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