Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: E, F
Locations: l0, l1, l10, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l9(X₀, X₁, X₂, X₃)
t₈: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, 1)
t₉: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁+1, X₃, X₃)
t₄: l3(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₁+1 ≤ X₀
t₅: l3(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁
t₆: l4(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃) :|: F+1 ≤ E
t₇: l4(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₂) :|: E ≤ F
t₁₁: l5(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₂+1 ≤ 0
t₁₂: l5(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: 1 ≤ X₂
t₁₀: l5(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0 ∧ 0 ≤ X₂
t₂: l6(X₀, X₁, X₂, X₃) → l3(X₀, 0, 0, X₃) :|: 1 ≤ X₀
t₃: l6(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0
t₁₃: l7(X₀, X₁, X₂, X₃) → l6(X₀-1, X₁, X₂, X₃)
t₁₄: l8(X₀, X₁, X₂, X₃) → l10(X₀, X₁, X₂, X₃)
t₁: l9(X₀, X₁, X₂, X₃) → l6(X₀-1, X₁, X₂, X₃)

Preprocessing

Found invariant X₃ ≤ 1 ∧ X₃ ≤ 1+X₂ ∧ X₂+X₃ ≤ 2 ∧ X₃ ≤ 1+X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l2

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

Found invariant X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l5

Found invariant X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l1

Found invariant X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l4

Found invariant X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l3

Cut unsatisfiable transition t₁₁: l5→l7

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: E, F
Locations: l0, l1, l10, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l9(X₀, X₁, X₂, X₃)
t₈: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, 1) :|: X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₉: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁+1, X₃, X₃) :|: X₃ ≤ 1 ∧ X₃ ≤ 1+X₂ ∧ X₂+X₃ ≤ 2 ∧ X₃ ≤ 1+X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₄: l3(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₁+1 ≤ X₀ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₅: l3(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₆: l4(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃) :|: F+1 ≤ E ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₇: l4(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₂) :|: E ≤ F ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₂: l5(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: 1 ≤ X₂ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀
t₁₀: l5(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀
t₂: l6(X₀, X₁, X₂, X₃) → l3(X₀, 0, 0, X₃) :|: 1 ≤ X₀
t₃: l6(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0
t₁₃: l7(X₀, X₁, X₂, X₃) → l6(X₀-1, X₁, X₂, X₃) :|: X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀
t₁₄: l8(X₀, X₁, X₂, X₃) → l10(X₀, X₁, X₂, X₃)
t₁: l9(X₀, X₁, X₂, X₃) → l6(X₀-1, X₁, X₂, X₃)

MPRF for transition t₂: l6(X₀, X₁, X₂, X₃) → l3(X₀, 0, 0, X₃) :|: 1 ≤ X₀ of depth 1:

new bound:

X₀+1 {O(n)}

MPRF for transition t₅: l3(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₀+2 {O(n)}

MPRF for transition t₁₂: l5(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: 1 ≤ X₂ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₀+2 {O(n)}

MPRF for transition t₁₃: l7(X₀, X₁, X₂, X₃) → l6(X₀-1, X₁, X₂, X₃) :|: X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

2⋅X₀+2 {O(n)}

MPRF for transition t₄: l3(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₁+1 ≤ X₀ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

2⋅X₀⋅X₀+7⋅X₀+6 {O(n^2)}

MPRF for transition t₆: l4(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃) :|: F+1 ≤ E ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

2⋅X₀⋅X₀+5⋅X₀+3 {O(n^2)}

MPRF for transition t₇: l4(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₂) :|: E ≤ F ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

2⋅X₀⋅X₀+5⋅X₀+3 {O(n^2)}

MPRF for transition t₈: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, 1) :|: X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

2⋅X₀⋅X₀+5⋅X₀+3 {O(n^2)}

MPRF for transition t₉: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁+1, X₃, X₃) :|: X₃ ≤ 1 ∧ X₃ ≤ 1+X₂ ∧ X₂+X₃ ≤ 2 ∧ X₃ ≤ 1+X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

2⋅X₀⋅X₀+5⋅X₀+3 {O(n^2)}

Chain transitions t₆: l4→l1 and t₈: l1→l2 to t₁₃₂: l4→l2

Chain transitions t₁₃₂: l4→l2 and t₉: l2→l3 to t₁₃₃: l4→l3

Chain transitions t₇: l4→l2 and t₉: l2→l3 to t₁₃₄: l4→l3

Chain transitions t₂: l6→l3 and t₅: l3→l5 to t₁₃₅: l6→l5

Chain transitions t₁₃₄: l4→l3 and t₅: l3→l5 to t₁₃₆: l4→l5

Chain transitions t₁₃₄: l4→l3 and t₄: l3→l4 to t₁₃₇: l4→l4

Chain transitions t₂: l6→l3 and t₄: l3→l4 to t₁₃₈: l6→l4

Chain transitions t₁₃₃: l4→l3 and t₄: l3→l4 to t₁₃₉: l4→l4

Chain transitions t₁₃₃: l4→l3 and t₅: l3→l5 to t₁₄₀: l4→l5

Chain transitions t₁₃₅: l6→l5 and t₁₀: l5→l8 to t₁₄₁: l6→l8

Chain transitions t₁₄₀: l4→l5 and t₁₀: l5→l8 to t₁₄₂: l4→l8

Chain transitions t₁₄₀: l4→l5 and t₁₂: l5→l7 to t₁₄₃: l4→l7

Chain transitions t₁₃₅: l6→l5 and t₁₂: l5→l7 to t₁₄₄: l6→l7

Chain transitions t₁₃₆: l4→l5 and t₁₂: l5→l7 to t₁₄₅: l4→l7

Chain transitions t₁₃₆: l4→l5 and t₁₀: l5→l8 to t₁₄₆: l4→l8

Chain transitions t₁: l9→l6 and t₁₄₁: l6→l8 to t₁₄₇: l9→l8

Chain transitions t₁₃: l7→l6 and t₁₄₁: l6→l8 to t₁₄₈: l7→l8

Chain transitions t₁₃: l7→l6 and t₃: l6→l8 to t₁₄₉: l7→l8

Chain transitions t₁: l9→l6 and t₃: l6→l8 to t₁₅₀: l9→l8

Chain transitions t₁₃: l7→l6 and t₁₄₄: l6→l7 to t₁₅₁: l7→l7

Chain transitions t₁: l9→l6 and t₁₄₄: l6→l7 to t₁₅₂: l9→l7

Chain transitions t₁₃: l7→l6 and t₁₃₅: l6→l5 to t₁₅₃: l7→l5

Chain transitions t₁: l9→l6 and t₁₃₅: l6→l5 to t₁₅₄: l9→l5

Chain transitions t₁₃: l7→l6 and t₁₃₈: l6→l4 to t₁₅₅: l7→l4

Chain transitions t₁: l9→l6 and t₁₃₈: l6→l4 to t₁₅₆: l9→l4

Chain transitions t₁₃: l7→l6 and t₂: l6→l3 to t₁₅₇: l7→l3

Chain transitions t₁: l9→l6 and t₂: l6→l3 to t₁₅₈: l9→l3

Analysing control-flow refined program

Cut unsatisfiable transition t₁₄₂: l4→l8

Cut unsatisfiable transition t₁₄₇: l9→l8

Cut unsatisfiable transition t₁₄₈: l7→l8

Cut unsatisfiable transition t₁₅₁: l7→l7

Cut unsatisfiable transition t₁₅₂: l9→l7

Cut unsatisfiable transition t₁₅₃: l7→l5

Cut unsatisfiable transition t₁₅₄: l9→l5

Eliminate variables {X₃} that do not contribute to the problem

Found invariant X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l2

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

Found invariant X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l5

Found invariant X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l1

Found invariant X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l4

Found invariant X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l3

MPRF for transition t₂₂₀: l4(X₀, X₁, X₂) -{5}> l7(X₀, 1+X₁, 1) :|: F+1 ≤ E ∧ X₀ ≤ X₁+1 ∧ 0 ≤ 0 ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

MPRF for transition t₂₂₁: l4(X₀, X₁, X₂) -{4}> l7(X₀, 1+X₁, X₂) :|: E ≤ F ∧ X₀ ≤ X₁+1 ∧ 1 ≤ X₂ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

MPRF for transition t₂₂₄: l7(X₀, X₁, X₂) -{3}> l4(X₀-1, 0, 0) :|: 2 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₀+1 {O(n)}

MPRF for transition t₂₁₆: l4(X₀, X₁, X₂) -{3}> l4(X₀, 1+X₁, X₂) :|: E ≤ F ∧ 2+X₁ ≤ X₀ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₀⋅X₀+2⋅X₀ {O(n^2)}

MPRF for transition t₂₁₇: l4(X₀, X₁, X₂) -{4}> l4(X₀, 1+X₁, 1) :|: F+1 ≤ E ∧ 2+X₁ ≤ X₀ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₀⋅X₀+2⋅X₀ {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 t₅: l3→l5

Found invariant X₃ ≤ 1 ∧ X₃ ≤ 1+X₂ ∧ X₂+X₃ ≤ 1 ∧ X₃ ≤ 1+X₁ ∧ X₁+X₃ ≤ 1 ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l2___6

Found invariant X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ X₁+X₃ ≤ 0 ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l2___7

Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l4___9

Found invariant X₃ ≤ 1 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 2 ∧ X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l4___4

Found invariant X₃ ≤ 1 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 2 ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l3___5

Found invariant X₃ ≤ 1 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 2 ∧ X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l1___3

Found invariant X₃ ≤ 1 ∧ X₃ ≤ 1+X₂ ∧ X₂+X₃ ≤ 2 ∧ X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l2___1

Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l1___8

Found invariant X₃ ≤ 1 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 2 ∧ X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l2___2

Found invariant X₃ ≤ 1 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 2 ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l7

Found invariant X₃ ≤ 1 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 2 ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l5

Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l3

knowledge_propagation leads to new time bound X₀+1 {O(n)} for transition t₃₄₈: l3(X₀, X₁, X₂, X₃) → n_l4___9(X₀, X₁, X₂, X₃) :|: 1+X₁ ≤ X₀ ∧ X₁ ≤ 0 ∧ X₂ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₂ ≤ 1 ∧ 0 ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ 1 ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀

knowledge_propagation leads to new time bound X₀+1 {O(n)} for transition t₃₅₂: n_l4___9(X₀, X₁, X₂, X₃) → n_l1___8(X₀, X₁, Arg2_P, X₃) :|: X₁ ≤ 0 ∧ X₂ ≤ 0 ∧ Arg2_P ≤ 1 ∧ 0 ≤ Arg2_P ∧ Arg2_P ≤ X₁ ∧ X₂ ≤ Arg2_P ∧ Arg2_P ≤ X₂ ∧ 1 ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀

knowledge_propagation leads to new time bound X₀+1 {O(n)} for transition t₃₅₃: n_l4___9(X₀, X₁, X₂, X₃) → n_l2___7(X₀, X₁, Arg2_P, Arg3_P) :|: X₁ ≤ 0 ∧ X₂ ≤ 0 ∧ Arg2_P ≤ 1 ∧ 0 ≤ Arg2_P ∧ Arg2_P ≤ X₁ ∧ X₂ ≤ Arg2_P ∧ Arg2_P ≤ X₂ ∧ Arg2_P ≤ Arg3_P ∧ Arg3_P ≤ Arg2_P ∧ 1 ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀

knowledge_propagation leads to new time bound X₀+1 {O(n)} for transition t₃₄₃: n_l1___8(X₀, X₁, X₂, X₃) → n_l2___6(X₀, X₁, X₂, 1) :|: X₁ ≤ 0 ∧ X₂ ≤ 0 ∧ 1 ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ 1 ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀

knowledge_propagation leads to new time bound X₀+1 {O(n)} for transition t₃₄₆: n_l2___6(X₀, X₁, X₂, X₃) → n_l3___5(X₀, X₁+1, X₃, X₃) :|: X₁ ≤ 0 ∧ X₂ ≤ 0 ∧ X₃ ≤ 1 ∧ 1 ≤ X₃ ∧ 1 ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂ ∧ X₃ ≤ 1 ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ X₃ ≤ 1 ∧ X₃ ≤ 1+X₂ ∧ X₂+X₃ ≤ 1 ∧ X₃ ≤ 1+X₁ ∧ X₁+X₃ ≤ 1 ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀

knowledge_propagation leads to new time bound X₀+1 {O(n)} for transition t₃₄₇: n_l2___7(X₀, X₁, X₂, X₃) → n_l3___5(X₀, X₁+1, X₃, X₃) :|: X₁ ≤ 0 ∧ X₂ ≤ 0 ∧ X₃ ≤ 0 ∧ 1 ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂ ∧ X₃ ≤ 1 ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ X₁+X₃ ≤ 0 ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀

MPRF for transition t₃₄₂: n_l1___3(X₀, X₁, X₂, X₃) → n_l2___1(X₀, X₁, X₂, 1) :|: 1 ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₂ ≤ 1 ∧ 0 ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ 1 ∧ X₃ ≤ 1 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 2 ∧ X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

2⋅X₀⋅X₀+5⋅X₀+3 {O(n^2)}

MPRF for transition t₃₄₄: n_l2___1(X₀, X₁, X₂, X₃) → n_l3___5(X₀, X₁+1, X₃, X₃) :|: 1 ≤ X₁ ∧ X₃ ≤ 1 ∧ 1 ≤ X₃ ∧ X₂ ≤ 1 ∧ 0 ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₃ ≤ 1 ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ X₃ ≤ 1 ∧ X₃ ≤ 1+X₂ ∧ X₂+X₃ ≤ 2 ∧ X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

2⋅X₀⋅X₀+5⋅X₀+4 {O(n^2)}

MPRF for transition t₃₄₅: n_l2___2(X₀, X₁, X₂, X₃) → n_l3___5(X₀, X₁+1, X₃, X₃) :|: 1 ≤ X₁ ∧ X₃ ≤ X₂ ∧ X₂ ≤ 1 ∧ 0 ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₃ ≤ 1 ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ X₃ ≤ 1 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 2 ∧ X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

2⋅X₀⋅X₀+5⋅X₀+3 {O(n^2)}

MPRF for transition t₃₄₉: n_l3___5(X₀, X₁, X₂, X₃) → n_l4___4(X₀, X₁, X₂, X₃) :|: X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ X₂ ≤ 1 ∧ 0 ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1 ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ 1 ∧ X₃ ≤ 1 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 2 ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

4⋅X₀⋅X₀+9⋅X₀+5 {O(n^2)}

MPRF for transition t₃₅₀: n_l4___4(X₀, X₁, X₂, X₃) → n_l1___3(X₀, X₁, Arg2_P, X₃) :|: 1 ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ Arg2_P ≤ 1 ∧ 0 ≤ Arg2_P ∧ Arg2_P ≤ X₁ ∧ X₂ ≤ Arg2_P ∧ Arg2_P ≤ X₂ ∧ X₂ ≤ 1 ∧ 0 ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₃ ≤ 1 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 2 ∧ X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

4⋅X₀⋅X₀+9⋅X₀+5 {O(n^2)}

MPRF for transition t₃₅₁: n_l4___4(X₀, X₁, X₂, X₃) → n_l2___2(X₀, X₁, Arg2_P, Arg3_P) :|: 1 ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ Arg2_P ≤ 1 ∧ 0 ≤ Arg2_P ∧ Arg2_P ≤ X₁ ∧ X₂ ≤ Arg2_P ∧ Arg2_P ≤ X₂ ∧ Arg2_P ≤ Arg3_P ∧ Arg3_P ≤ Arg2_P ∧ X₂ ≤ 1 ∧ 0 ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₃ ≤ 1 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 2 ∧ X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

2⋅X₀⋅X₀+4⋅X₀+2 {O(n^2)}

MPRF for transition t₃₆₁: n_l3___5(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ X₃ ≤ 1 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 2 ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₀+2 {O(n)}

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:10⋅X₀⋅X₀+32⋅X₀+30 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₀+1 {O(n)}
t₃: 1 {O(1)}
t₄: 2⋅X₀⋅X₀+7⋅X₀+6 {O(n^2)}
t₅: X₀+2 {O(n)}
t₆: 2⋅X₀⋅X₀+5⋅X₀+3 {O(n^2)}
t₇: 2⋅X₀⋅X₀+5⋅X₀+3 {O(n^2)}
t₈: 2⋅X₀⋅X₀+5⋅X₀+3 {O(n^2)}
t₉: 2⋅X₀⋅X₀+5⋅X₀+3 {O(n^2)}
t₁₀: 1 {O(1)}
t₁₂: X₀+2 {O(n)}
t₁₃: 2⋅X₀+2 {O(n)}
t₁₄: 1 {O(1)}

Costbounds

Overall costbound: 10⋅X₀⋅X₀+32⋅X₀+30 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₀+1 {O(n)}
t₃: 1 {O(1)}
t₄: 2⋅X₀⋅X₀+7⋅X₀+6 {O(n^2)}
t₅: X₀+2 {O(n)}
t₆: 2⋅X₀⋅X₀+5⋅X₀+3 {O(n^2)}
t₇: 2⋅X₀⋅X₀+5⋅X₀+3 {O(n^2)}
t₈: 2⋅X₀⋅X₀+5⋅X₀+3 {O(n^2)}
t₉: 2⋅X₀⋅X₀+5⋅X₀+3 {O(n^2)}
t₁₀: 1 {O(1)}
t₁₂: X₀+2 {O(n)}
t₁₃: 2⋅X₀+2 {O(n)}
t₁₄: 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+1 {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₂, X₀: X₀+1 {O(n)}
t₂, X₁: 0 {O(1)}
t₂, X₂: 0 {O(1)}
t₂, X₃: X₃+1 {O(n)}
t₃, X₀: 2⋅X₀+2 {O(n)}
t₃, X₁: 2⋅X₀⋅X₀+5⋅X₀+X₁+3 {O(n^2)}
t₃, X₂: X₂+1 {O(n)}
t₃, X₃: X₃+1 {O(n)}
t₄, X₀: X₀+1 {O(n)}
t₄, X₁: 2⋅X₀⋅X₀+5⋅X₀+3 {O(n^2)}
t₄, X₂: 1 {O(1)}
t₄, X₃: X₃+2 {O(n)}
t₅, X₀: X₀+1 {O(n)}
t₅, X₁: 2⋅X₀⋅X₀+5⋅X₀+3 {O(n^2)}
t₅, X₂: 1 {O(1)}
t₅, X₃: 1 {O(1)}
t₆, X₀: X₀+1 {O(n)}
t₆, X₁: 2⋅X₀⋅X₀+5⋅X₀+3 {O(n^2)}
t₆, X₂: 1 {O(1)}
t₆, X₃: X₃+2 {O(n)}
t₇, X₀: X₀+1 {O(n)}
t₇, X₁: 2⋅X₀⋅X₀+5⋅X₀+3 {O(n^2)}
t₇, X₂: 1 {O(1)}
t₇, X₃: 1 {O(1)}
t₈, X₀: X₀+1 {O(n)}
t₈, X₁: 2⋅X₀⋅X₀+5⋅X₀+3 {O(n^2)}
t₈, X₂: 1 {O(1)}
t₈, X₃: 1 {O(1)}
t₉, X₀: X₀+1 {O(n)}
t₉, X₁: 2⋅X₀⋅X₀+5⋅X₀+3 {O(n^2)}
t₉, X₂: 1 {O(1)}
t₉, X₃: 1 {O(1)}
t₁₀, X₀: X₀+1 {O(n)}
t₁₀, X₁: 2⋅X₀⋅X₀+5⋅X₀+3 {O(n^2)}
t₁₀, X₂: 0 {O(1)}
t₁₀, X₃: 1 {O(1)}
t₁₂, X₀: X₀+1 {O(n)}
t₁₂, X₁: 2⋅X₀⋅X₀+5⋅X₀+3 {O(n^2)}
t₁₂, X₂: 1 {O(1)}
t₁₂, X₃: 1 {O(1)}
t₁₃, X₀: X₀+1 {O(n)}
t₁₃, X₁: 2⋅X₀⋅X₀+5⋅X₀+3 {O(n^2)}
t₁₃, X₂: 1 {O(1)}
t₁₃, X₃: 1 {O(1)}
t₁₄, X₀: 3⋅X₀+3 {O(n)}
t₁₄, X₁: 4⋅X₀⋅X₀+10⋅X₀+X₁+6 {O(n^2)}
t₁₄, X₂: X₂+1 {O(n)}
t₁₄, X₃: X₃+2 {O(n)}