(from AG01 3.39) (VAR x y z) (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))) 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) )