Certification Problem

Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-146)

The rewrite relation of the following TRS is considered.

a(x1)	→	x1	(1)
a(b(x1))	→	a(c(b(b(a(a(x1))))))	(2)
b(x1)	→	x1	(3)
c(c(x1))	→	x1	(4)

Property / Task

Prove or disprove termination.

Answer / Result

No.

Proof (by ttt2 @ termCOMP 2023)

1 Loop

The following loop proves nontermination.

t₀	=	a(b(b(x10383)))
	→	a(c(b(b(a(a(b(x10383)))))))
	→	a(c(b(a(a(b(x10383))))))
	→	a(c(a(a(b(x10383)))))
	→	a(c(a(b(x10383))))
	→	a(c(a(c(b(b(a(a(x10383))))))))
	→	a(c(c(b(b(a(a(x10383)))))))
	→	a(b(b(a(a(x10383)))))
	=	t₇

where t₇ = t₀σ and σ = {x10383/a(a(x10383))}