/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:
            f(0(),0(),0(),0(),0()) -> 0()
            f(0(),0(),0(),0(),s(x5)) -> f(x5,x5,x5,x5,x5)
            f(0(),0(),0(),s(x4),x5) -> f(x4,x4,x4,x4,x5)
            f(0(),0(),s(x3),x4,x5) -> f(x3,x3,x3,x4,x5)
            f(0(),s(x2),x3,x4,x5) -> f(x2,x2,x3,x4,x5)
            f(s(x1),x2,x3,x4,x5) -> f(x1,x2,x3,x4,x5)
        - Signature:
            {f/5} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f} and constructors {0,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            f(0(),0(),0(),0(),0()) -> 0()
            f(0(),0(),0(),0(),s(x5)) -> f(x5,x5,x5,x5,x5)
            f(0(),0(),0(),s(x4),x5) -> f(x4,x4,x4,x4,x5)
            f(0(),0(),s(x3),x4,x5) -> f(x3,x3,x3,x4,x5)
            f(0(),s(x2),x3,x4,x5) -> f(x2,x2,x3,x4,x5)
            f(s(x1),x2,x3,x4,x5) -> f(x1,x2,x3,x4,x5)
        - Signature:
            {f/5} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f} and constructors {0,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 2.a:1: Ara.  MAYBE
    + Considered Problem:
        - Strict TRS:
            f(0(),0(),0(),0(),0()) -> 0()
            f(0(),0(),0(),0(),s(x5)) -> f(x5,x5,x5,x5,x5)
            f(0(),0(),0(),s(x4),x5) -> f(x4,x4,x4,x4,x5)
            f(0(),0(),s(x3),x4,x5) -> f(x3,x3,x3,x4,x5)
            f(0(),s(x2),x3,x4,x5) -> f(x2,x2,x3,x4,x5)
            f(s(x1),x2,x3,x4,x5) -> f(x1,x2,x3,x4,x5)
        - Signature:
            {f/5} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f} 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, 0, 0)
          F (TrsFun "0") :: [] -(0)-> "A"(1, 0, 0)
          F (TrsFun "0") :: [] -(0)-> "A"(1, 1, 0)
          F (TrsFun "0") :: [] -(0)-> "A"(1, 1, 1)
          F (TrsFun "f") :: ["A"(0, 0, 0) x "A"(1, 0, 0) x "A"(0, 0, 0) x "A"(1, 1, 0) x "A"(1, 1, 1)] -(1)-> "A"(0, 0, 0)
          F (TrsFun "main") :: ["A"(0, 0, 0) x "A"(0, 0, 0) x "A"(0, 0, 0) x "A"(0, 0, 0) x "A"(0, 0, 1)] -(1)-> "A"(0, 0, 0)
          F (TrsFun "s") :: ["A"(2, 2, 1)] -(1)-> "A"(1, 1, 1)
          F (TrsFun "s") :: ["A"(2, 1, 0)] -(1)-> "A"(1, 1, 0)
          F (TrsFun "s") :: ["A"(0, 0, 0)] -(0)-> "A"(0, 0, 0)
          F (TrsFun "s") :: ["A"(1, 0, 0)] -(1)-> "A"(1, 0, 0)
        
        
        Cost-free Signatures used:
        --------------------------
        
        
        
        Base Constructor Signatures used:
        ---------------------------------
        
        
        
        Following Still Strict Rules were Typed as:
        -------------------------------------------
        1. Strict:
          f(0(),0(),0(),0(),0()) -> 0()
          f(0(),0(),0(),0(),s(x5)) -> f(x5,x5,x5,x5,x5)
          f(0(),0(),0(),s(x4),x5) -> f(x4,x4,x4,x4,x5)
          f(0(),0(),s(x3),x4,x5) -> f(x3,x3,x3,x4,x5)
          f(0(),s(x2),x3,x4,x5) -> f(x2,x2,x3,x4,x5)
          f(s(x1),x2,x3,x4,x5) -> f(x1,x2,x3,x4,x5)
          main(x1,x2,x3,x4,x5) -> f(x1,x2,x3,x4,x5)
        2. Weak:
          
        

** Step 2.b:1: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            f(0(),0(),0(),0(),0()) -> 0()
            f(0(),0(),0(),0(),s(x5)) -> f(x5,x5,x5,x5,x5)
            f(0(),0(),0(),s(x4),x5) -> f(x4,x4,x4,x4,x5)
            f(0(),0(),s(x3),x4,x5) -> f(x3,x3,x3,x4,x5)
            f(0(),s(x2),x3,x4,x5) -> f(x2,x2,x3,x4,x5)
            f(s(x1),x2,x3,x4,x5) -> f(x1,x2,x3,x4,x5)
        - Signature:
            {f/5} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f} and constructors {0,s}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          f(x,y,z,u,v){x -> s(x)} =
            f(s(x),y,z,u,v) ->^+ f(x,y,z,u,v)
              = C[f(x,y,z,u,v) = f(x,y,z,u,v){}]

WORST_CASE(Omega(n^1),?)