(COMMENT 

  Claude Marché

  Sum and product of a list of integers

  Binary notation, + and * associative, * distributes over +, append

)
(VAR l2  l1  l  z  y  x)
(RULES

0(#) -> # 
+(x,#) -> x 
+(#,x) -> x 
+(0(x),0(y)) -> 0(+(x,y)) 
+(0(x),1(y)) -> 1(+(x,y)) 
+(1(x),0(y)) -> 1(+(x,y)) 
+(1(x),1(y)) -> 0(+(+(x,y),1(#))) 
+(+(x,y),z) -> +(x,+(y,z)) 
*(#,x) -> # 
*(0(x),y) -> 0(*(x,y)) 
*(1(x),y) -> +(0(*(x,y)),y) 
*(*(x,y),z) -> *(x,*(y,z)) 
*(x,+(y,z)) -> +(*(x,y),*(x,z)) 
app(nil,l) -> l 
app(cons(x,l1),l2) -> cons(x,app(l1,l2)) 
sum(nil) -> 0(#) 
sum(cons(x,l)) -> +(x,sum(l)) 
sum(app(l1,l2)) -> +(sum(l1),sum(l2)) 
prod(nil) -> 1(#) 
prod(cons(x,l)) -> *(x,prod(l)) 
prod(app(l1,l2)) -> *(prod(l1),prod(l2)) 

)