Term Rewriting System R:
[x, y]
f(x, y) -> f(x, x)
f(s(x), y) -> f(y, x)
Innermost Termination of R to be shown.
R
↳Dependency Pair Analysis
R contains the following Dependency Pairs:
F(x, y) -> F(x, x)
F(s(x), y) -> F(y, x)
Furthermore, R contains one SCC.
R
↳DPs
→DP Problem 1
↳Usable Rules (Innermost)
Dependency Pairs:
F(s(x), y) -> F(y, x)
F(x, y) -> F(x, x)
Rules:
f(x, y) -> f(x, x)
f(s(x), y) -> f(y, x)
Strategy:
innermost
As we are in the innermost case, we can delete all 2 non-usable-rules.
R
↳DPs
→DP Problem 1
↳UsableRules
→DP Problem 2
↳Non Termination
Dependency Pairs:
F(s(x), y) -> F(y, x)
F(x, y) -> F(x, x)
Rule:
none
Strategy:
innermost
Found an infinite P-chain over R:
P =
F(s(x), y) -> F(y, x)
F(x, y) -> F(x, x)
R = none
s = F(x', x')
evaluates to t =F(x', x')
Thus, s starts an infinite chain.
Innermost Non-Termination of R could be shown.
Duration:
0:00 minutes