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