YES Confluence Proof

Confluence Proof

by csi

Input

The rewrite relation of the following TRS is considered.

F(G(x,A,B)) x
G(F(H(C,D)),x,y) H(K1(x),K2(y))
K1(A) C
K2(B) D

Proof

1 Critical Pair Closing System

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

K2(B) D
K1(A) C

1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[C] = 0
[K2(x1)] = 2 · x1 + 0
[B] = 0
[D] = 0
[A] = 0
[K1(x1)] = 4 · x1 + 1
the rule
K2(B) D
remains.

1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[K2(x1)] = 1 · x1 + 1
[B] = 4
[D] = 0
all rules could be removed.

1.1.1.1 R is empty

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

Tool configuration

csi