MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            cons(x,cons(y,z)) -> big()
            inf(x) -> cons(x,inf(s(x)))
        - Signature:
            {cons/2,inf/1} / {big/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {cons,inf} and constructors {big,s}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          cons#(x,cons(y,z)) -> c_1()
          inf#(x) -> c_2(cons#(x,inf(s(x))),inf#(s(x)))
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            cons#(x,cons(y,z)) -> c_1()
            inf#(x) -> c_2(cons#(x,inf(s(x))),inf#(s(x)))
        - Weak TRS:
            cons(x,cons(y,z)) -> big()
            inf(x) -> cons(x,inf(s(x)))
        - Signature:
            {cons/2,inf/1,cons#/2,inf#/1} / {big/0,s/1,c_1/0,c_2/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {cons#,inf#} and constructors {big,s}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1}
        by application of
          Pre({1}) = {2}.
        Here rules are labelled as follows:
          1: cons#(x,cons(y,z)) -> c_1()
          2: inf#(x) -> c_2(cons#(x,inf(s(x))),inf#(s(x)))
* Step 3: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            inf#(x) -> c_2(cons#(x,inf(s(x))),inf#(s(x)))
        - Weak DPs:
            cons#(x,cons(y,z)) -> c_1()
        - Weak TRS:
            cons(x,cons(y,z)) -> big()
            inf(x) -> cons(x,inf(s(x)))
        - Signature:
            {cons/2,inf/1,cons#/2,inf#/1} / {big/0,s/1,c_1/0,c_2/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {cons#,inf#} and constructors {big,s}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:inf#(x) -> c_2(cons#(x,inf(s(x))),inf#(s(x)))
             -->_1 cons#(x,cons(y,z)) -> c_1():2
             -->_2 inf#(x) -> c_2(cons#(x,inf(s(x))),inf#(s(x))):1
          
          2:W:cons#(x,cons(y,z)) -> c_1()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          2: cons#(x,cons(y,z)) -> c_1()
* Step 4: SimplifyRHS MAYBE
    + Considered Problem:
        - Strict DPs:
            inf#(x) -> c_2(cons#(x,inf(s(x))),inf#(s(x)))
        - Weak TRS:
            cons(x,cons(y,z)) -> big()
            inf(x) -> cons(x,inf(s(x)))
        - Signature:
            {cons/2,inf/1,cons#/2,inf#/1} / {big/0,s/1,c_1/0,c_2/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {cons#,inf#} and constructors {big,s}
    + Applied Processor:
        SimplifyRHS
    + Details:
        Consider the dependency graph
          1:S:inf#(x) -> c_2(cons#(x,inf(s(x))),inf#(s(x)))
             -->_2 inf#(x) -> c_2(cons#(x,inf(s(x))),inf#(s(x))):1
          
        Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
          inf#(x) -> c_2(inf#(s(x)))
* Step 5: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            inf#(x) -> c_2(inf#(s(x)))
        - Weak TRS:
            cons(x,cons(y,z)) -> big()
            inf(x) -> cons(x,inf(s(x)))
        - Signature:
            {cons/2,inf/1,cons#/2,inf#/1} / {big/0,s/1,c_1/0,c_2/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {cons#,inf#} and constructors {big,s}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          inf#(x) -> c_2(inf#(s(x)))
* Step 6: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          inf#(x) -> c_2(inf#(s(x)))
      - Signature:
          {cons/2,inf/1,cons#/2,inf#/1} / {big/0,s/1,c_1/0,c_2/1}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {cons#,inf#} and constructors {big,s}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE