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Proof step 33 from proof termination-RED1 (previous step)

〈RED1(t1; tn)〉 tn = tn0, ∀ t0. #(t0) < #(t1 _ t2) → (¬ hasS(t0) → 〈RED1(t0; tn)〉 (tn ≠ none → ¬ hasS(tn) ∧ #(tn) < #(t0))), ¬ hasS(t1), ¬ hasS(t2), ¬ (ap(t1) ∧ t1 .1 = K ∧ value(t1 .2) ∧ value(t2)), ¬ (ap(t1) ∧ ap(t1 .1) ∧ t1 .1 .1 = S), tn0 ≠ none → ¬ hasS(tn0) ∧ #(tn0) < #(t1), tn0 ≠ none, ¬ (some(tn0 .t _ t2) ≠ none → ¬ hasS(some(tn0 .t _ t2)) ∧ ¬ #(t1) + #(t2) < #(some(tn0 .t _ t2))) ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 32:
〈RED1(t1; tn)〉 tn = tn0, ∀ t0. #(t0) < #(t1 _ t2) → (¬ hasS(t0) → 〈RED1(t0; tn)〉 (tn ≠ none → ¬ hasS(tn) ∧ #(tn) < #(t0))), tn0 ≠ none, #(tn0) < #(t1), ¬ hasS(tn0), ¬ hasS(t2), ¬ hasS(t1), ¬ (¬ hasS(tn0 .t) ∧ #(tn0 .t) < #(t1)), ¬ (ap(t1) ∧ ap(t1 .1) ∧ t1 .1 .1 = S), ¬ (ap(t1) ∧ t1 .1 = K ∧ value(t1 .2) ∧ 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 : ⊦ m + n < m + n0 ↔ n < n0], [CSIMPSEQ : ⊦ m +1 = m + 1], [CSIMPSEQ : ⊦ #(t _ t0) = (#(t) + #(t0)) +1], [CSIMPSEQ : ⊦ #(some(t)) = #(t)], [CSIMPSEQ : ⊦ hasS(t _ t0) ↔ hasS(t) ∨ hasS(t0)], [CSIMPSEQ : ⊦ hasS(some(t)) ↔ hasS(t)], [CSIMPSEQ : ⊦ some(t) ≠ none])]]