MAYBE

Problem:
 table() -> gen(s(0()))
 gen(x) -> if1(le(x,10()),x)
 if1(false(),x) -> nil()
 if1(true(),x) -> if2(x,x)
 if2(x,y) -> if3(le(y,10()),x,y)
 if3(true(),x,y) -> cons(entry(x,y,times(x,y)),if2(x,s(y)))
 if3(false(),x,y) -> gen(s(x))
 le(0(),y) -> true()
 le(s(x),0()) -> false()
 le(s(x),s(y)) -> le(x,y)
 plus(0(),y) -> y
 plus(s(x),y) -> s(plus(x,y))
 times(0(),y) -> 0()
 times(s(x),y) -> plus(y,times(x,y))
 10() -> s(s(s(s(s(s(s(s(s(s(0()))))))))))

Proof:
 DP Processor:
  DPs:
   table#() -> gen#(s(0()))
   gen#(x) -> 10#()
   gen#(x) -> le#(x,10())
   gen#(x) -> if1#(le(x,10()),x)
   if1#(true(),x) -> if2#(x,x)
   if2#(x,y) -> 10#()
   if2#(x,y) -> le#(y,10())
   if2#(x,y) -> if3#(le(y,10()),x,y)
   if3#(true(),x,y) -> if2#(x,s(y))
   if3#(true(),x,y) -> times#(x,y)
   if3#(false(),x,y) -> gen#(s(x))
   le#(s(x),s(y)) -> le#(x,y)
   plus#(s(x),y) -> plus#(x,y)
   times#(s(x),y) -> times#(x,y)
   times#(s(x),y) -> plus#(y,times(x,y))
  TRS:
   table() -> gen(s(0()))
   gen(x) -> if1(le(x,10()),x)
   if1(false(),x) -> nil()
   if1(true(),x) -> if2(x,x)
   if2(x,y) -> if3(le(y,10()),x,y)
   if3(true(),x,y) -> cons(entry(x,y,times(x,y)),if2(x,s(y)))
   if3(false(),x,y) -> gen(s(x))
   le(0(),y) -> true()
   le(s(x),0()) -> false()
   le(s(x),s(y)) -> le(x,y)
   plus(0(),y) -> y
   plus(s(x),y) -> s(plus(x,y))
   times(0(),y) -> 0()
   times(s(x),y) -> plus(y,times(x,y))
   10() -> s(s(s(s(s(s(s(s(s(s(0()))))))))))
  Open