/export/starexec/sandbox/solver/bin/starexec_run_tct_rci /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/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:
            dbl(0(),y) -> y
            dbl(S(0()),S(0())) -> S(S(S(S(0()))))
            save(0()) -> 0()
            save(S(x)) -> dbl(0(),save(x))
        - Signature:
            {dbl/2,save/1} / {0/0,S/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {dbl,save} and constructors {0,S}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            dbl(0(),y) -> y
            dbl(S(0()),S(0())) -> S(S(S(S(0()))))
            save(0()) -> 0()
            save(S(x)) -> dbl(0(),save(x))
        - Signature:
            {dbl/2,save/1} / {0/0,S/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {dbl,save} and constructors {0,S}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
*** Step 1.a:1.a:1: Ara.  MAYBE
    + Considered Problem:
        - Strict TRS:
            dbl(0(),y) -> y
            dbl(S(0()),S(0())) -> S(S(S(S(0()))))
            save(0()) -> 0()
            save(S(x)) -> dbl(0(),save(x))
        - Signature:
            {dbl/2,save/1} / {0/0,S/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {dbl,save} 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 "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 "dbl") :: ["A"(0) x "A"(0)] -(1)-> "A"(0)
          F (TrsFun "main") :: ["A"(1)] -(1)-> "A"(0)
          F (TrsFun "save") :: ["A"(1)] -(1)-> "A"(0)
        
        
        Cost-free Signatures used:
        --------------------------
        
        
        
        Base Constructor Signatures used:
        ---------------------------------
        
        
        
        Following Still Strict Rules were Typed as:
        -------------------------------------------
        1. Strict:
          dbl(0(),y) -> y
          dbl(S(0()),S(0())) -> S(S(S(S(0()))))
          save(0()) -> 0()
          save(S(x)) -> dbl(0(),save(x))
          main(x1) -> save(x1)
        2. Weak:
          
        

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

** Step 1.b:1: Ara.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            dbl(0(),y) -> y
            dbl(S(0()),S(0())) -> S(S(S(S(0()))))
            save(0()) -> 0()
            save(S(x)) -> dbl(0(),save(x))
        - Signature:
            {dbl/2,save/1} / {0/0,S/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {dbl,save} and constructors {0,S}
    + Applied Processor:
        Ara {minDegree = 1, maxDegree = 1, araTimeout = 8, araRuleShifting = Just 1, isBestCase = False, mkCompletelyDefined = False, verboseOutput = False}
    + Details:
        Signatures used:
        ----------------
          F (TrsFun "0") :: [] -(0)-> "A"(0)
          F (TrsFun "0") :: [] -(0)-> "A"(2)
          F (TrsFun "S") :: ["A"(0)] -(0)-> "A"(0)
          F (TrsFun "S") :: ["A"(2)] -(2)-> "A"(2)
          F (TrsFun "dbl") :: ["A"(0) x "A"(0)] -(1)-> "A"(0)
          F (TrsFun "save") :: ["A"(2)] -(1)-> "A"(0)
        
        
        Cost-free Signatures used:
        --------------------------
        
        
        
        Base Constructor Signatures used:
        ---------------------------------
        
        
        
        Following Still Strict Rules were Typed as:
        -------------------------------------------
        1. Strict:
          dbl(0(),y) -> y
          dbl(S(0()),S(0())) -> S(S(S(S(0()))))
          save(0()) -> 0()
          save(S(x)) -> dbl(0(),save(x))
        2. Weak:
          
        

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