/export/starexec/sandbox/solver/bin/starexec_run_tct_rc /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:
            app(x,y) -> helpa(0(),plus(length(x),length(y)),x,y)
            ge(x,0()) -> true()
            ge(0(),s(x)) -> false()
            ge(s(x),s(y)) -> ge(x,y)
            greater(ys,zs) -> helpc(ge(length(ys),length(zs)),ys,zs)
            helpa(c,l,ys,zs) -> if(ge(c,l),c,l,ys,zs)
            helpb(c,l,cons(y,ys),zs) -> cons(y,helpa(s(c),l,ys,zs))
            helpc(false(),ys,zs) -> zs
            helpc(true(),ys,zs) -> ys
            if(false(),c,l,ys,zs) -> helpb(c,l,greater(ys,zs),smaller(ys,zs))
            if(true(),c,l,ys,zs) -> nil()
            length(cons(x,y)) -> s(length(y))
            length(nil()) -> 0()
            plus(x,0()) -> x
            plus(x,s(y)) -> s(plus(x,y))
            smaller(ys,zs) -> helpc(ge(length(ys),length(zs)),zs,ys)
        - Signature:
            {app/2,ge/2,greater/2,helpa/4,helpb/4,helpc/3,if/5,length/1,plus/2,smaller/2} / {0/0,cons/2,false/0,nil/0
            ,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {app,ge,greater,helpa,helpb,helpc,if,length,plus
            ,smaller} 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:
            app(x,y) -> helpa(0(),plus(length(x),length(y)),x,y)
            ge(x,0()) -> true()
            ge(0(),s(x)) -> false()
            ge(s(x),s(y)) -> ge(x,y)
            greater(ys,zs) -> helpc(ge(length(ys),length(zs)),ys,zs)
            helpa(c,l,ys,zs) -> if(ge(c,l),c,l,ys,zs)
            helpb(c,l,cons(y,ys),zs) -> cons(y,helpa(s(c),l,ys,zs))
            helpc(false(),ys,zs) -> zs
            helpc(true(),ys,zs) -> ys
            if(false(),c,l,ys,zs) -> helpb(c,l,greater(ys,zs),smaller(ys,zs))
            if(true(),c,l,ys,zs) -> nil()
            length(cons(x,y)) -> s(length(y))
            length(nil()) -> 0()
            plus(x,0()) -> x
            plus(x,s(y)) -> s(plus(x,y))
            smaller(ys,zs) -> helpc(ge(length(ys),length(zs)),zs,ys)
        - Signature:
            {app/2,ge/2,greater/2,helpa/4,helpb/4,helpc/3,if/5,length/1,plus/2,smaller/2} / {0/0,cons/2,false/0,nil/0
            ,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {app,ge,greater,helpa,helpb,helpc,if,length,plus
            ,smaller} and constructors {0,cons,false,nil,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            app(x,y) -> helpa(0(),plus(length(x),length(y)),x,y)
            ge(x,0()) -> true()
            ge(0(),s(x)) -> false()
            ge(s(x),s(y)) -> ge(x,y)
            greater(ys,zs) -> helpc(ge(length(ys),length(zs)),ys,zs)
            helpa(c,l,ys,zs) -> if(ge(c,l),c,l,ys,zs)
            helpb(c,l,cons(y,ys),zs) -> cons(y,helpa(s(c),l,ys,zs))
            helpc(false(),ys,zs) -> zs
            helpc(true(),ys,zs) -> ys
            if(false(),c,l,ys,zs) -> helpb(c,l,greater(ys,zs),smaller(ys,zs))
            if(true(),c,l,ys,zs) -> nil()
            length(cons(x,y)) -> s(length(y))
            length(nil()) -> 0()
            plus(x,0()) -> x
            plus(x,s(y)) -> s(plus(x,y))
            smaller(ys,zs) -> helpc(ge(length(ys),length(zs)),zs,ys)
        - Signature:
            {app/2,ge/2,greater/2,helpa/4,helpb/4,helpc/3,if/5,length/1,plus/2,smaller/2} / {0/0,cons/2,false/0,nil/0
            ,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {app,ge,greater,helpa,helpb,helpc,if,length,plus
            ,smaller} and constructors {0,cons,false,nil,s,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          ge(x,y){x -> s(x),y -> s(y)} =
            ge(s(x),s(y)) ->^+ ge(x,y)
              = C[ge(x,y) = ge(x,y){}]

WORST_CASE(Omega(n^1),?)