/export/starexec/sandbox2/solver/bin/starexec_run_tct_rci /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


WORST_CASE(Omega(n^1),O(n^1))
* Step 1: Sum WORST_CASE(Omega(n^1),O(n^1))
    + Considered Problem:
        - Strict TRS:
            a(C(x1,x2),y,z) -> C(a(x1,y,z),a(x2,y,y))
            a(Z(),y,z) -> Z()
            eqZList(C(x1,x2),C(y1,y2)) -> and(eqZList(x1,y1),eqZList(x2,y2))
            eqZList(C(x1,x2),Z()) -> False()
            eqZList(Z(),C(y1,y2)) -> False()
            eqZList(Z(),Z()) -> True()
            first(C(x1,x2)) -> x1
            second(C(x1,x2)) -> x2
        - Weak TRS:
            and(False(),False()) -> False()
            and(False(),True()) -> False()
            and(True(),False()) -> False()
            and(True(),True()) -> True()
        - Signature:
            {a/3,and/2,eqZList/2,first/1,second/1} / {C/2,False/0,True/0,Z/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a,and,eqZList,first,second} and constructors {C,False
            ,True,Z}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            a(C(x1,x2),y,z) -> C(a(x1,y,z),a(x2,y,y))
            a(Z(),y,z) -> Z()
            eqZList(C(x1,x2),C(y1,y2)) -> and(eqZList(x1,y1),eqZList(x2,y2))
            eqZList(C(x1,x2),Z()) -> False()
            eqZList(Z(),C(y1,y2)) -> False()
            eqZList(Z(),Z()) -> True()
            first(C(x1,x2)) -> x1
            second(C(x1,x2)) -> x2
        - Weak TRS:
            and(False(),False()) -> False()
            and(False(),True()) -> False()
            and(True(),False()) -> False()
            and(True(),True()) -> True()
        - Signature:
            {a/3,and/2,eqZList/2,first/1,second/1} / {C/2,False/0,True/0,Z/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a,and,eqZList,first,second} and constructors {C,False
            ,True,Z}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          a(x,z,u){x -> C(x,y)} =
            a(C(x,y),z,u) ->^+ C(a(x,z,u),a(y,z,z))
              = C[a(x,z,u) = a(x,z,u){}]

** Step 1.b:1: Ara WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            a(C(x1,x2),y,z) -> C(a(x1,y,z),a(x2,y,y))
            a(Z(),y,z) -> Z()
            eqZList(C(x1,x2),C(y1,y2)) -> and(eqZList(x1,y1),eqZList(x2,y2))
            eqZList(C(x1,x2),Z()) -> False()
            eqZList(Z(),C(y1,y2)) -> False()
            eqZList(Z(),Z()) -> True()
            first(C(x1,x2)) -> x1
            second(C(x1,x2)) -> x2
        - Weak TRS:
            and(False(),False()) -> False()
            and(False(),True()) -> False()
            and(True(),False()) -> False()
            and(True(),True()) -> True()
        - Signature:
            {a/3,and/2,eqZList/2,first/1,second/1} / {C/2,False/0,True/0,Z/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a,and,eqZList,first,second} and constructors {C,False
            ,True,Z}
    + Applied Processor:
        Ara {araHeuristics = NoHeuristics, minDegree = 1, maxDegree = 2, araTimeout = 5, araRuleShifting = Nothing}
    + Details:
        Signatures used:
        ----------------
          C :: ["A"(15) x "A"(15)] -(15)-> "A"(15)
          C :: ["A"(9) x "A"(9)] -(9)-> "A"(9)
          C :: ["A"(3) x "A"(3)] -(3)-> "A"(3)
          C :: ["A"(0) x "A"(0)] -(0)-> "A"(0)
          C :: ["A"(2) x "A"(2)] -(2)-> "A"(2)
          False :: [] -(0)-> "A"(0)
          False :: [] -(0)-> "A"(1)
          True :: [] -(0)-> "A"(0)
          True :: [] -(0)-> "A"(6)
          Z :: [] -(0)-> "A"(15)
          Z :: [] -(0)-> "A"(9)
          Z :: [] -(0)-> "A"(6)
          a :: ["A"(15) x "A"(0) x "A"(0)] -(1)-> "A"(2)
          and :: ["A"(0) x "A"(0)] -(0)-> "A"(1)
          eqZList :: ["A"(9) x "A"(15)] -(2)-> "A"(0)
          first :: ["A"(3)] -(15)-> "A"(0)
          second :: ["A"(0)] -(8)-> "A"(0)
        
        
        Cost-free Signatures used:
        --------------------------
        
        
        
        Base Constructor Signatures used:
        ---------------------------------
          "C_A" :: ["A"(1) x "A"(1)] -(1)-> "A"(1)
          "False_A" :: [] -(0)-> "A"(1)
          "True_A" :: [] -(0)-> "A"(1)
          "Z_A" :: [] -(0)-> "A"(1)
        

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