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(cons1(X,cons(Y,Z))) -> Y
(2) 2nd(cons(X,X1)) -> 2nd(cons1(X,activate(X1)))
(3) from(X) -> cons(X,n__from(s(X)))
(4) from(X) -> n__from(X)
(5) activate(n__from(X)) -> from(X)
(6) activate(X) -> X

[2]  Eliminate dummy symbol <s>, to obtain the following TRS:
(1) 2nd(cons1(X,cons(Y,Z))) -> Y
(2) 2nd(cons(X,X1)) -> 2nd(cons1(X,activate(X1)))
(3a) from(X) -> cons(X,n__from(#0))
(3b) from(X) -> #1(X)
(4) from(X) -> n__from(X)
(5) activate(n__from(X)) -> from(X)
(6) 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:
[from(x)] = x + 1
[n__from(x)] = x + 1
rest default

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

[5]  Label this TRS using following interpretation that is a model:
[2nd(x)] = 0
[cons1(x,y)] = 1
[cons(x,y)] = 0
[from(x)] = 0
[n__from(x)] = 0
rest default

  thus obtaining new TRS:
(2a) 2nd$0(cons$11(X,X1)) -> 2nd$1(cons1$11(X,activate$1(X1)))
(2b) 2nd$0(cons$10(X,X1)) -> 2nd$1(cons1$10(X,activate$0(X1)))
(2c) 2nd$0(cons$01(X,X1)) -> 2nd$1(cons1$01(X,activate$1(X1)))
(2d) 2nd$0(cons$00(X,X1)) -> 2nd$1(cons1$00(X,activate$0(X1)))
(3aa) from$1(X) -> cons$10(X,n__from$0(#0))
(3ab) from$0(X) -> cons$00(X,n__from$0(#0))
(4a) from$1(X) -> n__from$1(X)
(4b) from$0(X) -> n__from$0(X)
(5a) activate$0(n__from$1(X)) -> from$1(X)
(5b) activate$0(n__from$0(X)) -> from$0(X)
(6a) activate$1(X) -> X
(6b) activate$0(X) -> X

[6]  Use following polynomial interpretation:
[cons$01(x,y)] = x + y + 1
rest default

  Remove rules with left hand side strictly bigger than right hand side:
(2c)

[7]  Use following polynomial interpretation:
[2nd$0(x)] = x + 1
rest default

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

[8]  Unlabel this TRS to obtain the one consisting of the rules:
(3)-(6)

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

  Remove rules with left hand side strictly bigger than right hand side:
(5)-(6)

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

  Remove rules with left hand side strictly bigger than right hand side:
(3)-(4)

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

../tpdb/TRS/TRCSR/Ex6_9_Luc02c_Z.trs, 0.01, Y
Couldn't open file <60>: 60: No such file or directory