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Proof step 547 from proof SII-loops (previous step)

〈if value(v4) ∧ value(v0) ∧ value(v) then tn0 := some(v4 _ v _ (v0 _ v)) else tn0 := none〉〈tn1 := tn0 ; if tn1 = none then { RED1(S _ (S _ K _ K) _ (S _ K _ K); tn1): m ; if tn1 ≠ none then tn1 := some(tn1 .t _ (S _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K)))) else { RED1(S _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K)); tn1): m ; if tn1 ≠ none then tn1 := some(S _ (S _ K _ K) _ (S _ K _ K) _ tn1 .t) } }〉〈if tn1 ≠ none then RED(tn1 .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, tn0 = tn1 ∧ t1 = S _ (S _ K _ K) _ (S _ K _ K) _ (S _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K))), v = t1 .2, v0 = t1 .1 .2, v4 = t1 .1 .1 .2 ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 546:
〈tn0 := none〉〈tn1 := tn0 ; if tn1 = none then { RED1(S _ (S _ K _ K) _ (S _ K _ K); tn1): m ; if tn1 ≠ none then tn1 := some(tn1 .t _ (S _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K)))) else { RED1(S _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K)); tn1): m ; if tn1 ≠ none then tn1 := some(S _ (S _ K _ K) _ (S _ K _ K) _ tn1 .t) } }〉〈if tn1 ≠ none then RED(tn1 .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

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ value ( S _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K) ))], [CSIMPSEQ : ⊦ value(S _ K _ K)], [CSIMPSEQ : ⊦ (t _ t0) .2 = t0], [CSIMPSEQ : ⊦ (t _ t0) .1 = t])]]