/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:
            rev(cons(X,L)) -> cons(rev1(X,L),rev2(X,L))
            rev(nil()) -> nil()
            rev1(X,cons(Y,L)) -> rev1(Y,L)
            rev1(0(),nil()) -> 0()
            rev1(s(X),nil()) -> s(X)
            rev2(X,cons(Y,L)) -> rev(cons(X,rev(rev2(Y,L))))
            rev2(X,nil()) -> nil()
        - Signature:
            {rev/1,rev1/2,rev2/2} / {0/0,cons/2,nil/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {rev,rev1,rev2} and constructors {0,cons,nil,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            rev(cons(X,L)) -> cons(rev1(X,L),rev2(X,L))
            rev(nil()) -> nil()
            rev1(X,cons(Y,L)) -> rev1(Y,L)
            rev1(0(),nil()) -> 0()
            rev1(s(X),nil()) -> s(X)
            rev2(X,cons(Y,L)) -> rev(cons(X,rev(rev2(Y,L))))
            rev2(X,nil()) -> nil()
        - Signature:
            {rev/1,rev1/2,rev2/2} / {0/0,cons/2,nil/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {rev,rev1,rev2} and constructors {0,cons,nil,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 2.a:1: Ara.  MAYBE
    + Considered Problem:
        - Strict TRS:
            rev(cons(X,L)) -> cons(rev1(X,L),rev2(X,L))
            rev(nil()) -> nil()
            rev1(X,cons(Y,L)) -> rev1(Y,L)
            rev1(0(),nil()) -> 0()
            rev1(s(X),nil()) -> s(X)
            rev2(X,cons(Y,L)) -> rev(cons(X,rev(rev2(Y,L))))
            rev2(X,nil()) -> nil()
        - Signature:
            {rev/1,rev1/2,rev2/2} / {0/0,cons/2,nil/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {rev,rev1,rev2} and constructors {0,cons,nil,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 "cons") :: ["A"(0) x "A"(0)] -(0)-> "A"(0)
          F (TrsFun "cons") :: ["A"(0) x "A"(1)] -(1)-> "A"(1)
          F (TrsFun "main") :: ["A"(0) x "A"(1)] -(1)-> "A"(0)
          F (TrsFun "nil") :: [] -(0)-> "A"(0)
          F (TrsFun "nil") :: [] -(0)-> "A"(1)
          F (TrsFun "rev") :: ["A"(0)] -(1)-> "A"(0)
          F (TrsFun "rev1") :: ["A"(0) x "A"(0)] -(1)-> "A"(0)
          F (TrsFun "rev2") :: ["A"(0) x "A"(1)] -(1)-> "A"(0)
          F (TrsFun "s") :: ["A"(0)] -(0)-> "A"(0)
        
        
        Cost-free Signatures used:
        --------------------------
        
        
        
        Base Constructor Signatures used:
        ---------------------------------
        
        
        
        Following Still Strict Rules were Typed as:
        -------------------------------------------
        1. Strict:
          rev(cons(X,L)) -> cons(rev1(X,L),rev2(X,L))
          rev(nil()) -> nil()
          rev1(X,cons(Y,L)) -> rev1(Y,L)
          rev1(0(),nil()) -> 0()
          rev1(s(X),nil()) -> s(X)
          rev2(X,cons(Y,L)) -> rev(cons(X,rev(rev2(Y,L))))
          rev2(X,nil()) -> nil()
          main(x1,x2) -> rev2(x1,x2)
        2. Weak:
          
        

** Step 2.b:1: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            rev(cons(X,L)) -> cons(rev1(X,L),rev2(X,L))
            rev(nil()) -> nil()
            rev1(X,cons(Y,L)) -> rev1(Y,L)
            rev1(0(),nil()) -> 0()
            rev1(s(X),nil()) -> s(X)
            rev2(X,cons(Y,L)) -> rev(cons(X,rev(rev2(Y,L))))
            rev2(X,nil()) -> nil()
        - Signature:
            {rev/1,rev1/2,rev2/2} / {0/0,cons/2,nil/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {rev,rev1,rev2} and constructors {0,cons,nil,s}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          rev1(x,z){z -> cons(y,z)} =
            rev1(x,cons(y,z)) ->^+ rev1(y,z)
              = C[rev1(y,z) = rev1(x,z){x -> y}]

WORST_CASE(Omega(n^1),?)