MAYBE
* Step 1: InnermostRuleRemoval MAYBE
    + Considered Problem:
        - Strict TRS:
            cons(x,y) -> y
            cons(x,cons(y,s(z))) -> cons(y,x)
            cons(cons(x,z),s(y)) -> transform(x)
            gcd(s(x),s(y)) -> gcd(minus(max(x,y),min(x,transform(y))),s(min(x,y)))
            max(x,0()) -> x
            max(0(),y) -> y
            max(s(x),s(y)) -> s(max(x,y))
            min(x,0()) -> 0()
            min(0(),y) -> 0()
            min(s(x),s(y)) -> s(min(x,y))
            minus(x,0()) -> x
            minus(s(x),s(y)) -> s(minus(x,y))
            transform(x) -> s(s(x))
            transform(cons(x,y)) -> y
            transform(cons(x,y)) -> cons(cons(x,x),x)
            transform(s(x)) -> s(s(transform(x)))
        - Signature:
            {cons/2,gcd/2,max/2,min/2,minus/2,transform/1} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {cons,gcd,max,min,minus,transform} and constructors {0,s}
    + Applied Processor:
        InnermostRuleRemoval
    + Details:
        Arguments of following rules are not normal-forms.
          cons(x,cons(y,s(z))) -> cons(y,x)
          cons(cons(x,z),s(y)) -> transform(x)
          transform(cons(x,y)) -> y
          transform(cons(x,y)) -> cons(cons(x,x),x)
        All above mentioned rules can be savely removed.
* Step 2: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            cons(x,y) -> y
            gcd(s(x),s(y)) -> gcd(minus(max(x,y),min(x,transform(y))),s(min(x,y)))
            max(x,0()) -> x
            max(0(),y) -> y
            max(s(x),s(y)) -> s(max(x,y))
            min(x,0()) -> 0()
            min(0(),y) -> 0()
            min(s(x),s(y)) -> s(min(x,y))
            minus(x,0()) -> x
            minus(s(x),s(y)) -> s(minus(x,y))
            transform(x) -> s(s(x))
            transform(s(x)) -> s(s(transform(x)))
        - Signature:
            {cons/2,gcd/2,max/2,min/2,minus/2,transform/1} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {cons,gcd,max,min,minus,transform} and constructors {0,s}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          cons#(x,y) -> c_1()
          gcd#(s(x),s(y)) -> c_2(gcd#(minus(max(x,y),min(x,transform(y))),s(min(x,y)))
                                ,minus#(max(x,y),min(x,transform(y)))
                                ,max#(x,y)
                                ,min#(x,transform(y))
                                ,transform#(y)
                                ,min#(x,y))
          max#(x,0()) -> c_3()
          max#(0(),y) -> c_4()
          max#(s(x),s(y)) -> c_5(max#(x,y))
          min#(x,0()) -> c_6()
          min#(0(),y) -> c_7()
          min#(s(x),s(y)) -> c_8(min#(x,y))
          minus#(x,0()) -> c_9()
          minus#(s(x),s(y)) -> c_10(minus#(x,y))
          transform#(x) -> c_11()
          transform#(s(x)) -> c_12(transform#(x))
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 3: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            cons#(x,y) -> c_1()
            gcd#(s(x),s(y)) -> c_2(gcd#(minus(max(x,y),min(x,transform(y))),s(min(x,y)))
                                  ,minus#(max(x,y),min(x,transform(y)))
                                  ,max#(x,y)
                                  ,min#(x,transform(y))
                                  ,transform#(y)
                                  ,min#(x,y))
            max#(x,0()) -> c_3()
            max#(0(),y) -> c_4()
            max#(s(x),s(y)) -> c_5(max#(x,y))
            min#(x,0()) -> c_6()
            min#(0(),y) -> c_7()
            min#(s(x),s(y)) -> c_8(min#(x,y))
            minus#(x,0()) -> c_9()
            minus#(s(x),s(y)) -> c_10(minus#(x,y))
            transform#(x) -> c_11()
            transform#(s(x)) -> c_12(transform#(x))
        - Weak TRS:
            cons(x,y) -> y
            gcd(s(x),s(y)) -> gcd(minus(max(x,y),min(x,transform(y))),s(min(x,y)))
            max(x,0()) -> x
            max(0(),y) -> y
            max(s(x),s(y)) -> s(max(x,y))
            min(x,0()) -> 0()
            min(0(),y) -> 0()
            min(s(x),s(y)) -> s(min(x,y))
            minus(x,0()) -> x
            minus(s(x),s(y)) -> s(minus(x,y))
            transform(x) -> s(s(x))
            transform(s(x)) -> s(s(transform(x)))
        - Signature:
            {cons/2,gcd/2,max/2,min/2,minus/2,transform/1,cons#/2,gcd#/2,max#/2,min#/2,minus#/2,transform#/1} / {0/0,s/1
            ,c_1/0,c_2/6,c_3/0,c_4/0,c_5/1,c_6/0,c_7/0,c_8/1,c_9/0,c_10/1,c_11/0,c_12/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {cons#,gcd#,max#,min#,minus#
            ,transform#} and constructors {0,s}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          max(x,0()) -> x
          max(0(),y) -> y
          max(s(x),s(y)) -> s(max(x,y))
          min(x,0()) -> 0()
          min(0(),y) -> 0()
          min(s(x),s(y)) -> s(min(x,y))
          minus(x,0()) -> x
          minus(s(x),s(y)) -> s(minus(x,y))
          transform(x) -> s(s(x))
          transform(s(x)) -> s(s(transform(x)))
          cons#(x,y) -> c_1()
          gcd#(s(x),s(y)) -> c_2(gcd#(minus(max(x,y),min(x,transform(y))),s(min(x,y)))
                                ,minus#(max(x,y),min(x,transform(y)))
                                ,max#(x,y)
                                ,min#(x,transform(y))
                                ,transform#(y)
                                ,min#(x,y))
          max#(x,0()) -> c_3()
          max#(0(),y) -> c_4()
          max#(s(x),s(y)) -> c_5(max#(x,y))
          min#(x,0()) -> c_6()
          min#(0(),y) -> c_7()
          min#(s(x),s(y)) -> c_8(min#(x,y))
          minus#(x,0()) -> c_9()
          minus#(s(x),s(y)) -> c_10(minus#(x,y))
          transform#(x) -> c_11()
          transform#(s(x)) -> c_12(transform#(x))
* Step 4: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            cons#(x,y) -> c_1()
            gcd#(s(x),s(y)) -> c_2(gcd#(minus(max(x,y),min(x,transform(y))),s(min(x,y)))
                                  ,minus#(max(x,y),min(x,transform(y)))
                                  ,max#(x,y)
                                  ,min#(x,transform(y))
                                  ,transform#(y)
                                  ,min#(x,y))
            max#(x,0()) -> c_3()
            max#(0(),y) -> c_4()
            max#(s(x),s(y)) -> c_5(max#(x,y))
            min#(x,0()) -> c_6()
            min#(0(),y) -> c_7()
            min#(s(x),s(y)) -> c_8(min#(x,y))
            minus#(x,0()) -> c_9()
            minus#(s(x),s(y)) -> c_10(minus#(x,y))
            transform#(x) -> c_11()
            transform#(s(x)) -> c_12(transform#(x))
        - Weak TRS:
            max(x,0()) -> x
            max(0(),y) -> y
            max(s(x),s(y)) -> s(max(x,y))
            min(x,0()) -> 0()
            min(0(),y) -> 0()
            min(s(x),s(y)) -> s(min(x,y))
            minus(x,0()) -> x
            minus(s(x),s(y)) -> s(minus(x,y))
            transform(x) -> s(s(x))
            transform(s(x)) -> s(s(transform(x)))
        - Signature:
            {cons/2,gcd/2,max/2,min/2,minus/2,transform/1,cons#/2,gcd#/2,max#/2,min#/2,minus#/2,transform#/1} / {0/0,s/1
            ,c_1/0,c_2/6,c_3/0,c_4/0,c_5/1,c_6/0,c_7/0,c_8/1,c_9/0,c_10/1,c_11/0,c_12/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {cons#,gcd#,max#,min#,minus#
            ,transform#} and constructors {0,s}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,3,4,6,7,9,11}
        by application of
          Pre({1,3,4,6,7,9,11}) = {2,5,8,10,12}.
        Here rules are labelled as follows:
          1: cons#(x,y) -> c_1()
          2: gcd#(s(x),s(y)) -> c_2(gcd#(minus(max(x,y),min(x,transform(y))),s(min(x,y)))
                                   ,minus#(max(x,y),min(x,transform(y)))
                                   ,max#(x,y)
                                   ,min#(x,transform(y))
                                   ,transform#(y)
                                   ,min#(x,y))
          3: max#(x,0()) -> c_3()
          4: max#(0(),y) -> c_4()
          5: max#(s(x),s(y)) -> c_5(max#(x,y))
          6: min#(x,0()) -> c_6()
          7: min#(0(),y) -> c_7()
          8: min#(s(x),s(y)) -> c_8(min#(x,y))
          9: minus#(x,0()) -> c_9()
          10: minus#(s(x),s(y)) -> c_10(minus#(x,y))
          11: transform#(x) -> c_11()
          12: transform#(s(x)) -> c_12(transform#(x))
* Step 5: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            gcd#(s(x),s(y)) -> c_2(gcd#(minus(max(x,y),min(x,transform(y))),s(min(x,y)))
                                  ,minus#(max(x,y),min(x,transform(y)))
                                  ,max#(x,y)
                                  ,min#(x,transform(y))
                                  ,transform#(y)
                                  ,min#(x,y))
            max#(s(x),s(y)) -> c_5(max#(x,y))
            min#(s(x),s(y)) -> c_8(min#(x,y))
            minus#(s(x),s(y)) -> c_10(minus#(x,y))
            transform#(s(x)) -> c_12(transform#(x))
        - Weak DPs:
            cons#(x,y) -> c_1()
            max#(x,0()) -> c_3()
            max#(0(),y) -> c_4()
            min#(x,0()) -> c_6()
            min#(0(),y) -> c_7()
            minus#(x,0()) -> c_9()
            transform#(x) -> c_11()
        - Weak TRS:
            max(x,0()) -> x
            max(0(),y) -> y
            max(s(x),s(y)) -> s(max(x,y))
            min(x,0()) -> 0()
            min(0(),y) -> 0()
            min(s(x),s(y)) -> s(min(x,y))
            minus(x,0()) -> x
            minus(s(x),s(y)) -> s(minus(x,y))
            transform(x) -> s(s(x))
            transform(s(x)) -> s(s(transform(x)))
        - Signature:
            {cons/2,gcd/2,max/2,min/2,minus/2,transform/1,cons#/2,gcd#/2,max#/2,min#/2,minus#/2,transform#/1} / {0/0,s/1
            ,c_1/0,c_2/6,c_3/0,c_4/0,c_5/1,c_6/0,c_7/0,c_8/1,c_9/0,c_10/1,c_11/0,c_12/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {cons#,gcd#,max#,min#,minus#
            ,transform#} and constructors {0,s}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:gcd#(s(x),s(y)) -> c_2(gcd#(minus(max(x,y),min(x,transform(y))),s(min(x,y)))
                                    ,minus#(max(x,y),min(x,transform(y)))
                                    ,max#(x,y)
                                    ,min#(x,transform(y))
                                    ,transform#(y)
                                    ,min#(x,y))
             -->_5 transform#(s(x)) -> c_12(transform#(x)):5
             -->_2 minus#(s(x),s(y)) -> c_10(minus#(x,y)):4
             -->_6 min#(s(x),s(y)) -> c_8(min#(x,y)):3
             -->_4 min#(s(x),s(y)) -> c_8(min#(x,y)):3
             -->_3 max#(s(x),s(y)) -> c_5(max#(x,y)):2
             -->_5 transform#(x) -> c_11():12
             -->_2 minus#(x,0()) -> c_9():11
             -->_6 min#(0(),y) -> c_7():10
             -->_4 min#(0(),y) -> c_7():10
             -->_6 min#(x,0()) -> c_6():9
             -->_4 min#(x,0()) -> c_6():9
             -->_3 max#(0(),y) -> c_4():8
             -->_3 max#(x,0()) -> c_3():7
             -->_1 gcd#(s(x),s(y)) -> c_2(gcd#(minus(max(x,y),min(x,transform(y))),s(min(x,y)))
                                         ,minus#(max(x,y),min(x,transform(y)))
                                         ,max#(x,y)
                                         ,min#(x,transform(y))
                                         ,transform#(y)
                                         ,min#(x,y)):1
          
          2:S:max#(s(x),s(y)) -> c_5(max#(x,y))
             -->_1 max#(0(),y) -> c_4():8
             -->_1 max#(x,0()) -> c_3():7
             -->_1 max#(s(x),s(y)) -> c_5(max#(x,y)):2
          
          3:S:min#(s(x),s(y)) -> c_8(min#(x,y))
             -->_1 min#(0(),y) -> c_7():10
             -->_1 min#(x,0()) -> c_6():9
             -->_1 min#(s(x),s(y)) -> c_8(min#(x,y)):3
          
          4:S:minus#(s(x),s(y)) -> c_10(minus#(x,y))
             -->_1 minus#(x,0()) -> c_9():11
             -->_1 minus#(s(x),s(y)) -> c_10(minus#(x,y)):4
          
          5:S:transform#(s(x)) -> c_12(transform#(x))
             -->_1 transform#(x) -> c_11():12
             -->_1 transform#(s(x)) -> c_12(transform#(x)):5
          
          6:W:cons#(x,y) -> c_1()
             
          
          7:W:max#(x,0()) -> c_3()
             
          
          8:W:max#(0(),y) -> c_4()
             
          
          9:W:min#(x,0()) -> c_6()
             
          
          10:W:min#(0(),y) -> c_7()
             
          
          11:W:minus#(x,0()) -> c_9()
             
          
          12:W:transform#(x) -> c_11()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          6: cons#(x,y) -> c_1()
          7: max#(x,0()) -> c_3()
          8: max#(0(),y) -> c_4()
          9: min#(x,0()) -> c_6()
          10: min#(0(),y) -> c_7()
          11: minus#(x,0()) -> c_9()
          12: transform#(x) -> c_11()
* Step 6: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          gcd#(s(x),s(y)) -> c_2(gcd#(minus(max(x,y),min(x,transform(y))),s(min(x,y)))
                                ,minus#(max(x,y),min(x,transform(y)))
                                ,max#(x,y)
                                ,min#(x,transform(y))
                                ,transform#(y)
                                ,min#(x,y))
          max#(s(x),s(y)) -> c_5(max#(x,y))
          min#(s(x),s(y)) -> c_8(min#(x,y))
          minus#(s(x),s(y)) -> c_10(minus#(x,y))
          transform#(s(x)) -> c_12(transform#(x))
      - Weak TRS:
          max(x,0()) -> x
          max(0(),y) -> y
          max(s(x),s(y)) -> s(max(x,y))
          min(x,0()) -> 0()
          min(0(),y) -> 0()
          min(s(x),s(y)) -> s(min(x,y))
          minus(x,0()) -> x
          minus(s(x),s(y)) -> s(minus(x,y))
          transform(x) -> s(s(x))
          transform(s(x)) -> s(s(transform(x)))
      - Signature:
          {cons/2,gcd/2,max/2,min/2,minus/2,transform/1,cons#/2,gcd#/2,max#/2,min#/2,minus#/2,transform#/1} / {0/0,s/1
          ,c_1/0,c_2/6,c_3/0,c_4/0,c_5/1,c_6/0,c_7/0,c_8/1,c_9/0,c_10/1,c_11/0,c_12/1}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {cons#,gcd#,max#,min#,minus#
          ,transform#} and constructors {0,s}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE