Problem: p(0()) -> 0() p(s(X)) -> X leq(0(),Y) -> true() leq(s(X),0()) -> false() leq(s(X),s(Y)) -> leq(X,Y) if(true(),X,Y) -> X if(false(),X,Y) -> Y diff(X,Y) -> if(leq(X,Y),0(),s(diff(p(X),Y))) Proof: Containment Processor: loop length: 1 terms: diff(X,Y) context: if(leq(X,Y),0(),s([])) substitution: X -> p(X) Y -> Y Qed