Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: nondef_0, nondef_1
Locations: l0, l1, l10, l11, l12, l13, l14, l15, l16, l17, l18, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃)
t₉: l10(X₀, X₁, X₂, X₃) → l13(X₀, X₁, 0, X₃) :|: 0 ≤ X₁
t₁₀: l10(X₀, X₁, X₂, X₃) → l14(X₀, X₁, X₂, X₃) :|: X₁ < 0
t₇: l11(X₀, X₁, X₂, X₃) → l12(X₀, X₁, X₂, X₃)
t₈: l12(X₀, X₁, X₂, X₃) → l10(X₀, X₃, X₂, X₃)
t₁₁: l13(X₀, X₁, X₂, X₃) → l15(X₀, X₁, X₂, X₃) :|: X₂+1 ≤ X₁
t₁₂: l13(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₁ < 1+X₂
t₂₀: l14(X₀, X₁, X₂, X₃) → l18(X₀, X₁, X₂, X₃)
t₁₄: l15(X₀, X₁, X₂, X₃) → l16(X₀, X₁, X₂, X₃) :|: nondef_0 ≤ nondef_1
t₁₃: l15(X₀, X₁, X₂, X₃) → l17(X₀, X₁, X₂, X₃) :|: nondef_1 < nondef_0
t₁₆: l16(X₀, X₁, X₂, X₃) → l13(X₀, X₁, X₂+1, X₃)
t₁₅: l17(X₀, X₁, X₂, X₃) → l16(X₀, X₁, X₂, X₃)
t₁: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃)
t₂: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃)
t₄: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₅: l5(X₀, X₁, X₂, X₃) → l9(X₀, X₁, X₂, X₃)
t₁₉: l6(X₀, X₁, X₂, X₃) → l10(X₀, X₀, X₂, X₃)
t₁₇: l7(X₀, X₁, X₂, X₃) → l8(X₁-1, X₁, X₂, X₃)
t₁₈: l8(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃)
t₆: l9(X₀, X₁, X₂, X₃) → l11(X₀, X₁, X₂, X₃)
Preprocessing
Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ 1+X₀ for location l6
Found invariant 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location l15
Found invariant 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location l17
Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁ for location l7
Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ for location l13
Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ 1+X₀ for location l8
Found invariant X₁ ≤ X₃ for location l10
Found invariant 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location l16
Found invariant X₁ ≤ X₃ ∧ 1+X₁ ≤ 0 for location l18
Found invariant X₁ ≤ X₃ ∧ 1+X₁ ≤ 0 for location l14
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: nondef_0, nondef_1
Locations: l0, l1, l10, l11, l12, l13, l14, l15, l16, l17, l18, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃)
t₉: l10(X₀, X₁, X₂, X₃) → l13(X₀, X₁, 0, X₃) :|: 0 ≤ X₁ ∧ X₁ ≤ X₃
t₁₀: l10(X₀, X₁, X₂, X₃) → l14(X₀, X₁, X₂, X₃) :|: X₁ < 0 ∧ X₁ ≤ X₃
t₇: l11(X₀, X₁, X₂, X₃) → l12(X₀, X₁, X₂, X₃)
t₈: l12(X₀, X₁, X₂, X₃) → l10(X₀, X₃, X₂, X₃)
t₁₁: l13(X₀, X₁, X₂, X₃) → l15(X₀, X₁, X₂, X₃) :|: X₂+1 ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁
t₁₂: l13(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₁ < 1+X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁
t₂₀: l14(X₀, X₁, X₂, X₃) → l18(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₃ ∧ 1+X₁ ≤ 0
t₁₄: l15(X₀, X₁, X₂, X₃) → l16(X₀, X₁, X₂, X₃) :|: nondef_0 ≤ nondef_1 ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁
t₁₃: l15(X₀, X₁, X₂, X₃) → l17(X₀, X₁, X₂, X₃) :|: nondef_1 < nondef_0 ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁
t₁₆: l16(X₀, X₁, X₂, X₃) → l13(X₀, X₁, X₂+1, X₃) :|: 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁
t₁₅: l17(X₀, X₁, X₂, X₃) → l16(X₀, X₁, X₂, X₃) :|: 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁
t₁: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃)
t₂: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃)
t₄: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₅: l5(X₀, X₁, X₂, X₃) → l9(X₀, X₁, X₂, X₃)
t₁₉: l6(X₀, X₁, X₂, X₃) → l10(X₀, X₀, X₂, X₃) :|: 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ 1+X₀
t₁₇: l7(X₀, X₁, X₂, X₃) → l8(X₁-1, X₁, X₂, X₃) :|: 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁
t₁₈: l8(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ 1+X₀
t₆: l9(X₀, X₁, X₂, X₃) → l11(X₀, X₁, X₂, X₃)
MPRF for transition t₉: l10(X₀, X₁, X₂, X₃) → l13(X₀, X₁, 0, X₃) :|: 0 ≤ X₁ ∧ X₁ ≤ X₃ of depth 1:
new bound:
X₃+1 {O(n)}
MPRF for transition t₁₂: l13(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₁ < 1+X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ of depth 1:
new bound:
X₃+1 {O(n)}
MPRF for transition t₁₇: l7(X₀, X₁, X₂, X₃) → l8(X₁-1, X₁, X₂, X₃) :|: 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁ of depth 1:
new bound:
X₃+1 {O(n)}
MPRF for transition t₁₈: l8(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ 1+X₀ of depth 1:
new bound:
X₃+1 {O(n)}
MPRF for transition t₁₉: l6(X₀, X₁, X₂, X₃) → l10(X₀, X₀, X₂, X₃) :|: 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ 1+X₀ of depth 1:
new bound:
X₃+1 {O(n)}
MPRF for transition t₁₁: l13(X₀, X₁, X₂, X₃) → l15(X₀, X₁, X₂, X₃) :|: X₂+1 ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ of depth 1:
new bound:
X₃⋅X₃+4⋅X₃+3 {O(n^2)}
MPRF for transition t₁₃: l15(X₀, X₁, X₂, X₃) → l17(X₀, X₁, X₂, X₃) :|: nondef_1 < nondef_0 ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ of depth 1:
new bound:
X₃⋅X₃+2⋅X₃ {O(n^2)}
MPRF for transition t₁₄: l15(X₀, X₁, X₂, X₃) → l16(X₀, X₁, X₂, X₃) :|: nondef_0 ≤ nondef_1 ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ of depth 1:
new bound:
X₃⋅X₃+3⋅X₃+1 {O(n^2)}
MPRF for transition t₁₅: l17(X₀, X₁, X₂, X₃) → l16(X₀, X₁, X₂, X₃) :|: 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ of depth 1:
new bound:
X₃⋅X₃+2⋅X₃ {O(n^2)}
MPRF for transition t₁₆: l16(X₀, X₁, X₂, X₃) → l13(X₀, X₁, X₂+1, X₃) :|: 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ of depth 1:
new bound:
X₃⋅X₃+2⋅X₃ {O(n^2)}
Chain transitions t₁₉: l6→l10 and t₁₀: l10→l14 to t₁₄₆: l6→l14
Chain transitions t₈: l12→l10 and t₁₀: l10→l14 to t₁₄₇: l12→l14
Chain transitions t₈: l12→l10 and t₉: l10→l13 to t₁₄₈: l12→l13
Chain transitions t₁₉: l6→l10 and t₉: l10→l13 to t₁₄₉: l6→l13
Chain transitions t₁₄₉: l6→l13 and t₁₂: l13→l7 to t₁₅₀: l6→l7
Chain transitions t₁₆: l16→l13 and t₁₂: l13→l7 to t₁₅₁: l16→l7
Chain transitions t₁₆: l16→l13 and t₁₁: l13→l15 to t₁₅₂: l16→l15
Chain transitions t₁₄₉: l6→l13 and t₁₁: l13→l15 to t₁₅₃: l6→l15
Chain transitions t₁₄₈: l12→l13 and t₁₁: l13→l15 to t₁₅₄: l12→l15
Chain transitions t₁₄₈: l12→l13 and t₁₂: l13→l7 to t₁₅₅: l12→l7
Chain transitions t₁₅₃: l6→l15 and t₁₃: l15→l17 to t₁₅₆: l6→l17
Chain transitions t₁₅₂: l16→l15 and t₁₃: l15→l17 to t₁₅₇: l16→l17
Chain transitions t₁₅₂: l16→l15 and t₁₄: l15→l16 to t₁₅₈: l16→l16
Chain transitions t₁₅₃: l6→l15 and t₁₄: l15→l16 to t₁₅₉: l6→l16
Chain transitions t₁₅₄: l12→l15 and t₁₄: l15→l16 to t₁₆₀: l12→l16
Chain transitions t₁₅₄: l12→l15 and t₁₃: l15→l17 to t₁₆₁: l12→l17
Chain transitions t₁₅₆: l6→l17 and t₁₅: l17→l16 to t₁₆₂: l6→l16
Chain transitions t₁₅₇: l16→l17 and t₁₅: l17→l16 to t₁₆₃: l16→l16
Chain transitions t₁₆₁: l12→l17 and t₁₅: l17→l16 to t₁₆₄: l12→l16
Chain transitions t₁₈: l8→l6 and t₁₅₀: l6→l7 to t₁₆₅: l8→l7
Chain transitions t₁₈: l8→l6 and t₁₅₆: l6→l17 to t₁₆₆: l8→l17
Chain transitions t₁₈: l8→l6 and t₁₆₂: l6→l16 to t₁₆₇: l8→l16
Chain transitions t₁₈: l8→l6 and t₁₅₉: l6→l16 to t₁₆₈: l8→l16
Chain transitions t₁₈: l8→l6 and t₁₅₃: l6→l15 to t₁₆₉: l8→l15
Chain transitions t₁₈: l8→l6 and t₁₄₆: l6→l14 to t₁₇₀: l8→l14
Chain transitions t₁₈: l8→l6 and t₁₄₉: l6→l13 to t₁₇₁: l8→l13
Chain transitions t₁₈: l8→l6 and t₁₉: l6→l10 to t₁₇₂: l8→l10
Chain transitions t₁₆₅: l8→l7 and t₁₇: l7→l8 to t₁₇₃: l8→l8
Chain transitions t₁₅₁: l16→l7 and t₁₇: l7→l8 to t₁₇₄: l16→l8
Chain transitions t₁₅₅: l12→l7 and t₁₇: l7→l8 to t₁₇₅: l12→l8
Analysing control-flow refined program
Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ 1+X₀ for location l6
Found invariant 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location l15
Found invariant 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location l17
Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁ for location l7
Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ for location l13
Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ 1+X₀ for location l8
Found invariant X₁ ≤ X₃ for location l10
Found invariant 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location l16
Found invariant X₁ ≤ X₃ ∧ 1+X₁ ≤ 0 for location l18
Found invariant X₁ ≤ X₃ ∧ 1+X₁ ≤ 0 for location l14
MPRF for transition t₁₆₇: l8(X₀, X₁, X₂, X₃) -{6}> l16(X₀, X₀, 0, X₃) :|: 0 ≤ X₀ ∧ 1 ≤ X₀ ∧ Temp_Int₆₀₀ < Temp_Int₆₀₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ 1+X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ 1+X₀ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₀ ∧ 0 ≤ 0 ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ ∧ 0 ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ ∧ 0 ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ 1+X₀ of depth 1:
new bound:
2⋅X₃ {O(n)}
MPRF for transition t₁₆₈: l8(X₀, X₁, X₂, X₃) -{5}> l16(X₀, X₀, 0, X₃) :|: 0 ≤ X₀ ∧ 1 ≤ X₀ ∧ Temp_Int₆₀₆ ≤ Temp_Int₆₀₇ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ 1+X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ 1+X₀ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₀ ∧ 0 ≤ 0 ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ ∧ 0 ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ 1+X₀ of depth 1:
new bound:
2⋅X₃ {O(n)}
MPRF for transition t₁₇₃: l8(X₀, X₁, X₂, X₃) -{5}> l8(X₀-1, X₀, 0, X₃) :|: 0 ≤ X₀ ∧ X₀ < 1 ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ 1+X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ 1+X₀ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₀ ∧ 0 ≤ 0 ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₀ ∧ 0 ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ 1+X₀ of depth 1:
new bound:
2⋅X₃ {O(n)}
MPRF for transition t₁₇₄: l16(X₀, X₁, X₂, X₃) -{3}> l8(X₁-1, X₁, 1+X₂, X₃) :|: X₁ < 2+X₂ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ 1+X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ X₂+1 ≤ X₁ ∧ 0 ≤ 1+X₂ ∧ 0 ≤ X₁+X₂+1 ∧ 0 ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ 1+X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ 1+X₂ ∧ 0 ≤ X₁+1+X₂ ∧ X₁ ≤ 1+X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ of depth 1:
new bound:
2⋅X₃+2 {O(n)}
TWN: t₁₅₈: l16→l16
cycle: [t₁₅₈: l16→l16; t₁₆₃: l16→l16]
loop: (2+X₂ ≤ X₁ ∨ 2+X₂ ≤ X₁,(X₁,X₂) -> (X₁,1+X₂)
order: [X₁; X₂]
closed-form:
X₁: X₁
X₂: X₂ + [[n != 0]] * n^1
Termination: true
Formula:
1 < 0
∨ 2+X₂ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2+X₂ ≤ X₁ ∧ X₁ ≤ 2+X₂
∨ 1 < 0
∨ 2+X₂ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2+X₂ ≤ X₁ ∧ X₁ ≤ 2+X₂
Stabilization-Threshold for: 2+X₂ ≤ X₁
alphas_abs: 2+X₂+X₁
M: 0
N: 1
Bound: 2⋅X₁+2⋅X₂+6 {O(n)}
loop: (2+X₂ ≤ X₁ ∨ 2+X₂ ≤ X₁,(X₁,X₂) -> (X₁,1+X₂)
order: [X₁; X₂]
closed-form:
X₁: X₁
X₂: X₂ + [[n != 0]] * n^1
Termination: true
Formula:
1 < 0
∨ 2+X₂ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2+X₂ ≤ X₁ ∧ X₁ ≤ 2+X₂
∨ 1 < 0
∨ 2+X₂ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2+X₂ ≤ X₁ ∧ X₁ ≤ 2+X₂
Stabilization-Threshold for: 2+X₂ ≤ X₁
alphas_abs: 2+X₂+X₁
M: 0
N: 1
Bound: 2⋅X₁+2⋅X₂+6 {O(n)}
loop: (2+X₂ ≤ X₁ ∨ 2+X₂ ≤ X₁,(X₁,X₂) -> (X₁,1+X₂)
order: [X₁; X₂]
closed-form:
X₁: X₁
X₂: X₂ + [[n != 0]] * n^1
Termination: true
Formula:
1 < 0
∨ 2+X₂ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2+X₂ ≤ X₁ ∧ X₁ ≤ 2+X₂
∨ 1 < 0
∨ 2+X₂ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2+X₂ ≤ X₁ ∧ X₁ ≤ 2+X₂
Stabilization-Threshold for: 2+X₂ ≤ X₁
alphas_abs: 2+X₂+X₁
M: 0
N: 1
Bound: 2⋅X₁+2⋅X₂+6 {O(n)}
loop: (2+X₂ ≤ X₁ ∨ 2+X₂ ≤ X₁,(X₁,X₂) -> (X₁,1+X₂)
order: [X₁; X₂]
closed-form:
X₁: X₁
X₂: X₂ + [[n != 0]] * n^1
Termination: true
Formula:
1 < 0
∨ 2+X₂ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2+X₂ ≤ X₁ ∧ X₁ ≤ 2+X₂
∨ 1 < 0
∨ 2+X₂ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2+X₂ ≤ X₁ ∧ X₁ ≤ 2+X₂
Stabilization-Threshold for: 2+X₂ ≤ X₁
alphas_abs: 2+X₂+X₁
M: 0
N: 1
Bound: 2⋅X₁+2⋅X₂+6 {O(n)}
loop: (2+X₂ ≤ X₁ ∨ 2+X₂ ≤ X₁,(X₁,X₂) -> (X₁,1+X₂)
order: [X₁; X₂]
closed-form:
X₁: X₁
X₂: X₂ + [[n != 0]] * n^1
Termination: true
Formula:
1 < 0
∨ 2+X₂ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2+X₂ ≤ X₁ ∧ X₁ ≤ 2+X₂
∨ 1 < 0
∨ 2+X₂ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2+X₂ ≤ X₁ ∧ X₁ ≤ 2+X₂
Stabilization-Threshold for: 2+X₂ ≤ X₁
alphas_abs: 2+X₂+X₁
M: 0
N: 1
Bound: 2⋅X₁+2⋅X₂+6 {O(n)}
loop: (2+X₂ ≤ X₁ ∨ 2+X₂ ≤ X₁,(X₁,X₂) -> (X₁,1+X₂)
order: [X₁; X₂]
closed-form:
X₁: X₁
X₂: X₂ + [[n != 0]] * n^1
Termination: true
Formula:
1 < 0
∨ 2+X₂ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2+X₂ ≤ X₁ ∧ X₁ ≤ 2+X₂
∨ 1 < 0
∨ 2+X₂ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2+X₂ ≤ X₁ ∧ X₁ ≤ 2+X₂
Stabilization-Threshold for: 2+X₂ ≤ X₁
alphas_abs: 2+X₂+X₁
M: 0
N: 1
Bound: 2⋅X₁+2⋅X₂+6 {O(n)}
loop: (2+X₂ ≤ X₁ ∨ 2+X₂ ≤ X₁,(X₁,X₂) -> (X₁,1+X₂)
order: [X₁; X₂]
closed-form:
X₁: X₁
X₂: X₂ + [[n != 0]] * n^1
Termination: true
Formula:
1 < 0
∨ 2+X₂ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2+X₂ ≤ X₁ ∧ X₁ ≤ 2+X₂
∨ 1 < 0
∨ 2+X₂ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2+X₂ ≤ X₁ ∧ X₁ ≤ 2+X₂
Stabilization-Threshold for: 2+X₂ ≤ X₁
alphas_abs: 2+X₂+X₁
M: 0
N: 1
Bound: 2⋅X₁+2⋅X₂+6 {O(n)}
loop: (2+X₂ ≤ X₁ ∨ 2+X₂ ≤ X₁,(X₁,X₂) -> (X₁,1+X₂)
order: [X₁; X₂]
closed-form:
X₁: X₁
X₂: X₂ + [[n != 0]] * n^1
Termination: true
Formula:
1 < 0
∨ 2+X₂ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2+X₂ ≤ X₁ ∧ X₁ ≤ 2+X₂
∨ 1 < 0
∨ 2+X₂ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2+X₂ ≤ X₁ ∧ X₁ ≤ 2+X₂
Stabilization-Threshold for: 2+X₂ ≤ X₁
alphas_abs: 2+X₂+X₁
M: 0
N: 1
Bound: 2⋅X₁+2⋅X₂+6 {O(n)}
TWN - Lifting for t₁₅₈: l16→l16 of 2⋅X₁+2⋅X₂+8 {O(n)}
relevant size-bounds w.r.t. t₁₆₈:
X₁: 2⋅X₃ {O(n)}
X₂: 0 {O(1)}
Runtime-bound of t₁₆₈: 2⋅X₃ {O(n)}
Results in: 8⋅X₃⋅X₃+16⋅X₃ {O(n^2)}
TWN - Lifting for t₁₅₈: l16→l16 of 2⋅X₁+2⋅X₂+8 {O(n)}
relevant size-bounds w.r.t. t₁₆₇:
X₁: 2⋅X₃ {O(n)}
X₂: 0 {O(1)}
Runtime-bound of t₁₆₇: 2⋅X₃ {O(n)}
Results in: 8⋅X₃⋅X₃+16⋅X₃ {O(n^2)}
TWN - Lifting for t₁₅₈: l16→l16 of 2⋅X₁+2⋅X₂+8 {O(n)}
relevant size-bounds w.r.t. t₁₆₄:
X₁: X₃ {O(n)}
X₂: 0 {O(1)}
Runtime-bound of t₁₆₄: 1 {O(1)}
Results in: 2⋅X₃+8 {O(n)}
TWN - Lifting for t₁₅₈: l16→l16 of 2⋅X₁+2⋅X₂+8 {O(n)}
relevant size-bounds w.r.t. t₁₆₀:
X₁: X₃ {O(n)}
X₂: 0 {O(1)}
Runtime-bound of t₁₆₀: 1 {O(1)}
Results in: 2⋅X₃+8 {O(n)}
TWN - Lifting for t₁₅₈: l16→l16 of 2⋅X₁+2⋅X₂+8 {O(n)}
relevant size-bounds w.r.t. t₁₆₈:
X₁: 2⋅X₃ {O(n)}
X₂: 0 {O(1)}
Runtime-bound of t₁₆₈: 2⋅X₃ {O(n)}
Results in: 8⋅X₃⋅X₃+16⋅X₃ {O(n^2)}
TWN - Lifting for t₁₅₈: l16→l16 of 2⋅X₁+2⋅X₂+8 {O(n)}
relevant size-bounds w.r.t. t₁₆₇:
X₁: 2⋅X₃ {O(n)}
X₂: 0 {O(1)}
Runtime-bound of t₁₆₇: 2⋅X₃ {O(n)}
Results in: 8⋅X₃⋅X₃+16⋅X₃ {O(n^2)}
TWN - Lifting for t₁₅₈: l16→l16 of 2⋅X₁+2⋅X₂+8 {O(n)}
relevant size-bounds w.r.t. t₁₆₄:
X₁: X₃ {O(n)}
X₂: 0 {O(1)}
Runtime-bound of t₁₆₄: 1 {O(1)}
Results in: 2⋅X₃+8 {O(n)}
TWN - Lifting for t₁₅₈: l16→l16 of 2⋅X₁+2⋅X₂+8 {O(n)}
relevant size-bounds w.r.t. t₁₆₀:
X₁: X₃ {O(n)}
X₂: 0 {O(1)}
Runtime-bound of t₁₆₀: 1 {O(1)}
Results in: 2⋅X₃+8 {O(n)}
TWN: t₁₆₃: l16→l16
TWN - Lifting for t₁₆₃: l16→l16 of 2⋅X₁+2⋅X₂+8 {O(n)}
relevant size-bounds w.r.t. t₁₆₈:
X₁: 2⋅X₃ {O(n)}
X₂: 0 {O(1)}
Runtime-bound of t₁₆₈: 2⋅X₃ {O(n)}
Results in: 8⋅X₃⋅X₃+16⋅X₃ {O(n^2)}
TWN - Lifting for t₁₆₃: l16→l16 of 2⋅X₁+2⋅X₂+8 {O(n)}
relevant size-bounds w.r.t. t₁₆₇:
X₁: 2⋅X₃ {O(n)}
X₂: 0 {O(1)}
Runtime-bound of t₁₆₇: 2⋅X₃ {O(n)}
Results in: 8⋅X₃⋅X₃+16⋅X₃ {O(n^2)}
TWN - Lifting for t₁₆₃: l16→l16 of 2⋅X₁+2⋅X₂+8 {O(n)}
relevant size-bounds w.r.t. t₁₆₄:
X₁: X₃ {O(n)}
X₂: 0 {O(1)}
Runtime-bound of t₁₆₄: 1 {O(1)}
Results in: 2⋅X₃+8 {O(n)}
TWN - Lifting for t₁₆₃: l16→l16 of 2⋅X₁+2⋅X₂+8 {O(n)}
relevant size-bounds w.r.t. t₁₆₀:
X₁: X₃ {O(n)}
X₂: 0 {O(1)}
Runtime-bound of t₁₆₀: 1 {O(1)}
Results in: 2⋅X₃+8 {O(n)}
TWN - Lifting for t₁₆₃: l16→l16 of 2⋅X₁+2⋅X₂+8 {O(n)}
relevant size-bounds w.r.t. t₁₆₈:
X₁: 2⋅X₃ {O(n)}
X₂: 0 {O(1)}
Runtime-bound of t₁₆₈: 2⋅X₃ {O(n)}
Results in: 8⋅X₃⋅X₃+16⋅X₃ {O(n^2)}
TWN - Lifting for t₁₆₃: l16→l16 of 2⋅X₁+2⋅X₂+8 {O(n)}
relevant size-bounds w.r.t. t₁₆₇:
X₁: 2⋅X₃ {O(n)}
X₂: 0 {O(1)}
Runtime-bound of t₁₆₇: 2⋅X₃ {O(n)}
Results in: 8⋅X₃⋅X₃+16⋅X₃ {O(n^2)}
TWN - Lifting for t₁₆₃: l16→l16 of 2⋅X₁+2⋅X₂+8 {O(n)}
relevant size-bounds w.r.t. t₁₆₄:
X₁: X₃ {O(n)}
X₂: 0 {O(1)}
Runtime-bound of t₁₆₄: 1 {O(1)}
Results in: 2⋅X₃+8 {O(n)}
TWN - Lifting for t₁₆₃: l16→l16 of 2⋅X₁+2⋅X₂+8 {O(n)}
relevant size-bounds w.r.t. t₁₆₀:
X₁: X₃ {O(n)}
X₂: 0 {O(1)}
Runtime-bound of t₁₆₀: 1 {O(1)}
Results in: 2⋅X₃+8 {O(n)}
CFR did not improve the program. Rolling back
CFR did not improve the program. Rolling back
Analysing control-flow refined program
Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₁ for location n_l16___2
Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ 1+X₀ for location l6
Found invariant 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location n_l15___7
Found invariant 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location n_l16___6
Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₁ for location n_l17___1
Found invariant 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location n_l13___4
Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₁ for location n_l15___3
Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁ for location l7
Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ for location l13
Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ 1+X₀ for location l8
Found invariant X₁ ≤ X₃ for location l10
Found invariant X₁ ≤ X₃ ∧ 1+X₁ ≤ 0 for location l18
Found invariant 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location n_l17___5
Found invariant X₁ ≤ X₃ ∧ 1+X₁ ≤ 0 for location l14
knowledge_propagation leads to new time bound X₃+1 {O(n)} for transition t₄₀₅: l13(X₀, X₁, X₂, X₃) → n_l15___7(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁
knowledge_propagation leads to new time bound X₃+1 {O(n)} for transition t₄₀₈: n_l15___7(X₀, X₁, X₂, X₃) → n_l16___6(X₀, X₁, Arg2_P, X₃) :|: X₂ ≤ 0 ∧ 1+Arg2_P ≤ X₁ ∧ 0 ≤ Arg2_P ∧ X₂ ≤ Arg2_P ∧ Arg2_P ≤ X₂ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₁ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁
knowledge_propagation leads to new time bound X₃+1 {O(n)} for transition t₄₀₉: n_l15___7(X₀, X₁, X₂, X₃) → n_l17___5(X₀, X₁, Arg2_P, X₃) :|: X₂ ≤ 0 ∧ 1+Arg2_P ≤ X₁ ∧ 0 ≤ Arg2_P ∧ X₂ ≤ Arg2_P ∧ Arg2_P ≤ X₂ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₁ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁
knowledge_propagation leads to new time bound X₃+1 {O(n)} for transition t₄₁₃: n_l17___5(X₀, X₁, X₂, X₃) → n_l16___6(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0 ∧ X₁ ≤ X₃ ∧ 1 ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁
knowledge_propagation leads to new time bound 2⋅X₃+2 {O(n)} for transition t₄₁₁: n_l16___6(X₀, X₁, X₂, X₃) → n_l13___4(X₀, X₁, X₂+1, X₃) :|: X₂ ≤ 0 ∧ X₁ ≤ X₃ ∧ 1 ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁
MPRF for transition t₄₀₄: n_l13___4(X₀, X₁, X₂, X₃) → n_l15___3(X₀, X₁, X₂, X₃) :|: 1 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ of depth 1:
new bound:
2⋅X₃⋅X₃+10⋅X₃+6 {O(n^2)}
MPRF for transition t₄₀₆: n_l15___3(X₀, X₁, X₂, X₃) → n_l16___2(X₀, X₁, Arg2_P, X₃) :|: 1 ≤ X₂ ∧ 1+Arg2_P ≤ X₁ ∧ 0 ≤ Arg2_P ∧ X₂ ≤ Arg2_P ∧ Arg2_P ≤ X₂ ∧ X₁ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₁ of depth 1:
new bound:
4⋅X₃⋅X₃+8⋅X₃+4 {O(n^2)}
MPRF for transition t₄₀₇: n_l15___3(X₀, X₁, X₂, X₃) → n_l17___1(X₀, X₁, Arg2_P, X₃) :|: 1 ≤ X₂ ∧ 1+Arg2_P ≤ X₁ ∧ 0 ≤ Arg2_P ∧ X₂ ≤ Arg2_P ∧ Arg2_P ≤ X₂ ∧ X₁ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₁ of depth 1:
new bound:
2⋅X₃⋅X₃+4⋅X₃+2 {O(n^2)}
MPRF for transition t₄₁₀: n_l16___2(X₀, X₁, X₂, X₃) → n_l13___4(X₀, X₁, X₂+1, X₃) :|: 1 ≤ X₂ ∧ X₁ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₁ of depth 1:
new bound:
2⋅X₃⋅X₃+7⋅X₃+4 {O(n^2)}
MPRF for transition t₄₁₂: n_l17___1(X₀, X₁, X₂, X₃) → n_l16___2(X₀, X₁, X₂, X₃) :|: 1 ≤ X₂ ∧ X₁ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₁ of depth 1:
new bound:
4⋅X₃⋅X₃+7⋅X₃+2 {O(n^2)}
MPRF for transition t₄₂₁: n_l13___4(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₁ < 1+X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ of depth 1:
new bound:
X₃+1 {O(n)}
CFR did not improve the program. Rolling back
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:5⋅X₃⋅X₃+18⋅X₃+20 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: X₃+1 {O(n)}
t₁₀: 1 {O(1)}
t₁₁: X₃⋅X₃+4⋅X₃+3 {O(n^2)}
t₁₂: X₃+1 {O(n)}
t₁₃: X₃⋅X₃+2⋅X₃ {O(n^2)}
t₁₄: X₃⋅X₃+3⋅X₃+1 {O(n^2)}
t₁₅: X₃⋅X₃+2⋅X₃ {O(n^2)}
t₁₆: X₃⋅X₃+2⋅X₃ {O(n^2)}
t₁₇: X₃+1 {O(n)}
t₁₈: X₃+1 {O(n)}
t₁₉: X₃+1 {O(n)}
t₂₀: 1 {O(1)}
Costbounds
Overall costbound: 5⋅X₃⋅X₃+18⋅X₃+20 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: X₃+1 {O(n)}
t₁₀: 1 {O(1)}
t₁₁: X₃⋅X₃+4⋅X₃+3 {O(n^2)}
t₁₂: X₃+1 {O(n)}
t₁₃: X₃⋅X₃+2⋅X₃ {O(n^2)}
t₁₄: X₃⋅X₃+3⋅X₃+1 {O(n^2)}
t₁₅: X₃⋅X₃+2⋅X₃ {O(n^2)}
t₁₆: X₃⋅X₃+2⋅X₃ {O(n^2)}
t₁₇: X₃+1 {O(n)}
t₁₈: X₃+1 {O(n)}
t₁₉: X₃+1 {O(n)}
t₂₀: 1 {O(1)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₅, X₀: X₀ {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₆, X₀: X₀ {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: X₃ {O(n)}
t₇, X₀: X₀ {O(n)}
t₇, X₁: X₁ {O(n)}
t₇, X₂: X₂ {O(n)}
t₇, X₃: X₃ {O(n)}
t₈, X₀: X₀ {O(n)}
t₈, X₁: X₃ {O(n)}
t₈, X₂: X₂ {O(n)}
t₈, X₃: X₃ {O(n)}
t₉, X₀: X₀+X₃+1 {O(n)}
t₉, X₁: X₃+1 {O(n)}
t₉, X₂: 0 {O(1)}
t₉, X₃: X₃ {O(n)}
t₁₀, X₀: X₀+X₃+1 {O(n)}
t₁₀, X₁: 2⋅X₃+1 {O(n)}
t₁₀, X₂: X₃⋅X₃+2⋅X₃+X₂ {O(n^2)}
t₁₀, X₃: 2⋅X₃ {O(n)}
t₁₁, X₀: X₀+X₃+1 {O(n)}
t₁₁, X₁: X₃+1 {O(n)}
t₁₁, X₂: X₃⋅X₃+2⋅X₃ {O(n^2)}
t₁₁, X₃: X₃ {O(n)}
t₁₂, X₀: 2⋅X₀+2⋅X₃+2 {O(n)}
t₁₂, X₁: X₃+1 {O(n)}
t₁₂, X₂: X₃⋅X₃+2⋅X₃ {O(n^2)}
t₁₂, X₃: X₃ {O(n)}
t₁₃, X₀: X₀+X₃+1 {O(n)}
t₁₃, X₁: X₃+1 {O(n)}
t₁₃, X₂: X₃⋅X₃+2⋅X₃ {O(n^2)}
t₁₃, X₃: X₃ {O(n)}
t₁₄, X₀: X₀+X₃+1 {O(n)}
t₁₄, X₁: X₃+1 {O(n)}
t₁₄, X₂: X₃⋅X₃+2⋅X₃ {O(n^2)}
t₁₄, X₃: X₃ {O(n)}
t₁₅, X₀: X₀+X₃+1 {O(n)}
t₁₅, X₁: X₃+1 {O(n)}
t₁₅, X₂: X₃⋅X₃+2⋅X₃ {O(n^2)}
t₁₅, X₃: X₃ {O(n)}
t₁₆, X₀: X₀+X₃+1 {O(n)}
t₁₆, X₁: X₃+1 {O(n)}
t₁₆, X₂: X₃⋅X₃+2⋅X₃ {O(n^2)}
t₁₆, X₃: X₃ {O(n)}
t₁₇, X₀: X₃+1 {O(n)}
t₁₇, X₁: X₃+1 {O(n)}
t₁₇, X₂: X₃⋅X₃+2⋅X₃ {O(n^2)}
t₁₇, X₃: X₃ {O(n)}
t₁₈, X₀: X₃+1 {O(n)}
t₁₈, X₁: X₃+1 {O(n)}
t₁₈, X₂: X₃⋅X₃+2⋅X₃ {O(n^2)}
t₁₈, X₃: X₃ {O(n)}
t₁₉, X₀: X₃+1 {O(n)}
t₁₉, X₁: X₃+1 {O(n)}
t₁₉, X₂: X₃⋅X₃+2⋅X₃ {O(n^2)}
t₁₉, X₃: X₃ {O(n)}
t₂₀, X₀: X₀+X₃+1 {O(n)}
t₂₀, X₁: 2⋅X₃+1 {O(n)}
t₂₀, X₂: X₃⋅X₃+2⋅X₃+X₂ {O(n^2)}
t₂₀, X₃: 2⋅X₃ {O(n)}