Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 0 < X₀+X₁
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀+X₁ ≤ 0
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₂, X₃, X₂, X₃)
t₄: l3(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₁ < X₀
t₅: l3(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁
t₁₆: l4(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃)
t₆: l5(X₀, X₁, X₂, X₃) → l1(X₀-1, X₁, X₂, X₃)
t₇: l6(X₀, X₁, X₂, X₃) → l1(X₀-1, X₁, X₂, X₃) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀
t₈: l6(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ < X₁
t₉: l6(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₁ < X₀
t₁₀: l6(X₀, X₁, X₂, X₃) → l1(X₀-1, X₁-1, X₂, X₃) :|: X₀ < X₁ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀
t₁₁: l6(X₀, X₁, X₂, X₃) → l1(X₀-1, X₁-1, X₂, X₃) :|: X₁ < X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀
t₁₂: l6(X₀, X₁, X₂, X₃) → l1(X₀, X₁-1, X₂, X₃) :|: X₀ < X₁ ∧ X₀ < X₁
t₁₃: l6(X₀, X₁, X₂, X₃) → l1(X₀, X₁-1, X₂, X₃) :|: X₀ < X₁ ∧ X₁ < X₀
t₁₄: l6(X₀, X₁, X₂, X₃) → l1(X₀, X₁-1, X₂, X₃) :|: X₁ < X₀ ∧ X₀ < X₁
t₁₅: l6(X₀, X₁, X₂, X₃) → l1(X₀, X₁-1, X₂, X₃) :|: X₁ < X₀ ∧ X₁ < X₀

Preprocessing

Cut unsatisfiable transition t₈: l6→l1

Cut unsatisfiable transition t₉: l6→l1

Cut unsatisfiable transition t₁₀: l6→l1

Cut unsatisfiable transition t₁₁: l6→l1

Cut unsatisfiable transition t₁₃: l6→l1

Cut unsatisfiable transition t₁₄: l6→l1

Cut unsatisfiable transition t₁₅: l6→l1

Found invariant 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₁+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ X₁ for location l6

Found invariant X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₀+X₁ ≤ 0 for location l7

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

Found invariant X₁ ≤ X₃ ∧ X₀ ≤ X₂ for location l1

Found invariant X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₀+X₁ ≤ 0 for location l4

Found invariant 1 ≤ X₂+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₁+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀+X₁ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 0 < X₀+X₁ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀+X₁ ≤ 0 ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₂, X₃, X₂, X₃)
t₄: l3(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₁ < X₀ ∧ 1 ≤ X₂+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₁+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀+X₁
t₅: l3(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁ ∧ 1 ≤ X₂+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₁+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀+X₁
t₁₆: l4(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₀+X₁ ≤ 0
t₆: l5(X₀, X₁, X₂, X₃) → l1(X₀-1, X₁, X₂, X₃) :|: 1 ≤ X₂+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₇: l6(X₀, X₁, X₂, X₃) → l1(X₀-1, X₁, X₂, X₃) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₁+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ X₁
t₁₂: l6(X₀, X₁, X₂, X₃) → l1(X₀, X₁-1, X₂, X₃) :|: X₀ < X₁ ∧ X₀ < X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₁+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ X₁

MPRF for transition t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 0 < X₀+X₁ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ of depth 1:

new bound:

X₂+X₃ {O(n)}

MPRF for transition t₄: l3(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₁ < X₀ ∧ 1 ≤ X₂+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₁+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀+X₁ of depth 1:

new bound:

2⋅X₂ {O(n)}

MPRF for transition t₅: l3(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁ ∧ 1 ≤ X₂+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₁+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀+X₁ of depth 1:

new bound:

X₂+X₃ {O(n)}

MPRF for transition t₆: l5(X₀, X₁, X₂, X₃) → l1(X₀-1, X₁, X₂, X₃) :|: 1 ≤ X₂+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₂ {O(n)}

MPRF for transition t₇: l6(X₀, X₁, X₂, X₃) → l1(X₀-1, X₁, X₂, X₃) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₁+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ X₁ of depth 1:

new bound:

2⋅X₂+1 {O(n)}

MPRF for transition t₁₂: l6(X₀, X₁, X₂, X₃) → l1(X₀, X₁-1, X₂, X₃) :|: X₀ < X₁ ∧ X₀ < X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₁+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ X₁ of depth 1:

new bound:

2⋅X₃ {O(n)}

All Bounds

Timebounds

Overall timebound:4⋅X₃+7⋅X₂+5 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₂+X₃ {O(n)}
t₃: 1 {O(1)}
t₄: 2⋅X₂ {O(n)}
t₅: X₂+X₃ {O(n)}
t₆: X₂ {O(n)}
t₇: 2⋅X₂+1 {O(n)}
t₁₂: 2⋅X₃ {O(n)}
t₁₆: 1 {O(1)}

Costbounds

Overall costbound: 4⋅X₃+7⋅X₂+5 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₂+X₃ {O(n)}
t₃: 1 {O(1)}
t₄: 2⋅X₂ {O(n)}
t₅: X₂+X₃ {O(n)}
t₆: X₂ {O(n)}
t₇: 2⋅X₂+1 {O(n)}
t₁₂: 2⋅X₃ {O(n)}
t₁₆: 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: X₂ {O(n)}
t₁, X₁: X₃ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₂, X₀: X₂ {O(n)}
t₂, X₁: X₃ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₃, X₀: 3⋅X₂ {O(n)}
t₃, X₁: 3⋅X₃ {O(n)}
t₃, X₂: 3⋅X₂ {O(n)}
t₃, X₃: 3⋅X₃ {O(n)}
t₄, X₀: X₂ {O(n)}
t₄, X₁: X₃ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₅, X₀: X₂ {O(n)}
t₅, X₁: X₃ {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₆, X₀: X₂ {O(n)}
t₆, X₁: X₃ {O(n)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: X₃ {O(n)}
t₇, X₀: X₂ {O(n)}
t₇, X₁: X₃ {O(n)}
t₇, X₂: X₂ {O(n)}
t₇, X₃: X₃ {O(n)}
t₁₂, X₀: X₂ {O(n)}
t₁₂, X₁: X₃ {O(n)}
t₁₂, X₂: X₂ {O(n)}
t₁₂, X₃: X₃ {O(n)}
t₁₆, X₀: 3⋅X₂ {O(n)}
t₁₆, X₁: 3⋅X₃ {O(n)}
t₁₆, X₂: 3⋅X₂ {O(n)}
t₁₆, X₃: 3⋅X₃ {O(n)}