/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),?)
* Step 1: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            add0(x,Nil()) -> x
            add0(x',Cons(x,xs)) -> Cons(Cons(Nil(),Nil()),add0(x',xs))
            goal(x,y) -> power(x,y)
            mult(x,Nil()) -> Nil()
            mult(x',Cons(x,xs)) -> add0(x',mult(x',xs))
            power(x,Nil()) -> Cons(Nil(),Nil())
            power(x',Cons(x,xs)) -> mult(x',power(x',xs))
        - Signature:
            {add0/2,goal/2,mult/2,power/2} / {Cons/2,Nil/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add0,goal,mult,power} and constructors {Cons,Nil}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            add0(x,Nil()) -> x
            add0(x',Cons(x,xs)) -> Cons(Cons(Nil(),Nil()),add0(x',xs))
            goal(x,y) -> power(x,y)
            mult(x,Nil()) -> Nil()
            mult(x',Cons(x,xs)) -> add0(x',mult(x',xs))
            power(x,Nil()) -> Cons(Nil(),Nil())
            power(x',Cons(x,xs)) -> mult(x',power(x',xs))
        - Signature:
            {add0/2,goal/2,mult/2,power/2} / {Cons/2,Nil/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add0,goal,mult,power} and constructors {Cons,Nil}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 2.a:1: Ara.  MAYBE
    + Considered Problem:
        - Strict TRS:
            add0(x,Nil()) -> x
            add0(x',Cons(x,xs)) -> Cons(Cons(Nil(),Nil()),add0(x',xs))
            goal(x,y) -> power(x,y)
            mult(x,Nil()) -> Nil()
            mult(x',Cons(x,xs)) -> add0(x',mult(x',xs))
            power(x,Nil()) -> Cons(Nil(),Nil())
            power(x',Cons(x,xs)) -> mult(x',power(x',xs))
        - Signature:
            {add0/2,goal/2,mult/2,power/2} / {Cons/2,Nil/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add0,goal,mult,power} and constructors {Cons,Nil}
    + Applied Processor:
        Ara {minDegree = 1, maxDegree = 3, araTimeout = 15, araRuleShifting = Just 1, isBestCase = True, mkCompletelyDefined = False, verboseOutput = False}
    + Details:
        Signatures used:
        ----------------
          F (TrsFun "Cons") :: ["A"(0) x "A"(0)] -(0)-> "A"(0)
          F (TrsFun "Cons") :: ["A"(0) x "A"(1)] -(1)-> "A"(1)
          F (TrsFun "Nil") :: [] -(0)-> "A"(0)
          F (TrsFun "Nil") :: [] -(0)-> "A"(1)
          F (TrsFun "add0") :: ["A"(0) x "A"(0)] -(1)-> "A"(0)
          F (TrsFun "goal") :: ["A"(0) x "A"(1)] -(1)-> "A"(0)
          F (TrsFun "main") :: ["A"(0) x "A"(1)] -(1)-> "A"(0)
          F (TrsFun "mult") :: ["A"(0) x "A"(0)] -(1)-> "A"(0)
          F (TrsFun "power") :: ["A"(0) x "A"(1)] -(1)-> "A"(0)
        
        
        Cost-free Signatures used:
        --------------------------
        
        
        
        Base Constructor Signatures used:
        ---------------------------------
        
        
        
        Following Still Strict Rules were Typed as:
        -------------------------------------------
        1. Strict:
          add0(x,Nil()) -> x
          add0(x',Cons(x,xs)) -> Cons(Cons(Nil(),Nil()),add0(x',xs))
          goal(x,y) -> power(x,y)
          mult(x,Nil()) -> Nil()
          mult(x',Cons(x,xs)) -> add0(x',mult(x',xs))
          power(x,Nil()) -> Cons(Nil(),Nil())
          power(x',Cons(x,xs)) -> mult(x',power(x',xs))
          main(x1,x2) -> power(x1,x2)
        2. Weak:
          
        

** Step 2.b:1: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            add0(x,Nil()) -> x
            add0(x',Cons(x,xs)) -> Cons(Cons(Nil(),Nil()),add0(x',xs))
            goal(x,y) -> power(x,y)
            mult(x,Nil()) -> Nil()
            mult(x',Cons(x,xs)) -> add0(x',mult(x',xs))
            power(x,Nil()) -> Cons(Nil(),Nil())
            power(x',Cons(x,xs)) -> mult(x',power(x',xs))
        - Signature:
            {add0/2,goal/2,mult/2,power/2} / {Cons/2,Nil/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add0,goal,mult,power} and constructors {Cons,Nil}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          add0(x,z){z -> Cons(y,z)} =
            add0(x,Cons(y,z)) ->^+ Cons(Cons(Nil(),Nil()),add0(x,z))
              = C[add0(x,z) = add0(x,z){}]

WORST_CASE(Omega(n^1),?)