(VAR k l x y )
(STRATEGY INNERMOST)
(RULES 
        app(nil,k) -> k
        app(l,nil) -> l
        app(cons(x,l),k) -> cons(x,app(l,k))
        sum(cons(x,nil)) -> cons(x,nil)
        sum(cons(x,cons(y,l))) -> sum(cons(plus(x,y),l))
        sum(app(l,cons(x,cons(y,k)))) -> sum(app(l,sum(cons(x,cons(y,k)))))
        sum(plus(cons(0,x),cons(y,l))) -> pred(sum(cons(s(x),cons(y,l))))
        pred(cons(s(x),nil)) -> cons(x,nil)
        plus(s(x),s(y)) -> s(s(plus(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y)))))
        plus(s(x),x) -> plus(if(gt(x,x),id(x),id(x)),s(x))
        plus(zero,y) -> y
        plus(id(x),s(y)) -> s(plus(x,if(gt(s(y),y),y,s(y))))
        id(x) -> x
        if(true,x,y) -> x
        if(false,x,y) -> y
        not(x) -> if(x,false,true)
        gt(s(x),zero) -> true
        gt(zero,y) -> false
        gt(s(x),s(y)) -> gt(x,y)
        
)