KoAT2 Proof Output

Initial Problem

Start: f9
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆, X₂₇, X₂₈, X₂₉, X₃₀, X₃₁, X₃₂, X₃₃, X₃₄, X₃₅, X₃₆, X₃₇
Temp_Vars: A2, B2, C2, D2, E2, M1, N1, O1, P1, Q1, R1, S1, T1, U1, V1, W1, X1, Y1, Z1
Locations: f1, f10, f12, f13, f16, f7, f8, f9
Transitions:
t₃: f1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆, X₂₇, X₂₈, X₂₉, X₃₀, X₃₁, X₃₂, X₃₃, X₃₄, X₃₅, X₃₆, X₃₇) → f1(1+X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₈, M1, X₁₈, O1, X₀, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆, X₂₇, X₂₈, X₂₉, X₃₀, X₃₁, X₃₂, X₃₃, X₃₄, X₃₅, X₃₆, X₃₇) :|: 1+X₀ ≤ X₁₆ ∧ 0 ≤ X₀
t₄: f1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆, X₂₇, X₂₈, X₂₉, X₃₀, X₃₁, X₃₂, X₃₃, X₃₄, X₃₅, X₃₆, X₃₇) → f16(X₆, 0, M1, X₁₇, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₇, X₁₃, X₁₄, X₁₅, O1, P1, S1, N1, X₂₀, X₂₁, Q1, T1, U1, R1, X₂₆, X₂₇, X₂₈, X₂₉, X₃₀, X₃₁, X₃₂, X₃₃, X₃₄, X₃₅, X₃₆, X₃₇) :|: 2 ≤ M1 ∧ M1 ≤ R1 ∧ M1 ≤ X₆ ∧ 0 ≤ X₀ ∧ X₁₆ ≤ X₀ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
t₀: f12(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆, X₂₇, X₂₈, X₂₉, X₃₀, X₃₁, X₃₂, X₃₃, X₃₄, X₃₅, X₃₆, X₃₇) → f16(X₀, 1, M1, O1, P1, 1+X₆, X₆, Q1, X₆, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆, X₂₇, X₂₈, X₂₉, X₃₀, X₃₁, X₃₂, X₃₃, X₃₄, X₃₅, X₃₆, X₃₇) :|: X₁ ≤ 1 ∧ 1 ≤ X₁ ∧ 2 ≤ M1 ∧ M1 ≤ N1 ∧ 0 ≤ X₀
t₁: f13(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆, X₂₇, X₂₈, X₂₉, X₃₀, X₃₁, X₃₂, X₃₃, X₃₄, X₃₅, X₃₆, X₃₇) → f16(X₀, X₁, M1, O1, X₄, X₅, X₆, X₇, X₈, P1, Q1, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆, X₂₇, X₂₈, X₂₉, X₃₀, X₃₁, X₃₂, X₃₃, X₃₄, X₃₅, X₃₆, X₃₇) :|: 2 ≤ M1 ∧ 0 ≤ X₈
t₉: f13(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆, X₂₇, X₂₈, X₂₉, X₃₀, X₃₁, X₃₂, X₃₃, X₃₄, X₃₅, X₃₆, X₃₇) → f8(X₀, 1+X₃₃, M1, X₃, X₄, X₅, X₆, X₇, 0, X₉, X₁₀, X₁₁, 0, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₃₃, 0, X₃, 0, X₃, X₃, X₃, X₃₃, X₃₄, X₃₅, X₃₆, X₃₇) :|: X₁ ≤ 1 ∧ 1 ≤ X₁ ∧ 2 ≤ M1 ∧ 2 ≤ O1 ∧ 0 ≤ X₈ ∧ X₈ ≤ 0 ∧ 0 ≤ X₁₂ ∧ X₁₂ ≤ 0
t₂: f16(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆, X₂₇, X₂₈, X₂₉, X₃₀, X₃₁, X₃₂, X₃₃, X₃₄, X₃₅, X₃₆, X₃₇) → f16(X₀, 1+X₁, M1, O1, P1, X₅, X₆-1, X₇, X₈, X₉, X₁₀, X₁₂, X₁₂, Q1, 1+X₁, X₆-1, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆, X₂₇, X₂₈, X₂₉, X₃₀, X₃₁, X₃₂, X₃₃, X₃₄, X₃₅, X₃₆, X₃₇) :|: 2 ≤ M1 ∧ 0 ≤ X₁ ∧ 0 ≤ X₆
t₁₀: f16(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆, X₂₇, X₂₈, X₂₉, X₃₀, X₃₁, X₃₂, X₃₃, X₃₄, X₃₅, X₃₆, X₃₇) → f8(X₀, 1+X₃₃, M1, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, 0, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₃₃, 0, X₃, 0, X₃, X₃, X₃, X₃₃, X₃₄, X₃₅, X₃₆, X₃₇) :|: 2 ≤ M1 ∧ 2 ≤ O1 ∧ 0 ≤ X₁ ∧ 0 ≤ X₆ ∧ 0 ≤ X₁₂ ∧ X₁₂ ≤ 0
t₆: f7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆, X₂₇, X₂₈, X₂₉, X₃₀, X₃₁, X₃₂, X₃₃, X₃₄, X₃₅, X₃₆, X₃₇) → f10(X₀, X₁, M1, T1, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, U1, X₂₅, X₂₆, N1, O1, P1, Q1, R1, S1, X₃₃, X₃₄, X₃₅, X₃₆, X₃₇) :|: 2 ≤ M1 ∧ 0 ≤ X₂₆ ∧ X₃₂ ≤ X₂₇ ∧ X₂₇ ≤ X₃₂
t₅: f7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆, X₂₇, X₂₈, X₂₉, X₃₀, X₃₁, X₃₂, X₃₃, X₃₄, X₃₅, X₃₆, X₃₇) → f8(X₀, X₁, M1, O1, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, 0, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆, 0, O1, 0, O1, X₃₂, X₃₂, X₃₃, X₃₄, X₃₅, X₃₆, X₃₇) :|: 2 ≤ M1 ∧ 0 ≤ X₂₆ ∧ 0 ≤ X₂₇ ∧ X₂₇ ≤ 0
t₈: f8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆, X₂₇, X₂₈, X₂₉, X₃₀, X₃₁, X₃₂, X₃₃, X₃₄, X₃₅, X₃₆, X₃₇) → f10(X₀, X₁, M1, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, T1, X₂₅, X₂₆, N1, O1, P1, Q1, U1, S1, X₃₃, X₃₄, X₃₅, X₃₆, X₃₇) :|: 2 ≤ M1 ∧ X₃₂ ≤ X₂₇ ∧ X₂₇ ≤ X₃₂ ∧ 0 ≤ X₃₃
t₇: f8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆, X₂₇, X₂₈, X₂₉, X₃₀, X₃₁, X₃₂, X₃₃, X₃₄, X₃₅, X₃₆, X₃₇) → f8(X₀, X₁, M1, O1, P1, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, 0, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆, 0, O1, 0, O1, X₃₂, X₃₂, X₃₃-1, X₃₃-1, X₃₅, X₃₆, X₃₇) :|: 2 ≤ M1 ∧ 0 ≤ X₂₇ ∧ X₂₇ ≤ 0 ∧ 0 ≤ X₃₃
t₁₁: f9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆, X₂₇, X₂₈, X₂₉, X₃₀, X₃₁, X₃₂, X₃₃, X₃₄, X₃₅, X₃₆, X₃₇) → f1(2, X₁, M1, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, M1, P1, Q1, P1, X₂₀, X₂₁, P1, X₂₃, X₂₄, X₂₅, X₂₆, X₂₇, X₂₈, X₂₉, X₃₀, X₃₁, X₃₂, X₃₃, X₃₄, O1, N1, 2) :|: 2 ≤ M1
t₁₂: f9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆, X₂₇, X₂₈, X₂₉, X₃₀, X₃₁, X₃₂, X₃₃, X₃₄, X₃₅, X₃₆, X₃₇) → f10(T1, X₁, M1, 0, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, 0, X₁₃, X₁₄, X₁₅, R1, Y1, B2, A2, X₂₀, X₂₁, Z1, C2, D2, X₂₅, X₂₆, N1, O1, P1, Q1, E2, S1, X₃₃, X₃₄, U1, X₃₆, X₃₇) :|: M1 ≤ 0 ∧ V1 ≤ 0 ∧ W1 ≤ 0 ∧ X1 ≤ 0
t₁₃: f9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆, X₂₇, X₂₈, X₂₉, X₃₀, X₃₁, X₃₂, X₃₃, X₃₄, X₃₅, X₃₆, X₃₇) → f10(T1, X₁, 1, S1, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, 0, X₁₃, X₁₄, X₁₅, R1, Y1, B2, A2, X₂₀, X₂₁, Z1, C2, D2, X₂₅, X₂₆, Q1, M1, O1, P1, E2, N1, X₃₃, X₃₄, U1, X₃₆, X₃₇) :|: 0 ≤ X₁₈ ∧ X₁₈ ≤ 0

Preprocessing

Cut unreachable locations [f12; f13; f7] from the program graph

Eliminate variables [A2; C2; D2; E2; U1; Z1; X₂; X₄; X₅; X₇; X₈; X₉; X₁₀; X₁₁; X₁₃; X₁₄; X₁₅; X₁₉; X₂₀; X₂₁; X₂₂; X₂₃; X₂₄; X₂₅; X₂₆; X₂₈; X₂₉; X₃₀; X₃₁; X₃₄; X₃₅; X₃₆; X₃₇] that do not contribute to the problem

Found invariant X₄ ≤ 0 ∧ 0 ≤ X₄ for location f10

Found invariant X₃ ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location f16

Found invariant X₈ ≤ 0 ∧ X₈ ≤ X₄ ∧ X₄+X₈ ≤ 0 ∧ X₈ ≤ X₃ ∧ 2+X₈ ≤ X₀ ∧ 0 ≤ X₈ ∧ 0 ≤ X₄+X₈ ∧ X₄ ≤ X₈ ∧ 0 ≤ X₃+X₈ ∧ 2 ≤ X₀+X₈ ∧ X₄ ≤ 0 ∧ X₄ ≤ X₃ ∧ 2+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 2 ≤ X₀+X₄ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 1+X₁₀ ≤ X₁ ∧ 2 ≤ X₀ for location f8

Found invariant 2 ≤ X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 2 ≤ X₀ for location f1

Problem after Preprocessing

Start: f9
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀
Temp_Vars: B2, M1, N1, O1, P1, Q1, R1, S1, T1, V1, W1, X1, Y1
Locations: f1, f10, f16, f8, f9
Transitions:
t₂₂: f1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f1(1+X₀, X₁, X₂, X₃, X₄, X₅, X₇, M1, X₈, X₉, X₁₀) :|: 1+X₀ ≤ X₅ ∧ 0 ≤ X₀ ∧ 2 ≤ X₀ ∧ 2 ≤ X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅
t₂₃: f1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f16(X₃, 0, X₆, X₃, X₆, O1, P1, S1, X₈, X₉, X₁₀) :|: 2 ≤ M1 ∧ M1 ≤ R1 ∧ M1 ≤ X₃ ∧ 0 ≤ X₀ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 2 ≤ X₀ ∧ 2 ≤ X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅
t₂₄: f16(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f16(X₀, 1+X₁, O1, X₃-1, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: 2 ≤ M1 ∧ 0 ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ 1+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₁+X₃ ∧ X₃ ≤ X₀
t₂₅: f16(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f8(X₀, 1+X₁₀, X₂, X₃, 0, X₅, X₆, X₇, 0, X₂, X₁₀) :|: 2 ≤ M1 ∧ 2 ≤ O1 ∧ 0 ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₄ ∧ X₄ ≤ 0 ∧ 0 ≤ 1+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₁+X₃ ∧ X₃ ≤ X₀
t₂₆: f8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, N1, S1, X₁₀) :|: 2 ≤ M1 ∧ X₉ ≤ X₈ ∧ X₈ ≤ X₉ ∧ 0 ≤ X₁₀ ∧ 1+X₁₀ ≤ X₁ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₀+X₄ ∧ 2+X₄ ≤ X₀ ∧ 2 ≤ X₀+X₈ ∧ 2+X₈ ≤ X₀ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₈ ∧ X₈ ≤ X₃ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₈ ∧ X₈ ≤ X₄ ∧ X₄ ≤ 0 ∧ X₄ ≤ X₈ ∧ X₄+X₈ ≤ 0 ∧ 0 ≤ X₈ ∧ X₈ ≤ 0
t₂₇: f8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f8(X₀, X₁, O1, X₃, 0, X₅, X₆, X₇, 0, X₉, X₁₀-1) :|: 2 ≤ M1 ∧ 0 ≤ X₈ ∧ X₈ ≤ 0 ∧ 0 ≤ X₁₀ ∧ 1+X₁₀ ≤ X₁ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₀+X₄ ∧ 2+X₄ ≤ X₀ ∧ 2 ≤ X₀+X₈ ∧ 2+X₈ ≤ X₀ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₈ ∧ X₈ ≤ X₃ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₈ ∧ X₈ ≤ X₄ ∧ X₄ ≤ 0 ∧ X₄ ≤ X₈ ∧ X₄+X₈ ≤ 0
t₂₈: f9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f1(2, X₁, X₂, X₃, X₄, M1, P1, Q1, X₈, X₉, X₁₀) :|: 2 ≤ M1
t₂₉: f9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f10(T1, X₁, 0, X₃, 0, R1, Y1, B2, N1, S1, X₁₀) :|: M1 ≤ 0 ∧ V1 ≤ 0 ∧ W1 ≤ 0 ∧ X1 ≤ 0
t₃₀: f9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f10(T1, X₁, S1, X₃, 0, R1, Y1, B2, Q1, N1, X₁₀) :|: 0 ≤ X₇ ∧ X₇ ≤ 0

Found invariant X₄ ≤ 0 ∧ 0 ≤ X₄ for location f10

Found invariant X₃ ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location f16

Found invariant 2 ≤ X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₀ ≤ 2 ∧ 2 ≤ X₀ for location f1

Found invariant 3 ≤ X₅ ∧ 6 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 3 ≤ X₀ for location f1_v1

MPRF for transition t₂₄: f16(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f16(X₀, 1+X₁, O1, X₃-1, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: 2 ≤ M1 ∧ 0 ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ 1+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₁+X₃ ∧ X₃ ≤ X₀ of depth 1:

new bound:

2⋅X₃+1 {O(n)}

MPRF:

• f16: [1+X₃]

MPRF for transition t₂₇: f8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f8(X₀, X₁, O1, X₃, 0, X₅, X₆, X₇, 0, X₉, X₁₀-1) :|: 2 ≤ M1 ∧ 0 ≤ X₈ ∧ X₈ ≤ 0 ∧ 0 ≤ X₁₀ ∧ 1+X₁₀ ≤ X₁ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₀+X₄ ∧ 2+X₄ ≤ X₀ ∧ 2 ≤ X₀+X₈ ∧ 2+X₈ ≤ X₀ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₈ ∧ X₈ ≤ X₃ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₈ ∧ X₈ ≤ X₄ ∧ X₄ ≤ 0 ∧ X₄ ≤ X₈ ∧ X₄+X₈ ≤ 0 of depth 1:

new bound:

4⋅X₁₀+1 {O(n)}

MPRF:

• f8: [1+X₁₀]

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₂₂: inf {Infinity}
t₂₃: 1 {O(1)}
t₂₄: 2⋅X₃+1 {O(n)}
t₂₅: 1 {O(1)}
t₂₆: 1 {O(1)}
t₂₇: 4⋅X₁₀+1 {O(n)}
t₂₈: 1 {O(1)}
t₂₉: 1 {O(1)}
t₃₀: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₂₂: inf {Infinity}
t₂₃: 1 {O(1)}
t₂₄: 2⋅X₃+1 {O(n)}
t₂₅: 1 {O(1)}
t₂₆: 1 {O(1)}
t₂₇: 4⋅X₁₀+1 {O(n)}
t₂₈: 1 {O(1)}
t₂₉: 1 {O(1)}
t₃₀: 1 {O(1)}

Sizebounds

t₂₂, X₁: X₁ {O(n)}
t₂₂, X₂: X₂ {O(n)}
t₂₂, X₃: X₃ {O(n)}
t₂₂, X₄: X₄ {O(n)}
t₂₂, X₈: X₈ {O(n)}
t₂₂, X₉: X₉ {O(n)}
t₂₂, X₁₀: X₁₀ {O(n)}
t₂₃, X₀: 2⋅X₃ {O(n)}
t₂₃, X₁: 0 {O(1)}
t₂₃, X₃: 2⋅X₃ {O(n)}
t₂₃, X₈: 2⋅X₈ {O(n)}
t₂₃, X₉: 2⋅X₉ {O(n)}
t₂₃, X₁₀: 2⋅X₁₀ {O(n)}
t₂₄, X₀: 2⋅X₃ {O(n)}
t₂₄, X₁: 2⋅X₃+1 {O(n)}
t₂₄, X₃: 2⋅X₃+1 {O(n)}
t₂₄, X₈: 2⋅X₈ {O(n)}
t₂₄, X₉: 2⋅X₉ {O(n)}
t₂₄, X₁₀: 2⋅X₁₀ {O(n)}
t₂₅, X₀: 4⋅X₃ {O(n)}
t₂₅, X₁: 4⋅X₁₀+2 {O(n)}
t₂₅, X₃: 4⋅X₃+1 {O(n)}
t₂₅, X₄: 0 {O(1)}
t₂₅, X₈: 0 {O(1)}
t₂₅, X₁₀: 4⋅X₁₀ {O(n)}
t₂₆, X₀: 8⋅X₃ {O(n)}
t₂₆, X₁: 8⋅X₁₀+4 {O(n)}
t₂₆, X₃: 8⋅X₃+2 {O(n)}
t₂₆, X₄: 0 {O(1)}
t₂₆, X₁₀: 8⋅X₁₀+1 {O(n)}
t₂₇, X₀: 4⋅X₃ {O(n)}
t₂₇, X₁: 4⋅X₁₀+2 {O(n)}
t₂₇, X₃: 4⋅X₃+1 {O(n)}
t₂₇, X₄: 0 {O(1)}
t₂₇, X₈: 0 {O(1)}
t₂₇, X₁₀: 4⋅X₁₀+1 {O(n)}
t₂₈, X₀: 2 {O(1)}
t₂₈, X₁: X₁ {O(n)}
t₂₈, X₂: X₂ {O(n)}
t₂₈, X₃: X₃ {O(n)}
t₂₈, X₄: X₄ {O(n)}
t₂₈, X₈: X₈ {O(n)}
t₂₈, X₉: X₉ {O(n)}
t₂₈, X₁₀: X₁₀ {O(n)}
t₂₉, X₁: X₁ {O(n)}
t₂₉, X₂: 0 {O(1)}
t₂₉, X₃: X₃ {O(n)}
t₂₉, X₄: 0 {O(1)}
t₂₉, X₁₀: X₁₀ {O(n)}
t₃₀, X₁: X₁ {O(n)}
t₃₀, X₃: X₃ {O(n)}
t₃₀, X₄: 0 {O(1)}
t₃₀, X₁₀: X₁₀ {O(n)}