Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄)
t₅: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: X₃ ≤ X₂
t₄: l1(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₃, X₄) :|: X₂+1 ≤ X₃
t₁₅: l2(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₁, X₂, X₃, X₄)
t₁₄: l3(X₀, X₁, X₂, X₃, X₄) → l5(X₂-10, X₃+2, X₂, X₃, X₄)
t₁: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₁, X₀, X₂, X₃, X₄)
t₂: l5(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₀, X₁, X₄) :|: X₁ ≤ 29
t₃: l5(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: 30 ≤ X₁
t₁₃: l6(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₄, X₃+10, X₄)
t₁₂: l7(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₄, X₃+1, X₄)
t₈: l8(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₂+7) :|: 6 ≤ X₂ ∧ 3 ≤ X₂ ∧ X₂ ≤ 5
t₁₁: l8(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₂+2) :|: X₂ ≤ 5 ∧ 8 ≤ X₂ ∧ X₂ ≤ 10
t₆: l8(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₂+7) :|: 6 ≤ X₂ ∧ X₂ ≤ 2
t₇: l8(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₂+7) :|: 6 ≤ X₂
t₉: l8(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₂+2) :|: X₂ ≤ 5 ∧ X₂ ≤ 7
t₁₀: l8(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₂+2) :|: X₂ ≤ 5 ∧ 11 ≤ X₂

Preprocessing

Cut unsatisfiable transition t₁₃: l6→l1

Cut unsatisfiable transition t₆: l8→l7

Cut unsatisfiable transition t₈: l8→l6

Cut unsatisfiable transition t₁₀: l8→l7

Cut unsatisfiable transition t₁₁: l8→l6

Cut unreachable locations [l6] from the program graph

Found invariant 30 ≤ X₁ for location l2

Found invariant X₄ ≤ 6+X₃ ∧ X₄ ≤ 7+X₂ ∧ 2+X₂ ≤ X₄ ∧ 2+X₀ ≤ X₄ ∧ 1+X₂ ≤ X₃ ∧ X₁ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 29 for location l7

Found invariant 1+X₂ ≤ X₃ ∧ X₁ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 29 for location l8

Found invariant X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 29 for location l1

Found invariant 30 ≤ X₁ for location l9

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

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄)
t₅: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: X₃ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 29
t₄: l1(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₃, X₄) :|: X₂+1 ≤ X₃ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 29
t₁₅: l2(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₁, X₂, X₃, X₄) :|: 30 ≤ X₁
t₁₄: l3(X₀, X₁, X₂, X₃, X₄) → l5(X₂-10, X₃+2, X₂, X₃, X₄) :|: X₃ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 29
t₁: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₁, X₀, X₂, X₃, X₄)
t₂: l5(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₀, X₁, X₄) :|: X₁ ≤ 29
t₃: l5(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: 30 ≤ X₁
t₁₂: l7(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₄, X₃+1, X₄) :|: X₄ ≤ 6+X₃ ∧ X₄ ≤ 7+X₂ ∧ 2+X₂ ≤ X₄ ∧ 2+X₀ ≤ X₄ ∧ 1+X₂ ≤ X₃ ∧ X₁ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 29
t₇: l8(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₂+7) :|: 6 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ X₁ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 29
t₉: l8(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₂+2) :|: X₂ ≤ 5 ∧ X₂ ≤ 7 ∧ 1+X₂ ≤ X₃ ∧ X₁ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 29

MPRF for transition t₄: l1(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₃, X₄) :|: X₂+1 ≤ X₃ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 29 of depth 1:

new bound:

5⋅X₀+X₁+174 {O(n)}

MPRF:

l3 [174-X₂-5⋅X₃ ]
l5 [174-X₀-5⋅X₁ ]
l1 [X₃+174-6⋅X₁-X₂ ]
l8 [X₃+173-6⋅X₁-X₂ ]
l7 [X₃+175-6⋅X₁-X₄ ]

MPRF for transition t₅: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: X₃ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 29 of depth 1:

new bound:

X₀+30 {O(n)}

MPRF:

l3 [28-X₁ ]
l5 [30-X₁ ]
l1 [30-X₁ ]
l8 [30-X₁ ]
l7 [30-X₁ ]

MPRF for transition t₁₄: l3(X₀, X₁, X₂, X₃, X₄) → l5(X₂-10, X₃+2, X₂, X₃, X₄) :|: X₃ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 29 of depth 1:

new bound:

X₀+30 {O(n)}

MPRF:

l3 [30-X₁ ]
l5 [30-X₁ ]
l1 [30-X₁ ]
l8 [30-X₁ ]
l7 [30-X₁ ]

MPRF for transition t₂: l5(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₀, X₁, X₄) :|: X₁ ≤ 29 of depth 1:

new bound:

X₀+30 {O(n)}

MPRF:

l3 [28-X₁ ]
l5 [30-X₁ ]
l1 [28-X₁ ]
l8 [28-X₁ ]
l7 [28-X₁ ]

MPRF for transition t₁₂: l7(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₄, X₃+1, X₄) :|: X₄ ≤ 6+X₃ ∧ X₄ ≤ 7+X₂ ∧ 2+X₂ ≤ X₄ ∧ 2+X₀ ≤ X₄ ∧ 1+X₂ ≤ X₃ ∧ X₁ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 29 of depth 1:

new bound:

5⋅X₀+X₁+179 {O(n)}

MPRF:

l3 [179-X₂-5⋅X₃ ]
l5 [179-X₀-5⋅X₁ ]
l1 [X₃+179-6⋅X₁-X₂ ]
l8 [X₃+179-6⋅X₁-X₂ ]
l7 [X₃+181-6⋅X₁-X₄ ]

MPRF for transition t₇: l8(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₂+7) :|: 6 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ X₁ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 29 of depth 1:

new bound:

5⋅X₀+X₁+174 {O(n)}

MPRF:

l3 [X₃+174-6⋅X₁-X₂ ]
l5 [174-X₀-5⋅X₁ ]
l1 [X₃+174-6⋅X₁-X₂ ]
l8 [X₃+174-6⋅X₁-X₂ ]
l7 [X₃+175-6⋅X₁-X₄ ]

MPRF for transition t₉: l8(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₂+2) :|: X₂ ≤ 5 ∧ X₂ ≤ 7 ∧ 1+X₂ ≤ X₃ ∧ X₁ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 29 of depth 1:

new bound:

5⋅X₀+X₁+151 {O(n)}

MPRF:

l3 [151-5⋅X₁-X₂ ]
l5 [151-X₀-5⋅X₁ ]
l1 [151-5⋅X₁-X₂ ]
l8 [151-5⋅X₁-X₂ ]
l7 [151-5⋅X₁-X₄ ]

All Bounds

Timebounds

Overall timebound:23⋅X₀+4⋅X₁+772 {O(n)}
t₀: 1 {O(1)}
t₄: 5⋅X₀+X₁+174 {O(n)}
t₅: X₀+30 {O(n)}
t₁₅: 1 {O(1)}
t₁₄: X₀+30 {O(n)}
t₁: 1 {O(1)}
t₂: X₀+30 {O(n)}
t₃: 1 {O(1)}
t₁₂: 5⋅X₀+X₁+179 {O(n)}
t₇: 5⋅X₀+X₁+174 {O(n)}
t₉: 5⋅X₀+X₁+151 {O(n)}

Costbounds

Overall costbound: 23⋅X₀+4⋅X₁+772 {O(n)}
t₀: 1 {O(1)}
t₄: 5⋅X₀+X₁+174 {O(n)}
t₅: X₀+30 {O(n)}
t₁₅: 1 {O(1)}
t₁₄: X₀+30 {O(n)}
t₁: 1 {O(1)}
t₂: X₀+30 {O(n)}
t₃: 1 {O(1)}
t₁₂: 5⋅X₀+X₁+179 {O(n)}
t₇: 5⋅X₀+X₁+174 {O(n)}
t₉: 5⋅X₀+X₁+151 {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)}
t₄, X₀: 45⋅X₀+9⋅X₁+1553 {O(n)}
t₄, X₁: 9⋅X₀+X₁+239 {O(n)}
t₄, X₂: 45⋅X₀+8⋅X₁+1553 {O(n)}
t₄, X₃: 8⋅X₀+X₁+239 {O(n)}
t₄, X₄: 180⋅X₀+32⋅X₁+X₄+6230 {O(n)}
t₅, X₀: 18⋅X₁+90⋅X₀+3106 {O(n)}
t₅, X₁: 18⋅X₀+2⋅X₁+478 {O(n)}
t₅, X₂: 45⋅X₀+8⋅X₁+1553 {O(n)}
t₅, X₃: 8⋅X₀+X₁+239 {O(n)}
t₅, X₄: 16⋅X₁+90⋅X₀+X₄+3115 {O(n)}
t₁₅, X₀: 45⋅X₀+9⋅X₁+1553 {O(n)}
t₁₅, X₁: 9⋅X₀+X₁+239 {O(n)}
t₁₅, X₂: 45⋅X₀+8⋅X₁+X₂+1553 {O(n)}
t₁₅, X₃: 8⋅X₀+X₁+X₃+239 {O(n)}
t₁₅, X₄: 16⋅X₁+2⋅X₄+90⋅X₀+3115 {O(n)}
t₁₄, X₀: 45⋅X₀+8⋅X₁+1553 {O(n)}
t₁₄, X₁: 8⋅X₀+X₁+239 {O(n)}
t₁₄, X₂: 45⋅X₀+8⋅X₁+1553 {O(n)}
t₁₄, X₃: 8⋅X₀+X₁+239 {O(n)}
t₁₄, X₄: 16⋅X₁+90⋅X₀+X₄+3115 {O(n)}
t₁, X₀: X₁ {O(n)}
t₁, X₁: X₀ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₂, X₀: 45⋅X₀+9⋅X₁+1553 {O(n)}
t₂, X₁: 9⋅X₀+X₁+239 {O(n)}
t₂, X₂: 45⋅X₀+8⋅X₁+1553 {O(n)}
t₂, X₃: 8⋅X₀+X₁+239 {O(n)}
t₂, X₄: 16⋅X₁+90⋅X₀+X₄+3115 {O(n)}
t₃, X₀: 45⋅X₀+9⋅X₁+1553 {O(n)}
t₃, X₁: 9⋅X₀+X₁+239 {O(n)}
t₃, X₂: 45⋅X₀+8⋅X₁+X₂+1553 {O(n)}
t₃, X₃: 8⋅X₀+X₁+X₃+239 {O(n)}
t₃, X₄: 16⋅X₁+2⋅X₄+90⋅X₀+3115 {O(n)}
t₁₂, X₀: 45⋅X₀+9⋅X₁+1553 {O(n)}
t₁₂, X₁: 9⋅X₀+X₁+239 {O(n)}
t₁₂, X₂: 45⋅X₀+8⋅X₁+1553 {O(n)}
t₁₂, X₃: 8⋅X₀+X₁+239 {O(n)}
t₁₂, X₄: 16⋅X₁+90⋅X₀+3115 {O(n)}
t₇, X₀: 45⋅X₀+9⋅X₁+1553 {O(n)}
t₇, X₁: 9⋅X₀+X₁+239 {O(n)}
t₇, X₂: 45⋅X₀+8⋅X₁+1553 {O(n)}
t₇, X₃: 8⋅X₀+X₁+239 {O(n)}
t₇, X₄: 45⋅X₀+8⋅X₁+1560 {O(n)}
t₉, X₀: 45⋅X₀+9⋅X₁+1553 {O(n)}
t₉, X₁: 9⋅X₀+X₁+239 {O(n)}
t₉, X₂: 45⋅X₀+8⋅X₁+1553 {O(n)}
t₉, X₃: 8⋅X₀+X₁+239 {O(n)}
t₉, X₄: 45⋅X₀+8⋅X₁+1555 {O(n)}