Certification Problem

Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-217)

The rewrite relation of the following TRS is considered.

a(x1)	→	x1	(1)
a(b(x1))	→	b(b(c(a(x1))))	(2)
b(x1)	→	x1	(3)
b(c(c(x1)))	→	a(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(b(c(b(b(x70479)))))))
	→	b(b(c(a(b(b(c(b(b(x70479)))))))))
	→	b(b(c(b(b(c(a(b(c(b(b(x70479)))))))))))
	→	b(b(c(b(c(a(b(c(b(b(x70479))))))))))
	→	b(b(c(c(a(b(c(b(b(x70479)))))))))
	→	b(a(a(b(c(b(b(x70479)))))))
	→	b(a(b(b(c(a(c(b(b(x70479)))))))))
	→	b(a(b(b(c(c(b(b(x70479))))))))
	→	b(a(b(a(b(b(x70479))))))
	→	b(a(b(b(b(c(a(b(x70479))))))))
	→	b(a(b(b(b(c(b(b(c(a(x70479))))))))))
	=	t₁₀

where t₁₀ = C[t₀σ] and σ = {x70479/c(a(x70479))} and C = b(☐)