MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            f(0()) -> 1()
            f(s(x)) -> +(f(x),s(f(x)))
            f(s(x)) -> g(f(x))
            g(x) -> +(x,s(x))
        - Signature:
            {f/1,g/1} / {+/2,0/0,1/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,g} and constructors {+,0,1,s}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          f#(0()) -> c_1()
          f#(s(x)) -> c_2(f#(x),f#(x))
          f#(s(x)) -> c_3(g#(f(x)),f#(x))
          g#(x) -> c_4()
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            f#(0()) -> c_1()
            f#(s(x)) -> c_2(f#(x),f#(x))
            f#(s(x)) -> c_3(g#(f(x)),f#(x))
            g#(x) -> c_4()
        - Weak TRS:
            f(0()) -> 1()
            f(s(x)) -> +(f(x),s(f(x)))
            f(s(x)) -> g(f(x))
            g(x) -> +(x,s(x))
        - Signature:
            {f/1,g/1,f#/1,g#/1} / {+/2,0/0,1/0,s/1,c_1/0,c_2/2,c_3/2,c_4/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f#,g#} and constructors {+,0,1,s}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,4}
        by application of
          Pre({1,4}) = {2,3}.
        Here rules are labelled as follows:
          1: f#(0()) -> c_1()
          2: f#(s(x)) -> c_2(f#(x),f#(x))
          3: f#(s(x)) -> c_3(g#(f(x)),f#(x))
          4: g#(x) -> c_4()
* Step 3: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            f#(s(x)) -> c_2(f#(x),f#(x))
            f#(s(x)) -> c_3(g#(f(x)),f#(x))
        - Weak DPs:
            f#(0()) -> c_1()
            g#(x) -> c_4()
        - Weak TRS:
            f(0()) -> 1()
            f(s(x)) -> +(f(x),s(f(x)))
            f(s(x)) -> g(f(x))
            g(x) -> +(x,s(x))
        - Signature:
            {f/1,g/1,f#/1,g#/1} / {+/2,0/0,1/0,s/1,c_1/0,c_2/2,c_3/2,c_4/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f#,g#} and constructors {+,0,1,s}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:f#(s(x)) -> c_2(f#(x),f#(x))
             -->_2 f#(s(x)) -> c_3(g#(f(x)),f#(x)):2
             -->_1 f#(s(x)) -> c_3(g#(f(x)),f#(x)):2
             -->_2 f#(0()) -> c_1():3
             -->_1 f#(0()) -> c_1():3
             -->_2 f#(s(x)) -> c_2(f#(x),f#(x)):1
             -->_1 f#(s(x)) -> c_2(f#(x),f#(x)):1
          
          2:S:f#(s(x)) -> c_3(g#(f(x)),f#(x))
             -->_1 g#(x) -> c_4():4
             -->_2 f#(0()) -> c_1():3
             -->_2 f#(s(x)) -> c_3(g#(f(x)),f#(x)):2
             -->_2 f#(s(x)) -> c_2(f#(x),f#(x)):1
          
          3:W:f#(0()) -> c_1()
             
          
          4:W:g#(x) -> c_4()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          3: f#(0()) -> c_1()
          4: g#(x) -> c_4()
* Step 4: SimplifyRHS MAYBE
    + Considered Problem:
        - Strict DPs:
            f#(s(x)) -> c_2(f#(x),f#(x))
            f#(s(x)) -> c_3(g#(f(x)),f#(x))
        - Weak TRS:
            f(0()) -> 1()
            f(s(x)) -> +(f(x),s(f(x)))
            f(s(x)) -> g(f(x))
            g(x) -> +(x,s(x))
        - Signature:
            {f/1,g/1,f#/1,g#/1} / {+/2,0/0,1/0,s/1,c_1/0,c_2/2,c_3/2,c_4/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f#,g#} and constructors {+,0,1,s}
    + Applied Processor:
        SimplifyRHS
    + Details:
        Consider the dependency graph
          1:S:f#(s(x)) -> c_2(f#(x),f#(x))
             -->_2 f#(s(x)) -> c_3(g#(f(x)),f#(x)):2
             -->_1 f#(s(x)) -> c_3(g#(f(x)),f#(x)):2
             -->_2 f#(s(x)) -> c_2(f#(x),f#(x)):1
             -->_1 f#(s(x)) -> c_2(f#(x),f#(x)):1
          
          2:S:f#(s(x)) -> c_3(g#(f(x)),f#(x))
             -->_2 f#(s(x)) -> c_3(g#(f(x)),f#(x)):2
             -->_2 f#(s(x)) -> c_2(f#(x),f#(x)):1
          
        Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
          f#(s(x)) -> c_3(f#(x))
* Step 5: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            f#(s(x)) -> c_2(f#(x),f#(x))
            f#(s(x)) -> c_3(f#(x))
        - Weak TRS:
            f(0()) -> 1()
            f(s(x)) -> +(f(x),s(f(x)))
            f(s(x)) -> g(f(x))
            g(x) -> +(x,s(x))
        - Signature:
            {f/1,g/1,f#/1,g#/1} / {+/2,0/0,1/0,s/1,c_1/0,c_2/2,c_3/1,c_4/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f#,g#} and constructors {+,0,1,s}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          f#(s(x)) -> c_2(f#(x),f#(x))
          f#(s(x)) -> c_3(f#(x))
* Step 6: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          f#(s(x)) -> c_2(f#(x),f#(x))
          f#(s(x)) -> c_3(f#(x))
      - Signature:
          {f/1,g/1,f#/1,g#/1} / {+/2,0/0,1/0,s/1,c_1/0,c_2/2,c_3/1,c_4/0}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {f#,g#} and constructors {+,0,1,s}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE