YES Confluence Proof

Confluence Proof

by csi

Input

The rewrite relation of the following TRS is considered.

or(x,T) → T
or(x,F) → x
or(x,y) → or(y,x)

Proof

1 Redundant Rules Transformation

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

or(x,y) → or(y,x)
or(x,F) → x
or(x,T) → T
or(T,x) → T
or(F,x) → x

All redundant rules that were added or removed can be simulated in 2 steps .

1.1 Critical Pair Closing System

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

or(F,x) → x
or(T,x) → T
or(x,T) → T
or(x,F) → x

1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[or(x1, x2)] = 4 · x1 + 1 · x2 + 0
[T] = 0
[F] = 4
the rules
or(T,x) → T
or(x,T) → T
remain.

1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[or(x1, x2)] = 4 · x1 + 2 · x2 + 6
[T] = 5
all rules could be removed.

1.1.1.1.1 R is empty

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

Tool configuration

csi