YES Confluence Proof

Confluence Proof

by csi

Input

The rewrite relation of the following TRS is considered.

f(a,a) → b
a → a'
f(a',x) → f(x,x)
f(x,a') → f(x,x)
f(a',a') → b
b → f(a',a')

Proof

1 Redundant Rules Transformation

To prove that the TRS is (non-)confluent, we show (non-)confluence of the following modified system:

a → a'
f(a',x) → f(x,x)
f(x,a') → f(x,x)
b → f(a',a')

All redundant rules that were added or removed can be simulated in 4 steps .

1.1 Critical Pair Closing System

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

There are no rules.

1.1.1 R is empty

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

Tool configuration

csi