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