Term Rewriting System R:
[]
g(a) -> g(b)
b -> f(a, a)
f(a, a) -> g(d)
Termination of R to be shown.
R
↳Dependency Pair Analysis
R contains the following Dependency Pairs:
G(a) -> G(b)
G(a) -> B
B -> F(a, a)
F(a, a) -> G(d)
Furthermore, R contains one SCC.
R
↳DPs
→DP Problem 1
↳Argument Filtering and Ordering
Dependency Pair:
G(a) -> G(b)
Rules:
g(a) -> g(b)
b -> f(a, a)
f(a, a) -> g(d)
The following dependency pair can be strictly oriented:
G(a) -> G(b)
The following usable rules using the Ce-refinement can be oriented:
b -> f(a, a)
f(a, a) -> g(d)
g(a) -> g(b)
Used ordering: Lexicographic Path Order with Non-Strict Precedence with Quasi Precedence:
a > {f, b} > d
a > {f, b} > g
resulting in one new DP problem.
Used Argument Filtering System: G(x1) -> G(x1)
b -> b
f(x1, x2) -> f
g(x1) -> g(x1)
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳Dependency Graph
Dependency Pair:
Rules:
g(a) -> g(b)
b -> f(a, a)
f(a, a) -> g(d)
Using the Dependency Graph resulted in no new DP problems.
Termination of R successfully shown.
Duration:
0:00 minutes