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