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