Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars: D
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂) → l8(X₀, X₁, X₂)
t₈: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₂+1 ≤ X₁
t₇: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₁ ≤ X₂
t₉: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: D+1 ≤ 0
t₁₀: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: 1 ≤ D
t₁₁: l2(X₀, X₁, X₂) → l4(X₀, X₁, X₂)
t₁₂: l3(X₀, X₁, X₂) → l1(X₀, X₁, X₂+1)
t₁₃: l4(X₀, X₁, X₂) → l6(X₂+1, X₁, X₂)
t₄: l5(X₀, X₁, X₂) → l1(X₀, X₁, X₀) :|: D+1 ≤ 0
t₅: l5(X₀, X₁, X₂) → l1(X₀, X₁, X₀) :|: 1 ≤ D
t₆: l5(X₀, X₁, X₂) → l7(X₀, X₁, X₂)
t₃: l6(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₀+1 ≤ X₁
t₂: l6(X₀, X₁, X₂) → l7(X₀, X₁, X₂) :|: X₁ ≤ X₀
t₁₄: l7(X₀, X₁, X₂) → l9(X₀, X₁, X₂)
t₁: l8(X₀, X₁, X₂) → l6(0, X₁, X₂)
Preprocessing
Found invariant 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l2
Found invariant 0 ≤ X₀ for location l6
Found invariant 0 ≤ X₀ for location l7
Found invariant 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l5
Found invariant X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l1
Found invariant X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l4
Found invariant 0 ≤ X₀ for location l9
Found invariant 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ 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, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂) → l8(X₀, X₁, X₂)
t₈: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₂+1 ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₇: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₉: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: D+1 ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₁₀: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: 1 ≤ D ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₁₁: l2(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₁₂: l3(X₀, X₁, X₂) → l1(X₀, X₁, X₂+1) :|: 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₁₃: l4(X₀, X₁, X₂) → l6(X₂+1, X₁, X₂) :|: X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₄: l5(X₀, X₁, X₂) → l1(X₀, X₁, X₀) :|: D+1 ≤ 0 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₅: l5(X₀, X₁, X₂) → l1(X₀, X₁, X₀) :|: 1 ≤ D ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₆: l5(X₀, X₁, X₂) → l7(X₀, X₁, X₂) :|: 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₃: l6(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₀+1 ≤ X₁ ∧ 0 ≤ X₀
t₂: l6(X₀, X₁, X₂) → l7(X₀, X₁, X₂) :|: X₁ ≤ X₀ ∧ 0 ≤ X₀
t₁₄: l7(X₀, X₁, X₂) → l9(X₀, X₁, X₂) :|: 0 ≤ X₀
t₁: l8(X₀, X₁, X₂) → l6(0, X₁, X₂)
MPRF for transition t₃: l6(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₀+1 ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₁ {O(n)}
MPRF for transition t₄: l5(X₀, X₁, X₂) → l1(X₀, X₁, X₀) :|: D+1 ≤ 0 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₁ {O(n)}
MPRF for transition t₅: l5(X₀, X₁, X₂) → l1(X₀, X₁, X₀) :|: 1 ≤ D ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₁+1 {O(n)}
MPRF for transition t₇: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₁+2 {O(n)}
MPRF for transition t₈: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₂+1 ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₁+1 {O(n)}
MPRF for transition t₉: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: D+1 ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₁ {O(n)}
MPRF for transition t₁₀: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: 1 ≤ D ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₁ {O(n)}
MPRF for transition t₁₁: l2(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₁ {O(n)}
MPRF for transition t₁₂: l3(X₀, X₁, X₂) → l1(X₀, X₁, X₂+1) :|: 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₁ {O(n)}
MPRF for transition t₁₃: l4(X₀, X₁, X₂) → l6(X₂+1, X₁, X₂) :|: X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₁+1 {O(n)}
All Bounds
Timebounds
Overall timebound:10⋅X₁+10 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: X₁ {O(n)}
t₄: X₁ {O(n)}
t₅: X₁+1 {O(n)}
t₆: 1 {O(1)}
t₇: X₁+2 {O(n)}
t₈: X₁+1 {O(n)}
t₉: X₁ {O(n)}
t₁₀: X₁ {O(n)}
t₁₁: X₁ {O(n)}
t₁₂: X₁ {O(n)}
t₁₃: X₁+1 {O(n)}
t₁₄: 1 {O(1)}
Costbounds
Overall costbound: 10⋅X₁+10 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: X₁ {O(n)}
t₄: X₁ {O(n)}
t₅: X₁+1 {O(n)}
t₆: 1 {O(1)}
t₇: X₁+2 {O(n)}
t₈: X₁+1 {O(n)}
t₉: X₁ {O(n)}
t₁₀: X₁ {O(n)}
t₁₁: X₁ {O(n)}
t₁₂: X₁ {O(n)}
t₁₃: X₁+1 {O(n)}
t₁₄: 1 {O(1)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₁, X₀: 0 {O(1)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₂, X₀: 2⋅X₁+1 {O(n)}
t₂, X₁: 2⋅X₁ {O(n)}
t₂, X₂: 4⋅X₁+X₂+2 {O(n)}
t₃, X₀: 2⋅X₁+1 {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: 4⋅X₁+X₂+2 {O(n)}
t₄, X₀: 2⋅X₁+1 {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: 2⋅X₁+1 {O(n)}
t₅, X₀: 2⋅X₁+1 {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: 2⋅X₁+1 {O(n)}
t₆, X₀: 2⋅X₁+1 {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: 4⋅X₁+X₂+2 {O(n)}
t₇, X₀: 4⋅X₁+2 {O(n)}
t₇, X₁: X₁ {O(n)}
t₇, X₂: 2⋅X₁+1 {O(n)}
t₈, X₀: 4⋅X₁+2 {O(n)}
t₈, X₁: X₁ {O(n)}
t₈, X₂: 2⋅X₁+1 {O(n)}
t₉, X₀: 4⋅X₁+2 {O(n)}
t₉, X₁: X₁ {O(n)}
t₉, X₂: 2⋅X₁+1 {O(n)}
t₁₀, X₀: 4⋅X₁+2 {O(n)}
t₁₀, X₁: X₁ {O(n)}
t₁₀, X₂: 2⋅X₁+1 {O(n)}
t₁₁, X₀: 4⋅X₁+2 {O(n)}
t₁₁, X₁: X₁ {O(n)}
t₁₁, X₂: 2⋅X₁+1 {O(n)}
t₁₂, X₀: 4⋅X₁+2 {O(n)}
t₁₂, X₁: X₁ {O(n)}
t₁₂, X₂: 2⋅X₁+1 {O(n)}
t₁₃, X₀: 2⋅X₁+1 {O(n)}
t₁₃, X₁: X₁ {O(n)}
t₁₃, X₂: 4⋅X₁+2 {O(n)}
t₁₄, X₀: 4⋅X₁+2 {O(n)}
t₁₄, X₁: 3⋅X₁ {O(n)}
t₁₄, X₂: 2⋅X₂+8⋅X₁+4 {O(n)}