Initial Problem

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

Preprocessing

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

Found invariant 0 ≤ X₂ for location l6

Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₂ for location l5

Found invariant 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location l8

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

Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ for location l10

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

Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ for location l9

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

Problem after Preprocessing

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

MPRF for transition t₂: l6(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₂ < X₁ ∧ 0 ≤ X₂ of depth 1:

new bound:

X₁ {O(n)}

MPRF for transition t₄: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ of depth 1:

new bound:

X₁ {O(n)}

MPRF for transition t₆: l3(X₀, X₁, X₂, X₃) → l1(nondef.0, X₁, X₂, X₃) :|: 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ of depth 1:

new bound:

X₁ {O(n)}

MPRF for transition t₈: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ of depth 1:

new bound:

X₁ {O(n)}

MPRF for transition t₉: l4(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂+1, X₃) :|: 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 of depth 1:

new bound:

X₁ {O(n)}

MPRF for transition t₁₀: l5(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃) :|: X₃ < X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₂ of depth 1:

new bound:

2⋅X₁ {O(n)}

MPRF for transition t₁₂: l8(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃+1) :|: 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ of depth 1:

new bound:

2⋅X₁ {O(n)}

All Bounds

Timebounds

Overall timebound:9⋅X₁+6 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₁ {O(n)}
t₃: 1 {O(1)}
t₄: X₁ {O(n)}
t₆: X₁ {O(n)}
t₇: 1 {O(1)}
t₈: X₁ {O(n)}
t₉: X₁ {O(n)}
t₁₀: 2⋅X₁ {O(n)}
t₁₁: 1 {O(1)}
t₁₂: 2⋅X₁ {O(n)}
t₁₃: 1 {O(1)}

Costbounds

Overall costbound: 9⋅X₁+6 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₁ {O(n)}
t₃: 1 {O(1)}
t₄: X₁ {O(n)}
t₆: X₁ {O(n)}
t₇: 1 {O(1)}
t₈: X₁ {O(n)}
t₉: X₁ {O(n)}
t₁₀: 2⋅X₁ {O(n)}
t₁₁: 1 {O(1)}
t₁₂: 2⋅X₁ {O(n)}
t₁₃: 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: 0 {O(1)}
t₁, X₃: X₃ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₁ {O(n)}
t₂, X₃: X₃ {O(n)}
t₃, X₁: 2⋅X₁ {O(n)}
t₃, X₂: X₁ {O(n)}
t₃, X₃: X₁ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₁ {O(n)}
t₄, X₃: X₃ {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: X₁ {O(n)}
t₆, X₃: X₃ {O(n)}
t₇, X₁: X₁ {O(n)}
t₇, X₂: X₁ {O(n)}
t₇, X₃: X₁ {O(n)}
t₈, X₁: X₁ {O(n)}
t₈, X₂: X₁ {O(n)}
t₈, X₃: X₃ {O(n)}
t₉, X₁: X₁ {O(n)}
t₉, X₂: X₁ {O(n)}
t₉, X₃: X₃ {O(n)}
t₁₀, X₁: X₁ {O(n)}
t₁₀, X₂: X₁ {O(n)}
t₁₀, X₃: 3⋅X₁ {O(n)}
t₁₁, X₁: 3⋅X₁ {O(n)}
t₁₁, X₂: 2⋅X₁ {O(n)}
t₁₁, X₃: 4⋅X₁ {O(n)}
t₁₂, X₁: X₁ {O(n)}
t₁₂, X₂: X₁ {O(n)}
t₁₂, X₃: 3⋅X₁ {O(n)}
t₁₃, X₁: 3⋅X₁ {O(n)}
t₁₃, X₂: 2⋅X₁ {O(n)}
t₁₃, X₃: 4⋅X₁ {O(n)}