Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
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, X₀, X₁, X₄, X₅) :|: X₀ < 30
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: 30 ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₄, X₅, X₂, X₃, X₄, X₅)
t₅: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂ ≤ X₃
t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₃ < X₂
t₁₃: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃, X₄, X₅)
t₁₂: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₂+2, X₃-10, X₂, X₃, X₄, X₅)
t₆: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂+10, X₃+7, X₄, X₅) :|: 5 < X₃ ∧ 3 ≤ X₃ ∧ X₃ ≤ 5
t₇: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂+1, X₃+7, X₄, X₅) :|: 5 < X₃ ∧ X₃ < 3
t₈: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂+1, X₃+7, X₄, X₅) :|: 5 < X₃ ∧ 5 < X₃
t₉: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂+10, X₃+2, X₄, X₅) :|: X₃ ≤ 5 ∧ 8 ≤ X₃ ∧ X₃ ≤ 10
t₁₀: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂+1, X₃+2, X₄, X₅) :|: X₃ ≤ 5 ∧ X₃ < 8
t₁₁: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂+1, X₃+2, X₄, X₅) :|: X₃ ≤ 5 ∧ 10 < X₃

Preprocessing

Cut unsatisfiable transition t₆: l6→l3

Cut unsatisfiable transition t₇: l6→l3

Cut unsatisfiable transition t₉: l6→l3

Cut unsatisfiable transition t₁₁: l6→l3

Found invariant X₄ ≤ 29 ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₀ ∧ X₀+X₄ ≤ 58 ∧ 1+X₃ ≤ X₂ ∧ X₁ ≤ X₃ ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 29 for location l6

Found invariant X₄ ≤ X₀ ∧ 30 ≤ X₀ for location l7

Found invariant X₄ ≤ 29 ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₀ ∧ X₀+X₄ ≤ 58 ∧ X₂ ≤ X₃ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 29 for location l5

Found invariant X₄ ≤ X₀ for location l1

Found invariant X₄ ≤ X₀ ∧ 30 ≤ X₀ for location l4

Found invariant X₄ ≤ 29 ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₀ ∧ X₀+X₄ ≤ 58 ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 29 for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
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, X₀, X₁, X₄, X₅) :|: X₀ < 30 ∧ X₄ ≤ X₀
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: 30 ≤ X₀ ∧ X₄ ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₄, X₅, X₂, X₃, X₄, X₅)
t₅: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂ ≤ X₃ ∧ X₄ ≤ 29 ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₀ ∧ X₀+X₄ ≤ 58 ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 29
t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₃ < X₂ ∧ X₄ ≤ 29 ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₀ ∧ X₀+X₄ ≤ 58 ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 29
t₁₃: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₄ ≤ X₀ ∧ 30 ≤ X₀
t₁₂: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₂+2, X₃-10, X₂, X₃, X₄, X₅) :|: X₄ ≤ 29 ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₀ ∧ X₀+X₄ ≤ 58 ∧ X₂ ≤ X₃ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 29
t₈: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂+1, X₃+7, X₄, X₅) :|: 5 < X₃ ∧ 5 < X₃ ∧ X₄ ≤ 29 ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₀ ∧ X₀+X₄ ≤ 58 ∧ 1+X₃ ≤ X₂ ∧ X₁ ≤ X₃ ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 29
t₁₀: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂+1, X₃+2, X₄, X₅) :|: X₃ ≤ 5 ∧ X₃ < 8 ∧ X₄ ≤ 29 ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₀ ∧ X₀+X₄ ≤ 58 ∧ 1+X₃ ≤ X₂ ∧ X₁ ≤ X₃ ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 29

MPRF for transition t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₀, X₁, X₄, X₅) :|: X₀ < 30 ∧ X₄ ≤ X₀ of depth 1:

new bound:

X₄+30 {O(n)}

MPRF:

l5 [28-X₂ ]
l1 [30-X₀ ]
l6 [27-X₂ ]
l3 [28-X₂ ]

MPRF for transition t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₃ < X₂ ∧ X₄ ≤ 29 ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₀ ∧ X₀+X₄ ≤ 58 ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 29 of depth 1:

new bound:

5⋅X₄+X₅+174 {O(n)}

MPRF:

l5 [X₂+174-6⋅X₀-X₃ ]
l1 [174-5⋅X₀-X₁ ]
l6 [X₂+173-6⋅X₀-X₃ ]
l3 [X₂+174-6⋅X₀-X₃ ]

MPRF for transition t₅: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂ ≤ X₃ ∧ X₄ ≤ 29 ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₀ ∧ X₀+X₄ ≤ 58 ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 29 of depth 1:

new bound:

X₄+30 {O(n)}

MPRF:

l5 [28-X₂ ]
l1 [30-X₀ ]
l6 [30-X₀ ]
l3 [30-X₀ ]

MPRF for transition t₁₂: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₂+2, X₃-10, X₂, X₃, X₄, X₅) :|: X₄ ≤ 29 ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₀ ∧ X₀+X₄ ≤ 58 ∧ X₂ ≤ X₃ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 29 of depth 1:

new bound:

X₄+30 {O(n)}

MPRF:

l5 [30-X₀ ]
l1 [30-X₀ ]
l6 [30-X₀ ]
l3 [30-X₀ ]

MPRF for transition t₈: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂+1, X₃+7, X₄, X₅) :|: 5 < X₃ ∧ 5 < X₃ ∧ X₄ ≤ 29 ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₀ ∧ X₀+X₄ ≤ 58 ∧ 1+X₃ ≤ X₂ ∧ X₁ ≤ X₃ ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 29 of depth 1:

new bound:

5⋅X₄+X₅+174 {O(n)}

MPRF:

l5 [X₂+174-6⋅X₀-X₃ ]
l1 [174-5⋅X₀-X₁ ]
l6 [X₂+174-6⋅X₀-X₃ ]
l3 [X₂+174-6⋅X₀-X₃ ]

MPRF for transition t₁₀: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂+1, X₃+2, X₄, X₅) :|: X₃ ≤ 5 ∧ X₃ < 8 ∧ X₄ ≤ 29 ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₀ ∧ X₀+X₄ ≤ 58 ∧ 1+X₃ ≤ X₂ ∧ X₁ ≤ X₃ ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 29 of depth 1:

new bound:

5⋅X₄+X₅+153 {O(n)}

MPRF:

l5 [153-5⋅X₀-X₃ ]
l1 [153-5⋅X₀-X₁ ]
l6 [153-5⋅X₀-X₃ ]
l3 [153-5⋅X₀-X₃ ]

All Bounds

Timebounds

Overall timebound:18⋅X₄+3⋅X₅+595 {O(n)}
t₀: 1 {O(1)}
t₂: X₄+30 {O(n)}
t₃: 1 {O(1)}
t₁: 1 {O(1)}
t₄: 5⋅X₄+X₅+174 {O(n)}
t₅: X₄+30 {O(n)}
t₁₃: 1 {O(1)}
t₁₂: X₄+30 {O(n)}
t₈: 5⋅X₄+X₅+174 {O(n)}
t₁₀: 5⋅X₄+X₅+153 {O(n)}

Costbounds

Overall costbound: 18⋅X₄+3⋅X₅+595 {O(n)}
t₀: 1 {O(1)}
t₂: X₄+30 {O(n)}
t₃: 1 {O(1)}
t₁: 1 {O(1)}
t₄: 5⋅X₄+X₅+174 {O(n)}
t₅: X₄+30 {O(n)}
t₁₃: 1 {O(1)}
t₁₂: X₄+30 {O(n)}
t₈: 5⋅X₄+X₅+174 {O(n)}
t₁₀: 5⋅X₄+X₅+153 {O(n)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₀, X₄: X₄ {O(n)}
t₀, X₅: X₅ {O(n)}
t₂, X₀: 14⋅X₄+2⋅X₅+387 {O(n)}
t₂, X₁: 11⋅X₅+55⋅X₄+1824 {O(n)}
t₂, X₂: 13⋅X₄+2⋅X₅+387 {O(n)}
t₂, X₃: 10⋅X₅+55⋅X₄+1824 {O(n)}
t₂, X₄: X₄ {O(n)}
t₂, X₅: X₅ {O(n)}
t₃, X₀: 14⋅X₄+2⋅X₅+387 {O(n)}
t₃, X₁: 11⋅X₅+55⋅X₄+1824 {O(n)}
t₃, X₂: 13⋅X₄+2⋅X₅+X₂+387 {O(n)}
t₃, X₃: 10⋅X₅+55⋅X₄+X₃+1824 {O(n)}
t₃, X₄: 2⋅X₄ {O(n)}
t₃, X₅: 2⋅X₅ {O(n)}
t₁, X₀: X₄ {O(n)}
t₁, X₁: X₅ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₁, X₅: X₅ {O(n)}
t₄, X₀: 14⋅X₄+2⋅X₅+387 {O(n)}
t₄, X₁: 11⋅X₅+55⋅X₄+1824 {O(n)}
t₄, X₂: 13⋅X₄+2⋅X₅+387 {O(n)}
t₄, X₃: 10⋅X₅+55⋅X₄+1824 {O(n)}
t₄, X₄: X₄ {O(n)}
t₄, X₅: X₅ {O(n)}
t₅, X₀: 42⋅X₄+6⋅X₅+1161 {O(n)}
t₅, X₁: 165⋅X₄+33⋅X₅+5472 {O(n)}
t₅, X₂: 13⋅X₄+2⋅X₅+387 {O(n)}
t₅, X₃: 10⋅X₅+55⋅X₄+1824 {O(n)}
t₅, X₄: X₄ {O(n)}
t₅, X₅: X₅ {O(n)}
t₁₃, X₀: 14⋅X₄+2⋅X₅+387 {O(n)}
t₁₃, X₁: 11⋅X₅+55⋅X₄+1824 {O(n)}
t₁₃, X₂: 13⋅X₄+2⋅X₅+X₂+387 {O(n)}
t₁₃, X₃: 10⋅X₅+55⋅X₄+X₃+1824 {O(n)}
t₁₃, X₄: 2⋅X₄ {O(n)}
t₁₃, X₅: 2⋅X₅ {O(n)}
t₁₂, X₀: 13⋅X₄+2⋅X₅+387 {O(n)}
t₁₂, X₁: 10⋅X₅+55⋅X₄+1824 {O(n)}
t₁₂, X₂: 13⋅X₄+2⋅X₅+387 {O(n)}
t₁₂, X₃: 10⋅X₅+55⋅X₄+1824 {O(n)}
t₁₂, X₄: X₄ {O(n)}
t₁₂, X₅: X₅ {O(n)}
t₈, X₀: 14⋅X₄+2⋅X₅+387 {O(n)}
t₈, X₁: 11⋅X₅+55⋅X₄+1824 {O(n)}
t₈, X₂: 13⋅X₄+2⋅X₅+387 {O(n)}
t₈, X₃: 10⋅X₅+55⋅X₄+1824 {O(n)}
t₈, X₄: X₄ {O(n)}
t₈, X₅: X₅ {O(n)}
t₁₀, X₀: 14⋅X₄+2⋅X₅+387 {O(n)}
t₁₀, X₁: 11⋅X₅+55⋅X₄+1824 {O(n)}
t₁₀, X₂: 13⋅X₄+2⋅X₅+387 {O(n)}
t₁₀, X₃: 10⋅X₅+55⋅X₄+1824 {O(n)}
t₁₀, X₄: X₄ {O(n)}
t₁₀, X₅: X₅ {O(n)}