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) f(X) -> if`1(X,if`2(c,n__f(true)))
(2) if`1(true,if`2(X,Y)) -> X
(3) if`1(false,if`2(X,Y)) -> activate(Y)
(4) f(X) -> n__f(X)
(5) activate(n__f(X)) -> f(X)
(6) activate(X) -> X

[2]  Use following polynomial interpretation:
[false] = 3
rest default

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

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

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

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

  Remove rules with left hand side strictly bigger than right hand side:
(1), (4)

[5]  Use following polynomial interpretation:
[if`1(x,y)] = x + y + 1
rest default

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

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

../tpdb/TRS/TRCSR/Ex5_Zan97_Z.trs, 0., Y
Couldn't open file <60>: 60: No such file or directory