/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

Problem:
 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))))

Proof:
 DP Processor:
  DPs:
   dx#(plus(ALPHA,BETA)) -> dx#(BETA)
   dx#(plus(ALPHA,BETA)) -> dx#(ALPHA)
   dx#(times(ALPHA,BETA)) -> dx#(BETA)
   dx#(times(ALPHA,BETA)) -> dx#(ALPHA)
   dx#(minus(ALPHA,BETA)) -> dx#(BETA)
   dx#(minus(ALPHA,BETA)) -> dx#(ALPHA)
   dx#(neg(ALPHA)) -> dx#(ALPHA)
   dx#(div(ALPHA,BETA)) -> dx#(BETA)
   dx#(div(ALPHA,BETA)) -> dx#(ALPHA)
   dx#(ln(ALPHA)) -> dx#(ALPHA)
   dx#(exp(ALPHA,BETA)) -> dx#(BETA)
   dx#(exp(ALPHA,BETA)) -> dx#(ALPHA)
  TRS:
   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))))
  Subterm Criterion Processor:
   simple projection:
    pi(dx#) = 0
   problem:
    DPs:
     
    TRS:
     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))))
   Qed