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

** Step 1.b:1: InnermostRuleRemoval WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            circ(s,id()) -> s
            circ(circ(s,t),u) -> circ(s,circ(t,u))
            circ(cons(a,s),t) -> cons(msubst(a,t),circ(s,t))
            circ(cons(lift(),s),circ(cons(lift(),t),u)) -> circ(cons(lift(),circ(s,t)),u)
            circ(cons(lift(),s),cons(a,t)) -> cons(a,circ(s,t))
            circ(cons(lift(),s),cons(lift(),t)) -> cons(lift(),circ(s,t))
            circ(id(),s) -> s
            msubst(a,id()) -> a
            msubst(msubst(a,s),t) -> msubst(a,circ(s,t))
            subst(a,id()) -> a
        - Signature:
            {circ/2,msubst/2,subst/2} / {cons/2,id/0,lift/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {circ,msubst,subst} and constructors {cons,id,lift}
    + Applied Processor:
        InnermostRuleRemoval
    + Details:
        Arguments of following rules are not normal-forms.
          circ(cons(lift(),s),circ(cons(lift(),t),u)) -> circ(cons(lift(),circ(s,t)),u)
        All above mentioned rules can be savely removed.
** Step 1.b:2: DependencyPairs WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            circ(s,id()) -> s
            circ(circ(s,t),u) -> circ(s,circ(t,u))
            circ(cons(a,s),t) -> cons(msubst(a,t),circ(s,t))
            circ(cons(lift(),s),cons(a,t)) -> cons(a,circ(s,t))
            circ(cons(lift(),s),cons(lift(),t)) -> cons(lift(),circ(s,t))
            circ(id(),s) -> s
            msubst(a,id()) -> a
            msubst(msubst(a,s),t) -> msubst(a,circ(s,t))
            subst(a,id()) -> a
        - Signature:
            {circ/2,msubst/2,subst/2} / {cons/2,id/0,lift/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {circ,msubst,subst} and constructors {cons,id,lift}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          circ#(s,id()) -> c_1()
          circ#(circ(s,t),u) -> c_2(circ#(s,circ(t,u)),circ#(t,u))
          circ#(cons(a,s),t) -> c_3(msubst#(a,t),circ#(s,t))
          circ#(cons(lift(),s),cons(a,t)) -> c_4(circ#(s,t))
          circ#(cons(lift(),s),cons(lift(),t)) -> c_5(circ#(s,t))
          circ#(id(),s) -> c_6()
          msubst#(a,id()) -> c_7()
          msubst#(msubst(a,s),t) -> c_8(msubst#(a,circ(s,t)),circ#(s,t))
          subst#(a,id()) -> c_9()
        Weak DPs
          
        
        and mark the set of starting terms.
** Step 1.b:3: UsableRules WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            circ#(s,id()) -> c_1()
            circ#(circ(s,t),u) -> c_2(circ#(s,circ(t,u)),circ#(t,u))
            circ#(cons(a,s),t) -> c_3(msubst#(a,t),circ#(s,t))
            circ#(cons(lift(),s),cons(a,t)) -> c_4(circ#(s,t))
            circ#(cons(lift(),s),cons(lift(),t)) -> c_5(circ#(s,t))
            circ#(id(),s) -> c_6()
            msubst#(a,id()) -> c_7()
            msubst#(msubst(a,s),t) -> c_8(msubst#(a,circ(s,t)),circ#(s,t))
            subst#(a,id()) -> c_9()
        - Weak TRS:
            circ(s,id()) -> s
            circ(circ(s,t),u) -> circ(s,circ(t,u))
            circ(cons(a,s),t) -> cons(msubst(a,t),circ(s,t))
            circ(cons(lift(),s),cons(a,t)) -> cons(a,circ(s,t))
            circ(cons(lift(),s),cons(lift(),t)) -> cons(lift(),circ(s,t))
            circ(id(),s) -> s
            msubst(a,id()) -> a
            msubst(msubst(a,s),t) -> msubst(a,circ(s,t))
            subst(a,id()) -> a
        - Signature:
            {circ/2,msubst/2,subst/2,circ#/2,msubst#/2,subst#/2} / {cons/2,id/0,lift/0,c_1/0,c_2/2,c_3/2,c_4/1,c_5/1
            ,c_6/0,c_7/0,c_8/2,c_9/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {circ#,msubst#,subst#} and constructors {cons,id,lift}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          circ(s,id()) -> s
          circ(circ(s,t),u) -> circ(s,circ(t,u))
          circ(cons(a,s),t) -> cons(msubst(a,t),circ(s,t))
          circ(cons(lift(),s),cons(a,t)) -> cons(a,circ(s,t))
          circ(cons(lift(),s),cons(lift(),t)) -> cons(lift(),circ(s,t))
          circ(id(),s) -> s
          msubst(a,id()) -> a
          msubst(msubst(a,s),t) -> msubst(a,circ(s,t))
          circ#(s,id()) -> c_1()
          circ#(circ(s,t),u) -> c_2(circ#(s,circ(t,u)),circ#(t,u))
          circ#(cons(a,s),t) -> c_3(msubst#(a,t),circ#(s,t))
          circ#(cons(lift(),s),cons(a,t)) -> c_4(circ#(s,t))
          circ#(cons(lift(),s),cons(lift(),t)) -> c_5(circ#(s,t))
          circ#(id(),s) -> c_6()
          msubst#(a,id()) -> c_7()
          msubst#(msubst(a,s),t) -> c_8(msubst#(a,circ(s,t)),circ#(s,t))
          subst#(a,id()) -> c_9()
** Step 1.b:4: PredecessorEstimation WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            circ#(s,id()) -> c_1()
            circ#(circ(s,t),u) -> c_2(circ#(s,circ(t,u)),circ#(t,u))
            circ#(cons(a,s),t) -> c_3(msubst#(a,t),circ#(s,t))
            circ#(cons(lift(),s),cons(a,t)) -> c_4(circ#(s,t))
            circ#(cons(lift(),s),cons(lift(),t)) -> c_5(circ#(s,t))
            circ#(id(),s) -> c_6()
            msubst#(a,id()) -> c_7()
            msubst#(msubst(a,s),t) -> c_8(msubst#(a,circ(s,t)),circ#(s,t))
            subst#(a,id()) -> c_9()
        - Weak TRS:
            circ(s,id()) -> s
            circ(circ(s,t),u) -> circ(s,circ(t,u))
            circ(cons(a,s),t) -> cons(msubst(a,t),circ(s,t))
            circ(cons(lift(),s),cons(a,t)) -> cons(a,circ(s,t))
            circ(cons(lift(),s),cons(lift(),t)) -> cons(lift(),circ(s,t))
            circ(id(),s) -> s
            msubst(a,id()) -> a
            msubst(msubst(a,s),t) -> msubst(a,circ(s,t))
        - Signature:
            {circ/2,msubst/2,subst/2,circ#/2,msubst#/2,subst#/2} / {cons/2,id/0,lift/0,c_1/0,c_2/2,c_3/2,c_4/1,c_5/1
            ,c_6/0,c_7/0,c_8/2,c_9/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {circ#,msubst#,subst#} and constructors {cons,id,lift}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,6,7,9}
        by application of
          Pre({1,6,7,9}) = {2,3,4,5,8}.
        Here rules are labelled as follows:
          1: circ#(s,id()) -> c_1()
          2: circ#(circ(s,t),u) -> c_2(circ#(s,circ(t,u)),circ#(t,u))
          3: circ#(cons(a,s),t) -> c_3(msubst#(a,t),circ#(s,t))
          4: circ#(cons(lift(),s),cons(a,t)) -> c_4(circ#(s,t))
          5: circ#(cons(lift(),s),cons(lift(),t)) -> c_5(circ#(s,t))
          6: circ#(id(),s) -> c_6()
          7: msubst#(a,id()) -> c_7()
          8: msubst#(msubst(a,s),t) -> c_8(msubst#(a,circ(s,t)),circ#(s,t))
          9: subst#(a,id()) -> c_9()
** Step 1.b:5: RemoveWeakSuffixes WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            circ#(circ(s,t),u) -> c_2(circ#(s,circ(t,u)),circ#(t,u))
            circ#(cons(a,s),t) -> c_3(msubst#(a,t),circ#(s,t))
            circ#(cons(lift(),s),cons(a,t)) -> c_4(circ#(s,t))
            circ#(cons(lift(),s),cons(lift(),t)) -> c_5(circ#(s,t))
            msubst#(msubst(a,s),t) -> c_8(msubst#(a,circ(s,t)),circ#(s,t))
        - Weak DPs:
            circ#(s,id()) -> c_1()
            circ#(id(),s) -> c_6()
            msubst#(a,id()) -> c_7()
            subst#(a,id()) -> c_9()
        - Weak TRS:
            circ(s,id()) -> s
            circ(circ(s,t),u) -> circ(s,circ(t,u))
            circ(cons(a,s),t) -> cons(msubst(a,t),circ(s,t))
            circ(cons(lift(),s),cons(a,t)) -> cons(a,circ(s,t))
            circ(cons(lift(),s),cons(lift(),t)) -> cons(lift(),circ(s,t))
            circ(id(),s) -> s
            msubst(a,id()) -> a
            msubst(msubst(a,s),t) -> msubst(a,circ(s,t))
        - Signature:
            {circ/2,msubst/2,subst/2,circ#/2,msubst#/2,subst#/2} / {cons/2,id/0,lift/0,c_1/0,c_2/2,c_3/2,c_4/1,c_5/1
            ,c_6/0,c_7/0,c_8/2,c_9/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {circ#,msubst#,subst#} and constructors {cons,id,lift}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:circ#(circ(s,t),u) -> c_2(circ#(s,circ(t,u)),circ#(t,u))
             -->_2 circ#(cons(lift(),s),cons(lift(),t)) -> c_5(circ#(s,t)):4
             -->_1 circ#(cons(lift(),s),cons(lift(),t)) -> c_5(circ#(s,t)):4
             -->_2 circ#(cons(lift(),s),cons(a,t)) -> c_4(circ#(s,t)):3
             -->_1 circ#(cons(lift(),s),cons(a,t)) -> c_4(circ#(s,t)):3
             -->_2 circ#(cons(a,s),t) -> c_3(msubst#(a,t),circ#(s,t)):2
             -->_1 circ#(cons(a,s),t) -> c_3(msubst#(a,t),circ#(s,t)):2
             -->_2 circ#(id(),s) -> c_6():7
             -->_1 circ#(id(),s) -> c_6():7
             -->_2 circ#(s,id()) -> c_1():6
             -->_1 circ#(s,id()) -> c_1():6
             -->_2 circ#(circ(s,t),u) -> c_2(circ#(s,circ(t,u)),circ#(t,u)):1
             -->_1 circ#(circ(s,t),u) -> c_2(circ#(s,circ(t,u)),circ#(t,u)):1
          
          2:S:circ#(cons(a,s),t) -> c_3(msubst#(a,t),circ#(s,t))
             -->_1 msubst#(msubst(a,s),t) -> c_8(msubst#(a,circ(s,t)),circ#(s,t)):5
             -->_2 circ#(cons(lift(),s),cons(lift(),t)) -> c_5(circ#(s,t)):4
             -->_2 circ#(cons(lift(),s),cons(a,t)) -> c_4(circ#(s,t)):3
             -->_1 msubst#(a,id()) -> c_7():8
             -->_2 circ#(id(),s) -> c_6():7
             -->_2 circ#(s,id()) -> c_1():6
             -->_2 circ#(cons(a,s),t) -> c_3(msubst#(a,t),circ#(s,t)):2
             -->_2 circ#(circ(s,t),u) -> c_2(circ#(s,circ(t,u)),circ#(t,u)):1
          
          3:S:circ#(cons(lift(),s),cons(a,t)) -> c_4(circ#(s,t))
             -->_1 circ#(cons(lift(),s),cons(lift(),t)) -> c_5(circ#(s,t)):4
             -->_1 circ#(id(),s) -> c_6():7
             -->_1 circ#(s,id()) -> c_1():6
             -->_1 circ#(cons(lift(),s),cons(a,t)) -> c_4(circ#(s,t)):3
             -->_1 circ#(cons(a,s),t) -> c_3(msubst#(a,t),circ#(s,t)):2
             -->_1 circ#(circ(s,t),u) -> c_2(circ#(s,circ(t,u)),circ#(t,u)):1
          
          4:S:circ#(cons(lift(),s),cons(lift(),t)) -> c_5(circ#(s,t))
             -->_1 circ#(id(),s) -> c_6():7
             -->_1 circ#(s,id()) -> c_1():6
             -->_1 circ#(cons(lift(),s),cons(lift(),t)) -> c_5(circ#(s,t)):4
             -->_1 circ#(cons(lift(),s),cons(a,t)) -> c_4(circ#(s,t)):3
             -->_1 circ#(cons(a,s),t) -> c_3(msubst#(a,t),circ#(s,t)):2
             -->_1 circ#(circ(s,t),u) -> c_2(circ#(s,circ(t,u)),circ#(t,u)):1
          
          5:S:msubst#(msubst(a,s),t) -> c_8(msubst#(a,circ(s,t)),circ#(s,t))
             -->_1 msubst#(a,id()) -> c_7():8
             -->_2 circ#(id(),s) -> c_6():7
             -->_2 circ#(s,id()) -> c_1():6
             -->_1 msubst#(msubst(a,s),t) -> c_8(msubst#(a,circ(s,t)),circ#(s,t)):5
             -->_2 circ#(cons(lift(),s),cons(lift(),t)) -> c_5(circ#(s,t)):4
             -->_2 circ#(cons(lift(),s),cons(a,t)) -> c_4(circ#(s,t)):3
             -->_2 circ#(cons(a,s),t) -> c_3(msubst#(a,t),circ#(s,t)):2
             -->_2 circ#(circ(s,t),u) -> c_2(circ#(s,circ(t,u)),circ#(t,u)):1
          
          6:W:circ#(s,id()) -> c_1()
             
          
          7:W:circ#(id(),s) -> c_6()
             
          
          8:W:msubst#(a,id()) -> c_7()
             
          
          9:W:subst#(a,id()) -> c_9()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          9: subst#(a,id()) -> c_9()
          8: msubst#(a,id()) -> c_7()
          6: circ#(s,id()) -> c_1()
          7: circ#(id(),s) -> c_6()
** Step 1.b:6: PredecessorEstimationCP WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            circ#(circ(s,t),u) -> c_2(circ#(s,circ(t,u)),circ#(t,u))
            circ#(cons(a,s),t) -> c_3(msubst#(a,t),circ#(s,t))
            circ#(cons(lift(),s),cons(a,t)) -> c_4(circ#(s,t))
            circ#(cons(lift(),s),cons(lift(),t)) -> c_5(circ#(s,t))
            msubst#(msubst(a,s),t) -> c_8(msubst#(a,circ(s,t)),circ#(s,t))
        - Weak TRS:
            circ(s,id()) -> s
            circ(circ(s,t),u) -> circ(s,circ(t,u))
            circ(cons(a,s),t) -> cons(msubst(a,t),circ(s,t))
            circ(cons(lift(),s),cons(a,t)) -> cons(a,circ(s,t))
            circ(cons(lift(),s),cons(lift(),t)) -> cons(lift(),circ(s,t))
            circ(id(),s) -> s
            msubst(a,id()) -> a
            msubst(msubst(a,s),t) -> msubst(a,circ(s,t))
        - Signature:
            {circ/2,msubst/2,subst/2,circ#/2,msubst#/2,subst#/2} / {cons/2,id/0,lift/0,c_1/0,c_2/2,c_3/2,c_4/1,c_5/1
            ,c_6/0,c_7/0,c_8/2,c_9/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {circ#,msubst#,subst#} and constructors {cons,id,lift}
    + 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: circ#(circ(s,t),u) -> c_2(circ#(s,circ(t,u)),circ#(t,u))
          2: circ#(cons(a,s),t) -> c_3(msubst#(a,t),circ#(s,t))
          3: circ#(cons(lift(),s),cons(a,t)) -> c_4(circ#(s,t))
          4: circ#(cons(lift(),s),cons(lift(),t)) -> c_5(circ#(s,t))
          5: msubst#(msubst(a,s),t) -> c_8(msubst#(a,circ(s,t)),circ#(s,t))
          
        The strictly oriented rules are moved into the weak component.
*** Step 1.b:6.a:1: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            circ#(circ(s,t),u) -> c_2(circ#(s,circ(t,u)),circ#(t,u))
            circ#(cons(a,s),t) -> c_3(msubst#(a,t),circ#(s,t))
            circ#(cons(lift(),s),cons(a,t)) -> c_4(circ#(s,t))
            circ#(cons(lift(),s),cons(lift(),t)) -> c_5(circ#(s,t))
            msubst#(msubst(a,s),t) -> c_8(msubst#(a,circ(s,t)),circ#(s,t))
        - Weak TRS:
            circ(s,id()) -> s
            circ(circ(s,t),u) -> circ(s,circ(t,u))
            circ(cons(a,s),t) -> cons(msubst(a,t),circ(s,t))
            circ(cons(lift(),s),cons(a,t)) -> cons(a,circ(s,t))
            circ(cons(lift(),s),cons(lift(),t)) -> cons(lift(),circ(s,t))
            circ(id(),s) -> s
            msubst(a,id()) -> a
            msubst(msubst(a,s),t) -> msubst(a,circ(s,t))
        - Signature:
            {circ/2,msubst/2,subst/2,circ#/2,msubst#/2,subst#/2} / {cons/2,id/0,lift/0,c_1/0,c_2/2,c_3/2,c_4/1,c_5/1
            ,c_6/0,c_7/0,c_8/2,c_9/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {circ#,msubst#,subst#} and constructors {cons,id,lift}
    + Applied Processor:
        NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just first alternative for predecessorEstimation on any intersect of rules of CDG leaf and strict-rules}
    + Details:
        We apply a matrix interpretation of kind constructor based matrix interpretation:
        The following argument positions are considered usable:
          uargs(c_2) = {1,2},
          uargs(c_3) = {1,2},
          uargs(c_4) = {1},
          uargs(c_5) = {1},
          uargs(c_8) = {1,2}
        
        Following symbols are considered usable:
          {circ#,msubst#,subst#}
        TcT has computed the following interpretation:
             p(circ) = [1] x1 + [3] x2 + [2]
             p(cons) = [1] x1 + [1] x2 + [2]
               p(id) = [3]                  
             p(lift) = [0]                  
           p(msubst) = [2] x1 + [4] x2 + [3]
            p(subst) = [1] x1 + [0]         
            p(circ#) = [4] x1 + [2]         
          p(msubst#) = [2] x1 + [0]         
           p(subst#) = [2]                  
              p(c_1) = [1]                  
              p(c_2) = [1] x1 + [2] x2 + [1]
              p(c_3) = [2] x1 + [1] x2 + [0]
              p(c_4) = [1] x1 + [1]         
              p(c_5) = [1] x1 + [4]         
              p(c_6) = [1]                  
              p(c_7) = [1]                  
              p(c_8) = [2] x1 + [2] x2 + [0]
              p(c_9) = [1]                  
        
        Following rules are strictly oriented:
                          circ#(circ(s,t),u) = [4] s + [12] t + [10]               
                                             > [4] s + [8] t + [7]                 
                                             = c_2(circ#(s,circ(t,u)),circ#(t,u))  
        
                          circ#(cons(a,s),t) = [4] a + [4] s + [10]                
                                             > [4] a + [4] s + [2]                 
                                             = c_3(msubst#(a,t),circ#(s,t))        
        
             circ#(cons(lift(),s),cons(a,t)) = [4] s + [10]                        
                                             > [4] s + [3]                         
                                             = c_4(circ#(s,t))                     
        
        circ#(cons(lift(),s),cons(lift(),t)) = [4] s + [10]                        
                                             > [4] s + [6]                         
                                             = c_5(circ#(s,t))                     
        
                      msubst#(msubst(a,s),t) = [4] a + [8] s + [6]                 
                                             > [4] a + [8] s + [4]                 
                                             = c_8(msubst#(a,circ(s,t)),circ#(s,t))
        
        
        Following rules are (at-least) weakly oriented:
        
*** Step 1.b:6.a:2: Assumption WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            circ#(circ(s,t),u) -> c_2(circ#(s,circ(t,u)),circ#(t,u))
            circ#(cons(a,s),t) -> c_3(msubst#(a,t),circ#(s,t))
            circ#(cons(lift(),s),cons(a,t)) -> c_4(circ#(s,t))
            circ#(cons(lift(),s),cons(lift(),t)) -> c_5(circ#(s,t))
            msubst#(msubst(a,s),t) -> c_8(msubst#(a,circ(s,t)),circ#(s,t))
        - Weak TRS:
            circ(s,id()) -> s
            circ(circ(s,t),u) -> circ(s,circ(t,u))
            circ(cons(a,s),t) -> cons(msubst(a,t),circ(s,t))
            circ(cons(lift(),s),cons(a,t)) -> cons(a,circ(s,t))
            circ(cons(lift(),s),cons(lift(),t)) -> cons(lift(),circ(s,t))
            circ(id(),s) -> s
            msubst(a,id()) -> a
            msubst(msubst(a,s),t) -> msubst(a,circ(s,t))
        - Signature:
            {circ/2,msubst/2,subst/2,circ#/2,msubst#/2,subst#/2} / {cons/2,id/0,lift/0,c_1/0,c_2/2,c_3/2,c_4/1,c_5/1
            ,c_6/0,c_7/0,c_8/2,c_9/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {circ#,msubst#,subst#} and constructors {cons,id,lift}
    + Applied Processor:
        Assumption {assumed = Certificate {spaceUB = Unknown, spaceLB = Unknown, timeUB = Poly (Just 0), timeLB = Unknown}}
    + Details:
        ()

*** Step 1.b:6.b:1: RemoveWeakSuffixes WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            circ#(circ(s,t),u) -> c_2(circ#(s,circ(t,u)),circ#(t,u))
            circ#(cons(a,s),t) -> c_3(msubst#(a,t),circ#(s,t))
            circ#(cons(lift(),s),cons(a,t)) -> c_4(circ#(s,t))
            circ#(cons(lift(),s),cons(lift(),t)) -> c_5(circ#(s,t))
            msubst#(msubst(a,s),t) -> c_8(msubst#(a,circ(s,t)),circ#(s,t))
        - Weak TRS:
            circ(s,id()) -> s
            circ(circ(s,t),u) -> circ(s,circ(t,u))
            circ(cons(a,s),t) -> cons(msubst(a,t),circ(s,t))
            circ(cons(lift(),s),cons(a,t)) -> cons(a,circ(s,t))
            circ(cons(lift(),s),cons(lift(),t)) -> cons(lift(),circ(s,t))
            circ(id(),s) -> s
            msubst(a,id()) -> a
            msubst(msubst(a,s),t) -> msubst(a,circ(s,t))
        - Signature:
            {circ/2,msubst/2,subst/2,circ#/2,msubst#/2,subst#/2} / {cons/2,id/0,lift/0,c_1/0,c_2/2,c_3/2,c_4/1,c_5/1
            ,c_6/0,c_7/0,c_8/2,c_9/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {circ#,msubst#,subst#} and constructors {cons,id,lift}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:W:circ#(circ(s,t),u) -> c_2(circ#(s,circ(t,u)),circ#(t,u))
             -->_2 circ#(cons(lift(),s),cons(lift(),t)) -> c_5(circ#(s,t)):4
             -->_1 circ#(cons(lift(),s),cons(lift(),t)) -> c_5(circ#(s,t)):4
             -->_2 circ#(cons(lift(),s),cons(a,t)) -> c_4(circ#(s,t)):3
             -->_1 circ#(cons(lift(),s),cons(a,t)) -> c_4(circ#(s,t)):3
             -->_2 circ#(cons(a,s),t) -> c_3(msubst#(a,t),circ#(s,t)):2
             -->_1 circ#(cons(a,s),t) -> c_3(msubst#(a,t),circ#(s,t)):2
             -->_2 circ#(circ(s,t),u) -> c_2(circ#(s,circ(t,u)),circ#(t,u)):1
             -->_1 circ#(circ(s,t),u) -> c_2(circ#(s,circ(t,u)),circ#(t,u)):1
          
          2:W:circ#(cons(a,s),t) -> c_3(msubst#(a,t),circ#(s,t))
             -->_1 msubst#(msubst(a,s),t) -> c_8(msubst#(a,circ(s,t)),circ#(s,t)):5
             -->_2 circ#(cons(lift(),s),cons(lift(),t)) -> c_5(circ#(s,t)):4
             -->_2 circ#(cons(lift(),s),cons(a,t)) -> c_4(circ#(s,t)):3
             -->_2 circ#(cons(a,s),t) -> c_3(msubst#(a,t),circ#(s,t)):2
             -->_2 circ#(circ(s,t),u) -> c_2(circ#(s,circ(t,u)),circ#(t,u)):1
          
          3:W:circ#(cons(lift(),s),cons(a,t)) -> c_4(circ#(s,t))
             -->_1 circ#(cons(lift(),s),cons(lift(),t)) -> c_5(circ#(s,t)):4
             -->_1 circ#(cons(lift(),s),cons(a,t)) -> c_4(circ#(s,t)):3
             -->_1 circ#(cons(a,s),t) -> c_3(msubst#(a,t),circ#(s,t)):2
             -->_1 circ#(circ(s,t),u) -> c_2(circ#(s,circ(t,u)),circ#(t,u)):1
          
          4:W:circ#(cons(lift(),s),cons(lift(),t)) -> c_5(circ#(s,t))
             -->_1 circ#(cons(lift(),s),cons(lift(),t)) -> c_5(circ#(s,t)):4
             -->_1 circ#(cons(lift(),s),cons(a,t)) -> c_4(circ#(s,t)):3
             -->_1 circ#(cons(a,s),t) -> c_3(msubst#(a,t),circ#(s,t)):2
             -->_1 circ#(circ(s,t),u) -> c_2(circ#(s,circ(t,u)),circ#(t,u)):1
          
          5:W:msubst#(msubst(a,s),t) -> c_8(msubst#(a,circ(s,t)),circ#(s,t))
             -->_1 msubst#(msubst(a,s),t) -> c_8(msubst#(a,circ(s,t)),circ#(s,t)):5
             -->_2 circ#(cons(lift(),s),cons(lift(),t)) -> c_5(circ#(s,t)):4
             -->_2 circ#(cons(lift(),s),cons(a,t)) -> c_4(circ#(s,t)):3
             -->_2 circ#(cons(a,s),t) -> c_3(msubst#(a,t),circ#(s,t)):2
             -->_2 circ#(circ(s,t),u) -> c_2(circ#(s,circ(t,u)),circ#(t,u)):1
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          1: circ#(circ(s,t),u) -> c_2(circ#(s,circ(t,u)),circ#(t,u))
          5: msubst#(msubst(a,s),t) -> c_8(msubst#(a,circ(s,t)),circ#(s,t))
          2: circ#(cons(a,s),t) -> c_3(msubst#(a,t),circ#(s,t))
          4: circ#(cons(lift(),s),cons(lift(),t)) -> c_5(circ#(s,t))
          3: circ#(cons(lift(),s),cons(a,t)) -> c_4(circ#(s,t))
*** Step 1.b:6.b:2: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            circ(s,id()) -> s
            circ(circ(s,t),u) -> circ(s,circ(t,u))
            circ(cons(a,s),t) -> cons(msubst(a,t),circ(s,t))
            circ(cons(lift(),s),cons(a,t)) -> cons(a,circ(s,t))
            circ(cons(lift(),s),cons(lift(),t)) -> cons(lift(),circ(s,t))
            circ(id(),s) -> s
            msubst(a,id()) -> a
            msubst(msubst(a,s),t) -> msubst(a,circ(s,t))
        - Signature:
            {circ/2,msubst/2,subst/2,circ#/2,msubst#/2,subst#/2} / {cons/2,id/0,lift/0,c_1/0,c_2/2,c_3/2,c_4/1,c_5/1
            ,c_6/0,c_7/0,c_8/2,c_9/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {circ#,msubst#,subst#} and constructors {cons,id,lift}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

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