MAYBE

Succeeded in reading "/export/starexec/sandbox/benchmark/theBenchmark.ari".
    (CONDITIONTYPE ORIENTED)
    (VAR x y ys xs zs x5 x4 x2 x3 x1)
    (RULES
      le(0,x) -> true
      le(s(x),0) -> false
      le(s(x),s(y)) -> le(x,y)
      app(nil,x) -> x
      app(cons(x,xs),ys) -> cons(x,app(xs,ys))
      split(x,nil) -> pair(nil,nil)
      qsort(nil) -> nil
      split(x,cons(y,ys)) -> pair(xs,cons(y,zs)) | split(x,ys) == pair(xs,zs), le(x,y) == true
      split(x,cons(y,ys)) -> pair(cons(y,xs),zs) | split(x,ys) == pair(xs,zs), le(x,y) == false
      qsort(cons(x,xs)) -> app(qsort(ys),cons(x,qsort(zs))) | split(x,xs) == pair(ys,zs)
    )

No "->="-rules.

Decomposed conditions and removed infeasible rules if possible.
    (CONDITIONTYPE ORIENTED)
    (VAR x y ys xs zs x5 x4 x2 x3 x1)
    (RULES
      le(0,x) -> true
      le(s(x),0) -> false
      le(s(x),s(y)) -> le(x,y)
      app(nil,x) -> x
      app(cons(x,xs),ys) -> cons(x,app(xs,ys))
      split(x,nil) -> pair(nil,nil)
      qsort(nil) -> nil
      split(x,cons(y,ys)) -> pair(xs,cons(y,zs)) | split(x,ys) == pair(xs,zs), le(x,y) == true
      split(x,cons(y,ys)) -> pair(cons(y,xs),zs) | split(x,ys) == pair(xs,zs), le(x,y) == false
      qsort(cons(x,xs)) -> app(qsort(ys),cons(x,qsort(zs))) | split(x,xs) == pair(ys,zs)
    )

(VAR x5 x4 x2 zs xs x3 x1)
(CONDITION 
split(x1,x3) == pair(xs,zs), le(x1,x2) == true, split(x1,x3) == pair(x4,x5), le(x1,x2) == false
)

Optimized the infeasibility problem if possible.

(VAR x5 x4 x2 zs xs x3 x1)
(CONDITION 
split(x1,x3) == pair(xs,zs), le(x1,x2) == true, split(x1,x3) == pair(x4,x5), le(x1,x2) == false
)

This is not ultra-RL and deterministic.


MAYBE