/home/nowonder/forschung/aprove/TPDB05/TRS/AG01/#3.55.trs

The program

(from AG01 3.55)
(VAR x y m n)
(RULES
minus(x,0)  -> x
minus(s(x),s(y)) -> minus(x,y)
quot(0,s(y)) -> 0
quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
le(0,y) -> true
le(s(x),0) -> false
le(s(x),s(y)) -> le(x,y)
app(nil,y) -> y
app(add(n,x),y) -> add(n,app(x,y))
low(n,nil) -> nil
low(n,add(m,x)) -> if_low(le(m,n),n,add(m,x))
if_low(true,n,add(m,x)) -> add(m,low(n,x))
if_low(false,n,add(m,x)) -> low(n,x)
high(n,nil) -> nil
high(n,add(m,x)) -> if_high(le(m,n),n,add(m,x))
if_high(true,n,add(m,x)) -> high(n,x)
if_high(false,n,add(m,x)) -> add(m,high(n,x))
quicksort(nil) -> nil
quicksort(add(n,x)) -> app(quicksort(low(n,x)), add(n,quicksort(high(n,x))))
)

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