YES Confluence Proof

Confluence Proof

by csi

Input

The rewrite relation of the following TRS is considered.

f(i(x),g(a)) f(j(x,x),g(b))
b a
i(x) j(x,x)

Proof

1 Redundant Rules Transformation

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

i(x) j(x,x)
b a
f(i(x),g(a)) f(j(x,x),g(b))
f(i(x),g(a)) f(j(x,x),g(a))

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:

b a

1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[a] = 0
[b] = 1
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