/0,false/0,logError/0,s/1,true/0
            ,c_1/0,c_2/1,c_3/2,c_4/0,c_5/0,c_6/0,c_7/1,c_8/0,c_9/1,c_10/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {double#,if#,le#,log#,loop#} and constructors {0,false
            ,logError,s,true}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          double(0()) -> 0()
          double(s(x)) -> s(s(double(x)))
          le(0(),y) -> true()
          le(s(x),0()) -> false()
          le(s(x),s(y)) -> le(x,y)
          double#(0()) -> c_1()
          double#(s(x)) -> c_2(double#(x))
          if#(false(),x,y,z) -> c_3(loop#(x,double(y),s(z)),double#(y))
          if#(true(),x,y,z) -> c_4()
          le#(0(),y) -> c_5()
          le#(s(x),0()) -> c_6()
          le#(s(x),s(y)) -> c_7(le#(x,y))
          log#(0()) -> c_8()
          log#(s(x)) -> c_9(loop#(s(x),s(0()),0()))
          loop#(x,s(y),z) -> c_10(if#(le(x,s(y)),x,s(y),z),le#(x,s(y)))
* Step 3: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            double#(0()) -> c_1()
            double#(s(x)) -> c_2(double#(x))
            if#(false(),x,y,z) -> c_3(loop#(x,double(y),s(z)),double#(y))
            if#(true(),x,y,z) -> c_4()
            le#(0(),y) -> c_5()
            le#(s(x),0()) -> c_6()
            le#(s(x),s(y)) -> c_7(le#(x,y))
            log#(0()) -> c_8()
            log#(s(x)) -> c_9(loop#(s(x),s(0()),0()))
            loop#(x,s(y),z) -> c_10(if#(le(x,s(y)),x,s(y),z),le#(x,s(y)))
        - Weak TRS:
            double(0()) -> 0()
            double(s(x)) -> s(s(double(x)))
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
        - Signature:
            {double/1,if/4,le/2,log/1,loop/3,double#/1,if#/4,le#/2,log#/1,loop#/3} / {0/0,false/0,logError/0,s/1,true/0
            ,c_1/0,c_2/1,c_3/2,c_4/0,c_5/0,c_6/0,c_7/1,c_8/0,c_9/1,c_10/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {double#,if#,le#,log#,loop#} and constructors {0,false
            ,logError,s,true}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,4,5,6,8}
        by application of
          Pre({1,4,5,6,8}) = {2,3,7,10}.
        Here rules are labelled as follows:
          1: double#(0()) -> c_1()
          2: double#(s(x)) -> c_2(double#(x))
          3: if#(false(),x,y,z) -> c_3(loop#(x,double(y),s(z)),double#(y))
          4: if#(true(),x,y,z) -> c_4()
          5: le#(0(),y) -> c_5()
          6: le#(s(x),0()) -> c_6()
          7: le#(s(x),s(y)) -> c_7(le#(x,y))
          8: log#(0()) -> c_8()
          9: log#(s(x)) -> c_9(loop#(s(x),s(0()),0()))
          10: loop#(x,s(y),z) -> c_10(if#(le(x,s(y)),x,s(y),z),le#(x,s(y)))
* Step 4: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            double#(s(x)) -> c_2(double#(x))
            if#(false(),x,y,z) -> c_3(loop#(x,double(y),s(z)),double#(y))
            le#(s(x),s(y)) -> c_7(le#(x,y))
            log#(s(x)) -> c_9(loop#(s(x),s(0()),0()))
            loop#(x,s(y),z) -> c_10(if#(le(x,s(y)),x,s(y),z),le#(x,s(y)))
        - Weak DPs:
            double#(0()) -> c_1()
            if#(true(),x,y,z) -> c_4()
            le#(0(),y) -> c_5()
            le#(s(x),0()) -> c_6()
            log#(0()) -> c_8()
        - Weak TRS:
            double(0()) -> 0()
            double(s(x)) -> s(s(double(x)))
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
        - Signature:
            {double/1,if/4,le/2,log/1,loop/3,double#/1,if#/4,le#/2,log#/1,loop#/3} / {0/0,false/0,logError/0,s/1,true/0
            ,c_1/0,c_2/1,c_3/2,c_4/0,c_5/0,c_6/0,c_7/1,c_8/0,c_9/1,c_10/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {double#,if#,le#,log#,loop#} and constructors {0,false
            ,logError,s,true}
    + 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:if#(false(),x,y,z) -> c_3(loop#(x,double(y),s(z)),double#(y))
             -->_1 loop#(x,s(y),z) -> c_10(if#(le(x,s(y)),x,s(y),z),le#(x,s(y))):5
             -->_2 double#(0()) -> c_1():6
             -->_2 double#(s(x)) -> c_2(double#(x)):1
          
          3:S:le#(s(x),s(y)) -> c_7(le#(x,y))
             -->_1 le#(s(x),0()) -> c_6():9
             -->_1 le#(0(),y) -> c_5():8
             -->_1 le#(s(x),s(y)) -> c_7(le#(x,y)):3
          
          4:S:log#(s(x)) -> c_9(loop#(s(x),s(0()),0()))
             -->_1 loop#(x,s(y),z) -> c_10(if#(le(x,s(y)),x,s(y),z),le#(x,s(y))):5
          
          5:S:loop#(x,s(y),z) -> c_10(if#(le(x,s(y)),x,s(y),z),le#(x,s(y)))
             -->_2 le#(0(),y) -> c_5():8
             -->_1 if#(true(),x,y,z) -> c_4():7
             -->_2 le#(s(x),s(y)) -> c_7(le#(x,y)):3
             -->_1 if#(false(),x,y,z) -> c_3(loop#(x,double(y),s(z)),double#(y)):2
          
          6:W:double#(0()) -> c_1()
             
          
          7:W:if#(true(),x,y,z) -> c_4()
             
          
          8:W:le#(0(),y) -> c_5()
             
          
          9:W:le#(s(x),0()) -> c_6()
             
          
          10:W:log#(0()) -> c_8()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          10: log#(0()) -> c_8()
          9: le#(s(x),0()) -> c_6()
          7: if#(true(),x,y,z) -> c_4()
          8: le#(0(),y) -> c_5()
          6: double#(0()) -> c_1()
* Step 5: RemoveHeads MAYBE
    + Considered Problem:
        - Strict DPs:
            double#(s(x)) -> c_2(double#(x))
            if#(false(),x,y,z) -> c_3(loop#(x,double(y),s(z)),double#(y))
            le#(s(x),s(y)) -> c_7(le#(x,y))
            log#(s(x)) -> c_9(loop#(s(x),s(0()),0()))
            loop#(x,s(y),z) -> c_10(if#(le(x,s(y)),x,s(y),z),le#(x,s(y)))
        - Weak TRS:
            double(0()) -> 0()
            double(s(x)) -> s(s(double(x)))
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
        - Signature:
            {double/1,if/4,le/2,log/1,loop/3,double#/1,if#/4,le#/2,log#/1,loop#/3} / {0/0,false/0,logError/0,s/1,true/0
            ,c_1/0,c_2/1,c_3/2,c_4/0,c_5/0,c_6/0,c_7/1,c_8/0,c_9/1,c_10/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {double#,if#,le#,log#,loop#} and constructors {0,false
            ,logError,s,true}
    + Applied Processor:
        RemoveHeads
    + 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:if#(false(),x,y,z) -> c_3(loop#(x,double(y),s(z)),double#(y))
           -->_1 loop#(x,s(y),z) -> c_10(if#(le(x,s(y)),x,s(y),z),le#(x,s(y))):5
           -->_2 double#(s(x)) -> c_2(double#(x)):1
        
        3:S:le#(s(x),s(y)) -> c_7(le#(x,y))
           -->_1 le#(s(x),s(y)) -> c_7(le#(x,y)):3
        
        4:S:log#(s(x)) -> c_9(loop#(s(x),s(0()),0()))
           -->_1 loop#(x,s(y),z) -> c_10(if#(le(x,s(y)),x,s(y),z),le#(x,s(y))):5
        
        5:S:loop#(x,s(y),z) -> c_10(if#(le(x,s(y)),x,s(y),z),le#(x,s(y)))
           -->_2 le#(s(x),s(y)) -> c_7(le#(x,y)):3
           -->_1 if#(false(),x,y,z) -> c_3(loop#(x,double(y),s(z)),double#(y)):2
        
        
        Following roots of the dependency graph are removed, as the considered set of starting terms is closed under reduction with respect to these rules (modulo compound contexts).
        
        [(4,log#(s(x)) -> c_9(loop#(s(x),s(0()),0())))]
* Step 6: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          double#(s(x)) -> c_2(double#(x))
          if#(false(),x,y,z) -> c_3(loop#(x,double(y),s(z)),double#(y))
          le#(s(x),s(y)) -> c_7(le#(x,y))
          loop#(x,s(y),z) -> c_10(if#(le(x,s(y)),x,s(y),z),le#(x,s(y)))
      - Weak TRS:
          double(0()) -> 0()
          double(s(x)) -> s(s(double(x)))
          le(0(),y) -> true()
          le(s(x),0()) -> false()
          le(s(x),s(y)) -> le(x,y)
      - Signature:
          {double/1,if/4,le/2,log/1,loop/3,double#/1,if#/4,le#/2,log#/1,loop#/3} / {0/0,false/0,logError/0,s/1,true/0
          ,c_1/0,c_2/1,c_3/2,c_4/0,c_5/0,c_6/0,c_7/1,c_8/0,c_9/1,c_10/2}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {double#,if#,le#,log#,loop#} and constructors {0,false
          ,logError,s,true}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE