MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            +(x,0()) -> x
            +(x,s(y)) -> s(+(x,y))
            fib(0()) -> 0()
            fib(s(0())) -> s(0())
            fib(s(s(x))) -> sp(g(x))
            fib(s(s(0()))) -> s(0())
            g(0()) -> pair(s(0()),0())
            g(s(x)) -> np(g(x))
            g(s(0())) -> pair(s(0()),s(0()))
            np(pair(x,y)) -> pair(+(x,y),x)
            sp(pair(x,y)) -> +(x,y)
        - Signature:
            {+/2,fib/1,g/1,np/1,sp/1} / {0/0,pair/2,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+,fib,g,np,sp} and constructors {0,pair,s}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          +#(x,0()) -> c_1()
          +#(x,s(y)) -> c_2(+#(x,y))
          fib#(0()) -> c_3()
          fib#(s(0())) -> c_4()
          fib#(s(s(x))) -> c_5(sp#(g(x)),g#(x))
          fib#(s(s(0()))) -> c_6()
          g#(0()) -> c_7()
          g#(s(x)) -> c_8(np#(g(x)),g#(x))
          g#(s(0())) -> c_9()
          np#(pair(x,y)) -> c_10(+#(x,y))
          sp#(pair(x,y)) -> c_11(+#(x,y))
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            +#(x,0()) -> c_1()
            +#(x,s(y)) -> c_2(+#(x,y))
            fib#(0()) -> c_3()
            fib#(s(0())) -> c_4()
            fib#(s(s(x))) -> c_5(sp#(g(x)),g#(x))
            fib#(s(s(0()))) -> c_6()
            g#(0()) -> c_7()
            g#(s(x)) -> c_8(np#(g(x)),g#(x))
            g#(s(0())) -> c_9()
            np#(pair(x,y)) -> c_10(+#(x,y))
            sp#(pair(x,y)) -> c_11(+#(x,y))
        - Weak TRS:
            +(x,0()) -> x
            +(x,s(y)) -> s(+(x,y))
            fib(0()) -> 0()
            fib(s(0())) -> s(0())
            fib(s(s(x))) -> sp(g(x))
            fib(s(s(0()))) -> s(0())
            g(0()) -> pair(s(0()),0())
            g(s(x)) -> np(g(x))
            g(s(0())) -> pair(s(0()),s(0()))
            np(pair(x,y)) -> pair(+(x,y),x)
            sp(pair(x,y)) -> +(x,y)
        - Signature:
            {+/2,fib/1,g/1,np/1,sp/1,+#/2,fib#/1,g#/1,np#/1,sp#/1} / {0/0,pair/2,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/2,c_6/0
            ,c_7/0,c_8/2,c_9/0,c_10/1,c_11/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+#,fib#,g#,np#,sp#} and constructors {0,pair,s}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          +(x,0()) -> x
          +(x,s(y)) -> s(+(x,y))
          g(0()) -> pair(s(0()),0())
          g(s(x)) -> np(g(x))
          g(s(0())) -> pair(s(0()),s(0()))
          np(pair(x,y)) -> pair(+(x,y),x)
          +#(x,0()) -> c_1()
          +#(x,s(y)) -> c_2(+#(x,y))
          fib#(0()) -> c_3()
          fib#(s(0())) -> c_4()
          fib#(s(s(x))) -> c_5(sp#(g(x)),g#(x))
          fib#(s(s(0()))) -> c_6()
          g#(0()) -> c_7()
          g#(s(x)) -> c_8(np#(g(x)),g#(x))
          g#(s(0())) -> c_9()
          np#(pair(x,y)) -> c_10(+#(x,y))
          sp#(pair(x,y)) -> c_11(+#(x,y))
* Step 3: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            +#(x,0()) -> c_1()
            +#(x,s(y)) -> c_2(+#(x,y))
            fib#(0()) -> c_3()
            fib#(s(0())) -> c_4()
            fib#(s(s(x))) -> c_5(sp#(g(x)),g#(x))
            fib#(s(s(0()))) -> c_6()
            g#(0()) -> c_7()
            g#(s(x)) -> c_8(np#(g(x)),g#(x))
            g#(s(0())) -> c_9()
            np#(pair(x,y)) -> c_10(+#(x,y))
            sp#(pair(x,y)) -> c_11(+#(x,y))
        - Weak TRS:
            +(x,0()) -> x
            +(x,s(y)) -> s(+(x,y))
            g(0()) -> pair(s(0()),0())
            g(s(x)) -> np(g(x))
            g(s(0())) -> pair(s(0()),s(0()))
            np(pair(x,y)) -> pair(+(x,y),x)
        - Signature:
            {+/2,fib/1,g/1,np/1,sp/1,+#/2,fib#/1,g#/1,np#/1,sp#/1} / {0/0,pair/2,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/2,c_6/0
            ,c_7/0,c_8/2,c_9/0,c_10/1,c_11/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+#,fib#,g#,np#,sp#} and constructors {0,pair,s}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,3,4,6,7,9}
        by application of
          Pre({1,3,4,6,7,9}) = {2,5,8,10,11}.
        Here rules are labelled as follows:
          1: +#(x,0()) -> c_1()
          2: +#(x,s(y)) -> c_2(+#(x,y))
          3: fib#(0()) -> c_3()
          4: fib#(s(0())) -> c_4()
          5: fib#(s(s(x))) -> c_5(sp#(g(x)),g#(x))
          6: fib#(s(s(0()))) -> c_6()
          7: g#(0()) -> c_7()
          8: g#(s(x)) -> c_8(np#(g(x)),g#(x))
          9: g#(s(0())) -> c_9()
          10: np#(pair(x,y)) -> c_10(+#(x,y))
          11: sp#(pair(x,y)) -> c_11(+#(x,y))
* Step 4: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            +#(x,s(y)) -> c_2(+#(x,y))
            fib#(s(s(x))) -> c_5(sp#(g(x)),g#(x))
            g#(s(x)) -> c_8(np#(g(x)),g#(x))
            np#(pair(x,y)) -> c_10(+#(x,y))
            sp#(pair(x,y)) -> c_11(+#(x,y))
        - Weak DPs:
            +#(x,0()) -> c_1()
            fib#(0()) -> c_3()
            fib#(s(0())) -> c_4()
            fib#(s(s(0()))) -> c_6()
            g#(0()) -> c_7()
            g#(s(0())) -> c_9()
        - Weak TRS:
            +(x,0()) -> x
            +(x,s(y)) -> s(+(x,y))
            g(0()) -> pair(s(0()),0())
            g(s(x)) -> np(g(x))
            g(s(0())) -> pair(s(0()),s(0()))
            np(pair(x,y)) -> pair(+(x,y),x)
        - Signature:
            {+/2,fib/1,g/1,np/1,sp/1,+#/2,fib#/1,g#/1,np#/1,sp#/1} / {0/0,pair/2,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/2,c_6/0
            ,c_7/0,c_8/2,c_9/0,c_10/1,c_11/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+#,fib#,g#,np#,sp#} and constructors {0,pair,s}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:+#(x,s(y)) -> c_2(+#(x,y))
             -->_1 +#(x,0()) -> c_1():6
             -->_1 +#(x,s(y)) -> c_2(+#(x,y)):1
          
          2:S:fib#(s(s(x))) -> c_5(sp#(g(x)),g#(x))
             -->_1 sp#(pair(x,y)) -> c_11(+#(x,y)):5
             -->_2 g#(s(x)) -> c_8(np#(g(x)),g#(x)):3
             -->_2 g#(s(0())) -> c_9():11
             -->_2 g#(0()) -> c_7():10
          
          3:S:g#(s(x)) -> c_8(np#(g(x)),g#(x))
             -->_1 np#(pair(x,y)) -> c_10(+#(x,y)):4
             -->_2 g#(s(0())) -> c_9():11
             -->_2 g#(0()) -> c_7():10
             -->_2 g#(s(x)) -> c_8(np#(g(x)),g#(x)):3
          
          4:S:np#(pair(x,y)) -> c_10(+#(x,y))
             -->_1 +#(x,0()) -> c_1():6
             -->_1 +#(x,s(y)) -> c_2(+#(x,y)):1
          
          5:S:sp#(pair(x,y)) -> c_11(+#(x,y))
             -->_1 +#(x,0()) -> c_1():6
             -->_1 +#(x,s(y)) -> c_2(+#(x,y)):1
          
          6:W:+#(x,0()) -> c_1()
             
          
          7:W:fib#(0()) -> c_3()
             
          
          8:W:fib#(s(0())) -> c_4()
             
          
          9:W:fib#(s(s(0()))) -> c_6()
             
          
          10:W:g#(0()) -> c_7()
             
          
          11:W:g#(s(0())) -> c_9()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          9: fib#(s(s(0()))) -> c_6()
          8: fib#(s(0())) -> c_4()
          7: fib#(0()) -> c_3()
          10: g#(0()) -> c_7()
          11: g#(s(0())) -> c_9()
          6: +#(x,0()) -> c_1()
* Step 5: Decompose MAYBE
    + Considered Problem:
        - Strict DPs:
            +#(x,s(y)) -> c_2(+#(x,y))
            fib#(s(s(x))) -> c_5(sp#(g(x)),g#(x))
            g#(s(x)) -> c_8(np#(g(x)),g#(x))
            np#(pair(x,y)) -> c_10(+#(x,y))
            sp#(pair(x,y)) -> c_11(+#(x,y))
        - Weak TRS:
            +(x,0()) -> x
            +(x,s(y)) -> s(+(x,y))
            g(0()) -> pair(s(0()),0())
            g(s(x)) -> np(g(x))
            g(s(0())) -> pair(s(0()),s(0()))
            np(pair(x,y)) -> pair(+(x,y),x)
        - Signature:
            {+/2,fib/1,g/1,np/1,sp/1,+#/2,fib#/1,g#/1,np#/1,sp#/1} / {0/0,pair/2,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/2,c_6/0
            ,c_7/0,c_8/2,c_9/0,c_10/1,c_11/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+#,fib#,g#,np#,sp#} and constructors {0,pair,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:
              +#(x,s(y)) -> c_2(+#(x,y))
          - Weak DPs:
              fib#(s(s(x))) -> c_5(sp#(g(x)),g#(x))
              g#(s(x)) -> c_8(np#(g(x)),g#(x))
              np#(pair(x,y)) -> c_10(+#(x,y))
              sp#(pair(x,y)) -> c_11(+#(x,y))
          - Weak TRS:
              +(x,0()) -> x
              +(x,s(y)) -> s(+(x,y))
              g(0()) -> pair(s(0()),0())
              g(s(x)) -> np(g(x))
              g(s(0())) -> pair(s(0()),s(0()))
              np(pair(x,y)) -> pair(+(x,y),x)
          - Signature:
              {+/2,fib/1,g/1,np/1,sp/1,+#/2,fib#/1,g#/1,np#/1,sp#/1} / {0/0,pair/2,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/2
              ,c_6/0,c_7/0,c_8/2,c_9/0,c_10/1,c_11/1}
          - Obligation:
              innermost runtime complexity wrt. defined symbols {+#,fib#,g#,np#,sp#} and constructors {0,pair,s}
        
        Problem (S)
          - Strict DPs:
              fib#(s(s(x))) -> c_5(sp#(g(x)),g#(x))
              g#(s(x)) -> c_8(np#(g(x)),g#(x))
              np#(pair(x,y)) -> c_10(+#(x,y))
              sp#(pair(x,y)) -> c_11(+#(x,y))
          - Weak DPs:
              +#(x,s(y)) -> c_2(+#(x,y))
          - Weak TRS:
              +(x,0()) -> x
              +(x,s(y)) -> s(+(x,y))
              g(0()) -> pair(s(0()),0())
              g(s(x)) -> np(g(x))
              g(s(0())) -> pair(s(0()),s(0()))
              np(pair(x,y)) -> pair(+(x,y),x)
          - Signature:
              {+/2,fib/1,g/1,np/1,sp/1,+#/2,fib#/1,g#/1,np#/1,sp#/1} / {0/0,pair/2,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/2
              ,c_6/0,c_7/0,c_8/2,c_9/0,c_10/1,c_11/1}
          - Obligation:
              innermost runtime complexity wrt. defined symbols {+#,fib#,g#,np#,sp#} and constructors {0,pair,s}
** Step 5.a:1: DecomposeDG MAYBE
    + Considered Problem:
        - Strict DPs:
            +#(x,s(y)) -> c_2(+#(x,y))
        - Weak DPs:
            fib#(s(s(x))) -> c_5(sp#(g(x)),g#(x))
            g#(s(x)) -> c_8(np#(g(x)),g#(x))
            np#(pair(x,y)) -> c_10(+#(x,y))
            sp#(pair(x,y)) -> c_11(+#(x,y))
        - Weak TRS:
            +(x,0()) -> x
            +(x,s(y)) -> s(+(x,y))
            g(0()) -> pair(s(0()),0())
            g(s(x)) -> np(g(x))
            g(s(0())) -> pair(s(0()),s(0()))
            np(pair(x,y)) -> pair(+(x,y),x)
        - Signature:
            {+/2,fib/1,g/1,np/1,sp/1,+#/2,fib#/1,g#/1,np#/1,sp#/1} / {0/0,pair/2,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/2,c_6/0
            ,c_7/0,c_8/2,c_9/0,c_10/1,c_11/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+#,fib#,g#,np#,sp#} and constructors {0,pair,s}
    + 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
          fib#(s(s(x))) -> c_5(sp#(g(x)),g#(x))
          g#(s(x)) -> c_8(np#(g(x)),g#(x))
          sp#(pair(x,y)) -> c_11(+#(x,y))
        and a lower component
          +#(x,s(y)) -> c_2(+#(x,y))
          np#(pair(x,y)) -> c_10(+#(x,y))
        Further, following extension rules are added to the lower component.
          fib#(s(s(x))) -> g#(x)
          fib#(s(s(x))) -> sp#(g(x))
          g#(s(x)) -> g#(x)
          g#(s(x)) -> np#(g(x))
          sp#(pair(x,y)) -> +#(x,y)
*** Step 5.a:1.a:1: PredecessorEstimationCP WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            g#(s(x)) -> c_8(np#(g(x)),g#(x))
            sp#(pair(x,y)) -> c_11(+#(x,y))
        - Weak DPs:
            fib#(s(s(x))) -> c_5(sp#(g(x)),g#(x))
        - Weak TRS:
            +(x,0()) -> x
            +(x,s(y)) -> s(+(x,y))
            g(0()) -> pair(s(0()),0())
            g(s(x)) -> np(g(x))
            g(s(0())) -> pair(s(0()),s(0()))
            np(pair(x,y)) -> pair(+(x,y),x)
        - Signature:
            {+/2,fib/1,g/1,np/1,sp/1,+#/2,fib#/1,g#/1,np#/1,sp#/1} / {0/0,pair/2,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/2,c_6/0
            ,c_7/0,c_8/2,c_9/0,c_10/1,c_11/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+#,fib#,g#,np#,sp#} and constructors {0,pair,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:
          2: sp#(pair(x,y)) -> c_11(+#(x,y))
          
        Consider the set of all dependency pairs
          1: g#(s(x)) -> c_8(np#(g(x)),g#(x))
          2: sp#(pair(x,y)) -> c_11(+#(x,y))
          3: fib#(s(s(x))) -> c_5(sp#(g(x)),g#(x))
        Processor NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing}induces the complexity certificateTIME (?,O(n^1))
        SPACE(?,?)on application of the dependency pairs
          {2}
        These cover all (indirect) predecessors of dependency pairs
          {2,3}
        their number of applications is equally bounded.
        The dependency pairs are shifted into the weak component.
**** Step 5.a:1.a:1.a:1: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            g#(s(x)) -> c_8(np#(g(x)),g#(x))
            sp#(pair(x,y)) -> c_11(+#(x,y))
        - Weak DPs:
            fib#(s(s(x))) -> c_5(sp#(g(x)),g#(x))
        - Weak TRS:
            +(x,0()) -> x
            +(x,s(y)) -> s(+(x,y))
            g(0()) -> pair(s(0()),0())
            g(s(x)) -> np(g(x))
            g(s(0())) -> pair(s(0()),s(0()))
            np(pair(x,y)) -> pair(+(x,y),x)
        - Signature:
            {+/2,fib/1,g/1,np/1,sp/1,+#/2,fib#/1,g#/1,np#/1,sp#/1} / {0/0,pair/2,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/2,c_6/0
            ,c_7/0,c_8/2,c_9/0,c_10/1,c_11/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+#,fib#,g#,np#,sp#} and constructors {0,pair,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) = {1,2},
          uargs(c_8) = {1,2}
        
        Following symbols are considered usable:
          {+#,fib#,g#,np#,sp#}
        TcT has computed the following interpretation:
             p(+) = [0]                   
             p(0) = [0]                   
           p(fib) = [0]                   
             p(g) = [5] x1 + [6]          
            p(np) = [2] x1 + [0]          
          p(pair) = [1] x2 + [9]          
             p(s) = [5]                   
            p(sp) = [0]                   
            p(+#) = [3]                   
          p(fib#) = [4] x1 + [1]          
            p(g#) = [0]                   
           p(np#) = [0]                   
           p(sp#) = [11]                  
           p(c_1) = [0]                   
           p(c_2) = [2]                   
           p(c_3) = [0]                   
           p(c_4) = [8]                   
           p(c_5) = [1] x1 + [1] x2 + [10]
           p(c_6) = [1]                   
           p(c_7) = [8]                   
           p(c_8) = [8] x1 + [8] x2 + [0] 
           p(c_9) = [1]                   
          p(c_10) = [1] x1 + [0]          
          p(c_11) = [1] x1 + [0]          
        
        Following rules are strictly oriented:
        sp#(pair(x,y)) = [11]         
                       > [3]          
                       = c_11(+#(x,y))
        
        
        Following rules are (at-least) weakly oriented:
        fib#(s(s(x))) =  [21]                
                      >= [21]                
                      =  c_5(sp#(g(x)),g#(x))
        
             g#(s(x)) =  [0]                 
                      >= [0]                 
                      =  c_8(np#(g(x)),g#(x))
        
**** Step 5.a:1.a:1.a:2: Assumption WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            g#(s(x)) -> c_8(np#(g(x)),g#(x))
        - Weak DPs:
            fib#(s(s(x))) -> c_5(sp#(g(x)),g#(x))
            sp#(pair(x,y)) -> c_11(+#(x,y))
        - Weak TRS:
            +(x,0()) -> x
            +(x,s(y)) -> s(+(x,y))
            g(0()) -> pair(s(0()),0())
            g(s(x)) -> np(g(x))
            g(s(0())) -> pair(s(0()),s(0()))
            np(pair(x,y)) -> pair(+(x,y),x)
        - Signature:
            {+/2,fib/1,g/1,np/1,sp/1,+#/2,fib#/1,g#/1,np#/1,sp#/1} / {0/0,pair/2,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/2,c_6/0
            ,c_7/0,c_8/2,c_9/0,c_10/1,c_11/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+#,fib#,g#,np#,sp#} and constructors {0,pair,s}
    + Applied Processor:
        Assumption {assumed = Certificate {spaceUB = Unknown, spaceLB = Unknown, timeUB = Poly (Just 0), timeLB = Unknown}}
    + Details:
        ()

**** Step 5.a:1.a:1.b:1: RemoveWeakSuffixes WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            g#(s(x)) -> c_8(np#(g(x)),g#(x))
        - Weak DPs:
            fib#(s(s(x))) -> c_5(sp#(g(x)),g#(x))
            sp#(pair(x,y)) -> c_11(+#(x,y))
        - Weak TRS:
            +(x,0()) -> x
            +(x,s(y)) -> s(+(x,y))
            g(0()) -> pair(s(0()),0())
            g(s(x)) -> np(g(x))
            g(s(0())) -> pair(s(0()),s(0()))
            np(pair(x,y)) -> pair(+(x,y),x)
        - Signature:
            {+/2,fib/1,g/1,np/1,sp/1,+#/2,fib#/1,g#/1,np#/1,sp#/1} / {0/0,pair/2,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/2,c_6/0
            ,c_7/0,c_8/2,c_9/0,c_10/1,c_11/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+#,fib#,g#,np#,sp#} and constructors {0,pair,s}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:g#(s(x)) -> c_8(np#(g(x)),g#(x))
             -->_2 g#(s(x)) -> c_8(np#(g(x)),g#(x)):1
          
          2:W:fib#(s(s(x))) -> c_5(sp#(g(x)),g#(x))
             -->_1 sp#(pair(x,y)) -> c_11(+#(x,y)):3
             -->_2 g#(s(x)) -> c_8(np#(g(x)),g#(x)):1
          
          3:W:sp#(pair(x,y)) -> c_11(+#(x,y))
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          3: sp#(pair(x,y)) -> c_11(+#(x,y))
**** Step 5.a:1.a:1.b:2: SimplifyRHS WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            g#(s(x)) -> c_8(np#(g(x)),g#(x))
        - Weak DPs:
            fib#(s(s(x))) -> c_5(sp#(g(x)),g#(x))
        - Weak TRS:
            +(x,0()) -> x
            +(x,s(y)) -> s(+(x,y))
            g(0()) -> pair(s(0()),0())
            g(s(x)) -> np(g(x))
            g(s(0())) -> pair(s(0()),s(0()))
            np(pair(x,y)) -> pair(+(x,y),x)
        - Signature:
            {+/2,fib/1,g/1,np/1,sp/1,+#/2,fib#/1,g#/1,np#/1,sp#/1} / {0/0,pair/2,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/2,c_6/0
            ,c_7/0,c_8/2,c_9/0,c_10/1,c_11/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+#,fib#,g#,np#,sp#} and constructors {0,pair,s}
    + Applied Processor:
        SimplifyRHS
    + Details:
        Consider the dependency graph
          1:S:g#(s(x)) -> c_8(np#(g(x)),g#(x))
             -->_2 g#(s(x)) -> c_8(np#(g(x)),g#(x)):1
          
          2:W:fib#(s(s(x))) -> c_5(sp#(g(x)),g#(x))
             -->_2 g#(s(x)) -> c_8(np#(g(x)),g#(x)):1
          
        Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
          fib#(s(s(x))) -> c_5(g#(x))
          g#(s(x)) -> c_8(g#(x))
**** Step 5.a:1.a:1.b:3: UsableRules WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            g#(s(x)) -> c_8(g#(x))
        - Weak DPs:
            fib#(s(s(x))) -> c_5(g#(x))
        - Weak TRS:
            +(x,0()) -> x
            +(x,s(y)) -> s(+(x,y))
            g(0()) -> pair(s(0()),0())
            g(s(x)) -> np(g(x))
            g(s(0())) -> pair(s(0()),s(0()))
            np(pair(x,y)) -> pair(+(x,y),x)
        - Signature:
            {+/2,fib/1,g/1,np/1,sp/1,+#/2,fib#/1,g#/1,np#/1,sp#/1} / {0/0,pair/2,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/1,c_6/0
            ,c_7/0,c_8/1,c_9/0,c_10/1,c_11/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+#,fib#,g#,np#,sp#} and constructors {0,pair,s}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          fib#(s(s(x))) -> c_5(g#(x))
          g#(s(x)) -> c_8(g#(x))
**** Step 5.a:1.a:1.b:4: PredecessorEstimationCP WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            g#(s(x)) -> c_8(g#(x))
        - Weak DPs:
            fib#(s(s(x))) -> c_5(g#(x))
        - Signature:
            {+/2,fib/1,g/1,np/1,sp/1,+#/2,fib#/1,g#/1,np#/1,sp#/1} / {0/0,pair/2,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/1,c_6/0
            ,c_7/0,c_8/1,c_9/0,c_10/1,c_11/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+#,fib#,g#,np#,sp#} and constructors {0,pair,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: g#(s(x)) -> c_8(g#(x))
          
        Consider the set of all dependency pairs
          1: g#(s(x)) -> c_8(g#(x))
          2: fib#(s(s(x))) -> c_5(g#(x))
        Processor NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing}induces the complexity certificateTIME (?,O(n^1))
        SPACE(?,?)on application of the dependency pairs
          {1}
        These cover all (indirect) predecessors of dependency pairs
          {1,2}
        their number of applications is equally bounded.
        The dependency pairs are shifted into the weak component.
***** Step 5.a:1.a:1.b:4.a:1: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            g#(s(x)) -> c_8(g#(x))
        - Weak DPs:
            fib#(s(s(x))) -> c_5(g#(x))
        - Signature:
            {+/2,fib/1,g/1,np/1,sp/1,+#/2,fib#/1,g#/1,np#/1,sp#/1} / {0/0,pair/2,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/1,c_6/0
            ,c_7/0,c_8/1,c_9/0,c_10/1,c_11/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+#,fib#,g#,np#,sp#} and constructors {0,pair,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},
          uargs(c_8) = {1}
        
        Following symbols are considered usable:
          {+#,fib#,g#,np#,sp#}
        TcT has computed the following interpretation:
             p(+) = [1] x1 + [1] x2 + [1]
             p(0) = [4]                  
           p(fib) = [2] x1 + [0]         
             p(g) = [1] x1 + [1]         
            p(np) = [4] x1 + [2]         
          p(pair) = [0]                  
             p(s) = [1] x1 + [2]         
            p(sp) = [1] x1 + [8]         
            p(+#) = [1] x1 + [1] x2 + [1]
          p(fib#) = [2] x1 + [4]         
            p(g#) = [2] x1 + [0]         
           p(np#) = [1] x1 + [8]         
           p(sp#) = [0]                  
           p(c_1) = [1]                  
           p(c_2) = [1]                  
           p(c_3) = [2]                  
           p(c_4) = [0]                  
           p(c_5) = [1] x1 + [12]        
           p(c_6) = [1]                  
           p(c_7) = [0]                  
           p(c_8) = [1] x1 + [1]         
           p(c_9) = [2]                  
          p(c_10) = [1] x1 + [1]         
          p(c_11) = [4] x1 + [0]         
        
        Following rules are strictly oriented:
        g#(s(x)) = [2] x + [4]
                 > [2] x + [1]
                 = c_8(g#(x)) 
        
        
        Following rules are (at-least) weakly oriented:
        fib#(s(s(x))) =  [2] x + [12]
                      >= [2] x + [12]
                      =  c_5(g#(x))  
        
***** Step 5.a:1.a:1.b:4.a:2: Assumption WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            fib#(s(s(x))) -> c_5(g#(x))
            g#(s(x)) -> c_8(g#(x))
        - Signature:
            {+/2,fib/1,g/1,np/1,sp/1,+#/2,fib#/1,g#/1,np#/1,sp#/1} / {0/0,pair/2,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/1,c_6/0
            ,c_7/0,c_8/1,c_9/0,c_10/1,c_11/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+#,fib#,g#,np#,sp#} and constructors {0,pair,s}
    + Applied Processor:
        Assumption {assumed = Certificate {spaceUB = Unknown, spaceLB = Unknown, timeUB = Poly (Just 0), timeLB = Unknown}}
    + Details:
        ()

***** Step 5.a:1.a:1.b:4.b:1: RemoveWeakSuffixes WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            fib#(s(s(x))) -> c_5(g#(x))
            g#(s(x)) -> c_8(g#(x))
        - Signature:
            {+/2,fib/1,g/1,np/1,sp/1,+#/2,fib#/1,g#/1,np#/1,sp#/1} / {0/0,pair/2,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/1,c_6/0
            ,c_7/0,c_8/1,c_9/0,c_10/1,c_11/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+#,fib#,g#,np#,sp#} and constructors {0,pair,s}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:W:fib#(s(s(x))) -> c_5(g#(x))
             -->_1 g#(s(x)) -> c_8(g#(x)):2
          
          2:W:g#(s(x)) -> c_8(g#(x))
             -->_1 g#(s(x)) -> c_8(g#(x)):2
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          1: fib#(s(s(x))) -> c_5(g#(x))
          2: g#(s(x)) -> c_8(g#(x))
***** Step 5.a:1.a:1.b:4.b:2: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        
        - Signature:
            {+/2,fib/1,g/1,np/1,sp/1,+#/2,fib#/1,g#/1,np#/1,sp#/1} / {0/0,pair/2,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/1,c_6/0
            ,c_7/0,c_8/1,c_9/0,c_10/1,c_11/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+#,fib#,g#,np#,sp#} and constructors {0,pair,s}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

*** Step 5.a:1.b:1: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          +#(x,s(y)) -> c_2(+#(x,y))
      - Weak DPs:
          fib#(s(s(x))) -> g#(x)
          fib#(s(s(x))) -> sp#(g(x))
          g#(s(x)) -> g#(x)
          g#(s(x)) -> np#(g(x))
          np#(pair(x,y)) -> c_10(+#(x,y))
          sp#(pair(x,y)) -> +#(x,y)
      - Weak TRS:
          +(x,0()) -> x
          +(x,s(y)) -> s(+(x,y))
          g(0()) -> pair(s(0()),0())
          g(s(x)) -> np(g(x))
          g(s(0())) -> pair(s(0()),s(0()))
          np(pair(x,y)) -> pair(+(x,y),x)
      - Signature:
          {+/2,fib/1,g/1,np/1,sp/1,+#/2,fib#/1,g#/1,np#/1,sp#/1} / {0/0,pair/2,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/2,c_6/0
          ,c_7/0,c_8/2,c_9/0,c_10/1,c_11/1}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {+#,fib#,g#,np#,sp#} and constructors {0,pair,s}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
** Step 5.b:1: PredecessorEstimation WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            fib#(s(s(x))) -> c_5(sp#(g(x)),g#(x))
            g#(s(x)) -> c_8(np#(g(x)),g#(x))
            np#(pair(x,y)) -> c_10(+#(x,y))
            sp#(pair(x,y)) -> c_11(+#(x,y))
        - Weak DPs:
            +#(x,s(y)) -> c_2(+#(x,y))
        - Weak TRS:
            +(x,0()) -> x
            +(x,s(y)) -> s(+(x,y))
            g(0()) -> pair(s(0()),0())
            g(s(x)) -> np(g(x))
            g(s(0())) -> pair(s(0()),s(0()))
            np(pair(x,y)) -> pair(+(x,y),x)
        - Signature:
            {+/2,fib/1,g/1,np/1,sp/1,+#/2,fib#/1,g#/1,np#/1,sp#/1} / {0/0,pair/2,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/2,c_6/0
            ,c_7/0,c_8/2,c_9/0,c_10/1,c_11/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+#,fib#,g#,np#,sp#} and constructors {0,pair,s}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {3,4}
        by application of
          Pre({3,4}) = {1,2}.
        Here rules are labelled as follows:
          1: fib#(s(s(x))) -> c_5(sp#(g(x)),g#(x))
          2: g#(s(x)) -> c_8(np#(g(x)),g#(x))
          3: np#(pair(x,y)) -> c_10(+#(x,y))
          4: sp#(pair(x,y)) -> c_11(+#(x,y))
          5: +#(x,s(y)) -> c_2(+#(x,y))
** Step 5.b:2: RemoveWeakSuffixes WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            fib#(s(s(x))) -> c_5(sp#(g(x)),g#(x))
            g#(s(x)) -> c_8(np#(g(x)),g#(x))
        - Weak DPs:
            +#(x,s(y)) -> c_2(+#(x,y))
            np#(pair(x,y)) -> c_10(+#(x,y))
            sp#(pair(x,y)) -> c_11(+#(x,y))
        - Weak TRS:
            +(x,0()) -> x
            +(x,s(y)) -> s(+(x,y))
            g(0()) -> pair(s(0()),0())
            g(s(x)) -> np(g(x))
            g(s(0())) -> pair(s(0()),s(0()))
            np(pair(x,y)) -> pair(+(x,y),x)
        - Signature:
            {+/2,fib/1,g/1,np/1,sp/1,+#/2,fib#/1,g#/1,np#/1,sp#/1} / {0/0,pair/2,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/2,c_6/0
            ,c_7/0,c_8/2,c_9/0,c_10/1,c_11/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+#,fib#,g#,np#,sp#} and constructors {0,pair,s}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:fib#(s(s(x))) -> c_5(sp#(g(x)),g#(x))
             -->_1 sp#(pair(x,y)) -> c_11(+#(x,y)):5
             -->_2 g#(s(x)) -> c_8(np#(g(x)),g#(x)):2
          
          2:S:g#(s(x)) -> c_8(np#(g(x)),g#(x))
             -->_1 np#(pair(x,y)) -> c_10(+#(x,y)):4
             -->_2 g#(s(x)) -> c_8(np#(g(x)),g#(x)):2
          
          3:W:+#(x,s(y)) -> c_2(+#(x,y))
             -->_1 +#(x,s(y)) -> c_2(+#(x,y)):3
          
          4:W:np#(pair(x,y)) -> c_10(+#(x,y))
             -->_1 +#(x,s(y)) -> c_2(+#(x,y)):3
          
          5:W:sp#(pair(x,y)) -> c_11(+#(x,y))
             -->_1 +#(x,s(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.
          4: np#(pair(x,y)) -> c_10(+#(x,y))
          5: sp#(pair(x,y)) -> c_11(+#(x,y))
          3: +#(x,s(y)) -> c_2(+#(x,y))
** Step 5.b:3: SimplifyRHS WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            fib#(s(s(x))) -> c_5(sp#(g(x)),g#(x))
            g#(s(x)) -> c_8(np#(g(x)),g#(x))
        - Weak TRS:
            +(x,0()) -> x
            +(x,s(y)) -> s(+(x,y))
            g(0()) -> pair(s(0()),0())
            g(s(x)) -> np(g(x))
            g(s(0())) -> pair(s(0()),s(0()))
            np(pair(x,y)) -> pair(+(x,y),x)
        - Signature:
            {+/2,fib/1,g/1,np/1,sp/1,+#/2,fib#/1,g#/1,np#/1,sp#/1} / {0/0,pair/2,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/2,c_6/0
            ,c_7/0,c_8/2,c_9/0,c_10/1,c_11/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+#,fib#,g#,np#,sp#} and constructors {0,pair,s}
    + Applied Processor:
        SimplifyRHS
    + Details:
        Consider the dependency graph
          1:S:fib#(s(s(x))) -> c_5(sp#(g(x)),g#(x))
             -->_2 g#(s(x)) -> c_8(np#(g(x)),g#(x)):2
          
          2:S:g#(s(x)) -> c_8(np#(g(x)),g#(x))
             -->_2 g#(s(x)) -> c_8(np#(g(x)),g#(x)):2
          
        Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
          fib#(s(s(x))) -> c_5(g#(x))
          g#(s(x)) -> c_8(g#(x))
** Step 5.b:4: UsableRules WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            fib#(s(s(x))) -> c_5(g#(x))
            g#(s(x)) -> c_8(g#(x))
        - Weak TRS:
            +(x,0()) -> x
            +(x,s(y)) -> s(+(x,y))
            g(0()) -> pair(s(0()),0())
            g(s(x)) -> np(g(x))
            g(s(0())) -> pair(s(0()),s(0()))
            np(pair(x,y)) -> pair(+(x,y),x)
        - Signature:
            {+/2,fib/1,g/1,np/1,sp/1,+#/2,fib#/1,g#/1,np#/1,sp#/1} / {0/0,pair/2,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/1,c_6/0
            ,c_7/0,c_8/1,c_9/0,c_10/1,c_11/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+#,fib#,g#,np#,sp#} and constructors {0,pair,s}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          fib#(s(s(x))) -> c_5(g#(x))
          g#(s(x)) -> c_8(g#(x))
** Step 5.b:5: PredecessorEstimationCP WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            fib#(s(s(x))) -> c_5(g#(x))
            g#(s(x)) -> c_8(g#(x))
        - Signature:
            {+/2,fib/1,g/1,np/1,sp/1,+#/2,fib#/1,g#/1,np#/1,sp#/1} / {0/0,pair/2,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/1,c_6/0
            ,c_7/0,c_8/1,c_9/0,c_10/1,c_11/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+#,fib#,g#,np#,sp#} and constructors {0,pair,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: fib#(s(s(x))) -> c_5(g#(x))
          2: g#(s(x)) -> c_8(g#(x))
          
        The strictly oriented rules are moved into the weak component.
*** Step 5.b:5.a:1: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            fib#(s(s(x))) -> c_5(g#(x))
            g#(s(x)) -> c_8(g#(x))
        - Signature:
            {+/2,fib/1,g/1,np/1,sp/1,+#/2,fib#/1,g#/1,np#/1,sp#/1} / {0/0,pair/2,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/1,c_6/0
            ,c_7/0,c_8/1,c_9/0,c_10/1,c_11/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+#,fib#,g#,np#,sp#} and constructors {0,pair,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},
          uargs(c_8) = {1}
        
        Following symbols are considered usable:
          {+#,fib#,g#,np#,sp#}
        TcT has computed the following interpretation:
             p(+) = [1] x1 + [4] 
             p(0) = [0]          
           p(fib) = [4] x1 + [1] 
             p(g) = [1]          
            p(np) = [1] x1 + [0] 
          p(pair) = [1] x1 + [1] 
             p(s) = [1] x1 + [1] 
            p(sp) = [2] x1 + [1] 
            p(+#) = [2] x2 + [2] 
          p(fib#) = [2] x1 + [15]
            p(g#) = [1] x1 + [8] 
           p(np#) = [1] x1 + [1] 
           p(sp#) = [2] x1 + [1] 
           p(c_1) = [0]          
           p(c_2) = [2] x1 + [0] 
           p(c_3) = [1]          
           p(c_4) = [1]          
           p(c_5) = [1] x1 + [0] 
           p(c_6) = [8]          
           p(c_7) = [1]          
           p(c_8) = [1] x1 + [0] 
           p(c_9) = [1]          
          p(c_10) = [1] x1 + [4] 
          p(c_11) = [1] x1 + [1] 
        
        Following rules are strictly oriented:
        fib#(s(s(x))) = [2] x + [19]
                      > [1] x + [8] 
                      = c_5(g#(x))  
        
             g#(s(x)) = [1] x + [9] 
                      > [1] x + [8] 
                      = c_8(g#(x))  
        
        
        Following rules are (at-least) weakly oriented:
        
*** Step 5.b:5.a:2: Assumption WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            fib#(s(s(x))) -> c_5(g#(x))
            g#(s(x)) -> c_8(g#(x))
        - Signature:
            {+/2,fib/1,g/1,np/1,sp/1,+#/2,fib#/1,g#/1,np#/1,sp#/1} / {0/0,pair/2,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/1,c_6/0
            ,c_7/0,c_8/1,c_9/0,c_10/1,c_11/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+#,fib#,g#,np#,sp#} and constructors {0,pair,s}
    + Applied Processor:
        Assumption {assumed = Certificate {spaceUB = Unknown, spaceLB = Unknown, timeUB = Poly (Just 0), timeLB = Unknown}}
    + Details:
        ()

*** Step 5.b:5.b:1: RemoveWeakSuffixes WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            fib#(s(s(x))) -> c_5(g#(x))
            g#(s(x)) -> c_8(g#(x))
        - Signature:
            {+/2,fib/1,g/1,np/1,sp/1,+#/2,fib#/1,g#/1,np#/1,sp#/1} / {0/0,pair/2,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/1,c_6/0
            ,c_7/0,c_8/1,c_9/0,c_10/1,c_11/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+#,fib#,g#,np#,sp#} and constructors {0,pair,s}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:W:fib#(s(s(x))) -> c_5(g#(x))
             -->_1 g#(s(x)) -> c_8(g#(x)):2
          
          2:W:g#(s(x)) -> c_8(g#(x))
             -->_1 g#(s(x)) -> c_8(g#(x)):2
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          1: fib#(s(s(x))) -> c_5(g#(x))
          2: g#(s(x)) -> c_8(g#(x))
*** Step 5.b:5.b:2: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        
        - Signature:
            {+/2,fib/1,g/1,np/1,sp/1,+#/2,fib#/1,g#/1,np#/1,sp#/1} / {0/0,pair/2,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/1,c_6/0
            ,c_7/0,c_8/1,c_9/0,c_10/1,c_11/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+#,fib#,g#,np#,sp#} and constructors {0,pair,s}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

MAYBE