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