Initial Problem

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

Preprocessing

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

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

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

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

Problem after Preprocessing

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

MPRF for transition t₃: l4(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₂ ≤ X₁ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ of depth 1:

new bound:

X₁+2 {O(n)}

MPRF for transition t₅: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ of depth 1:

new bound:

X₁+2 {O(n)}

MPRF for transition t₇: l3(X₀, X₁, X₂) → l1(nondef.0, X₁, X₂) :|: X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ of depth 1:

new bound:

2⋅X₁+1 {O(n)}

MPRF for transition t₈: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂+1) :|: 0 < X₀ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ of depth 1:

new bound:

X₁+2 {O(n)}

MPRF for transition t₉: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂+1) :|: X₀ ≤ 0 ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ of depth 1:

new bound:

X₁+2 {O(n)}

All Bounds

Timebounds

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

Costbounds

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

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: 1 {O(1)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: 2⋅X₁+5 {O(n)}
t₄, X₁: 2⋅X₁ {O(n)}
t₄, X₂: 4⋅X₁+10 {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: 2⋅X₁+5 {O(n)}
t₇, X₁: X₁ {O(n)}
t₇, X₂: 2⋅X₁+5 {O(n)}
t₈, X₁: X₁ {O(n)}
t₈, X₂: 2⋅X₁+5 {O(n)}
t₉, X₁: X₁ {O(n)}
t₉, X₂: 2⋅X₁+5 {O(n)}
t₁₀, X₁: 3⋅X₁ {O(n)}
t₁₀, X₂: 4⋅X₁+X₂+10 {O(n)}