KoAT2 Proof Output

Initial Problem

Start: f0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars: H, I
Locations: f0, f13, f17, f32, f5
Transitions:
t₀: f0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f5(0, X₁, X₂, X₃, X₄, X₅, X₆)
t₁₁: f17(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f13(X₀, X₁, X₂, X₁, X₄, X₁, H)
t₂: f17(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f17(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₃: f17(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f17(X₀, 1+X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+H ≤ 0
t₄: f17(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f17(X₀, 1+X₁, X₂, X₃, X₄, X₅, X₆)
t₉: f17(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f32(X₀, X₁, X₁, X₁, X₄, X₁, H) :|: 1+I ≤ 0
t₁₀: f17(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f32(X₀, X₁, X₁, X₁, X₄, X₁, H)
t₈: f32(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f13(X₀, X₁, X₂, X₂, X₂, X₅, X₆)
t₅: f32(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f32(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₆: f32(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f32(X₀, X₁, 1+X₂, X₃, X₄, X₅, X₆) :|: 1+H ≤ 0
t₇: f32(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f32(X₀, X₁, 1+X₂, X₃, X₄, X₅, X₆)
t₁₂: f5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f13(X₀, X₁, X₂, X₀-2, X₄, X₅, X₆) :|: 100 ≤ X₀
t₁₃: f5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f17(X₀, X₀-2, X₂, X₀-2, X₄, X₅, X₆) :|: 1+X₀ ≤ 0 ∧ 100 ≤ X₀
t₁: f5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f5(1+X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₀ ≤ 99

Preprocessing

Cut unsatisfiable transition [t₁₃: f5→f17]

Cut unreachable locations [f17; f32] from the program graph

Eliminate variables [X₁; X₂; X₃; X₄; X₅; X₆] that do not contribute to the problem

Found invariant X₀ ≤ 100 ∧ 100 ≤ X₀ for location f13

Found invariant X₀ ≤ 100 ∧ 0 ≤ X₀ for location f5

Problem after Preprocessing

Start: f0
Program_Vars: X₀
Temp_Vars:
Locations: f0, f13, f5
Transitions:
t₃₇: f0(X₀) → f5(0)
t₃₈: f5(X₀) → f13(X₀) :|: 100 ≤ X₀ ∧ X₀ ≤ 100 ∧ 0 ≤ X₀
t₃₉: f5(X₀) → f5(1+X₀) :|: X₀ ≤ 99 ∧ X₀ ≤ 100 ∧ 0 ≤ X₀

MPRF for transition t₃₉: f5(X₀) → f5(1+X₀) :|: X₀ ≤ 99 ∧ X₀ ≤ 100 ∧ 0 ≤ X₀ of depth 1:

new bound:

101 {O(1)}

MPRF:

• f5: [101-X₀]

All Bounds

Timebounds

Overall timebound:103 {O(1)}
t₃₇: 1 {O(1)}
t₃₈: 1 {O(1)}
t₃₉: 101 {O(1)}

Costbounds

Overall costbound: 103 {O(1)}
t₃₇: 1 {O(1)}
t₃₈: 1 {O(1)}
t₃₉: 101 {O(1)}

Sizebounds

t₃₇, X₀: 0 {O(1)}
t₃₈, X₀: 100 {O(1)}
t₃₉, X₀: 100 {O(1)}