YES
  TPA v.1.0

Result: TRS is terminating

Default interpretations for symbols are not printed. For polynomial interpretations
and semantic labelling over N\{0,1} defaults are 2 for constants, identity for unary
symbols and x+y-2 for binary symbols. For semantic labelling over {0,1} (booleans)
defaults are 0 for constants, identity for unary symbols and disjunction for binary symbols.

[1]  TRS loaded from input file:
(1) 2nd(cons(X,n__cons(Y,Z))) -> activate(Y)
(2) from(X) -> cons(X,n__from(s(X)))
(3) cons(X1,X2) -> n__cons(X1,X2)
(4) from(X) -> n__from(X)
(5) activate(n__cons(X1,X2)) -> cons(X1,X2)
(6) activate(n__from(X)) -> from(X)
(7) activate(X) -> X

[2]  Eliminate dummy symbol <s>, to obtain the following TRS:
(1) 2nd(cons(X,n__cons(Y,Z))) -> activate(Y)
(2a) from(X) -> cons(X,n__from(#0))
(2b) from(X) -> #1(X)
(3) cons(X1,X2) -> n__cons(X1,X2)
(4) from(X) -> n__from(X)
(5) activate(n__cons(X1,X2)) -> cons(X1,X2)
(6) activate(n__from(X)) -> from(X)
(7) activate(X) -> X

[3]  Use following polynomial interpretation:
[2nd(x)] = x + 1
rest default

  Remove rules with left hand side strictly bigger than right hand side:
(1)

[4]  Use following polynomial interpretation:
[activate(x)] = x + 1
rest default

  Remove rules with left hand side strictly bigger than right hand side:
(5)-(7)

[5]  Use following polynomial interpretation:
[from(x)] = x + 1
rest default

  Remove rules with left hand side strictly bigger than right hand side:
(2a)-(2b), (4)

[6]  Use following polynomial interpretation:
[cons(x,y)] = x + y + 1
rest default

  Remove rules with left hand side strictly bigger than right hand side:
(3)

[7]  Since there are no remaining rules, termination is proved!

../tpdb/TRS/TRCSR/Ex1_2_Luc02c_Z.trs, 0., Y
Couldn't open file <60>: 60: No such file or directory