/home/nowonder/forschung/aprove/TPDB05/TRS/Rubio/polo2.trs

The program

(VAR X ALPHA BETA)
(RULES

dx(X) -> one
dx(a) -> zero
dx(plus(ALPHA, BETA)) -> plus(dx(ALPHA), dx(BETA))
dx(times(ALPHA, BETA)) -> plus(times(BETA, dx(ALPHA)), times(ALPHA, dx(BETA)))
dx(minus(ALPHA, BETA)) -> minus(dx(ALPHA), dx(BETA))
dx(neg(ALPHA)) -> neg(dx(ALPHA))
dx(div(ALPHA, BETA)) -> 
     minus(div(dx(ALPHA), BETA), times(ALPHA, div(dx(BETA), exp(BETA,two))))
dx(ln(ALPHA)) -> div(dx(ALPHA), ALPHA)
dx(exp(ALPHA, BETA)) -> 
    plus(times(BETA, times(exp(ALPHA, minus(BETA, one)), dx(ALPHA))), 
           times(exp(ALPHA, BETA), times(ln(ALPHA), dx(BETA))))

)

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