YES Confluence Proof

Confluence Proof

by csi

Input

The rewrite relation of the following TRS is considered.

a c
b c
f(a,b) d
f(x,c) f(c,c)
f(c,x) f(c,c)
d f(a,c)
d f(c,b)

Proof

1 Redundant Rules Transformation

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

a c
b c
f(x,c) f(c,c)
f(c,x) f(c,c)
d f(c,b)

All redundant rules that were added or removed can be simulated in 4 steps .

1.1 Critical Pair Closing System

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

There are no rules.

1.1.1 R is empty

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

Tool configuration

csi