MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            half(0()) -> 0()
            half(s(0())) -> 0()
            half(s(s(x))) -> s(half(x))
            help(x,y) -> ifb(lt(y,x),x,y)
            ifa(false(),x) -> logZeroError()
            ifa(true(),x) -> help(x,1())
            ifb(false(),x,y) -> y
            ifb(true(),x,y) -> help(half(x),s(y))
            logarithm(x) -> ifa(lt(0(),x),x)
            lt(x,0()) -> false()
            lt(0(),s(x)) -> true()
            lt(s(x),s(y)) -> lt(x,y)
        - Signature:
            {half/1,help/2,ifa/2,ifb/3,logarithm/1,lt/2} / {0/0,1/0,false/0,logZeroError/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {half,help,ifa,ifb,logarithm,lt} and constructors {0,1
            ,false,logZeroError,s,true}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          half#(0()) -> c_1()
          half#(s(0())) -> c_2()
          half#(s(s(x))) -> c_3(half#(x))
          help#(x,y) -> c_4(ifb#(lt(y,x),x,y),lt#(y,x))
          ifa#(false(),x) -> c_5()
          ifa#(true(),x) -> c_6(help#(x,1()))
          ifb#(false(),x,y) -> c_7()
          ifb#(true(),x,y) -> c_8(help#(half(x),s(y)),half#(x))
          logarithm#(x) -> c_9(ifa#(lt(0(),x),x),lt#(0(),x))
          lt#(x,0()) -> c_10()
          lt#(0(),s(x)) -> c_11()
          lt#(s(x),s(y)) -> c_12(lt#(x,y))
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            half#(0()) -> c_1()
            half#(s(0())) -> c_2()
            half#(s(s(x))) -> c_3(half#(x))
            help#(x,y) -> c_4(ifb#(lt(y,x),x,y),lt#(y,x))
            ifa#(false(),x) -> c_5()
            ifa#(true(),x) -> c_6(help#(x,1()))
            ifb#(false(),x,y) -> c_7()
            ifb#(true(),x,y) -> c_8(help#(half(x),s(y)),half#(x))
            logarithm#(x) -> c_9(ifa#(lt(0(),x),x),lt#(0(),x))
            lt#(x,0()) -> c_10()
            lt#(0(),s(x)) -> c_11()
            lt#(s(x),s(y)) -> c_12(lt#(x,y))
        - Weak TRS:
            half(0()) -> 0()
            half(s(0())) -> 0()
            half(s(s(x))) -> s(half(x))
            help(x,y) -> ifb(lt(y,x),x,y)
            ifa(false(),x) -> logZeroError()
            ifa(true(),x) -> help(x,1())
            ifb(false(),x,y) -> y
            ifb(true(),x,y) -> help(half(x),s(y))
            logarithm(x) -> ifa(lt(0(),x),x)
            lt(x,0()) -> false()
            lt(0(),s(x)) -> true()
            lt(s(x),s(y)) -> lt(x,y)
        - Signature:
            {half/1,help/2,ifa/2,ifb/3,logarithm/1,lt/2,half#/1,help#/2,ifa#/2,ifb#/3,logarithm#/1,lt#/2} / {0/0,1/0
            ,false/0,logZeroError/0,s/1,true/0,c_1/0,c_2/0,c_3/1,c_4/2,c_5/0,c_6/1,c_7/0,c_8/2,c_9/2,c_10/0,c_11/0
            ,c_12/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {half#,help#,ifa#,ifb#,logarithm#,lt#} and constructors {0
            ,1,false,logZeroError,s,true}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          half(0()) -> 0()
          half(s(0())) -> 0()
          half(s(s(x))) -> s(half(x))
          lt(x,0()) -> false()
          lt(0(),s(x)) -> true()
          lt(s(x),s(y)) -> lt(x,y)
          half#(0()) -> c_1()
          half#(s(0())) -> c_2()
          half#(s(s(x))) -> c_3(half#(x))
          help#(x,y) -> c_4(ifb#(lt(y,x),x,y),lt#(y,x))
          ifa#(false(),x) -> c_5()
          ifa#(true(),x) -> c_6(help#(x,1()))
          ifb#(false(),x,y) -> c_7()
          ifb#(true(),x,y) -> c_8(help#(half(x),s(y)),half#(x))
          logarithm#(x) -> c_9(ifa#(lt(0(),x),x),lt#(0(),x))
          lt#(x,0()) -> c_10()
          lt#(0(),s(x)) -> c_11()
          lt#(s(x),s(y)) -> c_12(lt#(x,y))
* Step 3: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            half#(0()) -> c_1()
            half#(s(0())) -> c_2()
            half#(s(s(x))) -> c_3(half#(x))
            help#(x,y) -> c_4(ifb#(lt(y,x),x,y),lt#(y,x))
            ifa#(false(),x) -> c_5()
            ifa#(true(),x) -> c_6(help#(x,1()))
            ifb#(false(),x,y) -> c_7()
            ifb#(true(),x,y) -> c_8(help#(half(x),s(y)),half#(x))
            logarithm#(x) -> c_9(ifa#(lt(0(),x),x),lt#(0(),x))
            lt#(x,0()) -> c_10()
            lt#(0(),s(x)) -> c_11()
            lt#(s(x),s(y)) -> c_12(lt#(x,y))
        - Weak TRS:
            half(0()) -> 0()
            half(s(0())) -> 0()
            half(s(s(x))) -> s(half(x))
            lt(x,0()) -> false()
            lt(0(),s(x)) -> true()
            lt(s(x),s(y)) -> lt(x,y)
        - Signature:
            {half/1,help/2,ifa/2,ifb/3,logarithm/1,lt/2,half#/1,help#/2,ifa#/2,ifb#/3,logarithm#/1,lt#/2} / {0/0,1/0
            ,false/0,logZeroError/0,s/1,true/0,c_1/0,c_2/0,c_3/1,c_4/2,c_5/0,c_6/1,c_7/0,c_8/2,c_9/2,c_10/0,c_11/0
            ,c_12/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {half#,help#,ifa#,ifb#,logarithm#,lt#} and constructors {0
            ,1,false,logZeroError,s,true}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,2,5,7,10,11}
        by application of
          Pre({1,2,5,7,10,11}) = {3,4,8,9,12}.
        Here rules are labelled as follows:
          1: half#(0()) -> c_1()
          2: half#(s(0())) -> c_2()
          3: half#(s(s(x))) -> c_3(half#(x))
          4: help#(x,y) -> c_4(ifb#(lt(y,x),x,y),lt#(y,x))
          5: ifa#(false(),x) -> c_5()
          6: ifa#(true(),x) -> c_6(help#(x,1()))
          7: ifb#(false(),x,y) -> c_7()
          8: ifb#(true(),x,y) -> c_8(help#(half(x),s(y)),half#(x))
          9: logarithm#(x) -> c_9(ifa#(lt(0(),x),x),lt#(0(),x))
          10: lt#(x,0()) -> c_10()
          11: lt#(0(),s(x)) -> c_11()
          12: lt#(s(x),s(y)) -> c_12(lt#(x,y))
* Step 4: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            half#(s(s(x))) -> c_3(half#(x))
            help#(x,y) -> c_4(ifb#(lt(y,x),x,y),lt#(y,x))
            ifa#(true(),x) -> c_6(help#(x,1()))
            ifb#(true(),x,y) -> c_8(help#(half(x),s(y)),half#(x))
            logarithm#(x) -> c_9(ifa#(lt(0(),x),x),lt#(0(),x))
            lt#(s(x),s(y)) -> c_12(lt#(x,y))
        - Weak DPs:
            half#(0()) -> c_1()
            half#(s(0())) -> c_2()
            ifa#(false(),x) -> c_5()
            ifb#(false(),x,y) -> c_7()
            lt#(x,0()) -> c_10()
            lt#(0(),s(x)) -> c_11()
        - Weak TRS:
            half(0()) -> 0()
            half(s(0())) -> 0()
            half(s(s(x))) -> s(half(x))
            lt(x,0()) -> false()
            lt(0(),s(x)) -> true()
            lt(s(x),s(y)) -> lt(x,y)
        - Signature:
            {half/1,help/2,ifa/2,ifb/3,logarithm/1,lt/2,half#/1,help#/2,ifa#/2,ifb#/3,logarithm#/1,lt#/2} / {0/0,1/0
            ,false/0,logZeroError/0,s/1,true/0,c_1/0,c_2/0,c_3/1,c_4/2,c_5/0,c_6/1,c_7/0,c_8/2,c_9/2,c_10/0,c_11/0
            ,c_12/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {half#,help#,ifa#,ifb#,logarithm#,lt#} and constructors {0
            ,1,false,logZeroError,s,true}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:half#(s(s(x))) -> c_3(half#(x))
             -->_1 half#(s(0())) -> c_2():8
             -->_1 half#(0()) -> c_1():7
             -->_1 half#(s(s(x))) -> c_3(half#(x)):1
          
          2:S:help#(x,y) -> c_4(ifb#(lt(y,x),x,y),lt#(y,x))
             -->_2 lt#(s(x),s(y)) -> c_12(lt#(x,y)):6
             -->_1 ifb#(true(),x,y) -> c_8(help#(half(x),s(y)),half#(x)):4
             -->_2 lt#(0(),s(x)) -> c_11():12
             -->_2 lt#(x,0()) -> c_10():11
             -->_1 ifb#(false(),x,y) -> c_7():10
          
          3:S:ifa#(true(),x) -> c_6(help#(x,1()))
             -->_1 help#(x,y) -> c_4(ifb#(lt(y,x),x,y),lt#(y,x)):2
          
          4:S:ifb#(true(),x,y) -> c_8(help#(half(x),s(y)),half#(x))
             -->_2 half#(s(0())) -> c_2():8
             -->_2 half#(0()) -> c_1():7
             -->_1 help#(x,y) -> c_4(ifb#(lt(y,x),x,y),lt#(y,x)):2
             -->_2 half#(s(s(x))) -> c_3(half#(x)):1
          
          5:S:logarithm#(x) -> c_9(ifa#(lt(0(),x),x),lt#(0(),x))
             -->_2 lt#(0(),s(x)) -> c_11():12
             -->_2 lt#(x,0()) -> c_10():11
             -->_1 ifa#(false(),x) -> c_5():9
             -->_1 ifa#(true(),x) -> c_6(help#(x,1())):3
          
          6:S:lt#(s(x),s(y)) -> c_12(lt#(x,y))
             -->_1 lt#(0(),s(x)) -> c_11():12
             -->_1 lt#(x,0()) -> c_10():11
             -->_1 lt#(s(x),s(y)) -> c_12(lt#(x,y)):6
          
          7:W:half#(0()) -> c_1()
             
          
          8:W:half#(s(0())) -> c_2()
             
          
          9:W:ifa#(false(),x) -> c_5()
             
          
          10:W:ifb#(false(),x,y) -> c_7()
             
          
          11:W:lt#(x,0()) -> c_10()
             
          
          12:W:lt#(0(),s(x)) -> c_11()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          9: ifa#(false(),x) -> c_5()
          10: ifb#(false(),x,y) -> c_7()
          11: lt#(x,0()) -> c_10()
          12: lt#(0(),s(x)) -> c_11()
          7: half#(0()) -> c_1()
          8: half#(s(0())) -> c_2()
* Step 5: SimplifyRHS MAYBE
    + Considered Problem:
        - Strict DPs:
            half#(s(s(x))) -> c_3(half#(x))
            help#(x,y) -> c_4(ifb#(lt(y,x),x,y),lt#(y,x))
            ifa#(true(),x) -> c_6(help#(x,1()))
            ifb#(true(),x,y) -> c_8(help#(half(x),s(y)),half#(x))
            logarithm#(x) -> c_9(ifa#(lt(0(),x),x),lt#(0(),x))
            lt#(s(x),s(y)) -> c_12(lt#(x,y))
        - Weak TRS:
            half(0()) -> 0()
            half(s(0())) -> 0()
            half(s(s(x))) -> s(half(x))
            lt(x,0()) -> false()
            lt(0(),s(x)) -> true()
            lt(s(x),s(y)) -> lt(x,y)
        - Signature:
            {half/1,help/2,ifa/2,ifb/3,logarithm/1,lt/2,half#/1,help#/2,ifa#/2,ifb#/3,logarithm#/1,lt#/2} / {0/0,1/0
            ,false/0,logZeroError/0,s/1,true/0,c_1/0,c_2/0,c_3/1,c_4/2,c_5/0,c_6/1,c_7/0,c_8/2,c_9/2,c_10/0,c_11/0
            ,c_12/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {half#,help#,ifa#,ifb#,logarithm#,lt#} and constructors {0
            ,1,false,logZeroError,s,true}
    + Applied Processor:
        SimplifyRHS
    + Details:
        Consider the dependency graph
          1:S:half#(s(s(x))) -> c_3(half#(x))
             -->_1 half#(s(s(x))) -> c_3(half#(x)):1
          
          2:S:help#(x,y) -> c_4(ifb#(lt(y,x),x,y),lt#(y,x))
             -->_2 lt#(s(x),s(y)) -> c_12(lt#(x,y)):6
             -->_1 ifb#(true(),x,y) -> c_8(help#(half(x),s(y)),half#(x)):4
          
          3:S:ifa#(true(),x) -> c_6(help#(x,1()))
             -->_1 help#(x,y) -> c_4(ifb#(lt(y,x),x,y),lt#(y,x)):2
          
          4:S:ifb#(true(),x,y) -> c_8(help#(half(x),s(y)),half#(x))
             -->_1 help#(x,y) -> c_4(ifb#(lt(y,x),x,y),lt#(y,x)):2
             -->_2 half#(s(s(x))) -> c_3(half#(x)):1
          
          5:S:logarithm#(x) -> c_9(ifa#(lt(0(),x),x),lt#(0(),x))
             -->_1 ifa#(true(),x) -> c_6(help#(x,1())):3
          
          6:S:lt#(s(x),s(y)) -> c_12(lt#(x,y))
             -->_1 lt#(s(x),s(y)) -> c_12(lt#(x,y)):6
          
        Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
          logarithm#(x) -> c_9(ifa#(lt(0(),x),x))
* Step 6: NaturalMI MAYBE
    + Considered Problem:
        - Strict DPs:
            half#(s(s(x))) -> c_3(half#(x))
            help#(x,y) -> c_4(ifb#(lt(y,x),x,y),lt#(y,x))
            ifa#(true(),x) -> c_6(help#(x,1()))
            ifb#(true(),x,y) -> c_8(help#(half(x),s(y)),half#(x))
            logarithm#(x) -> c_9(ifa#(lt(0(),x),x))
            lt#(s(x),s(y)) -> c_12(lt#(x,y))
        - Weak TRS:
            half(0()) -> 0()
            half(s(0())) -> 0()
            half(s(s(x))) -> s(half(x))
            lt(x,0()) -> false()
            lt(0(),s(x)) -> true()
            lt(s(x),s(y)) -> lt(x,y)
        - Signature:
            {half/1,help/2,ifa/2,ifb/3,logarithm/1,lt/2,half#/1,help#/2,ifa#/2,ifb#/3,logarithm#/1,lt#/2} / {0/0,1/0
            ,false/0,logZeroError/0,s/1,true/0,c_1/0,c_2/0,c_3/1,c_4/2,c_5/0,c_6/1,c_7/0,c_8/2,c_9/1,c_10/0,c_11/0
            ,c_12/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {half#,help#,ifa#,ifb#,logarithm#,lt#} and constructors {0
            ,1,false,logZeroError,s,true}
    + Applied Processor:
        NaturalMI {miDimension = 1, miDegree = 0, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just any strict-rules}
    + Details:
        We apply a matrix interpretation of kind constructor based matrix interpretation (containing no more than 0 non-zero interpretation-entries in the diagonal of the component-wise maxima):
        The following argument positions are considered usable:
          uargs(c_3) = {1},
          uargs(c_4) = {1,2},
          uargs(c_6) = {1},
          uargs(c_8) = {1,2},
          uargs(c_9) = {1},
          uargs(c_12) = {1}
        
        Following symbols are considered usable:
          {half#,help#,ifa#,ifb#,logarithm#,lt#}
        TcT has computed the following interpretation:
                     p(0) = [1]                  
                     p(1) = [0]                  
                 p(false) = [8]                  
                  p(half) = [2]                  
                  p(help) = [1] x1 + [8] x2 + [4]
                   p(ifa) = [2] x1 + [1] x2 + [1]
                   p(ifb) = [1] x2 + [1] x3 + [1]
          p(logZeroError) = [0]                  
             p(logarithm) = [1] x1 + [1]         
                    p(lt) = [0]                  
                     p(s) = [0]                  
                  p(true) = [0]                  
                 p(half#) = [0]                  
                 p(help#) = [8] x2 + [10]        
                  p(ifa#) = [11]                 
                  p(ifb#) = [10]                 
            p(logarithm#) = [14]                 
                   p(lt#) = [0]                  
                   p(c_1) = [8]                  
                   p(c_2) = [1]                  
                   p(c_3) = [4] x1 + [0]         
                   p(c_4) = [1] x1 + [8] x2 + [0]
                   p(c_5) = [8]                  
                   p(c_6) = [1] x1 + [1]         
                   p(c_7) = [1]                  
                   p(c_8) = [1] x1 + [8] x2 + [0]
                   p(c_9) = [1] x1 + [2]         
                  p(c_10) = [1]                  
                  p(c_11) = [4]                  
                  p(c_12) = [8] x1 + [0]         
        
        Following rules are strictly oriented:
        logarithm#(x) = [14]                  
                      > [13]                  
                      = c_9(ifa#(lt(0(),x),x))
        
        
        Following rules are (at-least) weakly oriented:
          half#(s(s(x))) =  [0]                              
                         >= [0]                              
                         =  c_3(half#(x))                    
        
              help#(x,y) =  [8] y + [10]                     
                         >= [10]                             
                         =  c_4(ifb#(lt(y,x),x,y),lt#(y,x))  
        
          ifa#(true(),x) =  [11]                             
                         >= [11]                             
                         =  c_6(help#(x,1()))                
        
        ifb#(true(),x,y) =  [10]                             
                         >= [10]                             
                         =  c_8(help#(half(x),s(y)),half#(x))
        
          lt#(s(x),s(y)) =  [0]                              
                         >= [0]                              
                         =  c_12(lt#(x,y))                   
        
* Step 7: NaturalMI MAYBE
    + Considered Problem:
        - Strict DPs:
            half#(s(s(x))) -> c_3(half#(x))
            help#(x,y) -> c_4(ifb#(lt(y,x),x,y),lt#(y,x))
            ifa#(true(),x) -> c_6(help#(x,1()))
            ifb#(true(),x,y) -> c_8(help#(half(x),s(y)),half#(x))
            lt#(s(x),s(y)) -> c_12(lt#(x,y))
        - Weak DPs:
            logarithm#(x) -> c_9(ifa#(lt(0(),x),x))
        - Weak TRS:
            half(0()) -> 0()
            half(s(0())) -> 0()
            half(s(s(x))) -> s(half(x))
            lt(x,0()) -> false()
            lt(0(),s(x)) -> true()
            lt(s(x),s(y)) -> lt(x,y)
        - Signature:
            {half/1,help/2,ifa/2,ifb/3,logarithm/1,lt/2,half#/1,help#/2,ifa#/2,ifb#/3,logarithm#/1,lt#/2} / {0/0,1/0
            ,false/0,logZeroError/0,s/1,true/0,c_1/0,c_2/0,c_3/1,c_4/2,c_5/0,c_6/1,c_7/0,c_8/2,c_9/1,c_10/0,c_11/0
            ,c_12/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {half#,help#,ifa#,ifb#,logarithm#,lt#} and constructors {0
            ,1,false,logZeroError,s,true}
    + Applied Processor:
        NaturalMI {miDimension = 1, miDegree = 0, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just any strict-rules}
    + Details:
        We apply a matrix interpretation of kind constructor based matrix interpretation (containing no more than 0 non-zero interpretation-entries in the diagonal of the component-wise maxima):
        The following argument positions are considered usable:
          uargs(c_3) = {1},
          uargs(c_4) = {1,2},
          uargs(c_6) = {1},
          uargs(c_8) = {1,2},
          uargs(c_9) = {1},
          uargs(c_12) = {1}
        
        Following symbols are considered usable:
          {half#,help#,ifa#,ifb#,logarithm#,lt#}
        TcT has computed the following interpretation:
                     p(0) = [0]                  
                     p(1) = [1]                  
                 p(false) = [0]                  
                  p(half) = [7]                  
                  p(help) = [2] x1 + [1] x2 + [0]
                   p(ifa) = [1] x1 + [1] x2 + [8]
                   p(ifb) = [8] x1 + [1] x3 + [1]
          p(logZeroError) = [1]                  
             p(logarithm) = [0]                  
                    p(lt) = [8] x2 + [0]         
                     p(s) = [1]                  
                  p(true) = [0]                  
                 p(half#) = [0]                  
                 p(help#) = [0]                  
                  p(ifa#) = [15]                 
                  p(ifb#) = [0]                  
            p(logarithm#) = [15]                 
                   p(lt#) = [0]                  
                   p(c_1) = [0]                  
                   p(c_2) = [0]                  
                   p(c_3) = [4] x1 + [0]         
                   p(c_4) = [8] x1 + [4] x2 + [0]
                   p(c_5) = [4]                  
                   p(c_6) = [1] x1 + [11]        
                   p(c_7) = [1]                  
                   p(c_8) = [8] x1 + [2] x2 + [0]
                   p(c_9) = [1] x1 + [0]         
                  p(c_10) = [1]                  
                  p(c_11) = [2]                  
                  p(c_12) = [4] x1 + [0]         
        
        Following rules are strictly oriented:
        ifa#(true(),x) = [15]             
                       > [11]             
                       = c_6(help#(x,1()))
        
        
        Following rules are (at-least) weakly oriented:
          half#(s(s(x))) =  [0]                              
                         >= [0]                              
                         =  c_3(half#(x))                    
        
              help#(x,y) =  [0]                              
                         >= [0]                              
                         =  c_4(ifb#(lt(y,x),x,y),lt#(y,x))  
        
        ifb#(true(),x,y) =  [0]                              
                         >= [0]                              
                         =  c_8(help#(half(x),s(y)),half#(x))
        
           logarithm#(x) =  [15]                             
                         >= [15]                             
                         =  c_9(ifa#(lt(0(),x),x))           
        
          lt#(s(x),s(y)) =  [0]                              
                         >= [0]                              
                         =  c_12(lt#(x,y))                   
        
* Step 8: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          half#(s(s(x))) -> c_3(half#(x))
          help#(x,y) -> c_4(ifb#(lt(y,x),x,y),lt#(y,x))
          ifb#(true(),x,y) -> c_8(help#(half(x),s(y)),half#(x))
          lt#(s(x),s(y)) -> c_12(lt#(x,y))
      - Weak DPs:
          ifa#(true(),x) -> c_6(help#(x,1()))
          logarithm#(x) -> c_9(ifa#(lt(0(),x),x))
      - Weak TRS:
          half(0()) -> 0()
          half(s(0())) -> 0()
          half(s(s(x))) -> s(half(x))
          lt(x,0()) -> false()
          lt(0(),s(x)) -> true()
          lt(s(x),s(y)) -> lt(x,y)
      - Signature:
          {half/1,help/2,ifa/2,ifb/3,logarithm/1,lt/2,half#/1,help#/2,ifa#/2,ifb#/3,logarithm#/1,lt#/2} / {0/0,1/0
          ,false/0,logZeroError/0,s/1,true/0,c_1/0,c_2/0,c_3/1,c_4/2,c_5/0,c_6/1,c_7/0,c_8/2,c_9/1,c_10/0,c_11/0
          ,c_12/1}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {half#,help#,ifa#,ifb#,logarithm#,lt#} and constructors {0
          ,1,false,logZeroError,s,true}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE