/export/starexec/sandbox2/solver/bin/starexec_run_tct_rc /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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WORST_CASE(Omega(n^1),?)
* Step 1: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            dbl(0()) -> 0()
            dbl(s(X)) -> s(s(dbl(X)))
            dbl1(0()) -> 01()
            dbl1(s(X)) -> s1(s1(dbl1(X)))
            dbls(cons(X,Y)) -> cons(dbl(X),dbls(Y))
            dbls(nil()) -> nil()
            from(X) -> cons(X,from(s(X)))
            indx(cons(X,Y),Z) -> cons(sel(X,Z),indx(Y,Z))
            indx(nil(),X) -> nil()
            quote(0()) -> 01()
            quote(dbl(X)) -> dbl1(X)
            quote(s(X)) -> s1(quote(X))
            quote(sel(X,Y)) -> sel1(X,Y)
            sel(0(),cons(X,Y)) -> X
            sel(s(X),cons(Y,Z)) -> sel(X,Z)
            sel1(0(),cons(X,Y)) -> X
            sel1(s(X),cons(Y,Z)) -> sel1(X,Z)
        - Signature:
            {dbl/1,dbl1/1,dbls/1,from/1,indx/2,quote/1,sel/2,sel1/2} / {0/0,01/0,cons/2,nil/0,s/1,s1/1}
        - Obligation:
             runtime complexity wrt. defined symbols {dbl,dbl1,dbls,from,indx,quote,sel,sel1} and constructors {0,01
            ,cons,nil,s,s1}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            dbl(0()) -> 0()
            dbl(s(X)) -> s(s(dbl(X)))
            dbl1(0()) -> 01()
            dbl1(s(X)) -> s1(s1(dbl1(X)))
            dbls(cons(X,Y)) -> cons(dbl(X),dbls(Y))
            dbls(nil()) -> nil()
            from(X) -> cons(X,from(s(X)))
            indx(cons(X,Y),Z) -> cons(sel(X,Z),indx(Y,Z))
            indx(nil(),X) -> nil()
            quote(0()) -> 01()
            quote(dbl(X)) -> dbl1(X)
            quote(s(X)) -> s1(quote(X))
            quote(sel(X,Y)) -> sel1(X,Y)
            sel(0(),cons(X,Y)) -> X
            sel(s(X),cons(Y,Z)) -> sel(X,Z)
            sel1(0(),cons(X,Y)) -> X
            sel1(s(X),cons(Y,Z)) -> sel1(X,Z)
        - Signature:
            {dbl/1,dbl1/1,dbls/1,from/1,indx/2,quote/1,sel/2,sel1/2} / {0/0,01/0,cons/2,nil/0,s/1,s1/1}
        - Obligation:
             runtime complexity wrt. defined symbols {dbl,dbl1,dbls,from,indx,quote,sel,sel1} and constructors {0,01
            ,cons,nil,s,s1}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            dbl(0()) -> 0()
            dbl(s(X)) -> s(s(dbl(X)))
            dbl1(0()) -> 01()
            dbl1(s(X)) -> s1(s1(dbl1(X)))
            dbls(cons(X,Y)) -> cons(dbl(X),dbls(Y))
            dbls(nil()) -> nil()
            from(X) -> cons(X,from(s(X)))
            indx(cons(X,Y),Z) -> cons(sel(X,Z),indx(Y,Z))
            indx(nil(),X) -> nil()
            quote(0()) -> 01()
            quote(dbl(X)) -> dbl1(X)
            quote(s(X)) -> s1(quote(X))
            quote(sel(X,Y)) -> sel1(X,Y)
            sel(0(),cons(X,Y)) -> X
            sel(s(X),cons(Y,Z)) -> sel(X,Z)
            sel1(0(),cons(X,Y)) -> X
            sel1(s(X),cons(Y,Z)) -> sel1(X,Z)
        - Signature:
            {dbl/1,dbl1/1,dbls/1,from/1,indx/2,quote/1,sel/2,sel1/2} / {0/0,01/0,cons/2,nil/0,s/1,s1/1}
        - Obligation:
             runtime complexity wrt. defined symbols {dbl,dbl1,dbls,from,indx,quote,sel,sel1} and constructors {0,01
            ,cons,nil,s,s1}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          dbl(x){x -> s(x)} =
            dbl(s(x)) ->^+ s(s(dbl(x)))
              = C[dbl(x) = dbl(x){}]

WORST_CASE(Omega(n^1),?)