(GOAL COMPLEXITY) (STARTTERM CONSTRUCTOR-BASED) (STRATEGY INNERMOST) (STRATEGY INNERMOST) (VAR l l1 l2 x y z) (DATATYPES A = µX.< 0, s(X), nil, cons(X, X) >) (SIGNATURES + :: [A x A] -> A * :: [A x A] -> A app :: [A x A] -> A sum :: [A] -> A prod :: [A] -> A) (RULES +(x,0()) -> x +(0(),x) -> x +(s(x),s(y)) -> s(s(+(x,y))) +(+(x,y),z) -> +(x,+(y,z)) *(x,0()) -> 0() *(0(),x) -> 0() *(s(x),s(y)) -> s(+(*(x,y) ,+(x,y))) *(*(x,y),z) -> *(x,*(y,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()) -> s(0()) prod(cons(x,l)) -> *(x,prod(l)) prod(app(l1,l2)) -> *(prod(l1) ,prod(l2)))