Certification Problem

Input (TPDB TRS_Standard/Rubio_04/quotminus)

The rewrite relation of the following TRS is considered.

plus(0,Y) Y (1)
plus(s(X),Y) s(plus(X,Y)) (2)
min(X,0) X (3)
min(s(X),s(Y)) min(X,Y) (4)
min(min(X,Y),Z) min(X,plus(Y,Z)) (5)
quot(0,s(Y)) 0 (6)
quot(s(X),s(Y)) s(quot(min(X,Y),s(Y))) (7)

Property / Task

Prove or disprove termination.

Answer / Result

Yes.

Proof (by ttt2 @ termCOMP 2023)

1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.
plus#(s(X),Y) plus#(X,Y) (8)
min#(s(X),s(Y)) min#(X,Y) (9)
min#(min(X,Y),Z) plus#(Y,Z) (10)
min#(min(X,Y),Z) min#(X,plus(Y,Z)) (11)
quot#(s(X),s(Y)) min#(X,Y) (12)
quot#(s(X),s(Y)) quot#(min(X,Y),s(Y)) (13)

1.1 Dependency Graph Processor

The dependency pairs are split into 3 components.