YES

The TRS could be proven terminating. The proof took 19 ms.

The following DP Processors were used


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

Problem 1: SubtermCriterion



Dependency Pair Problem

Dependency Pairs

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

Rewrite Rules

if(true, x, y)xif(false, x, y)y
if(x, y, y)yif(if(x, y, z), u, v)if(x, if(y, u, v), if(z, u, v))

Original Signature

Termination of terms over the following signature is verified: v, u, if, true, false

Strategy


Projection

The following projection was used:

Thus, the following dependency pairs are removed:

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