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


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

** Step 1.b:1: Ara WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            +Full(0(),y) -> y
            +Full(S(x),y) -> +Full(x,S(y))
            f(x) -> *(x,x)
            goal(xs) -> map(xs)
            map(Cons(x,xs)) -> Cons(f(x),map(xs))
            map(Nil()) -> Nil()
        - Weak TRS:
            *(x,0()) -> 0()
            *(x,S(0())) -> x
            *(x,S(S(y))) -> +(x,*(x,S(y)))
            *(0(),y) -> 0()
        - Signature:
            {*/2,+Full/2,f/1,goal/1,map/1} / {+/2,0/0,Cons/2,Nil/0,S/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*,+Full,f,goal,map} and constructors {+,0,Cons,Nil,S}
    + Applied Processor:
        Ara {araHeuristics = NoHeuristics, minDegree = 1, maxDegree = 2, araTimeout = 5, araRuleShifting = Nothing}
    + Details:
        Signatures used:
        ----------------
          * :: ["A"(3) x "A"(7)] -(2)-> "A"(2)
          + :: ["A"(0) x "A"(0)] -(0)-> "A"(14)
          +Full :: ["A"(10) x "A"(1)] -(8)-> "A"(1)
          0 :: [] -(0)-> "A"(10)
          0 :: [] -(0)-> "A"(7)
          0 :: [] -(0)-> "A"(3)
          0 :: [] -(0)-> "A"(12)
          Cons :: ["A"(14) x "A"(14)] -(14)-> "A"(14)
          Cons :: ["A"(2) x "A"(2)] -(2)-> "A"(2)
          Nil :: [] -(0)-> "A"(14)
          Nil :: [] -(0)-> "A"(10)
          S :: ["A"(10)] -(10)-> "A"(10)
          S :: ["A"(7)] -(7)-> "A"(7)
          S :: ["A"(1)] -(1)-> "A"(1)
          f :: ["A"(11)] -(3)-> "A"(2)
          goal :: ["A"(14)] -(16)-> "A"(1)
          map :: ["A"(14)] -(2)-> "A"(2)
        
        
        Cost-free Signatures used:
        --------------------------
        
        
        
        Base Constructor Signatures used:
        ---------------------------------
          "+_A" :: ["A"(0) x "A"(0)] -(0)-> "A"(0)
          "0_A" :: [] -(0)-> "A"(1)
          "Cons_A" :: ["A"(1) x "A"(1)] -(1)-> "A"(1)
          "Nil_A" :: [] -(0)-> "A"(1)
          "S_A" :: ["A"(1)] -(1)-> "A"(1)
        

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