YES Confluence Proof

Confluence Proof

by csi

Input

The rewrite relation of the following TRS is considered.

a(x) x
a(a(x)) b(c(x))
b(x) x
c(x) x
c(b(x)) b(a(c(x)))

Proof

1 Critical Pair Closing System

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

a(x) x
c(x) x
b(x) x

1.1 Rule Removal

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