WORST_CASE(Omega(n^1),O(n^2))
* Step 1: Sum WORST_CASE(Omega(n^1),O(n^2))
    + Considered Problem:
        - Strict TRS:
            minus(x,0()) -> x
            minus(s(x),s(y)) -> minus(x,y)
            plus(0(),y) -> y
            plus(minus(x,s(0())),minus(y,s(s(z)))) -> plus(minus(y,s(s(z))),minus(x,s(0())))
            plus(plus(x,s(0())),plus(y,s(s(z)))) -> plus(plus(y,s(s(z))),plus(x,s(0())))
            plus(s(x),y) -> s(plus(x,y))
            quot(0(),s(y)) -> 0()
            quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
        - Signature:
            {minus/2,plus/2,quot/2} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {minus,plus,quot} and constructors {0,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            minus(x,0()) -> x
            minus(s(x),s(y)) -> minus(x,y)
            plus(0(),y) -> y
            plus(minus(x,s(0())),minus(y,s(s(z)))) -> plus(minus(y,s(s(z))),minus(x,s(0())))
            plus(plus(x,s(0())),plus(y,s(s(z)))) -> plus(plus(y,s(s(z))),plus(x,s(0())))
            plus(s(x),y) -> s(plus(x,y))
            quot(0(),s(y)) -> 0()
            quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
        - Signature:
            {minus/2,plus/2,quot/2} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {minus,plus,quot} and constructors {0,s}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          minus(x,y){x -> s(x),y -> s(y)} =
            minus(s(x),s(y)) ->^+ minus(x,y)
              = C[minus(x,y) = minus(x,y){}]

** Step 1.b:1: DependencyPairs WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict TRS:
            minus(x,0()) -> x
            minus(s(x),s(y)) -> minus(x,y)
            plus(0(),y) -> y
            plus(minus(x,s(0())),minus(y,s(s(z)))) -> plus(minus(y,s(s(z))),minus(x,s(0())))
            plus(plus(x,s(0())),plus(y,s(s(z)))) -> plus(plus(y,s(s(z))),plus(x,s(0())))
            plus(s(x),y) -> s(plus(x,y))
            quot(0(),s(y)) -> 0()
            quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
        - Signature:
            {minus/2,plus/2,quot/2} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {minus,plus,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#(s(x),s(y)) -> c_2(minus#(x,y))
          plus#(0(),y) -> c_3()
          plus#(minus(x,s(0())),minus(y,s(s(z)))) -> c_4(plus#(minus(y,s(s(z))),minus(x,s(0())))
                                                        ,minus#(y,s(s(z)))
                                                        ,minus#(x,s(0())))
          plus#(plus(x,s(0())),plus(y,s(s(z)))) -> c_5(plus#(plus(y,s(s(z))),plus(x,s(0())))
                                                      ,plus#(y,s(s(z)))
                                                      ,plus#(x,s(0())))
          plus#(s(x),y) -> c_6(plus#(x,y))
          quot#(0(),s(y)) -> c_7()
          quot#(s(x),s(y)) -> c_8(quot#(minus(x,y),s(y)),minus#(x,y))
        Weak DPs
          
        
        and mark the set of starting terms.
** Step 1.b:2: PredecessorEstimation WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict DPs:
            minus#(x,0()) -> c_1()
            minus#(s(x),s(y)) -> c_2(minus#(x,y))
            plus#(0(),y) -> c_3()
            plus#(minus(x,s(0())),minus(y,s(s(z)))) -> c_4(plus#(minus(y,s(s(z))),minus(x,s(0())))
                                                          ,minus#(y,s(s(z)))
                                                          ,minus#(x,s(0())))
            plus#(plus(x,s(0())),plus(y,s(s(z)))) -> c_5(plus#(plus(y,s(s(z))),plus(x,s(0())))
                                                        ,plus#(y,s(s(z)))
                                                        ,plus#(x,s(0())))
            plus#(s(x),y) -> c_6(plus#(x,y))
            quot#(0(),s(y)) -> c_7()
            quot#(s(x),s(y)) -> c_8(quot#(minus(x,y),s(y)),minus#(x,y))
        - Weak TRS:
            minus(x,0()) -> x
            minus(s(x),s(y)) -> minus(x,y)
            plus(0(),y) -> y
            plus(minus(x,s(0())),minus(y,s(s(z)))) -> plus(minus(y,s(s(z))),minus(x,s(0())))
            plus(plus(x,s(0())),plus(y,s(s(z)))) -> plus(plus(y,s(s(z))),plus(x,s(0())))
            plus(s(x),y) -> s(plus(x,y))
            quot(0(),s(y)) -> 0()
            quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
        - Signature:
            {minus/2,plus/2,quot/2,minus#/2,plus#/2,quot#/2} / {0/0,s/1,c_1/0,c_2/1,c_3/0,c_4/3,c_5/3,c_6/1,c_7/0,c_8/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {minus#,plus#,quot#} and constructors {0,s}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,3,7}
        by application of
          Pre({1,3,7}) = {2,4,5,6,8}.
        Here rules are labelled as follows:
          1: minus#(x,0()) -> c_1()
          2: minus#(s(x),s(y)) -> c_2(minus#(x,y))
          3: plus#(0(),y) -> c_3()
          4: plus#(minus(x,s(0())),minus(y,s(s(z)))) -> c_4(plus#(minus(y,s(s(z))),minus(x,s(0())))
                                                           ,minus#(y,s(s(z)))
                                                           ,minus#(x,s(0())))
          5: plus#(plus(x,s(0())),plus(y,s(s(z)))) -> c_5(plus#(plus(y,s(s(z))),plus(x,s(0())))
                                                         ,plus#(y,s(s(z)))
                                                         ,plus#(x,s(0())))
          6: plus#(s(x),y) -> c_6(plus#(x,y))
          7: quot#(0(),s(y)) -> c_7()
          8: quot#(s(x),s(y)) -> c_8(quot#(minus(x,y),s(y)),minus#(x,y))
** Step 1.b:3: RemoveWeakSuffixes WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict DPs:
            minus#(s(x),s(y)) -> c_2(minus#(x,y))
            plus#(minus(x,s(0())),minus(y,s(s(z)))) -> c_4(plus#(minus(y,s(s(z))),minus(x,s(0())))
                                                          ,minus#(y,s(s(z)))
                                                          ,minus#(x,s(0())))
            plus#(plus(x,s(0())),plus(y,s(s(z)))) -> c_5(plus#(plus(y,s(s(z))),plus(x,s(0())))
                                                        ,plus#(y,s(s(z)))
                                                        ,plus#(x,s(0())))
            plus#(s(x),y) -> c_6(plus#(x,y))
            quot#(s(x),s(y)) -> c_8(quot#(minus(x,y),s(y)),minus#(x,y))
        - Weak DPs:
            minus#(x,0()) -> c_1()
            plus#(0(),y) -> c_3()
            quot#(0(),s(y)) -> c_7()
        - Weak TRS:
            minus(x,0()) -> x
            minus(s(x),s(y)) -> minus(x,y)
            plus(0(),y) -> y
            plus(minus(x,s(0())),minus(y,s(s(z)))) -> plus(minus(y,s(s(z))),minus(x,s(0())))
            plus(plus(x,s(0())),plus(y,s(s(z)))) -> plus(plus(y,s(s(z))),plus(x,s(0())))
            plus(s(x),y) -> s(plus(x,y))
            quot(0(),s(y)) -> 0()
            quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
        - Signature:
            {minus/2,plus/2,quot/2,minus#/2,plus#/2,quot#/2} / {0/0,s/1,c_1/0,c_2/1,c_3/0,c_4/3,c_5/3,c_6/1,c_7/0,c_8/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {minus#,plus#,quot#} and constructors {0,s}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:minus#(s(x),s(y)) -> c_2(minus#(x,y))
             -->_1 minus#(x,0()) -> c_1():6
             -->_1 minus#(s(x),s(y)) -> c_2(minus#(x,y)):1
          
          2:S:plus#(minus(x,s(0())),minus(y,s(s(z)))) -> c_4(plus#(minus(y,s(s(z))),minus(x,s(0())))
                                                            ,minus#(y,s(s(z)))
                                                            ,minus#(x,s(0())))
             -->_1 plus#(s(x),y) -> c_6(plus#(x,y)):4
             -->_1 plus#(plus(x,s(0())),plus(y,s(s(z)))) -> c_5(plus#(plus(y,s(s(z))),plus(x,s(0())))
                                                               ,plus#(y,s(s(z)))
                                                               ,plus#(x,s(0()))):3
             -->_1 plus#(0(),y) -> c_3():7
             -->_1 plus#(minus(x,s(0())),minus(y,s(s(z)))) -> c_4(plus#(minus(y,s(s(z))),minus(x,s(0())))
                                                                 ,minus#(y,s(s(z)))
                                                                 ,minus#(x,s(0()))):2
             -->_3 minus#(s(x),s(y)) -> c_2(minus#(x,y)):1
          
          3:S:plus#(plus(x,s(0())),plus(y,s(s(z)))) -> c_5(plus#(plus(y,s(s(z))),plus(x,s(0())))
                                                          ,plus#(y,s(s(z)))
                                                          ,plus#(x,s(0())))
             -->_1 plus#(s(x),y) -> c_6(plus#(x,y)):4
             -->_1 plus#(0(),y) -> c_3():7
             -->_1 plus#(plus(x,s(0())),plus(y,s(s(z)))) -> c_5(plus#(plus(y,s(s(z))),plus(x,s(0())))
                                                               ,plus#(y,s(s(z)))
                                                               ,plus#(x,s(0()))):3
             -->_1 plus#(minus(x,s(0())),minus(y,s(s(z)))) -> c_4(plus#(minus(y,s(s(z))),minus(x,s(0())))
                                                                 ,minus#(y,s(s(z)))
                                                                 ,minus#(x,s(0()))):2
          
          4:S:plus#(s(x),y) -> c_6(plus#(x,y))
             -->_1 plus#(0(),y) -> c_3():7
             -->_1 plus#(s(x),y) -> c_6(plus#(x,y)):4
             -->_1 plus#(plus(x,s(0())),plus(y,s(s(z)))) -> c_5(plus#(plus(y,s(s(z))),plus(x,s(0())))
                                                               ,plus#(y,s(s(z)))
                                                               ,plus#(x,s(0()))):3
             -->_1 plus#(minus(x,s(0())),minus(y,s(s(z)))) -> c_4(plus#(minus(y,s(s(z))),minus(x,s(0())))
                                                                 ,minus#(y,s(s(z)))
                                                                 ,minus#(x,s(0()))):2
          
          5:S:quot#(s(x),s(y)) -> c_8(quot#(minus(x,y),s(y)),minus#(x,y))
             -->_1 quot#(0(),s(y)) -> c_7():8
             -->_2 minus#(x,0()) -> c_1():6
             -->_1 quot#(s(x),s(y)) -> c_8(quot#(minus(x,y),s(y)),minus#(x,y)):5
             -->_2 minus#(s(x),s(y)) -> c_2(minus#(x,y)):1
          
          6:W:minus#(x,0()) -> c_1()
             
          
          7:W:plus#(0(),y) -> c_3()
             
          
          8:W:quot#(0(),s(y)) -> c_7()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          8: quot#(0(),s(y)) -> c_7()
          7: plus#(0(),y) -> c_3()
          6: minus#(x,0()) -> c_1()
** Step 1.b:4: SimplifyRHS WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict DPs:
            minus#(s(x),s(y)) -> c_2(minus#(x,y))
            plus#(minus(x,s(0())),minus(y,s(s(z)))) -> c_4(plus#(minus(y,s(s(z))),minus(x,s(0())))
                                                          ,minus#(y,s(s(z)))
                                                          ,minus#(x,s(0())))
            plus#(plus(x,s(0())),plus(y,s(s(z)))) -> c_5(plus#(plus(y,s(s(z))),plus(x,s(0())))
                                                        ,plus#(y,s(s(z)))
                                                        ,plus#(x,s(0())))
            plus#(s(x),y) -> c_6(plus#(x,y))
            quot#(s(x),s(y)) -> c_8(quot#(minus(x,y),s(y)),minus#(x,y))
        - Weak TRS:
            minus(x,0()) -> x
            minus(s(x),s(y)) -> minus(x,y)
            plus(0(),y) -> y
            plus(minus(x,s(0())),minus(y,s(s(z)))) -> plus(minus(y,s(s(z))),minus(x,s(0())))
            plus(plus(x,s(0())),plus(y,s(s(z)))) -> plus(plus(y,s(s(z))),plus(x,s(0())))
            plus(s(x),y) -> s(plus(x,y))
            quot(0(),s(y)) -> 0()
            quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
        - Signature:
            {minus/2,plus/2,quot/2,minus#/2,plus#/2,quot#/2} / {0/0,s/1,c_1/0,c_2/1,c_3/0,c_4/3,c_5/3,c_6/1,c_7/0,c_8/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {minus#,plus#,quot#} and constructors {0,s}
    + Applied Processor:
        SimplifyRHS
    + Details:
        Consider the dependency graph
          1:S:minus#(s(x),s(y)) -> c_2(minus#(x,y))
             -->_1 minus#(s(x),s(y)) -> c_2(minus#(x,y)):1
          
          2:S:plus#(minus(x,s(0())),minus(y,s(s(z)))) -> c_4(plus#(minus(y,s(s(z))),minus(x,s(0())))
                                                            ,minus#(y,s(s(z)))
                                                            ,minus#(x,s(0())))
             -->_1 plus#(s(x),y) -> c_6(plus#(x,y)):4
             -->_1 plus#(plus(x,s(0())),plus(y,s(s(z)))) -> c_5(plus#(plus(y,s(s(z))),plus(x,s(0())))
                                                               ,plus#(y,s(s(z)))
                                                               ,plus#(x,s(0()))):3
             -->_1 plus#(minus(x,s(0())),minus(y,s(s(z)))) -> c_4(plus#(minus(y,s(s(z))),minus(x,s(0())))
                                                                 ,minus#(y,s(s(z)))
                                                                 ,minus#(x,s(0()))):2
             -->_3 minus#(s(x),s(y)) -> c_2(minus#(x,y)):1
          
          3:S:plus#(plus(x,s(0())),plus(y,s(s(z)))) -> c_5(plus#(plus(y,s(s(z))),plus(x,s(0())))
                                                          ,plus#(y,s(s(z)))
                                                          ,plus#(x,s(0())))
             -->_1 plus#(s(x),y) -> c_6(plus#(x,y)):4
             -->_1 plus#(plus(x,s(0())),plus(y,s(s(z)))) -> c_5(plus#(plus(y,s(s(z))),plus(x,s(0())))
                                                               ,plus#(y,s(s(z)))
                                                               ,plus#(x,s(0()))):3
             -->_1 plus#(minus(x,s(0())),minus(y,s(s(z)))) -> c_4(plus#(minus(y,s(s(z))),minus(x,s(0())))
                                                                 ,minus#(y,s(s(z)))
                                                                 ,minus#(x,s(0()))):2
          
          4:S:plus#(s(x),y) -> c_6(plus#(x,y))
             -->_1 plus#(s(x),y) -> c_6(plus#(x,y)):4
             -->_1 plus#(plus(x,s(0())),plus(y,s(s(z)))) -> c_5(plus#(plus(y,s(s(z))),plus(x,s(0())))
                                                               ,plus#(y,s(s(z)))
                                                               ,plus#(x,s(0()))):3
             -->_1 plus#(minus(x,s(0())),minus(y,s(s(z)))) -> c_4(plus#(minus(y,s(s(z))),minus(x,s(0())))
                                                                 ,minus#(y,s(s(z)))
                                                                 ,minus#(x,s(0()))):2
          
          5:S:quot#(s(x),s(y)) -> c_8(quot#(minus(x,y),s(y)),minus#(x,y))
             -->_1 quot#(s(x),s(y)) -> c_8(quot#(minus(x,y),s(y)),minus#(x,y)):5
             -->_2 minus#(s(x),s(y)) -> c_2(minus#(x,y)):1
          
        Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
          plus#(minus(x,s(0())),minus(y,s(s(z)))) -> c_4(plus#(minus(y,s(s(z))),minus(x,s(0()))),minus#(x,s(0())))
          plus#(plus(x,s(0())),plus(y,s(s(z)))) -> c_5(plus#(plus(y,s(s(z))),plus(x,s(0()))))
** Step 1.b:5: UsableRules WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict DPs:
            minus#(s(x),s(y)) -> c_2(minus#(x,y))
            plus#(minus(x,s(0())),minus(y,s(s(z)))) -> c_4(plus#(minus(y,s(s(z))),minus(x,s(0()))),minus#(x,s(0())))
            plus#(plus(x,s(0())),plus(y,s(s(z)))) -> c_5(plus#(plus(y,s(s(z))),plus(x,s(0()))))
            plus#(s(x),y) -> c_6(plus#(x,y))
            quot#(s(x),s(y)) -> c_8(quot#(minus(x,y),s(y)),minus#(x,y))
        - Weak TRS:
            minus(x,0()) -> x
            minus(s(x),s(y)) -> minus(x,y)
            plus(0(),y) -> y
            plus(minus(x,s(0())),minus(y,s(s(z)))) -> plus(minus(y,s(s(z))),minus(x,s(0())))
            plus(plus(x,s(0())),plus(y,s(s(z)))) -> plus(plus(y,s(s(z))),plus(x,s(0())))
            plus(s(x),y) -> s(plus(x,y))
            quot(0(),s(y)) -> 0()
            quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
        - Signature:
            {minus/2,plus/2,quot/2,minus#/2,plus#/2,quot#/2} / {0/0,s/1,c_1/0,c_2/1,c_3/0,c_4/2,c_5/1,c_6/1,c_7/0,c_8/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {minus#,plus#,quot#} and constructors {0,s}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          minus(x,0()) -> x
          minus(s(x),s(y)) -> minus(x,y)
          plus(0(),y) -> y
          plus(minus(x,s(0())),minus(y,s(s(z)))) -> plus(minus(y,s(s(z))),minus(x,s(0())))
          plus(plus(x,s(0())),plus(y,s(s(z)))) -> plus(plus(y,s(s(z))),plus(x,s(0())))
          plus(s(x),y) -> s(plus(x,y))
          minus#(s(x),s(y)) -> c_2(minus#(x,y))
          plus#(minus(x,s(0())),minus(y,s(s(z)))) -> c_4(plus#(minus(y,s(s(z))),minus(x,s(0()))),minus#(x,s(0())))
          plus#(plus(x,s(0())),plus(y,s(s(z)))) -> c_5(plus#(plus(y,s(s(z))),plus(x,s(0()))))
          plus#(s(x),y) -> c_6(plus#(x,y))
          quot#(s(x),s(y)) -> c_8(quot#(minus(x,y),s(y)),minus#(x,y))
** Step 1.b:6: DecomposeDG WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict DPs:
            minus#(s(x),s(y)) -> c_2(minus#(x,y))
            plus#(minus(x,s(0())),minus(y,s(s(z)))) -> c_4(plus#(minus(y,s(s(z))),minus(x,s(0()))),minus#(x,s(0())))
            plus#(plus(x,s(0())),plus(y,s(s(z)))) -> c_5(plus#(plus(y,s(s(z))),plus(x,s(0()))))
            plus#(s(x),y) -> c_6(plus#(x,y))
            quot#(s(x),s(y)) -> c_8(quot#(minus(x,y),s(y)),minus#(x,y))
        - Weak TRS:
            minus(x,0()) -> x
            minus(s(x),s(y)) -> minus(x,y)
            plus(0(),y) -> y
            plus(minus(x,s(0())),minus(y,s(s(z)))) -> plus(minus(y,s(s(z))),minus(x,s(0())))
            plus(plus(x,s(0())),plus(y,s(s(z)))) -> plus(plus(y,s(s(z))),plus(x,s(0())))
            plus(s(x),y) -> s(plus(x,y))
        - Signature:
            {minus/2,plus/2,quot/2,minus#/2,plus#/2,quot#/2} / {0/0,s/1,c_1/0,c_2/1,c_3/0,c_4/2,c_5/1,c_6/1,c_7/0,c_8/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {minus#,plus#,quot#} and constructors {0,s}
    + Applied Processor:
        DecomposeDG {onSelection = all below first cut in WDG, onUpper = Nothing, onLower = Nothing}
    + Details:
        We decompose the input problem according to the dependency graph into the upper component
          plus#(minus(x,s(0())),minus(y,s(s(z)))) -> c_4(plus#(minus(y,s(s(z))),minus(x,s(0()))),minus#(x,s(0())))
          plus#(plus(x,s(0())),plus(y,s(s(z)))) -> c_5(plus#(plus(y,s(s(z))),plus(x,s(0()))))
          plus#(s(x),y) -> c_6(plus#(x,y))
          quot#(s(x),s(y)) -> c_8(quot#(minus(x,y),s(y)),minus#(x,y))
        and a lower component
          minus#(s(x),s(y)) -> c_2(minus#(x,y))
        Further, following extension rules are added to the lower component.
          plus#(minus(x,s(0())),minus(y,s(s(z)))) -> minus#(x,s(0()))
          plus#(minus(x,s(0())),minus(y,s(s(z)))) -> plus#(minus(y,s(s(z))),minus(x,s(0())))
          plus#(plus(x,s(0())),plus(y,s(s(z)))) -> plus#(plus(y,s(s(z))),plus(x,s(0())))
          plus#(s(x),y) -> plus#(x,y)
          quot#(s(x),s(y)) -> minus#(x,y)
          quot#(s(x),s(y)) -> quot#(minus(x,y),s(y))
*** Step 1.b:6.a:1: SimplifyRHS WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            plus#(minus(x,s(0())),minus(y,s(s(z)))) -> c_4(plus#(minus(y,s(s(z))),minus(x,s(0()))),minus#(x,s(0())))
            plus#(plus(x,s(0())),plus(y,s(s(z)))) -> c_5(plus#(plus(y,s(s(z))),plus(x,s(0()))))
            plus#(s(x),y) -> c_6(plus#(x,y))
            quot#(s(x),s(y)) -> c_8(quot#(minus(x,y),s(y)),minus#(x,y))
        - Weak TRS:
            minus(x,0()) -> x
            minus(s(x),s(y)) -> minus(x,y)
            plus(0(),y) -> y
            plus(minus(x,s(0())),minus(y,s(s(z)))) -> plus(minus(y,s(s(z))),minus(x,s(0())))
            plus(plus(x,s(0())),plus(y,s(s(z)))) -> plus(plus(y,s(s(z))),plus(x,s(0())))
            plus(s(x),y) -> s(plus(x,y))
        - Signature:
            {minus/2,plus/2,quot/2,minus#/2,plus#/2,quot#/2} / {0/0,s/1,c_1/0,c_2/1,c_3/0,c_4/2,c_5/1,c_6/1,c_7/0,c_8/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {minus#,plus#,quot#} and constructors {0,s}
    + Applied Processor:
        SimplifyRHS
    + Details:
        Consider the dependency graph
          1:S:plus#(minus(x,s(0())),minus(y,s(s(z)))) -> c_4(plus#(minus(y,s(s(z))),minus(x,s(0())))
                                                            ,minus#(x,s(0())))
             -->_1 plus#(s(x),y) -> c_6(plus#(x,y)):3
             -->_1 plus#(plus(x,s(0())),plus(y,s(s(z)))) -> c_5(plus#(plus(y,s(s(z))),plus(x,s(0())))):2
             -->_1 plus#(minus(x,s(0())),minus(y,s(s(z)))) -> c_4(plus#(minus(y,s(s(z))),minus(x,s(0())))
                                                                 ,minus#(x,s(0()))):1
          
          2:S:plus#(plus(x,s(0())),plus(y,s(s(z)))) -> c_5(plus#(plus(y,s(s(z))),plus(x,s(0()))))
             -->_1 plus#(s(x),y) -> c_6(plus#(x,y)):3
             -->_1 plus#(plus(x,s(0())),plus(y,s(s(z)))) -> c_5(plus#(plus(y,s(s(z))),plus(x,s(0())))):2
             -->_1 plus#(minus(x,s(0())),minus(y,s(s(z)))) -> c_4(plus#(minus(y,s(s(z))),minus(x,s(0())))
                                                                 ,minus#(x,s(0()))):1
          
          3:S:plus#(s(x),y) -> c_6(plus#(x,y))
             -->_1 plus#(s(x),y) -> c_6(plus#(x,y)):3
             -->_1 plus#(plus(x,s(0())),plus(y,s(s(z)))) -> c_5(plus#(plus(y,s(s(z))),plus(x,s(0())))):2
             -->_1 plus#(minus(x,s(0())),minus(y,s(s(z)))) -> c_4(plus#(minus(y,s(s(z))),minus(x,s(0())))
                                                                 ,minus#(x,s(0()))):1
          
          4:S:quot#(s(x),s(y)) -> c_8(quot#(minus(x,y),s(y)),minus#(x,y))
             -->_1 quot#(s(x),s(y)) -> c_8(quot#(minus(x,y),s(y)),minus#(x,y)):4
          
        Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
          plus#(minus(x,s(0())),minus(y,s(s(z)))) -> c_4(plus#(minus(y,s(s(z))),minus(x,s(0()))))
          quot#(s(x),s(y)) -> c_8(quot#(minus(x,y),s(y)))
*** Step 1.b:6.a:2: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            plus#(minus(x,s(0())),minus(y,s(s(z)))) -> c_4(plus#(minus(y,s(s(z))),minus(x,s(0()))))
            plus#(plus(x,s(0())),plus(y,s(s(z)))) -> c_5(plus#(plus(y,s(s(z))),plus(x,s(0()))))
            plus#(s(x),y) -> c_6(plus#(x,y))
            quot#(s(x),s(y)) -> c_8(quot#(minus(x,y),s(y)))
        - Weak TRS:
            minus(x,0()) -> x
            minus(s(x),s(y)) -> minus(x,y)
            plus(0(),y) -> y
            plus(minus(x,s(0())),minus(y,s(s(z)))) -> plus(minus(y,s(s(z))),minus(x,s(0())))
            plus(plus(x,s(0())),plus(y,s(s(z)))) -> plus(plus(y,s(s(z))),plus(x,s(0())))
            plus(s(x),y) -> s(plus(x,y))
        - Signature:
            {minus/2,plus/2,quot/2,minus#/2,plus#/2,quot#/2} / {0/0,s/1,c_1/0,c_2/1,c_3/0,c_4/1,c_5/1,c_6/1,c_7/0,c_8/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {minus#,plus#,quot#} and constructors {0,s}
    + Applied Processor:
        NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just any strict-rules}
    + Details:
        We apply a matrix interpretation of kind constructor based matrix interpretation:
        The following argument positions are considered usable:
          uargs(c_6) = {1},
          uargs(c_8) = {1}
        
        Following symbols are considered usable:
          {minus#,plus#,quot#}
        TcT has computed the following interpretation:
               p(0) = [1]         
           p(minus) = [4]         
            p(plus) = [4]         
            p(quot) = [1] x2 + [1]
               p(s) = [0]         
          p(minus#) = [1] x2 + [4]
           p(plus#) = [1] x2 + [0]
           p(quot#) = [0]         
             p(c_1) = [0]         
             p(c_2) = [4]         
             p(c_3) = [1]         
             p(c_4) = [3]         
             p(c_5) = [4]         
             p(c_6) = [1] x1 + [0]
             p(c_7) = [1]         
             p(c_8) = [4] x1 + [0]
        
        Following rules are strictly oriented:
        plus#(minus(x,s(0())),minus(y,s(s(z)))) = [4]                                         
                                                > [3]                                         
                                                = c_4(plus#(minus(y,s(s(z))),minus(x,s(0()))))
        
        
        Following rules are (at-least) weakly oriented:
        plus#(plus(x,s(0())),plus(y,s(s(z)))) =  [4]                                       
                                              >= [4]                                       
                                              =  c_5(plus#(plus(y,s(s(z))),plus(x,s(0()))))
        
                                plus#(s(x),y) =  [1] y + [0]                               
                                              >= [1] y + [0]                               
                                              =  c_6(plus#(x,y))                           
        
                             quot#(s(x),s(y)) =  [0]                                       
                                              >= [0]                                       
                                              =  c_8(quot#(minus(x,y),s(y)))               
        
*** Step 1.b:6.a:3: NaturalPI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            plus#(plus(x,s(0())),plus(y,s(s(z)))) -> c_5(plus#(plus(y,s(s(z))),plus(x,s(0()))))
            plus#(s(x),y) -> c_6(plus#(x,y))
            quot#(s(x),s(y)) -> c_8(quot#(minus(x,y),s(y)))
        - Weak DPs:
            plus#(minus(x,s(0())),minus(y,s(s(z)))) -> c_4(plus#(minus(y,s(s(z))),minus(x,s(0()))))
        - Weak TRS:
            minus(x,0()) -> x
            minus(s(x),s(y)) -> minus(x,y)
            plus(0(),y) -> y
            plus(minus(x,s(0())),minus(y,s(s(z)))) -> plus(minus(y,s(s(z))),minus(x,s(0())))
            plus(plus(x,s(0())),plus(y,s(s(z)))) -> plus(plus(y,s(s(z))),plus(x,s(0())))
            plus(s(x),y) -> s(plus(x,y))
        - Signature:
            {minus/2,plus/2,quot/2,minus#/2,plus#/2,quot#/2} / {0/0,s/1,c_1/0,c_2/1,c_3/0,c_4/1,c_5/1,c_6/1,c_7/0,c_8/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {minus#,plus#,quot#} and constructors {0,s}
    + Applied Processor:
        NaturalPI {shape = Linear, restrict = Restrict, uargs = UArgs, urules = URules, selector = Just any strict-rules}
    + Details:
        We apply a polynomial interpretation of kind constructor-based(linear):
        The following argument positions are considered usable:
          uargs(c_6) = {1},
          uargs(c_8) = {1}
        
        Following symbols are considered usable:
          {minus#,plus#,quot#}
        TcT has computed the following interpretation:
               p(0) = 0 
           p(minus) = 0 
            p(plus) = 0 
            p(quot) = 0 
               p(s) = 0 
          p(minus#) = 0 
           p(plus#) = 4 
           p(quot#) = 0 
             p(c_1) = 0 
             p(c_2) = x1
             p(c_3) = 0 
             p(c_4) = 4 
             p(c_5) = 0 
             p(c_6) = x1
             p(c_7) = 0 
             p(c_8) = x1
        
        Following rules are strictly oriented:
        plus#(plus(x,s(0())),plus(y,s(s(z)))) = 4                                         
                                              > 0                                         
                                              = c_5(plus#(plus(y,s(s(z))),plus(x,s(0()))))
        
        
        Following rules are (at-least) weakly oriented:
        plus#(minus(x,s(0())),minus(y,s(s(z)))) =  4                                           
                                                >= 4                                           
                                                =  c_4(plus#(minus(y,s(s(z))),minus(x,s(0()))))
        
                                  plus#(s(x),y) =  4                                           
                                                >= 4                                           
                                                =  c_6(plus#(x,y))                             
        
                               quot#(s(x),s(y)) =  0                                           
                                                >= 0                                           
                                                =  c_8(quot#(minus(x,y),s(y)))                 
        
*** Step 1.b:6.a:4: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            plus#(s(x),y) -> c_6(plus#(x,y))
            quot#(s(x),s(y)) -> c_8(quot#(minus(x,y),s(y)))
        - Weak DPs:
            plus#(minus(x,s(0())),minus(y,s(s(z)))) -> c_4(plus#(minus(y,s(s(z))),minus(x,s(0()))))
            plus#(plus(x,s(0())),plus(y,s(s(z)))) -> c_5(plus#(plus(y,s(s(z))),plus(x,s(0()))))
        - Weak TRS:
            minus(x,0()) -> x
            minus(s(x),s(y)) -> minus(x,y)
            plus(0(),y) -> y
            plus(minus(x,s(0())),minus(y,s(s(z)))) -> plus(minus(y,s(s(z))),minus(x,s(0())))
            plus(plus(x,s(0())),plus(y,s(s(z)))) -> plus(plus(y,s(s(z))),plus(x,s(0())))
            plus(s(x),y) -> s(plus(x,y))
        - Signature:
            {minus/2,plus/2,quot/2,minus#/2,plus#/2,quot#/2} / {0/0,s/1,c_1/0,c_2/1,c_3/0,c_4/1,c_5/1,c_6/1,c_7/0,c_8/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {minus#,plus#,quot#} and constructors {0,s}
    + Applied Processor:
        NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just any strict-rules}
    + Details:
        We apply a matrix interpretation of kind constructor based matrix interpretation:
        The following argument positions are considered usable:
          uargs(c_6) = {1},
          uargs(c_8) = {1}
        
        Following symbols are considered usable:
          {minus,minus#,plus#,quot#}
        TcT has computed the following interpretation:
               p(0) = [3]                  
           p(minus) = [1] x1 + [0]         
            p(plus) = [1] x1 + [1] x2 + [2]
            p(quot) = [4] x1 + [2] x2 + [0]
               p(s) = [1] x1 + [1]         
          p(minus#) = [1] x1 + [1] x2 + [1]
           p(plus#) = [0]                  
           p(quot#) = [1] x1 + [0]         
             p(c_1) = [1]                  
             p(c_2) = [1] x1 + [1]         
             p(c_3) = [2]                  
             p(c_4) = [0]                  
             p(c_5) = [0]                  
             p(c_6) = [2] x1 + [0]         
             p(c_7) = [0]                  
             p(c_8) = [1] x1 + [0]         
        
        Following rules are strictly oriented:
        quot#(s(x),s(y)) = [1] x + [1]                
                         > [1] x + [0]                
                         = c_8(quot#(minus(x,y),s(y)))
        
        
        Following rules are (at-least) weakly oriented:
        plus#(minus(x,s(0())),minus(y,s(s(z)))) =  [0]                                         
                                                >= [0]                                         
                                                =  c_4(plus#(minus(y,s(s(z))),minus(x,s(0()))))
        
          plus#(plus(x,s(0())),plus(y,s(s(z)))) =  [0]                                         
                                                >= [0]                                         
                                                =  c_5(plus#(plus(y,s(s(z))),plus(x,s(0()))))  
        
                                  plus#(s(x),y) =  [0]                                         
                                                >= [0]                                         
                                                =  c_6(plus#(x,y))                             
        
                                   minus(x,0()) =  [1] x + [0]                                 
                                                >= [1] x + [0]                                 
                                                =  x                                           
        
                               minus(s(x),s(y)) =  [1] x + [1]                                 
                                                >= [1] x + [0]                                 
                                                =  minus(x,y)                                  
        
*** Step 1.b:6.a:5: WeightGap WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            plus#(s(x),y) -> c_6(plus#(x,y))
        - Weak DPs:
            plus#(minus(x,s(0())),minus(y,s(s(z)))) -> c_4(plus#(minus(y,s(s(z))),minus(x,s(0()))))
            plus#(plus(x,s(0())),plus(y,s(s(z)))) -> c_5(plus#(plus(y,s(s(z))),plus(x,s(0()))))
            quot#(s(x),s(y)) -> c_8(quot#(minus(x,y),s(y)))
        - Weak TRS:
            minus(x,0()) -> x
            minus(s(x),s(y)) -> minus(x,y)
            plus(0(),y) -> y
            plus(minus(x,s(0())),minus(y,s(s(z)))) -> plus(minus(y,s(s(z))),minus(x,s(0())))
            plus(plus(x,s(0())),plus(y,s(s(z)))) -> plus(plus(y,s(s(z))),plus(x,s(0())))
            plus(s(x),y) -> s(plus(x,y))
        - Signature:
            {minus/2,plus/2,quot/2,minus#/2,plus#/2,quot#/2} / {0/0,s/1,c_1/0,c_2/1,c_3/0,c_4/1,c_5/1,c_6/1,c_7/0,c_8/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {minus#,plus#,quot#} and constructors {0,s}
    + Applied Processor:
        WeightGap {wgDimension = 1, wgDegree = 1, wgKind = Algebraic, wgUArgs = UArgs, wgOn = WgOnAny}
    + Details:
        The weightgap principle applies using the following constant growth matrix-interpretation:
          We apply a matrix interpretation of kind constructor based matrix interpretation:
          The following argument positions are considered usable:
            uargs(s) = {1},
            uargs(quot#) = {1},
            uargs(c_6) = {1},
            uargs(c_8) = {1}
          
          Following symbols are considered usable:
            all
          TcT has computed the following interpretation:
                 p(0) = [2]                  
             p(minus) = [1] x1 + [0]         
              p(plus) = [1] x1 + [1] x2 + [0]
              p(quot) = [0]                  
                 p(s) = [1] x1 + [1]         
            p(minus#) = [0]                  
             p(plus#) = [5] x1 + [0]         
             p(quot#) = [1] x1 + [1] x2 + [2]
               p(c_1) = [0]                  
               p(c_2) = [2] x1 + [0]         
               p(c_3) = [2]                  
               p(c_4) = [0]                  
               p(c_5) = [0]                  
               p(c_6) = [1] x1 + [4]         
               p(c_7) = [1]                  
               p(c_8) = [1] x1 + [0]         
          
          Following rules are strictly oriented:
          plus#(s(x),y) = [5] x + [5]    
                        > [5] x + [4]    
                        = c_6(plus#(x,y))
          
          
          Following rules are (at-least) weakly oriented:
          plus#(minus(x,s(0())),minus(y,s(s(z)))) =  [5] x + [0]                                 
                                                  >= [0]                                         
                                                  =  c_4(plus#(minus(y,s(s(z))),minus(x,s(0()))))
          
            plus#(plus(x,s(0())),plus(y,s(s(z)))) =  [5] x + [15]                                
                                                  >= [0]                                         
                                                  =  c_5(plus#(plus(y,s(s(z))),plus(x,s(0()))))  
          
                                 quot#(s(x),s(y)) =  [1] x + [1] y + [4]                         
                                                  >= [1] x + [1] y + [3]                         
                                                  =  c_8(quot#(minus(x,y),s(y)))                 
          
                                     minus(x,0()) =  [1] x + [0]                                 
                                                  >= [1] x + [0]                                 
                                                  =  x                                           
          
                                 minus(s(x),s(y)) =  [1] x + [1]                                 
                                                  >= [1] x + [0]                                 
                                                  =  minus(x,y)                                  
          
                                      plus(0(),y) =  [1] y + [2]                                 
                                                  >= [1] y + [0]                                 
                                                  =  y                                           
          
           plus(minus(x,s(0())),minus(y,s(s(z)))) =  [1] x + [1] y + [0]                         
                                                  >= [1] x + [1] y + [0]                         
                                                  =  plus(minus(y,s(s(z))),minus(x,s(0())))      
          
             plus(plus(x,s(0())),plus(y,s(s(z)))) =  [1] x + [1] y + [1] z + [5]                 
                                                  >= [1] x + [1] y + [1] z + [5]                 
                                                  =  plus(plus(y,s(s(z))),plus(x,s(0())))        
          
                                     plus(s(x),y) =  [1] x + [1] y + [1]                         
                                                  >= [1] x + [1] y + [1]                         
                                                  =  s(plus(x,y))                                
          
        Further, it can be verified that all rules not oriented are covered by the weightgap condition.
*** Step 1.b:6.a:6: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            plus#(minus(x,s(0())),minus(y,s(s(z)))) -> c_4(plus#(minus(y,s(s(z))),minus(x,s(0()))))
            plus#(plus(x,s(0())),plus(y,s(s(z)))) -> c_5(plus#(plus(y,s(s(z))),plus(x,s(0()))))
            plus#(s(x),y) -> c_6(plus#(x,y))
            quot#(s(x),s(y)) -> c_8(quot#(minus(x,y),s(y)))
        - Weak TRS:
            minus(x,0()) -> x
            minus(s(x),s(y)) -> minus(x,y)
            plus(0(),y) -> y
            plus(minus(x,s(0())),minus(y,s(s(z)))) -> plus(minus(y,s(s(z))),minus(x,s(0())))
            plus(plus(x,s(0())),plus(y,s(s(z)))) -> plus(plus(y,s(s(z))),plus(x,s(0())))
            plus(s(x),y) -> s(plus(x,y))
        - Signature:
            {minus/2,plus/2,quot/2,minus#/2,plus#/2,quot#/2} / {0/0,s/1,c_1/0,c_2/1,c_3/0,c_4/1,c_5/1,c_6/1,c_7/0,c_8/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {minus#,plus#,quot#} and constructors {0,s}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

*** Step 1.b:6.b:1: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            minus#(s(x),s(y)) -> c_2(minus#(x,y))
        - Weak DPs:
            plus#(minus(x,s(0())),minus(y,s(s(z)))) -> minus#(x,s(0()))
            plus#(minus(x,s(0())),minus(y,s(s(z)))) -> plus#(minus(y,s(s(z))),minus(x,s(0())))
            plus#(plus(x,s(0())),plus(y,s(s(z)))) -> plus#(plus(y,s(s(z))),plus(x,s(0())))
            plus#(s(x),y) -> plus#(x,y)
            quot#(s(x),s(y)) -> minus#(x,y)
            quot#(s(x),s(y)) -> quot#(minus(x,y),s(y))
        - Weak TRS:
            minus(x,0()) -> x
            minus(s(x),s(y)) -> minus(x,y)
            plus(0(),y) -> y
            plus(minus(x,s(0())),minus(y,s(s(z)))) -> plus(minus(y,s(s(z))),minus(x,s(0())))
            plus(plus(x,s(0())),plus(y,s(s(z)))) -> plus(plus(y,s(s(z))),plus(x,s(0())))
            plus(s(x),y) -> s(plus(x,y))
        - Signature:
            {minus/2,plus/2,quot/2,minus#/2,plus#/2,quot#/2} / {0/0,s/1,c_1/0,c_2/1,c_3/0,c_4/2,c_5/1,c_6/1,c_7/0,c_8/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {minus#,plus#,quot#} and constructors {0,s}
    + Applied Processor:
        NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just any strict-rules}
    + Details:
        We apply a matrix interpretation of kind constructor based matrix interpretation:
        The following argument positions are considered usable:
          uargs(c_2) = {1}
        
        Following symbols are considered usable:
          {minus#,plus#,quot#}
        TcT has computed the following interpretation:
               p(0) = [0]         
           p(minus) = [4] x2 + [0]
            p(plus) = [1] x2 + [0]
            p(quot) = [0]         
               p(s) = [1] x1 + [1]
          p(minus#) = [1] x2 + [0]
           p(plus#) = [1]         
           p(quot#) = [4] x2 + [2]
             p(c_1) = [0]         
             p(c_2) = [1] x1 + [0]
             p(c_3) = [0]         
             p(c_4) = [0]         
             p(c_5) = [0]         
             p(c_6) = [0]         
             p(c_7) = [0]         
             p(c_8) = [0]         
        
        Following rules are strictly oriented:
        minus#(s(x),s(y)) = [1] y + [1]     
                          > [1] y + [0]     
                          = c_2(minus#(x,y))
        
        
        Following rules are (at-least) weakly oriented:
        plus#(minus(x,s(0())),minus(y,s(s(z)))) =  [1]                                    
                                                >= [1]                                    
                                                =  minus#(x,s(0()))                       
        
        plus#(minus(x,s(0())),minus(y,s(s(z)))) =  [1]                                    
                                                >= [1]                                    
                                                =  plus#(minus(y,s(s(z))),minus(x,s(0())))
        
          plus#(plus(x,s(0())),plus(y,s(s(z)))) =  [1]                                    
                                                >= [1]                                    
                                                =  plus#(plus(y,s(s(z))),plus(x,s(0())))  
        
                                  plus#(s(x),y) =  [1]                                    
                                                >= [1]                                    
                                                =  plus#(x,y)                             
        
                               quot#(s(x),s(y)) =  [4] y + [6]                            
                                                >= [1] y + [0]                            
                                                =  minus#(x,y)                            
        
                               quot#(s(x),s(y)) =  [4] y + [6]                            
                                                >= [4] y + [6]                            
                                                =  quot#(minus(x,y),s(y))                 
        
*** Step 1.b:6.b:2: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            minus#(s(x),s(y)) -> c_2(minus#(x,y))
            plus#(minus(x,s(0())),minus(y,s(s(z)))) -> minus#(x,s(0()))
            plus#(minus(x,s(0())),minus(y,s(s(z)))) -> plus#(minus(y,s(s(z))),minus(x,s(0())))
            plus#(plus(x,s(0())),plus(y,s(s(z)))) -> plus#(plus(y,s(s(z))),plus(x,s(0())))
            plus#(s(x),y) -> plus#(x,y)
            quot#(s(x),s(y)) -> minus#(x,y)
            quot#(s(x),s(y)) -> quot#(minus(x,y),s(y))
        - Weak TRS:
            minus(x,0()) -> x
            minus(s(x),s(y)) -> minus(x,y)
            plus(0(),y) -> y
            plus(minus(x,s(0())),minus(y,s(s(z)))) -> plus(minus(y,s(s(z))),minus(x,s(0())))
            plus(plus(x,s(0())),plus(y,s(s(z)))) -> plus(plus(y,s(s(z))),plus(x,s(0())))
            plus(s(x),y) -> s(plus(x,y))
        - Signature:
            {minus/2,plus/2,quot/2,minus#/2,plus#/2,quot#/2} / {0/0,s/1,c_1/0,c_2/1,c_3/0,c_4/2,c_5/1,c_6/1,c_7/0,c_8/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {minus#,plus#,quot#} and constructors {0,s}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(Omega(n^1),O(n^2))