Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l10, l11, l12, l13, l14, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l13(X₀, X₁, X₂, X₃)
t₄: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: 2+X₁ ≤ X₀
t₅: l1(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁+1
t₁₅: l10(X₀, X₁, X₂, X₃) → l11(X₀, X₁, X₂, 2⋅X₂+2)
t₁₆: l11(X₀, X₁, X₂, X₃) → l12(X₀, X₁, X₂, X₃)
t₁₇: l11(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₀, X₃)
t₁₈: l12(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₃, X₃)
t₂: l13(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₀ ≤ 2
t₁: l13(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: 3 ≤ X₀
t₈: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₀ ≤ 2⋅X₂+2+X₁
t₇: l2(X₀, X₁, X₂, X₃) → l9(X₀, X₁, X₂, X₃) :|: X₁+3+2⋅X₂ ≤ X₀
t₁₉: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁+1, X₂, X₃)
t₆: l4(X₀, X₁, X₂, X₃) → l2(X₀, X₁, 0, X₃)
t₂₀: l5(X₀, X₁, X₂, X₃) → l14(X₀, X₁, X₂, X₃)
t₃: l6(X₀, X₁, X₂, X₃) → l1(X₀, 0, X₂, X₃)
t₁₃: l7(X₀, X₁, X₂, X₃) → l10(X₀, X₁, X₂, X₃)
t₁₂: l7(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃)
t₁₄: l8(X₀, X₁, X₂, X₃) → l11(X₀, X₁, X₂, 2⋅X₂+1)
t₁₀: l9(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₁+4+2⋅X₂ ≤ X₀
t₁₁: l9(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₀ ≤ 2⋅X₂+2+X₁
t₉: l9(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃) :|: X₀ ≤ 2⋅X₂+3+X₁ ∧ 2⋅X₂+3+X₁ ≤ X₀
Preprocessing
Cut unsatisfiable transition t₁₁: l9→l7
Found invariant 0 ≤ X₁ for location l11
Found invariant 0 ≤ X₁ for location l2
Found invariant 3 ≤ X₀ for location l6
Found invariant 0 ≤ X₁ for location l12
Found invariant 0 ≤ X₁ for location l7
Found invariant 0 ≤ X₁ for location l8
Found invariant 0 ≤ X₁ for location l1
Found invariant 0 ≤ X₁ for location l10
Found invariant 2+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l4
Found invariant 0 ≤ X₁ for location l9
Found invariant 0 ≤ X₁ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l10, l11, l12, l13, l14, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l13(X₀, X₁, X₂, X₃)
t₄: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: 2+X₁ ≤ X₀ ∧ 0 ≤ X₁
t₅: l1(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁+1 ∧ 0 ≤ X₁
t₁₅: l10(X₀, X₁, X₂, X₃) → l11(X₀, X₁, X₂, 2⋅X₂+2) :|: 0 ≤ X₁
t₁₆: l11(X₀, X₁, X₂, X₃) → l12(X₀, X₁, X₂, X₃) :|: 0 ≤ X₁
t₁₇: l11(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₀, X₃) :|: 0 ≤ X₁
t₁₈: l12(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₃, X₃) :|: 0 ≤ X₁
t₂: l13(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₀ ≤ 2
t₁: l13(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: 3 ≤ X₀
t₈: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₀ ≤ 2⋅X₂+2+X₁ ∧ 0 ≤ X₁
t₇: l2(X₀, X₁, X₂, X₃) → l9(X₀, X₁, X₂, X₃) :|: X₁+3+2⋅X₂ ≤ X₀ ∧ 0 ≤ X₁
t₁₉: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁+1, X₂, X₃) :|: 0 ≤ X₁
t₆: l4(X₀, X₁, X₂, X₃) → l2(X₀, X₁, 0, X₃) :|: 2+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₂₀: l5(X₀, X₁, X₂, X₃) → l14(X₀, X₁, X₂, X₃)
t₃: l6(X₀, X₁, X₂, X₃) → l1(X₀, 0, X₂, X₃) :|: 3 ≤ X₀
t₁₃: l7(X₀, X₁, X₂, X₃) → l10(X₀, X₁, X₂, X₃) :|: 0 ≤ X₁
t₁₂: l7(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃) :|: 0 ≤ X₁
t₁₄: l8(X₀, X₁, X₂, X₃) → l11(X₀, X₁, X₂, 2⋅X₂+1) :|: 0 ≤ X₁
t₁₀: l9(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₁+4+2⋅X₂ ≤ X₀ ∧ 0 ≤ X₁
t₉: l9(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃) :|: X₀ ≤ 2⋅X₂+3+X₁ ∧ 2⋅X₂+3+X₁ ≤ X₀ ∧ 0 ≤ X₁
MPRF for transition t₄: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: 2+X₁ ≤ X₀ ∧ 0 ≤ X₁ of depth 1:
new bound:
X₀+1 {O(n)}
MPRF for transition t₆: l4(X₀, X₁, X₂, X₃) → l2(X₀, X₁, 0, X₃) :|: 2+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₀+1 {O(n)}
MPRF for transition t₈: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₀ ≤ 2⋅X₂+2+X₁ ∧ 0 ≤ X₁ of depth 1:
new bound:
2⋅X₀+3 {O(n)}
MPRF for transition t₁₉: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁+1, X₂, X₃) :|: 0 ≤ X₁ of depth 1:
new bound:
X₀+1 {O(n)}
Chain transitions t₃: l6→l1 and t₅: l1→l5 to t₄₀₀: l6→l5
Chain transitions t₁₉: l3→l1 and t₅: l1→l5 to t₄₀₁: l3→l5
Chain transitions t₁₉: l3→l1 and t₄: l1→l4 to t₄₀₂: l3→l4
Chain transitions t₃: l6→l1 and t₄: l1→l4 to t₄₀₃: l6→l4
Chain transitions t₁₃: l7→l10 and t₁₅: l10→l11 to t₄₀₄: l7→l11
Chain transitions t₁₄: l8→l11 and t₁₇: l11→l2 to t₄₀₅: l8→l2
Chain transitions t₄₀₄: l7→l11 and t₁₇: l11→l2 to t₄₀₆: l7→l2
Chain transitions t₄₀₄: l7→l11 and t₁₆: l11→l12 to t₄₀₇: l7→l12
Chain transitions t₁₄: l8→l11 and t₁₆: l11→l12 to t₄₀₈: l8→l12
Chain transitions t₄₀₈: l8→l12 and t₁₈: l12→l2 to t₄₀₉: l8→l2
Chain transitions t₄₀₇: l7→l12 and t₁₈: l12→l2 to t₄₁₀: l7→l2
Chain transitions t₄₀₉: l8→l2 and t₇: l2→l9 to t₄₁₁: l8→l9
Chain transitions t₄₀₅: l8→l2 and t₇: l2→l9 to t₄₁₂: l8→l9
Chain transitions t₄₀₅: l8→l2 and t₈: l2→l3 to t₄₁₃: l8→l3
Chain transitions t₄₀₉: l8→l2 and t₈: l2→l3 to t₄₁₄: l8→l3
Chain transitions t₄₁₀: l7→l2 and t₈: l2→l3 to t₄₁₅: l7→l3
Chain transitions t₄₁₀: l7→l2 and t₇: l2→l9 to t₄₁₆: l7→l9
Chain transitions t₄₀₆: l7→l2 and t₈: l2→l3 to t₄₁₇: l7→l3
Chain transitions t₄₀₆: l7→l2 and t₇: l2→l9 to t₄₁₈: l7→l9
Chain transitions t₆: l4→l2 and t₈: l2→l3 to t₄₁₉: l4→l3
Chain transitions t₆: l4→l2 and t₇: l2→l9 to t₄₂₀: l4→l9
Chain transitions t₄₁₄: l8→l3 and t₄₀₁: l3→l5 to t₄₂₁: l8→l5
Chain transitions t₄₁₃: l8→l3 and t₄₀₁: l3→l5 to t₄₂₂: l8→l5
Chain transitions t₄₁₃: l8→l3 and t₄₀₂: l3→l4 to t₄₂₃: l8→l4
Chain transitions t₄₁₄: l8→l3 and t₄₀₂: l3→l4 to t₄₂₄: l8→l4
Chain transitions t₄₁₇: l7→l3 and t₄₀₂: l3→l4 to t₄₂₅: l7→l4
Chain transitions t₄₁₇: l7→l3 and t₄₀₁: l3→l5 to t₄₂₆: l7→l5
Chain transitions t₄₁₇: l7→l3 and t₁₉: l3→l1 to t₄₂₇: l7→l1
Chain transitions t₄₁₃: l8→l3 and t₁₉: l3→l1 to t₄₂₈: l8→l1
Chain transitions t₄₁₄: l8→l3 and t₁₉: l3→l1 to t₄₂₉: l8→l1
Chain transitions t₄₁₅: l7→l3 and t₁₉: l3→l1 to t₄₃₀: l7→l1
Chain transitions t₄₁₅: l7→l3 and t₄₀₂: l3→l4 to t₄₃₁: l7→l4
Chain transitions t₄₁₅: l7→l3 and t₄₀₁: l3→l5 to t₄₃₂: l7→l5
Chain transitions t₄₁₉: l4→l3 and t₁₉: l3→l1 to t₄₃₃: l4→l1
Chain transitions t₄₁₉: l4→l3 and t₄₀₂: l3→l4 to t₄₃₄: l4→l4
Chain transitions t₄₁₉: l4→l3 and t₄₀₁: l3→l5 to t₄₃₅: l4→l5
Chain transitions t₁₀: l9→l7 and t₄₁₈: l7→l9 to t₄₃₆: l9→l9
Chain transitions t₁₀: l9→l7 and t₄₁₆: l7→l9 to t₄₃₇: l9→l9
Chain transitions t₁₀: l9→l7 and t₁₂: l7→l8 to t₄₃₈: l9→l8
Chain transitions t₁₀: l9→l7 and t₄₃₂: l7→l5 to t₄₃₉: l9→l5
Chain transitions t₁₀: l9→l7 and t₄₂₆: l7→l5 to t₄₄₀: l9→l5
Chain transitions t₁₀: l9→l7 and t₄₃₁: l7→l4 to t₄₄₁: l9→l4
Chain transitions t₁₀: l9→l7 and t₄₂₅: l7→l4 to t₄₄₂: l9→l4
Chain transitions t₁₀: l9→l7 and t₄₁₇: l7→l3 to t₄₄₃: l9→l3
Chain transitions t₁₀: l9→l7 and t₄₁₅: l7→l3 to t₄₄₄: l9→l3
Chain transitions t₁₀: l9→l7 and t₄₁₀: l7→l2 to t₄₄₅: l9→l2
Chain transitions t₁₀: l9→l7 and t₄₀₆: l7→l2 to t₄₄₆: l9→l2
Chain transitions t₁₀: l9→l7 and t₄₀₇: l7→l12 to t₄₄₇: l9→l12
Chain transitions t₁₀: l9→l7 and t₄₀₄: l7→l11 to t₄₄₈: l9→l11
Chain transitions t₁₀: l9→l7 and t₁₃: l7→l10 to t₄₄₉: l9→l10
Chain transitions t₁₀: l9→l7 and t₄₃₀: l7→l1 to t₄₅₀: l9→l1
Chain transitions t₁₀: l9→l7 and t₄₂₇: l7→l1 to t₄₅₁: l9→l1
Chain transitions t₄₃₈: l9→l8 and t₄₁₂: l8→l9 to t₄₅₂: l9→l9
Chain transitions t₉: l9→l8 and t₄₁₂: l8→l9 to t₄₅₃: l9→l9
Chain transitions t₉: l9→l8 and t₄₁₁: l8→l9 to t₄₅₄: l9→l9
Chain transitions t₄₃₈: l9→l8 and t₄₁₁: l8→l9 to t₄₅₅: l9→l9
Chain transitions t₉: l9→l8 and t₄₂₂: l8→l5 to t₄₅₆: l9→l5
Chain transitions t₄₃₈: l9→l8 and t₄₂₂: l8→l5 to t₄₅₇: l9→l5
Chain transitions t₉: l9→l8 and t₄₂₁: l8→l5 to t₄₅₈: l9→l5
Chain transitions t₄₃₈: l9→l8 and t₄₂₁: l8→l5 to t₄₅₉: l9→l5
Chain transitions t₉: l9→l8 and t₄₂₄: l8→l4 to t₄₆₀: l9→l4
Chain transitions t₄₃₈: l9→l8 and t₄₂₄: l8→l4 to t₄₆₁: l9→l4
Chain transitions t₉: l9→l8 and t₄₂₃: l8→l4 to t₄₆₂: l9→l4
Chain transitions t₄₃₈: l9→l8 and t₄₂₃: l8→l4 to t₄₆₃: l9→l4
Chain transitions t₉: l9→l8 and t₄₁₄: l8→l3 to t₄₆₄: l9→l3
Chain transitions t₄₃₈: l9→l8 and t₄₁₄: l8→l3 to t₄₆₅: l9→l3
Chain transitions t₉: l9→l8 and t₄₁₃: l8→l3 to t₄₆₆: l9→l3
Chain transitions t₄₃₈: l9→l8 and t₄₁₃: l8→l3 to t₄₆₇: l9→l3
Chain transitions t₉: l9→l8 and t₄₀₉: l8→l2 to t₄₆₈: l9→l2
Chain transitions t₄₃₈: l9→l8 and t₄₀₉: l8→l2 to t₄₆₉: l9→l2
Chain transitions t₉: l9→l8 and t₄₀₅: l8→l2 to t₄₇₀: l9→l2
Chain transitions t₄₃₈: l9→l8 and t₄₀₅: l8→l2 to t₄₇₁: l9→l2
Chain transitions t₉: l9→l8 and t₄₀₈: l8→l12 to t₄₇₂: l9→l12
Chain transitions t₄₃₈: l9→l8 and t₄₀₈: l8→l12 to t₄₇₃: l9→l12
Chain transitions t₉: l9→l8 and t₁₄: l8→l11 to t₄₇₄: l9→l11
Chain transitions t₄₃₈: l9→l8 and t₁₄: l8→l11 to t₄₇₅: l9→l11
Chain transitions t₉: l9→l8 and t₄₂₉: l8→l1 to t₄₇₆: l9→l1
Chain transitions t₄₃₈: l9→l8 and t₄₂₉: l8→l1 to t₄₇₇: l9→l1
Chain transitions t₉: l9→l8 and t₄₂₈: l8→l1 to t₄₇₈: l9→l1
Chain transitions t₄₃₈: l9→l8 and t₄₂₈: l8→l1 to t₄₇₉: l9→l1
Analysing control-flow refined program
Cut unsatisfiable transition t₄₀₀: l6→l5
Cut unsatisfiable transition t₄₃₄: l4→l4
Cut unsatisfiable transition t₄₅₈: l9→l5
Cut unsatisfiable transition t₄₅₉: l9→l5
Eliminate variables {X₃} that do not contribute to the problem
Found invariant 3+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀ for location l11
Found invariant 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀ for location l2
Found invariant 3 ≤ X₀ for location l6
Found invariant 3+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀ for location l12
Found invariant 4+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 4+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 4 ≤ X₀ for location l7
Found invariant 3+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀ for location l8
Found invariant 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀ for location l1
Found invariant 4+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 4+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 4 ≤ X₀ for location l10
Found invariant 2+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀ for location l4
Found invariant 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀ for location l9
Found invariant 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 2+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀ for location l3
Cut unsatisfiable transition t₆₀₈: l9→l5
Cut unsatisfiable transition t₆₀₉: l9→l5
Cut unsatisfiable transition t₆₁₀: l9→l5
Cut unsatisfiable transition t₆₁₁: l9→l5
Cut unsatisfiable transition t₆₁₅: l9→l9
Cut unsatisfiable transition t₆₁₇: l9→l9
Cut unsatisfiable transition t₆₁₈: l9→l9
Cut unsatisfiable transition t₆₁₉: l9→l9
MPRF for transition t₅₇₃: l4(X₀, X₁, X₂) -{2}> l9(X₀, X₁, 0) :|: X₁+3 ≤ X₀ ∧ 2+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀ of depth 1:
new bound:
X₀+1 {O(n)}
MPRF for transition t₆₀₂: l9(X₀, X₁, X₂) -{8}> l4(X₀, 1+X₁, 2+2⋅X₂) :|: X₁+4+2⋅X₂ ≤ X₀ ∧ X₀ ≤ 6+4⋅X₂+X₁ ∧ 3+X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀ of depth 1:
new bound:
X₀+2 {O(n)}
MPRF for transition t₆₀₃: l9(X₀, X₁, X₂) -{7}> l4(X₀, 1+X₁, X₀) :|: X₁+4+2⋅X₂ ≤ X₀ ∧ 0 ≤ X₀+2+X₁ ∧ 3+X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀ of depth 1:
new bound:
X₀+2 {O(n)}
MPRF for transition t₆₀₄: l9(X₀, X₁, X₂) -{7}> l4(X₀, 1+X₁, 1+2⋅X₂) :|: X₀ ≤ 2⋅X₂+3+X₁ ∧ 2⋅X₂+3+X₁ ≤ X₀ ∧ X₀ ≤ 4+4⋅X₂+X₁ ∧ 3+X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀ of depth 1:
new bound:
X₀+2 {O(n)}
MPRF for transition t₆₀₅: l9(X₀, X₁, X₂) -{8}> l4(X₀, 1+X₁, 1+2⋅X₂) :|: X₁+4+2⋅X₂ ≤ X₀ ∧ X₀ ≤ 4+4⋅X₂+X₁ ∧ 3+X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀ of depth 1:
new bound:
X₀+2 {O(n)}
MPRF for transition t₆₀₆: l9(X₀, X₁, X₂) -{6}> l4(X₀, 1+X₁, X₀) :|: X₀ ≤ 2⋅X₂+3+X₁ ∧ 2⋅X₂+3+X₁ ≤ X₀ ∧ 0 ≤ X₀+2+X₁ ∧ 3+X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀ of depth 1:
new bound:
X₀+2 {O(n)}
MPRF for transition t₆₀₇: l9(X₀, X₁, X₂) -{7}> l4(X₀, 1+X₁, X₀) :|: X₁+4+2⋅X₂ ≤ X₀ ∧ 0 ≤ X₀+2+X₁ ∧ 3+X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀ of depth 1:
new bound:
X₀+2 {O(n)}
MPRF for transition t₆₁₆: l9(X₀, X₁, X₂) -{6}> l9(X₀, X₁, 2+2⋅X₂) :|: X₁+4+2⋅X₂ ≤ X₀ ∧ X₁+7+4⋅X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀ of depth 1:
new bound:
42⋅X₀⋅X₀+193⋅X₀+222 {O(n^2)}
MPRF for transition t₆₂₀: l9(X₀, X₁, X₂) -{6}> l9(X₀, X₁, 1+2⋅X₂) :|: X₁+4+2⋅X₂ ≤ X₀ ∧ X₁+5+4⋅X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀ of depth 1:
new bound:
42⋅X₀⋅X₀+157⋅X₀+144 {O(n^2)}
Analysing control-flow refined program
Cut unsatisfiable transition t₁₀₄₀: n_l2___13→l3
Cut unsatisfiable transition t₁₀₄₁: n_l2___14→l3
Cut unsatisfiable transition t₁₀₄₄: n_l2___6→l3
Found invariant 4+X₂ ≤ 0 ∧ 4+X₂ ≤ X₁ ∧ 4+X₁+X₂ ≤ 0 ∧ X₂ ≤ X₀ ∧ 8+X₀+X₂ ≤ 0 ∧ X₀ ≤ X₂ ∧ 4+X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 4+X₀ ≤ X₁ ∧ 4+X₀ ≤ 0 for location n_l8___17
Found invariant 5+X₃ ≤ 0 ∧ 2+X₃ ≤ X₂ ∧ 8+X₂+X₃ ≤ 0 ∧ 5+X₃ ≤ X₁ ∧ 5+X₁+X₃ ≤ 0 ∧ 2+X₃ ≤ X₀ ∧ 8+X₀+X₃ ≤ 0 ∧ 3+X₂ ≤ 0 ∧ 3+X₂ ≤ X₁ ∧ 3+X₁+X₂ ≤ 0 ∧ X₂ ≤ X₀ ∧ 6+X₀+X₂ ≤ 0 ∧ 0 ≤ 3+X₁+X₂ ∧ X₀ ≤ X₂ ∧ 3+X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ 3+X₀+X₁ ∧ 3+X₀ ≤ X₁ ∧ 3+X₀ ≤ 0 for location n_l2___6
Found invariant X₃ ≤ 2 ∧ X₃ ≤ 2+X₂ ∧ X₂+X₃ ≤ 2 ∧ X₃ ≤ 2+X₁ ∧ 2+X₃ ≤ X₀ ∧ 2 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 6 ≤ X₀+X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 4+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 4+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 4 ≤ X₀ for location n_l11___36
Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 3+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀ for location n_l9___41
Found invariant 3 ≤ X₀ for location l6
Found invariant 6+X₃ ≤ 0 ∧ 2+X₃ ≤ X₂ ∧ 10+X₂+X₃ ≤ 0 ∧ 6+X₃ ≤ X₁ ∧ 6+X₁+X₃ ≤ 0 ∧ 2+X₃ ≤ X₀ ∧ 10+X₀+X₃ ≤ 0 ∧ 4+X₂ ≤ 0 ∧ 4+X₂ ≤ X₁ ∧ 4+X₁+X₂ ≤ 0 ∧ X₂ ≤ X₀ ∧ 8+X₀+X₂ ≤ 0 ∧ X₀ ≤ X₂ ∧ 4+X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 4+X₀ ≤ X₁ ∧ 4+X₀ ≤ 0 for location n_l2___14
Found invariant X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ for location n_l2___34
Found invariant X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁ for location n_l8___28
Found invariant X₃ ≤ 1 ∧ X₃ ≤ 1+X₂ ∧ X₂+X₃ ≤ 1 ∧ X₃ ≤ 1+X₁ ∧ 3+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 5 ≤ X₀+X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 4+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 4+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 4 ≤ X₀ for location n_l11___4
Found invariant 2+X₃ ≤ X₀ ∧ 0 ≤ X₁ for location n_l12___22
Found invariant X₃ ≤ 2 ∧ X₃ ≤ 2+X₂ ∧ X₂+X₃ ≤ 2 ∧ X₃ ≤ 2+X₁ ∧ 2+X₃ ≤ X₀ ∧ 2 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 6 ≤ X₀+X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 4+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 4+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 4 ≤ X₀ for location n_l12___35
Found invariant 4+X₂ ≤ 0 ∧ 4+X₂ ≤ X₁ ∧ 3+X₁+X₂ ≤ 0 ∧ X₂ ≤ X₀ ∧ 8+X₀+X₂ ≤ 0 ∧ X₀ ≤ X₂ ∧ 3+X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 4+X₀ ≤ X₁ ∧ 4+X₀ ≤ 0 for location n_l7___20
Found invariant 3+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ 3+X₁ ∧ 3 ≤ X₀ for location n_l8___39
Found invariant X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁ for location n_l9___32
Found invariant X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ for location n_l9___21
Found invariant 5+X₃ ≤ 0 ∧ 2+X₃ ≤ X₂ ∧ 8+X₂+X₃ ≤ 0 ∧ 5+X₃ ≤ X₁ ∧ 5+X₁+X₃ ≤ 0 ∧ 2+X₃ ≤ X₀ ∧ 8+X₀+X₃ ≤ 0 ∧ 3+X₂ ≤ 0 ∧ 3+X₂ ≤ X₁ ∧ 3+X₁+X₂ ≤ 0 ∧ X₂ ≤ X₀ ∧ 6+X₀+X₂ ≤ 0 ∧ 0 ≤ 3+X₁+X₂ ∧ X₀ ≤ X₂ ∧ 3+X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ 3+X₀+X₁ ∧ 3+X₀ ≤ X₁ ∧ 3+X₀ ≤ 0 for location n_l12___7
Found invariant 0 ≤ X₁ for location l1
Found invariant 2+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l4
Found invariant 0 ≤ X₁ for location n_l11___25
Found invariant 5+X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ 10+X₂+X₃ ≤ 0 ∧ 5+X₃ ≤ X₁ ∧ 5+X₁+X₃ ≤ 0 ∧ 2+X₃ ≤ X₀ ∧ 8+X₀+X₃ ≤ 0 ∧ X₂ ≤ X₃ ∧ 5+X₂ ≤ 0 ∧ 5+X₂ ≤ X₁ ∧ 5+X₁+X₂ ≤ 0 ∧ 2+X₂ ≤ X₀ ∧ 8+X₀+X₂ ≤ 0 ∧ 3+X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 3+X₀ ≤ X₁ ∧ 3+X₀ ≤ 0 for location n_l9___12
Found invariant 0 ≤ X₁ for location l3
Found invariant 5+X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ 10+X₂+X₃ ≤ 0 ∧ 5+X₃ ≤ X₁ ∧ 5+X₁+X₃ ≤ 0 ∧ 2+X₃ ≤ X₀ ∧ 8+X₀+X₃ ≤ 0 ∧ X₂ ≤ X₃ ∧ 5+X₂ ≤ 0 ∧ 5+X₂ ≤ X₁ ∧ 5+X₁+X₂ ≤ 0 ∧ 2+X₂ ≤ X₀ ∧ 8+X₀+X₂ ≤ 0 ∧ 3+X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 3+X₀ ≤ X₁ ∧ 3+X₀ ≤ 0 for location n_l2___13
Found invariant 3+X₂ ≤ 0 ∧ 3+X₂ ≤ X₁ ∧ 6+X₀+X₂ ≤ 0 ∧ 3+X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 3+X₀ ≤ X₁ ∧ 3+X₀ ≤ 0 for location n_l8___19
Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l2
Found invariant 0 ≤ X₁ for location n_l11___27
Found invariant X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁ for location n_l10___29
Found invariant 7+X₃ ≤ 0 ∧ 3+X₃ ≤ X₂ ∧ 11+X₂+X₃ ≤ 0 ∧ 7+X₃ ≤ X₁ ∧ 7+X₁+X₃ ≤ 0 ∧ 3+X₃ ≤ X₀ ∧ 11+X₀+X₃ ≤ 0 ∧ 4+X₂ ≤ 0 ∧ 4+X₂ ≤ X₁ ∧ 4+X₁+X₂ ≤ 0 ∧ X₂ ≤ X₀ ∧ 8+X₀+X₂ ≤ 0 ∧ X₀ ≤ X₂ ∧ 4+X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 4+X₀ ≤ X₁ ∧ 4+X₀ ≤ 0 for location n_l11___10
Found invariant 0 ≤ X₁ for location n_l11___23
Found invariant 0 ≤ X₁ for location n_l12___24
Found invariant 6+X₃ ≤ 0 ∧ 2+X₃ ≤ X₂ ∧ 10+X₂+X₃ ≤ 0 ∧ 6+X₃ ≤ X₁ ∧ 6+X₁+X₃ ≤ 0 ∧ 2+X₃ ≤ X₀ ∧ 10+X₀+X₃ ≤ 0 ∧ 4+X₂ ≤ 0 ∧ 4+X₂ ≤ X₁ ∧ 4+X₁+X₂ ≤ 0 ∧ X₂ ≤ X₀ ∧ 8+X₀+X₂ ≤ 0 ∧ X₀ ≤ X₂ ∧ 4+X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 4+X₀ ≤ X₁ ∧ 4+X₀ ≤ 0 for location n_l9___11
Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 4+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 4+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 4 ≤ X₀ for location n_l8___37
Found invariant X₃ ≤ 1 ∧ X₃ ≤ 1+X₂ ∧ X₂+X₃ ≤ 1 ∧ X₃ ≤ 1+X₁ ∧ 3+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 5 ≤ X₀+X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 4+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 4+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 4 ≤ X₀ for location n_l12___3
Found invariant X₃ ≤ 1 ∧ X₃ ≤ 1+X₂ ∧ X₂+X₃ ≤ 1 ∧ X₃ ≤ 1+X₁ ∧ 2+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 4 ≤ X₀+X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 3+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ 3+X₁ ∧ 3 ≤ X₀ for location n_l11___2
Found invariant 5+X₃ ≤ 0 ∧ 2+X₃ ≤ X₂ ∧ 8+X₂+X₃ ≤ 0 ∧ 5+X₃ ≤ X₁ ∧ 5+X₁+X₃ ≤ 0 ∧ 2+X₃ ≤ X₀ ∧ 8+X₀+X₃ ≤ 0 ∧ 3+X₂ ≤ 0 ∧ 3+X₂ ≤ X₁ ∧ 3+X₁+X₂ ≤ 0 ∧ X₂ ≤ X₀ ∧ 6+X₀+X₂ ≤ 0 ∧ 0 ≤ 3+X₁+X₂ ∧ X₀ ≤ X₂ ∧ 3+X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ 3+X₀+X₁ ∧ 3+X₀ ≤ X₁ ∧ 3+X₀ ≤ 0 for location n_l11___8
Found invariant 0 ≤ X₁ for location n_l8___30
Found invariant 4+X₂ ≤ 0 ∧ 4+X₂ ≤ X₁ ∧ 4+X₁+X₂ ≤ 0 ∧ X₂ ≤ X₀ ∧ 8+X₀+X₂ ≤ 0 ∧ X₀ ≤ X₂ ∧ 4+X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 4+X₀ ≤ X₁ ∧ 4+X₀ ≤ 0 for location n_l10___18
Found invariant 6+X₃ ≤ 0 ∧ 2+X₃ ≤ X₂ ∧ 10+X₂+X₃ ≤ 0 ∧ 6+X₃ ≤ X₁ ∧ 6+X₁+X₃ ≤ 0 ∧ 2+X₃ ≤ X₀ ∧ 10+X₀+X₃ ≤ 0 ∧ 4+X₂ ≤ 0 ∧ 4+X₂ ≤ X₁ ∧ 4+X₁+X₂ ≤ 0 ∧ X₂ ≤ X₀ ∧ 8+X₀+X₂ ≤ 0 ∧ X₀ ≤ X₂ ∧ 4+X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 4+X₀ ≤ X₁ ∧ 4+X₀ ≤ 0 for location n_l11___16
Found invariant X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁ for location n_l2___33
Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 4+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 4+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 4 ≤ X₀ for location n_l7___40
Found invariant X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁ for location n_l7___31
Found invariant X₃ ≤ 1 ∧ X₃ ≤ 1+X₂ ∧ X₂+X₃ ≤ 1 ∧ X₃ ≤ 1+X₁ ∧ 2+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 4 ≤ X₀+X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 3+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ 3+X₁ ∧ 3 ≤ X₀ for location n_l12___1
Found invariant 6+X₃ ≤ 0 ∧ 2+X₃ ≤ X₂ ∧ 10+X₂+X₃ ≤ 0 ∧ 6+X₃ ≤ X₁ ∧ 6+X₁+X₃ ≤ 0 ∧ 2+X₃ ≤ X₀ ∧ 10+X₀+X₃ ≤ 0 ∧ 4+X₂ ≤ 0 ∧ 4+X₂ ≤ X₁ ∧ 4+X₁+X₂ ≤ 0 ∧ X₂ ≤ X₀ ∧ 8+X₀+X₂ ≤ 0 ∧ X₀ ≤ X₂ ∧ 4+X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 4+X₀ ≤ X₁ ∧ 4+X₀ ≤ 0 for location n_l12___15
Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 4+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 4+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 4 ≤ X₀ for location n_l10___38
Found invariant 0 ≤ X₁ for location n_l12___26
Found invariant 5+X₃ ≤ 0 ∧ 2+X₃ ≤ X₂ ∧ 8+X₂+X₃ ≤ 0 ∧ 5+X₃ ≤ X₁ ∧ 5+X₁+X₃ ≤ 0 ∧ 2+X₃ ≤ X₀ ∧ 8+X₀+X₃ ≤ 0 ∧ 3+X₂ ≤ 0 ∧ 3+X₂ ≤ X₁ ∧ 3+X₁+X₂ ≤ 0 ∧ X₂ ≤ X₀ ∧ 6+X₀+X₂ ≤ 0 ∧ 0 ≤ 3+X₁+X₂ ∧ X₀ ≤ X₂ ∧ 3+X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ 3+X₀+X₁ ∧ 3+X₀ ≤ X₁ ∧ 3+X₀ ≤ 0 for location n_l9___5
Found invariant 7+X₃ ≤ 0 ∧ 3+X₃ ≤ X₂ ∧ 11+X₂+X₃ ≤ 0 ∧ 7+X₃ ≤ X₁ ∧ 7+X₁+X₃ ≤ 0 ∧ 3+X₃ ≤ X₀ ∧ 11+X₀+X₃ ≤ 0 ∧ 4+X₂ ≤ 0 ∧ 4+X₂ ≤ X₁ ∧ 4+X₁+X₂ ≤ 0 ∧ X₂ ≤ X₀ ∧ 8+X₀+X₂ ≤ 0 ∧ X₀ ≤ X₂ ∧ 4+X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 4+X₀ ≤ X₁ ∧ 4+X₀ ≤ 0 for location n_l12___9
knowledge_propagation leads to new time bound X₀+1 {O(n)} for transition t₁₀₀₁: l2(X₀, X₁, X₂, X₃) → n_l9___41(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 2+X₁ ≤ X₀ ∧ 3+X₁+2⋅X₂ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀
knowledge_propagation leads to new time bound X₀+1 {O(n)} for transition t₁₀₂₁: n_l9___41(X₀, X₁, X₂, X₃) → n_l7___40(X₀, X₁, X₂, X₃) :|: 3+X₁ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 4+X₁+2⋅X₂ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 3+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀
knowledge_propagation leads to new time bound X₀+1 {O(n)} for transition t₁₀₂₂: n_l9___41(X₀, X₁, X₂, X₃) → n_l8___39(X₀, X₁, Arg2_P, X₃) :|: 3+X₁ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₀ ≤ X₁+2⋅X₂+3 ∧ 3+X₁+2⋅X₂ ≤ X₀ ∧ X₀ ≤ X₁+2⋅Arg2_P+3 ∧ 3+X₁+2⋅Arg2_P ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 3+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀
knowledge_propagation leads to new time bound X₀+1 {O(n)} for transition t₁₀₀₇: n_l7___40(X₀, X₁, X₂, X₃) → n_l10___38(X₀, X₁, X₂, X₃) :|: 4+X₁ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 4+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 4+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 4 ≤ X₀
knowledge_propagation leads to new time bound X₀+1 {O(n)} for transition t₁₀₀₈: n_l7___40(X₀, X₁, X₂, X₃) → n_l8___37(X₀, X₁, X₂, X₃) :|: 4+X₁ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 4+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 4+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 4 ≤ X₀
knowledge_propagation leads to new time bound X₀+1 {O(n)} for transition t₁₀₁₃: n_l8___37(X₀, X₁, X₂, X₃) → n_l11___4(X₀, X₁, X₂, 2⋅X₂+1) :|: 4+X₁ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 4+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 4+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 4 ≤ X₀
knowledge_propagation leads to new time bound X₀+1 {O(n)} for transition t₁₀₁₄: n_l8___39(X₀, X₁, X₂, X₃) → n_l11___2(X₀, X₁, X₂, 2⋅X₂+1) :|: 3 ≤ X₀ ∧ X₀ ≤ X₁+3 ∧ 3+X₁ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₁ ∧ 3+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ 3+X₁ ∧ 3 ≤ X₀
knowledge_propagation leads to new time bound X₀+1 {O(n)} for transition t₉₆₉: n_l10___38(X₀, X₁, X₂, X₃) → n_l11___36(X₀, X₁, X₂, 2⋅X₂+2) :|: 4+X₁ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 4+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 4+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 4 ≤ X₀
knowledge_propagation leads to new time bound X₀+1 {O(n)} for transition t₉₇₄: n_l11___2(X₀, X₁, X₂, X₃) → n_l12___1(X₀, X₁, X₂, X₃) :|: 3 ≤ X₀ ∧ X₀ ≤ X₁+3 ∧ 3+X₁ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₃ ≤ 1 ∧ 1 ≤ X₃ ∧ 0 ≤ X₁ ∧ X₃ ≤ 1 ∧ X₃ ≤ 1+X₂ ∧ X₂+X₃ ≤ 1 ∧ X₃ ≤ 1+X₁ ∧ 2+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 4 ≤ X₀+X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 3+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ 3+X₁ ∧ 3 ≤ X₀
knowledge_propagation leads to new time bound X₀+1 {O(n)} for transition t₉₇₅: n_l11___2(X₀, X₁, X₂, X₃) → n_l2___34(X₀, X₁, X₀, X₃) :|: 3 ≤ X₀ ∧ X₀ ≤ X₁+3 ∧ 3+X₁ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₃ ≤ 1 ∧ 1 ≤ X₃ ∧ 0 ≤ X₁ ∧ X₃ ≤ 1 ∧ X₃ ≤ 1+X₂ ∧ X₂+X₃ ≤ 1 ∧ X₃ ≤ 1+X₁ ∧ 2+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 4 ≤ X₀+X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 3+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ 3+X₁ ∧ 3 ≤ X₀
knowledge_propagation leads to new time bound X₀+1 {O(n)} for transition t₉₈₂: n_l11___36(X₀, X₁, X₂, X₃) → n_l12___35(X₀, X₁, X₂, X₃) :|: 4+X₁ ≤ X₀ ∧ X₃ ≤ 2 ∧ 2 ≤ X₃ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ X₃ ≤ 2 ∧ X₃ ≤ 2+X₂ ∧ X₂+X₃ ≤ 2 ∧ X₃ ≤ 2+X₁ ∧ 2+X₃ ≤ X₀ ∧ 2 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 6 ≤ X₀+X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 4+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 4+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 4 ≤ X₀
knowledge_propagation leads to new time bound X₀+1 {O(n)} for transition t₉₈₃: n_l11___36(X₀, X₁, X₂, X₃) → n_l2___34(X₀, X₁, X₀, X₃) :|: 4+X₁ ≤ X₀ ∧ X₃ ≤ 2 ∧ 2 ≤ X₃ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ X₃ ≤ 2 ∧ X₃ ≤ 2+X₂ ∧ X₂+X₃ ≤ 2 ∧ X₃ ≤ 2+X₁ ∧ 2+X₃ ≤ X₀ ∧ 2 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 6 ≤ X₀+X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 4+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 4+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 4 ≤ X₀
knowledge_propagation leads to new time bound X₀+1 {O(n)} for transition t₉₈₄: n_l11___4(X₀, X₁, X₂, X₃) → n_l12___3(X₀, X₁, X₂, X₃) :|: 4+X₁ ≤ X₀ ∧ X₃ ≤ 1 ∧ 1 ≤ X₃ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ X₃ ≤ 1 ∧ X₃ ≤ 1+X₂ ∧ X₂+X₃ ≤ 1 ∧ X₃ ≤ 1+X₁ ∧ 3+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 5 ≤ X₀+X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 4+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 4+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 4 ≤ X₀
knowledge_propagation leads to new time bound X₀+1 {O(n)} for transition t₉₈₅: n_l11___4(X₀, X₁, X₂, X₃) → n_l2___34(X₀, X₁, X₀, X₃) :|: 4+X₁ ≤ X₀ ∧ X₃ ≤ 1 ∧ 1 ≤ X₃ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ X₃ ≤ 1 ∧ X₃ ≤ 1+X₂ ∧ X₂+X₃ ≤ 1 ∧ X₃ ≤ 1+X₁ ∧ 3+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 5 ≤ X₀+X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 4+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 4+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 4 ≤ X₀
knowledge_propagation leads to new time bound X₀+1 {O(n)} for transition t₉₈₈: n_l12___1(X₀, X₁, X₂, X₃) → n_l2___33(X₀, X₁, X₃, X₃) :|: 3 ≤ X₀ ∧ X₀ ≤ X₁+3 ∧ 3+X₁ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₃ ≤ 1 ∧ 1 ≤ X₃ ∧ 0 ≤ X₁ ∧ X₃ ≤ 1 ∧ X₃ ≤ 1+X₂ ∧ X₂+X₃ ≤ 1 ∧ X₃ ≤ 1+X₁ ∧ 2+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 4 ≤ X₀+X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 3+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ 3+X₁ ∧ 3 ≤ X₀
knowledge_propagation leads to new time bound X₀+1 {O(n)} for transition t₉₉₃: n_l12___3(X₀, X₁, X₂, X₃) → n_l2___33(X₀, X₁, X₃, X₃) :|: 4+X₁ ≤ X₀ ∧ X₃ ≤ 1 ∧ 1 ≤ X₃ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ X₃ ≤ 1 ∧ X₃ ≤ 1+X₂ ∧ X₂+X₃ ≤ 1 ∧ X₃ ≤ 1+X₁ ∧ 3+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 5 ≤ X₀+X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 4+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 4+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 4 ≤ X₀
knowledge_propagation leads to new time bound X₀+1 {O(n)} for transition t₉₉₄: n_l12___35(X₀, X₁, X₂, X₃) → n_l2___33(X₀, X₁, X₃, X₃) :|: 4+X₁ ≤ X₀ ∧ X₃ ≤ 2 ∧ 2 ≤ X₃ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ X₃ ≤ 2 ∧ X₃ ≤ 2+X₂ ∧ X₂+X₃ ≤ 2 ∧ X₃ ≤ 2+X₁ ∧ 2+X₃ ≤ X₀ ∧ 2 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 6 ≤ X₀+X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 4+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 4+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 4 ≤ X₀
MPRF for transition t₁₀₄₂: n_l2___33(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₀ ≤ 2⋅X₂+2+X₁ ∧ 0 ≤ X₁ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁ of depth 1:
new bound:
5⋅X₀⋅X₀+16⋅X₀+13 {O(n^2)}
MPRF for transition t₁₀₄₃: n_l2___34(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₀ ≤ 2⋅X₂+2+X₁ ∧ 0 ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ of depth 1:
new bound:
2⋅X₀⋅X₀+8⋅X₀+6 {O(n^2)}
CFR did not improve the program. Rolling back
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:inf {Infinity}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: X₀+1 {O(n)}
t₅: 1 {O(1)}
t₆: X₀+1 {O(n)}
t₇: inf {Infinity}
t₈: 2⋅X₀+3 {O(n)}
t₉: inf {Infinity}
t₁₀: inf {Infinity}
t₁₂: inf {Infinity}
t₁₃: inf {Infinity}
t₁₄: inf {Infinity}
t₁₅: inf {Infinity}
t₁₆: inf {Infinity}
t₁₇: inf {Infinity}
t₁₈: inf {Infinity}
t₁₉: X₀+1 {O(n)}
t₂₀: 1 {O(1)}
Costbounds
Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: X₀+1 {O(n)}
t₅: 1 {O(1)}
t₆: X₀+1 {O(n)}
t₇: inf {Infinity}
t₈: 2⋅X₀+3 {O(n)}
t₉: inf {Infinity}
t₁₀: inf {Infinity}
t₁₂: inf {Infinity}
t₁₃: inf {Infinity}
t₁₄: inf {Infinity}
t₁₅: inf {Infinity}
t₁₆: inf {Infinity}
t₁₇: inf {Infinity}
t₁₈: inf {Infinity}
t₁₉: X₀+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: 0 {O(1)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₀+1 {O(n)}
t₅, X₀: X₀ {O(n)}
t₅, X₁: X₀+1 {O(n)}
t₆, X₀: X₀ {O(n)}
t₆, X₁: X₀+1 {O(n)}
t₆, X₂: 0 {O(1)}
t₇, X₀: X₀ {O(n)}
t₇, X₁: X₀+1 {O(n)}
t₈, X₀: X₀ {O(n)}
t₈, X₁: X₀+1 {O(n)}
t₉, X₀: X₀ {O(n)}
t₉, X₁: X₀+1 {O(n)}
t₁₀, X₀: X₀ {O(n)}
t₁₀, X₁: X₀+1 {O(n)}
t₁₂, X₀: X₀ {O(n)}
t₁₂, X₁: X₀+1 {O(n)}
t₁₃, X₀: X₀ {O(n)}
t₁₃, X₁: X₀+1 {O(n)}
t₁₄, X₀: X₀ {O(n)}
t₁₄, X₁: X₀+1 {O(n)}
t₁₅, X₀: X₀ {O(n)}
t₁₅, X₁: X₀+1 {O(n)}
t₁₆, X₀: X₀ {O(n)}
t₁₆, X₁: X₀+1 {O(n)}
t₁₇, X₀: X₀ {O(n)}
t₁₇, X₁: X₀+1 {O(n)}
t₁₇, X₂: 2⋅X₀ {O(n)}
t₁₈, X₀: X₀ {O(n)}
t₁₈, X₁: X₀+1 {O(n)}
t₁₉, X₀: X₀ {O(n)}
t₁₉, X₁: X₀+1 {O(n)}
t₂₀, X₀: 2⋅X₀ {O(n)}
t₂₀, X₁: X₀+X₁+1 {O(n)}