ceta_eq: termination proof not accepted
1: error below switch to dependency pairs
1.1: error below the dependency graph processor
 1.1.4: error when applying the reduction pair processor with usable rules to remove from the DP problem
  pairs:
  
  +#(s(x), s(y)) -> +#(x, y)
  +#(+(x, y), z) -> +#(x, +(y, z))
  +#(+(x, y), z) -> +#(y, z)
  rules:
  
  *(x, 0) -> 0
  *(0, x) -> 0
  *(s(x), s(y)) -> s(+(*(x, y), +(x, y)))
  *(*(x, y), z) -> *(x, *(y, z))
  +(x, 0) -> x
  +(0, x) -> x
  +(s(x), s(y)) -> s(s(+(x, y)))
  +(+(x, y), z) -> +(x, +(y, z))
  app(nil, l) -> l
  app(cons(x, l1), l2) -> cons(x, app(l1, l2))
  prod(nil) -> s(0)
  prod(cons(x, l)) -> *(x, prod(l))
  prod(app(l1, l2)) -> *(prod(l1), prod(l2))
  sum(nil) -> 0
  sum(cons(x, l)) -> +(x, sum(l))
  sum(app(l1, l2)) -> +(sum(l1), sum(l2))
  
   the pairs 
  +#(+(x, y), z) -> +#(x, +(y, z))
  +#(+(x, y), z) -> +#(y, z)
  
  could not apply the generic root reduction pair processor with the following
  SCNP-version with mu = MS and the level mapping defined by 
  pi(+#) = [(epsilon,0),(1,0)]
  Argument Filter: 
  pi(+#/2) = []
  pi(+/2) = [1,2]
  pi(s/1) = 1
  pi(0/0) = []
  
  RPO with the following precedence
  precedence(+#[2]) = 0
  precedence(0[0]) = 1
  precedence(+[2]) = 2
  
  precedence(_) = 0
  and the following status
  status(+#[2]) = lex
  status(0[0]) = lex
  status(+[2]) = lex
  
  status(_) = lex
  
  problem when orienting DPs
  cannot orient pair +#(s(x), s(y)) -> +#(x, y) weakly:
  [(+#(s(x), s(y)),0),(s(x),0)] >=mu [(+#(x, y),0),(x,0)] could not be ensured