Initial Problem

Start: l0
Program_Vars: X₀, X₁
Temp_Vars: C
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁) → l4(X₀, X₁)
t₆: l1(X₀, X₁) → l2(X₀, X₁)
t₄: l1(X₀, X₁) → l3(X₀, X₁) :|: C+1 ≤ 0
t₅: l1(X₀, X₁) → l3(X₀, X₁) :|: 1 ≤ C
t₈: l2(X₀, X₁) → l6(X₀, X₁) :|: X₀+1 ≤ X₁
t₉: l2(X₀, X₁) → l7(X₀, X₁) :|: X₁ ≤ X₀
t₇: l3(X₀, X₁) → l5(X₀+1, X₁)
t₁: l4(X₀, X₁) → l5(0, X₁)
t₃: l5(X₀, X₁) → l1(X₀, X₁) :|: X₀+1 ≤ X₁
t₂: l5(X₀, X₁) → l2(X₀, X₁) :|: X₁ ≤ X₀
t₁₀: l6(X₀, X₁) → l2(X₀+1, X₁)
t₁₁: l7(X₀, X₁) → l8(X₀, X₁)

Preprocessing

Found invariant 0 ≤ X₀ for location l2

Found invariant 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l6

Found invariant X₁ ≤ X₀ ∧ 0 ≤ X₀ for location l7

Found invariant 0 ≤ X₀ for location l5

Found invariant X₁ ≤ X₀ ∧ 0 ≤ X₀ for location l8

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

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

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars: C
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁) → l4(X₀, X₁)
t₆: l1(X₀, X₁) → l2(X₀, X₁) :|: 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₄: l1(X₀, X₁) → l3(X₀, X₁) :|: C+1 ≤ 0 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₅: l1(X₀, X₁) → l3(X₀, X₁) :|: 1 ≤ C ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₈: l2(X₀, X₁) → l6(X₀, X₁) :|: X₀+1 ≤ X₁ ∧ 0 ≤ X₀
t₉: l2(X₀, X₁) → l7(X₀, X₁) :|: X₁ ≤ X₀ ∧ 0 ≤ X₀
t₇: l3(X₀, X₁) → l5(X₀+1, X₁) :|: 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₁: l4(X₀, X₁) → l5(0, X₁)
t₃: l5(X₀, X₁) → l1(X₀, X₁) :|: X₀+1 ≤ X₁ ∧ 0 ≤ X₀
t₂: l5(X₀, X₁) → l2(X₀, X₁) :|: X₁ ≤ X₀ ∧ 0 ≤ X₀
t₁₀: l6(X₀, X₁) → l2(X₀+1, X₁) :|: 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₁₁: l7(X₀, X₁) → l8(X₀, X₁) :|: X₁ ≤ X₀ ∧ 0 ≤ X₀

MPRF for transition t₄: l1(X₀, X₁) → l3(X₀, X₁) :|: C+1 ≤ 0 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁ {O(n)}

MPRF:

l3 [X₁-X₀-1 ]
l5 [X₁-X₀ ]
l1 [X₁-X₀ ]

MPRF for transition t₅: l1(X₀, X₁) → l3(X₀, X₁) :|: 1 ≤ C ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁ {O(n)}

MPRF:

l3 [X₁-X₀-1 ]
l5 [X₁-X₀ ]
l1 [X₁-X₀ ]

MPRF for transition t₇: l3(X₀, X₁) → l5(X₀+1, X₁) :|: 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁ {O(n)}

MPRF:

l3 [X₁-X₀ ]
l5 [X₁-X₀ ]
l1 [X₁-X₀ ]

MPRF for transition t₃: l5(X₀, X₁) → l1(X₀, X₁) :|: X₀+1 ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁ {O(n)}

MPRF:

l3 [X₁-X₀-1 ]
l5 [X₁-X₀ ]
l1 [X₁-X₀-1 ]

MPRF for transition t₈: l2(X₀, X₁) → l6(X₀, X₁) :|: X₀+1 ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

2⋅X₁ {O(n)}

MPRF:

l6 [X₁-X₀-1 ]
l2 [X₁-X₀ ]

MPRF for transition t₁₀: l6(X₀, X₁) → l2(X₀+1, X₁) :|: 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

2⋅X₁ {O(n)}

MPRF:

l6 [X₁-X₀ ]
l2 [X₁-X₀ ]

All Bounds

Timebounds

Overall timebound:8⋅X₁+6 {O(n)}
t₀: 1 {O(1)}
t₄: X₁ {O(n)}
t₅: X₁ {O(n)}
t₆: 1 {O(1)}
t₈: 2⋅X₁ {O(n)}
t₉: 1 {O(1)}
t₇: X₁ {O(n)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: X₁ {O(n)}
t₁₀: 2⋅X₁ {O(n)}
t₁₁: 1 {O(1)}

Costbounds

Overall costbound: 8⋅X₁+6 {O(n)}
t₀: 1 {O(1)}
t₄: X₁ {O(n)}
t₅: X₁ {O(n)}
t₆: 1 {O(1)}
t₈: 2⋅X₁ {O(n)}
t₉: 1 {O(1)}
t₇: X₁ {O(n)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: X₁ {O(n)}
t₁₀: 2⋅X₁ {O(n)}
t₁₁: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₄, X₀: X₁ {O(n)}
t₄, X₁: X₁ {O(n)}
t₅, X₀: X₁ {O(n)}
t₅, X₁: X₁ {O(n)}
t₆, X₀: X₁ {O(n)}
t₆, X₁: X₁ {O(n)}
t₈, X₀: 3⋅X₁ {O(n)}
t₈, X₁: X₁ {O(n)}
t₉, X₀: 4⋅X₁ {O(n)}
t₉, X₁: 3⋅X₁ {O(n)}
t₇, X₀: X₁ {O(n)}
t₇, X₁: X₁ {O(n)}
t₁, X₀: 0 {O(1)}
t₁, X₁: X₁ {O(n)}
t₂, X₀: X₁ {O(n)}
t₂, X₁: 2⋅X₁ {O(n)}
t₃, X₀: X₁ {O(n)}
t₃, X₁: X₁ {O(n)}
t₁₀, X₀: 3⋅X₁ {O(n)}
t₁₀, X₁: X₁ {O(n)}
t₁₁, X₀: 4⋅X₁ {O(n)}
t₁₁, X₁: 3⋅X₁ {O(n)}