Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅)
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1 < X₀
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ 1
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₄, X₁, X₂, X₃, X₄, X₅)
t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₀-2, X₂, X₃, X₄, X₅)
t₉: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l8(X₀, X₁, X₂, X₃, X₄, X₅)
t₈: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₁+1, X₁, X₂, X₃, X₄, X₅)
t₆: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ ≤ 1
t₅: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1 < X₁
t₇: l7(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁-2, X₂, X₃, X₄, X₅)

Preprocessing

Eliminate variables {X₂,X₃,X₅} that do not contribute to the problem

Found invariant 2 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l6

Found invariant 4 ≤ X₂ ∧ 6 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₂ ∧ 8 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2+X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 6 ≤ X₀+X₁ ∧ 4 ≤ X₀ for location l7

Found invariant 2 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 1 ∧ 2+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l5

Found invariant X₀ ≤ X₂ ∧ X₀ ≤ 1 for location l8

Found invariant X₀ ≤ X₂ for location l1

Found invariant X₀ ≤ X₂ ∧ X₀ ≤ 1 for location l4

Found invariant 2 ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₁₉: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₂₀: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: 1 < X₀ ∧ X₀ ≤ X₂
t₂₁: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₀ ≤ 1 ∧ X₀ ≤ X₂
t₂₂: l2(X₀, X₁, X₂) → l1(X₂, X₁, X₂)
t₂₃: l3(X₀, X₁, X₂) → l6(X₀, X₀-2, X₂) :|: 2 ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₀
t₂₄: l4(X₀, X₁, X₂) → l8(X₀, X₁, X₂) :|: X₀ ≤ X₂ ∧ X₀ ≤ 1
t₂₅: l5(X₀, X₁, X₂) → l1(X₁+1, X₁, X₂) :|: 2 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 1 ∧ 2+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₂₆: l6(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₁ ≤ 1 ∧ 2 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₂₇: l6(X₀, X₁, X₂) → l7(X₀, X₁, X₂) :|: 1 < X₁ ∧ 2 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₂₈: l7(X₀, X₁, X₂) → l6(X₀, X₁-2, X₂) :|: 4 ≤ X₂ ∧ 6 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₂ ∧ 8 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2+X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 6 ≤ X₀+X₁ ∧ 4 ≤ X₀

MPRF for transition t₂₀: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: 1 < X₀ ∧ X₀ ≤ X₂ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF for transition t₂₃: l3(X₀, X₁, X₂) → l6(X₀, X₀-2, X₂) :|: 2 ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF for transition t₂₅: l5(X₀, X₁, X₂) → l1(X₁+1, X₁, X₂) :|: 2 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 1 ∧ 2+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₂ {O(n)}

MPRF for transition t₂₆: l6(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₁ ≤ 1 ∧ 2 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF for transition t₂₇: l6(X₀, X₁, X₂) → l7(X₀, X₁, X₂) :|: 1 < X₁ ∧ 2 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

2⋅X₂+1 {O(n)}

MPRF for transition t₂₈: l7(X₀, X₁, X₂) → l6(X₀, X₁-2, X₂) :|: 4 ≤ X₂ ∧ 6 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₂ ∧ 8 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2+X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 6 ≤ X₀+X₁ ∧ 4 ≤ X₀ of depth 1:

new bound:

X₂+2 {O(n)}

All Bounds

Timebounds

Overall timebound:7⋅X₂+10 {O(n)}
t₁₉: 1 {O(1)}
t₂₀: X₂+1 {O(n)}
t₂₁: 1 {O(1)}
t₂₂: 1 {O(1)}
t₂₃: X₂+1 {O(n)}
t₂₄: 1 {O(1)}
t₂₅: X₂ {O(n)}
t₂₆: X₂+1 {O(n)}
t₂₇: 2⋅X₂+1 {O(n)}
t₂₈: X₂+2 {O(n)}

Costbounds

Overall costbound: 7⋅X₂+10 {O(n)}
t₁₉: 1 {O(1)}
t₂₀: X₂+1 {O(n)}
t₂₁: 1 {O(1)}
t₂₂: 1 {O(1)}
t₂₃: X₂+1 {O(n)}
t₂₄: 1 {O(1)}
t₂₅: X₂ {O(n)}
t₂₆: X₂+1 {O(n)}
t₂₇: 2⋅X₂+1 {O(n)}
t₂₈: X₂+2 {O(n)}

Sizebounds

t₁₉, X₀: X₀ {O(n)}
t₁₉, X₁: X₁ {O(n)}
t₁₉, X₂: X₂ {O(n)}
t₂₀, X₀: X₂+2 {O(n)}
t₂₀, X₁: X₁+1 {O(n)}
t₂₀, X₂: X₂ {O(n)}
t₂₁, X₀: X₂+2 {O(n)}
t₂₁, X₁: X₁+1 {O(n)}
t₂₁, X₂: 2⋅X₂ {O(n)}
t₂₂, X₀: X₂ {O(n)}
t₂₂, X₁: X₁ {O(n)}
t₂₂, X₂: X₂ {O(n)}
t₂₃, X₀: X₂+2 {O(n)}
t₂₃, X₁: X₂+2 {O(n)}
t₂₃, X₂: X₂ {O(n)}
t₂₄, X₀: X₂+2 {O(n)}
t₂₄, X₁: X₁+1 {O(n)}
t₂₄, X₂: 2⋅X₂ {O(n)}
t₂₅, X₀: 2 {O(1)}
t₂₅, X₁: 1 {O(1)}
t₂₅, X₂: X₂ {O(n)}
t₂₆, X₀: 2⋅X₂+4 {O(n)}
t₂₆, X₁: 1 {O(1)}
t₂₆, X₂: X₂ {O(n)}
t₂₇, X₀: X₂+2 {O(n)}
t₂₇, X₁: X₂+2 {O(n)}
t₂₇, X₂: X₂ {O(n)}
t₂₈, X₀: X₂+2 {O(n)}
t₂₈, X₁: X₂+2 {O(n)}
t₂₈, X₂: X₂ {O(n)}