* Step 1: DependencyPairs WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict TRS:
            minus(x,0()) -> x
            minus(x,s(y)) -> pred(minus(x,y))
            pred(s(x)) -> x
            quot(0(),s(y)) -> 0()
            quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
        - Signature:
            {minus/2,pred/1,quot/2} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {minus,pred,quot} and constructors {0,s}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          minus#(x,0()) -> c_1()
          minus#(x,s(y)) -> c_2(pred#(minus(x,y)),minus#(x,y))
          pred#(s(x)) -> c_3()
          quot#(0(),s(y)) -> c_4()
          quot#(s(x),s(y)) -> c_5(quot#(minus(x,y),s(y)),minus#(x,y))
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: UsableRules WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict DPs:
            minus#(x,0()) -> c_1()
            minus#(x,s(y)) -> c_2(pred#(minus(x,y)),minus#(x,y))
            pred#(s(x)) -> c_3()
            quot#(0(),s(y)) -> c_4()
            quot#(s(x),s(y)) -> c_5(quot#(minus(x,y),s(y)),minus#(x,y))
        - Weak TRS:
            minus(x,0()) -> x
            minus(x,s(y)) -> pred(minus(x,y))
            pred(s(x)) -> x
            quot(0(),s(y)) -> 0()
            quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
        - Signature:
            {minus/2,pred/1,quot/2,minus#/2,pred#/1,quot#/2} / {0/0,s/1,c_1/0,c_2/2,c_3/0,c_4/0,c_5/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {minus#,pred#,quot#} and constructors {0,s}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          minus(x,0()) -> x
          minus(x,s(y)) -> pred(minus(x,y))
          pred(s(x)) -> x
          minus#(x,0()) -> c_1()
          minus#(x,s(y)) -> c_2(pred#(minus(x,y)),minus#(x,y))
          pred#(s(x)) -> c_3()
          quot#(0(),s(y)) -> c_4()
          quot#(s(x),s(y)) -> c_5(quot#(minus(x,y),s(y)),minus#(x,y))
* Step 3: PredecessorEstimation WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict DPs:
            minus#(x,0()) -> c_1()
            minus#(x,s(y)) -> c_2(pred#(minus(x,y)),minus#(x,y))
            pred#(s(x)) -> c_3()
            quot#(0(),s(y)) -> c_4()
            quot#(s(x),s(y)) -> c_5(quot#(minus(x,y),s(y)),minus#(x,y))
        - Weak TRS:
            minus(x,0()) -> x
            minus(x,s(y)) -> pred(minus(x,y))
            pred(s(x)) -> x
        - Signature:
            {minus/2,pred/1,quot/2,minus#/2,pred#/1,quot#/2} / {0/0,s/1,c_1/0,c_2/2,c_3/0,c_4/0,c_5/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {minus#,pred#,quot#} and constructors {0,s}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,3,4}
        by application of
          Pre({1,3,4}) = {2,5}.
        Here rules are labelled as follows:
          1: minus#(x,0()) -> c_1()
          2: minus#(x,s(y)) -> c_2(pred#(minus(x,y)),minus#(x,y))
          3: pred#(s(x)) -> c_3()
          4: quot#(0(),s(y)) -> c_4()
          5: quot#(s(x),s(y)) -> c_5(quot#(minus(x,y),s(y)),minus#(x,y))
* Step 4: RemoveWeakSuffixes WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict DPs:
            minus#(x,s(y)) -> c_2(pred#(minus(x,y)),minus#(x,y))
            quot#(s(x),s(y)) -> c_5(quot#(minus(x,y),s(y)),minus#(x,y))
        - Weak DPs:
            minus#(x,0()) -> c_1()
            pred#(s(x)) -> c_3()
            quot#(0(),s(y)) -> c_4()
        - Weak TRS:
            minus(x,0()) -> x
            minus(x,s(y)) -> pred(minus(x,y))
            pred(s(x)) -> x
        - Signature:
            {minus/2,pred/1,quot/2,minus#/2,pred#/1,quot#/2} / {0/0,s/1,c_1/0,c_2/2,c_3/0,c_4/0,c_5/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {minus#,pred#,quot#} and constructors {0,s}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:minus#(x,s(y)) -> c_2(pred#(minus(x,y)),minus#(x,y))
             -->_1 pred#(s(x)) -> c_3():4
             -->_2 minus#(x,0()) -> c_1():3
             -->_2 minus#(x,s(y)) -> c_2(pred#(minus(x,y)),minus#(x,y)):1
          
          2:S:quot#(s(x),s(y)) -> c_5(quot#(minus(x,y),s(y)),minus#(x,y))
             -->_1 quot#(0(),s(y)) -> c_4():5
             -->_2 minus#(x,0()) -> c_1():3
             -->_1 quot#(s(x),s(y)) -> c_5(quot#(minus(x,y),s(y)),minus#(x,y)):2
             -->_2 minus#(x,s(y)) -> c_2(pred#(minus(x,y)),minus#(x,y)):1
          
          3:W:minus#(x,0()) -> c_1()
             
          
          4:W:pred#(s(x)) -> c_3()
             
          
          5:W:quot#(0(),s(y)) -> c_4()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          5: quot#(0(),s(y)) -> c_4()
          3: minus#(x,0()) -> c_1()
          4: pred#(s(x)) -> c_3()
* Step 5: SimplifyRHS WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict DPs:
            minus#(x,s(y)) -> c_2(pred#(minus(x,y)),minus#(x,y))
            quot#(s(x),s(y)) -> c_5(quot#(minus(x,y),s(y)),minus#(x,y))
        - Weak TRS:
            minus(x,0()) -> x
            minus(x,s(y)) -> pred(minus(x,y))
            pred(s(x)) -> x
        - Signature:
            {minus/2,pred/1,quot/2,minus#/2,pred#/1,quot#/2} / {0/0,s/1,c_1/0,c_2/2,c_3/0,c_4/0,c_5/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {minus#,pred#,quot#} and constructors {0,s}
    + Applied Processor:
        SimplifyRHS
    + Details:
        Consider the dependency graph
          1:S:minus#(x,s(y)) -> c_2(pred#(minus(x,y)),minus#(x,y))
             -->_2 minus#(x,s(y)) -> c_2(pred#(minus(x,y)),minus#(x,y)):1
          
          2:S:quot#(s(x),s(y)) -> c_5(quot#(minus(x,y),s(y)),minus#(x,y))
             -->_1 quot#(s(x),s(y)) -> c_5(quot#(minus(x,y),s(y)),minus#(x,y)):2
             -->_2 minus#(x,s(y)) -> c_2(pred#(minus(x,y)),minus#(x,y)):1
          
        Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
          minus#(x,s(y)) -> c_2(minus#(x,y))
* Step 6: Decompose WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict DPs:
            minus#(x,s(y)) -> c_2(minus#(x,y))
            quot#(s(x),s(y)) -> c_5(quot#(minus(x,y),s(y)),minus#(x,y))
        - Weak TRS:
            minus(x,0()) -> x
            minus(x,s(y)) -> pred(minus(x,y))
            pred(s(x)) -> x
        - Signature:
            {minus/2,pred/1,quot/2,minus#/2,pred#/1,quot#/2} / {0/0,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {minus#,pred#,quot#} 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:
              minus#(x,s(y)) -> c_2(minus#(x,y))
          - Weak DPs:
              quot#(s(x),s(y)) -> c_5(quot#(minus(x,y),s(y)),minus#(x,y))
          - Weak TRS:
              minus(x,0()) -> x
              minus(x,s(y)) -> pred(minus(x,y))
              pred(s(x)) -> x
          - Signature:
              {minus/2,pred/1,quot/2,minus#/2,pred#/1,quot#/2} / {0/0,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/2}
          - Obligation:
              innermost runtime complexity wrt. defined symbols {minus#,pred#,quot#} and constructors {0,s}
        
        Problem (S)
          - Strict DPs:
              quot#(s(x),s(y)) -> c_5(quot#(minus(x,y),s(y)),minus#(x,y))
          - Weak DPs:
              minus#(x,s(y)) -> c_2(minus#(x,y))
          - Weak TRS:
              minus(x,0()) -> x
              minus(x,s(y)) -> pred(minus(x,y))
              pred(s(x)) -> x
          - Signature:
              {minus/2,pred/1,quot/2,minus#/2,pred#/1,quot#/2} / {0/0,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/2}
          - Obligation:
              innermost runtime complexity wrt. defined symbols {minus#,pred#,quot#} and constructors {0,s}
** Step 6.a:1: PredecessorEstimationCP WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict DPs:
            minus#(x,s(y)) -> c_2(minus#(x,y))
        - Weak DPs:
            quot#(s(x),s(y)) -> c_5(quot#(minus(x,y),s(y)),minus#(x,y))
        - Weak TRS:
            minus(x,0()) -> x
            minus(x,s(y)) -> pred(minus(x,y))
            pred(s(x)) -> x
        - Signature:
            {minus/2,pred/1,quot/2,minus#/2,pred#/1,quot#/2} / {0/0,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {minus#,pred#,quot#} 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: minus#(x,s(y)) -> c_2(minus#(x,y))
          
        The strictly oriented rules are moved into the weak component.
*** Step 6.a:1.a:1: NaturalPI WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict DPs:
            minus#(x,s(y)) -> c_2(minus#(x,y))
        - Weak DPs:
            quot#(s(x),s(y)) -> c_5(quot#(minus(x,y),s(y)),minus#(x,y))
        - Weak TRS:
            minus(x,0()) -> x
            minus(x,s(y)) -> pred(minus(x,y))
            pred(s(x)) -> x
        - Signature:
            {minus/2,pred/1,quot/2,minus#/2,pred#/1,quot#/2} / {0/0,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {minus#,pred#,quot#} 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_5) = {1,2}
        
        Following symbols are considered usable:
          {minus,pred,minus#,pred#,quot#}
        TcT has computed the following interpretation:
               p(0) = 0                                    
           p(minus) = x1                                   
            p(pred) = x1                                   
            p(quot) = 1 + 2*x1 + 2*x1*x2 + x1^2 + x2 + x2^2
               p(s) = 1 + x1                               
          p(minus#) = 7 + x2                               
           p(pred#) = 1                                    
           p(quot#) = x1*x2 + 7*x1^2 + x2                  
             p(c_1) = 0                                    
             p(c_2) = x1                                   
             p(c_3) = 0                                    
             p(c_4) = 0                                    
             p(c_5) = 1 + x1 + x2                          
        
        Following rules are strictly oriented:
        minus#(x,s(y)) = 8 + y           
                       > 7 + y           
                       = c_2(minus#(x,y))
        
        
        Following rules are (at-least) weakly oriented:
        quot#(s(x),s(y)) =  9 + 15*x + x*y + 7*x^2 + 2*y           
                         >= 9 + x + x*y + 7*x^2 + 2*y              
                         =  c_5(quot#(minus(x,y),s(y)),minus#(x,y))
        
            minus(x,0()) =  x                                      
                         >= x                                      
                         =  x                                      
        
           minus(x,s(y)) =  x                                      
                         >= x                                      
                         =  pred(minus(x,y))                       
        
              pred(s(x)) =  1 + x                                  
                         >= x                                      
                         =  x                                      
        
*** Step 6.a:1.a:2: Assumption WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            minus#(x,s(y)) -> c_2(minus#(x,y))
            quot#(s(x),s(y)) -> c_5(quot#(minus(x,y),s(y)),minus#(x,y))
        - Weak TRS:
            minus(x,0()) -> x
            minus(x,s(y)) -> pred(minus(x,y))
            pred(s(x)) -> x
        - Signature:
            {minus/2,pred/1,quot/2,minus#/2,pred#/1,quot#/2} / {0/0,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {minus#,pred#,quot#} and constructors {0,s}
    + Applied Processor:
        Assumption {assumed = Certificate {spaceUB = Unknown, spaceLB = Unknown, timeUB = Poly (Just 0), timeLB = Unknown}}
    + Details:
        ()

*** Step 6.a:1.b:1: RemoveWeakSuffixes WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            minus#(x,s(y)) -> c_2(minus#(x,y))
            quot#(s(x),s(y)) -> c_5(quot#(minus(x,y),s(y)),minus#(x,y))
        - Weak TRS:
            minus(x,0()) -> x
            minus(x,s(y)) -> pred(minus(x,y))
            pred(s(x)) -> x
        - Signature:
            {minus/2,pred/1,quot/2,minus#/2,pred#/1,quot#/2} / {0/0,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {minus#,pred#,quot#} and constructors {0,s}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:W:minus#(x,s(y)) -> c_2(minus#(x,y))
             -->_1 minus#(x,s(y)) -> c_2(minus#(x,y)):1
          
          2:W:quot#(s(x),s(y)) -> c_5(quot#(minus(x,y),s(y)),minus#(x,y))
             -->_1 quot#(s(x),s(y)) -> c_5(quot#(minus(x,y),s(y)),minus#(x,y)):2
             -->_2 minus#(x,s(y)) -> c_2(minus#(x,y)):1
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          2: quot#(s(x),s(y)) -> c_5(quot#(minus(x,y),s(y)),minus#(x,y))
          1: minus#(x,s(y)) -> c_2(minus#(x,y))
*** Step 6.a:1.b:2: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            minus(x,0()) -> x
            minus(x,s(y)) -> pred(minus(x,y))
            pred(s(x)) -> x
        - Signature:
            {minus/2,pred/1,quot/2,minus#/2,pred#/1,quot#/2} / {0/0,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {minus#,pred#,quot#} and constructors {0,s}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

** Step 6.b:1: RemoveWeakSuffixes WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            quot#(s(x),s(y)) -> c_5(quot#(minus(x,y),s(y)),minus#(x,y))
        - Weak DPs:
            minus#(x,s(y)) -> c_2(minus#(x,y))
        - Weak TRS:
            minus(x,0()) -> x
            minus(x,s(y)) -> pred(minus(x,y))
            pred(s(x)) -> x
        - Signature:
            {minus/2,pred/1,quot/2,minus#/2,pred#/1,quot#/2} / {0/0,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {minus#,pred#,quot#} and constructors {0,s}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:quot#(s(x),s(y)) -> c_5(quot#(minus(x,y),s(y)),minus#(x,y))
             -->_2 minus#(x,s(y)) -> c_2(minus#(x,y)):2
             -->_1 quot#(s(x),s(y)) -> c_5(quot#(minus(x,y),s(y)),minus#(x,y)):1
          
          2:W:minus#(x,s(y)) -> c_2(minus#(x,y))
             -->_1 minus#(x,s(y)) -> c_2(minus#(x,y)):2
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          2: minus#(x,s(y)) -> c_2(minus#(x,y))
** Step 6.b:2: SimplifyRHS WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            quot#(s(x),s(y)) -> c_5(quot#(minus(x,y),s(y)),minus#(x,y))
        - Weak TRS:
            minus(x,0()) -> x
            minus(x,s(y)) -> pred(minus(x,y))
            pred(s(x)) -> x
        - Signature:
            {minus/2,pred/1,quot/2,minus#/2,pred#/1,quot#/2} / {0/0,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {minus#,pred#,quot#} and constructors {0,s}
    + Applied Processor:
        SimplifyRHS
    + Details:
        Consider the dependency graph
          1:S:quot#(s(x),s(y)) -> c_5(quot#(minus(x,y),s(y)),minus#(x,y))
             -->_1 quot#(s(x),s(y)) -> c_5(quot#(minus(x,y),s(y)),minus#(x,y)):1
          
        Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
          quot#(s(x),s(y)) -> c_5(quot#(minus(x,y),s(y)))
** Step 6.b:3: PredecessorEstimationCP WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            quot#(s(x),s(y)) -> c_5(quot#(minus(x,y),s(y)))
        - Weak TRS:
            minus(x,0()) -> x
            minus(x,s(y)) -> pred(minus(x,y))
            pred(s(x)) -> x
        - Signature:
            {minus/2,pred/1,quot/2,minus#/2,pred#/1,quot#/2} / {0/0,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {minus#,pred#,quot#} 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: quot#(s(x),s(y)) -> c_5(quot#(minus(x,y),s(y)))
          
        The strictly oriented rules are moved into the weak component.
*** Step 6.b:3.a:1: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            quot#(s(x),s(y)) -> c_5(quot#(minus(x,y),s(y)))
        - Weak TRS:
            minus(x,0()) -> x
            minus(x,s(y)) -> pred(minus(x,y))
            pred(s(x)) -> x
        - Signature:
            {minus/2,pred/1,quot/2,minus#/2,pred#/1,quot#/2} / {0/0,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {minus#,pred#,quot#} 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:
          {minus,pred,minus#,pred#,quot#}
        TcT has computed the following interpretation:
               p(0) = [0]                  
           p(minus) = [1] x1 + [0]         
            p(pred) = [1] x1 + [0]         
            p(quot) = [1] x1 + [8] x2 + [0]
               p(s) = [1] x1 + [8]         
          p(minus#) = [8] x1 + [0]         
           p(pred#) = [1] x1 + [1]         
           p(quot#) = [1] x1 + [0]         
             p(c_1) = [0]                  
             p(c_2) = [4] x1 + [2]         
             p(c_3) = [8]                  
             p(c_4) = [1]                  
             p(c_5) = [1] x1 + [0]         
        
        Following rules are strictly oriented:
        quot#(s(x),s(y)) = [1] x + [8]                
                         > [1] x + [0]                
                         = c_5(quot#(minus(x,y),s(y)))
        
        
        Following rules are (at-least) weakly oriented:
         minus(x,0()) =  [1] x + [0]     
                      >= [1] x + [0]     
                      =  x               
        
        minus(x,s(y)) =  [1] x + [0]     
                      >= [1] x + [0]     
                      =  pred(minus(x,y))
        
           pred(s(x)) =  [1] x + [8]     
                      >= [1] x + [0]     
                      =  x               
        
*** Step 6.b:3.a:2: Assumption WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            quot#(s(x),s(y)) -> c_5(quot#(minus(x,y),s(y)))
        - Weak TRS:
            minus(x,0()) -> x
            minus(x,s(y)) -> pred(minus(x,y))
            pred(s(x)) -> x
        - Signature:
            {minus/2,pred/1,quot/2,minus#/2,pred#/1,quot#/2} / {0/0,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {minus#,pred#,quot#} and constructors {0,s}
    + Applied Processor:
        Assumption {assumed = Certificate {spaceUB = Unknown, spaceLB = Unknown, timeUB = Poly (Just 0), timeLB = Unknown}}
    + Details:
        ()

*** Step 6.b:3.b:1: RemoveWeakSuffixes WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            quot#(s(x),s(y)) -> c_5(quot#(minus(x,y),s(y)))
        - Weak TRS:
            minus(x,0()) -> x
            minus(x,s(y)) -> pred(minus(x,y))
            pred(s(x)) -> x
        - Signature:
            {minus/2,pred/1,quot/2,minus#/2,pred#/1,quot#/2} / {0/0,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {minus#,pred#,quot#} and constructors {0,s}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:W:quot#(s(x),s(y)) -> c_5(quot#(minus(x,y),s(y)))
             -->_1 quot#(s(x),s(y)) -> c_5(quot#(minus(x,y),s(y))):1
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          1: quot#(s(x),s(y)) -> c_5(quot#(minus(x,y),s(y)))
*** Step 6.b:3.b:2: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            minus(x,0()) -> x
            minus(x,s(y)) -> pred(minus(x,y))
            pred(s(x)) -> x
        - Signature:
            {minus/2,pred/1,quot/2,minus#/2,pred#/1,quot#/2} / {0/0,s/1,c_1/0,c_2/1,c_3/0,c_4/0,c_5/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {minus#,pred#,quot#} and constructors {0,s}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^2))