Term Rewriting System R:
[X]
f(a) -> f(c(a))
f(c(X)) -> X
f(c(a)) -> f(d(b))
f(a) -> f(d(a))
f(d(X)) -> X
f(c(b)) -> f(d(a))
e(g(X)) -> e(X)
Termination of R to be shown.
R
↳Dependency Pair Analysis
R contains the following Dependency Pairs:
F(a) -> F(c(a))
F(c(a)) -> F(d(b))
F(a) -> F(d(a))
F(c(b)) -> F(d(a))
E(g(X)) -> E(X)
Furthermore, R contains one SCC.
R
↳DPs
→DP Problem 1
↳Argument Filtering and Ordering
Dependency Pair:
E(g(X)) -> E(X)
Rules:
f(a) -> f(c(a))
f(c(X)) -> X
f(c(a)) -> f(d(b))
f(a) -> f(d(a))
f(d(X)) -> X
f(c(b)) -> f(d(a))
e(g(X)) -> e(X)
The following dependency pair can be strictly oriented:
E(g(X)) -> E(X)
There are no usable rules w.r.t. to the AFS that need to be oriented.
Used ordering: Polynomial ordering with Polynomial interpretation:
POL(E(x1)) | = x1 |
POL(g(x1)) | = 1 + x1 |
resulting in one new DP problem.
Used Argument Filtering System: E(x1) -> E(x1)
g(x1) -> g(x1)
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳Dependency Graph
Dependency Pair:
Rules:
f(a) -> f(c(a))
f(c(X)) -> X
f(c(a)) -> f(d(b))
f(a) -> f(d(a))
f(d(X)) -> X
f(c(b)) -> f(d(a))
e(g(X)) -> e(X)
Using the Dependency Graph resulted in no new DP problems.
Termination of R successfully shown.
Duration:
0:00 minutes