Initial Problem

Start: start0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: E
Locations: a, b, cont1, start, start0, stop1, stop2, stop3
Transitions:
t₄: a(X₀, X₁, X₂, X₃) → b(X₀, X₁, E, X₃-1) :|: 1 ≤ X₃ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₂
t₅: b(X₀, X₁, X₂, X₃) → start(X₀, X₁, X₂, X₃) :|: 1+X₃ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
t₆: b(X₀, X₁, X₂, X₃) → stop3(X₀, X₁, X₂, X₃) :|: 1+X₃ ≤ X₀ ∧ 1+X₂ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₃
t₃: cont1(X₀, X₁, X₂, X₃) → a(X₀, X₁, X₂-1, X₃) :|: 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₂
t₂: cont1(X₀, X₁, X₂, X₃) → stop2(X₀, X₁, 1, X₃-1) :|: 1 ≤ X₃ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
t₁: start(X₀, X₁, X₂, X₃) → cont1(X₀, X₁, X₂, X₃) :|: 1 ≤ X₃ ∧ 0 ≤ X₀ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
t₀: start(X₀, X₁, X₂, X₃) → stop1(X₀, X₁, X₂, X₃) :|: 0 ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃ ∧ X₃ ≤ 0
t₇: start0(X₀, X₁, X₂, X₃) → start(X₀, X₁, X₁, X₀) :|: 0 ≤ X₀ ∧ 0 ≤ X₁

Preprocessing

Found invariant X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location stop1

Found invariant 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ 1+X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location stop2

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

Found invariant 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location stop3

Found invariant X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location start

Found invariant 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location b

Found invariant X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location cont1

Problem after Preprocessing

Start: start0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: E
Locations: a, b, cont1, start, start0, stop1, stop2, stop3
Transitions:
t₄: a(X₀, X₁, X₂, X₃) → b(X₀, X₁, E, X₃-1) :|: 1 ≤ X₃ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₀+X₃ ∧ 0 ≤ X₁+X₂
t₅: b(X₀, X₁, X₂, X₃) → start(X₀, X₁, X₂, X₃) :|: 1+X₃ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₃ ∧ 0 ≤ X₁+X₃
t₆: b(X₀, X₁, X₂, X₃) → stop3(X₀, X₁, X₂, X₃) :|: 1+X₃ ≤ X₀ ∧ 1+X₂ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₃ ∧ 0 ≤ X₁+X₃
t₃: cont1(X₀, X₁, X₂, X₃) → a(X₀, X₁, X₂-1, X₃) :|: 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₀+X₃ ∧ 0 ≤ X₁+X₂
t₂: cont1(X₀, X₁, X₂, X₃) → stop2(X₀, X₁, 1, X₃-1) :|: 1 ≤ X₃ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₀+X₃ ∧ 0 ≤ X₁+X₂
t₁: start(X₀, X₁, X₂, X₃) → cont1(X₀, X₁, X₂, X₃) :|: 1 ≤ X₃ ∧ 0 ≤ X₀ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₂+X₃
t₀: start(X₀, X₁, X₂, X₃) → stop1(X₀, X₁, X₂, X₃) :|: 0 ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃ ∧ X₃ ≤ 0 ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₀+X₃ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₂+X₃
t₇: start0(X₀, X₁, X₂, X₃) → start(X₀, X₁, X₁, X₀) :|: 0 ≤ X₀ ∧ 0 ≤ X₁

MPRF for transition t₁: start(X₀, X₁, X₂, X₃) → cont1(X₀, X₁, X₂, X₃) :|: 1 ≤ X₃ ∧ 0 ≤ X₀ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₂+X₃ of depth 1:

new bound:

X₀+1 {O(n)}

• a: [X₃]
• b: [1+X₃]
• cont1: [X₃]
• start: [1+X₃]

MPRF for transition t₃: cont1(X₀, X₁, X₂, X₃) → a(X₀, X₁, X₂-1, X₃) :|: 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₀+X₃ ∧ 0 ≤ X₁+X₂ of depth 1:

new bound:

X₀ {O(n)}

• a: [X₃-1]
• b: [X₃]
• cont1: [X₃]
• start: [X₃]

MPRF for transition t₄: a(X₀, X₁, X₂, X₃) → b(X₀, X₁, E, X₃-1) :|: 1 ≤ X₃ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₀+X₃ ∧ 0 ≤ X₁+X₂ of depth 1:

new bound:

X₀+X₁ {O(n)}

• a: [X₁+X₃]
• b: [X₁+X₃]
• cont1: [X₁+X₃]
• start: [X₁+X₃]

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

new bound:

X₀ {O(n)}

• a: [X₃]
• b: [1+X₃]
• cont1: [X₃]
• start: [X₃]

All Bounds

Timebounds

Overall timebound:4⋅X₀+X₁+5 {O(n)}
t₀: 1 {O(1)}
t₁: X₀+1 {O(n)}
t₂: 1 {O(1)}
t₃: X₀ {O(n)}
t₄: X₀+X₁ {O(n)}
t₅: X₀ {O(n)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}

Costbounds

Overall costbound: 4⋅X₀+X₁+5 {O(n)}
t₀: 1 {O(1)}
t₁: X₀+1 {O(n)}
t₂: 1 {O(1)}
t₃: X₀ {O(n)}
t₄: X₀+X₁ {O(n)}
t₅: X₀ {O(n)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}

Sizebounds

t₀, X₀: 2⋅X₀ {O(n)}
t₀, X₁: 2⋅X₁ {O(n)}
t₀, X₃: 0 {O(1)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₃: X₀ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: 1 {O(1)}
t₂, X₃: X₀ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₃: X₀ {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₃: X₀ {O(n)}
t₅, X₀: X₀ {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₃: X₀ {O(n)}
t₆, X₀: X₀ {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₃: X₀ {O(n)}
t₇, X₀: X₀ {O(n)}
t₇, X₁: X₁ {O(n)}
t₇, X₂: X₁ {O(n)}
t₇, X₃: X₀ {O(n)}