Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
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, X₄) → l2(X₀, X₁, X₂, X₃, X₄)
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄)
t₆: l10(X₀, X₁, X₂, X₃, X₄) → l11(X₀, X₁, X₂, X₃, X₄)
t₇: l11(X₀, X₁, X₂, X₃, X₄) → l12(X₀, X₁, X₂, X₃, X₄)
t₈: l12(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₁, 1, X₃, X₄)
t₁₁: l13(X₀, X₁, X₂, X₃, X₄) → l15(X₀, nondef_0, X₂, X₂-1, X₄)
t₂₀: l14(X₀, X₁, X₂, X₃, X₄) → l18(X₀, X₁, X₂, X₃, X₄)
t₁₂: l15(X₀, X₁, X₂, X₃, X₄) → l16(X₀, X₁, X₂, X₃, X₄) :|: 0 ≤ X₃
t₁₃: l15(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄) :|: X₃ < 0
t₁₄: l16(X₀, X₁, X₂, X₃, X₄) → l17(X₀, X₁, X₂, X₃, X₄) :|: X₁ < nondef_1
t₁₅: l16(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄) :|: nondef_1 ≤ X₁
t₁₆: l17(X₀, X₁, X₂, X₃, X₄) → l15(X₀, X₁, X₂, X₃-1, X₄)
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄)
t₂: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃, X₄)
t₄: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄)
t₅: l5(X₀, X₁, X₂, X₃, X₄) → l10(X₀, X₁, X₂, X₃, X₄)
t₁₉: l6(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₁, X₀, X₃, X₄)
t₁₇: l7(X₀, X₁, X₂, X₃, X₄) → l8(X₂+1, X₁, X₂, X₃, X₄)
t₁₈: l8(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄)
t₉: l9(X₀, X₁, X₂, X₃, X₄) → l13(X₀, X₁, X₂, X₃, X₄) :|: X₂ < X₄
t₁₀: l9(X₀, X₁, X₂, X₃, X₄) → l14(X₀, X₁, X₂, X₃, X₄) :|: X₄ ≤ X₂
Preprocessing
Found invariant 2 ≤ X₄ ∧ 2+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 4 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₀ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 2 ≤ X₀ for location l6
Found invariant 2 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ 1+X₃ ∧ 0 ≤ X₂+X₃ ∧ 1 ≤ X₂ for location l15
Found invariant 2 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₂ for location l17
Found invariant 2 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ 1+X₃ ∧ 0 ≤ X₂+X₃ ∧ 1 ≤ X₂ for location l7
Found invariant 2 ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 1 ≤ X₂ for location l13
Found invariant 2 ≤ X₄ ∧ 2+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 4 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₀ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 2 ≤ X₀ for location l8
Found invariant 2 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₂ for location l16
Found invariant X₄ ≤ X₂ ∧ 1 ≤ X₂ for location l18
Found invariant 1 ≤ X₂ for location l9
Found invariant X₄ ≤ X₂ ∧ 1 ≤ X₂ for location l14
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
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, X₄) → l2(X₀, X₁, X₂, X₃, X₄)
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄)
t₆: l10(X₀, X₁, X₂, X₃, X₄) → l11(X₀, X₁, X₂, X₃, X₄)
t₇: l11(X₀, X₁, X₂, X₃, X₄) → l12(X₀, X₁, X₂, X₃, X₄)
t₈: l12(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₁, 1, X₃, X₄)
t₁₁: l13(X₀, X₁, X₂, X₃, X₄) → l15(X₀, nondef_0, X₂, X₂-1, X₄) :|: 2 ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 1 ≤ X₂
t₂₀: l14(X₀, X₁, X₂, X₃, X₄) → l18(X₀, X₁, X₂, X₃, X₄) :|: X₄ ≤ X₂ ∧ 1 ≤ X₂
t₁₂: l15(X₀, X₁, X₂, X₃, X₄) → l16(X₀, X₁, X₂, X₃, X₄) :|: 0 ≤ X₃ ∧ 2 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ 1+X₃ ∧ 0 ≤ X₂+X₃ ∧ 1 ≤ X₂
t₁₃: l15(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄) :|: X₃ < 0 ∧ 2 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ 1+X₃ ∧ 0 ≤ X₂+X₃ ∧ 1 ≤ X₂
t₁₄: l16(X₀, X₁, X₂, X₃, X₄) → l17(X₀, X₁, X₂, X₃, X₄) :|: X₁ < nondef_1 ∧ 2 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₂
t₁₅: l16(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄) :|: nondef_1 ≤ X₁ ∧ 2 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₂
t₁₆: l17(X₀, X₁, X₂, X₃, X₄) → l15(X₀, X₁, X₂, X₃-1, X₄) :|: 2 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₂
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄)
t₂: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃, X₄)
t₄: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄)
t₅: l5(X₀, X₁, X₂, X₃, X₄) → l10(X₀, X₁, X₂, X₃, X₄)
t₁₉: l6(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₁, X₀, X₃, X₄) :|: 2 ≤ X₄ ∧ 2+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 4 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₀ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 2 ≤ X₀
t₁₇: l7(X₀, X₁, X₂, X₃, X₄) → l8(X₂+1, X₁, X₂, X₃, X₄) :|: 2 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ 1+X₃ ∧ 0 ≤ X₂+X₃ ∧ 1 ≤ X₂
t₁₈: l8(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: 2 ≤ X₄ ∧ 2+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 4 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₀ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 2 ≤ X₀
t₉: l9(X₀, X₁, X₂, X₃, X₄) → l13(X₀, X₁, X₂, X₃, X₄) :|: X₂ < X₄ ∧ 1 ≤ X₂
t₁₀: l9(X₀, X₁, X₂, X₃, X₄) → l14(X₀, X₁, X₂, X₃, X₄) :|: X₄ ≤ X₂ ∧ 1 ≤ X₂
MPRF for transition t₁₁: l13(X₀, X₁, X₂, X₃, X₄) → l15(X₀, nondef_0, X₂, X₂-1, X₄) :|: 2 ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 1 ≤ X₂ of depth 1:
new bound:
X₄+1 {O(n)}
MPRF:
l16 [X₄-X₂-1 ]
l17 [X₄-X₂-1 ]
l15 [X₄-X₂-1 ]
l7 [X₄-X₂-1 ]
l8 [X₄-X₀ ]
l6 [X₄-X₀ ]
l9 [X₄-X₂ ]
l13 [X₄-X₂ ]
MPRF for transition t₁₃: l15(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄) :|: X₃ < 0 ∧ 2 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ 1+X₃ ∧ 0 ≤ X₂+X₃ ∧ 1 ≤ X₂ of depth 1:
new bound:
X₄+1 {O(n)}
MPRF:
l16 [X₄-X₂ ]
l17 [X₄-X₂ ]
l15 [X₄-X₂ ]
l7 [X₄-X₂-1 ]
l8 [X₄-X₂-1 ]
l6 [X₄-X₀ ]
l9 [X₄-X₂ ]
l13 [X₄-X₂ ]
MPRF for transition t₁₅: l16(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄) :|: nondef_1 ≤ X₁ ∧ 2 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₂ of depth 1:
new bound:
X₄+1 {O(n)}
MPRF:
l16 [X₄-X₂ ]
l17 [X₄-X₂ ]
l15 [X₄-X₂ ]
l7 [X₄-X₂-1 ]
l8 [X₄-X₂-1 ]
l6 [X₄-X₂-1 ]
l9 [X₄-X₂ ]
l13 [X₄-X₂ ]
MPRF for transition t₁₉: l6(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₁, X₀, X₃, X₄) :|: 2 ≤ X₄ ∧ 2+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 4 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₀ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₄+1 {O(n)}
MPRF:
l16 [X₄-X₂ ]
l17 [X₄-X₂ ]
l15 [X₄-X₂ ]
l7 [X₄-X₂ ]
l8 [X₄-X₂ ]
l6 [X₄-X₂ ]
l9 [X₄-X₂ ]
l13 [X₄-X₂ ]
MPRF for transition t₁₇: l7(X₀, X₁, X₂, X₃, X₄) → l8(X₂+1, X₁, X₂, X₃, X₄) :|: 2 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ 1+X₃ ∧ 0 ≤ X₂+X₃ ∧ 1 ≤ X₂ of depth 1:
new bound:
X₄+1 {O(n)}
MPRF:
l16 [X₄-X₂ ]
l17 [X₄-X₂ ]
l15 [X₄-X₂ ]
l7 [X₄-X₂ ]
l8 [X₄-X₂-1 ]
l6 [X₄-X₂-1 ]
l9 [X₄-X₂ ]
l13 [X₄-X₂ ]
MPRF for transition t₁₈: l8(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: 2 ≤ X₄ ∧ 2+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 4 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₀ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₄+1 {O(n)}
MPRF:
l16 [X₄-X₂ ]
l17 [X₄-X₂ ]
l15 [X₄-X₂ ]
l7 [X₄-X₂ ]
l8 [X₄-X₂ ]
l6 [X₄-X₂-1 ]
l9 [X₄-X₂ ]
l13 [X₄-X₂ ]
MPRF for transition t₉: l9(X₀, X₁, X₂, X₃, X₄) → l13(X₀, X₁, X₂, X₃, X₄) :|: X₂ < X₄ ∧ 1 ≤ X₂ of depth 1:
new bound:
X₄+1 {O(n)}
MPRF:
l16 [X₄-X₂-1 ]
l17 [X₄-X₂-1 ]
l15 [X₄-X₂-1 ]
l7 [X₄-X₂-1 ]
l8 [X₄-X₂-1 ]
l6 [X₄-X₂-1 ]
l9 [X₄-X₂ ]
l13 [X₄-X₂-1 ]
MPRF for transition t₁₂: l15(X₀, X₁, X₂, X₃, X₄) → l16(X₀, X₁, X₂, X₃, X₄) :|: 0 ≤ X₃ ∧ 2 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ 1+X₃ ∧ 0 ≤ X₂+X₃ ∧ 1 ≤ X₂ of depth 1:
new bound:
2⋅X₄⋅X₄+6⋅X₄+4 {O(n^2)}
MPRF:
l13 [2⋅X₂ ]
l16 [X₂+X₃ ]
l17 [X₂+X₃ ]
l15 [X₂+X₃+1 ]
l9 [X₂-2 ]
l7 [X₂+X₃ ]
l8 [X₂-1 ]
l6 [X₀-2 ]
MPRF for transition t₁₄: l16(X₀, X₁, X₂, X₃, X₄) → l17(X₀, X₁, X₂, X₃, X₄) :|: X₁ < nondef_1 ∧ 2 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₂ of depth 1:
new bound:
X₄⋅X₄+3⋅X₄+2 {O(n^2)}
MPRF:
l13 [X₂ ]
l16 [X₃+1 ]
l17 [X₃ ]
l15 [X₃+1 ]
l9 [0 ]
l7 [0 ]
l8 [0 ]
l6 [0 ]
MPRF for transition t₁₆: l17(X₀, X₁, X₂, X₃, X₄) → l15(X₀, X₁, X₂, X₃-1, X₄) :|: 2 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₂ of depth 1:
new bound:
X₄⋅X₄+3⋅X₄+2 {O(n^2)}
MPRF:
l13 [X₂ ]
l16 [X₃+1 ]
l17 [X₃+1 ]
l15 [X₃+1 ]
l9 [0 ]
l7 [X₃+1 ]
l8 [0 ]
l6 [0 ]
Analysing control-flow refined program
Cut unsatisfiable transition t₁₃: l15→l7
Found invariant 3 ≤ X₄ ∧ 3 ≤ X₃+X₄ ∧ 3+X₃ ≤ X₄ ∧ 5 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₂ for location n_l16___2
Found invariant 2 ≤ X₄ ∧ 2+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 4 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₀ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 2 ≤ X₀ for location l6
Found invariant 2 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 1 ≤ X₂ for location l15
Found invariant 3 ≤ X₄ ∧ 3 ≤ X₃+X₄ ∧ 3+X₃ ≤ X₄ ∧ 5 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₂ for location n_l17___1
Found invariant 2 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 3+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2+X₃ ≤ X₂ ∧ 0 ≤ 1+X₃ ∧ 0 ≤ X₂+X₃ ∧ 1 ≤ X₂ for location n_l15___3
Found invariant 2 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ 1+X₃ ∧ 0 ≤ X₂+X₃ ∧ 1 ≤ X₂ for location l7
Found invariant 2 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 1 ≤ X₂ for location n_l16___5
Found invariant 2 ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 1 ≤ X₂ for location l13
Found invariant 2 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 4 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ 0 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 2 ≤ X₀ for location l8
Found invariant X₄ ≤ X₂ ∧ 1 ≤ X₂ for location l18
Found invariant 1 ≤ X₂ for location l9
Found invariant X₄ ≤ X₂ ∧ 1 ≤ X₂ for location l14
Found invariant 2 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 1 ≤ X₂ for location n_l17___4
knowledge_propagation leads to new time bound X₄+1 {O(n)} for transition t₁₂₉: l15(X₀, X₁, X₂, X₃, X₄) → n_l16___5(X₀, X₁, X₂, X₃, X₄) :|: 1+X₂ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ X₂ ≤ 1+X₃ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₄ ∧ 0 ≤ X₃ ∧ 1+X₃ ≤ X₂ ∧ 1+X₂ ≤ X₄ ∧ 0 ≤ X₃ ∧ 1+X₃ ≤ X₂ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 1 ≤ X₂
knowledge_propagation leads to new time bound X₄+1 {O(n)} for transition t₁₃₁: n_l16___5(X₀, X₁, X₂, X₃, X₄) → n_l17___4(X₀, X₁, X₂, Arg3_P, Arg4_P) :|: 1+X₂ ≤ X₄ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₃+1 ∧ 1+X₃ ≤ X₂ ∧ 1+X₂ ≤ Arg4_P ∧ 1+Arg3_P ≤ X₂ ∧ 0 ≤ Arg3_P ∧ X₃ ≤ Arg3_P ∧ Arg3_P ≤ X₃ ∧ X₄ ≤ Arg4_P ∧ Arg4_P ≤ X₄ ∧ 2 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 1 ≤ X₂
knowledge_propagation leads to new time bound X₄+1 {O(n)} for transition t₁₄₁: n_l16___5(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄) :|: nondef_1 ≤ X₁ ∧ 2 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 1 ≤ X₂
knowledge_propagation leads to new time bound X₄+1 {O(n)} for transition t₁₃₃: n_l17___4(X₀, X₁, X₂, X₃, X₄) → n_l15___3(X₀, X₁, X₂, X₃-1, X₄) :|: 1+X₂ ≤ X₄ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₃+1 ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1+X₃ ≤ X₂ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 1 ≤ X₂
MPRF for transition t₁₂₈: n_l15___3(X₀, X₁, X₂, X₃, X₄) → n_l16___2(X₀, X₁, X₂, X₃, X₄) :|: 1+X₂ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ 1+X₃ ∧ 2+X₃ ≤ X₂ ∧ 1+X₂ ≤ X₄ ∧ 0 ≤ X₃ ∧ 1+X₃ ≤ X₂ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 3+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2+X₃ ≤ X₂ ∧ 0 ≤ 1+X₃ ∧ 0 ≤ X₂+X₃ ∧ 1 ≤ X₂ of depth 1:
new bound:
X₄⋅X₄+5⋅X₄+4 {O(n^2)}
MPRF:
l15 [0 ]
l8 [0 ]
l6 [0 ]
l9 [0 ]
l13 [0 ]
n_l16___2 [X₃ ]
n_l17___4 [0 ]
n_l16___5 [0 ]
l7 [0 ]
n_l17___1 [X₃ ]
n_l15___3 [X₃+1 ]
MPRF for transition t₁₃₉: n_l15___3(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄) :|: X₃ < 0 ∧ 2 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ 1+X₃ ∧ 0 ≤ X₂+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 3+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2+X₃ ≤ X₂ ∧ 0 ≤ 1+X₃ ∧ 0 ≤ X₂+X₃ ∧ 1 ≤ X₂ of depth 1:
new bound:
X₄+1 {O(n)}
MPRF:
l15 [X₄-X₂ ]
l8 [X₄-X₀ ]
l6 [X₄-X₀ ]
l9 [X₄-X₂ ]
l13 [X₄-X₂ ]
n_l16___2 [X₄-X₂ ]
n_l16___5 [X₄-X₂ ]
l7 [X₄-X₂-1 ]
n_l17___1 [X₄-X₂ ]
n_l17___4 [X₄-X₂ ]
n_l15___3 [X₄-X₂ ]
MPRF for transition t₁₃₀: n_l16___2(X₀, X₁, X₂, X₃, X₄) → n_l17___1(X₀, X₁, X₂, Arg3_P, Arg4_P) :|: 1+X₂ ≤ X₄ ∧ 2+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1+X₂ ≤ Arg4_P ∧ 1+Arg3_P ≤ X₂ ∧ 0 ≤ Arg3_P ∧ X₃ ≤ Arg3_P ∧ Arg3_P ≤ X₃ ∧ X₄ ≤ Arg4_P ∧ Arg4_P ≤ X₄ ∧ 3 ≤ X₄ ∧ 3 ≤ X₃+X₄ ∧ 3+X₃ ≤ X₄ ∧ 5 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₂ of depth 1:
new bound:
X₄⋅X₄+5⋅X₄+4 {O(n^2)}
MPRF:
l15 [0 ]
l8 [0 ]
l6 [0 ]
l9 [0 ]
l13 [0 ]
n_l16___2 [X₃+1 ]
n_l17___4 [0 ]
n_l16___5 [0 ]
l7 [0 ]
n_l17___1 [X₃ ]
n_l15___3 [X₃+1 ]
MPRF for transition t₁₄₀: n_l16___2(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄) :|: nondef_1 ≤ X₁ ∧ 2 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₄ ∧ 3 ≤ X₃+X₄ ∧ 3+X₃ ≤ X₄ ∧ 5 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₂ of depth 1:
new bound:
X₄+1 {O(n)}
MPRF:
l15 [X₄-X₃-1 ]
l8 [X₄-X₂-1 ]
l6 [X₄-X₂-1 ]
l9 [X₄-X₂ ]
l13 [X₄-X₂ ]
n_l16___2 [X₄-X₂ ]
n_l16___5 [X₄-X₃-1 ]
l7 [X₄-X₂-1 ]
n_l17___1 [X₄-X₂ ]
n_l17___4 [X₄-X₂ ]
n_l15___3 [X₄-X₂ ]
MPRF for transition t₁₃₂: n_l17___1(X₀, X₁, X₂, X₃, X₄) → n_l15___3(X₀, X₁, X₂, X₃-1, X₄) :|: 1+X₂ ≤ X₄ ∧ 2+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃ ∧ 1+X₃ ≤ X₂ ∧ 1+X₂ ≤ X₄ ∧ 3 ≤ X₄ ∧ 3 ≤ X₃+X₄ ∧ 3+X₃ ≤ X₄ ∧ 5 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₂ of depth 1:
new bound:
X₄⋅X₄+5⋅X₄+4 {O(n^2)}
MPRF:
l15 [0 ]
l8 [0 ]
l6 [0 ]
l9 [0 ]
l13 [0 ]
n_l16___2 [X₃+1 ]
n_l17___4 [0 ]
n_l16___5 [0 ]
l7 [0 ]
n_l17___1 [X₃+1 ]
n_l15___3 [X₃+1 ]
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:4⋅X₄⋅X₄+19⋅X₄+26 {O(n^2)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₁₁: X₄+1 {O(n)}
t₂₀: 1 {O(1)}
t₁₂: 2⋅X₄⋅X₄+6⋅X₄+4 {O(n^2)}
t₁₃: X₄+1 {O(n)}
t₁₄: X₄⋅X₄+3⋅X₄+2 {O(n^2)}
t₁₅: X₄+1 {O(n)}
t₁₆: X₄⋅X₄+3⋅X₄+2 {O(n^2)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₁₉: X₄+1 {O(n)}
t₁₇: X₄+1 {O(n)}
t₁₈: X₄+1 {O(n)}
t₉: X₄+1 {O(n)}
t₁₀: 1 {O(1)}
Costbounds
Overall costbound: 4⋅X₄⋅X₄+19⋅X₄+26 {O(n^2)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₁₁: X₄+1 {O(n)}
t₂₀: 1 {O(1)}
t₁₂: 2⋅X₄⋅X₄+6⋅X₄+4 {O(n^2)}
t₁₃: X₄+1 {O(n)}
t₁₄: X₄⋅X₄+3⋅X₄+2 {O(n^2)}
t₁₅: X₄+1 {O(n)}
t₁₆: X₄⋅X₄+3⋅X₄+2 {O(n^2)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₁₉: X₄+1 {O(n)}
t₁₇: X₄+1 {O(n)}
t₁₈: X₄+1 {O(n)}
t₉: X₄+1 {O(n)}
t₁₀: 1 {O(1)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₀, X₄: X₄ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₃, X₄: X₄ {O(n)}
t₆, X₀: X₀ {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: X₃ {O(n)}
t₆, X₄: X₄ {O(n)}
t₇, X₀: X₀ {O(n)}
t₇, X₁: X₁ {O(n)}
t₇, X₂: X₂ {O(n)}
t₇, X₃: X₃ {O(n)}
t₇, X₄: X₄ {O(n)}
t₈, X₀: X₀ {O(n)}
t₈, X₁: X₁ {O(n)}
t₈, X₂: 1 {O(1)}
t₈, X₃: X₃ {O(n)}
t₈, X₄: X₄ {O(n)}
t₁₁, X₀: X₀+X₄+2 {O(n)}
t₁₁, X₂: X₄+2 {O(n)}
t₁₁, X₃: X₄+2 {O(n)}
t₁₁, X₄: X₄ {O(n)}
t₂₀, X₀: X₀+X₄+2 {O(n)}
t₂₀, X₂: X₄+3 {O(n)}
t₂₀, X₃: X₃+X₄+4 {O(n)}
t₂₀, X₄: 2⋅X₄ {O(n)}
t₁₂, X₀: X₀+X₄+2 {O(n)}
t₁₂, X₂: X₄+2 {O(n)}
t₁₂, X₃: X₄+3 {O(n)}
t₁₂, X₄: X₄ {O(n)}
t₁₃, X₀: X₀+X₄+2 {O(n)}
t₁₃, X₂: X₄+2 {O(n)}
t₁₃, X₃: 1 {O(1)}
t₁₃, X₄: X₄ {O(n)}
t₁₄, X₀: X₀+X₄+2 {O(n)}
t₁₄, X₂: X₄+2 {O(n)}
t₁₄, X₃: X₄+3 {O(n)}
t₁₄, X₄: X₄ {O(n)}
t₁₅, X₀: X₀+X₄+2 {O(n)}
t₁₅, X₂: X₄+2 {O(n)}
t₁₅, X₃: X₄+3 {O(n)}
t₁₅, X₄: X₄ {O(n)}
t₁₆, X₀: X₀+X₄+2 {O(n)}
t₁₆, X₂: X₄+2 {O(n)}
t₁₆, X₃: X₄+3 {O(n)}
t₁₆, X₄: X₄ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: X₄ {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₄, X₄: X₄ {O(n)}
t₅, X₀: X₀ {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₅, X₄: X₄ {O(n)}
t₁₉, X₀: X₄+2 {O(n)}
t₁₉, X₂: X₄+2 {O(n)}
t₁₉, X₃: X₄+4 {O(n)}
t₁₉, X₄: X₄ {O(n)}
t₁₇, X₀: X₄+2 {O(n)}
t₁₇, X₂: 2⋅X₄+4 {O(n)}
t₁₇, X₃: X₄+4 {O(n)}
t₁₇, X₄: X₄ {O(n)}
t₁₈, X₀: X₄+2 {O(n)}
t₁₈, X₂: 2⋅X₄+4 {O(n)}
t₁₈, X₃: X₄+4 {O(n)}
t₁₈, X₄: X₄ {O(n)}
t₉, X₀: X₀+X₄+2 {O(n)}
t₉, X₂: X₄+2 {O(n)}
t₉, X₃: X₃+X₄+4 {O(n)}
t₉, X₄: X₄ {O(n)}
t₁₀, X₀: X₀+X₄+2 {O(n)}
t₁₀, X₂: X₄+3 {O(n)}
t₁₀, X₃: X₃+X₄+4 {O(n)}
t₁₀, X₄: 2⋅X₄ {O(n)}