YES Confluence Proof

Confluence Proof

by csi

Input

The rewrite relation of the following TRS is considered.

f(f(a)) f(f(f(a)))
f(f(a)) f(a)

Proof

1 Critical Pair Closing System

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

f(f(a)) f(a)

1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[f(x1)] = 1 · x1 + 1
[a] = 7
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