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