Term Rewriting System R:
[x, y]
f(x, g(x)) -> x
f(x, h(y)) -> f(h(x), y)
Innermost Termination of R to be shown.
R
↳Dependency Pair Analysis
R contains the following Dependency Pairs:
F(x, h(y)) -> F(h(x), y)
Furthermore, R contains one SCC.
R
↳DPs
→DP Problem 1
↳Argument Filtering and Ordering
Dependency Pair:
F(x, h(y)) -> F(h(x), y)
Rules:
f(x, g(x)) -> x
f(x, h(y)) -> f(h(x), y)
Strategy:
innermost
The following dependency pair can be strictly oriented:
F(x, h(y)) -> F(h(x), y)
There are no usable rules for innermost w.r.t. to the AFS that need to be oriented.
Used ordering: Homeomorphic Embedding Order with EMB
resulting in one new DP problem.
Used Argument Filtering System: F(x1, x2) -> x2
h(x1) -> h(x1)
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳Dependency Graph
Dependency Pair:
Rules:
f(x, g(x)) -> x
f(x, h(y)) -> f(h(x), y)
Strategy:
innermost
Using the Dependency Graph resulted in no new DP problems.
Innermost Termination of R successfully shown.
Duration:
0:00 minutes