WORST_CASE(?,O(n^2))
* Step 1: DependencyPairs WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict TRS:
            *(0(),y) -> 0()
            *(s(x),y) -> +(y,*(x,y))
            -(x,0()) -> x
            -(0(),y) -> 0()
            -(s(x),s(y)) -> -(x,y)
            exp(x,0()) -> s(0())
            exp(x,s(y)) -> *(x,exp(x,y))
        - Signature:
            {*/2,-/2,exp/2} / {+/2,0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*,-,exp} and constructors {+,0,s}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          *#(0(),y) -> c_1()
          *#(s(x),y) -> c_2(*#(x,y))
          -#(x,0()) -> c_3()
          -#(0(),y) -> c_4()
          -#(s(x),s(y)) -> c_5(-#(x,y))
          exp#(x,0()) -> c_6()
          exp#(x,s(y)) -> c_7(*#(x,exp(x,y)),exp#(x,y))
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: UsableRules WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict DPs:
            *#(0(),y) -> c_1()
            *#(s(x),y) -> c_2(*#(x,y))
            -#(x,0()) -> c_3()
            -#(0(),y) -> c_4()
            -#(s(x),s(y)) -> c_5(-#(x,y))
            exp#(x,0()) -> c_6()
            exp#(x,s(y)) -> c_7(*#(x,exp(x,y)),exp#(x,y))
        - Weak TRS:
            *(0(),y) -> 0()
            *(s(x),y) -> +(y,*(x,y))
            -(x,0()) -> x
            -(0(),y) -> 0()
            -(s(x),s(y)) -> -(x,y)
            exp(x,0()) -> s(0())
            exp(x,s(y)) -> *(x,exp(x,y))
        - Signature:
            {*/2,-/2,exp/2,*#/2,-#/2,exp#/2} / {+/2,0/0,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/1,c_6/0,c_7/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#,-#,exp#} and constructors {+,0,s}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          *(0(),y) -> 0()
          *(s(x),y) -> +(y,*(x,y))
          exp(x,0()) -> s(0())
          exp(x,s(y)) -> *(x,exp(x,y))
          *#(0(),y) -> c_1()
          *#(s(x),y) -> c_2(*#(x,y))
          -#(x,0()) -> c_3()
          -#(0(),y) -> c_4()
          -#(s(x),s(y)) -> c_5(-#(x,y))
          exp#(x,0()) -> c_6()
          exp#(x,s(y)) -> c_7(*#(x,exp(x,y)),exp#(x,y))
* Step 3: PredecessorEstimation WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict DPs:
            *#(0(),y) -> c_1()
            *#(s(x),y) -> c_2(*#(x,y))
            -#(x,0()) -> c_3()
            -#(0(),y) -> c_4()
            -#(s(x),s(y)) -> c_5(-#(x,y))
            exp#(x,0()) -> c_6()
            exp#(x,s(y)) -> c_7(*#(x,exp(x,y)),exp#(x,y))
        - Weak TRS:
            *(0(),y) -> 0()
            *(s(x),y) -> +(y,*(x,y))
            exp(x,0()) -> s(0())
            exp(x,s(y)) -> *(x,exp(x,y))
        - Signature:
            {*/2,-/2,exp/2,*#/2,-#/2,exp#/2} / {+/2,0/0,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/1,c_6/0,c_7/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#,-#,exp#} and constructors {+,0,s}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,3,4,6}
        by application of
          Pre({1,3,4,6}) = {2,5,7}.
        Here rules are labelled as follows:
          1: *#(0(),y) -> c_1()
          2: *#(s(x),y) -> c_2(*#(x,y))
          3: -#(x,0()) -> c_3()
          4: -#(0(),y) -> c_4()
          5: -#(s(x),s(y)) -> c_5(-#(x,y))
          6: exp#(x,0()) -> c_6()
          7: exp#(x,s(y)) -> c_7(*#(x,exp(x,y)),exp#(x,y))
* Step 4: RemoveWeakSuffixes WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict DPs:
            *#(s(x),y) -> c_2(*#(x,y))
            -#(s(x),s(y)) -> c_5(-#(x,y))
            exp#(x,s(y)) -> c_7(*#(x,exp(x,y)),exp#(x,y))
        - Weak DPs:
            *#(0(),y) -> c_1()
            -#(x,0()) -> c_3()
            -#(0(),y) -> c_4()
            exp#(x,0()) -> c_6()
        - Weak TRS:
            *(0(),y) -> 0()
            *(s(x),y) -> +(y,*(x,y))
            exp(x,0()) -> s(0())
            exp(x,s(y)) -> *(x,exp(x,y))
        - Signature:
            {*/2,-/2,exp/2,*#/2,-#/2,exp#/2} / {+/2,0/0,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/1,c_6/0,c_7/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#,-#,exp#} and constructors {+,0,s}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:*#(s(x),y) -> c_2(*#(x,y))
             -->_1 *#(0(),y) -> c_1():4
             -->_1 *#(s(x),y) -> c_2(*#(x,y)):1
          
          2:S:-#(s(x),s(y)) -> c_5(-#(x,y))
             -->_1 -#(0(),y) -> c_4():6
             -->_1 -#(x,0()) -> c_3():5
             -->_1 -#(s(x),s(y)) -> c_5(-#(x,y)):2
          
          3:S:exp#(x,s(y)) -> c_7(*#(x,exp(x,y)),exp#(x,y))
             -->_2 exp#(x,0()) -> c_6():7
             -->_1 *#(0(),y) -> c_1():4
             -->_2 exp#(x,s(y)) -> c_7(*#(x,exp(x,y)),exp#(x,y)):3
             -->_1 *#(s(x),y) -> c_2(*#(x,y)):1
          
          4:W:*#(0(),y) -> c_1()
             
          
          5:W:-#(x,0()) -> c_3()
             
          
          6:W:-#(0(),y) -> c_4()
             
          
          7:W:exp#(x,0()) -> c_6()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          7: exp#(x,0()) -> c_6()
          5: -#(x,0()) -> c_3()
          6: -#(0(),y) -> c_4()
          4: *#(0(),y) -> c_1()
* Step 5: Decompose WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict DPs:
            *#(s(x),y) -> c_2(*#(x,y))
            -#(s(x),s(y)) -> c_5(-#(x,y))
            exp#(x,s(y)) -> c_7(*#(x,exp(x,y)),exp#(x,y))
        - Weak TRS:
            *(0(),y) -> 0()
            *(s(x),y) -> +(y,*(x,y))
            exp(x,0()) -> s(0())
            exp(x,s(y)) -> *(x,exp(x,y))
        - Signature:
            {*/2,-/2,exp/2,*#/2,-#/2,exp#/2} / {+/2,0/0,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/1,c_6/0,c_7/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#,-#,exp#} and constructors {+,0,s}
    + 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:
              *#(s(x),y) -> c_2(*#(x,y))
          - Weak DPs:
              -#(s(x),s(y)) -> c_5(-#(x,y))
              exp#(x,s(y)) -> c_7(*#(x,exp(x,y)),exp#(x,y))
          - Weak TRS:
              *(0(),y) -> 0()
              *(s(x),y) -> +(y,*(x,y))
              exp(x,0()) -> s(0())
              exp(x,s(y)) -> *(x,exp(x,y))
          - Signature:
              {*/2,-/2,exp/2,*#/2,-#/2,exp#/2} / {+/2,0/0,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/1,c_6/0,c_7/2}
          - Obligation:
              innermost runtime complexity wrt. defined symbols {*#,-#,exp#} and constructors {+,0,s}
        
        Problem (S)
          - Strict DPs:
              -#(s(x),s(y)) -> c_5(-#(x,y))
              exp#(x,s(y)) -> c_7(*#(x,exp(x,y)),exp#(x,y))
          - Weak DPs:
              *#(s(x),y) -> c_2(*#(x,y))
          - Weak TRS:
              *(0(),y) -> 0()
              *(s(x),y) -> +(y,*(x,y))
              exp(x,0()) -> s(0())
              exp(x,s(y)) -> *(x,exp(x,y))
          - Signature:
              {*/2,-/2,exp/2,*#/2,-#/2,exp#/2} / {+/2,0/0,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/1,c_6/0,c_7/2}
          - Obligation:
              innermost runtime complexity wrt. defined symbols {*#,-#,exp#} and constructors {+,0,s}
** Step 5.a:1: RemoveWeakSuffixes WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict DPs:
            *#(s(x),y) -> c_2(*#(x,y))
        - Weak DPs:
            -#(s(x),s(y)) -> c_5(-#(x,y))
            exp#(x,s(y)) -> c_7(*#(x,exp(x,y)),exp#(x,y))
        - Weak TRS:
            *(0(),y) -> 0()
            *(s(x),y) -> +(y,*(x,y))
            exp(x,0()) -> s(0())
            exp(x,s(y)) -> *(x,exp(x,y))
        - Signature:
            {*/2,-/2,exp/2,*#/2,-#/2,exp#/2} / {+/2,0/0,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/1,c_6/0,c_7/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#,-#,exp#} and constructors {+,0,s}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:*#(s(x),y) -> c_2(*#(x,y))
             -->_1 *#(s(x),y) -> c_2(*#(x,y)):1
          
          2:W:-#(s(x),s(y)) -> c_5(-#(x,y))
             -->_1 -#(s(x),s(y)) -> c_5(-#(x,y)):2
          
          3:W:exp#(x,s(y)) -> c_7(*#(x,exp(x,y)),exp#(x,y))
             -->_1 *#(s(x),y) -> c_2(*#(x,y)):1
             -->_2 exp#(x,s(y)) -> c_7(*#(x,exp(x,y)),exp#(x,y)):3
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          2: -#(s(x),s(y)) -> c_5(-#(x,y))
** Step 5.a:2: PredecessorEstimationCP WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict DPs:
            *#(s(x),y) -> c_2(*#(x,y))
        - Weak DPs:
            exp#(x,s(y)) -> c_7(*#(x,exp(x,y)),exp#(x,y))
        - Weak TRS:
            *(0(),y) -> 0()
            *(s(x),y) -> +(y,*(x,y))
            exp(x,0()) -> s(0())
            exp(x,s(y)) -> *(x,exp(x,y))
        - Signature:
            {*/2,-/2,exp/2,*#/2,-#/2,exp#/2} / {+/2,0/0,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/1,c_6/0,c_7/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#,-#,exp#} and constructors {+,0,s}
    + Applied Processor:
        PredecessorEstimationCP {onSelectionCP = any intersect of rules of CDG leaf and strict-rules, withComplexityPair = NaturalPI {shape = Mixed 2, restrict = Restrict, uargs = UArgs, urules = URules, selector = Nothing}}
    + Details:
        We first use the processor NaturalPI {shape = Mixed 2, restrict = Restrict, uargs = UArgs, urules = URules, selector = Nothing} to orient following rules strictly:
          1: *#(s(x),y) -> c_2(*#(x,y))
          
        The strictly oriented rules are moved into the weak component.
*** Step 5.a:2.a:1: NaturalPI WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict DPs:
            *#(s(x),y) -> c_2(*#(x,y))
        - Weak DPs:
            exp#(x,s(y)) -> c_7(*#(x,exp(x,y)),exp#(x,y))
        - Weak TRS:
            *(0(),y) -> 0()
            *(s(x),y) -> +(y,*(x,y))
            exp(x,0()) -> s(0())
            exp(x,s(y)) -> *(x,exp(x,y))
        - Signature:
            {*/2,-/2,exp/2,*#/2,-#/2,exp#/2} / {+/2,0/0,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/1,c_6/0,c_7/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#,-#,exp#} and constructors {+,0,s}
    + Applied Processor:
        NaturalPI {shape = Mixed 2, restrict = Restrict, 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 polynomial interpretation of kind constructor-based(mixed(2)):
        The following argument positions are considered usable:
          uargs(c_2) = {1},
          uargs(c_7) = {1,2}
        
        Following symbols are considered usable:
          {*#,-#,exp#}
        TcT has computed the following interpretation:
             p(*) = 2*x1^2 + 2*x2 + 2*x2^2          
             p(+) = x2                              
             p(-) = 2 + x1 + x1*x2 + x1^2 + 2*x2^2  
             p(0) = 0                               
           p(exp) = 0                               
             p(s) = 1 + x1                          
            p(*#) = 1 + x1                          
            p(-#) = 1 + x1 + x2 + x2^2              
          p(exp#) = 6 + 2*x1 + x1*x2 + 3*x2 + 2*x2^2
           p(c_1) = 0                               
           p(c_2) = x1                              
           p(c_3) = 4                               
           p(c_4) = 4                               
           p(c_5) = 0                               
           p(c_6) = 1                               
           p(c_7) = x1 + x2                         
        
        Following rules are strictly oriented:
        *#(s(x),y) = 2 + x       
                   > 1 + x       
                   = c_2(*#(x,y))
        
        
        Following rules are (at-least) weakly oriented:
        exp#(x,s(y)) =  11 + 3*x + x*y + 7*y + 2*y^2 
                     >= 7 + 3*x + x*y + 3*y + 2*y^2  
                     =  c_7(*#(x,exp(x,y)),exp#(x,y))
        
*** Step 5.a:2.a:2: Assumption WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            *#(s(x),y) -> c_2(*#(x,y))
            exp#(x,s(y)) -> c_7(*#(x,exp(x,y)),exp#(x,y))
        - Weak TRS:
            *(0(),y) -> 0()
            *(s(x),y) -> +(y,*(x,y))
            exp(x,0()) -> s(0())
            exp(x,s(y)) -> *(x,exp(x,y))
        - Signature:
            {*/2,-/2,exp/2,*#/2,-#/2,exp#/2} / {+/2,0/0,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/1,c_6/0,c_7/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#,-#,exp#} and constructors {+,0,s}
    + Applied Processor:
        Assumption {assumed = Certificate {spaceUB = Unknown, spaceLB = Unknown, timeUB = Poly (Just 0), timeLB = Unknown}}
    + Details:
        ()

*** Step 5.a:2.b:1: RemoveWeakSuffixes WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            *#(s(x),y) -> c_2(*#(x,y))
            exp#(x,s(y)) -> c_7(*#(x,exp(x,y)),exp#(x,y))
        - Weak TRS:
            *(0(),y) -> 0()
            *(s(x),y) -> +(y,*(x,y))
            exp(x,0()) -> s(0())
            exp(x,s(y)) -> *(x,exp(x,y))
        - Signature:
            {*/2,-/2,exp/2,*#/2,-#/2,exp#/2} / {+/2,0/0,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/1,c_6/0,c_7/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#,-#,exp#} and constructors {+,0,s}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:W:*#(s(x),y) -> c_2(*#(x,y))
             -->_1 *#(s(x),y) -> c_2(*#(x,y)):1
          
          2:W:exp#(x,s(y)) -> c_7(*#(x,exp(x,y)),exp#(x,y))
             -->_2 exp#(x,s(y)) -> c_7(*#(x,exp(x,y)),exp#(x,y)):2
             -->_1 *#(s(x),y) -> c_2(*#(x,y)):1
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          2: exp#(x,s(y)) -> c_7(*#(x,exp(x,y)),exp#(x,y))
          1: *#(s(x),y) -> c_2(*#(x,y))
*** Step 5.a:2.b:2: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            *(0(),y) -> 0()
            *(s(x),y) -> +(y,*(x,y))
            exp(x,0()) -> s(0())
            exp(x,s(y)) -> *(x,exp(x,y))
        - Signature:
            {*/2,-/2,exp/2,*#/2,-#/2,exp#/2} / {+/2,0/0,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/1,c_6/0,c_7/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#,-#,exp#} and constructors {+,0,s}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

** Step 5.b:1: RemoveWeakSuffixes WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            -#(s(x),s(y)) -> c_5(-#(x,y))
            exp#(x,s(y)) -> c_7(*#(x,exp(x,y)),exp#(x,y))
        - Weak DPs:
            *#(s(x),y) -> c_2(*#(x,y))
        - Weak TRS:
            *(0(),y) -> 0()
            *(s(x),y) -> +(y,*(x,y))
            exp(x,0()) -> s(0())
            exp(x,s(y)) -> *(x,exp(x,y))
        - Signature:
            {*/2,-/2,exp/2,*#/2,-#/2,exp#/2} / {+/2,0/0,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/1,c_6/0,c_7/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#,-#,exp#} and constructors {+,0,s}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:-#(s(x),s(y)) -> c_5(-#(x,y))
             -->_1 -#(s(x),s(y)) -> c_5(-#(x,y)):1
          
          2:S:exp#(x,s(y)) -> c_7(*#(x,exp(x,y)),exp#(x,y))
             -->_1 *#(s(x),y) -> c_2(*#(x,y)):3
             -->_2 exp#(x,s(y)) -> c_7(*#(x,exp(x,y)),exp#(x,y)):2
          
          3:W:*#(s(x),y) -> c_2(*#(x,y))
             -->_1 *#(s(x),y) -> c_2(*#(x,y)):3
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          3: *#(s(x),y) -> c_2(*#(x,y))
** Step 5.b:2: SimplifyRHS WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            -#(s(x),s(y)) -> c_5(-#(x,y))
            exp#(x,s(y)) -> c_7(*#(x,exp(x,y)),exp#(x,y))
        - Weak TRS:
            *(0(),y) -> 0()
            *(s(x),y) -> +(y,*(x,y))
            exp(x,0()) -> s(0())
            exp(x,s(y)) -> *(x,exp(x,y))
        - Signature:
            {*/2,-/2,exp/2,*#/2,-#/2,exp#/2} / {+/2,0/0,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/1,c_6/0,c_7/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#,-#,exp#} and constructors {+,0,s}
    + Applied Processor:
        SimplifyRHS
    + Details:
        Consider the dependency graph
          1:S:-#(s(x),s(y)) -> c_5(-#(x,y))
             -->_1 -#(s(x),s(y)) -> c_5(-#(x,y)):1
          
          2:S:exp#(x,s(y)) -> c_7(*#(x,exp(x,y)),exp#(x,y))
             -->_2 exp#(x,s(y)) -> c_7(*#(x,exp(x,y)),exp#(x,y)):2
          
        Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
          exp#(x,s(y)) -> c_7(exp#(x,y))
** Step 5.b:3: UsableRules WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            -#(s(x),s(y)) -> c_5(-#(x,y))
            exp#(x,s(y)) -> c_7(exp#(x,y))
        - Weak TRS:
            *(0(),y) -> 0()
            *(s(x),y) -> +(y,*(x,y))
            exp(x,0()) -> s(0())
            exp(x,s(y)) -> *(x,exp(x,y))
        - Signature:
            {*/2,-/2,exp/2,*#/2,-#/2,exp#/2} / {+/2,0/0,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/1,c_6/0,c_7/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#,-#,exp#} and constructors {+,0,s}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          -#(s(x),s(y)) -> c_5(-#(x,y))
          exp#(x,s(y)) -> c_7(exp#(x,y))
** Step 5.b:4: Decompose WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            -#(s(x),s(y)) -> c_5(-#(x,y))
            exp#(x,s(y)) -> c_7(exp#(x,y))
        - Signature:
            {*/2,-/2,exp/2,*#/2,-#/2,exp#/2} / {+/2,0/0,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/1,c_6/0,c_7/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#,-#,exp#} and constructors {+,0,s}
    + 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:
              -#(s(x),s(y)) -> c_5(-#(x,y))
          - Weak DPs:
              exp#(x,s(y)) -> c_7(exp#(x,y))
          - Signature:
              {*/2,-/2,exp/2,*#/2,-#/2,exp#/2} / {+/2,0/0,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/1,c_6/0,c_7/1}
          - Obligation:
              innermost runtime complexity wrt. defined symbols {*#,-#,exp#} and constructors {+,0,s}
        
        Problem (S)
          - Strict DPs:
              exp#(x,s(y)) -> c_7(exp#(x,y))
          - Weak DPs:
              -#(s(x),s(y)) -> c_5(-#(x,y))
          - Signature:
              {*/2,-/2,exp/2,*#/2,-#/2,exp#/2} / {+/2,0/0,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/1,c_6/0,c_7/1}
          - Obligation:
              innermost runtime complexity wrt. defined symbols {*#,-#,exp#} and constructors {+,0,s}
*** Step 5.b:4.a:1: RemoveWeakSuffixes WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            -#(s(x),s(y)) -> c_5(-#(x,y))
        - Weak DPs:
            exp#(x,s(y)) -> c_7(exp#(x,y))
        - Signature:
            {*/2,-/2,exp/2,*#/2,-#/2,exp#/2} / {+/2,0/0,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/1,c_6/0,c_7/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#,-#,exp#} and constructors {+,0,s}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:-#(s(x),s(y)) -> c_5(-#(x,y))
             -->_1 -#(s(x),s(y)) -> c_5(-#(x,y)):1
          
          2:W:exp#(x,s(y)) -> c_7(exp#(x,y))
             -->_1 exp#(x,s(y)) -> c_7(exp#(x,y)):2
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          2: exp#(x,s(y)) -> c_7(exp#(x,y))
*** Step 5.b:4.a:2: PredecessorEstimationCP WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            -#(s(x),s(y)) -> c_5(-#(x,y))
        - Signature:
            {*/2,-/2,exp/2,*#/2,-#/2,exp#/2} / {+/2,0/0,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/1,c_6/0,c_7/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#,-#,exp#} and constructors {+,0,s}
    + 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: -#(s(x),s(y)) -> c_5(-#(x,y))
          
        The strictly oriented rules are moved into the weak component.
**** Step 5.b:4.a:2.a:1: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            -#(s(x),s(y)) -> c_5(-#(x,y))
        - Signature:
            {*/2,-/2,exp/2,*#/2,-#/2,exp#/2} / {+/2,0/0,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/1,c_6/0,c_7/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#,-#,exp#} and constructors {+,0,s}
    + 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_5) = {1}
        
        Following symbols are considered usable:
          {*#,-#,exp#}
        TcT has computed the following interpretation:
             p(*) = [1] x1 + [2]         
             p(+) = [0]                  
             p(-) = [1] x2 + [0]         
             p(0) = [2]                  
           p(exp) = [2] x1 + [1] x2 + [2]
             p(s) = [1] x1 + [2]         
            p(*#) = [1] x1 + [4] x2 + [2]
            p(-#) = [8] x1 + [12]        
          p(exp#) = [1] x1 + [2] x2 + [1]
           p(c_1) = [4]                  
           p(c_2) = [4] x1 + [0]         
           p(c_3) = [1]                  
           p(c_4) = [0]                  
           p(c_5) = [1] x1 + [1]         
           p(c_6) = [1]                  
           p(c_7) = [1]                  
        
        Following rules are strictly oriented:
        -#(s(x),s(y)) = [8] x + [28]
                      > [8] x + [13]
                      = c_5(-#(x,y))
        
        
        Following rules are (at-least) weakly oriented:
        
**** Step 5.b:4.a:2.a:2: Assumption WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            -#(s(x),s(y)) -> c_5(-#(x,y))
        - Signature:
            {*/2,-/2,exp/2,*#/2,-#/2,exp#/2} / {+/2,0/0,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/1,c_6/0,c_7/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#,-#,exp#} and constructors {+,0,s}
    + Applied Processor:
        Assumption {assumed = Certificate {spaceUB = Unknown, spaceLB = Unknown, timeUB = Poly (Just 0), timeLB = Unknown}}
    + Details:
        ()

**** Step 5.b:4.a:2.b:1: RemoveWeakSuffixes WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            -#(s(x),s(y)) -> c_5(-#(x,y))
        - Signature:
            {*/2,-/2,exp/2,*#/2,-#/2,exp#/2} / {+/2,0/0,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/1,c_6/0,c_7/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#,-#,exp#} and constructors {+,0,s}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:W:-#(s(x),s(y)) -> c_5(-#(x,y))
             -->_1 -#(s(x),s(y)) -> c_5(-#(x,y)):1
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          1: -#(s(x),s(y)) -> c_5(-#(x,y))
**** Step 5.b:4.a:2.b:2: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        
        - Signature:
            {*/2,-/2,exp/2,*#/2,-#/2,exp#/2} / {+/2,0/0,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/1,c_6/0,c_7/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#,-#,exp#} and constructors {+,0,s}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

*** Step 5.b:4.b:1: RemoveWeakSuffixes WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            exp#(x,s(y)) -> c_7(exp#(x,y))
        - Weak DPs:
            -#(s(x),s(y)) -> c_5(-#(x,y))
        - Signature:
            {*/2,-/2,exp/2,*#/2,-#/2,exp#/2} / {+/2,0/0,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/1,c_6/0,c_7/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#,-#,exp#} and constructors {+,0,s}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:exp#(x,s(y)) -> c_7(exp#(x,y))
             -->_1 exp#(x,s(y)) -> c_7(exp#(x,y)):1
          
          2:W:-#(s(x),s(y)) -> c_5(-#(x,y))
             -->_1 -#(s(x),s(y)) -> c_5(-#(x,y)):2
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          2: -#(s(x),s(y)) -> c_5(-#(x,y))
*** Step 5.b:4.b:2: PredecessorEstimationCP WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            exp#(x,s(y)) -> c_7(exp#(x,y))
        - Signature:
            {*/2,-/2,exp/2,*#/2,-#/2,exp#/2} / {+/2,0/0,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/1,c_6/0,c_7/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#,-#,exp#} and constructors {+,0,s}
    + 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: exp#(x,s(y)) -> c_7(exp#(x,y))
          
        The strictly oriented rules are moved into the weak component.
**** Step 5.b:4.b:2.a:1: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            exp#(x,s(y)) -> c_7(exp#(x,y))
        - Signature:
            {*/2,-/2,exp/2,*#/2,-#/2,exp#/2} / {+/2,0/0,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/1,c_6/0,c_7/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#,-#,exp#} and constructors {+,0,s}
    + 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_7) = {1}
        
        Following symbols are considered usable:
          {*#,-#,exp#}
        TcT has computed the following interpretation:
             p(*) = [0]                  
             p(+) = [1] x1 + [1] x2 + [0]
             p(-) = [1] x1 + [1] x2 + [8]
             p(0) = [2]                  
           p(exp) = [2] x2 + [1]         
             p(s) = [1] x1 + [2]         
            p(*#) = [2]                  
            p(-#) = [1] x2 + [0]         
          p(exp#) = [8] x2 + [12]        
           p(c_1) = [0]                  
           p(c_2) = [1]                  
           p(c_3) = [1]                  
           p(c_4) = [0]                  
           p(c_5) = [1] x1 + [0]         
           p(c_6) = [1]                  
           p(c_7) = [1] x1 + [15]        
        
        Following rules are strictly oriented:
        exp#(x,s(y)) = [8] y + [28]  
                     > [8] y + [27]  
                     = c_7(exp#(x,y))
        
        
        Following rules are (at-least) weakly oriented:
        
**** Step 5.b:4.b:2.a:2: Assumption WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            exp#(x,s(y)) -> c_7(exp#(x,y))
        - Signature:
            {*/2,-/2,exp/2,*#/2,-#/2,exp#/2} / {+/2,0/0,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/1,c_6/0,c_7/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#,-#,exp#} and constructors {+,0,s}
    + Applied Processor:
        Assumption {assumed = Certificate {spaceUB = Unknown, spaceLB = Unknown, timeUB = Poly (Just 0), timeLB = Unknown}}
    + Details:
        ()

**** Step 5.b:4.b:2.b:1: RemoveWeakSuffixes WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            exp#(x,s(y)) -> c_7(exp#(x,y))
        - Signature:
            {*/2,-/2,exp/2,*#/2,-#/2,exp#/2} / {+/2,0/0,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/1,c_6/0,c_7/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#,-#,exp#} and constructors {+,0,s}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:W:exp#(x,s(y)) -> c_7(exp#(x,y))
             -->_1 exp#(x,s(y)) -> c_7(exp#(x,y)):1
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          1: exp#(x,s(y)) -> c_7(exp#(x,y))
**** Step 5.b:4.b:2.b:2: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        
        - Signature:
            {*/2,-/2,exp/2,*#/2,-#/2,exp#/2} / {+/2,0/0,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/1,c_6/0,c_7/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#,-#,exp#} and constructors {+,0,s}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^2))