YES(O(1), O(n^2)) 2.81/1.16 YES(O(1), O(n^2)) 2.81/1.19 2.81/1.19 2.81/1.19
2.81/1.19 2.81/1.190 CpxTRS2.81/1.19
↳1 CpxTrsToCdtProof (BOTH BOUNDS(ID, ID))2.81/1.19
↳2 CdtProblem2.81/1.19
↳3 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))2.81/1.19
↳4 CdtProblem2.81/1.19
↳5 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^2))))2.81/1.19
↳6 CdtProblem2.81/1.19
↳7 SIsEmptyProof (BOTH BOUNDS(ID, ID))2.81/1.19
↳8 BOUNDS(O(1), O(1))2.81/1.19
concat(leaf, Y) → Y 2.81/1.19
concat(cons(U, V), Y) → cons(U, concat(V, Y)) 2.81/1.19
lessleaves(X, leaf) → false 2.81/1.19
lessleaves(leaf, cons(W, Z)) → true 2.81/1.19
lessleaves(cons(U, V), cons(W, Z)) → lessleaves(concat(U, V), concat(W, Z))
Tuples:
concat(leaf, z0) → z0 2.81/1.19
concat(cons(z0, z1), z2) → cons(z0, concat(z1, z2)) 2.81/1.19
lessleaves(z0, leaf) → false 2.81/1.19
lessleaves(leaf, cons(z0, z1)) → true 2.81/1.19
lessleaves(cons(z0, z1), cons(z2, z3)) → lessleaves(concat(z0, z1), concat(z2, z3))
S tuples:
CONCAT(cons(z0, z1), z2) → c1(CONCAT(z1, z2)) 2.81/1.19
LESSLEAVES(cons(z0, z1), cons(z2, z3)) → c4(LESSLEAVES(concat(z0, z1), concat(z2, z3)), CONCAT(z0, z1), CONCAT(z2, z3))
K tuples:none
CONCAT(cons(z0, z1), z2) → c1(CONCAT(z1, z2)) 2.81/1.19
LESSLEAVES(cons(z0, z1), cons(z2, z3)) → c4(LESSLEAVES(concat(z0, z1), concat(z2, z3)), CONCAT(z0, z1), CONCAT(z2, z3))
concat, lessleaves
CONCAT, LESSLEAVES
c1, c4
We considered the (Usable) Rules:
LESSLEAVES(cons(z0, z1), cons(z2, z3)) → c4(LESSLEAVES(concat(z0, z1), concat(z2, z3)), CONCAT(z0, z1), CONCAT(z2, z3))
And the Tuples:
concat(leaf, z0) → z0 3.17/1.20
concat(cons(z0, z1), z2) → cons(z0, concat(z1, z2))
The order we found is given by the following interpretation:
CONCAT(cons(z0, z1), z2) → c1(CONCAT(z1, z2)) 3.17/1.20
LESSLEAVES(cons(z0, z1), cons(z2, z3)) → c4(LESSLEAVES(concat(z0, z1), concat(z2, z3)), CONCAT(z0, z1), CONCAT(z2, z3))
POL(CONCAT(x1, x2)) = [1] 3.17/1.20
POL(LESSLEAVES(x1, x2)) = x2 3.17/1.20
POL(c1(x1)) = x1 3.17/1.20
POL(c4(x1, x2, x3)) = x1 + x2 + x3 3.17/1.20
POL(concat(x1, x2)) = [1] + x1 + x2 3.17/1.20
POL(cons(x1, x2)) = [4] + x1 + x2 3.17/1.20
POL(leaf) = 0
Tuples:
concat(leaf, z0) → z0 3.17/1.20
concat(cons(z0, z1), z2) → cons(z0, concat(z1, z2)) 3.17/1.20
lessleaves(z0, leaf) → false 3.17/1.20
lessleaves(leaf, cons(z0, z1)) → true 3.17/1.20
lessleaves(cons(z0, z1), cons(z2, z3)) → lessleaves(concat(z0, z1), concat(z2, z3))
S tuples:
CONCAT(cons(z0, z1), z2) → c1(CONCAT(z1, z2)) 3.17/1.20
LESSLEAVES(cons(z0, z1), cons(z2, z3)) → c4(LESSLEAVES(concat(z0, z1), concat(z2, z3)), CONCAT(z0, z1), CONCAT(z2, z3))
K tuples:
CONCAT(cons(z0, z1), z2) → c1(CONCAT(z1, z2))
Defined Rule Symbols:
LESSLEAVES(cons(z0, z1), cons(z2, z3)) → c4(LESSLEAVES(concat(z0, z1), concat(z2, z3)), CONCAT(z0, z1), CONCAT(z2, z3))
concat, lessleaves
CONCAT, LESSLEAVES
c1, c4
We considered the (Usable) Rules:
CONCAT(cons(z0, z1), z2) → c1(CONCAT(z1, z2))
And the Tuples:
concat(leaf, z0) → z0 3.17/1.20
concat(cons(z0, z1), z2) → cons(z0, concat(z1, z2))
The order we found is given by the following interpretation:
CONCAT(cons(z0, z1), z2) → c1(CONCAT(z1, z2)) 3.17/1.20
LESSLEAVES(cons(z0, z1), cons(z2, z3)) → c4(LESSLEAVES(concat(z0, z1), concat(z2, z3)), CONCAT(z0, z1), CONCAT(z2, z3))
POL(CONCAT(x1, x2)) = x1 + x2 3.17/1.20
POL(LESSLEAVES(x1, x2)) = x1·x2 3.17/1.20
POL(c1(x1)) = x1 3.17/1.20
POL(c4(x1, x2, x3)) = x1 + x2 + x3 3.17/1.20
POL(concat(x1, x2)) = x1 + x2 3.17/1.20
POL(cons(x1, x2)) = [1] + x1 + x2 3.17/1.20
POL(leaf) = [3]
Tuples:
concat(leaf, z0) → z0 3.17/1.20
concat(cons(z0, z1), z2) → cons(z0, concat(z1, z2)) 3.17/1.20
lessleaves(z0, leaf) → false 3.17/1.20
lessleaves(leaf, cons(z0, z1)) → true 3.17/1.20
lessleaves(cons(z0, z1), cons(z2, z3)) → lessleaves(concat(z0, z1), concat(z2, z3))
S tuples:none
CONCAT(cons(z0, z1), z2) → c1(CONCAT(z1, z2)) 3.17/1.20
LESSLEAVES(cons(z0, z1), cons(z2, z3)) → c4(LESSLEAVES(concat(z0, z1), concat(z2, z3)), CONCAT(z0, z1), CONCAT(z2, z3))
Defined Rule Symbols:
LESSLEAVES(cons(z0, z1), cons(z2, z3)) → c4(LESSLEAVES(concat(z0, z1), concat(z2, z3)), CONCAT(z0, z1), CONCAT(z2, z3)) 3.17/1.20
CONCAT(cons(z0, z1), z2) → c1(CONCAT(z1, z2))
concat, lessleaves
CONCAT, LESSLEAVES
c1, c4