(STRATEGY
    INNERMOST)

(VAR
    x y z)
(DATATYPES
    A = µX.< #, 1(X), j(X) >)
(SIGNATURES
    0 :: [A] -> A
    + :: [A x A] -> A
    opp :: [A] -> A
    - :: [A x A] -> A
    * :: [A x 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))
    +(0(x),j(y)) -> j(+(x,y))
    +(j(x),0(y)) -> j(+(x,y))
    +(1(x),1(y)) -> j(+(+(x,y)
                       ,1(#())))
    +(j(x),j(y)) -> 1(+(+(x,y)
                       ,j(#())))
    +(1(x),j(y)) -> 0(+(x,y))
    +(j(x),1(y)) -> 0(+(x,y))
    +(+(x,y),z) -> +(x,+(y,z))
    opp(#()) -> #()
    opp(0(x)) -> 0(opp(x))
    opp(1(x)) -> j(opp(x))
    opp(j(x)) -> 1(opp(x))
    -(x,y) -> +(x,opp(y))
    *(#(),x) -> #()
    *(0(x),y) -> 0(*(x,y))
    *(1(x),y) -> +(0(*(x,y)),y)
    *(j(x),y) -> -(0(*(x,y)),y)
    *(*(x,y),z) -> *(x,*(y,z))
    *(+(x,y),z) -> +(*(x,z),*(y,z))
    *(x,+(y,z)) -> +(*(x,y),*(x,z)))