Termination w.r.t. Q proof of /tmp/tmpF6iK3g/lse.trs

Termination w.r.t. Q of the following Term Rewriting System could be proven:

Q restricted rewrite system:
The TRS R consists of the following rules:

Term_sub(Case(m, xi, n), s) → Frozen(m, Sum_sub(xi, s), n, s)
Frozen(m, Sum_constant(Left), n, s) → Term_sub(m, s)
Frozen(m, Sum_constant(Right), n, s) → Term_sub(n, s)
Frozen(m, Sum_term_var(xi), n, s) → Case(Term_sub(m, s), xi, Term_sub(n, s))
Term_sub(Term_app(m, n), s) → Term_app(Term_sub(m, s), Term_sub(n, s))
Term_sub(Term_pair(m, n), s) → Term_pair(Term_sub(m, s), Term_sub(n, s))
Term_sub(Term_inl(m), s) → Term_inl(Term_sub(m, s))
Term_sub(Term_inr(m), s) → Term_inr(Term_sub(m, s))
Term_sub(Term_var(x), Id) → Term_var(x)
Term_sub(Term_var(x), Cons_usual(y, m, s)) → m
Term_sub(Term_var(x), Cons_usual(y, m, s)) → Term_sub(Term_var(x), s)
Term_sub(Term_var(x), Cons_sum(xi, k, s)) → Term_sub(Term_var(x), s)
Term_sub(Term_sub(m, s), t) → Term_sub(m, Concat(s, t))
Sum_sub(xi, Id) → Sum_term_var(xi)
Sum_sub(xi, Cons_sum(psi, k, s)) → Sum_constant(k)
Sum_sub(xi, Cons_sum(psi, k, s)) → Sum_sub(xi, s)
Sum_sub(xi, Cons_usual(y, m, s)) → Sum_sub(xi, s)
Concat(Concat(s, t), u) → Concat(s, Concat(t, u))
Concat(Cons_usual(x, m, s), t) → Cons_usual(x, Term_sub(m, t), Concat(s, t))
Concat(Cons_sum(xi, k, s), t) → Cons_sum(xi, k, Concat(s, t))
Concat(Id, s) → s

Q is empty.

↳ QTRS

  ↳ DependencyPairsProof

Q restricted rewrite system:
The TRS R consists of the following rules:

Term_sub(Case(m, xi, n), s) → Frozen(m, Sum_sub(xi, s), n, s)
Frozen(m, Sum_constant(Left), n, s) → Term_sub(m, s)
Frozen(m, Sum_constant(Right), n, s) → Term_sub(n, s)
Frozen(m, Sum_term_var(xi), n, s) → Case(Term_sub(m, s), xi, Term_sub(n, s))
Term_sub(Term_app(m, n), s) → Term_app(Term_sub(m, s), Term_sub(n, s))
Term_sub(Term_pair(m, n), s) → Term_pair(Term_sub(m, s), Term_sub(n, s))
Term_sub(Term_inl(m), s) → Term_inl(Term_sub(m, s))
Term_sub(Term_inr(m), s) → Term_inr(Term_sub(m, s))
Term_sub(Term_var(x), Id) → Term_var(x)
Term_sub(Term_var(x), Cons_usual(y, m, s)) → m
Term_sub(Term_var(x), Cons_usual(y, m, s)) → Term_sub(Term_var(x), s)
Term_sub(Term_var(x), Cons_sum(xi, k, s)) → Term_sub(Term_var(x), s)
Term_sub(Term_sub(m, s), t) → Term_sub(m, Concat(s, t))
Sum_sub(xi, Id) → Sum_term_var(xi)
Sum_sub(xi, Cons_sum(psi, k, s)) → Sum_constant(k)
Sum_sub(xi, Cons_sum(psi, k, s)) → Sum_sub(xi, s)
Sum_sub(xi, Cons_usual(y, m, s)) → Sum_sub(xi, s)
Concat(Concat(s, t), u) → Concat(s, Concat(t, u))
Concat(Cons_usual(x, m, s), t) → Cons_usual(x, Term_sub(m, t), Concat(s, t))
Concat(Cons_sum(xi, k, s), t) → Cons_sum(xi, k, Concat(s, t))
Concat(Id, s) → s

Q is empty.

Using Dependency Pairs [1,15] we result in the following initial DP problem:
Q DP problem:
The TRS P consists of the following rules:

CONCAT(Cons_sum(xi, k, s), t) → CONCAT(s, t)
TERM_SUB(Case(m, xi, n), s) → FROZEN(m, Sum_sub(xi, s), n, s)
TERM_SUB(Term_var(x), Cons_usual(y, m, s)) → TERM_SUB(Term_var(x), s)
SUM_SUB(xi, Cons_usual(y, m, s)) → SUM_SUB(xi, s)
TERM_SUB(Term_var(x), Cons_sum(xi, k, s)) → TERM_SUB(Term_var(x), s)
CONCAT(Cons_usual(x, m, s), t) → CONCAT(s, t)
TERM_SUB(Term_inl(m), s) → TERM_SUB(m, s)
TERM_SUB(Term_inr(m), s) → TERM_SUB(m, s)
CONCAT(Concat(s, t), u) → CONCAT(s, Concat(t, u))
TERM_SUB(Term_sub(m, s), t) → CONCAT(s, t)
FROZEN(m, Sum_term_var(xi), n, s) → TERM_SUB(n, s)
SUM_SUB(xi, Cons_sum(psi, k, s)) → SUM_SUB(xi, s)
FROZEN(m, Sum_constant(Right), n, s) → TERM_SUB(n, s)
FROZEN(m, Sum_term_var(xi), n, s) → TERM_SUB(m, s)
CONCAT(Cons_usual(x, m, s), t) → TERM_SUB(m, t)
TERM_SUB(Case(m, xi, n), s) → SUM_SUB(xi, s)
TERM_SUB(Term_sub(m, s), t) → TERM_SUB(m, Concat(s, t))
TERM_SUB(Term_pair(m, n), s) → TERM_SUB(m, s)
CONCAT(Concat(s, t), u) → CONCAT(t, u)
TERM_SUB(Term_app(m, n), s) → TERM_SUB(n, s)
FROZEN(m, Sum_constant(Left), n, s) → TERM_SUB(m, s)
TERM_SUB(Term_app(m, n), s) → TERM_SUB(m, s)
TERM_SUB(Term_pair(m, n), s) → TERM_SUB(n, s)

The TRS R consists of the following rules:

Term_sub(Case(m, xi, n), s) → Frozen(m, Sum_sub(xi, s), n, s)
Frozen(m, Sum_constant(Left), n, s) → Term_sub(m, s)
Frozen(m, Sum_constant(Right), n, s) → Term_sub(n, s)
Frozen(m, Sum_term_var(xi), n, s) → Case(Term_sub(m, s), xi, Term_sub(n, s))
Term_sub(Term_app(m, n), s) → Term_app(Term_sub(m, s), Term_sub(n, s))
Term_sub(Term_pair(m, n), s) → Term_pair(Term_sub(m, s), Term_sub(n, s))
Term_sub(Term_inl(m), s) → Term_inl(Term_sub(m, s))
Term_sub(Term_inr(m), s) → Term_inr(Term_sub(m, s))
Term_sub(Term_var(x), Id) → Term_var(x)
Term_sub(Term_var(x), Cons_usual(y, m, s)) → m
Term_sub(Term_var(x), Cons_usual(y, m, s)) → Term_sub(Term_var(x), s)
Term_sub(Term_var(x), Cons_sum(xi, k, s)) → Term_sub(Term_var(x), s)
Term_sub(Term_sub(m, s), t) → Term_sub(m, Concat(s, t))
Sum_sub(xi, Id) → Sum_term_var(xi)
Sum_sub(xi, Cons_sum(psi, k, s)) → Sum_constant(k)
Sum_sub(xi, Cons_sum(psi, k, s)) → Sum_sub(xi, s)
Sum_sub(xi, Cons_usual(y, m, s)) → Sum_sub(xi, s)
Concat(Concat(s, t), u) → Concat(s, Concat(t, u))
Concat(Cons_usual(x, m, s), t) → Cons_usual(x, Term_sub(m, t), Concat(s, t))
Concat(Cons_sum(xi, k, s), t) → Cons_sum(xi, k, Concat(s, t))
Concat(Id, s) → s

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

↳ QTRS

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

Q DP problem:
The TRS P consists of the following rules:

CONCAT(Cons_sum(xi, k, s), t) → CONCAT(s, t)
TERM_SUB(Case(m, xi, n), s) → FROZEN(m, Sum_sub(xi, s), n, s)
TERM_SUB(Term_var(x), Cons_usual(y, m, s)) → TERM_SUB(Term_var(x), s)
SUM_SUB(xi, Cons_usual(y, m, s)) → SUM_SUB(xi, s)
TERM_SUB(Term_var(x), Cons_sum(xi, k, s)) → TERM_SUB(Term_var(x), s)
CONCAT(Cons_usual(x, m, s), t) → CONCAT(s, t)
TERM_SUB(Term_inl(m), s) → TERM_SUB(m, s)
TERM_SUB(Term_inr(m), s) → TERM_SUB(m, s)
CONCAT(Concat(s, t), u) → CONCAT(s, Concat(t, u))
TERM_SUB(Term_sub(m, s), t) → CONCAT(s, t)
FROZEN(m, Sum_term_var(xi), n, s) → TERM_SUB(n, s)
SUM_SUB(xi, Cons_sum(psi, k, s)) → SUM_SUB(xi, s)
FROZEN(m, Sum_constant(Right), n, s) → TERM_SUB(n, s)
FROZEN(m, Sum_term_var(xi), n, s) → TERM_SUB(m, s)
CONCAT(Cons_usual(x, m, s), t) → TERM_SUB(m, t)
TERM_SUB(Case(m, xi, n), s) → SUM_SUB(xi, s)
TERM_SUB(Term_sub(m, s), t) → TERM_SUB(m, Concat(s, t))
TERM_SUB(Term_pair(m, n), s) → TERM_SUB(m, s)
CONCAT(Concat(s, t), u) → CONCAT(t, u)
TERM_SUB(Term_app(m, n), s) → TERM_SUB(n, s)
FROZEN(m, Sum_constant(Left), n, s) → TERM_SUB(m, s)
TERM_SUB(Term_app(m, n), s) → TERM_SUB(m, s)
TERM_SUB(Term_pair(m, n), s) → TERM_SUB(n, s)

The TRS R consists of the following rules:

Term_sub(Case(m, xi, n), s) → Frozen(m, Sum_sub(xi, s), n, s)
Frozen(m, Sum_constant(Left), n, s) → Term_sub(m, s)
Frozen(m, Sum_constant(Right), n, s) → Term_sub(n, s)
Frozen(m, Sum_term_var(xi), n, s) → Case(Term_sub(m, s), xi, Term_sub(n, s))
Term_sub(Term_app(m, n), s) → Term_app(Term_sub(m, s), Term_sub(n, s))
Term_sub(Term_pair(m, n), s) → Term_pair(Term_sub(m, s), Term_sub(n, s))
Term_sub(Term_inl(m), s) → Term_inl(Term_sub(m, s))
Term_sub(Term_inr(m), s) → Term_inr(Term_sub(m, s))
Term_sub(Term_var(x), Id) → Term_var(x)
Term_sub(Term_var(x), Cons_usual(y, m, s)) → m
Term_sub(Term_var(x), Cons_usual(y, m, s)) → Term_sub(Term_var(x), s)
Term_sub(Term_var(x), Cons_sum(xi, k, s)) → Term_sub(Term_var(x), s)
Term_sub(Term_sub(m, s), t) → Term_sub(m, Concat(s, t))
Sum_sub(xi, Id) → Sum_term_var(xi)
Sum_sub(xi, Cons_sum(psi, k, s)) → Sum_constant(k)
Sum_sub(xi, Cons_sum(psi, k, s)) → Sum_sub(xi, s)
Sum_sub(xi, Cons_usual(y, m, s)) → Sum_sub(xi, s)
Concat(Concat(s, t), u) → Concat(s, Concat(t, u))
Concat(Cons_usual(x, m, s), t) → Cons_usual(x, Term_sub(m, t), Concat(s, t))
Concat(Cons_sum(xi, k, s), t) → Cons_sum(xi, k, Concat(s, t))
Concat(Id, s) → s

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 3 SCCs with 1 less node.

↳ QTRS

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ AND

          ↳ QDP

            ↳ UsableRulesProof

          ↳ QDP

          ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

SUM_SUB(xi, Cons_sum(psi, k, s)) → SUM_SUB(xi, s)
SUM_SUB(xi, Cons_usual(y, m, s)) → SUM_SUB(xi, s)

The TRS R consists of the following rules:

Term_sub(Case(m, xi, n), s) → Frozen(m, Sum_sub(xi, s), n, s)
Frozen(m, Sum_constant(Left), n, s) → Term_sub(m, s)
Frozen(m, Sum_constant(Right), n, s) → Term_sub(n, s)
Frozen(m, Sum_term_var(xi), n, s) → Case(Term_sub(m, s), xi, Term_sub(n, s))
Term_sub(Term_app(m, n), s) → Term_app(Term_sub(m, s), Term_sub(n, s))
Term_sub(Term_pair(m, n), s) → Term_pair(Term_sub(m, s), Term_sub(n, s))
Term_sub(Term_inl(m), s) → Term_inl(Term_sub(m, s))
Term_sub(Term_inr(m), s) → Term_inr(Term_sub(m, s))
Term_sub(Term_var(x), Id) → Term_var(x)
Term_sub(Term_var(x), Cons_usual(y, m, s)) → m
Term_sub(Term_var(x), Cons_usual(y, m, s)) → Term_sub(Term_var(x), s)
Term_sub(Term_var(x), Cons_sum(xi, k, s)) → Term_sub(Term_var(x), s)
Term_sub(Term_sub(m, s), t) → Term_sub(m, Concat(s, t))
Sum_sub(xi, Id) → Sum_term_var(xi)
Sum_sub(xi, Cons_sum(psi, k, s)) → Sum_constant(k)
Sum_sub(xi, Cons_sum(psi, k, s)) → Sum_sub(xi, s)
Sum_sub(xi, Cons_usual(y, m, s)) → Sum_sub(xi, s)
Concat(Concat(s, t), u) → Concat(s, Concat(t, u))
Concat(Cons_usual(x, m, s), t) → Cons_usual(x, Term_sub(m, t), Concat(s, t))
Concat(Cons_sum(xi, k, s), t) → Cons_sum(xi, k, Concat(s, t))
Concat(Id, s) → s

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
We can use the usable rules and reduction pair processor [15] with the Ce-compatible extension of the polynomial order that maps every function symbol to the sum of its argument. Then, we can delete all non-usable rules [17] from R.

↳ QTRS

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ AND

          ↳ QDP

            ↳ UsableRulesProof

              ↳ QDP

                ↳ QDPSizeChangeProof

          ↳ QDP

          ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

SUM_SUB(xi, Cons_sum(psi, k, s)) → SUM_SUB(xi, s)
SUM_SUB(xi, Cons_usual(y, m, s)) → SUM_SUB(xi, s)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs:

SUM_SUB(xi, Cons_sum(psi, k, s)) → SUM_SUB(xi, s)
The graph contains the following edges 1 >= 1, 2 > 2
SUM_SUB(xi, Cons_usual(y, m, s)) → SUM_SUB(xi, s)
The graph contains the following edges 1 >= 1, 2 > 2

↳ QTRS

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ AND

          ↳ QDP

          ↳ QDP

            ↳ UsableRulesProof

          ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

TERM_SUB(Term_var(x), Cons_usual(y, m, s)) → TERM_SUB(Term_var(x), s)
TERM_SUB(Term_var(x), Cons_sum(xi, k, s)) → TERM_SUB(Term_var(x), s)

The TRS R consists of the following rules:

Term_sub(Case(m, xi, n), s) → Frozen(m, Sum_sub(xi, s), n, s)
Frozen(m, Sum_constant(Left), n, s) → Term_sub(m, s)
Frozen(m, Sum_constant(Right), n, s) → Term_sub(n, s)
Frozen(m, Sum_term_var(xi), n, s) → Case(Term_sub(m, s), xi, Term_sub(n, s))
Term_sub(Term_app(m, n), s) → Term_app(Term_sub(m, s), Term_sub(n, s))
Term_sub(Term_pair(m, n), s) → Term_pair(Term_sub(m, s), Term_sub(n, s))
Term_sub(Term_inl(m), s) → Term_inl(Term_sub(m, s))
Term_sub(Term_inr(m), s) → Term_inr(Term_sub(m, s))
Term_sub(Term_var(x), Id) → Term_var(x)
Term_sub(Term_var(x), Cons_usual(y, m, s)) → m
Term_sub(Term_var(x), Cons_usual(y, m, s)) → Term_sub(Term_var(x), s)
Term_sub(Term_var(x), Cons_sum(xi, k, s)) → Term_sub(Term_var(x), s)
Term_sub(Term_sub(m, s), t) → Term_sub(m, Concat(s, t))
Sum_sub(xi, Id) → Sum_term_var(xi)
Sum_sub(xi, Cons_sum(psi, k, s)) → Sum_constant(k)
Sum_sub(xi, Cons_sum(psi, k, s)) → Sum_sub(xi, s)
Sum_sub(xi, Cons_usual(y, m, s)) → Sum_sub(xi, s)
Concat(Concat(s, t), u) → Concat(s, Concat(t, u))
Concat(Cons_usual(x, m, s), t) → Cons_usual(x, Term_sub(m, t), Concat(s, t))
Concat(Cons_sum(xi, k, s), t) → Cons_sum(xi, k, Concat(s, t))
Concat(Id, s) → s

↳ QTRS

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ AND

          ↳ QDP

          ↳ QDP

            ↳ UsableRulesProof

              ↳ QDP

                ↳ QDPSizeChangeProof

          ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

TERM_SUB(Term_var(x), Cons_usual(y, m, s)) → TERM_SUB(Term_var(x), s)
TERM_SUB(Term_var(x), Cons_sum(xi, k, s)) → TERM_SUB(Term_var(x), s)

From the DPs we obtained the following set of size-change graphs:

TERM_SUB(Term_var(x), Cons_usual(y, m, s)) → TERM_SUB(Term_var(x), s)
The graph contains the following edges 1 >= 1, 2 > 2
TERM_SUB(Term_var(x), Cons_sum(xi, k, s)) → TERM_SUB(Term_var(x), s)
The graph contains the following edges 1 >= 1, 2 > 2

↳ QTRS

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ AND

          ↳ QDP

          ↳ QDP

          ↳ QDP

            ↳ QDPSizeChangeProof

Q DP problem:
The TRS P consists of the following rules:

CONCAT(Cons_sum(xi, k, s), t) → CONCAT(s, t)
TERM_SUB(Case(m, xi, n), s) → FROZEN(m, Sum_sub(xi, s), n, s)
CONCAT(Cons_usual(x, m, s), t) → CONCAT(s, t)
TERM_SUB(Term_inl(m), s) → TERM_SUB(m, s)
TERM_SUB(Term_inr(m), s) → TERM_SUB(m, s)
TERM_SUB(Term_sub(m, s), t) → CONCAT(s, t)
CONCAT(Concat(s, t), u) → CONCAT(s, Concat(t, u))
FROZEN(m, Sum_term_var(xi), n, s) → TERM_SUB(n, s)
FROZEN(m, Sum_term_var(xi), n, s) → TERM_SUB(m, s)
FROZEN(m, Sum_constant(Right), n, s) → TERM_SUB(n, s)
CONCAT(Cons_usual(x, m, s), t) → TERM_SUB(m, t)
TERM_SUB(Term_sub(m, s), t) → TERM_SUB(m, Concat(s, t))
TERM_SUB(Term_pair(m, n), s) → TERM_SUB(m, s)
TERM_SUB(Term_app(m, n), s) → TERM_SUB(n, s)
CONCAT(Concat(s, t), u) → CONCAT(t, u)
FROZEN(m, Sum_constant(Left), n, s) → TERM_SUB(m, s)
TERM_SUB(Term_app(m, n), s) → TERM_SUB(m, s)
TERM_SUB(Term_pair(m, n), s) → TERM_SUB(n, s)

The TRS R consists of the following rules:

Term_sub(Case(m, xi, n), s) → Frozen(m, Sum_sub(xi, s), n, s)
Frozen(m, Sum_constant(Left), n, s) → Term_sub(m, s)
Frozen(m, Sum_constant(Right), n, s) → Term_sub(n, s)
Frozen(m, Sum_term_var(xi), n, s) → Case(Term_sub(m, s), xi, Term_sub(n, s))
Term_sub(Term_app(m, n), s) → Term_app(Term_sub(m, s), Term_sub(n, s))
Term_sub(Term_pair(m, n), s) → Term_pair(Term_sub(m, s), Term_sub(n, s))
Term_sub(Term_inl(m), s) → Term_inl(Term_sub(m, s))
Term_sub(Term_inr(m), s) → Term_inr(Term_sub(m, s))
Term_sub(Term_var(x), Id) → Term_var(x)
Term_sub(Term_var(x), Cons_usual(y, m, s)) → m
Term_sub(Term_var(x), Cons_usual(y, m, s)) → Term_sub(Term_var(x), s)
Term_sub(Term_var(x), Cons_sum(xi, k, s)) → Term_sub(Term_var(x), s)
Term_sub(Term_sub(m, s), t) → Term_sub(m, Concat(s, t))
Sum_sub(xi, Id) → Sum_term_var(xi)
Sum_sub(xi, Cons_sum(psi, k, s)) → Sum_constant(k)
Sum_sub(xi, Cons_sum(psi, k, s)) → Sum_sub(xi, s)
Sum_sub(xi, Cons_usual(y, m, s)) → Sum_sub(xi, s)
Concat(Concat(s, t), u) → Concat(s, Concat(t, u))
Concat(Cons_usual(x, m, s), t) → Cons_usual(x, Term_sub(m, t), Concat(s, t))
Concat(Cons_sum(xi, k, s), t) → Cons_sum(xi, k, Concat(s, t))
Concat(Id, s) → s

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs:

TERM_SUB(Case(m, xi, n), s) → FROZEN(m, Sum_sub(xi, s), n, s)
The graph contains the following edges 1 > 1, 1 > 3, 2 >= 4
TERM_SUB(Term_sub(m, s), t) → CONCAT(s, t)
The graph contains the following edges 1 > 1, 2 >= 2
CONCAT(Cons_usual(x, m, s), t) → TERM_SUB(m, t)
The graph contains the following edges 1 > 1, 2 >= 2
TERM_SUB(Term_app(m, n), s) → TERM_SUB(m, s)
The graph contains the following edges 1 > 1, 2 >= 2
TERM_SUB(Term_app(m, n), s) → TERM_SUB(n, s)
The graph contains the following edges 1 > 1, 2 >= 2
TERM_SUB(Term_pair(m, n), s) → TERM_SUB(m, s)
The graph contains the following edges 1 > 1, 2 >= 2
TERM_SUB(Term_pair(m, n), s) → TERM_SUB(n, s)
The graph contains the following edges 1 > 1, 2 >= 2
TERM_SUB(Term_inl(m), s) → TERM_SUB(m, s)
The graph contains the following edges 1 > 1, 2 >= 2
TERM_SUB(Term_inr(m), s) → TERM_SUB(m, s)
The graph contains the following edges 1 > 1, 2 >= 2
TERM_SUB(Term_sub(m, s), t) → TERM_SUB(m, Concat(s, t))
The graph contains the following edges 1 > 1
FROZEN(m, Sum_constant(Left), n, s) → TERM_SUB(m, s)
The graph contains the following edges 1 >= 1, 4 >= 2
FROZEN(m, Sum_constant(Right), n, s) → TERM_SUB(n, s)
The graph contains the following edges 3 >= 1, 4 >= 2
FROZEN(m, Sum_term_var(xi), n, s) → TERM_SUB(m, s)
The graph contains the following edges 1 >= 1, 4 >= 2
FROZEN(m, Sum_term_var(xi), n, s) → TERM_SUB(n, s)
The graph contains the following edges 3 >= 1, 4 >= 2
CONCAT(Concat(s, t), u) → CONCAT(s, Concat(t, u))
The graph contains the following edges 1 > 1
CONCAT(Concat(s, t), u) → CONCAT(t, u)
The graph contains the following edges 1 > 1, 2 >= 2
CONCAT(Cons_usual(x, m, s), t) → CONCAT(s, t)
The graph contains the following edges 1 > 1, 2 >= 2
CONCAT(Cons_sum(xi, k, s), t) → CONCAT(s, t)
The graph contains the following edges 1 > 1, 2 >= 2