Term Rewriting System R:
[x, y]
f(x, x) -> f(i(x), g(g(x)))
f(x, y) -> x
f(x, i(x)) -> f(x, x)
f(i(x), i(g(x))) -> a
g(x) -> i(x)
Innermost Termination of R to be shown.
R
↳Dependency Pair Analysis
R contains the following Dependency Pairs:
F(x, x) -> F(i(x), g(g(x)))
F(x, x) -> G(g(x))
F(x, x) -> G(x)
F(x, i(x)) -> F(x, x)
Furthermore, R contains one SCC.
R
↳DPs
→DP Problem 1
↳Remaining Obligation(s)
The following remains to be proven:
Dependency Pairs:
F(x, i(x)) -> F(x, x)
F(x, x) -> F(i(x), g(g(x)))
Rules:
f(x, x) -> f(i(x), g(g(x)))
f(x, y) -> x
f(x, i(x)) -> f(x, x)
f(i(x), i(g(x))) -> a
g(x) -> i(x)
Strategy:
innermost
Innermost Termination of R could not be shown.
Duration:
0:00 minutes