Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l10, l11, l12, l13, l14, l15, l16, 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)
t₁₃: l10(X₀, X₁, X₂, X₃) → l13(X₀, X₁, X₂, X₃+1)
t₁₁: l11(X₀, X₁, X₂, X₃) → l12(X₀, X₁, X₂, X₃)
t₁₂: l12(X₀, X₁, X₂, X₃) → l10(X₀, X₁, X₂, X₃)
t₉: l13(X₀, X₁, X₂, X₃) → l11(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₁
t₁₀: l13(X₀, X₁, X₂, X₃) → l14(X₀, X₁, X₂, X₃) :|: X₁ < X₃
t₁₄: l14(X₀, X₁, X₂, X₃) → l6(X₂+1, X₁, X₂, X₃)
t₁₇: l15(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) → l8(X₀, X₁, X₂, X₃)
t₇: l5(X₀, X₁, X₂, X₃) → l13(X₀, X₁, X₂, X₂) :|: X₂ ≤ X₁
t₈: l5(X₀, X₁, X₂, X₃) → l15(X₀, X₁, X₂, X₃) :|: X₁ < X₂
t₁₅: l6(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃)
t₁₆: l7(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₀, X₃)
t₅: l8(X₀, X₁, X₂, X₃) → l9(X₀, X₁, X₂, X₃)
t₆: l9(X₀, X₁, X₂, X₃) → l5(X₀, X₁, 1, X₃)
Preprocessing
Found invariant X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location l11
Found invariant X₃ ≤ 1+X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 2 ≤ X₀ for location l6
Found invariant 1 ≤ X₂ ∧ 1+X₁ ≤ X₂ for location l15
Found invariant X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location l12
Found invariant X₃ ≤ 1+X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 2 ≤ X₀ for location l7
Found invariant 1 ≤ X₂ for location l5
Found invariant X₃ ≤ 1+X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location l13
Found invariant X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location l10
Found invariant 1 ≤ X₂ ∧ 1+X₁ ≤ X₂ for location l16
Found invariant X₃ ≤ 1+X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location l14
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l10, l11, l12, l13, l14, l15, l16, 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)
t₁₃: l10(X₀, X₁, X₂, X₃) → l13(X₀, X₁, X₂, X₃+1) :|: X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁
t₁₁: l11(X₀, X₁, X₂, X₃) → l12(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁
t₁₂: l12(X₀, X₁, X₂, X₃) → l10(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁
t₉: l13(X₀, X₁, X₂, X₃) → l11(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₁ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁
t₁₀: l13(X₀, X₁, X₂, X₃) → l14(X₀, X₁, X₂, X₃) :|: X₁ < X₃ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁
t₁₄: l14(X₀, X₁, X₂, X₃) → l6(X₂+1, X₁, X₂, X₃) :|: X₃ ≤ 1+X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁
t₁₇: l15(X₀, X₁, X₂, X₃) → l16(X₀, X₁, X₂, X₃) :|: 1 ≤ X₂ ∧ 1+X₁ ≤ X₂
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) → l8(X₀, X₁, X₂, X₃)
t₇: l5(X₀, X₁, X₂, X₃) → l13(X₀, X₁, X₂, X₂) :|: X₂ ≤ X₁ ∧ 1 ≤ X₂
t₈: l5(X₀, X₁, X₂, X₃) → l15(X₀, X₁, X₂, X₃) :|: X₁ < X₂ ∧ 1 ≤ X₂
t₁₅: l6(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₃ ≤ 1+X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 2 ≤ X₀
t₁₆: l7(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₀, X₃) :|: X₃ ≤ 1+X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 2 ≤ X₀
t₅: l8(X₀, X₁, X₂, X₃) → l9(X₀, X₁, X₂, X₃)
t₆: l9(X₀, X₁, X₂, X₃) → l5(X₀, X₁, 1, X₃)
MPRF for transition t₁₀: l13(X₀, X₁, X₂, X₃) → l14(X₀, X₁, X₂, X₃) :|: X₁ < X₃ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ of depth 1:
new bound:
X₁+2 {O(n)}
MPRF:
l12 [X₁+1-X₂ ]
l10 [X₁+1-X₂ ]
l11 [X₁+1-X₂ ]
l14 [X₁-X₂ ]
l13 [X₁+1-X₂ ]
l6 [X₁-X₂ ]
l7 [X₁-X₂ ]
l5 [X₁+1-X₂ ]
MPRF for transition t₁₄: l14(X₀, X₁, X₂, X₃) → l6(X₂+1, X₁, X₂, X₃) :|: X₃ ≤ 1+X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ of depth 1:
new bound:
2⋅X₁+1 {O(n)}
MPRF:
l12 [2⋅X₁-X₂ ]
l10 [2⋅X₁-X₂ ]
l11 [2⋅X₁-X₂ ]
l14 [2⋅X₁-X₂ ]
l13 [2⋅X₁-X₂ ]
l6 [2⋅X₁-X₀ ]
l7 [2⋅X₁-X₀ ]
l5 [2⋅X₁-X₂ ]
MPRF for transition t₇: l5(X₀, X₁, X₂, X₃) → l13(X₀, X₁, X₂, X₂) :|: X₂ ≤ X₁ ∧ 1 ≤ X₂ of depth 1:
new bound:
X₁+2 {O(n)}
MPRF:
l12 [X₁-X₂ ]
l10 [X₁-X₂ ]
l11 [X₁-X₂ ]
l14 [X₁-X₂ ]
l13 [X₁-X₂ ]
l6 [X₁-X₂ ]
l7 [X₁-X₂ ]
l5 [X₁+1-X₂ ]
MPRF for transition t₁₅: l6(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₃ ≤ 1+X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
2⋅X₁+1 {O(n)}
MPRF:
l12 [2⋅X₁-X₂ ]
l10 [2⋅X₁-X₂ ]
l11 [2⋅X₁-X₂ ]
l14 [X₁+X₃-X₂-1 ]
l13 [2⋅X₁-X₂ ]
l6 [2⋅X₁-X₂ ]
l7 [2⋅X₁-X₂-1 ]
l5 [2⋅X₁-X₂ ]
MPRF for transition t₁₆: l7(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₀, X₃) :|: X₃ ≤ 1+X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₁+2 {O(n)}
MPRF:
l12 [X₁+1-X₂ ]
l10 [X₁+1-X₂ ]
l11 [X₁+1-X₂ ]
l14 [X₃-X₂ ]
l13 [X₁+1-X₂ ]
l6 [X₃-X₂ ]
l7 [X₃-X₂ ]
l5 [X₁+1-X₂ ]
MPRF for transition t₁₃: l10(X₀, X₁, X₂, X₃) → l13(X₀, X₁, X₂, X₃+1) :|: X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ of depth 1:
new bound:
X₁⋅X₁+3⋅X₁ {O(n^2)}
MPRF:
l12 [X₁+1-X₃ ]
l10 [X₁+1-X₃ ]
l11 [X₁+1-X₃ ]
l14 [X₁-X₃ ]
l5 [X₁ ]
l13 [X₁+1-X₃ ]
l6 [X₁-X₃ ]
l7 [X₁-X₃ ]
MPRF for transition t₁₁: l11(X₀, X₁, X₂, X₃) → l12(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ of depth 1:
new bound:
X₁⋅X₁+3⋅X₁ {O(n^2)}
MPRF:
l12 [X₁-X₃ ]
l10 [X₁-X₃ ]
l11 [X₁+1-X₃ ]
l14 [X₁-X₃ ]
l5 [X₁ ]
l13 [X₁+1-X₃ ]
l6 [X₁-X₃ ]
l7 [X₁-X₃ ]
MPRF for transition t₁₂: l12(X₀, X₁, X₂, X₃) → l10(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ of depth 1:
new bound:
4⋅X₁⋅X₁+12⋅X₁+5 {O(n^2)}
MPRF:
l12 [2⋅X₁-X₃ ]
l10 [2⋅X₁-X₃-1 ]
l11 [2⋅X₁-X₃ ]
l14 [2⋅X₁-X₃ ]
l5 [2⋅X₁-X₂ ]
l13 [2⋅X₁-X₃ ]
l6 [2⋅X₁-X₃ ]
l7 [2⋅X₁-X₃ ]
MPRF for transition t₉: l13(X₀, X₁, X₂, X₃) → l11(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₁ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ of depth 1:
new bound:
X₁⋅X₁+3⋅X₁ {O(n^2)}
MPRF:
l12 [X₁-X₃ ]
l10 [X₁-X₃ ]
l11 [X₁-X₃ ]
l14 [X₁-X₃ ]
l5 [X₁ ]
l13 [X₁+1-X₃ ]
l6 [X₁-X₃ ]
l7 [X₁-X₃ ]
Analysing control-flow refined program
Cut unsatisfiable transition t₁₀: l13→l14
Found invariant X₃ ≤ 1+X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 2 ≤ X₀ for location l6
Found invariant 1 ≤ X₂ ∧ 1+X₁ ≤ X₂ for location l15
Found invariant X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₁ for location n_l10___1
Found invariant X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₁ for location n_l12___2
Found invariant X₃ ≤ 1+X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location n_l13___4
Found invariant X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location n_l10___5
Found invariant X₃ ≤ 1+X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 2 ≤ X₀ for location l7
Found invariant X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location n_l11___7
Found invariant 1 ≤ X₂ for location l5
Found invariant X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location l13
Found invariant 1 ≤ X₂ ∧ 1+X₁ ≤ X₂ for location l16
Found invariant X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₁ for location n_l11___3
Found invariant X₃ ≤ 1+X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location l14
Found invariant X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location n_l12___6
knowledge_propagation leads to new time bound X₁+2 {O(n)} for transition t₁₂₂: l13(X₀, X₁, X₂, X₃) → n_l11___7(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₁ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁
knowledge_propagation leads to new time bound X₁+2 {O(n)} for transition t₁₁₈: n_l11___7(X₀, X₁, X₂, X₃) → n_l12___6(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 1 ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁
knowledge_propagation leads to new time bound X₁+2 {O(n)} for transition t₁₂₀: n_l12___6(X₀, X₁, X₂, X₃) → n_l10___5(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 1 ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁
knowledge_propagation leads to new time bound X₁+2 {O(n)} for transition t₁₁₆: n_l10___5(X₀, X₁, X₂, X₃) → n_l13___4(X₀, X₁, X₂, X₃+1) :|: X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 1 ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁
MPRF for transition t₁₁₅: n_l10___1(X₀, X₁, X₂, X₃) → n_l13___4(X₀, X₁, X₂, X₃+1) :|: X₃ ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₁ of depth 1:
new bound:
X₁⋅X₁+5⋅X₁+1 {O(n^2)}
MPRF:
l13 [X₃-3⋅X₁ ]
l6 [X₁-X₃ ]
l7 [X₁-X₃ ]
l5 [X₂-3⋅X₁ ]
n_l10___5 [X₁ ]
n_l11___7 [X₂-3⋅X₁ ]
n_l12___6 [X₂-3⋅X₁-X₃ ]
n_l12___2 [X₁+X₂-X₃ ]
n_l10___1 [X₁+X₂-X₃ ]
n_l11___3 [X₁+X₂-X₃ ]
n_l13___4 [X₁+X₂-X₃ ]
l14 [X₁-X₃ ]
MPRF for transition t₁₁₇: n_l11___3(X₀, X₁, X₂, X₃) → n_l12___2(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₁ of depth 1:
new bound:
3⋅X₁⋅X₁+10⋅X₁+6 {O(n^2)}
MPRF:
l13 [-X₁ ]
l6 [X₁-X₃ ]
l7 [-X₁ ]
l5 [-X₁ ]
n_l10___5 [X₁-X₃ ]
n_l11___7 [-X₁-X₃ ]
n_l12___6 [-X₁-X₃ ]
n_l12___2 [X₁-X₃ ]
n_l10___1 [X₁-X₃ ]
n_l11___3 [X₁+1-X₃ ]
n_l13___4 [X₁+1-X₃ ]
l14 [X₁-X₃ ]
MPRF for transition t₁₁₉: n_l12___2(X₀, X₁, X₂, X₃) → n_l10___1(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₁ of depth 1:
new bound:
4⋅X₁⋅X₁+11⋅X₁+6 {O(n^2)}
MPRF:
l13 [0 ]
l6 [0 ]
l7 [0 ]
l5 [0 ]
n_l10___5 [2⋅X₁-X₃ ]
n_l11___7 [-X₃ ]
n_l12___6 [-X₃ ]
n_l12___2 [2⋅X₁-X₃ ]
n_l10___1 [2⋅X₁-X₃-1 ]
n_l11___3 [2⋅X₁-X₃ ]
n_l13___4 [2⋅X₁-X₃ ]
l14 [2⋅X₁-X₃ ]
MPRF for transition t₁₂₁: n_l13___4(X₀, X₁, X₂, X₃) → n_l11___3(X₀, X₁, X₂, X₃) :|: X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₃ ≤ 1+X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ of depth 1:
new bound:
3⋅X₁⋅X₁+10⋅X₁+6 {O(n^2)}
MPRF:
l13 [-X₁ ]
l6 [-X₁ ]
l7 [-X₁ ]
l5 [-X₁ ]
n_l10___5 [X₁-X₃ ]
n_l11___7 [-X₁ ]
n_l12___6 [-X₁-X₃ ]
n_l12___2 [X₁-X₃ ]
n_l10___1 [X₁-X₃ ]
n_l11___3 [X₁-X₃ ]
n_l13___4 [X₁+1-X₃ ]
l14 [X₁-X₃ ]
MPRF for transition t₁₂₈: n_l13___4(X₀, X₁, X₂, X₃) → l14(X₀, X₁, X₂, X₃) :|: X₁ < X₃ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ ∧ X₃ ≤ 1+X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ of depth 1:
new bound:
X₁+2 {O(n)}
MPRF:
l13 [X₁+1-X₂ ]
l6 [X₁-X₂ ]
l7 [X₁-X₂ ]
l5 [X₁+1-X₂ ]
n_l11___7 [X₁+1-X₂ ]
n_l12___2 [X₁+1-X₂ ]
n_l10___1 [X₁+1-X₂ ]
n_l12___6 [X₁+1-X₂ ]
n_l10___5 [X₁+1-X₂ ]
n_l11___3 [X₁+1-X₂ ]
n_l13___4 [X₁+1-X₂ ]
l14 [X₁-X₂ ]
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:7⋅X₁⋅X₁+28⋅X₁+22 {O(n^2)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₁₃: X₁⋅X₁+3⋅X₁ {O(n^2)}
t₁₁: X₁⋅X₁+3⋅X₁ {O(n^2)}
t₁₂: 4⋅X₁⋅X₁+12⋅X₁+5 {O(n^2)}
t₉: X₁⋅X₁+3⋅X₁ {O(n^2)}
t₁₀: X₁+2 {O(n)}
t₁₄: 2⋅X₁+1 {O(n)}
t₁₇: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₄: 1 {O(1)}
t₇: X₁+2 {O(n)}
t₈: 1 {O(1)}
t₁₅: 2⋅X₁+1 {O(n)}
t₁₆: X₁+2 {O(n)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
Costbounds
Overall costbound: 7⋅X₁⋅X₁+28⋅X₁+22 {O(n^2)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₁₃: X₁⋅X₁+3⋅X₁ {O(n^2)}
t₁₁: X₁⋅X₁+3⋅X₁ {O(n^2)}
t₁₂: 4⋅X₁⋅X₁+12⋅X₁+5 {O(n^2)}
t₉: X₁⋅X₁+3⋅X₁ {O(n^2)}
t₁₀: X₁+2 {O(n)}
t₁₄: 2⋅X₁+1 {O(n)}
t₁₇: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₄: 1 {O(1)}
t₇: X₁+2 {O(n)}
t₈: 1 {O(1)}
t₁₅: 2⋅X₁+1 {O(n)}
t₁₆: X₁+2 {O(n)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₁₃, X₀: 2⋅X₁+X₀+2 {O(n)}
t₁₃, X₁: X₁ {O(n)}
t₁₃, X₂: 2⋅X₁+2 {O(n)}
t₁₃, X₃: X₁⋅X₁+5⋅X₁+3 {O(n^2)}
t₁₁, X₀: 2⋅X₁+X₀+2 {O(n)}
t₁₁, X₁: X₁ {O(n)}
t₁₁, X₂: 2⋅X₁+2 {O(n)}
t₁₁, X₃: X₁⋅X₁+5⋅X₁+3 {O(n^2)}
t₁₂, X₀: 2⋅X₁+X₀+2 {O(n)}
t₁₂, X₁: X₁ {O(n)}
t₁₂, X₂: 2⋅X₁+2 {O(n)}
t₁₂, X₃: X₁⋅X₁+5⋅X₁+3 {O(n^2)}
t₉, X₀: 2⋅X₁+X₀+2 {O(n)}
t₉, X₁: X₁ {O(n)}
t₉, X₂: 2⋅X₁+2 {O(n)}
t₉, X₃: X₁⋅X₁+5⋅X₁+3 {O(n^2)}
t₁₀, X₀: 2⋅X₁+X₀+2 {O(n)}
t₁₀, X₁: X₁ {O(n)}
t₁₀, X₂: 2⋅X₁+2 {O(n)}
t₁₀, X₃: X₁⋅X₁+5⋅X₁+3 {O(n^2)}
t₁₄, X₀: 2⋅X₁+2 {O(n)}
t₁₄, X₁: X₁ {O(n)}
t₁₄, X₂: 2⋅X₁+2 {O(n)}
t₁₄, X₃: X₁⋅X₁+5⋅X₁+3 {O(n^2)}
t₁₇, X₀: 2⋅X₁+X₀+2 {O(n)}
t₁₇, X₁: 2⋅X₁ {O(n)}
t₁₇, X₂: 2⋅X₁+3 {O(n)}
t₁₇, X₃: X₁⋅X₁+5⋅X₁+X₃+3 {O(n^2)}
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)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₇, X₀: 2⋅X₁+X₀+2 {O(n)}
t₇, X₁: X₁ {O(n)}
t₇, X₂: 2⋅X₁+2 {O(n)}
t₇, X₃: 2⋅X₁+3 {O(n)}
t₈, X₀: 2⋅X₁+X₀+2 {O(n)}
t₈, X₁: 2⋅X₁ {O(n)}
t₈, X₂: 2⋅X₁+3 {O(n)}
t₈, X₃: X₁⋅X₁+5⋅X₁+X₃+3 {O(n^2)}
t₁₅, X₀: 2⋅X₁+2 {O(n)}
t₁₅, X₁: X₁ {O(n)}
t₁₅, X₂: 2⋅X₁+2 {O(n)}
t₁₅, X₃: X₁⋅X₁+5⋅X₁+3 {O(n^2)}
t₁₆, X₀: 2⋅X₁+2 {O(n)}
t₁₆, X₁: X₁ {O(n)}
t₁₆, X₂: 2⋅X₁+2 {O(n)}
t₁₆, X₃: X₁⋅X₁+5⋅X₁+3 {O(n^2)}
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: 1 {O(1)}
t₆, X₃: X₃ {O(n)}