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

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

WORST_CASE(Omega(n^1),?)