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