YES Confluence Proof

Confluence Proof

by csi

Input

The rewrite relation of the following TRS is considered.

F(c(x)) G(x)
G(x) F(x)
c(x) x

Proof

1 Critical Pair Closing System

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

G(x) F(x)

1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[F(x1)] = 4 · x1 + 0
[G(x1)] = 4 · x1 + 1
all rules could be removed.

1.1.1 R is empty

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

Tool configuration

csi