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