/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(cons(x,xs),ys) -> cons(x,append(xs,ys))
            append(nil(),ys) -> ys
            dropLast(cons(x,cons(y,ys))) -> cons(x,dropLast(cons(y,ys)))
            dropLast(cons(x,nil())) -> nil()
            dropLast(nil()) -> nil()
            if(false(),xs,ys,zs) -> rev(xs,ys)
            if(true(),xs,ys,zs) -> zs
            isEmpty(cons(x,xs)) -> false()
            isEmpty(nil()) -> true()
            last(cons(x,cons(y,ys))) -> last(cons(y,ys))
            last(cons(x,nil())) -> x
            rev(xs,ys) -> if(isEmpty(xs),dropLast(xs),append(ys,last(xs)),ys)
            reverse(xs) -> rev(xs,nil())
        - Signature:
            {append/2,dropLast/1,if/4,isEmpty/1,last/1,rev/2,reverse/1} / {cons/2,false/0,nil/0,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {append,dropLast,if,isEmpty,last,rev
            ,reverse} 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(cons(x,xs),ys) -> cons(x,append(xs,ys))
            append(nil(),ys) -> ys
            dropLast(cons(x,cons(y,ys))) -> cons(x,dropLast(cons(y,ys)))
            dropLast(cons(x,nil())) -> nil()
            dropLast(nil()) -> nil()
            if(false(),xs,ys,zs) -> rev(xs,ys)
            if(true(),xs,ys,zs) -> zs
            isEmpty(cons(x,xs)) -> false()
            isEmpty(nil()) -> true()
            last(cons(x,cons(y,ys))) -> last(cons(y,ys))
            last(cons(x,nil())) -> x
            rev(xs,ys) -> if(isEmpty(xs),dropLast(xs),append(ys,last(xs)),ys)
            reverse(xs) -> rev(xs,nil())
        - Signature:
            {append/2,dropLast/1,if/4,isEmpty/1,last/1,rev/2,reverse/1} / {cons/2,false/0,nil/0,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {append,dropLast,if,isEmpty,last,rev
            ,reverse} 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(cons(x,xs),ys) -> cons(x,append(xs,ys))
            append(nil(),ys) -> ys
            dropLast(cons(x,cons(y,ys))) -> cons(x,dropLast(cons(y,ys)))
            dropLast(cons(x,nil())) -> nil()
            dropLast(nil()) -> nil()
            if(false(),xs,ys,zs) -> rev(xs,ys)
            if(true(),xs,ys,zs) -> zs
            isEmpty(cons(x,xs)) -> false()
            isEmpty(nil()) -> true()
            last(cons(x,cons(y,ys))) -> last(cons(y,ys))
            last(cons(x,nil())) -> x
            rev(xs,ys) -> if(isEmpty(xs),dropLast(xs),append(ys,last(xs)),ys)
            reverse(xs) -> rev(xs,nil())
        - Signature:
            {append/2,dropLast/1,if/4,isEmpty/1,last/1,rev/2,reverse/1} / {cons/2,false/0,nil/0,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {append,dropLast,if,isEmpty,last,rev
            ,reverse} and constructors {cons,false,nil,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          append(y,z){y -> cons(x,y)} =
            append(cons(x,y),z) ->^+ cons(x,append(y,z))
              = C[append(y,z) = append(y,z){}]

WORST_CASE(Omega(n^1),?)