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