YES Confluence Proof

Confluence Proof

by csi

Input

The rewrite relation of the following TRS is considered.

W(B(x)) W(x)
B(I(x)) J(x)
W(I(x)) W(J(x))

Proof

1 Redundant Rules Transformation

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

W(I(x)) W(J(x))
B(I(x)) J(x)
W(B(x)) W(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:

W(I(x)) W(J(x))

1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[W(x1)] = 4 · x1 + 2
[J(x1)] = 1 · x1 + 1
[I(x1)] = 1 · x1 + 2
all rules could be removed.

1.1.1.1 R is empty

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

Tool configuration

csi