Initial Problem

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

Preprocessing

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

Found invariant X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l7

Found invariant X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l5

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

Found invariant X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l4

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

Problem after Preprocessing

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

MPRF for transition t₃: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: 1 ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

2⋅X₀+1 {O(n)}

MPRF:

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

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

new bound:

X₀+X₁+1 {O(n)}

MPRF:

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

MPRF for transition t₈: l2(X₀, X₁, X₂) → l1(X₀, X₁, 0) :|: X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

MPRF:

l3 [X₁+X₂ ]
l1 [X₁+X₂ ]
l4 [X₁+X₂ ]
l2 [X₁+X₂ ]

MPRF for transition t₉: l3(X₀, X₁, X₂) → l1(X₀, X₁-1, X₂+1) :|: 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

MPRF:

l3 [X₁ ]
l1 [X₁ ]
l4 [X₁ ]
l2 [X₁ ]

MPRF for transition t₄: l4(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: D+1 ≤ 0 ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

2⋅X₀+1 {O(n)}

MPRF:

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

MPRF for transition t₅: l4(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: 1 ≤ D ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

2⋅X₀+X₁+1 {O(n)}

MPRF:

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

All Bounds

Timebounds

Overall timebound:2⋅X₁+9⋅X₀+9 {O(n)}
t₀: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 2⋅X₀+1 {O(n)}
t₇: X₀+X₁+1 {O(n)}
t₈: X₀ {O(n)}
t₉: X₀ {O(n)}
t₄: 2⋅X₀+1 {O(n)}
t₅: 2⋅X₀+X₁+1 {O(n)}
t₆: 1 {O(1)}
t₁₀: 1 {O(1)}
t₁: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₁+9⋅X₀+9 {O(n)}
t₀: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 2⋅X₀+1 {O(n)}
t₇: X₀+X₁+1 {O(n)}
t₈: X₀ {O(n)}
t₉: X₀ {O(n)}
t₄: 2⋅X₀+1 {O(n)}
t₅: 2⋅X₀+X₁+1 {O(n)}
t₆: 1 {O(1)}
t₁₀: 1 {O(1)}
t₁: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₂, X₀: X₁ {O(n)}
t₂, X₁: 0 {O(1)}
t₂, X₂: X₀ {O(n)}
t₃, X₀: X₁ {O(n)}
t₃, X₁: X₀ {O(n)}
t₃, X₂: X₀ {O(n)}
t₇, X₀: X₁ {O(n)}
t₇, X₁: X₀ {O(n)}
t₇, X₂: X₀ {O(n)}
t₈, X₀: X₁ {O(n)}
t₈, X₁: X₀ {O(n)}
t₈, X₂: 0 {O(1)}
t₉, X₀: X₁ {O(n)}
t₉, X₁: X₀ {O(n)}
t₉, X₂: X₀ {O(n)}
t₄, X₀: X₁ {O(n)}
t₄, X₁: X₀ {O(n)}
t₄, X₂: X₀ {O(n)}
t₅, X₀: X₁ {O(n)}
t₅, X₁: X₀ {O(n)}
t₅, X₂: X₀ {O(n)}
t₆, X₀: X₁ {O(n)}
t₆, X₁: X₀ {O(n)}
t₆, X₂: X₀ {O(n)}
t₁₀, X₀: 2⋅X₁ {O(n)}
t₁₀, X₁: X₀ {O(n)}
t₁₀, X₂: 2⋅X₀ {O(n)}
t₁, X₀: X₁ {O(n)}
t₁, X₁: X₀ {O(n)}
t₁, X₂: 0 {O(1)}