Certification Problem

Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-158)

The rewrite relation of the following TRS is considered.

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

Property / Task

Prove or disprove termination.

Answer / Result

No.

Proof (by ttt2 @ termCOMP 2023)

1 Loop

The following loop proves nontermination.

t₀	=	a(b(c(x9997)))
	→	b(a(a(c(a(a(c(x9997)))))))
	→	b(a(a(c(a(c(x9997))))))
	→	b(a(a(c(c(x9997)))))
	→	b(a(a(b(x9997))))
	→	b(a(b(a(a(c(a(a(x9997))))))))
	→	b(a(b(a(c(a(a(x9997)))))))
	→	b(a(b(c(a(a(x9997))))))
	=	t₇

where t₇ = C[t₀σ] and σ = {x9997/a(a(x9997))} and C = b(☐)