Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 < X₀+X₁
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₀+X₁ ≤ 0
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₅, X₆, X₂, X₃, X₄, X₅, X₆)
t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 < X₀
t₅: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₀ ≤ 0
t₁₀: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₉: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₂, X₃, X₂, X₃, X₄, X₅, X₆)
t₆: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₀-1, X₁, X₄, X₅, X₆)
t₇: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₀, X₁-1, X₄, X₅, X₆) :|: 0 < X₁
t₈: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₀, X₁, X₄, X₅, X₆) :|: X₁ ≤ 0

Preprocessing

Eliminate variables {X₄} that do not contribute to the problem

Found invariant 1 ≤ X₄+X₅ ∧ X₁ ≤ X₅ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l6

Found invariant 1 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 1 ≤ X₀+X₅ ∧ 1+X₀ ≤ X₅ ∧ 1 ≤ X₁+X₄ ∧ X₀ ≤ X₄ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l7

Found invariant 1 ≤ X₄+X₅ ∧ X₃ ≤ X₅ ∧ 0 ≤ X₂+X₅ ∧ X₁ ≤ X₅ ∧ 1 ≤ X₀+X₅ ∧ 0 ≤ X₃+X₄ ∧ X₂ ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ X₀ ≤ X₄ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₂+X₃ ∧ X₁ ≤ 1+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₀+X₁ for location l5

Found invariant X₁ ≤ X₅ ∧ X₀ ≤ X₄ ∧ X₀+X₁ ≤ 0 for location l8

Found invariant X₁ ≤ X₅ ∧ X₀ ≤ X₄ for location l1

Found invariant X₁ ≤ X₅ ∧ X₀ ≤ X₄ ∧ X₀+X₁ ≤ 0 for location l4

Found invariant 1 ≤ X₄+X₅ ∧ X₁ ≤ X₅ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₁+X₄ ∧ X₀ ≤ X₄ ∧ 1 ≤ X₀+X₁ for location l3

Cut unsatisfiable transition t₃₁: l7→l5

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₂₁: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅)
t₂₂: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₀+X₁ ∧ X₁ ≤ X₅ ∧ X₀ ≤ X₄
t₂₃: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀+X₁ ≤ 0 ∧ X₁ ≤ X₅ ∧ X₀ ≤ X₄
t₂₄: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₄, X₅, X₂, X₃, X₄, X₅)
t₂₅: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₀ ∧ 1 ≤ X₄+X₅ ∧ X₁ ≤ X₅ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₁+X₄ ∧ X₀ ≤ X₄ ∧ 1 ≤ X₀+X₁
t₂₆: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ 0 ∧ 1 ≤ X₄+X₅ ∧ X₁ ≤ X₅ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₁+X₄ ∧ X₀ ≤ X₄ ∧ 1 ≤ X₀+X₁
t₂₇: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l8(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ ≤ X₅ ∧ X₀ ≤ X₄ ∧ X₀+X₁ ≤ 0
t₂₈: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₂, X₃, X₂, X₃, X₄, X₅) :|: 1 ≤ X₄+X₅ ∧ X₃ ≤ X₅ ∧ 0 ≤ X₂+X₅ ∧ X₁ ≤ X₅ ∧ 1 ≤ X₀+X₅ ∧ 0 ≤ X₃+X₄ ∧ X₂ ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ X₀ ≤ X₄ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₂+X₃ ∧ X₁ ≤ 1+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₀+X₁
t₂₉: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₀-1, X₁, X₄, X₅) :|: 1 ≤ X₄+X₅ ∧ X₁ ≤ X₅ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₃₀: l7(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₀, X₁-1, X₄, X₅) :|: 0 < X₁ ∧ 1 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 1 ≤ X₀+X₅ ∧ 1+X₀ ≤ X₅ ∧ 1 ≤ X₁+X₄ ∧ X₀ ≤ X₄ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0

MPRF for transition t₂₂: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₀+X₁ ∧ X₁ ≤ X₅ ∧ X₀ ≤ X₄ of depth 1:

new bound:

X₄+X₅ {O(n)}

MPRF for transition t₂₅: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₀ ∧ 1 ≤ X₄+X₅ ∧ X₁ ≤ X₅ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₁+X₄ ∧ X₀ ≤ X₄ ∧ 1 ≤ X₀+X₁ of depth 1:

new bound:

X₄ {O(n)}

MPRF for transition t₂₆: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ 0 ∧ 1 ≤ X₄+X₅ ∧ X₁ ≤ X₅ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₁+X₄ ∧ X₀ ≤ X₄ ∧ 1 ≤ X₀+X₁ of depth 1:

new bound:

X₅ {O(n)}

MPRF for transition t₂₈: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₂, X₃, X₂, X₃, X₄, X₅) :|: 1 ≤ X₄+X₅ ∧ X₃ ≤ X₅ ∧ 0 ≤ X₂+X₅ ∧ X₁ ≤ X₅ ∧ 1 ≤ X₀+X₅ ∧ 0 ≤ X₃+X₄ ∧ X₂ ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ X₀ ≤ X₄ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₂+X₃ ∧ X₁ ≤ 1+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₀+X₁ of depth 1:

new bound:

2⋅X₄+2⋅X₅+1 {O(n)}

MPRF for transition t₂₉: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₀-1, X₁, X₄, X₅) :|: 1 ≤ X₄+X₅ ∧ X₁ ≤ X₅ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

2⋅X₄+1 {O(n)}

MPRF for transition t₃₀: l7(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₀, X₁-1, X₄, X₅) :|: 0 < X₁ ∧ 1 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 1 ≤ X₀+X₅ ∧ 1+X₀ ≤ X₅ ∧ 1 ≤ X₁+X₄ ∧ X₀ ≤ X₄ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 of depth 1:

new bound:

X₅ {O(n)}

All Bounds

Timebounds

Overall timebound:5⋅X₅+6⋅X₄+6 {O(n)}
t₂₁: 1 {O(1)}
t₂₂: X₄+X₅ {O(n)}
t₂₃: 1 {O(1)}
t₂₄: 1 {O(1)}
t₂₅: X₄ {O(n)}
t₂₆: X₅ {O(n)}
t₂₇: 1 {O(1)}
t₂₈: 2⋅X₄+2⋅X₅+1 {O(n)}
t₂₉: 2⋅X₄+1 {O(n)}
t₃₀: X₅ {O(n)}

Costbounds

Overall costbound: 5⋅X₅+6⋅X₄+6 {O(n)}
t₂₁: 1 {O(1)}
t₂₂: X₄+X₅ {O(n)}
t₂₃: 1 {O(1)}
t₂₄: 1 {O(1)}
t₂₅: X₄ {O(n)}
t₂₆: X₅ {O(n)}
t₂₇: 1 {O(1)}
t₂₈: 2⋅X₄+2⋅X₅+1 {O(n)}
t₂₉: 2⋅X₄+1 {O(n)}
t₃₀: X₅ {O(n)}

Sizebounds

t₂₁, X₀: X₀ {O(n)}
t₂₁, X₁: X₁ {O(n)}
t₂₁, X₂: X₂ {O(n)}
t₂₁, X₃: X₃ {O(n)}
t₂₁, X₄: X₄ {O(n)}
t₂₁, X₅: X₅ {O(n)}
t₂₂, X₀: 2⋅X₅+3⋅X₄+1 {O(n)}
t₂₂, X₁: 2⋅X₄+3⋅X₅+1 {O(n)}
t₂₂, X₂: 4⋅X₅+6⋅X₄+X₂+2 {O(n)}
t₂₂, X₃: 4⋅X₄+6⋅X₅+X₃+2 {O(n)}
t₂₂, X₄: X₄ {O(n)}
t₂₂, X₅: X₅ {O(n)}
t₂₃, X₀: 2⋅X₅+4⋅X₄+1 {O(n)}
t₂₃, X₁: 2⋅X₄+4⋅X₅+1 {O(n)}
t₂₃, X₂: 4⋅X₅+6⋅X₄+X₂+2 {O(n)}
t₂₃, X₃: 4⋅X₄+6⋅X₅+X₃+2 {O(n)}
t₂₃, X₄: 2⋅X₄ {O(n)}
t₂₃, X₅: 2⋅X₅ {O(n)}
t₂₄, X₀: X₄ {O(n)}
t₂₄, X₁: X₅ {O(n)}
t₂₄, X₂: X₂ {O(n)}
t₂₄, X₃: X₃ {O(n)}
t₂₄, X₄: X₄ {O(n)}
t₂₄, X₅: X₅ {O(n)}
t₂₅, X₀: 2⋅X₅+3⋅X₄+1 {O(n)}
t₂₅, X₁: 2⋅X₄+3⋅X₅+1 {O(n)}
t₂₅, X₂: 4⋅X₅+6⋅X₄+X₂+2 {O(n)}
t₂₅, X₃: 4⋅X₄+6⋅X₅+X₃+2 {O(n)}
t₂₅, X₄: X₄ {O(n)}
t₂₅, X₅: X₅ {O(n)}
t₂₆, X₀: 2⋅X₅+3⋅X₄+1 {O(n)}
t₂₆, X₁: 2⋅X₄+3⋅X₅+1 {O(n)}
t₂₆, X₂: 4⋅X₅+6⋅X₄+X₂+2 {O(n)}
t₂₆, X₃: 4⋅X₄+6⋅X₅+X₃+2 {O(n)}
t₂₆, X₄: X₄ {O(n)}
t₂₆, X₅: X₅ {O(n)}
t₂₇, X₀: 2⋅X₅+4⋅X₄+1 {O(n)}
t₂₇, X₁: 2⋅X₄+4⋅X₅+1 {O(n)}
t₂₇, X₂: 4⋅X₅+6⋅X₄+X₂+2 {O(n)}
t₂₇, X₃: 4⋅X₄+6⋅X₅+X₃+2 {O(n)}
t₂₇, X₄: 2⋅X₄ {O(n)}
t₂₇, X₅: 2⋅X₅ {O(n)}
t₂₈, X₀: 2⋅X₅+3⋅X₄+1 {O(n)}
t₂₈, X₁: 2⋅X₄+3⋅X₅+1 {O(n)}
t₂₈, X₂: 4⋅X₅+6⋅X₄+2 {O(n)}
t₂₈, X₃: 4⋅X₄+6⋅X₅+2 {O(n)}
t₂₈, X₄: X₄ {O(n)}
t₂₈, X₅: X₅ {O(n)}
t₂₉, X₀: 2⋅X₅+3⋅X₄+1 {O(n)}
t₂₉, X₁: 2⋅X₄+3⋅X₅+1 {O(n)}
t₂₉, X₂: 2⋅X₅+3⋅X₄+1 {O(n)}
t₂₉, X₃: 2⋅X₄+3⋅X₅+1 {O(n)}
t₂₉, X₄: X₄ {O(n)}
t₂₉, X₅: X₅ {O(n)}
t₃₀, X₀: 2⋅X₅+3⋅X₄+1 {O(n)}
t₃₀, X₁: 2⋅X₄+3⋅X₅+1 {O(n)}
t₃₀, X₂: 2⋅X₅+3⋅X₄+1 {O(n)}
t₃₀, X₃: 2⋅X₄+3⋅X₅+1 {O(n)}
t₃₀, X₄: X₄ {O(n)}
t₃₀, X₅: X₅ {O(n)}