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

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

WORST_CASE(Omega(n^1),?)