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(c(s(x),y)) -> f(c(x,s(y)))
(2) g(c(x,s(y))) -> g(c(s(x),y))
(3) g(s(f(x))) -> g(f(x))

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

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

[3]  Apply the Dependency Pair transformation resulting in the following dependency pairs:
<F(c(s(x),y)), F(c(x,s(y)))>
<G(c(x,s(y))), G(c(s(x),y))>
 and 2 SCCs in the dependency graph. Proofs for those SCCs follow.

[3a-1]  Consider the following SCC obtained from analysis of dependency graph:
(1) f(c(s(x),y)) ->= f(c(x,s(y)))
(2) g(c(x,s(y))) ->= g(c(s(x),y))
(DP2) G(c(x,s(y))) -> G(c(s(x),y))

[3a-2]  Use following polynomial interpretation:
[f(x)] = 2
[c(x,y)] = y
[s(x)] = x + 1
rest default

  Remove rules with left hand side strictly bigger than right hand side:
(2), (DP2)

[3a-3]  Since there are no remaining strict rules, relative termination is proved!

[3b-1]  Consider the following SCC obtained from analysis of dependency graph:
(1) f(c(s(x),y)) ->= f(c(x,s(y)))
(2) g(c(x,s(y))) ->= g(c(s(x),y))
(DP1) F(c(s(x),y)) -> F(c(x,s(y)))

[3b-2]  Use following polynomial interpretation:
[c(x,y)] = x
[s(x)] = x + 1
[g(x)] = 2
rest default

  Remove rules with left hand side strictly bigger than right hand side:
(1), (DP1)

[3b-3]  Since there are no remaining strict rules, relative termination is proved!



../tpdb/TRS/nontermin/AG01/#4.37a.trs, 0.01, Y
Couldn't open file <60>: 60: No such file or directory