Term Rewriting System R:
[x, y, z]
f(s(a), s(b), x) -> f(x, x, x)
g(f(s(x), s(y), z)) -> g(f(x, y, z))
cons(x, y) -> x
cons(x, y) -> y
Innermost Termination of R to be shown.
R
↳Dependency Pair Analysis
R contains the following Dependency Pairs:
F(s(a), s(b), x) -> F(x, x, x)
G(f(s(x), s(y), z)) -> G(f(x, y, z))
G(f(s(x), s(y), z)) -> F(x, y, z)
Furthermore, R contains one SCC.
R
↳DPs
→DP Problem 1
↳Usable Rules (Innermost)
Dependency Pair:
G(f(s(x), s(y), z)) -> G(f(x, y, z))
Rules:
f(s(a), s(b), x) -> f(x, x, x)
g(f(s(x), s(y), z)) -> g(f(x, y, z))
cons(x, y) -> x
cons(x, y) -> y
Strategy:
innermost
As we are in the innermost case, we can delete all 3 non-usable-rules.
R
↳DPs
→DP Problem 1
↳UsableRules
→DP Problem 2
↳Remaining Obligation(s)
The following remains to be proven:
Dependency Pair:
G(f(s(x), s(y), z)) -> G(f(x, y, z))
Rule:
f(s(a), s(b), x) -> f(x, x, x)
Strategy:
innermost
Innermost Termination of R could not be shown.
Duration:
0:16 minutes