Initial Problem

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁) → l6(X₀, X₁)
t₉: l1(X₀, X₁) → l3(X₀, X₁+1)
t₁₀: l2(X₀, X₁) → l3(X₀+1, X₁)
t₄: l3(X₀, X₁) → l4(X₀, X₁) :|: X₀+3 ≤ X₁
t₅: l3(X₀, X₁) → l4(X₀, X₁) :|: X₁+3 ≤ X₀
t₆: l3(X₀, X₁) → l5(X₀, X₁) :|: X₁ ≤ 2+X₀ ∧ X₀ ≤ 2+X₁
t₇: l4(X₀, X₁) → l1(X₀, X₁) :|: X₁+1 ≤ X₀
t₈: l4(X₀, X₁) → l2(X₀, X₁) :|: X₀ ≤ X₁
t₁₁: l5(X₀, X₁) → l7(X₀, X₁)
t₃: l6(X₀, X₁) → l3(X₁, X₀) :|: 0 ≤ X₀ ∧ 0 ≤ X₁
t₁: l6(X₀, X₁) → l5(X₀, X₁) :|: X₀+1 ≤ 0
t₂: l6(X₀, X₁) → l5(X₀, X₁) :|: X₁+1 ≤ 0

Preprocessing

Found invariant 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l2

Found invariant 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l1

Found invariant 0 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l4

Found invariant 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁) → l6(X₀, X₁)
t₉: l1(X₀, X₁) → l3(X₀, X₁+1) :|: 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₁₀: l2(X₀, X₁) → l3(X₀+1, X₁) :|: 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀
t₄: l3(X₀, X₁) → l4(X₀, X₁) :|: X₀+3 ≤ X₁ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₅: l3(X₀, X₁) → l4(X₀, X₁) :|: X₁+3 ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₆: l3(X₀, X₁) → l5(X₀, X₁) :|: X₁ ≤ 2+X₀ ∧ X₀ ≤ 2+X₁ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₇: l4(X₀, X₁) → l1(X₀, X₁) :|: X₁+1 ≤ X₀ ∧ 0 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₈: l4(X₀, X₁) → l2(X₀, X₁) :|: X₀ ≤ X₁ ∧ 0 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₁₁: l5(X₀, X₁) → l7(X₀, X₁)
t₃: l6(X₀, X₁) → l3(X₁, X₀) :|: 0 ≤ X₀ ∧ 0 ≤ X₁
t₁: l6(X₀, X₁) → l5(X₀, X₁) :|: X₀+1 ≤ 0
t₂: l6(X₀, X₁) → l5(X₀, X₁) :|: X₁+1 ≤ 0

MPRF for transition t₉: l1(X₀, X₁) → l3(X₀, X₁+1) :|: 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₀+X₁+2 {O(n)}

MPRF:

l3 [X₀+2-X₁ ]
l4 [X₀+2-X₁ ]
l1 [X₀+2-X₁ ]

MPRF for transition t₁₀: l2(X₀, X₁) → l3(X₀+1, X₁) :|: 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₀+X₁+1 {O(n)}

MPRF:

l3 [X₁+1-X₀ ]
l4 [X₁+1-X₀ ]
l2 [X₁+1-X₀ ]

MPRF for transition t₄: l3(X₀, X₁) → l4(X₀, X₁) :|: X₀+3 ≤ X₁ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₀+X₁+2 {O(n)}

MPRF:

l3 [X₁-X₀-2 ]
l4 [X₁-X₀-3 ]
l2 [X₁-X₀-3 ]

MPRF for transition t₅: l3(X₀, X₁) → l4(X₀, X₁) :|: X₁+3 ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₀+X₁+14 {O(n)}

MPRF:

l3 [X₀+14-X₁ ]
l4 [X₀+13-X₁ ]
l1 [X₀+13-X₁ ]

MPRF for transition t₇: l4(X₀, X₁) → l1(X₀, X₁) :|: X₁+1 ≤ X₀ ∧ 0 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₀+X₁ {O(n)}

MPRF:

l3 [X₀-X₁ ]
l4 [X₀-X₁ ]
l1 [X₀-X₁-1 ]

MPRF for transition t₈: l4(X₀, X₁) → l2(X₀, X₁) :|: X₀ ≤ X₁ ∧ 0 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₀+X₁+1 {O(n)}

MPRF:

l3 [X₁+1-X₀ ]
l4 [X₁+1-X₀ ]
l2 [X₁-X₀ ]

All Bounds

Timebounds

Overall timebound:6⋅X₀+6⋅X₁+26 {O(n)}
t₀: 1 {O(1)}
t₉: X₀+X₁+2 {O(n)}
t₁₀: X₀+X₁+1 {O(n)}
t₄: X₀+X₁+2 {O(n)}
t₅: X₀+X₁+14 {O(n)}
t₆: 1 {O(1)}
t₇: X₀+X₁ {O(n)}
t₈: X₀+X₁+1 {O(n)}
t₁₁: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}

Costbounds

Overall costbound: 6⋅X₀+6⋅X₁+26 {O(n)}
t₀: 1 {O(1)}
t₉: X₀+X₁+2 {O(n)}
t₁₀: X₀+X₁+1 {O(n)}
t₄: X₀+X₁+2 {O(n)}
t₅: X₀+X₁+14 {O(n)}
t₆: 1 {O(1)}
t₇: X₀+X₁ {O(n)}
t₈: X₀+X₁+1 {O(n)}
t₁₁: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₉, X₀: X₁ {O(n)}
t₉, X₁: 2⋅X₀+X₁+2 {O(n)}
t₁₀, X₀: 2⋅X₁+X₀+1 {O(n)}
t₁₀, X₁: X₀ {O(n)}
t₄, X₀: 2⋅X₁+X₀+1 {O(n)}
t₄, X₁: X₀ {O(n)}
t₅, X₀: X₁ {O(n)}
t₅, X₁: 2⋅X₀+X₁+2 {O(n)}
t₆, X₀: 4⋅X₁+X₀+1 {O(n)}
t₆, X₁: 4⋅X₀+X₁+2 {O(n)}
t₇, X₀: X₁ {O(n)}
t₇, X₁: 2⋅X₀+X₁+2 {O(n)}
t₈, X₀: 2⋅X₁+X₀+1 {O(n)}
t₈, X₁: X₀ {O(n)}
t₁₁, X₀: 3⋅X₀+4⋅X₁+1 {O(n)}
t₁₁, X₁: 3⋅X₁+4⋅X₀+2 {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₃, X₀: X₁ {O(n)}
t₃, X₁: X₀ {O(n)}