isLeaf(leaf) → true
isLeaf(cons(u, v)) → false
left(cons(u, v)) → u
right(cons(u, v)) → v
concat(leaf, y) → y
concat(cons(u, v), y) → cons(u, concat(v, y))
less_leaves(u, v) → if1(isLeaf(u), isLeaf(v), u, v)
if1(b, true, u, v) → false
if1(b, false, u, v) → if2(b, u, v)
if2(true, u, v) → true
if2(false, u, v) → less_leaves(concat(left(u), right(u)), concat(left(v), right(v)))
↳ QTRS
↳ DependencyPairsProof
isLeaf(leaf) → true
isLeaf(cons(u, v)) → false
left(cons(u, v)) → u
right(cons(u, v)) → v
concat(leaf, y) → y
concat(cons(u, v), y) → cons(u, concat(v, y))
less_leaves(u, v) → if1(isLeaf(u), isLeaf(v), u, v)
if1(b, true, u, v) → false
if1(b, false, u, v) → if2(b, u, v)
if2(true, u, v) → true
if2(false, u, v) → less_leaves(concat(left(u), right(u)), concat(left(v), right(v)))
IF2(false, u, v) → LEFT(u)
LESS_LEAVES(u, v) → ISLEAF(u)
LESS_LEAVES(u, v) → IF1(isLeaf(u), isLeaf(v), u, v)
IF2(false, u, v) → RIGHT(u)
IF2(false, u, v) → RIGHT(v)
CONCAT(cons(u, v), y) → CONCAT(v, y)
IF2(false, u, v) → LEFT(v)
IF2(false, u, v) → CONCAT(left(u), right(u))
LESS_LEAVES(u, v) → ISLEAF(v)
IF2(false, u, v) → CONCAT(left(v), right(v))
IF1(b, false, u, v) → IF2(b, u, v)
IF2(false, u, v) → LESS_LEAVES(concat(left(u), right(u)), concat(left(v), right(v)))
isLeaf(leaf) → true
isLeaf(cons(u, v)) → false
left(cons(u, v)) → u
right(cons(u, v)) → v
concat(leaf, y) → y
concat(cons(u, v), y) → cons(u, concat(v, y))
less_leaves(u, v) → if1(isLeaf(u), isLeaf(v), u, v)
if1(b, true, u, v) → false
if1(b, false, u, v) → if2(b, u, v)
if2(true, u, v) → true
if2(false, u, v) → less_leaves(concat(left(u), right(u)), concat(left(v), right(v)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
IF2(false, u, v) → LEFT(u)
LESS_LEAVES(u, v) → ISLEAF(u)
LESS_LEAVES(u, v) → IF1(isLeaf(u), isLeaf(v), u, v)
IF2(false, u, v) → RIGHT(u)
IF2(false, u, v) → RIGHT(v)
CONCAT(cons(u, v), y) → CONCAT(v, y)
IF2(false, u, v) → LEFT(v)
IF2(false, u, v) → CONCAT(left(u), right(u))
LESS_LEAVES(u, v) → ISLEAF(v)
IF2(false, u, v) → CONCAT(left(v), right(v))
IF1(b, false, u, v) → IF2(b, u, v)
IF2(false, u, v) → LESS_LEAVES(concat(left(u), right(u)), concat(left(v), right(v)))
isLeaf(leaf) → true
isLeaf(cons(u, v)) → false
left(cons(u, v)) → u
right(cons(u, v)) → v
concat(leaf, y) → y
concat(cons(u, v), y) → cons(u, concat(v, y))
less_leaves(u, v) → if1(isLeaf(u), isLeaf(v), u, v)
if1(b, true, u, v) → false
if1(b, false, u, v) → if2(b, u, v)
if2(true, u, v) → true
if2(false, u, v) → less_leaves(concat(left(u), right(u)), concat(left(v), right(v)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
CONCAT(cons(u, v), y) → CONCAT(v, y)
isLeaf(leaf) → true
isLeaf(cons(u, v)) → false
left(cons(u, v)) → u
right(cons(u, v)) → v
concat(leaf, y) → y
concat(cons(u, v), y) → cons(u, concat(v, y))
less_leaves(u, v) → if1(isLeaf(u), isLeaf(v), u, v)
if1(b, true, u, v) → false
if1(b, false, u, v) → if2(b, u, v)
if2(true, u, v) → true
if2(false, u, v) → less_leaves(concat(left(u), right(u)), concat(left(v), right(v)))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
CONCAT(cons(u, v), y) → CONCAT(v, y)
The value of delta used in the strict ordering is 1/2.
POL(cons(x1, x2)) = 1/4 + (7/2)x_2
POL(CONCAT(x1, x2)) = (2)x_1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
isLeaf(leaf) → true
isLeaf(cons(u, v)) → false
left(cons(u, v)) → u
right(cons(u, v)) → v
concat(leaf, y) → y
concat(cons(u, v), y) → cons(u, concat(v, y))
less_leaves(u, v) → if1(isLeaf(u), isLeaf(v), u, v)
if1(b, true, u, v) → false
if1(b, false, u, v) → if2(b, u, v)
if2(true, u, v) → true
if2(false, u, v) → less_leaves(concat(left(u), right(u)), concat(left(v), right(v)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
LESS_LEAVES(u, v) → IF1(isLeaf(u), isLeaf(v), u, v)
IF1(b, false, u, v) → IF2(b, u, v)
IF2(false, u, v) → LESS_LEAVES(concat(left(u), right(u)), concat(left(v), right(v)))
isLeaf(leaf) → true
isLeaf(cons(u, v)) → false
left(cons(u, v)) → u
right(cons(u, v)) → v
concat(leaf, y) → y
concat(cons(u, v), y) → cons(u, concat(v, y))
less_leaves(u, v) → if1(isLeaf(u), isLeaf(v), u, v)
if1(b, true, u, v) → false
if1(b, false, u, v) → if2(b, u, v)
if2(true, u, v) → true
if2(false, u, v) → less_leaves(concat(left(u), right(u)), concat(left(v), right(v)))