/export/starexec/sandbox/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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MAYBE

Problem:
 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))
 head(add(n,x)) -> n
 tail(add(n,x)) -> x
 isempty(nil()) -> true()
 isempty(add(n,x)) -> false()
 quicksort(x) -> if_qs(isempty(x),low(head(x),tail(x)),head(x),high(head(x),tail(x)))
 if_qs(true(),x,n,y) -> nil()
 if_qs(false(),x,n,y) -> app(quicksort(x),add(n,quicksort(y)))

Proof:
 Open