YES Confluence Proof

Confluence Proof

by csi

Input

The rewrite relation of the following TRS is considered.

b c
a a

Proof

1 Persistent Decomposition (Many-Sorted)

Confluence is proven, because the maximal systems induced by the sorts in the following many-sorted sort attachment are confluent.
b : 0
c : 0
a : 1
The subsystems are

(1.1)

b c

(1.2)

a a

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.

1.2 Redundant Rules Transformation

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

There are no rules.

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

1.2.1 Parallel Closed

Confluence is proven since the TRS is (almost) parallel closed. The joins can be performed by approximating rewrite sequences by a parallel rewrite step.

Tool configuration

csi