YES

The TRS could be proven terminating. The proof took 17 ms.

The following DP Processors were used


Problem 1 was processed with processor SubtermCriterion (1ms).

Problem 1: SubtermCriterion



Dependency Pair Problem

Dependency Pairs

f#(f(x, y, z), u, f(x, y, v))f#(z, u, v)f#(f(x, y, z), u, f(x, y, v))f#(x, y, f(z, u, v))

Rewrite Rules

f(f(x, y, z), u, f(x, y, v))f(x, y, f(z, u, v))f(x, y, y)y
f(x, y, g(y))xf(x, x, y)x
f(g(x), x, y)y

Original Signature

Termination of terms over the following signature is verified: f, g

Strategy


Projection

The following projection was used:

Thus, the following dependency pairs are removed:

f#(f(x, y, z), u, f(x, y, v))f#(z, u, v)f#(f(x, y, z), u, f(x, y, v))f#(x, y, f(z, u, v))