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Proof step 649 from proof SII-loops (previous step)

〈TOPRED(S _ (S _ K _ K) _ (S _ K _ K) _ (S _ (S _ K _ K) _ (S _ K _ K)); tn1): m0 〉〈if tn1 = none then { RED1(S _ (S _ K _ K) _ (S _ K _ K); tn1): m0 ; if tn1 ≠ none then tn1 := some(tn1 .t _ (S _ (S _ K _ K) _ (S _ K _ K))) else { RED1(S _ (S _ K _ K) _ (S _ K _ K); tn1): m0 ; if tn1 ≠ none then tn1 := some(S _ (S _ K _ K) _ (S _ K _ K) _ tn1 .t) } }〉〈if tn1 ≠ none then RED(tn1 .t; t3): m0 + 1 else t3 := S _ (S _ K _ K) _ (S _ K _ K) _ (S _ (S _ K _ K) _ (S _ K _ K))〉 t3 = t, ∀ kappa0, t. kappa0 < (m0 + 1) + 1 → (〈RED(S _ (S _ K _ K) _ (S _ K _ K) _ (S _ (S _ K _ K) _ (S _ K _ K)); t3): kappa0 〉 t3 = t → false) ⊦

Heuristic weak unfold applied rule call left

And obtained the following new goals

Proof step 7:
⊦
Proof step 648:
〈tn := tn1, t0 := S _ (S _ K _ K) _ (S _ K _ K) _ (S _ (S _ K _ K) _ (S _ K _ K))〉〈if m0 = 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) _ (S _ K _ K); tn1): m0 ; if tn1 ≠ none then tn1 := some(tn1 .t _ (S _ (S _ K _ K) _ (S _ K _ K))) else { RED1(S _ (S _ K _ K) _ (S _ K _ K); tn1): m0 ; if tn1 ≠ none then tn1 := some(S _ (S _ K _ K) _ (S _ K _ K) _ tn1 .t) } }〉〈if tn1 ≠ none then RED(tn1 .t; t3): m0 + 1 else t3 := S _ (S _ K _ K) _ (S _ K _ K) _ (S _ (S _ K _ K) _ (S _ K _ K))〉 t3 = t, ∀ kappa0, t. kappa0 < (m0 + 1) + 1 → (〈RED(S _ (S _ K _ K) _ (S _ K _ K) _ (S _ (S _ K _ K) _ (S _ K _ K)); t3): kappa0 〉 t3 = t → false) ⊦

Rule argument

[fmapos-arg: pos: left 1]

Additional information

[[CONCRETESIMPRULES : ()]]