Certification Problem

Input (COPS 4)

We consider the TRS containing the following rules:

or(true,true) → true (1)
or(x,y) → or(y,x) (2)

The underlying signature is as follows:

{or/2, true/0}

Property / Task

Prove or disprove confluence.

Answer / Result

Yes.

Proof (by csi @ CoCo 2021)

1 Critical Pair Closing System

Confluence is proven using the following terminating critical-pair-closing-system R:

or(true,true) → true (1)

1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[or(x1, x2)] = 1 · x1 + 2 · x2 + 1
[true] = 4
all of the following rules can be deleted.
or(true,true) → true (1)

1.1.1 R is empty

There are no rules in the TRS. Hence, it is terminating.