ceta_equiv: termination proof not accepted
1: error below switch to dependency pairs
1.1: error below the dependency graph processor
 1.1.1: error when applying the reduction pair processor with usable rules to remove from the DP problem
  pairs:
  
  inter#(app(l1, l2), l3) -> inter#(l1, l3)
  inter#(app(l1, l2), l3) -> inter#(l2, l3)
  inter#(l1, app(l2, l3)) -> inter#(l1, l2)
  inter#(l1, app(l2, l3)) -> inter#(l1, l3)
  inter#(cons(x, l1), l2) -> ifinter#(mem(x, l2), x, l1, l2)
  inter#(l1, cons(x, l2)) -> ifinter#(mem(x, l1), x, l2, l1)
  ifinter#(true, x, l1, l2) -> inter#(l1, l2)
  ifinter#(false, x, l1, l2) -> inter#(l1, l2)
  rules:
  
  app(nil, l) -> l
  app(cons(x, l1), l2) -> cons(x, app(l1, l2))
  app(app(l1, l2), l3) -> app(l1, app(l2, l3))
  eq(0, 0) -> true
  eq(0, s(x)) -> false
  eq(s(x), 0) -> false
  eq(s(x), s(y)) -> eq(x, y)
  if(true, x, y) -> x
  if(false, x, y) -> y
  ifinter(true, x, l1, l2) -> cons(x, inter(l1, l2))
  ifinter(false, x, l1, l2) -> inter(l1, l2)
  ifmem(true, x, l) -> true
  ifmem(false, x, l) -> mem(x, l)
  inter(x, nil) -> nil
  inter(nil, x) -> nil
  inter(app(l1, l2), l3) -> app(inter(l1, l3), inter(l2, l3))
  inter(l1, app(l2, l3)) -> app(inter(l1, l2), inter(l1, l3))
  inter(cons(x, l1), l2) -> ifinter(mem(x, l2), x, l1, l2)
  inter(l1, cons(x, l2)) -> ifinter(mem(x, l1), x, l2, l1)
  mem(x, nil) -> false
  mem(x, cons(y, l)) -> ifmem(eq(x, y), x, l)
  
   the pairs 
  inter#(cons(x, l1), l2) -> ifinter#(mem(x, l2), x, l1, l2)
  inter#(l1, cons(x, l2)) -> ifinter#(mem(x, l1), x, l2, l1)
  ifinter#(true, x, l1, l2) -> inter#(l1, l2)
  ifinter#(false, x, l1, l2) -> inter#(l1, l2)
  
  could not apply the generic root reduction pair processor with the following
  SCNP-version with mu = MS and the level mapping defined by 
  pi(inter#) = [(1,0),(2,0)]
  pi(ifinter#) = [(epsilon,0),(1,2),(3,7)]
  polynomial interpretration over naturals with negative constants
  Pol(inter#(x_1, x_2)) = 0
  Pol(app(x_1, x_2)) = x_2 + x_1
  Pol(cons(x_1, x_2)) = 1 + x_2
  Pol(ifinter#(x_1, x_2, x_3, x_4)) = x_4
  Pol(mem(x_1, x_2)) = 0
  Pol(true) = 0
  Pol(false) = 0
  Pol(nil) = 0
  Pol(ifmem(x_1, x_2, x_3)) = 0
  Pol(eq(x_1, x_2)) = x_2
  Pol(0) = 1
  Pol(s(x_1)) = 0
  problem when orienting DPs
  cannot orient pair inter#(app(l1, l2), l3) -> inter#(l1, l3) weakly:
  [(app(l1, l2),0),(l3,0)] >=mu [(l1,0),(l3,0)] could not be ensured