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


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YES

Problem:
 D(t()) -> s(h())
 D(constant()) -> h()
 D(b(x,y)) -> b(D(x),D(y))
 D(c(x,y)) -> b(c(y,D(x)),c(x,D(y)))
 D(m(x,y)) -> m(D(x),D(y))
 D(opp(x)) -> opp(D(x))
 D(div(x,y)) -> m(div(D(x),y),div(c(x,D(y)),pow(y,2())))
 D(ln(x)) -> div(D(x),x)
 D(pow(x,y)) -> b(c(c(y,pow(x,m(y,1()))),D(x)),c(c(pow(x,y),ln(x)),D(y)))
 b(h(),x) -> x
 b(x,h()) -> x
 b(s(x),s(y)) -> s(s(b(x,y)))
 b(b(x,y),z) -> b(x,b(y,z))

Proof:
 DP Processor:
  DPs:
   D#(b(x,y)) -> D#(y)
   D#(b(x,y)) -> D#(x)
   D#(b(x,y)) -> b#(D(x),D(y))
   D#(c(x,y)) -> D#(y)
   D#(c(x,y)) -> D#(x)
   D#(c(x,y)) -> b#(c(y,D(x)),c(x,D(y)))
   D#(m(x,y)) -> D#(y)
   D#(m(x,y)) -> D#(x)
   D#(opp(x)) -> D#(x)
   D#(div(x,y)) -> D#(y)
   D#(div(x,y)) -> D#(x)
   D#(ln(x)) -> D#(x)
   D#(pow(x,y)) -> D#(y)
   D#(pow(x,y)) -> D#(x)
   D#(pow(x,y)) -> b#(c(c(y,pow(x,m(y,1()))),D(x)),c(c(pow(x,y),ln(x)),D(y)))
   b#(s(x),s(y)) -> b#(x,y)
   b#(b(x,y),z) -> b#(y,z)
   b#(b(x,y),z) -> b#(x,b(y,z))
  TRS:
   D(t()) -> s(h())
   D(constant()) -> h()
   D(b(x,y)) -> b(D(x),D(y))
   D(c(x,y)) -> b(c(y,D(x)),c(x,D(y)))
   D(m(x,y)) -> m(D(x),D(y))
   D(opp(x)) -> opp(D(x))
   D(div(x,y)) -> m(div(D(x),y),div(c(x,D(y)),pow(y,2())))
   D(ln(x)) -> div(D(x),x)
   D(pow(x,y)) -> b(c(c(y,pow(x,m(y,1()))),D(x)),c(c(pow(x,y),ln(x)),D(y)))
   b(h(),x) -> x
   b(x,h()) -> x
   b(s(x),s(y)) -> s(s(b(x,y)))
   b(b(x,y),z) -> b(x,b(y,z))
  TDG Processor:
   DPs:
    D#(b(x,y)) -> D#(y)
    D#(b(x,y)) -> D#(x)
    D#(b(x,y)) -> b#(D(x),D(y))
    D#(c(x,y)) -> D#(y)
    D#(c(x,y)) -> D#(x)
    D#(c(x,y)) -> b#(c(y,D(x)),c(x,D(y)))
    D#(m(x,y)) -> D#(y)
    D#(m(x,y)) -> D#(x)
    D#(opp(x)) -> D#(x)
    D#(div(x,y)) -> D#(y)
    D#(div(x,y)) -> D#(x)
    D#(ln(x)) -> D#(x)
    D#(pow(x,y)) -> D#(y)
    D#(pow(x,y)) -> D#(x)
    D#(pow(x,y)) -> b#(c(c(y,pow(x,m(y,1()))),D(x)),c(c(pow(x,y),ln(x)),D(y)))
    b#(s(x),s(y)) -> b#(x,y)
    b#(b(x,y),z) -> b#(y,z)
    b#(b(x,y),z) -> b#(x,b(y,z))
   TRS:
    D(t()) -> s(h())
    D(constant()) -> h()
    D(b(x,y)) -> b(D(x),D(y))
    D(c(x,y)) -> b(c(y,D(x)),c(x,D(y)))
    D(m(x,y)) -> m(D(x),D(y))
    D(opp(x)) -> opp(D(x))
    D(div(x,y)) -> m(div(D(x),y),div(c(x,D(y)),pow(y,2())))
    D(ln(x)) -> div(D(x),x)
    D(pow(x,y)) -> b(c(c(y,pow(x,m(y,1()))),D(x)),c(c(pow(x,y),ln(x)),D(y)))
    b(h(),x) -> x
    b(x,h()) -> x
    b(s(x),s(y)) -> s(s(b(x,y)))
    b(b(x,y),z) -> b(x,b(y,z))
   graph:
    b#(b(x,y),z) -> b#(y,z) -> b#(b(x,y),z) -> b#(x,b(y,z))
    b#(b(x,y),z) -> b#(y,z) -> b#(b(x,y),z) -> b#(y,z)
    b#(b(x,y),z) -> b#(y,z) -> b#(s(x),s(y)) -> b#(x,y)
    b#(b(x,y),z) -> b#(x,b(y,z)) -> b#(b(x,y),z) -> b#(x,b(y,z))
    b#(b(x,y),z) -> b#(x,b(y,z)) -> b#(b(x,y),z) -> b#(y,z)
    b#(b(x,y),z) -> b#(x,b(y,z)) -> b#(s(x),s(y)) -> b#(x,y)
    b#(s(x),s(y)) -> b#(x,y) -> b#(b(x,y),z) -> b#(x,b(y,z))
    b#(s(x),s(y)) -> b#(x,y) -> b#(b(x,y),z) -> b#(y,z)
    b#(s(x),s(y)) -> b#(x,y) -> b#(s(x),s(y)) -> b#(x,y)
    D#(ln(x)) -> D#(x) ->
    D#(pow(x,y)) -> b#(c(c(y,pow(x,m(y,1()))),D(x)),c(c(pow(x,y),ln(x)),D(y)))
    D#(ln(x)) -> D#(x) -> D#(pow(x,y)) -> D#(x)
    D#(ln(x)) -> D#(x) -> D#(pow(x,y)) -> D#(y)
    D#(ln(x)) -> D#(x) -> D#(ln(x)) -> D#(x)
    D#(ln(x)) -> D#(x) -> D#(div(x,y)) -> D#(x)
    D#(ln(x)) -> D#(x) -> D#(div(x,y)) -> D#(y)
    D#(ln(x)) -> D#(x) -> D#(opp(x)) -> D#(x)
    D#(ln(x)) -> D#(x) -> D#(m(x,y)) -> D#(x)
    D#(ln(x)) -> D#(x) -> D#(m(x,y)) -> D#(y)
    D#(ln(x)) -> D#(x) -> D#(c(x,y)) -> b#(c(y,D(x)),c(x,D(y)))
    D#(ln(x)) -> D#(x) -> D#(c(x,y)) -> D#(x)
    D#(ln(x)) -> D#(x) -> D#(c(x,y)) -> D#(y)
    D#(ln(x)) -> D#(x) -> D#(b(x,y)) -> b#(D(x),D(y))
    D#(ln(x)) -> D#(x) -> D#(b(x,y)) -> D#(x)
    D#(ln(x)) -> D#(x) ->
    D#(b(x,y)) -> D#(y)
    D#(pow(x,y)) -> b#(c(c(y,pow(x,m(y,1()))),D(x)),c(c(pow(x,y),ln(x)),D(y))) ->
    b#(b(x,y),z) -> b#(x,b(y,z))
    D#(pow(x,y)) -> b#(c(c(y,pow(x,m(y,1()))),D(x)),c(c(pow(x,y),ln(x)),D(y))) ->
    b#(b(x,y),z) -> b#(y,z)
    D#(pow(x,y)) -> b#(c(c(y,pow(x,m(y,1()))),D(x)),c(c(pow(x,y),ln(x)),D(y))) ->
    b#(s(x),s(y)) -> b#(x,y)
    D#(pow(x,y)) -> D#(y) ->
    D#(pow(x,y)) -> b#(c(c(y,pow(x,m(y,1()))),D(x)),c(c(pow(x,y),ln(x)),D(y)))
    D#(pow(x,y)) -> D#(y) -> D#(pow(x,y)) -> D#(x)
    D#(pow(x,y)) -> D#(y) -> D#(pow(x,y)) -> D#(y)
    D#(pow(x,y)) -> D#(y) -> D#(ln(x)) -> D#(x)
    D#(pow(x,y)) -> D#(y) -> D#(div(x,y)) -> D#(x)
    D#(pow(x,y)) -> D#(y) -> D#(div(x,y)) -> D#(y)
    D#(pow(x,y)) -> D#(y) -> D#(opp(x)) -> D#(x)
    D#(pow(x,y)) -> D#(y) -> D#(m(x,y)) -> D#(x)
    D#(pow(x,y)) -> D#(y) -> D#(m(x,y)) -> D#(y)
    D#(pow(x,y)) -> D#(y) -> D#(c(x,y)) -> b#(c(y,D(x)),c(x,D(y)))
    D#(pow(x,y)) -> D#(y) -> D#(c(x,y)) -> D#(x)
    D#(pow(x,y)) -> D#(y) -> D#(c(x,y)) -> D#(y)
    D#(pow(x,y)) -> D#(y) -> D#(b(x,y)) -> b#(D(x),D(y))
    D#(pow(x,y)) -> D#(y) -> D#(b(x,y)) -> D#(x)
    D#(pow(x,y)) -> D#(y) -> D#(b(x,y)) -> D#(y)
    D#(pow(x,y)) -> D#(x) ->
    D#(pow(x,y)) -> b#(c(c(y,pow(x,m(y,1()))),D(x)),c(c(pow(x,y),ln(x)),D(y)))
    D#(pow(x,y)) -> D#(x) -> D#(pow(x,y)) -> D#(x)
    D#(pow(x,y)) -> D#(x) -> D#(pow(x,y)) -> D#(y)
    D#(pow(x,y)) -> D#(x) -> D#(ln(x)) -> D#(x)
    D#(pow(x,y)) -> D#(x) -> D#(div(x,y)) -> D#(x)
    D#(pow(x,y)) -> D#(x) -> D#(div(x,y)) -> D#(y)
    D#(pow(x,y)) -> D#(x) -> D#(opp(x)) -> D#(x)
    D#(pow(x,y)) -> D#(x) -> D#(m(x,y)) -> D#(x)
    D#(pow(x,y)) -> D#(x) -> D#(m(x,y)) -> D#(y)
    D#(pow(x,y)) -> D#(x) -> D#(c(x,y)) -> b#(c(y,D(x)),c(x,D(y)))
    D#(pow(x,y)) -> D#(x) -> D#(c(x,y)) -> D#(x)
    D#(pow(x,y)) -> D#(x) -> D#(c(x,y)) -> D#(y)
    D#(pow(x,y)) -> D#(x) -> D#(b(x,y)) -> b#(D(x),D(y))
    D#(pow(x,y)) -> D#(x) -> D#(b(x,y)) -> D#(x)
    D#(pow(x,y)) -> D#(x) -> D#(b(x,y)) -> D#(y)
    D#(div(x,y)) -> D#(y) ->
    D#(pow(x,y)) -> b#(c(c(y,pow(x,m(y,1()))),D(x)),c(c(pow(x,y),ln(x)),D(y)))
    D#(div(x,y)) -> D#(y) -> D#(pow(x,y)) -> D#(x)
    D#(div(x,y)) -> D#(y) -> D#(pow(x,y)) -> D#(y)
    D#(div(x,y)) -> D#(y) -> D#(ln(x)) -> D#(x)
    D#(div(x,y)) -> D#(y) -> D#(div(x,y)) -> D#(x)
    D#(div(x,y)) -> D#(y) -> D#(div(x,y)) -> D#(y)
    D#(div(x,y)) -> D#(y) -> D#(opp(x)) -> D#(x)
    D#(div(x,y)) -> D#(y) -> D#(m(x,y)) -> D#(x)
    D#(div(x,y)) -> D#(y) -> D#(m(x,y)) -> D#(y)
    D#(div(x,y)) -> D#(y) -> D#(c(x,y)) -> b#(c(y,D(x)),c(x,D(y)))
    D#(div(x,y)) -> D#(y) -> D#(c(x,y)) -> D#(x)
    D#(div(x,y)) -> D#(y) -> D#(c(x,y)) -> D#(y)
    D#(div(x,y)) -> D#(y) -> D#(b(x,y)) -> b#(D(x),D(y))
    D#(div(x,y)) -> D#(y) -> D#(b(x,y)) -> D#(x)
    D#(div(x,y)) -> D#(y) -> D#(b(x,y)) -> D#(y)
    D#(div(x,y)) -> D#(x) ->
    D#(pow(x,y)) -> b#(c(c(y,pow(x,m(y,1()))),D(x)),c(c(pow(x,y),ln(x)),D(y)))
    D#(div(x,y)) -> D#(x) -> D#(pow(x,y)) -> D#(x)
    D#(div(x,y)) -> D#(x) -> D#(pow(x,y)) -> D#(y)
    D#(div(x,y)) -> D#(x) -> D#(ln(x)) -> D#(x)
    D#(div(x,y)) -> D#(x) -> D#(div(x,y)) -> D#(x)
    D#(div(x,y)) -> D#(x) -> D#(div(x,y)) -> D#(y)
    D#(div(x,y)) -> D#(x) -> D#(opp(x)) -> D#(x)
    D#(div(x,y)) -> D#(x) -> D#(m(x,y)) -> D#(x)
    D#(div(x,y)) -> D#(x) -> D#(m(x,y)) -> D#(y)
    D#(div(x,y)) -> D#(x) -> D#(c(x,y)) -> b#(c(y,D(x)),c(x,D(y)))
    D#(div(x,y)) -> D#(x) -> D#(c(x,y)) -> D#(x)
    D#(div(x,y)) -> D#(x) -> D#(c(x,y)) -> D#(y)
    D#(div(x,y)) -> D#(x) -> D#(b(x,y)) -> b#(D(x),D(y))
    D#(div(x,y)) -> D#(x) -> D#(b(x,y)) -> D#(x)
    D#(div(x,y)) -> D#(x) -> D#(b(x,y)) -> D#(y)
    D#(opp(x)) -> D#(x) ->
    D#(pow(x,y)) -> b#(c(c(y,pow(x,m(y,1()))),D(x)),c(c(pow(x,y),ln(x)),D(y)))
    D#(opp(x)) -> D#(x) -> D#(pow(x,y)) -> D#(x)
    D#(opp(x)) -> D#(x) -> D#(pow(x,y)) -> D#(y)
    D#(opp(x)) -> D#(x) -> D#(ln(x)) -> D#(x)
    D#(opp(x)) -> D#(x) -> D#(div(x,y)) -> D#(x)
    D#(opp(x)) -> D#(x) -> D#(div(x,y)) -> D#(y)
    D#(opp(x)) -> D#(x) -> D#(opp(x)) -> D#(x)
    D#(opp(x)) -> D#(x) -> D#(m(x,y)) -> D#(x)
    D#(opp(x)) -> D#(x) -> D#(m(x,y)) -> D#(y)
    D#(opp(x)) -> D#(x) -> D#(c(x,y)) -> b#(c(y,D(x)),c(x,D(y)))
    D#(opp(x)) -> D#(x) -> D#(c(x,y)) -> D#(x)
    D#(opp(x)) -> D#(x) -> D#(c(x,y)) -> D#(y)
    D#(opp(x)) -> D#(x) -> D#(b(x,y)) -> b#(D(x),D(y))
    D#(opp(x)) -> D#(x) -> D#(b(x,y)) -> D#(x)
    D#(opp(x)) -> D#(x) -> D#(b(x,y)) -> D#(y)
    D#(m(x,y)) -> D#(y) ->
    D#(pow(x,y)) -> b#(c(c(y,pow(x,m(y,1()))),D(x)),c(c(pow(x,y),ln(x)),D(y)))
    D#(m(x,y)) -> D#(y) -> D#(pow(x,y)) -> D#(x)
    D#(m(x,y)) -> D#(y) -> D#(pow(x,y)) -> D#(y)
    D#(m(x,y)) -> D#(y) -> D#(ln(x)) -> D#(x)
    D#(m(x,y)) -> D#(y) -> D#(div(x,y)) -> D#(x)
    D#(m(x,y)) -> D#(y) -> D#(div(x,y)) -> D#(y)
    D#(m(x,y)) -> D#(y) -> D#(opp(x)) -> D#(x)
    D#(m(x,y)) -> D#(y) -> D#(m(x,y)) -> D#(x)
    D#(m(x,y)) -> D#(y) -> D#(m(x,y)) -> D#(y)
    D#(m(x,y)) -> D#(y) -> D#(c(x,y)) -> b#(c(y,D(x)),c(x,D(y)))
    D#(m(x,y)) -> D#(y) -> D#(c(x,y)) -> D#(x)
    D#(m(x,y)) -> D#(y) -> D#(c(x,y)) -> D#(y)
    D#(m(x,y)) -> D#(y) -> D#(b(x,y)) -> b#(D(x),D(y))
    D#(m(x,y)) -> D#(y) -> D#(b(x,y)) -> D#(x)
    D#(m(x,y)) -> D#(y) -> D#(b(x,y)) -> D#(y)
    D#(m(x,y)) -> D#(x) ->
    D#(pow(x,y)) -> b#(c(c(y,pow(x,m(y,1()))),D(x)),c(c(pow(x,y),ln(x)),D(y)))
    D#(m(x,y)) -> D#(x) -> D#(pow(x,y)) -> D#(x)
    D#(m(x,y)) -> D#(x) -> D#(pow(x,y)) -> D#(y)
    D#(m(x,y)) -> D#(x) -> D#(ln(x)) -> D#(x)
    D#(m(x,y)) -> D#(x) -> D#(div(x,y)) -> D#(x)
    D#(m(x,y)) -> D#(x) -> D#(div(x,y)) -> D#(y)
    D#(m(x,y)) -> D#(x) -> D#(opp(x)) -> D#(x)
    D#(m(x,y)) -> D#(x) -> D#(m(x,y)) -> D#(x)
    D#(m(x,y)) -> D#(x) -> D#(m(x,y)) -> D#(y)
    D#(m(x,y)) -> D#(x) -> D#(c(x,y)) -> b#(c(y,D(x)),c(x,D(y)))
    D#(m(x,y)) -> D#(x) -> D#(c(x,y)) -> D#(x)
    D#(m(x,y)) -> D#(x) -> D#(c(x,y)) -> D#(y)
    D#(m(x,y)) -> D#(x) -> D#(b(x,y)) -> b#(D(x),D(y))
    D#(m(x,y)) -> D#(x) -> D#(b(x,y)) -> D#(x)
    D#(m(x,y)) -> D#(x) -> D#(b(x,y)) -> D#(y)
    D#(c(x,y)) -> b#(c(y,D(x)),c(x,D(y))) ->
    b#(b(x,y),z) -> b#(x,b(y,z))
    D#(c(x,y)) -> b#(c(y,D(x)),c(x,D(y))) ->
    b#(b(x,y),z) -> b#(y,z)
    D#(c(x,y)) -> b#(c(y,D(x)),c(x,D(y))) -> b#(s(x),s(y)) -> b#(x,y)
    D#(c(x,y)) -> D#(y) ->
    D#(pow(x,y)) -> b#(c(c(y,pow(x,m(y,1()))),D(x)),c(c(pow(x,y),ln(x)),D(y)))
    D#(c(x,y)) -> D#(y) -> D#(pow(x,y)) -> D#(x)
    D#(c(x,y)) -> D#(y) -> D#(pow(x,y)) -> D#(y)
    D#(c(x,y)) -> D#(y) -> D#(ln(x)) -> D#(x)
    D#(c(x,y)) -> D#(y) -> D#(div(x,y)) -> D#(x)
    D#(c(x,y)) -> D#(y) -> D#(div(x,y)) -> D#(y)
    D#(c(x,y)) -> D#(y) -> D#(opp(x)) -> D#(x)
    D#(c(x,y)) -> D#(y) -> D#(m(x,y)) -> D#(x)
    D#(c(x,y)) -> D#(y) -> D#(m(x,y)) -> D#(y)
    D#(c(x,y)) -> D#(y) -> D#(c(x,y)) -> b#(c(y,D(x)),c(x,D(y)))
    D#(c(x,y)) -> D#(y) -> D#(c(x,y)) -> D#(x)
    D#(c(x,y)) -> D#(y) -> D#(c(x,y)) -> D#(y)
    D#(c(x,y)) -> D#(y) -> D#(b(x,y)) -> b#(D(x),D(y))
    D#(c(x,y)) -> D#(y) -> D#(b(x,y)) -> D#(x)
    D#(c(x,y)) -> D#(y) -> D#(b(x,y)) -> D#(y)
    D#(c(x,y)) -> D#(x) ->
    D#(pow(x,y)) -> b#(c(c(y,pow(x,m(y,1()))),D(x)),c(c(pow(x,y),ln(x)),D(y)))
    D#(c(x,y)) -> D#(x) -> D#(pow(x,y)) -> D#(x)
    D#(c(x,y)) -> D#(x) -> D#(pow(x,y)) -> D#(y)
    D#(c(x,y)) -> D#(x) -> D#(ln(x)) -> D#(x)
    D#(c(x,y)) -> D#(x) -> D#(div(x,y)) -> D#(x)
    D#(c(x,y)) -> D#(x) -> D#(div(x,y)) -> D#(y)
    D#(c(x,y)) -> D#(x) -> D#(opp(x)) -> D#(x)
    D#(c(x,y)) -> D#(x) -> D#(m(x,y)) -> D#(x)
    D#(c(x,y)) -> D#(x) -> D#(m(x,y)) -> D#(y)
    D#(c(x,y)) -> D#(x) -> D#(c(x,y)) -> b#(c(y,D(x)),c(x,D(y)))
    D#(c(x,y)) -> D#(x) -> D#(c(x,y)) -> D#(x)
    D#(c(x,y)) -> D#(x) -> D#(c(x,y)) -> D#(y)
    D#(c(x,y)) -> D#(x) -> D#(b(x,y)) -> b#(D(x),D(y))
    D#(c(x,y)) -> D#(x) -> D#(b(x,y)) -> D#(x)
    D#(c(x,y)) -> D#(x) -> D#(b(x,y)) -> D#(y)
    D#(b(x,y)) -> b#(D(x),D(y)) -> b#(b(x,y),z) -> b#(x,b(y,z))
    D#(b(x,y)) -> b#(D(x),D(y)) -> b#(b(x,y),z) -> b#(y,z)
    D#(b(x,y)) -> b#(D(x),D(y)) -> b#(s(x),s(y)) -> b#(x,y)
    D#(b(x,y)) -> D#(y) ->
    D#(pow(x,y)) -> b#(c(c(y,pow(x,m(y,1()))),D(x)),c(c(pow(x,y),ln(x)),D(y)))
    D#(b(x,y)) -> D#(y) -> D#(pow(x,y)) -> D#(x)
    D#(b(x,y)) -> D#(y) -> D#(pow(x,y)) -> D#(y)
    D#(b(x,y)) -> D#(y) -> D#(ln(x)) -> D#(x)
    D#(b(x,y)) -> D#(y) -> D#(div(x,y)) -> D#(x)
    D#(b(x,y)) -> D#(y) -> D#(div(x,y)) -> D#(y)
    D#(b(x,y)) -> D#(y) -> D#(opp(x)) -> D#(x)
    D#(b(x,y)) -> D#(y) -> D#(m(x,y)) -> D#(x)
    D#(b(x,y)) -> D#(y) -> D#(m(x,y)) -> D#(y)
    D#(b(x,y)) -> D#(y) -> D#(c(x,y)) -> b#(c(y,D(x)),c(x,D(y)))
    D#(b(x,y)) -> D#(y) -> D#(c(x,y)) -> D#(x)
    D#(b(x,y)) -> D#(y) -> D#(c(x,y)) -> D#(y)
    D#(b(x,y)) -> D#(y) -> D#(b(x,y)) -> b#(D(x),D(y))
    D#(b(x,y)) -> D#(y) -> D#(b(x,y)) -> D#(x)
    D#(b(x,y)) -> D#(y) -> D#(b(x,y)) -> D#(y)
    D#(b(x,y)) -> D#(x) ->
    D#(pow(x,y)) -> b#(c(c(y,pow(x,m(y,1()))),D(x)),c(c(pow(x,y),ln(x)),D(y)))
    D#(b(x,y)) -> D#(x) -> D#(pow(x,y)) -> D#(x)
    D#(b(x,y)) -> D#(x) -> D#(pow(x,y)) -> D#(y)
    D#(b(x,y)) -> D#(x) -> D#(ln(x)) -> D#(x)
    D#(b(x,y)) -> D#(x) -> D#(div(x,y)) -> D#(x)
    D#(b(x,y)) -> D#(x) -> D#(div(x,y)) -> D#(y)
    D#(b(x,y)) -> D#(x) -> D#(opp(x)) -> D#(x)
    D#(b(x,y)) -> D#(x) -> D#(m(x,y)) -> D#(x)
    D#(b(x,y)) -> D#(x) -> D#(m(x,y)) -> D#(y)
    D#(b(x,y)) -> D#(x) -> D#(c(x,y)) -> b#(c(y,D(x)),c(x,D(y)))
    D#(b(x,y)) -> D#(x) -> D#(c(x,y)) -> D#(x)
    D#(b(x,y)) -> D#(x) -> D#(c(x,y)) -> D#(y)
    D#(b(x,y)) -> D#(x) -> D#(b(x,y)) -> b#(D(x),D(y))
    D#(b(x,y)) -> D#(x) -> D#(b(x,y)) -> D#(x)
    D#(b(x,y)) -> D#(x) -> D#(b(x,y)) -> D#(y)
   SCC Processor:
    #sccs: 2
    #rules: 15
    #arcs: 198/324
    DPs:
     D#(ln(x)) -> D#(x)
     D#(b(x,y)) -> D#(y)
     D#(b(x,y)) -> D#(x)
     D#(c(x,y)) -> D#(y)
     D#(c(x,y)) -> D#(x)
     D#(m(x,y)) -> D#(y)
     D#(m(x,y)) -> D#(x)
     D#(opp(x)) -> D#(x)
     D#(div(x,y)) -> D#(y)
     D#(div(x,y)) -> D#(x)
     D#(pow(x,y)) -> D#(y)
     D#(pow(x,y)) -> D#(x)
    TRS:
     D(t()) -> s(h())
     D(constant()) -> h()
     D(b(x,y)) -> b(D(x),D(y))
     D(c(x,y)) -> b(c(y,D(x)),c(x,D(y)))
     D(m(x,y)) -> m(D(x),D(y))
     D(opp(x)) -> opp(D(x))
     D(div(x,y)) -> m(div(D(x),y),div(c(x,D(y)),pow(y,2())))
     D(ln(x)) -> div(D(x),x)
     D(pow(x,y)) -> b(c(c(y,pow(x,m(y,1()))),D(x)),c(c(pow(x,y),ln(x)),D(y)))
     b(h(),x) -> x
     b(x,h()) -> x
     b(s(x),s(y)) -> s(s(b(x,y)))
     b(b(x,y),z) -> b(x,b(y,z))
    Subterm Criterion Processor:
     simple projection:
      pi(D#) = 0
     problem:
      DPs:
       
      TRS:
       D(t()) -> s(h())
       D(constant()) -> h()
       D(b(x,y)) -> b(D(x),D(y))
       D(c(x,y)) -> b(c(y,D(x)),c(x,D(y)))
       D(m(x,y)) -> m(D(x),D(y))
       D(opp(x)) -> opp(D(x))
       D(div(x,y)) -> m(div(D(x),y),div(c(x,D(y)),pow(y,2())))
       D(ln(x)) -> div(D(x),x)
       D(pow(x,y)) -> b(c(c(y,pow(x,m(y,1()))),D(x)),c(c(pow(x,y),ln(x)),D(y)))
       b(h(),x) -> x
       b(x,h()) -> x
       b(s(x),s(y)) -> s(s(b(x,y)))
       b(b(x,y),z) -> b(x,b(y,z))
     Qed
    
    DPs:
     b#(b(x,y),z) -> b#(y,z)
     b#(s(x),s(y)) -> b#(x,y)
     b#(b(x,y),z) -> b#(x,b(y,z))
    TRS:
     D(t()) -> s(h())
     D(constant()) -> h()
     D(b(x,y)) -> b(D(x),D(y))
     D(c(x,y)) -> b(c(y,D(x)),c(x,D(y)))
     D(m(x,y)) -> m(D(x),D(y))
     D(opp(x)) -> opp(D(x))
     D(div(x,y)) -> m(div(D(x),y),div(c(x,D(y)),pow(y,2())))
     D(ln(x)) -> div(D(x),x)
     D(pow(x,y)) -> b(c(c(y,pow(x,m(y,1()))),D(x)),c(c(pow(x,y),ln(x)),D(y)))
     b(h(),x) -> x
     b(x,h()) -> x
     b(s(x),s(y)) -> s(s(b(x,y)))
     b(b(x,y),z) -> b(x,b(y,z))
    Subterm Criterion Processor:
     simple projection:
      pi(b#) = 0
     problem:
      DPs:
       
      TRS:
       D(t()) -> s(h())
       D(constant()) -> h()
       D(b(x,y)) -> b(D(x),D(y))
       D(c(x,y)) -> b(c(y,D(x)),c(x,D(y)))
       D(m(x,y)) -> m(D(x),D(y))
       D(opp(x)) -> opp(D(x))
       D(div(x,y)) -> m(div(D(x),y),div(c(x,D(y)),pow(y,2())))
       D(ln(x)) -> div(D(x),x)
       D(pow(x,y)) -> b(c(c(y,pow(x,m(y,1()))),D(x)),c(c(pow(x,y),ln(x)),D(y)))
       b(h(),x) -> x
       b(x,h()) -> x
       b(s(x),s(y)) -> s(s(b(x,y)))
       b(b(x,y),z) -> b(x,b(y,z))
     Qed