YES

The TRS could be proven terminating. The proof took 27 ms.

The following DP Processors were used


Problem 1 was processed with processor DependencyGraph (7ms).
 | – Problem 2 was processed with processor SubtermCriterion (0ms).

Problem 1: DependencyGraph



Dependency Pair Problem

Dependency Pairs

f#(a)f#(c(a))f#(a)f#(d(a))
f#(c(a))f#(d(b))f#(c(b))f#(d(a))
e#(g(X))e#(X)

Rewrite Rules

f(a)f(c(a))f(c(X))X
f(c(a))f(d(b))f(a)f(d(a))
f(d(X))Xf(c(b))f(d(a))
e(g(X))e(X)

Original Signature

Termination of terms over the following signature is verified: f, g, d, e, b, c, a

Strategy


The following SCCs where found

e#(g(X)) → e#(X)

Problem 2: SubtermCriterion



Dependency Pair Problem

Dependency Pairs

e#(g(X))e#(X)

Rewrite Rules

f(a)f(c(a))f(c(X))X
f(c(a))f(d(b))f(a)f(d(a))
f(d(X))Xf(c(b))f(d(a))
e(g(X))e(X)

Original Signature

Termination of terms over the following signature is verified: f, g, d, e, b, c, a

Strategy


Projection

The following projection was used:

Thus, the following dependency pairs are removed:

e#(g(X))e#(X)