YES

Problem 1:

(VAR x)
(STRATEGY CONTEXTSENSITIVE
 (a)
 (b)
 (c)
 (d)
 (f 1)
 (g 1 2)
 (h 1 2)
)
(RULES
 a -> c
 a -> d
 b -> c
 b -> d
 f(x) -> x | x -> c
 g(x,x) -> h(x,x)
 h(x,f(x)) -> x
)


Problem 1:

Dependency Pair Processor:
-> Rules:
 a -> c
 a -> d
 b -> c
 b -> d
 f(x) -> x | x -> c
 g(x,x) -> h(x,x)
 h(x,f(x)) -> x
-> Infeasible Rules:
 Empty.
-> Equations:
 Empty.
-> Horn Clauses:
 Empty.

Problem 1:

SCC Processor:
-> Rules:
 a -> c
 a -> d
 b -> c
 b -> d
 f(x) -> x | x -> c
 g(x,x) -> h(x,x)
 h(x,f(x)) -> x
-> Infeasible Rules:
 Empty.
-> Equations:
 Empty.
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.
19.87user 0.19system 0:20.20elapsed 99%CPU (0avgtext+0avgdata 460548maxresident)k
9872inputs+96outputs (43major+53432minor)pagefaults 0swaps