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Proof step 119 from proof termination-RED1 (previous step)

〈RED1(t1; tn)〉 (tn ≠ none → ¬ hasS(tn) ∧ #(tn) < #(t1)), ∀ 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) ⊦ 〈RED1(t1; tn)〉〈if tn ≠ none then tn := some(tn .t _ t2) else if value(t1) then { RED1(t2; tn) ; if tn ≠ none then tn := some(t1 _ tn .t) }〉 (tn ≠ none → ¬ hasS(tn) ∧ ¬ #(t1) + #(t2) < #(tn))

Heuristic contract and execute applied rule execute call

And obtained the following new goals

Proof step 118:
〈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) ⊦ 〈if tn0 ≠ none then tn0 := some(tn0 .t _ t2) else if value(t1) then { RED1(t2; tn0) ; if tn0 ≠ none then tn0 := some(t1 _ tn0 .t) }〉 (tn0 ≠ none → ¬ hasS(tn0) ∧ ¬ #(t1) + #(t2) < #(tn0))

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ()]]