ceta_eq: termination proof not accepted
1: error below switch to dependency pairs
1.1: error below the dependency graph processor
 1.1.2: error when applying the reduction pair processor with usable rules to remove from the DP problem
  pairs:
  
  mem#(x, cons(y, l)) -> ifmem#(eq(x, y), x, l)
  ifmem#(false, x, l) -> mem#(x, l)
  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 
  mem#(x, cons(y, l)) -> ifmem#(eq(x, y), x, l)
  ifmem#(false, x, l) -> mem#(x, l)
  
  could not apply the generic root reduction pair processor with the following
  SCNP-version with mu = MS and the level mapping defined by 
  pi(mem#) = [(epsilon,0),(1,0)]
  pi(ifmem#) = [(epsilon,0),(2,0),(3,1)]
  Argument Filter: 
  pi(mem#/2) = [2]
  pi(cons/2) = [2]
  pi(ifmem#/3) = [3]
  pi(eq/2) = [1,2]
  pi(false/0) = []
  pi(0/0) = []
  pi(true/0) = []
  pi(s/1) = []
  
  RPO with the following precedence
  precedence(mem#[2]) = 1
  precedence(cons[2]) = 0
  precedence(ifmem#[3]) = 1
  precedence(eq[2]) = 0
  precedence(false[0]) = 1
  precedence(0[0]) = 1
  precedence(true[0]) = 2
  precedence(s[1]) = 1
  
  precedence(_) = 0
  and the following status
  status(mem#[2]) = lex
  status(cons[2]) = lex
  status(ifmem#[3]) = lex
  status(eq[2]) = lex
  status(false[0]) = lex
  status(0[0]) = lex
  status(true[0]) = lex
  status(s[1]) = lex
  
  status(_) = lex
  
  problem when orienting DPs
  cannot orient pair ifmem#(false, x, l) -> mem#(x, l) strictly:
  [(ifmem#(false, x, l),0),(x,0),(l,1)] >mu [(mem#(x, l),0),(x,0)] could not be ensured