concat2(leaf, y) -> y
concat2(cons2(u, v), y) -> cons2(u, concat2(v, y))
less_leaves2(x, leaf) -> false
less_leaves2(leaf, cons2(w, z)) -> true
less_leaves2(cons2(u, v), cons2(w, z)) -> less_leaves2(concat2(u, v), concat2(w, z))
↳ QTRS
↳ DependencyPairsProof
concat2(leaf, y) -> y
concat2(cons2(u, v), y) -> cons2(u, concat2(v, y))
less_leaves2(x, leaf) -> false
less_leaves2(leaf, cons2(w, z)) -> true
less_leaves2(cons2(u, v), cons2(w, z)) -> less_leaves2(concat2(u, v), concat2(w, z))
LESS_LEAVES2(cons2(u, v), cons2(w, z)) -> CONCAT2(u, v)
LESS_LEAVES2(cons2(u, v), cons2(w, z)) -> LESS_LEAVES2(concat2(u, v), concat2(w, z))
LESS_LEAVES2(cons2(u, v), cons2(w, z)) -> CONCAT2(w, z)
CONCAT2(cons2(u, v), y) -> CONCAT2(v, y)
concat2(leaf, y) -> y
concat2(cons2(u, v), y) -> cons2(u, concat2(v, y))
less_leaves2(x, leaf) -> false
less_leaves2(leaf, cons2(w, z)) -> true
less_leaves2(cons2(u, v), cons2(w, z)) -> less_leaves2(concat2(u, v), concat2(w, z))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
LESS_LEAVES2(cons2(u, v), cons2(w, z)) -> CONCAT2(u, v)
LESS_LEAVES2(cons2(u, v), cons2(w, z)) -> LESS_LEAVES2(concat2(u, v), concat2(w, z))
LESS_LEAVES2(cons2(u, v), cons2(w, z)) -> CONCAT2(w, z)
CONCAT2(cons2(u, v), y) -> CONCAT2(v, y)
concat2(leaf, y) -> y
concat2(cons2(u, v), y) -> cons2(u, concat2(v, y))
less_leaves2(x, leaf) -> false
less_leaves2(leaf, cons2(w, z)) -> true
less_leaves2(cons2(u, v), cons2(w, z)) -> less_leaves2(concat2(u, v), concat2(w, z))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
CONCAT2(cons2(u, v), y) -> CONCAT2(v, y)
concat2(leaf, y) -> y
concat2(cons2(u, v), y) -> cons2(u, concat2(v, y))
less_leaves2(x, leaf) -> false
less_leaves2(leaf, cons2(w, z)) -> true
less_leaves2(cons2(u, v), cons2(w, z)) -> less_leaves2(concat2(u, v), concat2(w, z))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
CONCAT2(cons2(u, v), y) -> CONCAT2(v, y)
POL(CONCAT2(x1, x2)) = 2·x1
POL(cons2(x1, x2)) = 1 + 2·x2
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
concat2(leaf, y) -> y
concat2(cons2(u, v), y) -> cons2(u, concat2(v, y))
less_leaves2(x, leaf) -> false
less_leaves2(leaf, cons2(w, z)) -> true
less_leaves2(cons2(u, v), cons2(w, z)) -> less_leaves2(concat2(u, v), concat2(w, z))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
LESS_LEAVES2(cons2(u, v), cons2(w, z)) -> LESS_LEAVES2(concat2(u, v), concat2(w, z))
concat2(leaf, y) -> y
concat2(cons2(u, v), y) -> cons2(u, concat2(v, y))
less_leaves2(x, leaf) -> false
less_leaves2(leaf, cons2(w, z)) -> true
less_leaves2(cons2(u, v), cons2(w, z)) -> less_leaves2(concat2(u, v), concat2(w, z))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
LESS_LEAVES2(cons2(u, v), cons2(w, z)) -> LESS_LEAVES2(concat2(u, v), concat2(w, z))
POL(LESS_LEAVES2(x1, x2)) = 2·x1 + x2
POL(concat2(x1, x2)) = 2·x1 + x2
POL(cons2(x1, x2)) = 3 + 2·x1 + x2
POL(leaf) = 0
concat2(leaf, y) -> y
concat2(cons2(u, v), y) -> cons2(u, concat2(v, y))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
concat2(leaf, y) -> y
concat2(cons2(u, v), y) -> cons2(u, concat2(v, y))
less_leaves2(x, leaf) -> false
less_leaves2(leaf, cons2(w, z)) -> true
less_leaves2(cons2(u, v), cons2(w, z)) -> less_leaves2(concat2(u, v), concat2(w, z))