/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:
            append(l1,l2) -> ifappend(l1,l2,is_empty(l1))
            hd(cons(x,l)) -> x
            ifappend(l1,l2,false()) -> cons(hd(l1),append(tl(l1),l2))
            ifappend(l1,l2,true()) -> l2
            is_empty(cons(x,l)) -> false()
            is_empty(nil()) -> true()
            tl(cons(x,l)) -> l
        - Signature:
            {append/2,hd/1,ifappend/3,is_empty/1,tl/1} / {cons/2,false/0,nil/0,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {append,hd,ifappend,is_empty,tl} and constructors {cons,false,nil
            ,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            append(l1,l2) -> ifappend(l1,l2,is_empty(l1))
            hd(cons(x,l)) -> x
            ifappend(l1,l2,false()) -> cons(hd(l1),append(tl(l1),l2))
            ifappend(l1,l2,true()) -> l2
            is_empty(cons(x,l)) -> false()
            is_empty(nil()) -> true()
            tl(cons(x,l)) -> l
        - Signature:
            {append/2,hd/1,ifappend/3,is_empty/1,tl/1} / {cons/2,false/0,nil/0,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {append,hd,ifappend,is_empty,tl} and constructors {cons,false,nil
            ,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            append(l1,l2) -> ifappend(l1,l2,is_empty(l1))
            hd(cons(x,l)) -> x
            ifappend(l1,l2,false()) -> cons(hd(l1),append(tl(l1),l2))
            ifappend(l1,l2,true()) -> l2
            is_empty(cons(x,l)) -> false()
            is_empty(nil()) -> true()
            tl(cons(x,l)) -> l
        - Signature:
            {append/2,hd/1,ifappend/3,is_empty/1,tl/1} / {cons/2,false/0,nil/0,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {append,hd,ifappend,is_empty,tl} and constructors {cons,false,nil
            ,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          append(z,w){z -> cons(x,z)} =
            append(cons(x,z),w) ->^+ cons(hd(cons(x,z)),append(z,w))
              = C[append(z,w) = append(z,w){}]

WORST_CASE(Omega(n^1),?)