NO

Problem 1:

(VAR vu95NonEmpty x y)
(RULES
b -> b
f(x,y) -> g(x) | c(g(x)) ->* c(a)
f(x,y) -> h(x) | c(h(x)) ->* c(a)
g(s(x)) -> x
h(s(x)) -> x
)

Problem 1:
Valid CTRS Processor:
-> Rules:
 b -> b
 f(x,y) -> g(x) | c(g(x)) ->* c(a)
 f(x,y) -> h(x) | c(h(x)) ->* c(a)
 g(s(x)) -> x
 h(s(x)) -> x
-> The system is a 2-CTRS.

Problem 1:
-> Pairs:
 B -> B
 F(x,y) -> G(x) | c(g(x)) ->* c(a)
 F(x,y) -> H(x) | c(h(x)) ->* c(a)
-> QPairs:
 Empty
-> Rules:
 b -> b
 f(x,y) -> g(x) | c(g(x)) ->* c(a)
 f(x,y) -> h(x) | c(h(x)) ->* c(a)
 g(s(x)) -> x
 h(s(x)) -> x

Problem 1:

SCC Processor:
-> Pairs:
 B -> B
 F(x,y) -> G(x) | c(g(x)) ->* c(a)
 F(x,y) -> H(x) | c(h(x)) ->* c(a)
-> QPairs:
 Empty
-> Rules:
 b -> b
 f(x,y) -> g(x) | c(g(x)) ->* c(a)
 f(x,y) -> h(x) | c(h(x)) ->* c(a)
 g(s(x)) -> x
 h(s(x)) -> x
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 B -> B
-> QPairs:
 Empty
->->-> Rules:
 b -> b
 f(x,y) -> g(x) | c(g(x)) ->* c(a)
 f(x,y) -> h(x) | c(h(x)) ->* c(a)
 g(s(x)) -> x
 h(s(x)) -> x

Problem 1:

Infiniteness Processor:
-> Pairs:
 B -> B
-> QPairs:
 Empty
-> Rules:
 b -> b
 f(x,y) -> g(x) | c(g(x)) ->* c(a)
 f(x,y) -> h(x) | c(h(x)) ->* c(a)
 g(s(x)) -> x
 h(s(x)) -> x
-> Pairs in cycle:
 B -> B

The problem is infinite.
29.90user 0.27system 0:30.47elapsed 99%CPU (0avgtext+0avgdata 89200maxresident)k
26320inputs+120outputs (117major+24002minor)pagefaults 0swaps