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Proof step 54 from proof termination-RED1 (previous step)

〈RED1(t2; tn)〉 (tn ≠ none → ¬ hasS(tn) ∧ #(tn) < #(t2)), 〈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) ⊦ 〈RED1(t2; tn0)〉〈t1 := t3 _ t4 ; if tn0 ≠ none then tn0 := some(t1 _ tn0 .t)〉 (tn0 ≠ none → ¬ hasS(tn0) ∧ ¬ #(t1) + #(t2) < #(tn0))

Heuristic contract and execute applied rule execute call

And obtained the following new goals

Proof step 53:
〈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) ⊦ 〈t1 := t3 _ t4〉〈if tn3 ≠ none then tn3 := some(t1 _ tn3 .t)〉 (tn3 ≠ none → ¬ hasS(tn3) ∧ ¬ #(t1) + #(t2) < #(tn3))

Rule argument

[fmaposlist-arg: (pos: left 1, pos: right 1)]

Additional information

[[CONCRETESIMPRULES : ()]]