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)
t₉: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂-X₀-1)
t₁₀: l2(X₀, X₁, X₂) → l3(X₀, X₁+X₀+1, X₂)
t₅: l3(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₁ ≤ X₂ ∧ 0 ≤ X₀
t₃: l3(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₂+1 ≤ X₁
t₄: l3(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₀+1 ≤ 0
t₆: l4(X₀, X₁, X₂) → l1(X₀, X₁, X₂) :|: D+1 ≤ 0
t₇: l4(X₀, X₁, X₂) → l1(X₀, X₁, X₂) :|: 1 ≤ D
t₈: l4(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₁₁: l5(X₀, X₁, X₂) → l7(X₀, X₁, X₂)
t₁: l6(X₀, X₁, X₂) → l3(X₀, X₂, X₁) :|: 0 ≤ X₀
t₂: l6(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₀+1 ≤ 0

Preprocessing

Found invariant X₁ ≤ X₂ ∧ 0 ≤ X₀ for location l2

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

Found invariant X₁ ≤ X₂ ∧ 0 ≤ X₀ for location l4

Found invariant 0 ≤ X₀ for location l3

Cut unsatisfiable transition t₄: l3→l5

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)
t₉: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂-X₀-1) :|: X₁ ≤ X₂ ∧ 0 ≤ X₀
t₁₀: l2(X₀, X₁, X₂) → l3(X₀, X₁+X₀+1, X₂) :|: X₁ ≤ X₂ ∧ 0 ≤ X₀
t₅: l3(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₁ ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀
t₃: l3(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₂+1 ≤ X₁ ∧ 0 ≤ X₀
t₆: l4(X₀, X₁, X₂) → l1(X₀, X₁, X₂) :|: D+1 ≤ 0 ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀
t₇: l4(X₀, X₁, X₂) → l1(X₀, X₁, X₂) :|: 1 ≤ D ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀
t₈: l4(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₁ ≤ X₂ ∧ 0 ≤ X₀
t₁₁: l5(X₀, X₁, X₂) → l7(X₀, X₁, X₂)
t₁: l6(X₀, X₁, X₂) → l3(X₀, X₂, X₁) :|: 0 ≤ X₀
t₂: l6(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₀+1 ≤ 0

MPRF for transition t₅: l3(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₁ ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁+X₂+1 {O(n)}

MPRF for transition t₆: l4(X₀, X₁, X₂) → l1(X₀, X₁, X₂) :|: D+1 ≤ 0 ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁+X₂+1 {O(n)}

MPRF for transition t₇: l4(X₀, X₁, X₂) → l1(X₀, X₁, X₂) :|: 1 ≤ D ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁+X₂+1 {O(n)}

MPRF for transition t₈: l4(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₁ ≤ X₂ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁+X₂+1 {O(n)}

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

new bound:

X₁+X₂+1 {O(n)}

MPRF for transition t₁₀: l2(X₀, X₁, X₂) → l3(X₀, X₁+X₀+1, X₂) :|: X₁ ≤ X₂ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁+X₂+1 {O(n)}

All Bounds

Timebounds

Overall timebound:6⋅X₁+6⋅X₂+11 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₅: X₁+X₂+1 {O(n)}
t₆: X₁+X₂+1 {O(n)}
t₇: X₁+X₂+1 {O(n)}
t₈: X₁+X₂+1 {O(n)}
t₉: X₁+X₂+1 {O(n)}
t₁₀: X₁+X₂+1 {O(n)}
t₁₁: 1 {O(1)}

Costbounds

Overall costbound: 6⋅X₁+6⋅X₂+11 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₅: X₁+X₂+1 {O(n)}
t₆: X₁+X₂+1 {O(n)}
t₇: X₁+X₂+1 {O(n)}
t₈: X₁+X₂+1 {O(n)}
t₉: X₁+X₂+1 {O(n)}
t₁₀: X₁+X₂+1 {O(n)}
t₁₁: 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: X₂ {O(n)}
t₁, X₂: X₁ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₃, X₀: 3⋅X₀ {O(n)}
t₃, X₁: 2⋅X₀⋅X₁+2⋅X₀⋅X₂+2⋅X₁+4⋅X₀+5⋅X₂+2 {O(n^2)}
t₃, X₂: 4⋅X₀⋅X₁+4⋅X₀⋅X₂+2⋅X₂+5⋅X₁+8⋅X₀+2 {O(n^2)}
t₅, X₀: X₀ {O(n)}
t₅, X₁: X₀⋅X₁+X₀⋅X₂+2⋅X₀+2⋅X₂+X₁+1 {O(n^2)}
t₅, X₂: 2⋅X₀⋅X₁+2⋅X₀⋅X₂+2⋅X₁+4⋅X₀+X₂+1 {O(n^2)}
t₆, X₀: X₀ {O(n)}
t₆, X₁: X₀⋅X₁+X₀⋅X₂+2⋅X₀+2⋅X₂+X₁+1 {O(n^2)}
t₆, X₂: 2⋅X₀⋅X₁+2⋅X₀⋅X₂+2⋅X₁+4⋅X₀+X₂+1 {O(n^2)}
t₇, X₀: X₀ {O(n)}
t₇, X₁: X₀⋅X₁+X₀⋅X₂+2⋅X₀+2⋅X₂+X₁+1 {O(n^2)}
t₇, X₂: 2⋅X₀⋅X₁+2⋅X₀⋅X₂+2⋅X₁+4⋅X₀+X₂+1 {O(n^2)}
t₈, X₀: X₀ {O(n)}
t₈, X₁: X₀⋅X₁+X₀⋅X₂+2⋅X₀+2⋅X₂+X₁+1 {O(n^2)}
t₈, X₂: 2⋅X₀⋅X₁+2⋅X₀⋅X₂+2⋅X₁+4⋅X₀+X₂+1 {O(n^2)}
t₉, X₀: X₀ {O(n)}
t₉, X₁: X₀⋅X₁+X₀⋅X₂+2⋅X₀+2⋅X₂+X₁+1 {O(n^2)}
t₉, X₂: 2⋅X₀⋅X₁+2⋅X₀⋅X₂+2⋅X₁+4⋅X₀+X₂+1 {O(n^2)}
t₁₀, X₀: X₀ {O(n)}
t₁₀, X₁: X₀⋅X₁+X₀⋅X₂+2⋅X₀+2⋅X₂+X₁+1 {O(n^2)}
t₁₀, X₂: 2⋅X₀⋅X₁+2⋅X₀⋅X₂+2⋅X₁+4⋅X₀+X₂+1 {O(n^2)}
t₁₁, X₀: 4⋅X₀ {O(n)}
t₁₁, X₁: 2⋅X₀⋅X₁+2⋅X₀⋅X₂+3⋅X₁+4⋅X₀+5⋅X₂+2 {O(n^2)}
t₁₁, X₂: 4⋅X₀⋅X₁+4⋅X₀⋅X₂+3⋅X₂+5⋅X₁+8⋅X₀+2 {O(n^2)}