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:

l15 [X₁ ]
l13 [X₁ ]
l17 [X₁ ]
l16 [X₁ ]
l10 [X₁+1 ]
l7 [X₂ ]
l8 [X₂ ]
l6 [X₀+1 ]

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:

l15 [X₁+1 ]
l13 [X₁+1 ]
l17 [X₁+1 ]
l16 [X₁+1 ]
l10 [X₁+1 ]
l7 [X₁ ]
l8 [X₀+1 ]
l6 [X₀+1 ]

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:

l15 [X₁+1 ]
l13 [X₁+1 ]
l17 [X₁+1 ]
l16 [X₁+1 ]
l10 [X₁+1 ]
l7 [X₂+1 ]
l8 [X₂+1 ]
l6 [X₁+1 ]

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:

l15 [X₁+1 ]
l13 [X₁+1 ]
l17 [X₁+1 ]
l16 [X₁+1 ]
l10 [X₁+1 ]
l7 [X₂+1 ]
l8 [X₀+1 ]
l6 [X₀+1 ]

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:

l15 [X₁+1 ]
l13 [X₁+1 ]
l17 [X₁+1 ]
l16 [X₁+1 ]
l10 [X₁+1 ]
l7 [X₂+1 ]
l8 [X₁+1 ]
l6 [X₂ ]

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+3⋅X₃+2 {O(n^2)}

MPRF:

l15 [X₃-X₂ ]
l13 [X₃+1-X₂ ]
l17 [X₃-X₂ ]
l16 [X₃-X₂ ]
l6 [X₃+1 ]
l10 [X₃+1 ]
l7 [X₃-X₂ ]
l8 [X₃-X₂ ]

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+4⋅X₃+4 {O(n^2)}

MPRF:

l15 [X₃+2-X₂ ]
l13 [X₃+2-X₂ ]
l17 [X₃+1-X₂ ]
l16 [X₃+1-X₂ ]
l6 [X₃+2 ]
l10 [X₃+2 ]
l7 [X₃-X₂ ]
l8 [X₃-X₂ ]

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+2⋅X₃ {O(n^2)}

MPRF:

l15 [X₃-X₂ ]
l13 [X₃-X₂ ]
l17 [X₃-X₂ ]
l16 [X₃-X₂-1 ]
l6 [X₃ ]
l10 [X₃ ]
l7 [X₃-X₂ ]
l8 [X₁+X₃-X₀-X₂-1 ]

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+3⋅X₃+1 {O(n^2)}

MPRF:

l15 [X₁-X₂ ]
l13 [X₁-X₂ ]
l17 [X₁-X₂ ]
l16 [X₁-X₂ ]
l6 [X₀ ]
l10 [X₁ ]
l7 [0 ]
l8 [0 ]

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:

l15 [X₃-X₂ ]
l13 [X₃-X₂ ]
l17 [X₃-X₂ ]
l16 [X₃-X₂-1 ]
l6 [X₃ ]
l10 [X₃ ]
l7 [X₃-X₂ ]
l8 [X₃-X₂ ]

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 t₁₃₅: l13(X₀, X₁, X₂, X₃) → n_l15___7(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₁ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 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 t₁₃₈: n_l15___7(X₀, X₁, X₂, X₃) → n_l16___6(X₀, X₁, Arg2_P, X₃) :|: X₁ ≤ X₃ ∧ 1 ≤ X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₁ ≤ X₃ ∧ 1+Arg2_P ≤ X₁ ∧ 0 ≤ Arg2_P ∧ X₂ ≤ Arg2_P ∧ Arg2_P ≤ X₂ ∧ 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 t₁₃₉: n_l15___7(X₀, X₁, X₂, X₃) → n_l17___5(X₀, X₁, Arg2_P, X₃) :|: X₁ ≤ X₃ ∧ 1 ≤ X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₁ ≤ X₃ ∧ 1+Arg2_P ≤ X₁ ∧ 0 ≤ Arg2_P ∧ X₂ ≤ Arg2_P ∧ Arg2_P ≤ X₂ ∧ 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 t₁₄₃: n_l17___5(X₀, X₁, X₂, X₃) → n_l16___6(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₃ ∧ 1 ≤ X₁ ∧ X₂ ≤ 0 ∧ 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 t₁₄₁: n_l16___6(X₀, X₁, X₂, X₃) → n_l13___4(X₀, X₁, X₂+1, X₃) :|: X₁ ≤ X₃ ∧ 1 ≤ X₁ ∧ X₂ ≤ 0 ∧ 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 t₁₃₄: n_l13___4(X₀, X₁, X₂, X₃) → n_l15___3(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 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+8 {O(n^2)}

MPRF:

l13 [0 ]
l10 [0 ]
l8 [0 ]
l6 [0 ]
l7 [0 ]
n_l15___3 [X₁+1-X₂ ]
n_l15___7 [0 ]
n_l13___4 [X₁+2-X₂ ]
n_l17___1 [X₁+1-X₂ ]
n_l16___2 [X₁+1-X₂ ]
n_l17___5 [0 ]
n_l16___6 [0 ]

MPRF for transition t₁₅₁: 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)}

MPRF:

l13 [X₁+1 ]
l10 [X₁+1 ]
l8 [X₁ ]
l6 [X₂ ]
l7 [X₂ ]
n_l15___3 [X₁+1 ]
n_l15___7 [X₁+1 ]
n_l13___4 [X₁+1 ]
n_l17___1 [X₁+1 ]
n_l16___2 [X₁+1 ]
n_l17___5 [X₁+1 ]
n_l16___6 [X₁+1 ]

MPRF for transition t₁₃₆: n_l15___3(X₀, X₁, X₂, X₃) → n_l16___2(X₀, X₁, Arg2_P, X₃) :|: X₁ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ X₁ ≤ X₃ ∧ 1+Arg2_P ≤ X₁ ∧ 0 ≤ Arg2_P ∧ X₂ ≤ Arg2_P ∧ Arg2_P ≤ X₂ ∧ 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+6⋅X₃+4 {O(n^2)}

MPRF:

l13 [0 ]
l10 [0 ]
l8 [0 ]
l6 [0 ]
l7 [0 ]
n_l15___3 [X₁-X₂ ]
n_l15___7 [0 ]
n_l13___4 [X₁-X₂ ]
n_l17___1 [X₁-X₂ ]
n_l16___2 [X₁-X₂-1 ]
n_l17___5 [0 ]
n_l16___6 [0 ]

MPRF for transition t₁₃₇: n_l15___3(X₀, X₁, X₂, X₃) → n_l17___1(X₀, X₁, Arg2_P, X₃) :|: X₁ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ X₁ ≤ X₃ ∧ 1+Arg2_P ≤ X₁ ∧ 0 ≤ Arg2_P ∧ X₂ ≤ Arg2_P ∧ Arg2_P ≤ X₂ ∧ 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+10⋅X₃+8 {O(n^2)}

MPRF:

l13 [0 ]
l10 [0 ]
l8 [0 ]
l6 [0 ]
l7 [0 ]
n_l15___3 [X₁+2-X₂ ]
n_l15___7 [0 ]
n_l13___4 [X₁+2-X₂ ]
n_l17___1 [X₁+1-X₂ ]
n_l16___2 [X₁+1-X₂ ]
n_l17___5 [0 ]
n_l16___6 [0 ]

MPRF for transition t₁₄₀: n_l16___2(X₀, X₁, X₂, X₃) → n_l13___4(X₀, X₁, X₂+1, X₃) :|: X₁ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 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+11⋅X₃+6 {O(n^2)}

MPRF:

l13 [X₁ ]
l10 [X₁ ]
l8 [X₁ ]
l6 [X₂ ]
l7 [X₂ ]
n_l15___3 [2⋅X₁-X₂ ]
n_l15___7 [X₁ ]
n_l13___4 [2⋅X₁-X₂ ]
n_l17___1 [2⋅X₁-X₂ ]
n_l16___2 [2⋅X₁-X₂ ]
n_l17___5 [X₁ ]
n_l16___6 [X₁ ]

MPRF for transition t₁₄₂: n_l17___1(X₀, X₁, X₂, X₃) → n_l16___2(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 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:

6⋅X₃⋅X₃+12⋅X₃+4 {O(n^2)}

MPRF:

l13 [2⋅X₃ ]
l10 [2⋅X₃ ]
l8 [2⋅X₃ ]
l6 [2⋅X₃ ]
l7 [2⋅X₃ ]
n_l15___3 [X₁+2⋅X₃-X₂ ]
n_l15___7 [2⋅X₃ ]
n_l13___4 [X₁+2⋅X₃-X₂ ]
n_l17___1 [X₁+2⋅X₃-X₂ ]
n_l16___2 [X₁+2⋅X₃-X₂-1 ]
n_l17___5 [2⋅X₃ ]
n_l16___6 [2⋅X₃ ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:5⋅X₃⋅X₃+19⋅X₃+23 {O(n^2)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₉: X₃+1 {O(n)}
t₁₀: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₁₁: X₃⋅X₃+3⋅X₃+2 {O(n^2)}
t₁₂: X₃+1 {O(n)}
t₂₀: 1 {O(1)}
t₁₃: X₃⋅X₃+4⋅X₃+4 {O(n^2)}
t₁₄: X₃⋅X₃+2⋅X₃ {O(n^2)}
t₁₆: X₃⋅X₃+3⋅X₃+1 {O(n^2)}
t₁₅: X₃⋅X₃+2⋅X₃ {O(n^2)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₁₉: X₃+1 {O(n)}
t₁₇: X₃+1 {O(n)}
t₁₈: X₃+1 {O(n)}
t₆: 1 {O(1)}

Costbounds

Overall costbound: 5⋅X₃⋅X₃+19⋅X₃+23 {O(n^2)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₉: X₃+1 {O(n)}
t₁₀: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₁₁: X₃⋅X₃+3⋅X₃+2 {O(n^2)}
t₁₂: X₃+1 {O(n)}
t₂₀: 1 {O(1)}
t₁₃: X₃⋅X₃+4⋅X₃+4 {O(n^2)}
t₁₄: X₃⋅X₃+2⋅X₃ {O(n^2)}
t₁₆: X₃⋅X₃+3⋅X₃+1 {O(n^2)}
t₁₅: X₃⋅X₃+2⋅X₃ {O(n^2)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₁₉: X₃+1 {O(n)}
t₁₇: X₃+1 {O(n)}
t₁₈: X₃+1 {O(n)}
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)}
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+3⋅X₃+X₂+1 {O(n^2)}
t₁₀, X₃: 2⋅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)}
t₁₁, X₀: X₀+X₃+1 {O(n)}
t₁₁, X₁: X₃+1 {O(n)}
t₁₁, X₂: X₃⋅X₃+3⋅X₃+1 {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+3⋅X₃+1 {O(n^2)}
t₁₂, X₃: X₃ {O(n)}
t₂₀, X₀: X₀+X₃+1 {O(n)}
t₂₀, X₁: 2⋅X₃+1 {O(n)}
t₂₀, X₂: X₃⋅X₃+3⋅X₃+X₂+1 {O(n^2)}
t₂₀, X₃: 2⋅X₃ {O(n)}
t₁₃, X₀: X₀+X₃+1 {O(n)}
t₁₃, X₁: X₃+1 {O(n)}
t₁₃, X₂: X₃⋅X₃+3⋅X₃+1 {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+3⋅X₃+1 {O(n^2)}
t₁₄, X₃: X₃ {O(n)}
t₁₆, X₀: X₀+X₃+1 {O(n)}
t₁₆, X₁: X₃+1 {O(n)}
t₁₆, X₂: X₃⋅X₃+3⋅X₃+1 {O(n^2)}
t₁₆, X₃: X₃ {O(n)}
t₁₅, X₀: X₀+X₃+1 {O(n)}
t₁₅, X₁: X₃+1 {O(n)}
t₁₅, X₂: X₃⋅X₃+3⋅X₃+1 {O(n^2)}
t₁₅, 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)}
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)}
t₁₉, X₀: X₃+1 {O(n)}
t₁₉, X₁: X₃+1 {O(n)}
t₁₉, X₂: X₃⋅X₃+3⋅X₃+1 {O(n^2)}
t₁₉, X₃: X₃ {O(n)}
t₁₇, X₀: X₃+1 {O(n)}
t₁₇, X₁: X₃+1 {O(n)}
t₁₇, X₂: X₃⋅X₃+3⋅X₃+1 {O(n^2)}
t₁₇, X₃: X₃ {O(n)}
t₁₈, X₀: X₃+1 {O(n)}
t₁₈, X₁: X₃+1 {O(n)}
t₁₈, X₂: X₃⋅X₃+3⋅X₃+1 {O(n^2)}
t₁₈, X₃: X₃ {O(n)}
t₆, X₀: X₀ {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: X₃ {O(n)}