(GOAL COMPLEXITY) (STARTTERM CONSTRUCTORBASED) (VAR l l1 l2 l3 x y z ) (STRATEGY INNERMOST) (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) -> # -(x, #) -> x -(0(x), 0(y)) -> 0(-(x, y)) -(0(x), 1(y)) -> 1(-(-(x, y), 1(#))) -(1(x), 0(y)) -> 1(-(x, y)) -(1(x), 1(y)) -> 0(-(x, y)) not(true) -> false not(false) -> true if(true, x, y) -> x if(false, x, y) -> y eq(#, #) -> true eq(#, 1(y)) -> false eq(1(x), #) -> false eq(#, 0(y)) -> eq(#, y) eq(0(x), #) -> eq(x, #) eq(1(x), 1(y)) -> eq(x, y) eq(0(x), 1(y)) -> false eq(1(x), 0(y)) -> false eq(0(x), 0(y)) -> eq(x, y) ge(0(x), 0(y)) -> ge(x, y) ge(0(x), 1(y)) -> not(ge(y, x)) ge(1(x), 0(y)) -> ge(x, y) ge(1(x), 1(y)) -> ge(x, y) ge(x, #) -> true ge(#, 0(x)) -> ge(#, x) ge(#, 1(x)) -> false log(x) -> -(log'(x), 1(#)) log'(#) -> # log'(1(x)) -> +(log'(x), 1(#)) log'(0(x)) -> if(ge(x, 1(#)), +(log'(x), 1(#)), #) *(#, 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)) mem(x, nil) -> false mem(x, cons(y, l)) -> if(eq(x, y), true, mem(x, l)) inter(x, nil) -> nil inter(nil, x) -> nil inter(app(l1, l2), l3) -> app(inter(l1, l3), inter(l2, l3)) inter(l1, app(l2, l3)) -> app(inter(l1, l2), inter(l1, l3)) inter(cons(x, l1), l2) -> ifinter(mem(x, l2), x, l1, l2) inter(l1, cons(x, l2)) -> ifinter(mem(x, l1), x, l2, l1) ifinter(true, x, l1, l2) -> cons(x, inter(l1, l2)) ifinter(false, x, l1, l2) -> inter(l1, l2) )