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Proof step 538 from proof SII-loops (previous step)

〈TOPRED(S _ (S _ K _ K) _ (S _ K _ K); tn1): m - 1 〉〈if tn1 = none then { RED1(S _ (S _ K _ K); tn1): m - 1 ; if tn1 ≠ none then tn1 := some(tn1 .t _ (S _ K _ K)) else { RED1(S _ K _ K; tn1): m - 1 ; if tn1 ≠ none then tn1 := some(S _ (S _ K _ K) _ tn1 .t) } }〉〈tn := tn1 ; if tn ≠ none then tn := some(tn .t _ (S _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K)))) else { RED1(S _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K)); tn): m ; if tn ≠ none then tn := some(S _ (S _ K _ K) _ (S _ K _ K) _ tn .t) }〉〈if tn ≠ none then RED(tn .t; t2): 1 + m else t2 := S _ (S _ K _ K) _ (S _ K _ K) _ (S _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K)))〉 t2 = t, ∀ kappa0, t. kappa0 < ((((m + 1) + 1) + 1) + 1) + 1 → (〈RED(S _ (S _ K _ K) _ (S _ K _ K) _ (S _ (S _ K _ K) _ (S _ K _ K)); t2): kappa0 〉 t2 = t → false), m ≠ 0 ⊦

Heuristic nonrecursive calls applied rule call left

And obtained the following new goals

Proof step 26:
⊦
Proof step 537:
〈tn := tn1, t0 := S _ (S _ K _ K) _ (S _ K _ K)〉〈if m - 1 = 0 then abort else if ap(t0) ∧ ap(t0 .1) ∧ t0 .1 .1 = K ∧ value(t0 .1 .2) ∧ value(t0 .2) then tn := some(t0 .1 .2) else if ap(t0) ∧ ap(t0 .1) ∧ ap(t0 .1 .1) ∧ t0 .1 .1 .1 = S then let v1 = t0 .1 .1 .2, v2 = t0 .1 .2, v3 = t0 .2 in if value(v1) ∧ value(v2) ∧ value(v3) then tn := some(v1 _ v3 _ (v2 _ v3)) else tn := none else tn := none〉〈tn1 := tn ; if tn1 = none then { RED1(S _ (S _ K _ K); tn1): m - 1 ; if tn1 ≠ none then tn1 := some(tn1 .t _ (S _ K _ K)) else { RED1(S _ K _ K; tn1): m - 1 ; if tn1 ≠ none then tn1 := some(S _ (S _ K _ K) _ tn1 .t) } }〉〈tn := tn1 ; if tn ≠ none then tn := some(tn .t _ (S _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K)))) else { RED1(S _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K)); tn): m ; if tn ≠ none then tn := some(S _ (S _ K _ K) _ (S _ K _ K) _ tn .t) }〉〈if tn ≠ none then RED(tn .t; t2): 1 + m else t2 := S _ (S _ K _ K) _ (S _ K _ K) _ (S _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K)))〉 t2 = t, ∀ kappa0, t. kappa0 < ((((m + 1) + 1) + 1) + 1) + 1 → (〈RED(S _ (S _ K _ K) _ (S _ K _ K) _ (S _ (S _ K _ K) _ (S _ K _ K)); t2): kappa0 〉 t2 = t → false), m ≠ 0 ⊦

Rule argument

[fmapos-arg: pos: left 1]

Additional information

[[CONCRETESIMPRULES : ()]]