NO Non-Confluence Proof

Non-Confluence Proof

by ACP

Input

The rewrite relation of the following TRS is considered.

0(1(2(1(x)))) 1(2(1(1(0(1(2(0(1(2(x))))))))))
0(1(2(1(x)))) 1(2(1(1(0(1(2(0(1(2(0(1(2(x)))))))))))))
0(1(2(1(x)))) 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(x))))))))))))))))
0(1(2(1(x)))) 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x)))))))))))))))))))
0(1(2(1(x)))) 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x))))))))))))))))))))))
0(1(2(1(x)))) 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x)))))))))))))))))))))))))

Proof

1 Non-Joinable Fork

The system is not confluent due to the following forking derivations.

t0 = 0(1(2(1(c_1))))
ε 1(2(1(1(0(1(2(0(1(2(0(1(2(c_1)))))))))))))
= t1

t0 = 0(1(2(1(c_1))))
ε 1(2(1(1(0(1(2(0(1(2(c_1))))))))))
= t1

The two resulting terms cannot be joined for the following reason:

Tool configuration

ACP