Initial Problem
Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁) → l2(X₀, X₁)
t₂: l1(X₀, X₁) → l3(X₀, X₁) :|: 0 < X₀
t₃: l1(X₀, X₁) → l4(X₀, X₁) :|: X₀ ≤ 0
t₁: l2(X₀, X₁) → l1(X₁, X₁)
t₄: l3(X₀, X₁) → l1(X₀+1, X₁) :|: 3 < X₀
t₅: l3(X₀, X₁) → l1(X₀-1, X₁) :|: X₀ ≤ 3
t₆: l4(X₀, X₁) → l5(X₀, X₁)
Preprocessing
Found invariant X₀ ≤ 0 for location l5
Found invariant X₀ ≤ 0 for location l4
Found invariant 1 ≤ X₀ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁) → l2(X₀, X₁)
t₂: l1(X₀, X₁) → l3(X₀, X₁) :|: 0 < X₀
t₃: l1(X₀, X₁) → l4(X₀, X₁) :|: X₀ ≤ 0
t₁: l2(X₀, X₁) → l1(X₁, X₁)
t₄: l3(X₀, X₁) → l1(X₀+1, X₁) :|: 3 < X₀ ∧ 1 ≤ X₀
t₅: l3(X₀, X₁) → l1(X₀-1, X₁) :|: X₀ ≤ 3 ∧ 1 ≤ X₀
t₆: l4(X₀, X₁) → l5(X₀, X₁) :|: X₀ ≤ 0
Chain transitions t₅: l3→l1 and t₃: l1→l4 to t₅₂: l3→l4
Chain transitions t₄: l3→l1 and t₃: l1→l4 to t₅₃: l3→l4
Chain transitions t₄: l3→l1 and t₂: l1→l3 to t₅₄: l3→l3
Chain transitions t₅: l3→l1 and t₂: l1→l3 to t₅₅: l3→l3
Chain transitions t₁: l2→l1 and t₂: l1→l3 to t₅₆: l2→l3
Chain transitions t₁: l2→l1 and t₃: l1→l4 to t₅₇: l2→l4
Analysing control-flow refined program
Cut unsatisfiable transition t₅₃: l3→l4
Found invariant X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l5
Found invariant X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l4
Found invariant 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l3
MPRF for transition t₅₅: l3(X₀, X₁) -{2}> l3(X₀-1, X₁) :|: X₀ ≤ 3 ∧ 1 < X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁ {O(n)}
CFR did not improve the program. Rolling back
CFR did not improve the program. Rolling back
Analysing control-flow refined program
Cut unsatisfiable transition t₁₄₃: n_l1___4→l4
Found invariant 1+X₁ ≤ X₀ ∧ 4 ≤ X₁ ∧ 9 ≤ X₀+X₁ ∧ 5 ≤ X₀ for location n_l1___4
Found invariant X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l3___5
Found invariant X₁ ≤ 3 ∧ X₁ ≤ 3+X₀ ∧ X₀+X₁ ≤ 5 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 2 ∧ 0 ≤ X₀ for location n_l1___3
Found invariant X₁ ≤ 3 ∧ X₁ ≤ 3+X₀ ∧ X₀+X₁ ≤ 3 ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l5
Found invariant 1+X₁ ≤ X₀ ∧ 4 ≤ X₁ ∧ 9 ≤ X₀+X₁ ∧ 5 ≤ X₀ for location n_l3___2
Found invariant X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l1
Found invariant X₁ ≤ 3 ∧ X₁ ≤ 3+X₀ ∧ X₀+X₁ ≤ 3 ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l4
Found invariant X₁ ≤ 3 ∧ X₁ ≤ 2+X₀ ∧ X₀+X₁ ≤ 5 ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 2 ∧ 1 ≤ X₀ for location n_l3___1
MPRF for transition t₁₂₉: n_l1___3(X₀, X₁) → n_l3___1(X₀, X₁) :|: X₀ ≤ 3 ∧ 0 ≤ X₀ ∧ X₀ ≤ 2 ∧ 0 < X₀ ∧ X₁ ≤ 3 ∧ X₁ ≤ 3+X₀ ∧ X₀+X₁ ≤ 5 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 2 ∧ 0 ≤ X₀ of depth 1:
new bound:
3 {O(1)}
MPRF for transition t₁₃₂: n_l3___1(X₀, X₁) → n_l1___3(X₀-1, X₁) :|: X₀ ≤ 2 ∧ 0 < X₀ ∧ X₀ ≤ 3 ∧ 1 ≤ X₀ ∧ X₁ ≤ 3 ∧ X₁ ≤ 2+X₀ ∧ X₀+X₁ ≤ 5 ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 2 ∧ 1 ≤ X₀ of depth 1:
new bound:
2 {O(1)}
CFR did not improve the program. Rolling back
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:inf {Infinity}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: inf {Infinity}
t₃: 1 {O(1)}
t₄: inf {Infinity}
t₅: inf {Infinity}
t₆: 1 {O(1)}
Costbounds
Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: inf {Infinity}
t₃: 1 {O(1)}
t₄: inf {Infinity}
t₅: inf {Infinity}
t₆: 1 {O(1)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₁, X₀: X₁ {O(n)}
t₁, X₁: X₁ {O(n)}
t₂, X₁: X₁ {O(n)}
t₃, X₀: X₁+2 {O(n)}
t₃, X₁: 2⋅X₁ {O(n)}
t₄, X₁: X₁ {O(n)}
t₅, X₀: 2 {O(1)}
t₅, X₁: X₁ {O(n)}
t₆, X₀: X₁+2 {O(n)}
t₆, X₁: 2⋅X₁ {O(n)}