Certification Problem

Input (TPDB TRS_Standard/SK90/2.05)

The rewrite relation of the following TRS is considered.

+(x,+(y,z))	→	+(+(x,y),z)	(1)
*(x,+(y,z))	→	+((x,y),(x,z))	(2)
+(+(x,(y,z)),(y,u))	→	+(x,*(y,+(z,u)))	(3)

Property / Task

Prove or disprove termination.

Answer / Result

No.

Proof (by ttt2 @ termCOMP 2023)

1 Loop

The following loop proves nontermination.

t₀	=	+(x245,*(x282,+(x283,x284)))
	→	+(x245,+((x282,x283),(x282,x284)))
	→	+(+(x245,(x282,x283)),(x282,x284))
	→	+(x245,*(x282,+(x283,x284)))
	=	t₃

where t₃ = t₀σ and σ = {x284/x284, x283/x283, x282/x282, x245/x245}