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