(GOAL COMPLEXITY) (STARTTERM CONSTRUCTOR-BASED) (STRATEGY INNERMOST) (STRATEGY INNERMOST) (VAR l x y) (DATATYPES A = µX.< #, 1(X), nil, cons(X, X) >) (SIGNATURES 0 :: [A] -> A + :: [A x A] -> A * :: [A x A] -> A sum :: [A] -> A prod :: [A] -> A) (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) -> #() *(0(x),y) -> 0(*(x,y)) *(1(x),y) -> +(0(*(x,y)),y) sum(nil()) -> 0(#()) sum(cons(x,l)) -> +(x,sum(l)) prod(nil()) -> 1(#()) prod(cons(x,l)) -> *(x,prod(l)))