YES

The TRS could be proven terminating. The proof took 387 ms.

The following DP Processors were used


Problem 1 was processed with processor DependencyGraph (8ms).
 | – Problem 2 was processed with processor SubtermCriterion (1ms).
 | – Problem 3 was processed with processor PolynomialLinearRange4iUR (229ms).

Problem 1: DependencyGraph



Dependency Pair Problem

Dependency Pairs

concat#(cons(U, V), Y)concat#(V, Y)lessleaves#(cons(U, V), cons(W, Z))lessleaves#(concat(U, V), concat(W, Z))
lessleaves#(cons(U, V), cons(W, Z))concat#(U, V)lessleaves#(cons(U, V), cons(W, Z))concat#(W, Z)

Rewrite Rules

concat(leaf, Y)Yconcat(cons(U, V), Y)cons(U, concat(V, Y))
lessleaves(X, leaf)falselessleaves(leaf, cons(W, Z))true
lessleaves(cons(U, V), cons(W, Z))lessleaves(concat(U, V), concat(W, Z))

Original Signature

Termination of terms over the following signature is verified: false, true, leaf, lessleaves, concat, cons

Strategy


The following SCCs where found

concat#(cons(U, V), Y) → concat#(V, Y)

lessleaves#(cons(U, V), cons(W, Z)) → lessleaves#(concat(U, V), concat(W, Z))

Problem 2: SubtermCriterion



Dependency Pair Problem

Dependency Pairs

concat#(cons(U, V), Y)concat#(V, Y)

Rewrite Rules

concat(leaf, Y)Yconcat(cons(U, V), Y)cons(U, concat(V, Y))
lessleaves(X, leaf)falselessleaves(leaf, cons(W, Z))true
lessleaves(cons(U, V), cons(W, Z))lessleaves(concat(U, V), concat(W, Z))

Original Signature

Termination of terms over the following signature is verified: false, true, leaf, lessleaves, concat, cons

Strategy


Projection

The following projection was used:

Thus, the following dependency pairs are removed:

concat#(cons(U, V), Y)concat#(V, Y)

Problem 3: PolynomialLinearRange4iUR



Dependency Pair Problem

Dependency Pairs

lessleaves#(cons(U, V), cons(W, Z))lessleaves#(concat(U, V), concat(W, Z))

Rewrite Rules

concat(leaf, Y)Yconcat(cons(U, V), Y)cons(U, concat(V, Y))
lessleaves(X, leaf)falselessleaves(leaf, cons(W, Z))true
lessleaves(cons(U, V), cons(W, Z))lessleaves(concat(U, V), concat(W, Z))

Original Signature

Termination of terms over the following signature is verified: false, true, leaf, lessleaves, concat, cons

Strategy


Polynomial Interpretation

Improved Usable rules

concat(cons(U, V), Y)cons(U, concat(V, Y))concat(leaf, Y)Y

The following dependency pairs are strictly oriented by an ordering on the given polynomial interpretation, thus they are removed:

lessleaves#(cons(U, V), cons(W, Z))lessleaves#(concat(U, V), concat(W, Z))