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_ = WIDP}
    + Details:
        We add the following weak innermost dependency pairs:
        
        Strict DPs
          *#(X,+(Y,1())) -> c_1(*#(X,+(Y,*(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()))))
            *#(X,0()) -> c_2()
            *#(X,0()) -> c_3()
            *#(X,1()) -> c_4()
        - Strict 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_1/1,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()))))
          *#(X,0()) -> c_2()
          *#(X,0()) -> c_3()
          *#(X,1()) -> c_4()
* Step 3: WeightGap MAYBE
    + Considered Problem:
        - Strict DPs:
            *#(X,+(Y,1())) -> c_1(*#(X,+(Y,*(1(),0()))))
            *#(X,0()) -> c_2()
            *#(X,0()) -> c_3()
            *#(X,1()) -> c_4()
        - Strict 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:
        WeightGap {wgDimension = 1, wgDegree = 1, wgKind = Algebraic, wgUArgs = UArgs, wgOn = WgOnTrs}
    + Details:
        The weightgap principle applies using the following constant growth matrix-interpretation:
          We apply a matrix interpretation of kind constructor based matrix interpretation:
          The following argument positions are considered usable:
            uargs(+) = {2},
            uargs(*#) = {2},
            uargs(c_1) = {1}
          
          Following symbols are considered usable:
            all
          TcT has computed the following interpretation:
              p(*) = [2] x1 + [3]         
              p(+) = [1] x1 + [1] x2 + [0]
              p(0) = [0]                  
              p(1) = [0]                  
             p(*#) = [1] x2 + [0]         
            p(c_1) = [1] x1 + [0]         
            p(c_2) = [0]                  
            p(c_3) = [0]                  
            p(c_4) = [0]                  
          
          Following rules are strictly oriented:
          *(X,0()) = [2] X + [3]
                   > [1] X + [0]
                   = X          
          
          *(X,0()) = [2] X + [3]
                   > [0]        
                   = 0()        
          
          
          Following rules are (at-least) weakly oriented:
          *#(X,+(Y,1())) =  [1] Y + [0]               
                         >= [1] Y + [3]               
                         =  c_1(*#(X,+(Y,*(1(),0()))))
          
               *#(X,0()) =  [0]                       
                         >= [0]                       
                         =  c_2()                     
          
               *#(X,0()) =  [0]                       
                         >= [0]                       
                         =  c_3()                     
          
               *#(X,1()) =  [0]                       
                         >= [0]                       
                         =  c_4()                     
          
        Further, it can be verified that all rules not oriented are covered by the weightgap condition.
* Step 4: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            *#(X,+(Y,1())) -> c_1(*#(X,+(Y,*(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_1/1,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}) = {}.
        Here rules are labelled as follows:
          1: *#(X,+(Y,1())) -> c_1(*#(X,+(Y,*(1(),0()))))
          2: *#(X,0()) -> c_2()
          3: *#(X,0()) -> c_3()
          4: *#(X,1()) -> c_4()
* Step 5: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            *#(X,+(Y,1())) -> c_1(*#(X,+(Y,*(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_1/1,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 *#(X,+(Y,1())) -> c_1(*#(X,+(Y,*(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()
          3: *#(X,0()) -> c_3()
          2: *#(X,0()) -> c_2()
* 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