Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars: nondef_0
Locations: l0, l1, l10, l11, l12, l13, l14, l15, l16, l17, l18, l19, l2, l20, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅)
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅)
t₂₀: l10(X₀, X₁, X₂, X₃, X₄, X₅) → l9(X₀, X₁, X₂, X₃, X₄, X₅)
t₉: l11(X₀, X₁, X₂, X₃, X₄, X₅) → l18(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂ < X₅
t₁₀: l11(X₀, X₁, X₂, X₃, X₄, X₅) → l19(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₅ ≤ X₂
t₅: l12(X₀, X₁, X₂, X₃, X₄, X₅) → l13(X₀, X₁, X₂, X₃, X₄, X₅)
t₆: l13(X₀, X₁, X₂, X₃, X₄, X₅) → l14(X₀, X₁, X₂, X₃, X₄, X₅)
t₇: l14(X₀, X₁, X₂, X₃, X₄, X₅) → l15(X₀, X₁, X₂, X₃, X₄, X₅)
t₈: l15(X₀, X₁, X₂, X₃, X₄, X₅) → l11(X₀, X₁, 0, X₃, X₄, X₅)
t₁₄: l16(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃, X₄, X₅)
t₁₂: l17(X₀, X₁, X₂, X₃, X₄, X₅) → l16(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₃ < X₅
t₁₃: l17(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₅ ≤ X₃
t₁₁: l18(X₀, X₁, X₂, X₃, X₄, X₅) → l17(X₀, X₁, X₂, X₂+1, 0, X₅)
t₂₃: l19(X₀, X₁, X₂, X₃, X₄, X₅) → l20(X₀, X₁, X₂, X₃, X₄, X₅)
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅)
t₂: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₃, X₄, X₅)
t₄: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l12(X₀, X₁, X₂, X₃, X₄, X₅)
t₁₉: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l10(X₀, X₃-1, X₂, X₃, X₄, X₅)
t₁₈: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l17(X₀, X₁, X₂, X₃+1, X₄+1, X₅)
t₁₅: l7(X₀, X₁, X₂, X₃, X₄, X₅) → l8(nondef_0, X₁, X₂, X₃, X₄, X₅)
t₁₇: l8(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ 0
t₁₆: l8(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₀
t₂₁: l9(X₀, X₁, X₂, X₃, X₄, X₅) → l11(X₀, X₁, X₁, X₃, X₄, X₅) :|: 0 < X₄
t₂₂: l9(X₀, X₁, X₂, X₃, X₄, X₅) → l11(X₀, X₁, X₃, X₃, X₄, X₅) :|: X₄ ≤ 0
Preprocessing
Found invariant 0 ≤ X₂ for location l11
Found invariant 2 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2+X₄ ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ 2+X₂ ≤ X₅ ∧ 3 ≤ X₀+X₅ ∧ 1+X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀ for location l6
Found invariant X₅ ≤ X₂ ∧ 0 ≤ X₂ for location l19
Found invariant 1 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ 1+X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ for location l17
Found invariant 2 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2+X₄ ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ 2+X₂ ≤ X₅ ∧ 1+X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ for location l7
Found invariant X₅ ≤ X₂ ∧ 0 ≤ X₂ for location l20
Found invariant 1 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ 1+X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ for location l5
Found invariant 2 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2+X₄ ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ 2+X₂ ≤ X₅ ∧ 1+X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ for location l8
Found invariant 1+X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₁+X₄ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ for location l10
Found invariant 2 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2+X₄ ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ 2+X₂ ≤ X₅ ∧ 1+X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ for location l16
Found invariant 1 ≤ X₅ ∧ 1 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ 0 ≤ X₂ for location l18
Found invariant 1+X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₁+X₄ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ for location l9
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars: nondef_0
Locations: l0, l1, l10, l11, l12, l13, l14, l15, l16, l17, l18, l19, l2, l20, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅)
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅)
t₂₀: l10(X₀, X₁, X₂, X₃, X₄, X₅) → l9(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₁+X₄ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁
t₉: l11(X₀, X₁, X₂, X₃, X₄, X₅) → l18(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂ < X₅ ∧ 0 ≤ X₂
t₁₀: l11(X₀, X₁, X₂, X₃, X₄, X₅) → l19(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₅ ≤ X₂ ∧ 0 ≤ X₂
t₅: l12(X₀, X₁, X₂, X₃, X₄, X₅) → l13(X₀, X₁, X₂, X₃, X₄, X₅)
t₆: l13(X₀, X₁, X₂, X₃, X₄, X₅) → l14(X₀, X₁, X₂, X₃, X₄, X₅)
t₇: l14(X₀, X₁, X₂, X₃, X₄, X₅) → l15(X₀, X₁, X₂, X₃, X₄, X₅)
t₈: l15(X₀, X₁, X₂, X₃, X₄, X₅) → l11(X₀, X₁, 0, X₃, X₄, X₅)
t₁₄: l16(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃, X₄, X₅) :|: 2 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2+X₄ ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ 2+X₂ ≤ X₅ ∧ 1+X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂
t₁₂: l17(X₀, X₁, X₂, X₃, X₄, X₅) → l16(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₃ < X₅ ∧ 1 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ 1+X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂
t₁₃: l17(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₅ ≤ X₃ ∧ 1 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ 1+X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂
t₁₁: l18(X₀, X₁, X₂, X₃, X₄, X₅) → l17(X₀, X₁, X₂, X₂+1, 0, X₅) :|: 1 ≤ X₅ ∧ 1 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ 0 ≤ X₂
t₂₃: l19(X₀, X₁, X₂, X₃, X₄, X₅) → l20(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₅ ≤ X₂ ∧ 0 ≤ X₂
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅)
t₂: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₃, X₄, X₅)
t₄: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l12(X₀, X₁, X₂, X₃, X₄, X₅)
t₁₉: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l10(X₀, X₃-1, X₂, X₃, X₄, X₅) :|: 1 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ 1+X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂
t₁₈: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l17(X₀, X₁, X₂, X₃+1, X₄+1, X₅) :|: 2 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2+X₄ ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ 2+X₂ ≤ X₅ ∧ 3 ≤ X₀+X₅ ∧ 1+X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀
t₁₅: l7(X₀, X₁, X₂, X₃, X₄, X₅) → l8(nondef_0, X₁, X₂, X₃, X₄, X₅) :|: 2 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2+X₄ ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ 2+X₂ ≤ X₅ ∧ 1+X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂
t₁₇: l8(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ 0 ∧ 2 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2+X₄ ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ 2+X₂ ≤ X₅ ∧ 1+X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂
t₁₆: l8(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₀ ∧ 2 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2+X₄ ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ 2+X₂ ≤ X₅ ∧ 1+X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂
t₂₁: l9(X₀, X₁, X₂, X₃, X₄, X₅) → l11(X₀, X₁, X₁, X₃, X₄, X₅) :|: 0 < X₄ ∧ 1+X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₁+X₄ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁
t₂₂: l9(X₀, X₁, X₂, X₃, X₄, X₅) → l11(X₀, X₁, X₃, X₃, X₄, X₅) :|: X₄ ≤ 0 ∧ 1+X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₁+X₄ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁
MPRF for transition t₉: l11(X₀, X₁, X₂, X₃, X₄, X₅) → l18(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂ < X₅ ∧ 0 ≤ X₂ of depth 1:
new bound:
X₅ {O(n)}
MPRF:
l16 [X₄+X₅-X₃ ]
l18 [X₅-X₂-1 ]
l10 [X₄+X₅-X₃ ]
l17 [X₄+X₅-X₃ ]
l7 [X₄+X₅-X₃ ]
l6 [X₄+X₅-X₃ ]
l8 [X₄+X₅-X₃ ]
l5 [X₄+X₅-X₃ ]
l9 [X₄+X₅-X₃ ]
l11 [X₅-X₂ ]
MPRF for transition t₁₄: l16(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃, X₄, X₅) :|: 2 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2+X₄ ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ 2+X₂ ≤ X₅ ∧ 1+X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ of depth 1:
new bound:
2⋅X₅+1 {O(n)}
MPRF:
l16 [X₄+2⋅X₅+1-2⋅X₃ ]
l18 [2⋅X₅-2⋅X₂-1 ]
l10 [X₄+2⋅X₅-2⋅X₃ ]
l17 [X₄+2⋅X₅+1-2⋅X₃ ]
l7 [X₄+2⋅X₅-2⋅X₃ ]
l6 [X₄+2⋅X₅-2⋅X₃ ]
l8 [X₄+2⋅X₅-2⋅X₃ ]
l5 [X₄+2⋅X₅-2⋅X₃ ]
l9 [X₄+2⋅X₅-2⋅X₁-2 ]
l11 [2⋅X₅-2⋅X₂-1 ]
MPRF for transition t₁₂: l17(X₀, X₁, X₂, X₃, X₄, X₅) → l16(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₃ < X₅ ∧ 1 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ 1+X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ of depth 1:
new bound:
2⋅X₅+1 {O(n)}
MPRF:
l16 [X₄+2⋅X₅-2⋅X₃ ]
l18 [2⋅X₅-2⋅X₂-1 ]
l10 [X₄+2⋅X₅-2⋅X₃ ]
l17 [X₄+2⋅X₅+1-2⋅X₃ ]
l7 [X₄+2⋅X₅-2⋅X₃ ]
l6 [X₄+2⋅X₅-2⋅X₃ ]
l8 [X₄+2⋅X₅-2⋅X₃ ]
l5 [X₄+2⋅X₅-2⋅X₃ ]
l9 [X₄+2⋅X₅-2⋅X₃ ]
l11 [2⋅X₅-2⋅X₂-1 ]
MPRF for transition t₁₃: l17(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₅ ≤ X₃ ∧ 1 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ 1+X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ of depth 1:
new bound:
X₅ {O(n)}
MPRF:
l16 [X₄+X₅+1-X₃ ]
l18 [X₅-X₂ ]
l10 [X₄+X₅-X₁-1 ]
l17 [X₄+X₅+1-X₃ ]
l7 [X₄+X₅+1-X₃ ]
l6 [X₄+X₅+1-X₃ ]
l8 [X₄+X₅+1-X₃ ]
l5 [X₄+X₅-X₃ ]
l9 [X₄+X₅-X₁-1 ]
l11 [X₅-X₂ ]
MPRF for transition t₁₁: l18(X₀, X₁, X₂, X₃, X₄, X₅) → l17(X₀, X₁, X₂, X₂+1, 0, X₅) :|: 1 ≤ X₅ ∧ 1 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ 0 ≤ X₂ of depth 1:
new bound:
X₅ {O(n)}
MPRF:
l16 [X₄+X₅-X₃ ]
l18 [X₅-X₂ ]
l10 [X₄+X₅-X₁-1 ]
l17 [X₄+X₅-X₃ ]
l7 [X₄+X₅-X₃ ]
l6 [X₄+X₅-X₃ ]
l8 [X₄+X₅-X₃ ]
l5 [X₄+X₅-X₃ ]
l9 [X₄+X₅-X₁-1 ]
l11 [X₅-X₂ ]
MPRF for transition t₁₉: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l10(X₀, X₃-1, X₂, X₃, X₄, X₅) :|: 1 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ 1+X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ of depth 1:
new bound:
2⋅X₅+1 {O(n)}
MPRF:
l16 [X₄+2⋅X₅-X₂-X₃ ]
l18 [2⋅X₅-2⋅X₂-1 ]
l10 [X₄+2⋅X₅-2⋅X₃ ]
l17 [X₄+2⋅X₅-X₂-X₃ ]
l7 [X₄+2⋅X₅-X₂-X₃ ]
l6 [X₄+2⋅X₅-X₂-X₃ ]
l8 [X₄+2⋅X₅-X₂-X₃ ]
l5 [X₄+2⋅X₅+1-2⋅X₃ ]
l9 [X₄+2⋅X₅-2⋅X₃ ]
l11 [2⋅X₅-2⋅X₂-1 ]
MPRF for transition t₁₈: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l17(X₀, X₁, X₂, X₃+1, X₄+1, X₅) :|: 2 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2+X₄ ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ 2+X₂ ≤ X₅ ∧ 3 ≤ X₀+X₅ ∧ 1+X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀ of depth 1:
new bound:
2⋅X₅+2 {O(n)}
MPRF:
l16 [2⋅X₅-2⋅X₃ ]
l18 [2⋅X₅-2⋅X₂-2 ]
l10 [2⋅X₅-2⋅X₃ ]
l17 [2⋅X₅-2⋅X₃ ]
l7 [2⋅X₅-2⋅X₃ ]
l6 [2⋅X₅-2⋅X₃ ]
l8 [2⋅X₅-2⋅X₃ ]
l5 [2⋅X₅-2⋅X₃ ]
l9 [2⋅X₅-2⋅X₃ ]
l11 [2⋅X₅-2⋅X₂-2 ]
MPRF for transition t₁₅: l7(X₀, X₁, X₂, X₃, X₄, X₅) → l8(nondef_0, X₁, X₂, X₃, X₄, X₅) :|: 2 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2+X₄ ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ 2+X₂ ≤ X₅ ∧ 1+X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ of depth 1:
new bound:
2⋅X₅+3 {O(n)}
MPRF:
l16 [X₄+2⋅X₅-2⋅X₃-1 ]
l18 [2⋅X₅-2⋅X₂-3 ]
l10 [2⋅X₁+X₄+2⋅X₅-4⋅X₃ ]
l17 [X₄+2⋅X₅-2⋅X₃-1 ]
l7 [X₄+2⋅X₅-2⋅X₃-1 ]
l6 [X₄+2⋅X₅-2⋅X₃-2 ]
l8 [X₄+2⋅X₅-2⋅X₃-2 ]
l5 [X₄+2⋅X₅-2⋅X₃-2 ]
l9 [2⋅X₁+X₄+2⋅X₅-4⋅X₃ ]
l11 [2⋅X₅-2⋅X₂-3 ]
MPRF for transition t₁₆: l8(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₀ ∧ 2 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2+X₄ ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ 2+X₂ ≤ X₅ ∧ 1+X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ of depth 1:
new bound:
X₅+1 {O(n)}
MPRF:
l16 [X₅-X₃ ]
l18 [X₅-X₂-1 ]
l10 [X₅-X₁-1 ]
l17 [X₅-X₃ ]
l7 [X₅-X₃ ]
l6 [X₅-X₃-1 ]
l8 [X₅-X₃ ]
l5 [X₅-X₃ ]
l9 [X₅-X₁-1 ]
l11 [X₅-X₂-1 ]
MPRF for transition t₁₇: l8(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ 0 ∧ 2 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2+X₄ ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ 2+X₂ ≤ X₅ ∧ 1+X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ of depth 1:
new bound:
X₅ {O(n)}
MPRF:
l16 [X₄+X₅+1-X₃ ]
l18 [X₅-X₂ ]
l10 [X₄+X₅-X₃ ]
l17 [X₄+X₅+1-X₃ ]
l7 [X₄+X₅+1-X₃ ]
l6 [X₄+X₅+1-X₃ ]
l8 [X₄+X₅+1-X₃ ]
l5 [X₄+X₅-X₃ ]
l9 [X₄+X₅-X₃ ]
l11 [X₅-X₂ ]
knowledge_propagation leads to new time bound 2⋅X₅+1 {O(n)} for transition t₂₀: l10(X₀, X₁, X₂, X₃, X₄, X₅) → l9(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₁+X₄ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁
knowledge_propagation leads to new time bound 2⋅X₅+1 {O(n)} for transition t₂₁: l9(X₀, X₁, X₂, X₃, X₄, X₅) → l11(X₀, X₁, X₁, X₃, X₄, X₅) :|: 0 < X₄ ∧ 1+X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₁+X₄ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁
knowledge_propagation leads to new time bound 2⋅X₅+1 {O(n)} for transition t₂₂: l9(X₀, X₁, X₂, X₃, X₄, X₅) → l11(X₀, X₁, X₃, X₃, X₄, X₅) :|: X₄ ≤ 0 ∧ 1+X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₁+X₄ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁
All Bounds
Timebounds
Overall timebound:21⋅X₅+23 {O(n)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₂₀: 2⋅X₅+1 {O(n)}
t₉: X₅ {O(n)}
t₁₀: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₁₄: 2⋅X₅+1 {O(n)}
t₁₂: 2⋅X₅+1 {O(n)}
t₁₃: X₅ {O(n)}
t₁₁: X₅ {O(n)}
t₂₃: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₄: 1 {O(1)}
t₁₉: 2⋅X₅+1 {O(n)}
t₁₈: 2⋅X₅+2 {O(n)}
t₁₅: 2⋅X₅+3 {O(n)}
t₁₆: X₅+1 {O(n)}
t₁₇: X₅ {O(n)}
t₂₁: 2⋅X₅+1 {O(n)}
t₂₂: 2⋅X₅+1 {O(n)}
Costbounds
Overall costbound: 21⋅X₅+23 {O(n)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₂₀: 2⋅X₅+1 {O(n)}
t₉: X₅ {O(n)}
t₁₀: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₁₄: 2⋅X₅+1 {O(n)}
t₁₂: 2⋅X₅+1 {O(n)}
t₁₃: X₅ {O(n)}
t₁₁: X₅ {O(n)}
t₂₃: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₄: 1 {O(1)}
t₁₉: 2⋅X₅+1 {O(n)}
t₁₈: 2⋅X₅+2 {O(n)}
t₁₅: 2⋅X₅+3 {O(n)}
t₁₆: X₅+1 {O(n)}
t₁₇: X₅ {O(n)}
t₂₁: 2⋅X₅+1 {O(n)}
t₂₂: 2⋅X₅+1 {O(n)}
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)}
t₀, X₅: X₅ {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)}
t₃, X₅: X₅ {O(n)}
t₂₀, X₁: 3⋅X₅+2 {O(n)}
t₂₀, X₂: 9⋅X₅+6 {O(n)}
t₂₀, X₃: 3⋅X₅+2 {O(n)}
t₂₀, X₄: 4⋅X₅+4 {O(n)}
t₂₀, X₅: X₅ {O(n)}
t₉, X₁: 6⋅X₅+X₁+4 {O(n)}
t₉, X₂: 3⋅X₅+2 {O(n)}
t₉, X₃: 6⋅X₅+X₃+4 {O(n)}
t₉, X₄: 4⋅X₅+X₄+4 {O(n)}
t₉, X₅: X₅ {O(n)}
t₁₀, X₁: 6⋅X₅+X₁+4 {O(n)}
t₁₀, X₂: 6⋅X₅+4 {O(n)}
t₁₀, X₃: 6⋅X₅+X₃+4 {O(n)}
t₁₀, X₄: 4⋅X₅+X₄+4 {O(n)}
t₁₀, X₅: 3⋅X₅ {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)}
t₅, X₅: X₅ {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)}
t₆, X₅: X₅ {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)}
t₇, X₅: X₅ {O(n)}
t₈, X₀: X₀ {O(n)}
t₈, X₁: X₁ {O(n)}
t₈, X₂: 0 {O(1)}
t₈, X₃: X₃ {O(n)}
t₈, X₄: X₄ {O(n)}
t₈, X₅: X₅ {O(n)}
t₁₄, X₁: 6⋅X₅+X₁+4 {O(n)}
t₁₄, X₂: 3⋅X₅+2 {O(n)}
t₁₄, X₃: 3⋅X₅+2 {O(n)}
t₁₄, X₄: 2⋅X₅+2 {O(n)}
t₁₄, X₅: X₅ {O(n)}
t₁₂, X₁: 6⋅X₅+X₁+4 {O(n)}
t₁₂, X₂: 3⋅X₅+2 {O(n)}
t₁₂, X₃: 3⋅X₅+2 {O(n)}
t₁₂, X₄: 2⋅X₅+2 {O(n)}
t₁₂, X₅: X₅ {O(n)}
t₁₃, X₁: 12⋅X₅+2⋅X₁+8 {O(n)}
t₁₃, X₂: 6⋅X₅+4 {O(n)}
t₁₃, X₃: 3⋅X₅+2 {O(n)}
t₁₃, X₄: 2⋅X₅+2 {O(n)}
t₁₃, X₅: X₅ {O(n)}
t₁₁, X₁: 6⋅X₅+X₁+4 {O(n)}
t₁₁, X₂: 3⋅X₅+2 {O(n)}
t₁₁, X₃: 3⋅X₅+2 {O(n)}
t₁₁, X₄: 0 {O(1)}
t₁₁, X₅: X₅ {O(n)}
t₂₃, X₁: 6⋅X₅+X₁+4 {O(n)}
t₂₃, X₂: 6⋅X₅+4 {O(n)}
t₂₃, X₃: 6⋅X₅+X₃+4 {O(n)}
t₂₃, X₄: 4⋅X₅+X₄+4 {O(n)}
t₂₃, X₅: 3⋅X₅ {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)}
t₁, X₅: X₅ {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)}
t₂, X₅: X₅ {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)}
t₄, X₅: X₅ {O(n)}
t₁₉, X₁: 3⋅X₅+2 {O(n)}
t₁₉, X₂: 9⋅X₅+6 {O(n)}
t₁₉, X₃: 3⋅X₅+2 {O(n)}
t₁₉, X₄: 4⋅X₅+4 {O(n)}
t₁₉, X₅: X₅ {O(n)}
t₁₈, X₁: 6⋅X₅+X₁+4 {O(n)}
t₁₈, X₂: 3⋅X₅+2 {O(n)}
t₁₈, X₃: 3⋅X₅+2 {O(n)}
t₁₈, X₄: 2⋅X₅+2 {O(n)}
t₁₈, X₅: X₅ {O(n)}
t₁₅, X₁: 6⋅X₅+X₁+4 {O(n)}
t₁₅, X₂: 3⋅X₅+2 {O(n)}
t₁₅, X₃: 3⋅X₅+2 {O(n)}
t₁₅, X₄: 2⋅X₅+2 {O(n)}
t₁₅, X₅: X₅ {O(n)}
t₁₆, X₁: 6⋅X₅+X₁+4 {O(n)}
t₁₆, X₂: 3⋅X₅+2 {O(n)}
t₁₆, X₃: 3⋅X₅+2 {O(n)}
t₁₆, X₄: 2⋅X₅+2 {O(n)}
t₁₆, X₅: X₅ {O(n)}
t₁₇, X₁: 6⋅X₅+X₁+4 {O(n)}
t₁₇, X₂: 3⋅X₅+2 {O(n)}
t₁₇, X₃: 3⋅X₅+2 {O(n)}
t₁₇, X₄: 2⋅X₅+2 {O(n)}
t₁₇, X₅: X₅ {O(n)}
t₂₁, X₁: 3⋅X₅+2 {O(n)}
t₂₁, X₂: 3⋅X₅+2 {O(n)}
t₂₁, X₃: 3⋅X₅+2 {O(n)}
t₂₁, X₄: 4⋅X₅+4 {O(n)}
t₂₁, X₅: X₅ {O(n)}
t₂₂, X₁: 3⋅X₅+2 {O(n)}
t₂₂, X₂: 3⋅X₅+2 {O(n)}
t₂₂, X₃: 3⋅X₅+2 {O(n)}
t₂₂, X₄: 0 {O(1)}
t₂₂, X₅: X₅ {O(n)}