Certification Problem

Input (TPDB SRS_Standard/Zantema_04/z044)

The rewrite relation of the following TRS is considered.

c(a(b(a(x1))))

→

a(b(a(b(c(c(a(x1)))))))

(1)

Property / Task

Prove or disprove termination.

Answer / Result

No.

Proof (by matchbox @ termCOMP 2023)

1 Loop

The following loop proves nontermination.

t₀	=	a(b(a(b(c(c(a(b(a(b(a(x1)))))))))))
	→	a(b(a(b(c(a(b(a(b(c(c(a(b(a(x1))))))))))))))
	→	a(b(a(b(a(b(a(b(c(c(a(b(c(c(a(b(a(x1)))))))))))))))))
	→	a(b(a(b(a(b(a(b(c(c(a(b(c(a(b(a(b(c(c(a(x1))))))))))))))))))))
	→	a(b(a(b(a(b(a(b(c(c(a(b(a(b(a(b(c(c(a(b(c(c(a(x1)))))))))))))))))))))))
	=	t₄

where t₄ = C[t₀σ] and σ = {x1/b(c(c(a(b(c(c(a(x1))))))))} and C = a(b(a(b(☐))))