YES Confluence Proof

Confluence Proof

by csi

Input

The rewrite relation of the following TRS is considered.

c c
h(a,h(f(b),c)) c

Proof

1 Critical Pair Closing System

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

h(a,h(f(b),c)) c

1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[h(x1, x2)] = 1 · x1 + 1 · x2 + 2
[a] = 1
[f(x1)] = 1 · x1 + 4
[c] = 2
[b] = 0
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