0 QTRS
↳1 Overlay + Local Confluence (⇔)
↳2 QTRS
↳3 DependencyPairsProof (⇔)
↳4 QDP
↳5 DependencyGraphProof (⇔)
↳6 AND
↳7 QDP
↳8 QDPOrderProof (⇔)
↳9 QDP
↳10 PisEmptyProof (⇔)
↳11 TRUE
↳12 QDP
le(0, y) → true
le(s(x), 0) → false
le(s(x), s(y)) → le(x, y)
int(x, y) → if(le(x, y), x, y)
if(true, x, y) → cons(x, int(s(x), y))
if(false, x, y) → nil
le(0, y) → true
le(s(x), 0) → false
le(s(x), s(y)) → le(x, y)
int(x, y) → if(le(x, y), x, y)
if(true, x, y) → cons(x, int(s(x), y))
if(false, x, y) → nil
le(0, x0)
le(s(x0), 0)
le(s(x0), s(x1))
int(x0, x1)
if(true, x0, x1)
if(false, x0, x1)
LE(s(x), s(y)) → LE(x, y)
INT(x, y) → IF(le(x, y), x, y)
INT(x, y) → LE(x, y)
IF(true, x, y) → INT(s(x), y)
le(0, y) → true
le(s(x), 0) → false
le(s(x), s(y)) → le(x, y)
int(x, y) → if(le(x, y), x, y)
if(true, x, y) → cons(x, int(s(x), y))
if(false, x, y) → nil
le(0, x0)
le(s(x0), 0)
le(s(x0), s(x1))
int(x0, x1)
if(true, x0, x1)
if(false, x0, x1)
LE(s(x), s(y)) → LE(x, y)
le(0, y) → true
le(s(x), 0) → false
le(s(x), s(y)) → le(x, y)
int(x, y) → if(le(x, y), x, y)
if(true, x, y) → cons(x, int(s(x), y))
if(false, x, y) → nil
le(0, x0)
le(s(x0), 0)
le(s(x0), s(x1))
int(x0, x1)
if(true, x0, x1)
if(false, x0, x1)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
LE(s(x), s(y)) → LE(x, y)
le1 > false > true
0 > true
int1 > if1 > s1 > true
int1 > if1 > nil > true
s1: multiset
le1: [1]
0: multiset
true: multiset
false: multiset
int1: multiset
if1: multiset
nil: multiset
le(0, y) → true
le(s(x), 0) → false
le(s(x), s(y)) → le(x, y)
int(x, y) → if(le(x, y), x, y)
if(true, x, y) → cons(x, int(s(x), y))
if(false, x, y) → nil
le(0, y) → true
le(s(x), 0) → false
le(s(x), s(y)) → le(x, y)
int(x, y) → if(le(x, y), x, y)
if(true, x, y) → cons(x, int(s(x), y))
if(false, x, y) → nil
le(0, x0)
le(s(x0), 0)
le(s(x0), s(x1))
int(x0, x1)
if(true, x0, x1)
if(false, x0, x1)
INT(x, y) → IF(le(x, y), x, y)
IF(true, x, y) → INT(s(x), y)
le(0, y) → true
le(s(x), 0) → false
le(s(x), s(y)) → le(x, y)
int(x, y) → if(le(x, y), x, y)
if(true, x, y) → cons(x, int(s(x), y))
if(false, x, y) → nil
le(0, x0)
le(s(x0), 0)
le(s(x0), s(x1))
int(x0, x1)
if(true, x0, x1)
if(false, x0, x1)