R

     ↳Dependency Pair Analysis

ACTIVE(sel(s(X), cons(Y, Z))) -> SEL(X, Z)
ACTIVE(first(s(X), cons(Y, Z))) -> CONS(Y, first(X, Z))
ACTIVE(first(s(X), cons(Y, Z))) -> FIRST(X, Z)
ACTIVE(from(X)) -> CONS(X, from(s(X)))
ACTIVE(from(X)) -> FROM(s(X))
ACTIVE(from(X)) -> S(X)
ACTIVE(sel1(s(X), cons(Y, Z))) -> SEL1(X, Z)
ACTIVE(sel1(0, cons(X, Z))) -> QUOTE(X)
ACTIVE(first1(s(X), cons(Y, Z))) -> CONS1(quote(Y), first1(X, Z))
ACTIVE(first1(s(X), cons(Y, Z))) -> QUOTE(Y)
ACTIVE(first1(s(X), cons(Y, Z))) -> FIRST1(X, Z)
ACTIVE(quote1(cons(X, Z))) -> CONS1(quote(X), quote1(Z))
ACTIVE(quote1(cons(X, Z))) -> QUOTE(X)
ACTIVE(quote1(cons(X, Z))) -> QUOTE1(Z)
ACTIVE(quote(s(X))) -> S1(quote(X))
ACTIVE(quote(s(X))) -> QUOTE(X)
ACTIVE(quote(sel(X, Z))) -> SEL1(X, Z)
ACTIVE(quote1(first(X, Z))) -> FIRST1(X, Z)
ACTIVE(unquote(s1(X))) -> S(unquote(X))
ACTIVE(unquote(s1(X))) -> UNQUOTE(X)
ACTIVE(unquote1(cons1(X, Z))) -> FCONS(unquote(X), unquote1(Z))
ACTIVE(unquote1(cons1(X, Z))) -> UNQUOTE(X)
ACTIVE(unquote1(cons1(X, Z))) -> UNQUOTE1(Z)
ACTIVE(fcons(X, Z)) -> CONS(X, Z)
ACTIVE(sel(X1, X2)) -> SEL(active(X1), X2)
ACTIVE(sel(X1, X2)) -> ACTIVE(X1)
ACTIVE(sel(X1, X2)) -> SEL(X1, active(X2))
ACTIVE(sel(X1, X2)) -> ACTIVE(X2)
ACTIVE(s(X)) -> S(active(X))
ACTIVE(s(X)) -> ACTIVE(X)
ACTIVE(cons(X1, X2)) -> CONS(active(X1), X2)
ACTIVE(cons(X1, X2)) -> ACTIVE(X1)
ACTIVE(first(X1, X2)) -> FIRST(active(X1), X2)
ACTIVE(first(X1, X2)) -> ACTIVE(X1)
ACTIVE(first(X1, X2)) -> FIRST(X1, active(X2))
ACTIVE(first(X1, X2)) -> ACTIVE(X2)
ACTIVE(from(X)) -> FROM(active(X))
ACTIVE(from(X)) -> ACTIVE(X)
ACTIVE(sel1(X1, X2)) -> SEL1(active(X1), X2)
ACTIVE(sel1(X1, X2)) -> ACTIVE(X1)
ACTIVE(sel1(X1, X2)) -> SEL1(X1, active(X2))
ACTIVE(sel1(X1, X2)) -> ACTIVE(X2)
ACTIVE(first1(X1, X2)) -> FIRST1(active(X1), X2)
ACTIVE(first1(X1, X2)) -> ACTIVE(X1)
ACTIVE(first1(X1, X2)) -> FIRST1(X1, active(X2))
ACTIVE(first1(X1, X2)) -> ACTIVE(X2)
ACTIVE(cons1(X1, X2)) -> CONS1(active(X1), X2)
ACTIVE(cons1(X1, X2)) -> ACTIVE(X1)
ACTIVE(cons1(X1, X2)) -> CONS1(X1, active(X2))
ACTIVE(cons1(X1, X2)) -> ACTIVE(X2)
ACTIVE(s1(X)) -> S1(active(X))
ACTIVE(s1(X)) -> ACTIVE(X)
ACTIVE(unquote(X)) -> UNQUOTE(active(X))
ACTIVE(unquote(X)) -> ACTIVE(X)
ACTIVE(unquote1(X)) -> UNQUOTE1(active(X))
ACTIVE(unquote1(X)) -> ACTIVE(X)
ACTIVE(fcons(X1, X2)) -> FCONS(active(X1), X2)
ACTIVE(fcons(X1, X2)) -> ACTIVE(X1)
ACTIVE(fcons(X1, X2)) -> FCONS(X1, active(X2))
ACTIVE(fcons(X1, X2)) -> ACTIVE(X2)
SEL(mark(X1), X2) -> SEL(X1, X2)
SEL(X1, mark(X2)) -> SEL(X1, X2)
SEL(ok(X1), ok(X2)) -> SEL(X1, X2)
S(mark(X)) -> S(X)
S(ok(X)) -> S(X)
CONS(mark(X1), X2) -> CONS(X1, X2)
CONS(ok(X1), ok(X2)) -> CONS(X1, X2)
FIRST(mark(X1), X2) -> FIRST(X1, X2)
FIRST(X1, mark(X2)) -> FIRST(X1, X2)
FIRST(ok(X1), ok(X2)) -> FIRST(X1, X2)
FROM(mark(X)) -> FROM(X)
FROM(ok(X)) -> FROM(X)
SEL1(mark(X1), X2) -> SEL1(X1, X2)
SEL1(X1, mark(X2)) -> SEL1(X1, X2)
SEL1(ok(X1), ok(X2)) -> SEL1(X1, X2)
FIRST1(mark(X1), X2) -> FIRST1(X1, X2)
FIRST1(X1, mark(X2)) -> FIRST1(X1, X2)
FIRST1(ok(X1), ok(X2)) -> FIRST1(X1, X2)
CONS1(mark(X1), X2) -> CONS1(X1, X2)
CONS1(X1, mark(X2)) -> CONS1(X1, X2)
CONS1(ok(X1), ok(X2)) -> CONS1(X1, X2)
S1(mark(X)) -> S1(X)
S1(ok(X)) -> S1(X)
UNQUOTE(mark(X)) -> UNQUOTE(X)
UNQUOTE(ok(X)) -> UNQUOTE(X)
UNQUOTE1(mark(X)) -> UNQUOTE1(X)
UNQUOTE1(ok(X)) -> UNQUOTE1(X)
FCONS(mark(X1), X2) -> FCONS(X1, X2)
FCONS(X1, mark(X2)) -> FCONS(X1, X2)
FCONS(ok(X1), ok(X2)) -> FCONS(X1, X2)
PROPER(sel(X1, X2)) -> SEL(proper(X1), proper(X2))
PROPER(sel(X1, X2)) -> PROPER(X1)
PROPER(sel(X1, X2)) -> PROPER(X2)
PROPER(s(X)) -> S(proper(X))
PROPER(s(X)) -> PROPER(X)
PROPER(cons(X1, X2)) -> CONS(proper(X1), proper(X2))
PROPER(cons(X1, X2)) -> PROPER(X1)
PROPER(cons(X1, X2)) -> PROPER(X2)
PROPER(first(X1, X2)) -> FIRST(proper(X1), proper(X2))
PROPER(first(X1, X2)) -> PROPER(X1)
PROPER(first(X1, X2)) -> PROPER(X2)
PROPER(from(X)) -> FROM(proper(X))
PROPER(from(X)) -> PROPER(X)
PROPER(sel1(X1, X2)) -> SEL1(proper(X1), proper(X2))
PROPER(sel1(X1, X2)) -> PROPER(X1)
PROPER(sel1(X1, X2)) -> PROPER(X2)
PROPER(quote(X)) -> QUOTE(proper(X))
PROPER(quote(X)) -> PROPER(X)
PROPER(first1(X1, X2)) -> FIRST1(proper(X1), proper(X2))
PROPER(first1(X1, X2)) -> PROPER(X1)
PROPER(first1(X1, X2)) -> PROPER(X2)
PROPER(cons1(X1, X2)) -> CONS1(proper(X1), proper(X2))
PROPER(cons1(X1, X2)) -> PROPER(X1)
PROPER(cons1(X1, X2)) -> PROPER(X2)
PROPER(quote1(X)) -> QUOTE1(proper(X))
PROPER(quote1(X)) -> PROPER(X)
PROPER(s1(X)) -> S1(proper(X))
PROPER(s1(X)) -> PROPER(X)
PROPER(unquote(X)) -> UNQUOTE(proper(X))
PROPER(unquote(X)) -> PROPER(X)
PROPER(unquote1(X)) -> UNQUOTE1(proper(X))
PROPER(unquote1(X)) -> PROPER(X)
PROPER(fcons(X1, X2)) -> FCONS(proper(X1), proper(X2))
PROPER(fcons(X1, X2)) -> PROPER(X1)
PROPER(fcons(X1, X2)) -> PROPER(X2)
QUOTE(ok(X)) -> QUOTE(X)
QUOTE1(ok(X)) -> QUOTE1(X)
TOP(mark(X)) -> TOP(proper(X))
TOP(mark(X)) -> PROPER(X)
TOP(ok(X)) -> TOP(active(X))
TOP(ok(X)) -> ACTIVE(X)

   R

     ↳DPs

       →DP Problem 1

         ↳Remaining Obligation(s)

       →DP Problem 2

         ↳Remaining Obligation(s)

       →DP Problem 3

         ↳Remaining Obligation(s)

       →DP Problem 4

         ↳Remaining Obligation(s)

       →DP Problem 5

         ↳Remaining Obligation(s)

       →DP Problem 6

         ↳Remaining Obligation(s)

       →DP Problem 7

         ↳Remaining Obligation(s)

       →DP Problem 8

         ↳Remaining Obligation(s)

       →DP Problem 9

         ↳Remaining Obligation(s)

       →DP Problem 10

         ↳Remaining Obligation(s)

       →DP Problem 11

         ↳Remaining Obligation(s)

       →DP Problem 12

         ↳Remaining Obligation(s)

       →DP Problem 13

         ↳Remaining Obligation(s)

       →DP Problem 14

         ↳Remaining Obligation(s)

       →DP Problem 15

         ↳Remaining Obligation(s)

       →DP Problem 16

         ↳Remaining Obligation(s)

       →DP Problem 17

         ↳Remaining Obligation(s)

• Dependency Pairs:
  

  SEL(ok(X1), ok(X2)) -> SEL(X1, X2)
  SEL(X1, mark(X2)) -> SEL(X1, X2)
  SEL(mark(X1), X2) -> SEL(X1, X2)

  
  Rules:
  

  
  active(sel(s(X), cons(Y, Z))) -> mark(sel(X, Z))
  active(sel(0, cons(X, Z))) -> mark(X)
  active(first(0, Z)) -> mark(nil)
  active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
  active(from(X)) -> mark(cons(X, from(s(X))))
  active(sel1(s(X), cons(Y, Z))) -> mark(sel1(X, Z))
  active(sel1(0, cons(X, Z))) -> mark(quote(X))
  active(first1(0, Z)) -> mark(nil1)
  active(first1(s(X), cons(Y, Z))) -> mark(cons1(quote(Y), first1(X, Z)))
  active(quote(0)) -> mark(01)
  active(quote1(cons(X, Z))) -> mark(cons1(quote(X), quote1(Z)))
  active(quote1(nil)) -> mark(nil1)
  active(quote(s(X))) -> mark(s1(quote(X)))
  active(quote(sel(X, Z))) -> mark(sel1(X, Z))
  active(quote1(first(X, Z))) -> mark(first1(X, Z))
  active(unquote(01)) -> mark(0)
  active(unquote(s1(X))) -> mark(s(unquote(X)))
  active(unquote1(nil1)) -> mark(nil)
  active(unquote1(cons1(X, Z))) -> mark(fcons(unquote(X), unquote1(Z)))
  active(fcons(X, Z)) -> mark(cons(X, Z))
  active(sel(X1, X2)) -> sel(active(X1), X2)
  active(sel(X1, X2)) -> sel(X1, active(X2))
  active(s(X)) -> s(active(X))
  active(cons(X1, X2)) -> cons(active(X1), X2)
  active(first(X1, X2)) -> first(active(X1), X2)
  active(first(X1, X2)) -> first(X1, active(X2))
  active(from(X)) -> from(active(X))
  active(sel1(X1, X2)) -> sel1(active(X1), X2)
  active(sel1(X1, X2)) -> sel1(X1, active(X2))
  active(first1(X1, X2)) -> first1(active(X1), X2)
  active(first1(X1, X2)) -> first1(X1, active(X2))
  active(cons1(X1, X2)) -> cons1(active(X1), X2)
  active(cons1(X1, X2)) -> cons1(X1, active(X2))
  active(s1(X)) -> s1(active(X))
  active(unquote(X)) -> unquote(active(X))
  active(unquote1(X)) -> unquote1(active(X))
  active(fcons(X1, X2)) -> fcons(active(X1), X2)
  active(fcons(X1, X2)) -> fcons(X1, active(X2))
  sel(mark(X1), X2) -> mark(sel(X1, X2))
  sel(X1, mark(X2)) -> mark(sel(X1, X2))
  sel(ok(X1), ok(X2)) -> ok(sel(X1, X2))
  s(mark(X)) -> mark(s(X))
  s(ok(X)) -> ok(s(X))
  cons(mark(X1), X2) -> mark(cons(X1, X2))
  cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
  first(mark(X1), X2) -> mark(first(X1, X2))
  first(X1, mark(X2)) -> mark(first(X1, X2))
  first(ok(X1), ok(X2)) -> ok(first(X1, X2))
  from(mark(X)) -> mark(from(X))
  from(ok(X)) -> ok(from(X))
  sel1(mark(X1), X2) -> mark(sel1(X1, X2))
  sel1(X1, mark(X2)) -> mark(sel1(X1, X2))
  sel1(ok(X1), ok(X2)) -> ok(sel1(X1, X2))
  first1(mark(X1), X2) -> mark(first1(X1, X2))
  first1(X1, mark(X2)) -> mark(first1(X1, X2))
  first1(ok(X1), ok(X2)) -> ok(first1(X1, X2))
  cons1(mark(X1), X2) -> mark(cons1(X1, X2))
  cons1(X1, mark(X2)) -> mark(cons1(X1, X2))
  cons1(ok(X1), ok(X2)) -> ok(cons1(X1, X2))
  s1(mark(X)) -> mark(s1(X))
  s1(ok(X)) -> ok(s1(X))
  unquote(mark(X)) -> mark(unquote(X))
  unquote(ok(X)) -> ok(unquote(X))
  unquote1(mark(X)) -> mark(unquote1(X))
  unquote1(ok(X)) -> ok(unquote1(X))
  fcons(mark(X1), X2) -> mark(fcons(X1, X2))
  fcons(X1, mark(X2)) -> mark(fcons(X1, X2))
  fcons(ok(X1), ok(X2)) -> ok(fcons(X1, X2))
  proper(sel(X1, X2)) -> sel(proper(X1), proper(X2))
  proper(s(X)) -> s(proper(X))
  proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
  proper(0) -> ok(0)
  proper(first(X1, X2)) -> first(proper(X1), proper(X2))
  proper(nil) -> ok(nil)
  proper(from(X)) -> from(proper(X))
  proper(sel1(X1, X2)) -> sel1(proper(X1), proper(X2))
  proper(quote(X)) -> quote(proper(X))
  proper(first1(X1, X2)) -> first1(proper(X1), proper(X2))
  proper(nil1) -> ok(nil1)
  proper(cons1(X1, X2)) -> cons1(proper(X1), proper(X2))
  proper(01) -> ok(01)
  proper(quote1(X)) -> quote1(proper(X))
  proper(s1(X)) -> s1(proper(X))
  proper(unquote(X)) -> unquote(proper(X))
  proper(unquote1(X)) -> unquote1(proper(X))
  proper(fcons(X1, X2)) -> fcons(proper(X1), proper(X2))
  quote(ok(X)) -> ok(quote(X))
  quote1(ok(X)) -> ok(quote1(X))
  top(mark(X)) -> top(proper(X))
  top(ok(X)) -> top(active(X))

  
  
  
• Dependency Pairs:
  

  CONS(ok(X1), ok(X2)) -> CONS(X1, X2)
  CONS(mark(X1), X2) -> CONS(X1, X2)

  
  Rules:
  

  
  active(sel(s(X), cons(Y, Z))) -> mark(sel(X, Z))
  active(sel(0, cons(X, Z))) -> mark(X)
  active(first(0, Z)) -> mark(nil)
  active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
  active(from(X)) -> mark(cons(X, from(s(X))))
  active(sel1(s(X), cons(Y, Z))) -> mark(sel1(X, Z))
  active(sel1(0, cons(X, Z))) -> mark(quote(X))
  active(first1(0, Z)) -> mark(nil1)
  active(first1(s(X), cons(Y, Z))) -> mark(cons1(quote(Y), first1(X, Z)))
  active(quote(0)) -> mark(01)
  active(quote1(cons(X, Z))) -> mark(cons1(quote(X), quote1(Z)))
  active(quote1(nil)) -> mark(nil1)
  active(quote(s(X))) -> mark(s1(quote(X)))
  active(quote(sel(X, Z))) -> mark(sel1(X, Z))
  active(quote1(first(X, Z))) -> mark(first1(X, Z))
  active(unquote(01)) -> mark(0)
  active(unquote(s1(X))) -> mark(s(unquote(X)))
  active(unquote1(nil1)) -> mark(nil)
  active(unquote1(cons1(X, Z))) -> mark(fcons(unquote(X), unquote1(Z)))
  active(fcons(X, Z)) -> mark(cons(X, Z))
  active(sel(X1, X2)) -> sel(active(X1), X2)
  active(sel(X1, X2)) -> sel(X1, active(X2))
  active(s(X)) -> s(active(X))
  active(cons(X1, X2)) -> cons(active(X1), X2)
  active(first(X1, X2)) -> first(active(X1), X2)
  active(first(X1, X2)) -> first(X1, active(X2))
  active(from(X)) -> from(active(X))
  active(sel1(X1, X2)) -> sel1(active(X1), X2)
  active(sel1(X1, X2)) -> sel1(X1, active(X2))
  active(first1(X1, X2)) -> first1(active(X1), X2)
  active(first1(X1, X2)) -> first1(X1, active(X2))
  active(cons1(X1, X2)) -> cons1(active(X1), X2)
  active(cons1(X1, X2)) -> cons1(X1, active(X2))
  active(s1(X)) -> s1(active(X))
  active(unquote(X)) -> unquote(active(X))
  active(unquote1(X)) -> unquote1(active(X))
  active(fcons(X1, X2)) -> fcons(active(X1), X2)
  active(fcons(X1, X2)) -> fcons(X1, active(X2))
  sel(mark(X1), X2) -> mark(sel(X1, X2))
  sel(X1, mark(X2)) -> mark(sel(X1, X2))
  sel(ok(X1), ok(X2)) -> ok(sel(X1, X2))
  s(mark(X)) -> mark(s(X))
  s(ok(X)) -> ok(s(X))
  cons(mark(X1), X2) -> mark(cons(X1, X2))
  cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
  first(mark(X1), X2) -> mark(first(X1, X2))
  first(X1, mark(X2)) -> mark(first(X1, X2))
  first(ok(X1), ok(X2)) -> ok(first(X1, X2))
  from(mark(X)) -> mark(from(X))
  from(ok(X)) -> ok(from(X))
  sel1(mark(X1), X2) -> mark(sel1(X1, X2))
  sel1(X1, mark(X2)) -> mark(sel1(X1, X2))
  sel1(ok(X1), ok(X2)) -> ok(sel1(X1, X2))
  first1(mark(X1), X2) -> mark(first1(X1, X2))
  first1(X1, mark(X2)) -> mark(first1(X1, X2))
  first1(ok(X1), ok(X2)) -> ok(first1(X1, X2))
  cons1(mark(X1), X2) -> mark(cons1(X1, X2))
  cons1(X1, mark(X2)) -> mark(cons1(X1, X2))
  cons1(ok(X1), ok(X2)) -> ok(cons1(X1, X2))
  s1(mark(X)) -> mark(s1(X))
  s1(ok(X)) -> ok(s1(X))
  unquote(mark(X)) -> mark(unquote(X))
  unquote(ok(X)) -> ok(unquote(X))
  unquote1(mark(X)) -> mark(unquote1(X))
  unquote1(ok(X)) -> ok(unquote1(X))
  fcons(mark(X1), X2) -> mark(fcons(X1, X2))
  fcons(X1, mark(X2)) -> mark(fcons(X1, X2))
  fcons(ok(X1), ok(X2)) -> ok(fcons(X1, X2))
  proper(sel(X1, X2)) -> sel(proper(X1), proper(X2))
  proper(s(X)) -> s(proper(X))
  proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
  proper(0) -> ok(0)
  proper(first(X1, X2)) -> first(proper(X1), proper(X2))
  proper(nil) -> ok(nil)
  proper(from(X)) -> from(proper(X))
  proper(sel1(X1, X2)) -> sel1(proper(X1), proper(X2))
  proper(quote(X)) -> quote(proper(X))
  proper(first1(X1, X2)) -> first1(proper(X1), proper(X2))
  proper(nil1) -> ok(nil1)
  proper(cons1(X1, X2)) -> cons1(proper(X1), proper(X2))
  proper(01) -> ok(01)
  proper(quote1(X)) -> quote1(proper(X))
  proper(s1(X)) -> s1(proper(X))
  proper(unquote(X)) -> unquote(proper(X))
  proper(unquote1(X)) -> unquote1(proper(X))
  proper(fcons(X1, X2)) -> fcons(proper(X1), proper(X2))
  quote(ok(X)) -> ok(quote(X))
  quote1(ok(X)) -> ok(quote1(X))
  top(mark(X)) -> top(proper(X))
  top(ok(X)) -> top(active(X))

  
  
  
• Dependency Pairs:
  

  FIRST(ok(X1), ok(X2)) -> FIRST(X1, X2)
  FIRST(X1, mark(X2)) -> FIRST(X1, X2)
  FIRST(mark(X1), X2) -> FIRST(X1, X2)

  
  Rules:
  

  
  active(sel(s(X), cons(Y, Z))) -> mark(sel(X, Z))
  active(sel(0, cons(X, Z))) -> mark(X)
  active(first(0, Z)) -> mark(nil)
  active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
  active(from(X)) -> mark(cons(X, from(s(X))))
  active(sel1(s(X), cons(Y, Z))) -> mark(sel1(X, Z))
  active(sel1(0, cons(X, Z))) -> mark(quote(X))
  active(first1(0, Z)) -> mark(nil1)
  active(first1(s(X), cons(Y, Z))) -> mark(cons1(quote(Y), first1(X, Z)))
  active(quote(0)) -> mark(01)
  active(quote1(cons(X, Z))) -> mark(cons1(quote(X), quote1(Z)))
  active(quote1(nil)) -> mark(nil1)
  active(quote(s(X))) -> mark(s1(quote(X)))
  active(quote(sel(X, Z))) -> mark(sel1(X, Z))
  active(quote1(first(X, Z))) -> mark(first1(X, Z))
  active(unquote(01)) -> mark(0)
  active(unquote(s1(X))) -> mark(s(unquote(X)))
  active(unquote1(nil1)) -> mark(nil)
  active(unquote1(cons1(X, Z))) -> mark(fcons(unquote(X), unquote1(Z)))
  active(fcons(X, Z)) -> mark(cons(X, Z))
  active(sel(X1, X2)) -> sel(active(X1), X2)
  active(sel(X1, X2)) -> sel(X1, active(X2))
  active(s(X)) -> s(active(X))
  active(cons(X1, X2)) -> cons(active(X1), X2)
  active(first(X1, X2)) -> first(active(X1), X2)
  active(first(X1, X2)) -> first(X1, active(X2))
  active(from(X)) -> from(active(X))
  active(sel1(X1, X2)) -> sel1(active(X1), X2)
  active(sel1(X1, X2)) -> sel1(X1, active(X2))
  active(first1(X1, X2)) -> first1(active(X1), X2)
  active(first1(X1, X2)) -> first1(X1, active(X2))
  active(cons1(X1, X2)) -> cons1(active(X1), X2)
  active(cons1(X1, X2)) -> cons1(X1, active(X2))
  active(s1(X)) -> s1(active(X))
  active(unquote(X)) -> unquote(active(X))
  active(unquote1(X)) -> unquote1(active(X))
  active(fcons(X1, X2)) -> fcons(active(X1), X2)
  active(fcons(X1, X2)) -> fcons(X1, active(X2))
  sel(mark(X1), X2) -> mark(sel(X1, X2))
  sel(X1, mark(X2)) -> mark(sel(X1, X2))
  sel(ok(X1), ok(X2)) -> ok(sel(X1, X2))
  s(mark(X)) -> mark(s(X))
  s(ok(X)) -> ok(s(X))
  cons(mark(X1), X2) -> mark(cons(X1, X2))
  cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
  first(mark(X1), X2) -> mark(first(X1, X2))
  first(X1, mark(X2)) -> mark(first(X1, X2))
  first(ok(X1), ok(X2)) -> ok(first(X1, X2))
  from(mark(X)) -> mark(from(X))
  from(ok(X)) -> ok(from(X))
  sel1(mark(X1), X2) -> mark(sel1(X1, X2))
  sel1(X1, mark(X2)) -> mark(sel1(X1, X2))
  sel1(ok(X1), ok(X2)) -> ok(sel1(X1, X2))
  first1(mark(X1), X2) -> mark(first1(X1, X2))
  first1(X1, mark(X2)) -> mark(first1(X1, X2))
  first1(ok(X1), ok(X2)) -> ok(first1(X1, X2))
  cons1(mark(X1), X2) -> mark(cons1(X1, X2))
  cons1(X1, mark(X2)) -> mark(cons1(X1, X2))
  cons1(ok(X1), ok(X2)) -> ok(cons1(X1, X2))
  s1(mark(X)) -> mark(s1(X))
  s1(ok(X)) -> ok(s1(X))
  unquote(mark(X)) -> mark(unquote(X))
  unquote(ok(X)) -> ok(unquote(X))
  unquote1(mark(X)) -> mark(unquote1(X))
  unquote1(ok(X)) -> ok(unquote1(X))
  fcons(mark(X1), X2) -> mark(fcons(X1, X2))
  fcons(X1, mark(X2)) -> mark(fcons(X1, X2))
  fcons(ok(X1), ok(X2)) -> ok(fcons(X1, X2))
  proper(sel(X1, X2)) -> sel(proper(X1), proper(X2))
  proper(s(X)) -> s(proper(X))
  proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
  proper(0) -> ok(0)
  proper(first(X1, X2)) -> first(proper(X1), proper(X2))
  proper(nil) -> ok(nil)
  proper(from(X)) -> from(proper(X))
  proper(sel1(X1, X2)) -> sel1(proper(X1), proper(X2))
  proper(quote(X)) -> quote(proper(X))
  proper(first1(X1, X2)) -> first1(proper(X1), proper(X2))
  proper(nil1) -> ok(nil1)
  proper(cons1(X1, X2)) -> cons1(proper(X1), proper(X2))
  proper(01) -> ok(01)
  proper(quote1(X)) -> quote1(proper(X))
  proper(s1(X)) -> s1(proper(X))
  proper(unquote(X)) -> unquote(proper(X))
  proper(unquote1(X)) -> unquote1(proper(X))
  proper(fcons(X1, X2)) -> fcons(proper(X1), proper(X2))
  quote(ok(X)) -> ok(quote(X))
  quote1(ok(X)) -> ok(quote1(X))
  top(mark(X)) -> top(proper(X))
  top(ok(X)) -> top(active(X))

  
  
  
• Dependency Pairs:
  

  FROM(ok(X)) -> FROM(X)
  FROM(mark(X)) -> FROM(X)

  
  Rules:
  

  
  active(sel(s(X), cons(Y, Z))) -> mark(sel(X, Z))
  active(sel(0, cons(X, Z))) -> mark(X)
  active(first(0, Z)) -> mark(nil)
  active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
  active(from(X)) -> mark(cons(X, from(s(X))))
  active(sel1(s(X), cons(Y, Z))) -> mark(sel1(X, Z))
  active(sel1(0, cons(X, Z))) -> mark(quote(X))
  active(first1(0, Z)) -> mark(nil1)
  active(first1(s(X), cons(Y, Z))) -> mark(cons1(quote(Y), first1(X, Z)))
  active(quote(0)) -> mark(01)
  active(quote1(cons(X, Z))) -> mark(cons1(quote(X), quote1(Z)))
  active(quote1(nil)) -> mark(nil1)
  active(quote(s(X))) -> mark(s1(quote(X)))
  active(quote(sel(X, Z))) -> mark(sel1(X, Z))
  active(quote1(first(X, Z))) -> mark(first1(X, Z))
  active(unquote(01)) -> mark(0)
  active(unquote(s1(X))) -> mark(s(unquote(X)))
  active(unquote1(nil1)) -> mark(nil)
  active(unquote1(cons1(X, Z))) -> mark(fcons(unquote(X), unquote1(Z)))
  active(fcons(X, Z)) -> mark(cons(X, Z))
  active(sel(X1, X2)) -> sel(active(X1), X2)
  active(sel(X1, X2)) -> sel(X1, active(X2))
  active(s(X)) -> s(active(X))
  active(cons(X1, X2)) -> cons(active(X1), X2)
  active(first(X1, X2)) -> first(active(X1), X2)
  active(first(X1, X2)) -> first(X1, active(X2))
  active(from(X)) -> from(active(X))
  active(sel1(X1, X2)) -> sel1(active(X1), X2)
  active(sel1(X1, X2)) -> sel1(X1, active(X2))
  active(first1(X1, X2)) -> first1(active(X1), X2)
  active(first1(X1, X2)) -> first1(X1, active(X2))
  active(cons1(X1, X2)) -> cons1(active(X1), X2)
  active(cons1(X1, X2)) -> cons1(X1, active(X2))
  active(s1(X)) -> s1(active(X))
  active(unquote(X)) -> unquote(active(X))
  active(unquote1(X)) -> unquote1(active(X))
  active(fcons(X1, X2)) -> fcons(active(X1), X2)
  active(fcons(X1, X2)) -> fcons(X1, active(X2))
  sel(mark(X1), X2) -> mark(sel(X1, X2))
  sel(X1, mark(X2)) -> mark(sel(X1, X2))
  sel(ok(X1), ok(X2)) -> ok(sel(X1, X2))
  s(mark(X)) -> mark(s(X))
  s(ok(X)) -> ok(s(X))
  cons(mark(X1), X2) -> mark(cons(X1, X2))
  cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
  first(mark(X1), X2) -> mark(first(X1, X2))
  first(X1, mark(X2)) -> mark(first(X1, X2))
  first(ok(X1), ok(X2)) -> ok(first(X1, X2))
  from(mark(X)) -> mark(from(X))
  from(ok(X)) -> ok(from(X))
  sel1(mark(X1), X2) -> mark(sel1(X1, X2))
  sel1(X1, mark(X2)) -> mark(sel1(X1, X2))
  sel1(ok(X1), ok(X2)) -> ok(sel1(X1, X2))
  first1(mark(X1), X2) -> mark(first1(X1, X2))
  first1(X1, mark(X2)) -> mark(first1(X1, X2))
  first1(ok(X1), ok(X2)) -> ok(first1(X1, X2))
  cons1(mark(X1), X2) -> mark(cons1(X1, X2))
  cons1(X1, mark(X2)) -> mark(cons1(X1, X2))
  cons1(ok(X1), ok(X2)) -> ok(cons1(X1, X2))
  s1(mark(X)) -> mark(s1(X))
  s1(ok(X)) -> ok(s1(X))
  unquote(mark(X)) -> mark(unquote(X))
  unquote(ok(X)) -> ok(unquote(X))
  unquote1(mark(X)) -> mark(unquote1(X))
  unquote1(ok(X)) -> ok(unquote1(X))
  fcons(mark(X1), X2) -> mark(fcons(X1, X2))
  fcons(X1, mark(X2)) -> mark(fcons(X1, X2))
  fcons(ok(X1), ok(X2)) -> ok(fcons(X1, X2))
  proper(sel(X1, X2)) -> sel(proper(X1), proper(X2))
  proper(s(X)) -> s(proper(X))
  proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
  proper(0) -> ok(0)
  proper(first(X1, X2)) -> first(proper(X1), proper(X2))
  proper(nil) -> ok(nil)
  proper(from(X)) -> from(proper(X))
  proper(sel1(X1, X2)) -> sel1(proper(X1), proper(X2))
  proper(quote(X)) -> quote(proper(X))
  proper(first1(X1, X2)) -> first1(proper(X1), proper(X2))
  proper(nil1) -> ok(nil1)
  proper(cons1(X1, X2)) -> cons1(proper(X1), proper(X2))
  proper(01) -> ok(01)
  proper(quote1(X)) -> quote1(proper(X))
  proper(s1(X)) -> s1(proper(X))
  proper(unquote(X)) -> unquote(proper(X))
  proper(unquote1(X)) -> unquote1(proper(X))
  proper(fcons(X1, X2)) -> fcons(proper(X1), proper(X2))
  quote(ok(X)) -> ok(quote(X))
  quote1(ok(X)) -> ok(quote1(X))
  top(mark(X)) -> top(proper(X))
  top(ok(X)) -> top(active(X))

  
  
  
• Dependency Pairs:
  

  S(ok(X)) -> S(X)
  S(mark(X)) -> S(X)

  
  Rules:
  

  
  active(sel(s(X), cons(Y, Z))) -> mark(sel(X, Z))
  active(sel(0, cons(X, Z))) -> mark(X)
  active(first(0, Z)) -> mark(nil)
  active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
  active(from(X)) -> mark(cons(X, from(s(X))))
  active(sel1(s(X), cons(Y, Z))) -> mark(sel1(X, Z))
  active(sel1(0, cons(X, Z))) -> mark(quote(X))
  active(first1(0, Z)) -> mark(nil1)
  active(first1(s(X), cons(Y, Z))) -> mark(cons1(quote(Y), first1(X, Z)))
  active(quote(0)) -> mark(01)
  active(quote1(cons(X, Z))) -> mark(cons1(quote(X), quote1(Z)))
  active(quote1(nil)) -> mark(nil1)
  active(quote(s(X))) -> mark(s1(quote(X)))
  active(quote(sel(X, Z))) -> mark(sel1(X, Z))
  active(quote1(first(X, Z))) -> mark(first1(X, Z))
  active(unquote(01)) -> mark(0)
  active(unquote(s1(X))) -> mark(s(unquote(X)))
  active(unquote1(nil1)) -> mark(nil)
  active(unquote1(cons1(X, Z))) -> mark(fcons(unquote(X), unquote1(Z)))
  active(fcons(X, Z)) -> mark(cons(X, Z))
  active(sel(X1, X2)) -> sel(active(X1), X2)
  active(sel(X1, X2)) -> sel(X1, active(X2))
  active(s(X)) -> s(active(X))
  active(cons(X1, X2)) -> cons(active(X1), X2)
  active(first(X1, X2)) -> first(active(X1), X2)
  active(first(X1, X2)) -> first(X1, active(X2))
  active(from(X)) -> from(active(X))
  active(sel1(X1, X2)) -> sel1(active(X1), X2)
  active(sel1(X1, X2)) -> sel1(X1, active(X2))
  active(first1(X1, X2)) -> first1(active(X1), X2)
  active(first1(X1, X2)) -> first1(X1, active(X2))
  active(cons1(X1, X2)) -> cons1(active(X1), X2)
  active(cons1(X1, X2)) -> cons1(X1, active(X2))
  active(s1(X)) -> s1(active(X))
  active(unquote(X)) -> unquote(active(X))
  active(unquote1(X)) -> unquote1(active(X))
  active(fcons(X1, X2)) -> fcons(active(X1), X2)
  active(fcons(X1, X2)) -> fcons(X1, active(X2))
  sel(mark(X1), X2) -> mark(sel(X1, X2))
  sel(X1, mark(X2)) -> mark(sel(X1, X2))
  sel(ok(X1), ok(X2)) -> ok(sel(X1, X2))
  s(mark(X)) -> mark(s(X))
  s(ok(X)) -> ok(s(X))
  cons(mark(X1), X2) -> mark(cons(X1, X2))
  cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
  first(mark(X1), X2) -> mark(first(X1, X2))
  first(X1, mark(X2)) -> mark(first(X1, X2))
  first(ok(X1), ok(X2)) -> ok(first(X1, X2))
  from(mark(X)) -> mark(from(X))
  from(ok(X)) -> ok(from(X))
  sel1(mark(X1), X2) -> mark(sel1(X1, X2))
  sel1(X1, mark(X2)) -> mark(sel1(X1, X2))
  sel1(ok(X1), ok(X2)) -> ok(sel1(X1, X2))
  first1(mark(X1), X2) -> mark(first1(X1, X2))
  first1(X1, mark(X2)) -> mark(first1(X1, X2))
  first1(ok(X1), ok(X2)) -> ok(first1(X1, X2))
  cons1(mark(X1), X2) -> mark(cons1(X1, X2))
  cons1(X1, mark(X2)) -> mark(cons1(X1, X2))
  cons1(ok(X1), ok(X2)) -> ok(cons1(X1, X2))
  s1(mark(X)) -> mark(s1(X))
  s1(ok(X)) -> ok(s1(X))
  unquote(mark(X)) -> mark(unquote(X))
  unquote(ok(X)) -> ok(unquote(X))
  unquote1(mark(X)) -> mark(unquote1(X))
  unquote1(ok(X)) -> ok(unquote1(X))
  fcons(mark(X1), X2) -> mark(fcons(X1, X2))
  fcons(X1, mark(X2)) -> mark(fcons(X1, X2))
  fcons(ok(X1), ok(X2)) -> ok(fcons(X1, X2))
  proper(sel(X1, X2)) -> sel(proper(X1), proper(X2))
  proper(s(X)) -> s(proper(X))
  proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
  proper(0) -> ok(0)
  proper(first(X1, X2)) -> first(proper(X1), proper(X2))
  proper(nil) -> ok(nil)
  proper(from(X)) -> from(proper(X))
  proper(sel1(X1, X2)) -> sel1(proper(X1), proper(X2))
  proper(quote(X)) -> quote(proper(X))
  proper(first1(X1, X2)) -> first1(proper(X1), proper(X2))
  proper(nil1) -> ok(nil1)
  proper(cons1(X1, X2)) -> cons1(proper(X1), proper(X2))
  proper(01) -> ok(01)
  proper(quote1(X)) -> quote1(proper(X))
  proper(s1(X)) -> s1(proper(X))
  proper(unquote(X)) -> unquote(proper(X))
  proper(unquote1(X)) -> unquote1(proper(X))
  proper(fcons(X1, X2)) -> fcons(proper(X1), proper(X2))
  quote(ok(X)) -> ok(quote(X))
  quote1(ok(X)) -> ok(quote1(X))
  top(mark(X)) -> top(proper(X))
  top(ok(X)) -> top(active(X))

  
  
  
• Dependency Pairs:
  

  SEL1(ok(X1), ok(X2)) -> SEL1(X1, X2)
  SEL1(X1, mark(X2)) -> SEL1(X1, X2)
  SEL1(mark(X1), X2) -> SEL1(X1, X2)

  
  Rules:
  

  
  active(sel(s(X), cons(Y, Z))) -> mark(sel(X, Z))
  active(sel(0, cons(X, Z))) -> mark(X)
  active(first(0, Z)) -> mark(nil)
  active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
  active(from(X)) -> mark(cons(X, from(s(X))))
  active(sel1(s(X), cons(Y, Z))) -> mark(sel1(X, Z))
  active(sel1(0, cons(X, Z))) -> mark(quote(X))
  active(first1(0, Z)) -> mark(nil1)
  active(first1(s(X), cons(Y, Z))) -> mark(cons1(quote(Y), first1(X, Z)))
  active(quote(0)) -> mark(01)
  active(quote1(cons(X, Z))) -> mark(cons1(quote(X), quote1(Z)))
  active(quote1(nil)) -> mark(nil1)
  active(quote(s(X))) -> mark(s1(quote(X)))
  active(quote(sel(X, Z))) -> mark(sel1(X, Z))
  active(quote1(first(X, Z))) -> mark(first1(X, Z))
  active(unquote(01)) -> mark(0)
  active(unquote(s1(X))) -> mark(s(unquote(X)))
  active(unquote1(nil1)) -> mark(nil)
  active(unquote1(cons1(X, Z))) -> mark(fcons(unquote(X), unquote1(Z)))
  active(fcons(X, Z)) -> mark(cons(X, Z))
  active(sel(X1, X2)) -> sel(active(X1), X2)
  active(sel(X1, X2)) -> sel(X1, active(X2))
  active(s(X)) -> s(active(X))
  active(cons(X1, X2)) -> cons(active(X1), X2)
  active(first(X1, X2)) -> first(active(X1), X2)
  active(first(X1, X2)) -> first(X1, active(X2))
  active(from(X)) -> from(active(X))
  active(sel1(X1, X2)) -> sel1(active(X1), X2)
  active(sel1(X1, X2)) -> sel1(X1, active(X2))
  active(first1(X1, X2)) -> first1(active(X1), X2)
  active(first1(X1, X2)) -> first1(X1, active(X2))
  active(cons1(X1, X2)) -> cons1(active(X1), X2)
  active(cons1(X1, X2)) -> cons1(X1, active(X2))
  active(s1(X)) -> s1(active(X))
  active(unquote(X)) -> unquote(active(X))
  active(unquote1(X)) -> unquote1(active(X))
  active(fcons(X1, X2)) -> fcons(active(X1), X2)
  active(fcons(X1, X2)) -> fcons(X1, active(X2))
  sel(mark(X1), X2) -> mark(sel(X1, X2))
  sel(X1, mark(X2)) -> mark(sel(X1, X2))
  sel(ok(X1), ok(X2)) -> ok(sel(X1, X2))
  s(mark(X)) -> mark(s(X))
  s(ok(X)) -> ok(s(X))
  cons(mark(X1), X2) -> mark(cons(X1, X2))
  cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
  first(mark(X1), X2) -> mark(first(X1, X2))
  first(X1, mark(X2)) -> mark(first(X1, X2))
  first(ok(X1), ok(X2)) -> ok(first(X1, X2))
  from(mark(X)) -> mark(from(X))
  from(ok(X)) -> ok(from(X))
  sel1(mark(X1), X2) -> mark(sel1(X1, X2))
  sel1(X1, mark(X2)) -> mark(sel1(X1, X2))
  sel1(ok(X1), ok(X2)) -> ok(sel1(X1, X2))
  first1(mark(X1), X2) -> mark(first1(X1, X2))
  first1(X1, mark(X2)) -> mark(first1(X1, X2))
  first1(ok(X1), ok(X2)) -> ok(first1(X1, X2))
  cons1(mark(X1), X2) -> mark(cons1(X1, X2))
  cons1(X1, mark(X2)) -> mark(cons1(X1, X2))
  cons1(ok(X1), ok(X2)) -> ok(cons1(X1, X2))
  s1(mark(X)) -> mark(s1(X))
  s1(ok(X)) -> ok(s1(X))
  unquote(mark(X)) -> mark(unquote(X))
  unquote(ok(X)) -> ok(unquote(X))
  unquote1(mark(X)) -> mark(unquote1(X))
  unquote1(ok(X)) -> ok(unquote1(X))
  fcons(mark(X1), X2) -> mark(fcons(X1, X2))
  fcons(X1, mark(X2)) -> mark(fcons(X1, X2))
  fcons(ok(X1), ok(X2)) -> ok(fcons(X1, X2))
  proper(sel(X1, X2)) -> sel(proper(X1), proper(X2))
  proper(s(X)) -> s(proper(X))
  proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
  proper(0) -> ok(0)
  proper(first(X1, X2)) -> first(proper(X1), proper(X2))
  proper(nil) -> ok(nil)
  proper(from(X)) -> from(proper(X))
  proper(sel1(X1, X2)) -> sel1(proper(X1), proper(X2))
  proper(quote(X)) -> quote(proper(X))
  proper(first1(X1, X2)) -> first1(proper(X1), proper(X2))
  proper(nil1) -> ok(nil1)
  proper(cons1(X1, X2)) -> cons1(proper(X1), proper(X2))
  proper(01) -> ok(01)
  proper(quote1(X)) -> quote1(proper(X))
  proper(s1(X)) -> s1(proper(X))
  proper(unquote(X)) -> unquote(proper(X))
  proper(unquote1(X)) -> unquote1(proper(X))
  proper(fcons(X1, X2)) -> fcons(proper(X1), proper(X2))
  quote(ok(X)) -> ok(quote(X))
  quote1(ok(X)) -> ok(quote1(X))
  top(mark(X)) -> top(proper(X))
  top(ok(X)) -> top(active(X))

  
  
  
• Dependency Pair:
  

  QUOTE(ok(X)) -> QUOTE(X)

  
  Rules:
  

  
  active(sel(s(X), cons(Y, Z))) -> mark(sel(X, Z))
  active(sel(0, cons(X, Z))) -> mark(X)
  active(first(0, Z)) -> mark(nil)
  active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
  active(from(X)) -> mark(cons(X, from(s(X))))
  active(sel1(s(X), cons(Y, Z))) -> mark(sel1(X, Z))
  active(sel1(0, cons(X, Z))) -> mark(quote(X))
  active(first1(0, Z)) -> mark(nil1)
  active(first1(s(X), cons(Y, Z))) -> mark(cons1(quote(Y), first1(X, Z)))
  active(quote(0)) -> mark(01)
  active(quote1(cons(X, Z))) -> mark(cons1(quote(X), quote1(Z)))
  active(quote1(nil)) -> mark(nil1)
  active(quote(s(X))) -> mark(s1(quote(X)))
  active(quote(sel(X, Z))) -> mark(sel1(X, Z))
  active(quote1(first(X, Z))) -> mark(first1(X, Z))
  active(unquote(01)) -> mark(0)
  active(unquote(s1(X))) -> mark(s(unquote(X)))
  active(unquote1(nil1)) -> mark(nil)
  active(unquote1(cons1(X, Z))) -> mark(fcons(unquote(X), unquote1(Z)))
  active(fcons(X, Z)) -> mark(cons(X, Z))
  active(sel(X1, X2)) -> sel(active(X1), X2)
  active(sel(X1, X2)) -> sel(X1, active(X2))
  active(s(X)) -> s(active(X))
  active(cons(X1, X2)) -> cons(active(X1), X2)
  active(first(X1, X2)) -> first(active(X1), X2)
  active(first(X1, X2)) -> first(X1, active(X2))
  active(from(X)) -> from(active(X))
  active(sel1(X1, X2)) -> sel1(active(X1), X2)
  active(sel1(X1, X2)) -> sel1(X1, active(X2))
  active(first1(X1, X2)) -> first1(active(X1), X2)
  active(first1(X1, X2)) -> first1(X1, active(X2))
  active(cons1(X1, X2)) -> cons1(active(X1), X2)
  active(cons1(X1, X2)) -> cons1(X1, active(X2))
  active(s1(X)) -> s1(active(X))
  active(unquote(X)) -> unquote(active(X))
  active(unquote1(X)) -> unquote1(active(X))
  active(fcons(X1, X2)) -> fcons(active(X1), X2)
  active(fcons(X1, X2)) -> fcons(X1, active(X2))
  sel(mark(X1), X2) -> mark(sel(X1, X2))
  sel(X1, mark(X2)) -> mark(sel(X1, X2))
  sel(ok(X1), ok(X2)) -> ok(sel(X1, X2))
  s(mark(X)) -> mark(s(X))
  s(ok(X)) -> ok(s(X))
  cons(mark(X1), X2) -> mark(cons(X1, X2))
  cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
  first(mark(X1), X2) -> mark(first(X1, X2))
  first(X1, mark(X2)) -> mark(first(X1, X2))
  first(ok(X1), ok(X2)) -> ok(first(X1, X2))
  from(mark(X)) -> mark(from(X))
  from(ok(X)) -> ok(from(X))
  sel1(mark(X1), X2) -> mark(sel1(X1, X2))
  sel1(X1, mark(X2)) -> mark(sel1(X1, X2))
  sel1(ok(X1), ok(X2)) -> ok(sel1(X1, X2))
  first1(mark(X1), X2) -> mark(first1(X1, X2))
  first1(X1, mark(X2)) -> mark(first1(X1, X2))
  first1(ok(X1), ok(X2)) -> ok(first1(X1, X2))
  cons1(mark(X1), X2) -> mark(cons1(X1, X2))
  cons1(X1, mark(X2)) -> mark(cons1(X1, X2))
  cons1(ok(X1), ok(X2)) -> ok(cons1(X1, X2))
  s1(mark(X)) -> mark(s1(X))
  s1(ok(X)) -> ok(s1(X))
  unquote(mark(X)) -> mark(unquote(X))
  unquote(ok(X)) -> ok(unquote(X))
  unquote1(mark(X)) -> mark(unquote1(X))
  unquote1(ok(X)) -> ok(unquote1(X))
  fcons(mark(X1), X2) -> mark(fcons(X1, X2))
  fcons(X1, mark(X2)) -> mark(fcons(X1, X2))
  fcons(ok(X1), ok(X2)) -> ok(fcons(X1, X2))
  proper(sel(X1, X2)) -> sel(proper(X1), proper(X2))
  proper(s(X)) -> s(proper(X))
  proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
  proper(0) -> ok(0)
  proper(first(X1, X2)) -> first(proper(X1), proper(X2))
  proper(nil) -> ok(nil)
  proper(from(X)) -> from(proper(X))
  proper(sel1(X1, X2)) -> sel1(proper(X1), proper(X2))
  proper(quote(X)) -> quote(proper(X))
  proper(first1(X1, X2)) -> first1(proper(X1), proper(X2))
  proper(nil1) -> ok(nil1)
  proper(cons1(X1, X2)) -> cons1(proper(X1), proper(X2))
  proper(01) -> ok(01)
  proper(quote1(X)) -> quote1(proper(X))
  proper(s1(X)) -> s1(proper(X))
  proper(unquote(X)) -> unquote(proper(X))
  proper(unquote1(X)) -> unquote1(proper(X))
  proper(fcons(X1, X2)) -> fcons(proper(X1), proper(X2))
  quote(ok(X)) -> ok(quote(X))
  quote1(ok(X)) -> ok(quote1(X))
  top(mark(X)) -> top(proper(X))
  top(ok(X)) -> top(active(X))

  
  
  
• Dependency Pairs:
  

  CONS1(ok(X1), ok(X2)) -> CONS1(X1, X2)
  CONS1(X1, mark(X2)) -> CONS1(X1, X2)
  CONS1(mark(X1), X2) -> CONS1(X1, X2)

  
  Rules:
  

  
  active(sel(s(X), cons(Y, Z))) -> mark(sel(X, Z))
  active(sel(0, cons(X, Z))) -> mark(X)
  active(first(0, Z)) -> mark(nil)
  active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
  active(from(X)) -> mark(cons(X, from(s(X))))
  active(sel1(s(X), cons(Y, Z))) -> mark(sel1(X, Z))
  active(sel1(0, cons(X, Z))) -> mark(quote(X))
  active(first1(0, Z)) -> mark(nil1)
  active(first1(s(X), cons(Y, Z))) -> mark(cons1(quote(Y), first1(X, Z)))
  active(quote(0)) -> mark(01)
  active(quote1(cons(X, Z))) -> mark(cons1(quote(X), quote1(Z)))
  active(quote1(nil)) -> mark(nil1)
  active(quote(s(X))) -> mark(s1(quote(X)))
  active(quote(sel(X, Z))) -> mark(sel1(X, Z))
  active(quote1(first(X, Z))) -> mark(first1(X, Z))
  active(unquote(01)) -> mark(0)
  active(unquote(s1(X))) -> mark(s(unquote(X)))
  active(unquote1(nil1)) -> mark(nil)
  active(unquote1(cons1(X, Z))) -> mark(fcons(unquote(X), unquote1(Z)))
  active(fcons(X, Z)) -> mark(cons(X, Z))
  active(sel(X1, X2)) -> sel(active(X1), X2)
  active(sel(X1, X2)) -> sel(X1, active(X2))
  active(s(X)) -> s(active(X))
  active(cons(X1, X2)) -> cons(active(X1), X2)
  active(first(X1, X2)) -> first(active(X1), X2)
  active(first(X1, X2)) -> first(X1, active(X2))
  active(from(X)) -> from(active(X))
  active(sel1(X1, X2)) -> sel1(active(X1), X2)
  active(sel1(X1, X2)) -> sel1(X1, active(X2))
  active(first1(X1, X2)) -> first1(active(X1), X2)
  active(first1(X1, X2)) -> first1(X1, active(X2))
  active(cons1(X1, X2)) -> cons1(active(X1), X2)
  active(cons1(X1, X2)) -> cons1(X1, active(X2))
  active(s1(X)) -> s1(active(X))
  active(unquote(X)) -> unquote(active(X))
  active(unquote1(X)) -> unquote1(active(X))
  active(fcons(X1, X2)) -> fcons(active(X1), X2)
  active(fcons(X1, X2)) -> fcons(X1, active(X2))
  sel(mark(X1), X2) -> mark(sel(X1, X2))
  sel(X1, mark(X2)) -> mark(sel(X1, X2))
  sel(ok(X1), ok(X2)) -> ok(sel(X1, X2))
  s(mark(X)) -> mark(s(X))
  s(ok(X)) -> ok(s(X))
  cons(mark(X1), X2) -> mark(cons(X1, X2))
  cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
  first(mark(X1), X2) -> mark(first(X1, X2))
  first(X1, mark(X2)) -> mark(first(X1, X2))
  first(ok(X1), ok(X2)) -> ok(first(X1, X2))
  from(mark(X)) -> mark(from(X))
  from(ok(X)) -> ok(from(X))
  sel1(mark(X1), X2) -> mark(sel1(X1, X2))
  sel1(X1, mark(X2)) -> mark(sel1(X1, X2))
  sel1(ok(X1), ok(X2)) -> ok(sel1(X1, X2))
  first1(mark(X1), X2) -> mark(first1(X1, X2))
  first1(X1, mark(X2)) -> mark(first1(X1, X2))
  first1(ok(X1), ok(X2)) -> ok(first1(X1, X2))
  cons1(mark(X1), X2) -> mark(cons1(X1, X2))
  cons1(X1, mark(X2)) -> mark(cons1(X1, X2))
  cons1(ok(X1), ok(X2)) -> ok(cons1(X1, X2))
  s1(mark(X)) -> mark(s1(X))
  s1(ok(X)) -> ok(s1(X))
  unquote(mark(X)) -> mark(unquote(X))
  unquote(ok(X)) -> ok(unquote(X))
  unquote1(mark(X)) -> mark(unquote1(X))
  unquote1(ok(X)) -> ok(unquote1(X))
  fcons(mark(X1), X2) -> mark(fcons(X1, X2))
  fcons(X1, mark(X2)) -> mark(fcons(X1, X2))
  fcons(ok(X1), ok(X2)) -> ok(fcons(X1, X2))
  proper(sel(X1, X2)) -> sel(proper(X1), proper(X2))
  proper(s(X)) -> s(proper(X))
  proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
  proper(0) -> ok(0)
  proper(first(X1, X2)) -> first(proper(X1), proper(X2))
  proper(nil) -> ok(nil)
  proper(from(X)) -> from(proper(X))
  proper(sel1(X1, X2)) -> sel1(proper(X1), proper(X2))
  proper(quote(X)) -> quote(proper(X))
  proper(first1(X1, X2)) -> first1(proper(X1), proper(X2))
  proper(nil1) -> ok(nil1)
  proper(cons1(X1, X2)) -> cons1(proper(X1), proper(X2))
  proper(01) -> ok(01)
  proper(quote1(X)) -> quote1(proper(X))
  proper(s1(X)) -> s1(proper(X))
  proper(unquote(X)) -> unquote(proper(X))
  proper(unquote1(X)) -> unquote1(proper(X))
  proper(fcons(X1, X2)) -> fcons(proper(X1), proper(X2))
  quote(ok(X)) -> ok(quote(X))
  quote1(ok(X)) -> ok(quote1(X))
  top(mark(X)) -> top(proper(X))
  top(ok(X)) -> top(active(X))

  
  
  
• Dependency Pairs:
  

  FIRST1(ok(X1), ok(X2)) -> FIRST1(X1, X2)
  FIRST1(X1, mark(X2)) -> FIRST1(X1, X2)
  FIRST1(mark(X1), X2) -> FIRST1(X1, X2)

  
  Rules:
  

  
  active(sel(s(X), cons(Y, Z))) -> mark(sel(X, Z))
  active(sel(0, cons(X, Z))) -> mark(X)
  active(first(0, Z)) -> mark(nil)
  active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
  active(from(X)) -> mark(cons(X, from(s(X))))
  active(sel1(s(X), cons(Y, Z))) -> mark(sel1(X, Z))
  active(sel1(0, cons(X, Z))) -> mark(quote(X))
  active(first1(0, Z)) -> mark(nil1)
  active(first1(s(X), cons(Y, Z))) -> mark(cons1(quote(Y), first1(X, Z)))
  active(quote(0)) -> mark(01)
  active(quote1(cons(X, Z))) -> mark(cons1(quote(X), quote1(Z)))
  active(quote1(nil)) -> mark(nil1)
  active(quote(s(X))) -> mark(s1(quote(X)))
  active(quote(sel(X, Z))) -> mark(sel1(X, Z))
  active(quote1(first(X, Z))) -> mark(first1(X, Z))
  active(unquote(01)) -> mark(0)
  active(unquote(s1(X))) -> mark(s(unquote(X)))
  active(unquote1(nil1)) -> mark(nil)
  active(unquote1(cons1(X, Z))) -> mark(fcons(unquote(X), unquote1(Z)))
  active(fcons(X, Z)) -> mark(cons(X, Z))
  active(sel(X1, X2)) -> sel(active(X1), X2)
  active(sel(X1, X2)) -> sel(X1, active(X2))
  active(s(X)) -> s(active(X))
  active(cons(X1, X2)) -> cons(active(X1), X2)
  active(first(X1, X2)) -> first(active(X1), X2)
  active(first(X1, X2)) -> first(X1, active(X2))
  active(from(X)) -> from(active(X))
  active(sel1(X1, X2)) -> sel1(active(X1), X2)
  active(sel1(X1, X2)) -> sel1(X1, active(X2))
  active(first1(X1, X2)) -> first1(active(X1), X2)
  active(first1(X1, X2)) -> first1(X1, active(X2))
  active(cons1(X1, X2)) -> cons1(active(X1), X2)
  active(cons1(X1, X2)) -> cons1(X1, active(X2))
  active(s1(X)) -> s1(active(X))
  active(unquote(X)) -> unquote(active(X))
  active(unquote1(X)) -> unquote1(active(X))
  active(fcons(X1, X2)) -> fcons(active(X1), X2)
  active(fcons(X1, X2)) -> fcons(X1, active(X2))
  sel(mark(X1), X2) -> mark(sel(X1, X2))
  sel(X1, mark(X2)) -> mark(sel(X1, X2))
  sel(ok(X1), ok(X2)) -> ok(sel(X1, X2))
  s(mark(X)) -> mark(s(X))
  s(ok(X)) -> ok(s(X))
  cons(mark(X1), X2) -> mark(cons(X1, X2))
  cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
  first(mark(X1), X2) -> mark(first(X1, X2))
  first(X1, mark(X2)) -> mark(first(X1, X2))
  first(ok(X1), ok(X2)) -> ok(first(X1, X2))
  from(mark(X)) -> mark(from(X))
  from(ok(X)) -> ok(from(X))
  sel1(mark(X1), X2) -> mark(sel1(X1, X2))
  sel1(X1, mark(X2)) -> mark(sel1(X1, X2))
  sel1(ok(X1), ok(X2)) -> ok(sel1(X1, X2))
  first1(mark(X1), X2) -> mark(first1(X1, X2))
  first1(X1, mark(X2)) -> mark(first1(X1, X2))
  first1(ok(X1), ok(X2)) -> ok(first1(X1, X2))
  cons1(mark(X1), X2) -> mark(cons1(X1, X2))
  cons1(X1, mark(X2)) -> mark(cons1(X1, X2))
  cons1(ok(X1), ok(X2)) -> ok(cons1(X1, X2))
  s1(mark(X)) -> mark(s1(X))
  s1(ok(X)) -> ok(s1(X))
  unquote(mark(X)) -> mark(unquote(X))
  unquote(ok(X)) -> ok(unquote(X))
  unquote1(mark(X)) -> mark(unquote1(X))
  unquote1(ok(X)) -> ok(unquote1(X))
  fcons(mark(X1), X2) -> mark(fcons(X1, X2))
  fcons(X1, mark(X2)) -> mark(fcons(X1, X2))
  fcons(ok(X1), ok(X2)) -> ok(fcons(X1, X2))
  proper(sel(X1, X2)) -> sel(proper(X1), proper(X2))
  proper(s(X)) -> s(proper(X))
  proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
  proper(0) -> ok(0)
  proper(first(X1, X2)) -> first(proper(X1), proper(X2))
  proper(nil) -> ok(nil)
  proper(from(X)) -> from(proper(X))
  proper(sel1(X1, X2)) -> sel1(proper(X1), proper(X2))
  proper(quote(X)) -> quote(proper(X))
  proper(first1(X1, X2)) -> first1(proper(X1), proper(X2))
  proper(nil1) -> ok(nil1)
  proper(cons1(X1, X2)) -> cons1(proper(X1), proper(X2))
  proper(01) -> ok(01)
  proper(quote1(X)) -> quote1(proper(X))
  proper(s1(X)) -> s1(proper(X))
  proper(unquote(X)) -> unquote(proper(X))
  proper(unquote1(X)) -> unquote1(proper(X))
  proper(fcons(X1, X2)) -> fcons(proper(X1), proper(X2))
  quote(ok(X)) -> ok(quote(X))
  quote1(ok(X)) -> ok(quote1(X))
  top(mark(X)) -> top(proper(X))
  top(ok(X)) -> top(active(X))

  
  
  
• Dependency Pair:
  

  QUOTE1(ok(X)) -> QUOTE1(X)

  
  Rules:
  

  
  active(sel(s(X), cons(Y, Z))) -> mark(sel(X, Z))
  active(sel(0, cons(X, Z))) -> mark(X)
  active(first(0, Z)) -> mark(nil)
  active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
  active(from(X)) -> mark(cons(X, from(s(X))))
  active(sel1(s(X), cons(Y, Z))) -> mark(sel1(X, Z))
  active(sel1(0, cons(X, Z))) -> mark(quote(X))
  active(first1(0, Z)) -> mark(nil1)
  active(first1(s(X), cons(Y, Z))) -> mark(cons1(quote(Y), first1(X, Z)))
  active(quote(0)) -> mark(01)
  active(quote1(cons(X, Z))) -> mark(cons1(quote(X), quote1(Z)))
  active(quote1(nil)) -> mark(nil1)
  active(quote(s(X))) -> mark(s1(quote(X)))
  active(quote(sel(X, Z))) -> mark(sel1(X, Z))
  active(quote1(first(X, Z))) -> mark(first1(X, Z))
  active(unquote(01)) -> mark(0)
  active(unquote(s1(X))) -> mark(s(unquote(X)))
  active(unquote1(nil1)) -> mark(nil)
  active(unquote1(cons1(X, Z))) -> mark(fcons(unquote(X), unquote1(Z)))
  active(fcons(X, Z)) -> mark(cons(X, Z))
  active(sel(X1, X2)) -> sel(active(X1), X2)
  active(sel(X1, X2)) -> sel(X1, active(X2))
  active(s(X)) -> s(active(X))
  active(cons(X1, X2)) -> cons(active(X1), X2)
  active(first(X1, X2)) -> first(active(X1), X2)
  active(first(X1, X2)) -> first(X1, active(X2))
  active(from(X)) -> from(active(X))
  active(sel1(X1, X2)) -> sel1(active(X1), X2)
  active(sel1(X1, X2)) -> sel1(X1, active(X2))
  active(first1(X1, X2)) -> first1(active(X1), X2)
  active(first1(X1, X2)) -> first1(X1, active(X2))
  active(cons1(X1, X2)) -> cons1(active(X1), X2)
  active(cons1(X1, X2)) -> cons1(X1, active(X2))
  active(s1(X)) -> s1(active(X))
  active(unquote(X)) -> unquote(active(X))
  active(unquote1(X)) -> unquote1(active(X))
  active(fcons(X1, X2)) -> fcons(active(X1), X2)
  active(fcons(X1, X2)) -> fcons(X1, active(X2))
  sel(mark(X1), X2) -> mark(sel(X1, X2))
  sel(X1, mark(X2)) -> mark(sel(X1, X2))
  sel(ok(X1), ok(X2)) -> ok(sel(X1, X2))
  s(mark(X)) -> mark(s(X))
  s(ok(X)) -> ok(s(X))
  cons(mark(X1), X2) -> mark(cons(X1, X2))
  cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
  first(mark(X1), X2) -> mark(first(X1, X2))
  first(X1, mark(X2)) -> mark(first(X1, X2))
  first(ok(X1), ok(X2)) -> ok(first(X1, X2))
  from(mark(X)) -> mark(from(X))
  from(ok(X)) -> ok(from(X))
  sel1(mark(X1), X2) -> mark(sel1(X1, X2))
  sel1(X1, mark(X2)) -> mark(sel1(X1, X2))
  sel1(ok(X1), ok(X2)) -> ok(sel1(X1, X2))
  first1(mark(X1), X2) -> mark(first1(X1, X2))
  first1(X1, mark(X2)) -> mark(first1(X1, X2))
  first1(ok(X1), ok(X2)) -> ok(first1(X1, X2))
  cons1(mark(X1), X2) -> mark(cons1(X1, X2))
  cons1(X1, mark(X2)) -> mark(cons1(X1, X2))
  cons1(ok(X1), ok(X2)) -> ok(cons1(X1, X2))
  s1(mark(X)) -> mark(s1(X))
  s1(ok(X)) -> ok(s1(X))
  unquote(mark(X)) -> mark(unquote(X))
  unquote(ok(X)) -> ok(unquote(X))
  unquote1(mark(X)) -> mark(unquote1(X))
  unquote1(ok(X)) -> ok(unquote1(X))
  fcons(mark(X1), X2) -> mark(fcons(X1, X2))
  fcons(X1, mark(X2)) -> mark(fcons(X1, X2))
  fcons(ok(X1), ok(X2)) -> ok(fcons(X1, X2))
  proper(sel(X1, X2)) -> sel(proper(X1), proper(X2))
  proper(s(X)) -> s(proper(X))
  proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
  proper(0) -> ok(0)
  proper(first(X1, X2)) -> first(proper(X1), proper(X2))
  proper(nil) -> ok(nil)
  proper(from(X)) -> from(proper(X))
  proper(sel1(X1, X2)) -> sel1(proper(X1), proper(X2))
  proper(quote(X)) -> quote(proper(X))
  proper(first1(X1, X2)) -> first1(proper(X1), proper(X2))
  proper(nil1) -> ok(nil1)
  proper(cons1(X1, X2)) -> cons1(proper(X1), proper(X2))
  proper(01) -> ok(01)
  proper(quote1(X)) -> quote1(proper(X))
  proper(s1(X)) -> s1(proper(X))
  proper(unquote(X)) -> unquote(proper(X))
  proper(unquote1(X)) -> unquote1(proper(X))
  proper(fcons(X1, X2)) -> fcons(proper(X1), proper(X2))
  quote(ok(X)) -> ok(quote(X))
  quote1(ok(X)) -> ok(quote1(X))
  top(mark(X)) -> top(proper(X))
  top(ok(X)) -> top(active(X))

  
  
  
• Dependency Pairs:
  

  S1(ok(X)) -> S1(X)
  S1(mark(X)) -> S1(X)

  
  Rules:
  

  
  active(sel(s(X), cons(Y, Z))) -> mark(sel(X, Z))
  active(sel(0, cons(X, Z))) -> mark(X)
  active(first(0, Z)) -> mark(nil)
  active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
  active(from(X)) -> mark(cons(X, from(s(X))))
  active(sel1(s(X), cons(Y, Z))) -> mark(sel1(X, Z))
  active(sel1(0, cons(X, Z))) -> mark(quote(X))
  active(first1(0, Z)) -> mark(nil1)
  active(first1(s(X), cons(Y, Z))) -> mark(cons1(quote(Y), first1(X, Z)))
  active(quote(0)) -> mark(01)
  active(quote1(cons(X, Z))) -> mark(cons1(quote(X), quote1(Z)))
  active(quote1(nil)) -> mark(nil1)
  active(quote(s(X))) -> mark(s1(quote(X)))
  active(quote(sel(X, Z))) -> mark(sel1(X, Z))
  active(quote1(first(X, Z))) -> mark(first1(X, Z))
  active(unquote(01)) -> mark(0)
  active(unquote(s1(X))) -> mark(s(unquote(X)))
  active(unquote1(nil1)) -> mark(nil)
  active(unquote1(cons1(X, Z))) -> mark(fcons(unquote(X), unquote1(Z)))
  active(fcons(X, Z)) -> mark(cons(X, Z))
  active(sel(X1, X2)) -> sel(active(X1), X2)
  active(sel(X1, X2)) -> sel(X1, active(X2))
  active(s(X)) -> s(active(X))
  active(cons(X1, X2)) -> cons(active(X1), X2)
  active(first(X1, X2)) -> first(active(X1), X2)
  active(first(X1, X2)) -> first(X1, active(X2))
  active(from(X)) -> from(active(X))
  active(sel1(X1, X2)) -> sel1(active(X1), X2)
  active(sel1(X1, X2)) -> sel1(X1, active(X2))
  active(first1(X1, X2)) -> first1(active(X1), X2)
  active(first1(X1, X2)) -> first1(X1, active(X2))
  active(cons1(X1, X2)) -> cons1(active(X1), X2)
  active(cons1(X1, X2)) -> cons1(X1, active(X2))
  active(s1(X)) -> s1(active(X))
  active(unquote(X)) -> unquote(active(X))
  active(unquote1(X)) -> unquote1(active(X))
  active(fcons(X1, X2)) -> fcons(active(X1), X2)
  active(fcons(X1, X2)) -> fcons(X1, active(X2))
  sel(mark(X1), X2) -> mark(sel(X1, X2))
  sel(X1, mark(X2)) -> mark(sel(X1, X2))
  sel(ok(X1), ok(X2)) -> ok(sel(X1, X2))
  s(mark(X)) -> mark(s(X))
  s(ok(X)) -> ok(s(X))
  cons(mark(X1), X2) -> mark(cons(X1, X2))
  cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
  first(mark(X1), X2) -> mark(first(X1, X2))
  first(X1, mark(X2)) -> mark(first(X1, X2))
  first(ok(X1), ok(X2)) -> ok(first(X1, X2))
  from(mark(X)) -> mark(from(X))
  from(ok(X)) -> ok(from(X))
  sel1(mark(X1), X2) -> mark(sel1(X1, X2))
  sel1(X1, mark(X2)) -> mark(sel1(X1, X2))
  sel1(ok(X1), ok(X2)) -> ok(sel1(X1, X2))
  first1(mark(X1), X2) -> mark(first1(X1, X2))
  first1(X1, mark(X2)) -> mark(first1(X1, X2))
  first1(ok(X1), ok(X2)) -> ok(first1(X1, X2))
  cons1(mark(X1), X2) -> mark(cons1(X1, X2))
  cons1(X1, mark(X2)) -> mark(cons1(X1, X2))
  cons1(ok(X1), ok(X2)) -> ok(cons1(X1, X2))
  s1(mark(X)) -> mark(s1(X))
  s1(ok(X)) -> ok(s1(X))
  unquote(mark(X)) -> mark(unquote(X))
  unquote(ok(X)) -> ok(unquote(X))
  unquote1(mark(X)) -> mark(unquote1(X))
  unquote1(ok(X)) -> ok(unquote1(X))
  fcons(mark(X1), X2) -> mark(fcons(X1, X2))
  fcons(X1, mark(X2)) -> mark(fcons(X1, X2))
  fcons(ok(X1), ok(X2)) -> ok(fcons(X1, X2))
  proper(sel(X1, X2)) -> sel(proper(X1), proper(X2))
  proper(s(X)) -> s(proper(X))
  proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
  proper(0) -> ok(0)
  proper(first(X1, X2)) -> first(proper(X1), proper(X2))
  proper(nil) -> ok(nil)
  proper(from(X)) -> from(proper(X))
  proper(sel1(X1, X2)) -> sel1(proper(X1), proper(X2))
  proper(quote(X)) -> quote(proper(X))
  proper(first1(X1, X2)) -> first1(proper(X1), proper(X2))
  proper(nil1) -> ok(nil1)
  proper(cons1(X1, X2)) -> cons1(proper(X1), proper(X2))
  proper(01) -> ok(01)
  proper(quote1(X)) -> quote1(proper(X))
  proper(s1(X)) -> s1(proper(X))
  proper(unquote(X)) -> unquote(proper(X))
  proper(unquote1(X)) -> unquote1(proper(X))
  proper(fcons(X1, X2)) -> fcons(proper(X1), proper(X2))
  quote(ok(X)) -> ok(quote(X))
  quote1(ok(X)) -> ok(quote1(X))
  top(mark(X)) -> top(proper(X))
  top(ok(X)) -> top(active(X))

  
  
  
• Dependency Pairs:
  

  UNQUOTE(ok(X)) -> UNQUOTE(X)
  UNQUOTE(mark(X)) -> UNQUOTE(X)

  
  Rules:
  

  
  active(sel(s(X), cons(Y, Z))) -> mark(sel(X, Z))
  active(sel(0, cons(X, Z))) -> mark(X)
  active(first(0, Z)) -> mark(nil)
  active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
  active(from(X)) -> mark(cons(X, from(s(X))))
  active(sel1(s(X), cons(Y, Z))) -> mark(sel1(X, Z))
  active(sel1(0, cons(X, Z))) -> mark(quote(X))
  active(first1(0, Z)) -> mark(nil1)
  active(first1(s(X), cons(Y, Z))) -> mark(cons1(quote(Y), first1(X, Z)))
  active(quote(0)) -> mark(01)
  active(quote1(cons(X, Z))) -> mark(cons1(quote(X), quote1(Z)))
  active(quote1(nil)) -> mark(nil1)
  active(quote(s(X))) -> mark(s1(quote(X)))
  active(quote(sel(X, Z))) -> mark(sel1(X, Z))
  active(quote1(first(X, Z))) -> mark(first1(X, Z))
  active(unquote(01)) -> mark(0)
  active(unquote(s1(X))) -> mark(s(unquote(X)))
  active(unquote1(nil1)) -> mark(nil)
  active(unquote1(cons1(X, Z))) -> mark(fcons(unquote(X), unquote1(Z)))
  active(fcons(X, Z)) -> mark(cons(X, Z))
  active(sel(X1, X2)) -> sel(active(X1), X2)
  active(sel(X1, X2)) -> sel(X1, active(X2))
  active(s(X)) -> s(active(X))
  active(cons(X1, X2)) -> cons(active(X1), X2)
  active(first(X1, X2)) -> first(active(X1), X2)
  active(first(X1, X2)) -> first(X1, active(X2))
  active(from(X)) -> from(active(X))
  active(sel1(X1, X2)) -> sel1(active(X1), X2)
  active(sel1(X1, X2)) -> sel1(X1, active(X2))
  active(first1(X1, X2)) -> first1(active(X1), X2)
  active(first1(X1, X2)) -> first1(X1, active(X2))
  active(cons1(X1, X2)) -> cons1(active(X1), X2)
  active(cons1(X1, X2)) -> cons1(X1, active(X2))
  active(s1(X)) -> s1(active(X))
  active(unquote(X)) -> unquote(active(X))
  active(unquote1(X)) -> unquote1(active(X))
  active(fcons(X1, X2)) -> fcons(active(X1), X2)
  active(fcons(X1, X2)) -> fcons(X1, active(X2))
  sel(mark(X1), X2) -> mark(sel(X1, X2))
  sel(X1, mark(X2)) -> mark(sel(X1, X2))
  sel(ok(X1), ok(X2)) -> ok(sel(X1, X2))
  s(mark(X)) -> mark(s(X))
  s(ok(X)) -> ok(s(X))
  cons(mark(X1), X2) -> mark(cons(X1, X2))
  cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
  first(mark(X1), X2) -> mark(first(X1, X2))
  first(X1, mark(X2)) -> mark(first(X1, X2))
  first(ok(X1), ok(X2)) -> ok(first(X1, X2))
  from(mark(X)) -> mark(from(X))
  from(ok(X)) -> ok(from(X))
  sel1(mark(X1), X2) -> mark(sel1(X1, X2))
  sel1(X1, mark(X2)) -> mark(sel1(X1, X2))
  sel1(ok(X1), ok(X2)) -> ok(sel1(X1, X2))
  first1(mark(X1), X2) -> mark(first1(X1, X2))
  first1(X1, mark(X2)) -> mark(first1(X1, X2))
  first1(ok(X1), ok(X2)) -> ok(first1(X1, X2))
  cons1(mark(X1), X2) -> mark(cons1(X1, X2))
  cons1(X1, mark(X2)) -> mark(cons1(X1, X2))
  cons1(ok(X1), ok(X2)) -> ok(cons1(X1, X2))
  s1(mark(X)) -> mark(s1(X))
  s1(ok(X)) -> ok(s1(X))
  unquote(mark(X)) -> mark(unquote(X))
  unquote(ok(X)) -> ok(unquote(X))
  unquote1(mark(X)) -> mark(unquote1(X))
  unquote1(ok(X)) -> ok(unquote1(X))
  fcons(mark(X1), X2) -> mark(fcons(X1, X2))
  fcons(X1, mark(X2)) -> mark(fcons(X1, X2))
  fcons(ok(X1), ok(X2)) -> ok(fcons(X1, X2))
  proper(sel(X1, X2)) -> sel(proper(X1), proper(X2))
  proper(s(X)) -> s(proper(X))
  proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
  proper(0) -> ok(0)
  proper(first(X1, X2)) -> first(proper(X1), proper(X2))
  proper(nil) -> ok(nil)
  proper(from(X)) -> from(proper(X))
  proper(sel1(X1, X2)) -> sel1(proper(X1), proper(X2))
  proper(quote(X)) -> quote(proper(X))
  proper(first1(X1, X2)) -> first1(proper(X1), proper(X2))
  proper(nil1) -> ok(nil1)
  proper(cons1(X1, X2)) -> cons1(proper(X1), proper(X2))
  proper(01) -> ok(01)
  proper(quote1(X)) -> quote1(proper(X))
  proper(s1(X)) -> s1(proper(X))
  proper(unquote(X)) -> unquote(proper(X))
  proper(unquote1(X)) -> unquote1(proper(X))
  proper(fcons(X1, X2)) -> fcons(proper(X1), proper(X2))
  quote(ok(X)) -> ok(quote(X))
  quote1(ok(X)) -> ok(quote1(X))
  top(mark(X)) -> top(proper(X))
  top(ok(X)) -> top(active(X))

  
  
  
• Dependency Pairs:
  

  FCONS(ok(X1), ok(X2)) -> FCONS(X1, X2)
  FCONS(X1, mark(X2)) -> FCONS(X1, X2)
  FCONS(mark(X1), X2) -> FCONS(X1, X2)

  
  Rules:
  

  
  active(sel(s(X), cons(Y, Z))) -> mark(sel(X, Z))
  active(sel(0, cons(X, Z))) -> mark(X)
  active(first(0, Z)) -> mark(nil)
  active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
  active(from(X)) -> mark(cons(X, from(s(X))))
  active(sel1(s(X), cons(Y, Z))) -> mark(sel1(X, Z))
  active(sel1(0, cons(X, Z))) -> mark(quote(X))
  active(first1(0, Z)) -> mark(nil1)
  active(first1(s(X), cons(Y, Z))) -> mark(cons1(quote(Y), first1(X, Z)))
  active(quote(0)) -> mark(01)
  active(quote1(cons(X, Z))) -> mark(cons1(quote(X), quote1(Z)))
  active(quote1(nil)) -> mark(nil1)
  active(quote(s(X))) -> mark(s1(quote(X)))
  active(quote(sel(X, Z))) -> mark(sel1(X, Z))
  active(quote1(first(X, Z))) -> mark(first1(X, Z))
  active(unquote(01)) -> mark(0)
  active(unquote(s1(X))) -> mark(s(unquote(X)))
  active(unquote1(nil1)) -> mark(nil)
  active(unquote1(cons1(X, Z))) -> mark(fcons(unquote(X), unquote1(Z)))
  active(fcons(X, Z)) -> mark(cons(X, Z))
  active(sel(X1, X2)) -> sel(active(X1), X2)
  active(sel(X1, X2)) -> sel(X1, active(X2))
  active(s(X)) -> s(active(X))
  active(cons(X1, X2)) -> cons(active(X1), X2)
  active(first(X1, X2)) -> first(active(X1), X2)
  active(first(X1, X2)) -> first(X1, active(X2))
  active(from(X)) -> from(active(X))
  active(sel1(X1, X2)) -> sel1(active(X1), X2)
  active(sel1(X1, X2)) -> sel1(X1, active(X2))
  active(first1(X1, X2)) -> first1(active(X1), X2)
  active(first1(X1, X2)) -> first1(X1, active(X2))
  active(cons1(X1, X2)) -> cons1(active(X1), X2)
  active(cons1(X1, X2)) -> cons1(X1, active(X2))
  active(s1(X)) -> s1(active(X))
  active(unquote(X)) -> unquote(active(X))
  active(unquote1(X)) -> unquote1(active(X))
  active(fcons(X1, X2)) -> fcons(active(X1), X2)
  active(fcons(X1, X2)) -> fcons(X1, active(X2))
  sel(mark(X1), X2) -> mark(sel(X1, X2))
  sel(X1, mark(X2)) -> mark(sel(X1, X2))
  sel(ok(X1), ok(X2)) -> ok(sel(X1, X2))
  s(mark(X)) -> mark(s(X))
  s(ok(X)) -> ok(s(X))
  cons(mark(X1), X2) -> mark(cons(X1, X2))
  cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
  first(mark(X1), X2) -> mark(first(X1, X2))
  first(X1, mark(X2)) -> mark(first(X1, X2))
  first(ok(X1), ok(X2)) -> ok(first(X1, X2))
  from(mark(X)) -> mark(from(X))
  from(ok(X)) -> ok(from(X))
  sel1(mark(X1), X2) -> mark(sel1(X1, X2))
  sel1(X1, mark(X2)) -> mark(sel1(X1, X2))
  sel1(ok(X1), ok(X2)) -> ok(sel1(X1, X2))
  first1(mark(X1), X2) -> mark(first1(X1, X2))
  first1(X1, mark(X2)) -> mark(first1(X1, X2))
  first1(ok(X1), ok(X2)) -> ok(first1(X1, X2))
  cons1(mark(X1), X2) -> mark(cons1(X1, X2))
  cons1(X1, mark(X2)) -> mark(cons1(X1, X2))
  cons1(ok(X1), ok(X2)) -> ok(cons1(X1, X2))
  s1(mark(X)) -> mark(s1(X))
  s1(ok(X)) -> ok(s1(X))
  unquote(mark(X)) -> mark(unquote(X))
  unquote(ok(X)) -> ok(unquote(X))
  unquote1(mark(X)) -> mark(unquote1(X))
  unquote1(ok(X)) -> ok(unquote1(X))
  fcons(mark(X1), X2) -> mark(fcons(X1, X2))
  fcons(X1, mark(X2)) -> mark(fcons(X1, X2))
  fcons(ok(X1), ok(X2)) -> ok(fcons(X1, X2))
  proper(sel(X1, X2)) -> sel(proper(X1), proper(X2))
  proper(s(X)) -> s(proper(X))
  proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
  proper(0) -> ok(0)
  proper(first(X1, X2)) -> first(proper(X1), proper(X2))
  proper(nil) -> ok(nil)
  proper(from(X)) -> from(proper(X))
  proper(sel1(X1, X2)) -> sel1(proper(X1), proper(X2))
  proper(quote(X)) -> quote(proper(X))
  proper(first1(X1, X2)) -> first1(proper(X1), proper(X2))
  proper(nil1) -> ok(nil1)
  proper(cons1(X1, X2)) -> cons1(proper(X1), proper(X2))
  proper(01) -> ok(01)
  proper(quote1(X)) -> quote1(proper(X))
  proper(s1(X)) -> s1(proper(X))
  proper(unquote(X)) -> unquote(proper(X))
  proper(unquote1(X)) -> unquote1(proper(X))
  proper(fcons(X1, X2)) -> fcons(proper(X1), proper(X2))
  quote(ok(X)) -> ok(quote(X))
  quote1(ok(X)) -> ok(quote1(X))
  top(mark(X)) -> top(proper(X))
  top(ok(X)) -> top(active(X))

  
  
  
• Dependency Pairs:
  

  UNQUOTE1(ok(X)) -> UNQUOTE1(X)
  UNQUOTE1(mark(X)) -> UNQUOTE1(X)

  
  Rules:
  

  
  active(sel(s(X), cons(Y, Z))) -> mark(sel(X, Z))
  active(sel(0, cons(X, Z))) -> mark(X)
  active(first(0, Z)) -> mark(nil)
  active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
  active(from(X)) -> mark(cons(X, from(s(X))))
  active(sel1(s(X), cons(Y, Z))) -> mark(sel1(X, Z))
  active(sel1(0, cons(X, Z))) -> mark(quote(X))
  active(first1(0, Z)) -> mark(nil1)
  active(first1(s(X), cons(Y, Z))) -> mark(cons1(quote(Y), first1(X, Z)))
  active(quote(0)) -> mark(01)
  active(quote1(cons(X, Z))) -> mark(cons1(quote(X), quote1(Z)))
  active(quote1(nil)) -> mark(nil1)
  active(quote(s(X))) -> mark(s1(quote(X)))
  active(quote(sel(X, Z))) -> mark(sel1(X, Z))
  active(quote1(first(X, Z))) -> mark(first1(X, Z))
  active(unquote(01)) -> mark(0)
  active(unquote(s1(X))) -> mark(s(unquote(X)))
  active(unquote1(nil1)) -> mark(nil)
  active(unquote1(cons1(X, Z))) -> mark(fcons(unquote(X), unquote1(Z)))
  active(fcons(X, Z)) -> mark(cons(X, Z))
  active(sel(X1, X2)) -> sel(active(X1), X2)
  active(sel(X1, X2)) -> sel(X1, active(X2))
  active(s(X)) -> s(active(X))
  active(cons(X1, X2)) -> cons(active(X1), X2)
  active(first(X1, X2)) -> first(active(X1), X2)
  active(first(X1, X2)) -> first(X1, active(X2))
  active(from(X)) -> from(active(X))
  active(sel1(X1, X2)) -> sel1(active(X1), X2)
  active(sel1(X1, X2)) -> sel1(X1, active(X2))
  active(first1(X1, X2)) -> first1(active(X1), X2)
  active(first1(X1, X2)) -> first1(X1, active(X2))
  active(cons1(X1, X2)) -> cons1(active(X1), X2)
  active(cons1(X1, X2)) -> cons1(X1, active(X2))
  active(s1(X)) -> s1(active(X))
  active(unquote(X)) -> unquote(active(X))
  active(unquote1(X)) -> unquote1(active(X))
  active(fcons(X1, X2)) -> fcons(active(X1), X2)
  active(fcons(X1, X2)) -> fcons(X1, active(X2))
  sel(mark(X1), X2) -> mark(sel(X1, X2))
  sel(X1, mark(X2)) -> mark(sel(X1, X2))
  sel(ok(X1), ok(X2)) -> ok(sel(X1, X2))
  s(mark(X)) -> mark(s(X))
  s(ok(X)) -> ok(s(X))
  cons(mark(X1), X2) -> mark(cons(X1, X2))
  cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
  first(mark(X1), X2) -> mark(first(X1, X2))
  first(X1, mark(X2)) -> mark(first(X1, X2))
  first(ok(X1), ok(X2)) -> ok(first(X1, X2))
  from(mark(X)) -> mark(from(X))
  from(ok(X)) -> ok(from(X))
  sel1(mark(X1), X2) -> mark(sel1(X1, X2))
  sel1(X1, mark(X2)) -> mark(sel1(X1, X2))
  sel1(ok(X1), ok(X2)) -> ok(sel1(X1, X2))
  first1(mark(X1), X2) -> mark(first1(X1, X2))
  first1(X1, mark(X2)) -> mark(first1(X1, X2))
  first1(ok(X1), ok(X2)) -> ok(first1(X1, X2))
  cons1(mark(X1), X2) -> mark(cons1(X1, X2))
  cons1(X1, mark(X2)) -> mark(cons1(X1, X2))
  cons1(ok(X1), ok(X2)) -> ok(cons1(X1, X2))
  s1(mark(X)) -> mark(s1(X))
  s1(ok(X)) -> ok(s1(X))
  unquote(mark(X)) -> mark(unquote(X))
  unquote(ok(X)) -> ok(unquote(X))
  unquote1(mark(X)) -> mark(unquote1(X))
  unquote1(ok(X)) -> ok(unquote1(X))
  fcons(mark(X1), X2) -> mark(fcons(X1, X2))
  fcons(X1, mark(X2)) -> mark(fcons(X1, X2))
  fcons(ok(X1), ok(X2)) -> ok(fcons(X1, X2))
  proper(sel(X1, X2)) -> sel(proper(X1), proper(X2))
  proper(s(X)) -> s(proper(X))
  proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
  proper(0) -> ok(0)
  proper(first(X1, X2)) -> first(proper(X1), proper(X2))
  proper(nil) -> ok(nil)
  proper(from(X)) -> from(proper(X))
  proper(sel1(X1, X2)) -> sel1(proper(X1), proper(X2))
  proper(quote(X)) -> quote(proper(X))
  proper(first1(X1, X2)) -> first1(proper(X1), proper(X2))
  proper(nil1) -> ok(nil1)
  proper(cons1(X1, X2)) -> cons1(proper(X1), proper(X2))
  proper(01) -> ok(01)
  proper(quote1(X)) -> quote1(proper(X))
  proper(s1(X)) -> s1(proper(X))
  proper(unquote(X)) -> unquote(proper(X))
  proper(unquote1(X)) -> unquote1(proper(X))
  proper(fcons(X1, X2)) -> fcons(proper(X1), proper(X2))
  quote(ok(X)) -> ok(quote(X))
  quote1(ok(X)) -> ok(quote1(X))
  top(mark(X)) -> top(proper(X))
  top(ok(X)) -> top(active(X))

  
  
  
• Dependency Pairs:
  

  ACTIVE(fcons(X1, X2)) -> ACTIVE(X2)
  ACTIVE(fcons(X1, X2)) -> ACTIVE(X1)
  ACTIVE(unquote1(X)) -> ACTIVE(X)
  ACTIVE(unquote(X)) -> ACTIVE(X)
  ACTIVE(s1(X)) -> ACTIVE(X)
  ACTIVE(cons1(X1, X2)) -> ACTIVE(X2)
  ACTIVE(cons1(X1, X2)) -> ACTIVE(X1)
  ACTIVE(first1(X1, X2)) -> ACTIVE(X2)
  ACTIVE(first1(X1, X2)) -> ACTIVE(X1)
  ACTIVE(sel1(X1, X2)) -> ACTIVE(X2)
  ACTIVE(sel1(X1, X2)) -> ACTIVE(X1)
  ACTIVE(from(X)) -> ACTIVE(X)
  ACTIVE(first(X1, X2)) -> ACTIVE(X2)
  ACTIVE(first(X1, X2)) -> ACTIVE(X1)
  ACTIVE(cons(X1, X2)) -> ACTIVE(X1)
  ACTIVE(s(X)) -> ACTIVE(X)
  ACTIVE(sel(X1, X2)) -> ACTIVE(X2)
  ACTIVE(sel(X1, X2)) -> ACTIVE(X1)

  
  Rules:
  

  
  active(sel(s(X), cons(Y, Z))) -> mark(sel(X, Z))
  active(sel(0, cons(X, Z))) -> mark(X)
  active(first(0, Z)) -> mark(nil)
  active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
  active(from(X)) -> mark(cons(X, from(s(X))))
  active(sel1(s(X), cons(Y, Z))) -> mark(sel1(X, Z))
  active(sel1(0, cons(X, Z))) -> mark(quote(X))
  active(first1(0, Z)) -> mark(nil1)
  active(first1(s(X), cons(Y, Z))) -> mark(cons1(quote(Y), first1(X, Z)))
  active(quote(0)) -> mark(01)
  active(quote1(cons(X, Z))) -> mark(cons1(quote(X), quote1(Z)))
  active(quote1(nil)) -> mark(nil1)
  active(quote(s(X))) -> mark(s1(quote(X)))
  active(quote(sel(X, Z))) -> mark(sel1(X, Z))
  active(quote1(first(X, Z))) -> mark(first1(X, Z))
  active(unquote(01)) -> mark(0)
  active(unquote(s1(X))) -> mark(s(unquote(X)))
  active(unquote1(nil1)) -> mark(nil)
  active(unquote1(cons1(X, Z))) -> mark(fcons(unquote(X), unquote1(Z)))
  active(fcons(X, Z)) -> mark(cons(X, Z))
  active(sel(X1, X2)) -> sel(active(X1), X2)
  active(sel(X1, X2)) -> sel(X1, active(X2))
  active(s(X)) -> s(active(X))
  active(cons(X1, X2)) -> cons(active(X1), X2)
  active(first(X1, X2)) -> first(active(X1), X2)
  active(first(X1, X2)) -> first(X1, active(X2))
  active(from(X)) -> from(active(X))
  active(sel1(X1, X2)) -> sel1(active(X1), X2)
  active(sel1(X1, X2)) -> sel1(X1, active(X2))
  active(first1(X1, X2)) -> first1(active(X1), X2)
  active(first1(X1, X2)) -> first1(X1, active(X2))
  active(cons1(X1, X2)) -> cons1(active(X1), X2)
  active(cons1(X1, X2)) -> cons1(X1, active(X2))
  active(s1(X)) -> s1(active(X))
  active(unquote(X)) -> unquote(active(X))
  active(unquote1(X)) -> unquote1(active(X))
  active(fcons(X1, X2)) -> fcons(active(X1), X2)
  active(fcons(X1, X2)) -> fcons(X1, active(X2))
  sel(mark(X1), X2) -> mark(sel(X1, X2))
  sel(X1, mark(X2)) -> mark(sel(X1, X2))
  sel(ok(X1), ok(X2)) -> ok(sel(X1, X2))
  s(mark(X)) -> mark(s(X))
  s(ok(X)) -> ok(s(X))
  cons(mark(X1), X2) -> mark(cons(X1, X2))
  cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
  first(mark(X1), X2) -> mark(first(X1, X2))
  first(X1, mark(X2)) -> mark(first(X1, X2))
  first(ok(X1), ok(X2)) -> ok(first(X1, X2))
  from(mark(X)) -> mark(from(X))
  from(ok(X)) -> ok(from(X))
  sel1(mark(X1), X2) -> mark(sel1(X1, X2))
  sel1(X1, mark(X2)) -> mark(sel1(X1, X2))
  sel1(ok(X1), ok(X2)) -> ok(sel1(X1, X2))
  first1(mark(X1), X2) -> mark(first1(X1, X2))
  first1(X1, mark(X2)) -> mark(first1(X1, X2))
  first1(ok(X1), ok(X2)) -> ok(first1(X1, X2))
  cons1(mark(X1), X2) -> mark(cons1(X1, X2))
  cons1(X1, mark(X2)) -> mark(cons1(X1, X2))
  cons1(ok(X1), ok(X2)) -> ok(cons1(X1, X2))
  s1(mark(X)) -> mark(s1(X))
  s1(ok(X)) -> ok(s1(X))
  unquote(mark(X)) -> mark(unquote(X))
  unquote(ok(X)) -> ok(unquote(X))
  unquote1(mark(X)) -> mark(unquote1(X))
  unquote1(ok(X)) -> ok(unquote1(X))
  fcons(mark(X1), X2) -> mark(fcons(X1, X2))
  fcons(X1, mark(X2)) -> mark(fcons(X1, X2))
  fcons(ok(X1), ok(X2)) -> ok(fcons(X1, X2))
  proper(sel(X1, X2)) -> sel(proper(X1), proper(X2))
  proper(s(X)) -> s(proper(X))
  proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
  proper(0) -> ok(0)
  proper(first(X1, X2)) -> first(proper(X1), proper(X2))
  proper(nil) -> ok(nil)
  proper(from(X)) -> from(proper(X))
  proper(sel1(X1, X2)) -> sel1(proper(X1), proper(X2))
  proper(quote(X)) -> quote(proper(X))
  proper(first1(X1, X2)) -> first1(proper(X1), proper(X2))
  proper(nil1) -> ok(nil1)
  proper(cons1(X1, X2)) -> cons1(proper(X1), proper(X2))
  proper(01) -> ok(01)
  proper(quote1(X)) -> quote1(proper(X))
  proper(s1(X)) -> s1(proper(X))
  proper(unquote(X)) -> unquote(proper(X))
  proper(unquote1(X)) -> unquote1(proper(X))
  proper(fcons(X1, X2)) -> fcons(proper(X1), proper(X2))
  quote(ok(X)) -> ok(quote(X))
  quote1(ok(X)) -> ok(quote1(X))
  top(mark(X)) -> top(proper(X))
  top(ok(X)) -> top(active(X))

  
  
  
• Dependency Pairs:
  

  PROPER(fcons(X1, X2)) -> PROPER(X2)
  PROPER(fcons(X1, X2)) -> PROPER(X1)
  PROPER(unquote1(X)) -> PROPER(X)
  PROPER(unquote(X)) -> PROPER(X)
  PROPER(s1(X)) -> PROPER(X)
  PROPER(quote1(X)) -> PROPER(X)
  PROPER(cons1(X1, X2)) -> PROPER(X2)
  PROPER(cons1(X1, X2)) -> PROPER(X1)
  PROPER(first1(X1, X2)) -> PROPER(X2)
  PROPER(first1(X1, X2)) -> PROPER(X1)
  PROPER(quote(X)) -> PROPER(X)
  PROPER(sel1(X1, X2)) -> PROPER(X2)
  PROPER(sel1(X1, X2)) -> PROPER(X1)
  PROPER(from(X)) -> PROPER(X)
  PROPER(first(X1, X2)) -> PROPER(X2)
  PROPER(first(X1, X2)) -> PROPER(X1)
  PROPER(cons(X1, X2)) -> PROPER(X2)
  PROPER(cons(X1, X2)) -> PROPER(X1)
  PROPER(s(X)) -> PROPER(X)
  PROPER(sel(X1, X2)) -> PROPER(X2)
  PROPER(sel(X1, X2)) -> PROPER(X1)

  
  Rules:
  

  
  active(sel(s(X), cons(Y, Z))) -> mark(sel(X, Z))
  active(sel(0, cons(X, Z))) -> mark(X)
  active(first(0, Z)) -> mark(nil)
  active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
  active(from(X)) -> mark(cons(X, from(s(X))))
  active(sel1(s(X), cons(Y, Z))) -> mark(sel1(X, Z))
  active(sel1(0, cons(X, Z))) -> mark(quote(X))
  active(first1(0, Z)) -> mark(nil1)
  active(first1(s(X), cons(Y, Z))) -> mark(cons1(quote(Y), first1(X, Z)))
  active(quote(0)) -> mark(01)
  active(quote1(cons(X, Z))) -> mark(cons1(quote(X), quote1(Z)))
  active(quote1(nil)) -> mark(nil1)
  active(quote(s(X))) -> mark(s1(quote(X)))
  active(quote(sel(X, Z))) -> mark(sel1(X, Z))
  active(quote1(first(X, Z))) -> mark(first1(X, Z))
  active(unquote(01)) -> mark(0)
  active(unquote(s1(X))) -> mark(s(unquote(X)))
  active(unquote1(nil1)) -> mark(nil)
  active(unquote1(cons1(X, Z))) -> mark(fcons(unquote(X), unquote1(Z)))
  active(fcons(X, Z)) -> mark(cons(X, Z))
  active(sel(X1, X2)) -> sel(active(X1), X2)
  active(sel(X1, X2)) -> sel(X1, active(X2))
  active(s(X)) -> s(active(X))
  active(cons(X1, X2)) -> cons(active(X1), X2)
  active(first(X1, X2)) -> first(active(X1), X2)
  active(first(X1, X2)) -> first(X1, active(X2))
  active(from(X)) -> from(active(X))
  active(sel1(X1, X2)) -> sel1(active(X1), X2)
  active(sel1(X1, X2)) -> sel1(X1, active(X2))
  active(first1(X1, X2)) -> first1(active(X1), X2)
  active(first1(X1, X2)) -> first1(X1, active(X2))
  active(cons1(X1, X2)) -> cons1(active(X1), X2)
  active(cons1(X1, X2)) -> cons1(X1, active(X2))
  active(s1(X)) -> s1(active(X))
  active(unquote(X)) -> unquote(active(X))
  active(unquote1(X)) -> unquote1(active(X))
  active(fcons(X1, X2)) -> fcons(active(X1), X2)
  active(fcons(X1, X2)) -> fcons(X1, active(X2))
  sel(mark(X1), X2) -> mark(sel(X1, X2))
  sel(X1, mark(X2)) -> mark(sel(X1, X2))
  sel(ok(X1), ok(X2)) -> ok(sel(X1, X2))
  s(mark(X)) -> mark(s(X))
  s(ok(X)) -> ok(s(X))
  cons(mark(X1), X2) -> mark(cons(X1, X2))
  cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
  first(mark(X1), X2) -> mark(first(X1, X2))
  first(X1, mark(X2)) -> mark(first(X1, X2))
  first(ok(X1), ok(X2)) -> ok(first(X1, X2))
  from(mark(X)) -> mark(from(X))
  from(ok(X)) -> ok(from(X))
  sel1(mark(X1), X2) -> mark(sel1(X1, X2))
  sel1(X1, mark(X2)) -> mark(sel1(X1, X2))
  sel1(ok(X1), ok(X2)) -> ok(sel1(X1, X2))
  first1(mark(X1), X2) -> mark(first1(X1, X2))
  first1(X1, mark(X2)) -> mark(first1(X1, X2))
  first1(ok(X1), ok(X2)) -> ok(first1(X1, X2))
  cons1(mark(X1), X2) -> mark(cons1(X1, X2))
  cons1(X1, mark(X2)) -> mark(cons1(X1, X2))
  cons1(ok(X1), ok(X2)) -> ok(cons1(X1, X2))
  s1(mark(X)) -> mark(s1(X))
  s1(ok(X)) -> ok(s1(X))
  unquote(mark(X)) -> mark(unquote(X))
  unquote(ok(X)) -> ok(unquote(X))
  unquote1(mark(X)) -> mark(unquote1(X))
  unquote1(ok(X)) -> ok(unquote1(X))
  fcons(mark(X1), X2) -> mark(fcons(X1, X2))
  fcons(X1, mark(X2)) -> mark(fcons(X1, X2))
  fcons(ok(X1), ok(X2)) -> ok(fcons(X1, X2))
  proper(sel(X1, X2)) -> sel(proper(X1), proper(X2))
  proper(s(X)) -> s(proper(X))
  proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
  proper(0) -> ok(0)
  proper(first(X1, X2)) -> first(proper(X1), proper(X2))
  proper(nil) -> ok(nil)
  proper(from(X)) -> from(proper(X))
  proper(sel1(X1, X2)) -> sel1(proper(X1), proper(X2))
  proper(quote(X)) -> quote(proper(X))
  proper(first1(X1, X2)) -> first1(proper(X1), proper(X2))
  proper(nil1) -> ok(nil1)
  proper(cons1(X1, X2)) -> cons1(proper(X1), proper(X2))
  proper(01) -> ok(01)
  proper(quote1(X)) -> quote1(proper(X))
  proper(s1(X)) -> s1(proper(X))
  proper(unquote(X)) -> unquote(proper(X))
  proper(unquote1(X)) -> unquote1(proper(X))
  proper(fcons(X1, X2)) -> fcons(proper(X1), proper(X2))
  quote(ok(X)) -> ok(quote(X))
  quote1(ok(X)) -> ok(quote1(X))
  top(mark(X)) -> top(proper(X))
  top(ok(X)) -> top(active(X))

  
  
  
• Dependency Pairs:
  

  TOP(ok(X)) -> TOP(active(X))
  TOP(mark(X)) -> TOP(proper(X))

  
  Rules:
  

  
  active(sel(s(X), cons(Y, Z))) -> mark(sel(X, Z))
  active(sel(0, cons(X, Z))) -> mark(X)
  active(first(0, Z)) -> mark(nil)
  active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
  active(from(X)) -> mark(cons(X, from(s(X))))
  active(sel1(s(X), cons(Y, Z))) -> mark(sel1(X, Z))
  active(sel1(0, cons(X, Z))) -> mark(quote(X))
  active(first1(0, Z)) -> mark(nil1)
  active(first1(s(X), cons(Y, Z))) -> mark(cons1(quote(Y), first1(X, Z)))
  active(quote(0)) -> mark(01)
  active(quote1(cons(X, Z))) -> mark(cons1(quote(X), quote1(Z)))
  active(quote1(nil)) -> mark(nil1)
  active(quote(s(X))) -> mark(s1(quote(X)))
  active(quote(sel(X, Z))) -> mark(sel1(X, Z))
  active(quote1(first(X, Z))) -> mark(first1(X, Z))
  active(unquote(01)) -> mark(0)
  active(unquote(s1(X))) -> mark(s(unquote(X)))
  active(unquote1(nil1)) -> mark(nil)
  active(unquote1(cons1(X, Z))) -> mark(fcons(unquote(X), unquote1(Z)))
  active(fcons(X, Z)) -> mark(cons(X, Z))
  active(sel(X1, X2)) -> sel(active(X1), X2)
  active(sel(X1, X2)) -> sel(X1, active(X2))
  active(s(X)) -> s(active(X))
  active(cons(X1, X2)) -> cons(active(X1), X2)
  active(first(X1, X2)) -> first(active(X1), X2)
  active(first(X1, X2)) -> first(X1, active(X2))
  active(from(X)) -> from(active(X))
  active(sel1(X1, X2)) -> sel1(active(X1), X2)
  active(sel1(X1, X2)) -> sel1(X1, active(X2))
  active(first1(X1, X2)) -> first1(active(X1), X2)
  active(first1(X1, X2)) -> first1(X1, active(X2))
  active(cons1(X1, X2)) -> cons1(active(X1), X2)
  active(cons1(X1, X2)) -> cons1(X1, active(X2))
  active(s1(X)) -> s1(active(X))
  active(unquote(X)) -> unquote(active(X))
  active(unquote1(X)) -> unquote1(active(X))
  active(fcons(X1, X2)) -> fcons(active(X1), X2)
  active(fcons(X1, X2)) -> fcons(X1, active(X2))
  sel(mark(X1), X2) -> mark(sel(X1, X2))
  sel(X1, mark(X2)) -> mark(sel(X1, X2))
  sel(ok(X1), ok(X2)) -> ok(sel(X1, X2))
  s(mark(X)) -> mark(s(X))
  s(ok(X)) -> ok(s(X))
  cons(mark(X1), X2) -> mark(cons(X1, X2))
  cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
  first(mark(X1), X2) -> mark(first(X1, X2))
  first(X1, mark(X2)) -> mark(first(X1, X2))
  first(ok(X1), ok(X2)) -> ok(first(X1, X2))
  from(mark(X)) -> mark(from(X))
  from(ok(X)) -> ok(from(X))
  sel1(mark(X1), X2) -> mark(sel1(X1, X2))
  sel1(X1, mark(X2)) -> mark(sel1(X1, X2))
  sel1(ok(X1), ok(X2)) -> ok(sel1(X1, X2))
  first1(mark(X1), X2) -> mark(first1(X1, X2))
  first1(X1, mark(X2)) -> mark(first1(X1, X2))
  first1(ok(X1), ok(X2)) -> ok(first1(X1, X2))
  cons1(mark(X1), X2) -> mark(cons1(X1, X2))
  cons1(X1, mark(X2)) -> mark(cons1(X1, X2))
  cons1(ok(X1), ok(X2)) -> ok(cons1(X1, X2))
  s1(mark(X)) -> mark(s1(X))
  s1(ok(X)) -> ok(s1(X))
  unquote(mark(X)) -> mark(unquote(X))
  unquote(ok(X)) -> ok(unquote(X))
  unquote1(mark(X)) -> mark(unquote1(X))
  unquote1(ok(X)) -> ok(unquote1(X))
  fcons(mark(X1), X2) -> mark(fcons(X1, X2))
  fcons(X1, mark(X2)) -> mark(fcons(X1, X2))
  fcons(ok(X1), ok(X2)) -> ok(fcons(X1, X2))
  proper(sel(X1, X2)) -> sel(proper(X1), proper(X2))
  proper(s(X)) -> s(proper(X))
  proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
  proper(0) -> ok(0)
  proper(first(X1, X2)) -> first(proper(X1), proper(X2))
  proper(nil) -> ok(nil)
  proper(from(X)) -> from(proper(X))
  proper(sel1(X1, X2)) -> sel1(proper(X1), proper(X2))
  proper(quote(X)) -> quote(proper(X))
  proper(first1(X1, X2)) -> first1(proper(X1), proper(X2))
  proper(nil1) -> ok(nil1)
  proper(cons1(X1, X2)) -> cons1(proper(X1), proper(X2))
  proper(01) -> ok(01)
  proper(quote1(X)) -> quote1(proper(X))
  proper(s1(X)) -> s1(proper(X))
  proper(unquote(X)) -> unquote(proper(X))
  proper(unquote1(X)) -> unquote1(proper(X))
  proper(fcons(X1, X2)) -> fcons(proper(X1), proper(X2))
  quote(ok(X)) -> ok(quote(X))
  quote1(ok(X)) -> ok(quote1(X))
  top(mark(X)) -> top(proper(X))
  top(ok(X)) -> top(active(X))