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

** Step 1.b:1: Ara WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            merge(x,nil()) -> x
            merge(++(x,y),++(u(),v())) -> ++(x,merge(y,++(u(),v())))
            merge(++(x,y),++(u(),v())) -> ++(u(),merge(++(x,y),v()))
            merge(nil(),y) -> y
        - Signature:
            {merge/2} / {++/2,nil/0,u/0,v/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {merge} and constructors {++,nil,u,v}
    + Applied Processor:
        Ara {araHeuristics = NoHeuristics, minDegree = 1, maxDegree = 2, araTimeout = 5, araRuleShifting = Nothing}
    + Details:
        Signatures used:
        ----------------
          ++ :: ["A"(13) x "A"(13)] -(13)-> "A"(13)
          ++ :: ["A"(7) x "A"(7)] -(7)-> "A"(7)
          ++ :: ["A"(4) x "A"(4)] -(4)-> "A"(4)
          merge :: ["A"(13) x "A"(7)] -(1)-> "A"(4)
          nil :: [] -(0)-> "A"(7)
          nil :: [] -(0)-> "A"(13)
          u :: [] -(0)-> "A"(7)
          u :: [] -(0)-> "A"(15)
          u :: [] -(0)-> "A"(14)
          v :: [] -(0)-> "A"(7)
          v :: [] -(0)-> "A"(12)
          v :: [] -(0)-> "A"(14)
        
        
        Cost-free Signatures used:
        --------------------------
        
        
        
        Base Constructor Signatures used:
        ---------------------------------
          "++_A" :: ["A"(0) x "A"(0)] -(0)-> "A"(0)
          "nil_A" :: [] -(0)-> "A"(1)
          "u_A" :: [] -(0)-> "A"(1)
          "v_A" :: [] -(0)-> "A"(1)
        

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