Term Rewriting System R:
[X, Y]
f(g(X), Y) -> f(X, f(g(X), Y))
Innermost Termination of R to be shown.
R
↳Dependency Pair Analysis
R contains the following Dependency Pairs:
F(g(X), Y) -> F(X, f(g(X), Y))
F(g(X), Y) -> F(g(X), Y)
Furthermore, R contains one SCC.
R
↳DPs
→DP Problem 1
↳Argument Filtering and Ordering
Dependency Pairs:
F(g(X), Y) -> F(g(X), Y)
F(g(X), Y) -> F(X, f(g(X), Y))
Rule:
f(g(X), Y) -> f(X, f(g(X), Y))
Strategy:
innermost
The following dependency pair can be strictly oriented:
F(g(X), Y) -> F(X, f(g(X), Y))
The following usable rule for innermost w.r.t. to the AFS can be oriented:
f(g(X), Y) -> f(X, f(g(X), Y))
Used ordering: Lexicographic Path Order with Non-Strict Precedence with Quasi Precedence:
trivial
resulting in one new DP problem.
Used Argument Filtering System: F(x1, x2) -> F(x1, x2)
g(x1) -> g(x1)
f(x1, x2) -> x1
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳Remaining Obligation(s)
The following remains to be proven:
Dependency Pair:
F(g(X), Y) -> F(g(X), Y)
Rule:
f(g(X), Y) -> f(X, f(g(X), Y))
Strategy:
innermost
Innermost Termination of R could not be shown.
Duration:
0:00 minutes