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

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

** Step 1.b:1: Ara.  WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict TRS:
            f(x,c(y)) -> f(x,s(f(y,y)))
            f(s(x),y) -> f(x,s(c(y)))
        - Signature:
            {f/2} / {c/1,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f} and constructors {c,s}
    + Applied Processor:
        Ara {minDegree = 1, maxDegree = 2, araTimeout = 5, araRuleShifting = Nothing, isBestCase = False, mkCompletelyDefined = False, verboseOutput = False}
    + Details:
        Signatures used:
        ----------------
          F (TrsFun "c") :: ["A"(15, 15)] -(15)-> "A"(0, 15)
          F (TrsFun "c") :: ["A"(0, 0)] -(0)-> "A"(0, 0)
          F (TrsFun "f") :: ["A"(15, 0) x "A"(0, 15)] -(5)-> "A"(12, 14)
          F (TrsFun "s") :: ["A"(15, 0)] -(15)-> "A"(15, 0)
          F (TrsFun "s") :: ["A"(0, 0)] -(0)-> "A"(0, 15)
        
        
        Cost-free Signatures used:
        --------------------------
        
        
        
        Base Constructor Signatures used:
        ---------------------------------
          "F (TrsFun \"c\")_A" :: ["A"(1, 0)] -(0)-> "A"(1, 0)
          "F (TrsFun \"c\")_A" :: ["A"(1, 1)] -(1)-> "A"(0, 1)
          "F (TrsFun \"s\")_A" :: ["A"(1, 0)] -(1)-> "A"(1, 0)
          "F (TrsFun \"s\")_A" :: ["A"(0, 0)] -(0)-> "A"(0, 1)
        
        

WORST_CASE(Omega(n^1),O(n^2))