/export/starexec/sandbox2/solver/bin/starexec_run_tct_rci /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/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:
            -(x,0()) -> x
            -(s(x),s(y)) -> -(x,y)
            f(x,s(y)) -> f(p(-(x,s(y))),p(-(s(y),x)))
            f(s(x),y) -> f(p(-(s(x),y)),p(-(y,s(x))))
            p(s(x)) -> x
        - Signature:
            {-/2,f/2,p/1} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {-,f,p} 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:
            -(x,0()) -> x
            -(s(x),s(y)) -> -(x,y)
            f(x,s(y)) -> f(p(-(x,s(y))),p(-(s(y),x)))
            f(s(x),y) -> f(p(-(s(x),y)),p(-(y,s(x))))
            p(s(x)) -> x
        - Signature:
            {-/2,f/2,p/1} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {-,f,p} and constructors {0,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:2: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            -(x,0()) -> x
            -(s(x),s(y)) -> -(x,y)
            f(x,s(y)) -> f(p(-(x,s(y))),p(-(s(y),x)))
            f(s(x),y) -> f(p(-(s(x),y)),p(-(y,s(x))))
            p(s(x)) -> x
        - Signature:
            {-/2,f/2,p/1} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {-,f,p} and constructors {0,s}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          -(x,y){x -> s(x),y -> s(y)} =
            -(s(x),s(y)) ->^+ -(x,y)
              = C[-(x,y) = -(x,y){}]

** Step 1.b:1: Ara.  WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict TRS:
            -(x,0()) -> x
            -(s(x),s(y)) -> -(x,y)
            f(x,s(y)) -> f(p(-(x,s(y))),p(-(s(y),x)))
            f(s(x),y) -> f(p(-(s(x),y)),p(-(y,s(x))))
            p(s(x)) -> x
        - Signature:
            {-/2,f/2,p/1} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {-,f,p} and constructors {0,s}
    + Applied Processor:
        Ara {minDegree = 1, maxDegree = 2, araTimeout = 3, araRuleShifting = Nothing, isBestCase = False, mkCompletelyDefined = False, verboseOutput = False}
    + Details:
        Signatures used:
        ----------------
          F (TrsFun "-") :: ["A"(7, 6) x "A"(0, 0)] -(1)-> "A"(7, 6)
          F (TrsFun "0") :: [] -(0)-> "A"(0, 0)
          F (TrsFun "f") :: ["A"(12, 6) x "A"(12, 6)] -(0)-> "A"(0, 0)
          F (TrsFun "p") :: ["A"(7, 6)] -(1)-> "A"(12, 6)
          F (TrsFun "s") :: ["A"(13, 6)] -(7)-> "A"(7, 6)
          F (TrsFun "s") :: ["A"(0, 0)] -(0)-> "A"(0, 0)
          F (TrsFun "s") :: ["A"(18, 6)] -(12)-> "A"(12, 6)
        
        
        Cost-free Signatures used:
        --------------------------
        
        
        
        Base Constructor Signatures used:
        ---------------------------------
        
        
        

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