Initial Problem
Start: l0
Program_Vars: X₀, X₁
Temp_Vars: C
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁) → l1(0, X₁)
t₁: l1(X₀, X₁) → l1(C+1, X₁) :|: X₀ ≤ 5 ∧ 5 ≤ X₀
t₂: l1(X₀, X₁) → l1(X₀+1, X₀) :|: X₀ ≤ 9 ∧ X₀ ≤ 4
t₃: l1(X₀, X₁) → l1(X₀+1, X₀) :|: X₀ ≤ 9 ∧ 6 ≤ X₀
t₄: l1(X₀, X₁) → l2(X₀, X₁) :|: 10 ≤ X₀
Preprocessing
Eliminate variables {X₁} that do not contribute to the problem
Found invariant 10 ≤ X₀ for location l2
Problem after Preprocessing
Start: l0
Program_Vars: X₀
Temp_Vars: C
Locations: l0, l1, l2
Transitions:
t₁₅: l0(X₀) → l1(0)
t₁₆: l1(X₀) → l1(C+1) :|: X₀ ≤ 5 ∧ 5 ≤ X₀
t₁₇: l1(X₀) → l1(X₀+1) :|: X₀ ≤ 9 ∧ X₀ ≤ 4
t₁₈: l1(X₀) → l1(X₀+1) :|: X₀ ≤ 9 ∧ 6 ≤ X₀
t₁₉: l1(X₀) → l2(X₀) :|: 10 ≤ X₀
Analysing control-flow refined program
Cut unsatisfiable transition t₁₉: l1→l2
Cut unsatisfiable transition t₁₄₅: n_l1___3→l2
Cut unsatisfiable transition t₁₄₆: n_l1___4→l2
Found invariant 10 ≤ X₀ for location l2
Found invariant X₀ ≤ 1 ∧ 1 ≤ X₀ for location n_l1___4
Found invariant X₀ ≤ 5 for location n_l1___3
Found invariant X₀ ≤ 0 ∧ 0 ≤ X₀ for location l1
Found invariant X₀ ≤ 10 ∧ 7 ≤ X₀ for location n_l1___1
Found invariant 10 ≤ X₀ for location l2
Found invariant X₀ ≤ 1 ∧ 1 ≤ X₀ for location n_l1___4
Found invariant X₀ ≤ 5 for location n_l1___3
Found invariant X₀ ≤ 0 ∧ 0 ≤ X₀ for location l1
Found invariant X₀ ≤ 10 ∧ 7 ≤ X₀ for location n_l1___1
Time-Bound by TWN-Loops:
TWN-Loops: t₁₂₃ 114 {O(1)}
TWN-Loops:
entry: t₁₂₄: n_l1___2(X₀) → n_l1___1(X₀+1) :|: 6 ≤ X₀ ∧ X₀ ≤ 9
results in twn-loop: twn:Inv: [X₀ ≤ 10 ∧ 7 ≤ X₀] , (X₀) -> (X₀+1) :|: 6 ≤ X₀ ∧ 7 ≤ X₀ ∧ X₀ ≤ 10 ∧ 6 ≤ X₀ ∧ X₀ ≤ 9
order: [X₀]
closed-form:
X₀: X₀ + [[n != 0]] * n^1
Termination: true
Formula:
1 < 0 ∧ 0 < 1
∨ 0 < 1 ∧ 1 < 0 ∧ 7 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 0 < 1 ∧ 1 < 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 7 ≤ X₀ ∧ X₀ ≤ 7
∨ 1 < 0 ∧ X₀ < 10 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 1
∨ 1 < 0 ∧ 0 < 1 ∧ X₀ < 10 ∧ 7 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 1 < 0 ∧ 0 < 1 ∧ X₀ < 10 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 7 ≤ X₀ ∧ X₀ ≤ 7
∨ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 10 ∧ 10 ≤ X₀ ∧ 0 < 1
∨ 1 < 0 ∧ 0 < 1 ∧ X₀ ≤ 10 ∧ 10 ≤ X₀ ∧ 7 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 1 < 0 ∧ 0 < 1 ∧ X₀ ≤ 10 ∧ 10 ≤ X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 7 ≤ X₀ ∧ X₀ ≤ 7
∨ 6 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 < 0 ∧ 0 < 1
∨ 6 < X₀ ∧ 1 < 0 ∧ 7 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 6 < X₀ ∧ 1 < 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 7 ≤ X₀ ∧ X₀ ≤ 7
∨ 1 < 0 ∧ 6 < X₀ ∧ X₀ < 10 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 1
∨ 1 < 0 ∧ 6 < X₀ ∧ X₀ < 10 ∧ 7 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 1 < 0 ∧ 6 < X₀ ∧ X₀ < 10 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 7 ≤ X₀ ∧ X₀ ≤ 7
∨ 1 < 0 ∧ 6 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 10 ∧ 10 ≤ X₀ ∧ 0 < 1
∨ 1 < 0 ∧ 6 < X₀ ∧ X₀ ≤ 10 ∧ 10 ≤ X₀ ∧ 7 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 1 < 0 ∧ 6 < X₀ ∧ X₀ ≤ 10 ∧ 10 ≤ X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 7 ≤ X₀ ∧ X₀ ≤ 7
∨ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 6 ≤ X₀ ∧ X₀ ≤ 6 ∧ 1 < 0 ∧ 0 < 1
∨ 6 ≤ X₀ ∧ X₀ ≤ 6 ∧ 1 < 0 ∧ 7 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 6 ≤ X₀ ∧ X₀ ≤ 6 ∧ 1 < 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 7 ≤ X₀ ∧ X₀ ≤ 7
∨ 1 < 0 ∧ 6 ≤ X₀ ∧ X₀ ≤ 6 ∧ X₀ < 10 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 1
∨ 1 < 0 ∧ 6 ≤ X₀ ∧ X₀ ≤ 6 ∧ X₀ < 10 ∧ 7 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 1 < 0 ∧ 6 ≤ X₀ ∧ X₀ ≤ 6 ∧ X₀ < 10 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 7 ≤ X₀ ∧ X₀ ≤ 7
∨ 1 < 0 ∧ 6 ≤ X₀ ∧ X₀ ≤ 6 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 10 ∧ 10 ≤ X₀ ∧ 0 < 1
∨ 1 < 0 ∧ 6 ≤ X₀ ∧ X₀ ≤ 6 ∧ X₀ ≤ 10 ∧ 10 ≤ X₀ ∧ 7 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 1 < 0 ∧ 6 ≤ X₀ ∧ X₀ ≤ 6 ∧ X₀ ≤ 10 ∧ 10 ≤ X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 7 ≤ X₀ ∧ X₀ ≤ 7
∨ X₀ < 9 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0 ∧ 0 < 1
∨ X₀ < 9 ∧ 0 < 1 ∧ 1 < 0 ∧ 7 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ < 9 ∧ 0 < 1 ∧ 1 < 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 7 ≤ X₀ ∧ X₀ ≤ 7
∨ X₀ < 9 ∧ X₀ < 10 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 1
∨ X₀ < 9 ∧ 0 < 1 ∧ X₀ < 10 ∧ 7 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ < 9 ∧ 0 < 1 ∧ X₀ < 10 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 7 ≤ X₀ ∧ X₀ ≤ 7
∨ X₀ < 9 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 10 ∧ 10 ≤ X₀ ∧ 0 < 1
∨ X₀ < 9 ∧ 0 < 1 ∧ X₀ ≤ 10 ∧ 10 ≤ X₀ ∧ 7 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ < 9 ∧ 0 < 1 ∧ X₀ ≤ 10 ∧ 10 ≤ X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 7 ≤ X₀ ∧ X₀ ≤ 7
∨ X₀ < 9 ∧ 6 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 < 0 ∧ 0 < 1
∨ X₀ < 9 ∧ 6 < X₀ ∧ 1 < 0 ∧ 7 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ < 9 ∧ 6 < X₀ ∧ 1 < 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 7 ≤ X₀ ∧ X₀ ≤ 7
∨ X₀ < 9 ∧ 6 < X₀ ∧ X₀ < 10 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 1
∨ X₀ < 9 ∧ 6 < X₀ ∧ X₀ < 10 ∧ 7 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ < 9 ∧ 6 < X₀ ∧ X₀ < 10 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 7 ≤ X₀ ∧ X₀ ≤ 7
∨ X₀ < 9 ∧ 6 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 10 ∧ 10 ≤ X₀ ∧ 0 < 1
∨ X₀ < 9 ∧ 6 < X₀ ∧ X₀ ≤ 10 ∧ 10 ≤ X₀ ∧ 7 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ < 9 ∧ 6 < X₀ ∧ X₀ ≤ 10 ∧ 10 ≤ X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 7 ≤ X₀ ∧ X₀ ≤ 7
∨ X₀ < 9 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 6 ≤ X₀ ∧ X₀ ≤ 6 ∧ 1 < 0 ∧ 0 < 1
∨ X₀ < 9 ∧ 6 ≤ X₀ ∧ X₀ ≤ 6 ∧ 1 < 0 ∧ 7 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ < 9 ∧ 6 ≤ X₀ ∧ X₀ ≤ 6 ∧ 1 < 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 7 ≤ X₀ ∧ X₀ ≤ 7
∨ X₀ < 9 ∧ 6 ≤ X₀ ∧ X₀ ≤ 6 ∧ X₀ < 10 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 1
∨ X₀ < 9 ∧ 6 ≤ X₀ ∧ X₀ ≤ 6 ∧ X₀ < 10 ∧ 7 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ < 9 ∧ 6 ≤ X₀ ∧ X₀ ≤ 6 ∧ X₀ < 10 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 7 ≤ X₀ ∧ X₀ ≤ 7
∨ X₀ < 9 ∧ 6 ≤ X₀ ∧ X₀ ≤ 6 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 10 ∧ 10 ≤ X₀ ∧ 0 < 1
∨ X₀ < 9 ∧ 6 ≤ X₀ ∧ X₀ ≤ 6 ∧ X₀ ≤ 10 ∧ 10 ≤ X₀ ∧ 7 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ < 9 ∧ 6 ≤ X₀ ∧ X₀ ≤ 6 ∧ X₀ ≤ 10 ∧ 10 ≤ X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 7 ≤ X₀ ∧ X₀ ≤ 7
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 9 ∧ 9 ≤ X₀ ∧ 1 < 0 ∧ 0 < 1
∨ X₀ ≤ 9 ∧ 9 ≤ X₀ ∧ 0 < 1 ∧ 1 < 0 ∧ 7 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ ≤ 9 ∧ 9 ≤ X₀ ∧ 0 < 1 ∧ 1 < 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 7 ≤ X₀ ∧ X₀ ≤ 7
∨ X₀ ≤ 9 ∧ 9 ≤ X₀ ∧ X₀ < 10 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 1
∨ X₀ ≤ 9 ∧ 9 ≤ X₀ ∧ 0 < 1 ∧ X₀ < 10 ∧ 7 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ ≤ 9 ∧ 9 ≤ X₀ ∧ 0 < 1 ∧ X₀ < 10 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 7 ≤ X₀ ∧ X₀ ≤ 7
∨ X₀ ≤ 9 ∧ 9 ≤ X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 10 ∧ 10 ≤ X₀ ∧ 0 < 1
∨ X₀ ≤ 9 ∧ 9 ≤ X₀ ∧ 0 < 1 ∧ X₀ ≤ 10 ∧ 10 ≤ X₀ ∧ 7 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ ≤ 9 ∧ 9 ≤ X₀ ∧ 0 < 1 ∧ X₀ ≤ 10 ∧ 10 ≤ X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 7 ≤ X₀ ∧ X₀ ≤ 7
∨ X₀ ≤ 9 ∧ 9 ≤ X₀ ∧ 6 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 < 0 ∧ 0 < 1
∨ X₀ ≤ 9 ∧ 9 ≤ X₀ ∧ 6 < X₀ ∧ 1 < 0 ∧ 7 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ ≤ 9 ∧ 9 ≤ X₀ ∧ 6 < X₀ ∧ 1 < 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 7 ≤ X₀ ∧ X₀ ≤ 7
∨ X₀ ≤ 9 ∧ 9 ≤ X₀ ∧ 6 < X₀ ∧ X₀ < 10 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 1
∨ X₀ ≤ 9 ∧ 9 ≤ X₀ ∧ 6 < X₀ ∧ X₀ < 10 ∧ 7 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ ≤ 9 ∧ 9 ≤ X₀ ∧ 6 < X₀ ∧ X₀ < 10 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 7 ≤ X₀ ∧ X₀ ≤ 7
∨ X₀ ≤ 9 ∧ 9 ≤ X₀ ∧ 6 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 10 ∧ 10 ≤ X₀ ∧ 0 < 1
∨ X₀ ≤ 9 ∧ 9 ≤ X₀ ∧ 6 < X₀ ∧ X₀ ≤ 10 ∧ 10 ≤ X₀ ∧ 7 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ ≤ 9 ∧ 9 ≤ X₀ ∧ 6 < X₀ ∧ X₀ ≤ 10 ∧ 10 ≤ X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 7 ≤ X₀ ∧ X₀ ≤ 7
∨ X₀ ≤ 9 ∧ 9 ≤ X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 6 ≤ X₀ ∧ X₀ ≤ 6 ∧ 1 < 0 ∧ 0 < 1
∨ X₀ ≤ 9 ∧ 9 ≤ X₀ ∧ 6 ≤ X₀ ∧ X₀ ≤ 6 ∧ 1 < 0 ∧ 7 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ ≤ 9 ∧ 9 ≤ X₀ ∧ 6 ≤ X₀ ∧ X₀ ≤ 6 ∧ 1 < 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 7 ≤ X₀ ∧ X₀ ≤ 7
∨ X₀ ≤ 9 ∧ 9 ≤ X₀ ∧ 6 ≤ X₀ ∧ X₀ ≤ 6 ∧ X₀ < 10 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 1
∨ X₀ ≤ 9 ∧ 9 ≤ X₀ ∧ 6 ≤ X₀ ∧ X₀ ≤ 6 ∧ X₀ < 10 ∧ 7 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ ≤ 9 ∧ 9 ≤ X₀ ∧ 6 ≤ X₀ ∧ X₀ ≤ 6 ∧ X₀ < 10 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 7 ≤ X₀ ∧ X₀ ≤ 7
∨ X₀ ≤ 9 ∧ 9 ≤ X₀ ∧ 6 ≤ X₀ ∧ X₀ ≤ 6 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 10 ∧ 10 ≤ X₀ ∧ 0 < 1
∨ X₀ ≤ 9 ∧ 9 ≤ X₀ ∧ 6 ≤ X₀ ∧ X₀ ≤ 6 ∧ X₀ ≤ 10 ∧ 10 ≤ X₀ ∧ 7 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ ≤ 9 ∧ 9 ≤ X₀ ∧ 6 ≤ X₀ ∧ X₀ ≤ 6 ∧ X₀ ≤ 10 ∧ 10 ≤ X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 7 ≤ X₀ ∧ X₀ ≤ 7
Stabilization-Threshold for: X₀ ≤ 9
alphas_abs: 9
M: 0
N: 1
Bound: 20 {O(1)}
Stabilization-Threshold for: 6 ≤ X₀
alphas_abs: 6+X₀
M: 0
N: 1
Bound: 2⋅X₀+14 {O(n)}
Stabilization-Threshold for: X₀ ≤ 10
alphas_abs: 10
M: 0
N: 1
Bound: 22 {O(1)}
Stabilization-Threshold for: 7 ≤ X₀
alphas_abs: 7+X₀
M: 0
N: 1
Bound: 2⋅X₀+16 {O(n)}
relevant size-bounds w.r.t. t₁₂₄:
X₀: 10 {O(1)}
Runtime-bound of t₁₂₄: 1 {O(1)}
Results in: 114 {O(1)}
114 {O(1)}
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:inf {Infinity}
t₁₅: 1 {O(1)}
t₁₆: inf {Infinity}
t₁₇: inf {Infinity}
t₁₈: inf {Infinity}
t₁₉: 1 {O(1)}
Costbounds
Overall costbound: inf {Infinity}
t₁₅: 1 {O(1)}
t₁₆: inf {Infinity}
t₁₇: inf {Infinity}
t₁₈: inf {Infinity}
t₁₉: 1 {O(1)}
Sizebounds
t₁₅, X₀: 0 {O(1)}
t₁₈, X₀: 10 {O(1)}