MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            *(x,+(y,f(z))) -> *(g(x,z),+(y,y))
            *(*(x,y),z) -> *(x,*(y,z))
            *(+(x,y),z) -> +(*(x,z),*(y,z))
        - Signature:
            {*/2} / {+/2,f/1,g/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*} and constructors {+,f,g}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          *#(x,+(y,f(z))) -> c_1(*#(g(x,z),+(y,y)))
          *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z))
          *#(+(x,y),z) -> c_3(*#(x,z),*#(y,z))
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: Decompose MAYBE
    + Considered Problem:
        - Strict DPs:
            *#(x,+(y,f(z))) -> c_1(*#(g(x,z),+(y,y)))
            *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z))
            *#(+(x,y),z) -> c_3(*#(x,z),*#(y,z))
        - Weak TRS:
            *(x,+(y,f(z))) -> *(g(x,z),+(y,y))
            *(*(x,y),z) -> *(x,*(y,z))
            *(+(x,y),z) -> +(*(x,z),*(y,z))
        - Signature:
            {*/2,*#/2} / {+/2,f/1,g/2,c_1/1,c_2/2,c_3/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#} and constructors {+,f,g}
    + Applied Processor:
        Decompose {onSelection = all cycle independent sub-graph, withBound = RelativeAdd}
    + Details:
        We analyse the complexity of following sub-problems (R) and (S).
        Problem (S) is obtained from the input problem by shifting strict rules from (R) into the weak component.
        
        Problem (R)
          - Strict DPs:
              *#(x,+(y,f(z))) -> c_1(*#(g(x,z),+(y,y)))
          - Weak DPs:
              *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z))
              *#(+(x,y),z) -> c_3(*#(x,z),*#(y,z))
          - Weak TRS:
              *(x,+(y,f(z))) -> *(g(x,z),+(y,y))
              *(*(x,y),z) -> *(x,*(y,z))
              *(+(x,y),z) -> +(*(x,z),*(y,z))
          - Signature:
              {*/2,*#/2} / {+/2,f/1,g/2,c_1/1,c_2/2,c_3/2}
          - Obligation:
              innermost runtime complexity wrt. defined symbols {*#} and constructors {+,f,g}
        
        Problem (S)
          - Strict DPs:
              *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z))
              *#(+(x,y),z) -> c_3(*#(x,z),*#(y,z))
          - Weak DPs:
              *#(x,+(y,f(z))) -> c_1(*#(g(x,z),+(y,y)))
          - Weak TRS:
              *(x,+(y,f(z))) -> *(g(x,z),+(y,y))
              *(*(x,y),z) -> *(x,*(y,z))
              *(+(x,y),z) -> +(*(x,z),*(y,z))
          - Signature:
              {*/2,*#/2} / {+/2,f/1,g/2,c_1/1,c_2/2,c_3/2}
          - Obligation:
              innermost runtime complexity wrt. defined symbols {*#} and constructors {+,f,g}
** Step 2.a:1: DecomposeDG MAYBE
    + Considered Problem:
        - Strict DPs:
            *#(x,+(y,f(z))) -> c_1(*#(g(x,z),+(y,y)))
        - Weak DPs:
            *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z))
            *#(+(x,y),z) -> c_3(*#(x,z),*#(y,z))
        - Weak TRS:
            *(x,+(y,f(z))) -> *(g(x,z),+(y,y))
            *(*(x,y),z) -> *(x,*(y,z))
            *(+(x,y),z) -> +(*(x,z),*(y,z))
        - Signature:
            {*/2,*#/2} / {+/2,f/1,g/2,c_1/1,c_2/2,c_3/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#} and constructors {+,f,g}
    + Applied Processor:
        DecomposeDG {onSelection = all below first cut in WDG, onUpper = Just someStrategy, onLower = Nothing}
    + Details:
        We decompose the input problem according to the dependency graph into the upper component
          *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z))
          *#(+(x,y),z) -> c_3(*#(x,z),*#(y,z))
        and a lower component
          *#(x,+(y,f(z))) -> c_1(*#(g(x,z),+(y,y)))
        Further, following extension rules are added to the lower component.
          *#(*(x,y),z) -> *#(x,*(y,z))
          *#(*(x,y),z) -> *#(y,z)
          *#(+(x,y),z) -> *#(x,z)
          *#(+(x,y),z) -> *#(y,z)
*** Step 2.a:1.a:1: PredecessorEstimationCP WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z))
            *#(+(x,y),z) -> c_3(*#(x,z),*#(y,z))
        - Weak TRS:
            *(x,+(y,f(z))) -> *(g(x,z),+(y,y))
            *(*(x,y),z) -> *(x,*(y,z))
            *(+(x,y),z) -> +(*(x,z),*(y,z))
        - Signature:
            {*/2,*#/2} / {+/2,f/1,g/2,c_1/1,c_2/2,c_3/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#} and constructors {+,f,g}
    + Applied Processor:
        PredecessorEstimationCP {onSelectionCP = any intersect of rules of CDG leaf and strict-rules, withComplexityPair = NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing}}
    + Details:
        We first use the processor NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing} to orient following rules strictly:
          1: *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z))
          
        The strictly oriented rules are moved into the weak component.
**** Step 2.a:1.a:1.a:1: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z))
            *#(+(x,y),z) -> c_3(*#(x,z),*#(y,z))
        - Weak TRS:
            *(x,+(y,f(z))) -> *(g(x,z),+(y,y))
            *(*(x,y),z) -> *(x,*(y,z))
            *(+(x,y),z) -> +(*(x,z),*(y,z))
        - Signature:
            {*/2,*#/2} / {+/2,f/1,g/2,c_1/1,c_2/2,c_3/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#} and constructors {+,f,g}
    + Applied Processor:
        NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just first alternative for predecessorEstimation on any intersect of rules of CDG leaf and strict-rules}
    + Details:
        We apply a matrix interpretation of kind constructor based matrix interpretation:
        The following argument positions are considered usable:
          uargs(c_2) = {1,2},
          uargs(c_3) = {1,2}
        
        Following symbols are considered usable:
          {*#}
        TcT has computed the following interpretation:
            p(*) = [4] x1 + [4] x2 + [2]
            p(+) = [1] x1 + [1] x2 + [0]
            p(f) = [0]                  
            p(g) = [1] x2 + [4]         
           p(*#) = [4] x1 + [0]         
          p(c_1) = [1] x1 + [0]         
          p(c_2) = [2] x1 + [4] x2 + [0]
          p(c_3) = [1] x1 + [1] x2 + [0]
        
        Following rules are strictly oriented:
        *#(*(x,y),z) = [16] x + [16] y + [8]    
                     > [8] x + [16] y + [0]     
                     = c_2(*#(x,*(y,z)),*#(y,z))
        
        
        Following rules are (at-least) weakly oriented:
        *#(+(x,y),z) =  [4] x + [4] y + [0] 
                     >= [4] x + [4] y + [0] 
                     =  c_3(*#(x,z),*#(y,z))
        
**** Step 2.a:1.a:1.a:2: Assumption WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            *#(+(x,y),z) -> c_3(*#(x,z),*#(y,z))
        - Weak DPs:
            *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z))
        - Weak TRS:
            *(x,+(y,f(z))) -> *(g(x,z),+(y,y))
            *(*(x,y),z) -> *(x,*(y,z))
            *(+(x,y),z) -> +(*(x,z),*(y,z))
        - Signature:
            {*/2,*#/2} / {+/2,f/1,g/2,c_1/1,c_2/2,c_3/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#} and constructors {+,f,g}
    + Applied Processor:
        Assumption {assumed = Certificate {spaceUB = Unknown, spaceLB = Unknown, timeUB = Poly (Just 0), timeLB = Unknown}}
    + Details:
        ()

**** Step 2.a:1.a:1.b:1: PredecessorEstimationCP WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            *#(+(x,y),z) -> c_3(*#(x,z),*#(y,z))
        - Weak DPs:
            *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z))
        - Weak TRS:
            *(x,+(y,f(z))) -> *(g(x,z),+(y,y))
            *(*(x,y),z) -> *(x,*(y,z))
            *(+(x,y),z) -> +(*(x,z),*(y,z))
        - Signature:
            {*/2,*#/2} / {+/2,f/1,g/2,c_1/1,c_2/2,c_3/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#} and constructors {+,f,g}
    + Applied Processor:
        PredecessorEstimationCP {onSelectionCP = any intersect of rules of CDG leaf and strict-rules, withComplexityPair = NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing}}
    + Details:
        We first use the processor NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing} to orient following rules strictly:
          1: *#(+(x,y),z) -> c_3(*#(x,z),*#(y,z))
          
        The strictly oriented rules are moved into the weak component.
***** Step 2.a:1.a:1.b:1.a:1: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            *#(+(x,y),z) -> c_3(*#(x,z),*#(y,z))
        - Weak DPs:
            *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z))
        - Weak TRS:
            *(x,+(y,f(z))) -> *(g(x,z),+(y,y))
            *(*(x,y),z) -> *(x,*(y,z))
            *(+(x,y),z) -> +(*(x,z),*(y,z))
        - Signature:
            {*/2,*#/2} / {+/2,f/1,g/2,c_1/1,c_2/2,c_3/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#} and constructors {+,f,g}
    + Applied Processor:
        NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just first alternative for predecessorEstimation on any intersect of rules of CDG leaf and strict-rules}
    + Details:
        We apply a matrix interpretation of kind constructor based matrix interpretation:
        The following argument positions are considered usable:
          uargs(c_2) = {1,2},
          uargs(c_3) = {1,2}
        
        Following symbols are considered usable:
          {*#}
        TcT has computed the following interpretation:
            p(*) = [1] x1 + [1] x2 + [3]
            p(+) = [1] x1 + [1] x2 + [1]
            p(f) = [0]                  
            p(g) = [1] x2 + [9]         
           p(*#) = [8] x1 + [0]         
          p(c_1) = [8]                  
          p(c_2) = [1] x1 + [1] x2 + [1]
          p(c_3) = [1] x1 + [1] x2 + [1]
        
        Following rules are strictly oriented:
        *#(+(x,y),z) = [8] x + [8] y + [8] 
                     > [8] x + [8] y + [1] 
                     = c_3(*#(x,z),*#(y,z))
        
        
        Following rules are (at-least) weakly oriented:
        *#(*(x,y),z) =  [8] x + [8] y + [24]     
                     >= [8] x + [8] y + [1]      
                     =  c_2(*#(x,*(y,z)),*#(y,z))
        
***** Step 2.a:1.a:1.b:1.a:2: Assumption WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z))
            *#(+(x,y),z) -> c_3(*#(x,z),*#(y,z))
        - Weak TRS:
            *(x,+(y,f(z))) -> *(g(x,z),+(y,y))
            *(*(x,y),z) -> *(x,*(y,z))
            *(+(x,y),z) -> +(*(x,z),*(y,z))
        - Signature:
            {*/2,*#/2} / {+/2,f/1,g/2,c_1/1,c_2/2,c_3/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#} and constructors {+,f,g}
    + Applied Processor:
        Assumption {assumed = Certificate {spaceUB = Unknown, spaceLB = Unknown, timeUB = Poly (Just 0), timeLB = Unknown}}
    + Details:
        ()

***** Step 2.a:1.a:1.b:1.b:1: RemoveWeakSuffixes WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z))
            *#(+(x,y),z) -> c_3(*#(x,z),*#(y,z))
        - Weak TRS:
            *(x,+(y,f(z))) -> *(g(x,z),+(y,y))
            *(*(x,y),z) -> *(x,*(y,z))
            *(+(x,y),z) -> +(*(x,z),*(y,z))
        - Signature:
            {*/2,*#/2} / {+/2,f/1,g/2,c_1/1,c_2/2,c_3/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#} and constructors {+,f,g}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:W:*#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z))
             -->_2 *#(+(x,y),z) -> c_3(*#(x,z),*#(y,z)):2
             -->_1 *#(+(x,y),z) -> c_3(*#(x,z),*#(y,z)):2
             -->_2 *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z)):1
             -->_1 *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z)):1
          
          2:W:*#(+(x,y),z) -> c_3(*#(x,z),*#(y,z))
             -->_2 *#(+(x,y),z) -> c_3(*#(x,z),*#(y,z)):2
             -->_1 *#(+(x,y),z) -> c_3(*#(x,z),*#(y,z)):2
             -->_2 *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z)):1
             -->_1 *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z)):1
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          1: *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z))
          2: *#(+(x,y),z) -> c_3(*#(x,z),*#(y,z))
***** Step 2.a:1.a:1.b:1.b:2: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            *(x,+(y,f(z))) -> *(g(x,z),+(y,y))
            *(*(x,y),z) -> *(x,*(y,z))
            *(+(x,y),z) -> +(*(x,z),*(y,z))
        - Signature:
            {*/2,*#/2} / {+/2,f/1,g/2,c_1/1,c_2/2,c_3/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#} and constructors {+,f,g}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

*** Step 2.a:1.b:1: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          *#(x,+(y,f(z))) -> c_1(*#(g(x,z),+(y,y)))
      - Weak DPs:
          *#(*(x,y),z) -> *#(x,*(y,z))
          *#(*(x,y),z) -> *#(y,z)
          *#(+(x,y),z) -> *#(x,z)
          *#(+(x,y),z) -> *#(y,z)
      - Weak TRS:
          *(x,+(y,f(z))) -> *(g(x,z),+(y,y))
          *(*(x,y),z) -> *(x,*(y,z))
          *(+(x,y),z) -> +(*(x,z),*(y,z))
      - Signature:
          {*/2,*#/2} / {+/2,f/1,g/2,c_1/1,c_2/2,c_3/2}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {*#} and constructors {+,f,g}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
** Step 2.b:1: RemoveWeakSuffixes WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z))
            *#(+(x,y),z) -> c_3(*#(x,z),*#(y,z))
        - Weak DPs:
            *#(x,+(y,f(z))) -> c_1(*#(g(x,z),+(y,y)))
        - Weak TRS:
            *(x,+(y,f(z))) -> *(g(x,z),+(y,y))
            *(*(x,y),z) -> *(x,*(y,z))
            *(+(x,y),z) -> +(*(x,z),*(y,z))
        - Signature:
            {*/2,*#/2} / {+/2,f/1,g/2,c_1/1,c_2/2,c_3/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#} and constructors {+,f,g}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:*#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z))
             -->_2 *#(x,+(y,f(z))) -> c_1(*#(g(x,z),+(y,y))):3
             -->_1 *#(x,+(y,f(z))) -> c_1(*#(g(x,z),+(y,y))):3
             -->_2 *#(+(x,y),z) -> c_3(*#(x,z),*#(y,z)):2
             -->_1 *#(+(x,y),z) -> c_3(*#(x,z),*#(y,z)):2
             -->_2 *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z)):1
             -->_1 *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z)):1
          
          2:S:*#(+(x,y),z) -> c_3(*#(x,z),*#(y,z))
             -->_2 *#(x,+(y,f(z))) -> c_1(*#(g(x,z),+(y,y))):3
             -->_1 *#(x,+(y,f(z))) -> c_1(*#(g(x,z),+(y,y))):3
             -->_2 *#(+(x,y),z) -> c_3(*#(x,z),*#(y,z)):2
             -->_1 *#(+(x,y),z) -> c_3(*#(x,z),*#(y,z)):2
             -->_2 *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z)):1
             -->_1 *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z)):1
          
          3:W:*#(x,+(y,f(z))) -> c_1(*#(g(x,z),+(y,y)))
             -->_1 *#(x,+(y,f(z))) -> c_1(*#(g(x,z),+(y,y))):3
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          3: *#(x,+(y,f(z))) -> c_1(*#(g(x,z),+(y,y)))
** Step 2.b:2: PredecessorEstimationCP WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z))
            *#(+(x,y),z) -> c_3(*#(x,z),*#(y,z))
        - Weak TRS:
            *(x,+(y,f(z))) -> *(g(x,z),+(y,y))
            *(*(x,y),z) -> *(x,*(y,z))
            *(+(x,y),z) -> +(*(x,z),*(y,z))
        - Signature:
            {*/2,*#/2} / {+/2,f/1,g/2,c_1/1,c_2/2,c_3/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#} and constructors {+,f,g}
    + Applied Processor:
        PredecessorEstimationCP {onSelectionCP = any intersect of rules of CDG leaf and strict-rules, withComplexityPair = NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing}}
    + Details:
        We first use the processor NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing} to orient following rules strictly:
          1: *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z))
          
        The strictly oriented rules are moved into the weak component.
*** Step 2.b:2.a:1: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z))
            *#(+(x,y),z) -> c_3(*#(x,z),*#(y,z))
        - Weak TRS:
            *(x,+(y,f(z))) -> *(g(x,z),+(y,y))
            *(*(x,y),z) -> *(x,*(y,z))
            *(+(x,y),z) -> +(*(x,z),*(y,z))
        - Signature:
            {*/2,*#/2} / {+/2,f/1,g/2,c_1/1,c_2/2,c_3/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#} and constructors {+,f,g}
    + Applied Processor:
        NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just first alternative for predecessorEstimation on any intersect of rules of CDG leaf and strict-rules}
    + Details:
        We apply a matrix interpretation of kind constructor based matrix interpretation:
        The following argument positions are considered usable:
          uargs(c_2) = {1,2},
          uargs(c_3) = {1,2}
        
        Following symbols are considered usable:
          {*#}
        TcT has computed the following interpretation:
            p(*) = [4] x1 + [4] x2 + [2]
            p(+) = [1] x1 + [1] x2 + [0]
            p(f) = [0]                  
            p(g) = [1] x2 + [4]         
           p(*#) = [4] x1 + [0]         
          p(c_1) = [1] x1 + [0]         
          p(c_2) = [2] x1 + [4] x2 + [0]
          p(c_3) = [1] x1 + [1] x2 + [0]
        
        Following rules are strictly oriented:
        *#(*(x,y),z) = [16] x + [16] y + [8]    
                     > [8] x + [16] y + [0]     
                     = c_2(*#(x,*(y,z)),*#(y,z))
        
        
        Following rules are (at-least) weakly oriented:
        *#(+(x,y),z) =  [4] x + [4] y + [0] 
                     >= [4] x + [4] y + [0] 
                     =  c_3(*#(x,z),*#(y,z))
        
*** Step 2.b:2.a:2: Assumption WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            *#(+(x,y),z) -> c_3(*#(x,z),*#(y,z))
        - Weak DPs:
            *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z))
        - Weak TRS:
            *(x,+(y,f(z))) -> *(g(x,z),+(y,y))
            *(*(x,y),z) -> *(x,*(y,z))
            *(+(x,y),z) -> +(*(x,z),*(y,z))
        - Signature:
            {*/2,*#/2} / {+/2,f/1,g/2,c_1/1,c_2/2,c_3/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#} and constructors {+,f,g}
    + Applied Processor:
        Assumption {assumed = Certificate {spaceUB = Unknown, spaceLB = Unknown, timeUB = Poly (Just 0), timeLB = Unknown}}
    + Details:
        ()

*** Step 2.b:2.b:1: PredecessorEstimationCP WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            *#(+(x,y),z) -> c_3(*#(x,z),*#(y,z))
        - Weak DPs:
            *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z))
        - Weak TRS:
            *(x,+(y,f(z))) -> *(g(x,z),+(y,y))
            *(*(x,y),z) -> *(x,*(y,z))
            *(+(x,y),z) -> +(*(x,z),*(y,z))
        - Signature:
            {*/2,*#/2} / {+/2,f/1,g/2,c_1/1,c_2/2,c_3/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#} and constructors {+,f,g}
    + Applied Processor:
        PredecessorEstimationCP {onSelectionCP = any intersect of rules of CDG leaf and strict-rules, withComplexityPair = NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing}}
    + Details:
        We first use the processor NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing} to orient following rules strictly:
          1: *#(+(x,y),z) -> c_3(*#(x,z),*#(y,z))
          
        The strictly oriented rules are moved into the weak component.
**** Step 2.b:2.b:1.a:1: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            *#(+(x,y),z) -> c_3(*#(x,z),*#(y,z))
        - Weak DPs:
            *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z))
        - Weak TRS:
            *(x,+(y,f(z))) -> *(g(x,z),+(y,y))
            *(*(x,y),z) -> *(x,*(y,z))
            *(+(x,y),z) -> +(*(x,z),*(y,z))
        - Signature:
            {*/2,*#/2} / {+/2,f/1,g/2,c_1/1,c_2/2,c_3/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#} and constructors {+,f,g}
    + Applied Processor:
        NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just first alternative for predecessorEstimation on any intersect of rules of CDG leaf and strict-rules}
    + Details:
        We apply a matrix interpretation of kind constructor based matrix interpretation:
        The following argument positions are considered usable:
          uargs(c_2) = {1,2},
          uargs(c_3) = {1,2}
        
        Following symbols are considered usable:
          {*#}
        TcT has computed the following interpretation:
            p(*) = [1] x1 + [1] x2 + [3]
            p(+) = [1] x1 + [1] x2 + [1]
            p(f) = [0]                  
            p(g) = [1] x2 + [9]         
           p(*#) = [8] x1 + [0]         
          p(c_1) = [8]                  
          p(c_2) = [1] x1 + [1] x2 + [1]
          p(c_3) = [1] x1 + [1] x2 + [1]
        
        Following rules are strictly oriented:
        *#(+(x,y),z) = [8] x + [8] y + [8] 
                     > [8] x + [8] y + [1] 
                     = c_3(*#(x,z),*#(y,z))
        
        
        Following rules are (at-least) weakly oriented:
        *#(*(x,y),z) =  [8] x + [8] y + [24]     
                     >= [8] x + [8] y + [1]      
                     =  c_2(*#(x,*(y,z)),*#(y,z))
        
**** Step 2.b:2.b:1.a:2: Assumption WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z))
            *#(+(x,y),z) -> c_3(*#(x,z),*#(y,z))
        - Weak TRS:
            *(x,+(y,f(z))) -> *(g(x,z),+(y,y))
            *(*(x,y),z) -> *(x,*(y,z))
            *(+(x,y),z) -> +(*(x,z),*(y,z))
        - Signature:
            {*/2,*#/2} / {+/2,f/1,g/2,c_1/1,c_2/2,c_3/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#} and constructors {+,f,g}
    + Applied Processor:
        Assumption {assumed = Certificate {spaceUB = Unknown, spaceLB = Unknown, timeUB = Poly (Just 0), timeLB = Unknown}}
    + Details:
        ()

**** Step 2.b:2.b:1.b:1: RemoveWeakSuffixes WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z))
            *#(+(x,y),z) -> c_3(*#(x,z),*#(y,z))
        - Weak TRS:
            *(x,+(y,f(z))) -> *(g(x,z),+(y,y))
            *(*(x,y),z) -> *(x,*(y,z))
            *(+(x,y),z) -> +(*(x,z),*(y,z))
        - Signature:
            {*/2,*#/2} / {+/2,f/1,g/2,c_1/1,c_2/2,c_3/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#} and constructors {+,f,g}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:W:*#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z))
             -->_2 *#(+(x,y),z) -> c_3(*#(x,z),*#(y,z)):2
             -->_1 *#(+(x,y),z) -> c_3(*#(x,z),*#(y,z)):2
             -->_2 *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z)):1
             -->_1 *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z)):1
          
          2:W:*#(+(x,y),z) -> c_3(*#(x,z),*#(y,z))
             -->_2 *#(+(x,y),z) -> c_3(*#(x,z),*#(y,z)):2
             -->_1 *#(+(x,y),z) -> c_3(*#(x,z),*#(y,z)):2
             -->_2 *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z)):1
             -->_1 *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z)):1
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          1: *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z))
          2: *#(+(x,y),z) -> c_3(*#(x,z),*#(y,z))
**** Step 2.b:2.b:1.b:2: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            *(x,+(y,f(z))) -> *(g(x,z),+(y,y))
            *(*(x,y),z) -> *(x,*(y,z))
            *(+(x,y),z) -> +(*(x,z),*(y,z))
        - Signature:
            {*/2,*#/2} / {+/2,f/1,g/2,c_1/1,c_2/2,c_3/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#} and constructors {+,f,g}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

MAYBE