Certification Problem

Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-99)

The rewrite relation of the following TRS is considered.

a(x1)	→	x1	(1)
a(a(a(x1)))	→	b(x1)	(2)
b(c(x1))	→	a(c(c(b(x1))))	(3)
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(a(a(c(c(c(c(x69305)))))))
	→	b(c(c(c(c(x69305)))))
	→	a(c(c(b(c(c(c(x69305)))))))
	→	a(c(b(c(c(c(x69305))))))
	→	a(b(c(c(c(x69305)))))
	→	a(a(c(c(b(c(c(x69305)))))))
	→	a(a(c(b(c(c(x69305))))))
	→	a(a(b(c(c(x69305)))))
	→	a(a(a(c(c(b(c(x69305)))))))
	→	a(a(a(c(c(a(c(c(b(x69305)))))))))
	→	a(a(a(c(c(c(c(b(x69305))))))))
	=	t₁₀

where t₁₀ = t₀σ and σ = {x69305/b(x69305)}