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Proof step 10 from proof termination-TOPRED (previous step)

t = t0 _ t1, t0 .1 .1 = S, ap(t), ap(t0), ap(t0 .1), value(t0 .1 .2), value(t0 .2), value(t1) ⊦ t0 .1 = K, hasS(t), ¬ hasS(t0 .1 .2 _ t1 _ (t0 .2 _ t1)) ∧ 3 + #(t0 .1 .2) + #(t0 .2) + 2 * #(t1) < #(t)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
t0 .1 .1 = S, ap(t0), ap(t0 .1), value(t0 .1 .2), value(t0 .2), value(t1) ⊦ t0 .1 = K, hasS(t0), hasS(t1), ¬ hasS(t0 .1 .2 _ t1 _ (t0 .2 _ t1)) ∧ ¬ #(t0) ≤ #(t1) + #(t0 .1 .2) + #(t0 .2) + 2

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ ¬ m < n ↔ n ≤ m], [CSIMPSEQ : ⊦ m * n = n * m], [CSIMPSEQ : ⊦ m0 * m * n = (m0 * m) * n], [CSIMPSEQ : ⊦ m0 * 1 = m0], [CSIMPSEQ : m2 ≠ 0 ⊦ ((* m2)) * m + n < m + n0 ↔ (m2 - 1) * m + n < n0], [CSIMPSEQ : n0 < n ⊦ m + ((* n)) < m0 + ((* n0)) ↔ m + (n - n0) < m0], [CSIMPSEQ : ⊦ m +1 = m + 1], [CSIMPSEQ : ⊦ #(t _ t0) = (#(t) + #(t0)) +1], [CSIMPSEQ : ⊦ hasS(t _ t0) ↔ hasS(t) ∨ hasS(t0)], [CSIMPSEQ : ⊦ ap(t _ t0)])]]