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