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Proof step 49 from proof termination-RED1 (previous step)

〈RED1(t2; tn)〉 tn = tn3, 〈RED1(t4; tn2)〉 tn2 = none, 〈RED1(t3; tn1)〉 tn1 = none, ∀ t0. #(t0) < #(t3 _ t4 _ t2) → (¬ hasS(t0) → 〈RED1(t0; tn)〉 (tn ≠ none → ¬ hasS(tn) ∧ #(tn) < #(t0))), value(t3 _ t4), value(t3), ¬ hasS(t2), ¬ hasS(t3), ¬ hasS(t4), ¬ (t3 = K ∧ value(t4) ∧ value(t2)), ¬ (ap(t3) ∧ t3 .1 = S), ¬ (ap(t3) ∧ t3 .1 = K ∧ value(t3 .2) ∧ value(t4)), ¬ (ap(t3) ∧ ap(t3 .1) ∧ t3 .1 .1 = S), tn3 ≠ none → ¬ hasS(tn3) ∧ #(tn3) < #(t2), t = t3 _ t4, tn3 ≠ none, ¬ (some(t _ tn3 .t) ≠ none → ¬ hasS(some(t _ tn3 .t)) ∧ ¬ #(t) + #(t2) < #(some(t _ tn3 .t))) ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 48:
〈RED1(t3; tn1)〉 tn1 = none, 〈RED1(t4; tn2)〉 tn2 = none, 〈RED1(t2; tn)〉 tn = tn3, ∀ t0. #(t0) < #(t3 _ t4 _ t2) → (¬ hasS(t0) → 〈RED1(t0; tn)〉 (tn ≠ none → ¬ hasS(tn) ∧ #(tn) < #(t0))), tn3 ≠ none, #(tn3) < #(t2), value(t3), value(t3 _ t4), ¬ hasS(tn3), ¬ hasS(t4), ¬ hasS(t3), ¬ hasS(t2), ¬ (¬ hasS(t3 _ t4 _ tn3 .t) ∧ #(tn3 .t) < #(t2)), ¬ (ap(t3) ∧ ap(t3 .1) ∧ t3 .1 .1 = S), ¬ (ap(t3) ∧ t3 .1 = K ∧ value(t3 .2) ∧ value(t4)), ¬ (ap(t3) ∧ t3 .1 = S), ¬ (t3 = K ∧ value(t4) ∧ value(t2)) ⊦

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ m < n → n ≠ 0], [CSIMPFORWARD : ⊦ m < n → n ≠ 0], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m < n + 1 ↔ ¬ n < m], [CSIMPSEQ : n < n0 ⊦ m + ((* n)) < m0 + ((* n0)) ↔ m < m0 + (n0 - n)], [CSIMPSEQ : ⊦ m + n < m + n0 ↔ n < n0], [CSIMPSEQ : ⊦ #(some(t)) = #(t)], [CSIMPSEQ : ⊦ m +1 = m + 1], [CSIMPSEQ : ⊦ #(t _ t0) = (#(t) + #(t0)) +1], [CSIMPSEQ : ⊦ hasS(some(t)) ↔ hasS(t)], [CSIMPSEQ : ⊦ some(t) ≠ none])]]