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(a,a) -> f(a,b)
(2) f(a,b) -> f(s(a),c)
(3) f(s(X),c) -> f(X,c)
(4) f(c,c) -> f(a,a)

[2]  Label this TRS using following interpretation over N\{0,1}:
[f(x,y)] = 2
[c] = 3
rest default

  This interpretation is a model and yields following TRS:
(1) f{2,2}(a,a) -> f{2,2}(a,b)
(2) f{2,2}(a,b) -> f{2,3}(s{2}(a),c)
(3) f{i,3}(s{i}(X),c) -> f{i,3}(X,c)
(4) f{3,3}(c,c) -> f{2,2}(a,a)

[3]  Use following polynomial interpretation:
[f_{i,j}(x,y)] = x + y - 2 + i
[s_{i}(x)] = x
rest default

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

[4]  Unlabel this TRS to obtain the one consisting of the rules:
(1)-(3)

[5]  Use following polynomial interpretation:
[a] = 3
rest default

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

[6]  Use following polynomial interpretation:
[b] = 3
rest default

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

[7]  Use following polynomial interpretation:
[s(x)] = x + 1
rest default

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

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

../tpdb/TRS/Rubio/test4.trs, 0.01, Y
Couldn't open file <60>: 60: No such file or directory