Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: E
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃)
t₆: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: 1 ≤ X₃
t₅: l1(X₀, X₁, X₂, X₃) → l4(X₂, X₃, X₂, X₃) :|: X₃ ≤ 0
t₇: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: E+1 ≤ 0
t₈: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 1 ≤ E
t₉: l2(X₀, X₁, X₂, X₃) → l4(X₂, X₃, X₂, X₃)
t₁₀: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, 1, X₃-1)
t₂: l4(X₀, X₁, X₂, X₃) → l1(X₀, X₁, 0, X₁) :|: X₀ ≤ 1 ∧ 1 ≤ X₀
t₃: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0
t₄: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: 2 ≤ X₀
t₁₁: l5(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃)
t₁: l6(X₀, X₁, X₂, X₃) → l4(1, X₀, X₂, X₃)

Preprocessing

Found invariant X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 2 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location l2

Found invariant X₀ ≤ 0 ∧ 0 ≤ X₀ for location l7

Found invariant X₀ ≤ 0 ∧ 0 ≤ X₀ for location l5

Found invariant X₃ ≤ X₁ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 2 ∧ 0 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location l1

Found invariant X₀ ≤ 1 ∧ 0 ≤ X₀ for location l4

Found invariant X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 2 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location l3

Cut unsatisfiable transition t₄: l4→l5

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: E
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃)
t₆: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: 1 ≤ X₃ ∧ X₃ ≤ X₁ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 2 ∧ 0 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀
t₅: l1(X₀, X₁, X₂, X₃) → l4(X₂, X₃, X₂, X₃) :|: X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 2 ∧ 0 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀
t₇: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: E+1 ≤ 0 ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 2 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀
t₈: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 1 ≤ E ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 2 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀
t₉: l2(X₀, X₁, X₂, X₃) → l4(X₂, X₃, X₂, X₃) :|: X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 2 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀
t₁₀: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, 1, X₃-1) :|: X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 2 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀
t₂: l4(X₀, X₁, X₂, X₃) → l1(X₀, X₁, 0, X₁) :|: X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 0 ≤ X₀
t₃: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0 ∧ X₀ ≤ 1 ∧ 0 ≤ X₀
t₁₁: l5(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0 ∧ 0 ≤ X₀
t₁: l6(X₀, X₁, X₂, X₃) → l4(1, X₀, X₂, X₃)

MPRF for transition t₆: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: 1 ≤ X₃ ∧ X₃ ≤ X₁ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 2 ∧ 0 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ of depth 1:

new bound:

2⋅X₀+2 {O(n)}

MPRF:

l2 [X₂+2⋅X₃-1 ]
l3 [2⋅X₃-X₀ ]
l4 [X₀+2⋅X₁-1 ]
l1 [X₂+2⋅X₃ ]

MPRF for transition t₇: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: E+1 ≤ 0 ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 2 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ of depth 1:

new bound:

X₀+1 {O(n)}

MPRF:

l2 [X₃+1 ]
l3 [X₃ ]
l4 [X₁+1 ]
l1 [X₀+X₃ ]

MPRF for transition t₈: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 1 ≤ E ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 2 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ of depth 1:

new bound:

X₀+1 {O(n)}

MPRF:

l2 [X₃+1 ]
l3 [X₃ ]
l4 [X₁+1 ]
l1 [X₀+X₃ ]

MPRF for transition t₉: l2(X₀, X₁, X₂, X₃) → l4(X₂, X₃, X₂, X₃) :|: X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 2 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ of depth 1:

new bound:

2⋅X₀+1 {O(n)}

MPRF:

l2 [X₂+2⋅X₃+1 ]
l3 [2⋅X₃ ]
l4 [X₀+2⋅X₁ ]
l1 [X₀+X₂+2⋅X₃ ]

MPRF for transition t₁₀: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, 1, X₃-1) :|: X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 2 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ of depth 1:

new bound:

4⋅X₀ {O(n)}

MPRF:

l2 [2⋅X₁+2⋅X₃ ]
l3 [2⋅X₁+2⋅X₃-X₀ ]
l4 [4⋅X₁ ]
l1 [2⋅X₁+2⋅X₃ ]

MPRF for transition t₅: l1(X₀, X₁, X₂, X₃) → l4(X₂, X₃, X₂, X₃) :|: X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 2 ∧ 0 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ of depth 1:

new bound:

8⋅X₀+1 {O(n)}

MPRF:

l3 [X₀+X₂ ]
l2 [X₂+1 ]
l4 [X₀ ]
l1 [X₂+1 ]

MPRF for transition t₂: l4(X₀, X₁, X₂, X₃) → l1(X₀, X₁, 0, X₁) :|: X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 0 ≤ X₀ of depth 1:

new bound:

8⋅X₀+2 {O(n)}

MPRF:

l3 [X₀ ]
l2 [X₀+X₂ ]
l4 [X₀+1 ]
l1 [X₀+X₂ ]

All Bounds

Timebounds

Overall timebound:26⋅X₀+12 {O(n)}
t₀: 1 {O(1)}
t₅: 8⋅X₀+1 {O(n)}
t₆: 2⋅X₀+2 {O(n)}
t₇: X₀+1 {O(n)}
t₈: X₀+1 {O(n)}
t₉: 2⋅X₀+1 {O(n)}
t₁₀: 4⋅X₀ {O(n)}
t₂: 8⋅X₀+2 {O(n)}
t₃: 1 {O(1)}
t₁₁: 1 {O(1)}
t₁: 1 {O(1)}

Costbounds

Overall costbound: 26⋅X₀+12 {O(n)}
t₀: 1 {O(1)}
t₅: 8⋅X₀+1 {O(n)}
t₆: 2⋅X₀+2 {O(n)}
t₇: X₀+1 {O(n)}
t₈: X₀+1 {O(n)}
t₉: 2⋅X₀+1 {O(n)}
t₁₀: 4⋅X₀ {O(n)}
t₂: 8⋅X₀+2 {O(n)}
t₃: 1 {O(1)}
t₁₁: 1 {O(1)}
t₁: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₅, X₀: 1 {O(1)}
t₅, X₁: 2⋅X₀ {O(n)}
t₅, X₂: 1 {O(1)}
t₅, X₃: 4⋅X₀ {O(n)}
t₆, X₀: 1 {O(1)}
t₆, X₁: 2⋅X₀ {O(n)}
t₆, X₂: 1 {O(1)}
t₆, X₃: 2⋅X₀ {O(n)}
t₇, X₀: 1 {O(1)}
t₇, X₁: 2⋅X₀ {O(n)}
t₇, X₂: 1 {O(1)}
t₇, X₃: 2⋅X₀ {O(n)}
t₈, X₀: 1 {O(1)}
t₈, X₁: 2⋅X₀ {O(n)}
t₈, X₂: 1 {O(1)}
t₈, X₃: 2⋅X₀ {O(n)}
t₉, X₀: 1 {O(1)}
t₉, X₁: 2⋅X₀ {O(n)}
t₉, X₂: 1 {O(1)}
t₉, X₃: 2⋅X₀ {O(n)}
t₁₀, X₀: 1 {O(1)}
t₁₀, X₁: 2⋅X₀ {O(n)}
t₁₀, X₂: 1 {O(1)}
t₁₀, X₃: 2⋅X₀ {O(n)}
t₂, X₀: 1 {O(1)}
t₂, X₁: 2⋅X₀ {O(n)}
t₂, X₂: 0 {O(1)}
t₂, X₃: 2⋅X₀ {O(n)}
t₃, X₀: 0 {O(1)}
t₃, X₁: 4⋅X₀ {O(n)}
t₃, X₂: 2 {O(1)}
t₃, X₃: 6⋅X₀ {O(n)}
t₁₁, X₀: 0 {O(1)}
t₁₁, X₁: 4⋅X₀ {O(n)}
t₁₁, X₂: 2 {O(1)}
t₁₁, X₃: 6⋅X₀ {O(n)}
t₁, X₀: 1 {O(1)}
t₁, X₁: X₀ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}