Term Rewriting System R:
[x, y, z]
f(x, y, z) -> g(x, y, z)
g(0, 1, x) -> f(x, x, x)
a -> b
a -> c
Termination of R to be shown.
R
↳Dependency Pair Analysis
R contains the following Dependency Pairs:
F(x, y, z) -> G(x, y, z)
G(0, 1, x) -> F(x, x, x)
Furthermore, R contains one SCC.
R
↳DPs
→DP Problem 1
↳Forward Instantiation Transformation
Dependency Pairs:
G(0, 1, x) -> F(x, x, x)
F(x, y, z) -> G(x, y, z)
Rules:
f(x, y, z) -> g(x, y, z)
g(0, 1, x) -> f(x, x, x)
a -> b
a -> c
On this DP problem, a Forward Instantiation SCC transformation can be performed.
As a result of transforming the rule
F(x, y, z) -> G(x, y, z)
one new Dependency Pair
is created:
F(0, 1, z') -> G(0, 1, z')
The transformation is resulting in one new DP problem:
R
↳DPs
→DP Problem 1
↳FwdInst
→DP Problem 2
↳Forward Instantiation Transformation
Dependency Pairs:
F(0, 1, z') -> G(0, 1, z')
G(0, 1, x) -> F(x, x, x)
Rules:
f(x, y, z) -> g(x, y, z)
g(0, 1, x) -> f(x, x, x)
a -> b
a -> c
On this DP problem, a Forward Instantiation SCC transformation can be performed.
As a result of transforming the rule
G(0, 1, x) -> F(x, x, x)
no new Dependency Pairs
are created.
The transformation is resulting in no new DP problems.
Termination of R successfully shown.
Duration:
0:00 minutes