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 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 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+3 {O(n)}

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:

X₁+2 {O(n)}

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:

X₁+2 {O(n)}

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:

2⋅X₁+1 {O(n)}

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:

4⋅X₁⋅X₁+13⋅X₁+8 {O(n^2)}

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:

4⋅X₁⋅X₁+11⋅X₁+6 {O(n^2)}

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:

6⋅X₁⋅X₁+11⋅X₁+4 {O(n^2)}

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:

2⋅X₁⋅X₁+2⋅X₁ {O(n^2)}

Chain transitions t₁₂: l12→l10 and t₁₃: l10→l13 to t₁₀₄: l12→l13

Chain transitions t₉: l13→l11 and t₁₁: l11→l12 to t₁₀₅: l13→l12

Chain transitions t₁₀₅: l13→l12 and t₁₀₄: l12→l13 to t₁₀₆: l13→l13

Chain transitions t₁₀₅: l13→l12 and t₁₂: l12→l10 to t₁₀₇: l13→l10

Chain transitions t₁₀: l13→l14 and t₁₄: l14→l6 to t₁₀₈: l13→l6

Chain transitions t₆: l9→l5 and t₈: l5→l15 to t₁₀₉: l9→l15

Chain transitions t₁₆: l7→l5 and t₈: l5→l15 to t₁₁₀: l7→l15

Chain transitions t₁₆: l7→l5 and t₇: l5→l13 to t₁₁₁: l7→l13

Chain transitions t₆: l9→l5 and t₇: l5→l13 to t₁₁₂: l9→l13

Chain transitions t₁₀₈: l13→l6 and t₁₅: l6→l7 to t₁₁₃: l13→l7

Chain transitions t₁₁₃: l13→l7 and t₁₆: l7→l5 to t₁₁₄: l13→l5

Chain transitions t₁₁₃: l13→l7 and t₁₁₀: l7→l15 to t₁₁₅: l13→l15

Chain transitions t₁₁₃: l13→l7 and t₁₁₁: l7→l13 to t₁₁₆: l13→l13

Analysing control-flow refined program

Eliminate variables {X₀} that do not contribute to the problem

Found invariant X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l11

Found invariant X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l6

Found invariant 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ for location l15

Found invariant X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l12

Found invariant X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l7

Found invariant 1 ≤ X₁ for location l5

Found invariant X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l13

Found invariant X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l10

Found invariant 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ for location l16

Found invariant X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l14

MPRF for transition t₁₅₄: l13(X₀, X₁, X₂) -{5}> l13(X₀, 1+X₁, 1+X₁) :|: X₀ < X₂ ∧ 1+X₁ ≤ X₀ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₀+3 {O(n)}

MPRF for transition t₁₅₃: l13(X₀, X₁, X₂) -{4}> l13(X₀, X₁, X₂+1) :|: X₂ ≤ X₀ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

2⋅X₀⋅X₀+13⋅X₀+20 {O(n^2)}

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

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 t₂₆₄: l13(X₀, X₁, X₂, X₃) → n_l11___7(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₁ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ 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 t₂₆₀: n_l11___7(X₀, X₁, X₂, X₃) → n_l12___6(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ X₂ ≤ X₃ ∧ 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 t₂₆₂: n_l12___6(X₀, X₁, X₂, X₃) → n_l10___5(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ X₂ ≤ X₃ ∧ 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 t₂₅₈: n_l10___5(X₀, X₁, X₂, X₃) → n_l13___4(X₀, X₁, X₂, X₃+1) :|: X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ X₂ ≤ X₃ ∧ 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 t₂₅₇: n_l10___1(X₀, X₁, X₂, X₃) → n_l13___4(X₀, X₁, X₂, X₃+1) :|: 1+X₂ ≤ X₃ ∧ X₃ ≤ X₁ ∧ 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:

2⋅X₁⋅X₁+9⋅X₁+8 {O(n^2)}

MPRF for transition t₂₅₉: n_l11___3(X₀, X₁, X₂, X₃) → n_l12___2(X₀, X₁, X₂, X₃) :|: 1+X₂ ≤ X₃ ∧ X₃ ≤ X₁ ∧ 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+8 {O(n^2)}

MPRF for transition t₂₆₁: n_l12___2(X₀, X₁, X₂, X₃) → n_l10___1(X₀, X₁, X₂, X₃) :|: 1+X₂ ≤ X₃ ∧ X₃ ≤ X₁ ∧ 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:

5⋅X₁⋅X₁+24⋅X₁+28 {O(n^2)}

MPRF for transition t₂₆₃: n_l13___4(X₀, X₁, X₂, X₃) → n_l11___3(X₀, X₁, X₂, X₃) :|: 1+X₂ ≤ X₃ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₂ ∧ 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:

2⋅X₁⋅X₁+9⋅X₁+8 {O(n^2)}

MPRF for transition t₂₇₀: 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)}

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:16⋅X₁⋅X₁+43⋅X₁+37 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: X₁+2 {O(n)}
t₈: 1 {O(1)}
t₉: 4⋅X₁⋅X₁+13⋅X₁+8 {O(n^2)}
t₁₀: X₁+3 {O(n)}
t₁₁: 4⋅X₁⋅X₁+11⋅X₁+6 {O(n^2)}
t₁₂: 6⋅X₁⋅X₁+11⋅X₁+4 {O(n^2)}
t₁₃: 2⋅X₁⋅X₁+2⋅X₁ {O(n^2)}
t₁₄: X₁+2 {O(n)}
t₁₅: X₁+2 {O(n)}
t₁₆: 2⋅X₁+1 {O(n)}
t₁₇: 1 {O(1)}

Costbounds

Overall costbound: 16⋅X₁⋅X₁+43⋅X₁+37 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: X₁+2 {O(n)}
t₈: 1 {O(1)}
t₉: 4⋅X₁⋅X₁+13⋅X₁+8 {O(n^2)}
t₁₀: X₁+3 {O(n)}
t₁₁: 4⋅X₁⋅X₁+11⋅X₁+6 {O(n^2)}
t₁₂: 6⋅X₁⋅X₁+11⋅X₁+4 {O(n^2)}
t₁₃: 2⋅X₁⋅X₁+2⋅X₁ {O(n^2)}
t₁₄: X₁+2 {O(n)}
t₁₅: X₁+2 {O(n)}
t₁₆: 2⋅X₁+1 {O(n)}
t₁₇: 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: X₁ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, 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)}
t₆, X₀: X₀ {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: 1 {O(1)}
t₆, X₃: X₃ {O(n)}
t₇, X₀: X₀+X₁+3 {O(n)}
t₇, X₁: X₁ {O(n)}
t₇, X₂: X₁+3 {O(n)}
t₇, X₃: X₁+4 {O(n)}
t₈, X₀: X₀+X₁+3 {O(n)}
t₈, X₁: 2⋅X₁ {O(n)}
t₈, X₂: X₁+4 {O(n)}
t₈, X₃: 2⋅X₁⋅X₁+3⋅X₁+X₃+4 {O(n^2)}
t₉, X₀: X₀+X₁+3 {O(n)}
t₉, X₁: X₁ {O(n)}
t₉, X₂: X₁+3 {O(n)}
t₉, X₃: 2⋅X₁⋅X₁+3⋅X₁+4 {O(n^2)}
t₁₀, X₀: X₀+X₁+3 {O(n)}
t₁₀, X₁: X₁ {O(n)}
t₁₀, X₂: X₁+3 {O(n)}
t₁₀, X₃: 2⋅X₁⋅X₁+3⋅X₁+4 {O(n^2)}
t₁₁, X₀: X₀+X₁+3 {O(n)}
t₁₁, X₁: X₁ {O(n)}
t₁₁, X₂: X₁+3 {O(n)}
t₁₁, X₃: 2⋅X₁⋅X₁+3⋅X₁+4 {O(n^2)}
t₁₂, X₀: X₀+X₁+3 {O(n)}
t₁₂, X₁: X₁ {O(n)}
t₁₂, X₂: X₁+3 {O(n)}
t₁₂, X₃: 2⋅X₁⋅X₁+3⋅X₁+4 {O(n^2)}
t₁₃, X₀: X₀+X₁+3 {O(n)}
t₁₃, X₁: X₁ {O(n)}
t₁₃, X₂: X₁+3 {O(n)}
t₁₃, X₃: 2⋅X₁⋅X₁+3⋅X₁+4 {O(n^2)}
t₁₄, X₀: X₁+3 {O(n)}
t₁₄, X₁: X₁ {O(n)}
t₁₄, X₂: X₁+3 {O(n)}
t₁₄, X₃: 2⋅X₁⋅X₁+3⋅X₁+4 {O(n^2)}
t₁₅, X₀: X₁+3 {O(n)}
t₁₅, X₁: X₁ {O(n)}
t₁₅, X₂: X₁+3 {O(n)}
t₁₅, X₃: 2⋅X₁⋅X₁+3⋅X₁+4 {O(n^2)}
t₁₆, X₀: X₁+3 {O(n)}
t₁₆, X₁: X₁ {O(n)}
t₁₆, X₂: X₁+3 {O(n)}
t₁₆, X₃: 2⋅X₁⋅X₁+3⋅X₁+4 {O(n^2)}
t₁₇, X₀: X₀+X₁+3 {O(n)}
t₁₇, X₁: 2⋅X₁ {O(n)}
t₁₇, X₂: X₁+4 {O(n)}
t₁₇, X₃: 2⋅X₁⋅X₁+3⋅X₁+X₃+4 {O(n^2)}