div(0,

div(

quot(0, s(

quot(s(

quot(

R

↳Dependency Pair Analysis

DIV(x,y) -> QUOT(x,y,y)

QUOT(s(x), s(y),z) -> QUOT(x,y,z)

QUOT(x, 0, s(z)) -> DIV(x, s(z))

Furthermore,

R

↳DPs

→DP Problem 1

↳Remaining Obligation(s)

The following remains to be proven:

**QUOT( x, 0, s(z)) -> DIV(x, s(z))**

div(0,y) -> 0

div(x,y) -> quot(x,y,y)

quot(0, s(y),z) -> 0

quot(s(x), s(y),z) -> quot(x,y,z)

quot(x, 0, s(z)) -> s(div(x, s(z)))

Duration:

0:02 minutes