Term Rewriting System R:
[x, y, z]
f(x, y, z) -> g(<=(x, y), x, y, z)
g(true, x, y, z) -> z
g(false, x, y, z) -> f(f(p(x), y, z), f(p(y), z, x), f(p(z), x, y))
p(0) -> 0
p(s(x)) -> x
Termination of R to be shown.
R
↳Overlay and local confluence Check
The TRS is overlay and locally confluent (all critical pairs are trivially joinable).Hence, we can switch to innermost.
R
↳OC
→TRS2
↳Dependency Pair Analysis
R contains the following Dependency Pairs:
F(x, y, z) -> G(<=(x, y), x, y, z)
G(false, x, y, z) -> F(f(p(x), y, z), f(p(y), z, x), f(p(z), x, y))
G(false, x, y, z) -> F(p(x), y, z)
G(false, x, y, z) -> P(x)
G(false, x, y, z) -> F(p(y), z, x)
G(false, x, y, z) -> P(y)
G(false, x, y, z) -> F(p(z), x, y)
G(false, x, y, z) -> P(z)
R contains no SCCs.
Termination of R successfully shown.
Duration:
0:00 minutes