YES Confluence Proof

Confluence Proof

by csi

Input

The rewrite relation of the following TRS is considered.

c → b
a → a
b → b
f(f(a)) → c

Proof

1 Redundant Rules Transformation

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

f(f(a)) → c
c → b

All redundant rules that were added or removed can be simulated in 1 steps .

1.1 Redundant Rules Transformation

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

f(f(a)) → c
c → b
f(f(a)) → b

All redundant rules that were added or removed can be simulated in 2 steps .

1.1.1 Critical Pair Closing System

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

c → b

1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[b] = 0
[c] = 1
all rules could be removed.

1.1.1.1.1 R is empty

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

Tool configuration

csi