KoAT2 Proof Output

Initial Problem

Start: f2
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
Temp_Vars: A2, B1, B2, C1, C2, D1, D2, E1, E2, F1, F2, G1, G2, H1, H2, I1, I2, J1, J2, K1, K2, L1, L2, M1, N1, O1, P1, Q1, R1, S1, T1, U1, V1, W1, X1, Y1, Z1
Locations: f1, f101, f110, f119, f132, f17, f2, f27, f31, f34, f46, f5, f50, f53, f69, f8, f80, f92
Transitions:
t₂₃: f101(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) → f101(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, B1, X₁₁, X₁₂, X₁₃, X₁₄, C1, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, 1+X₂₆) :|: 1+X₂₆ ≤ X₂
t₃₀: f101(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) → f110(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) :|: X₂ ≤ X₂₆
t₂₄: f110(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) → f110(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, B1, X₁₁, X₁₂, X₁₃, X₁₄, C1, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, 1+X₂₆) :|: X₂₆ ≤ X₀
t₂₉: f110(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) → f119(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) :|: 1+X₀ ≤ X₂₆
t₂₅: f119(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) → f119(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, B1, X₁₁, X₁₂, X₁₃, X₁₄, C1, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, 1+X₂₆) :|: X₂₆ ≤ X₀
t₂₈: f119(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) → f53(X₀, X₁, 1+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) :|: 1+X₀ ≤ X₂₆
t₂₆: f132(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) → f132(X₀, 1+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) :|: X₁ ≤ X₀
t₂₇: f132(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) → f27(X₀, X₁, X₂, X₃, 1+X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) :|: 1+X₀ ≤ X₁
t₃: f17(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) → f17(X₀, 1+X₁, X₂, B1, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) :|: X₁ ≤ X₀
t₃₉: f17(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) → f27(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) :|: 1+X₀ ≤ X₁
t₀: f2(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) → f5(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)
t₃₈: f27(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) → 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) :|: 51 ≤ X₄
t₄: f27(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) → f31(X₀, X₁, X₂, X₃, X₄, 0, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) :|: X₄ ≤ 50
t₃₇: f31(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) → f1(X₀, X₁, X₂, X₃, X₄, 0, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) :|: X₀ ≤ X₁ ∧ 0 ≤ X₅ ∧ X₅ ≤ 0
t₅: f31(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) → f34(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) :|: 1+X₁ ≤ X₀
t₃₅: f31(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) → f46(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) :|: 1+X₅ ≤ 0 ∧ X₀ ≤ X₁
t₃₆: f31(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) → f46(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) :|: 1 ≤ X₅ ∧ X₀ ≤ X₁
t₃₄: f34(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) → f31(X₀, 1+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) :|: 1+X₀ ≤ X₂
t₆: f34(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) → f34(X₀, X₁, 1+X₂, X₃, X₄, B1+X₅, B1, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) :|: X₂ ≤ X₀
t₇: f46(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) → f50(X₀, X₁, X₂, X₃, X₄, X₅, X₆, B1, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) :|: X₄ ≤ 3
t₈: f46(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) → f50(X₀, X₁, X₂, X₃, X₄, X₅, X₆, 0, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) :|: 4 ≤ X₄
t₄₁: f5(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) → f17(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) :|: 1+X₀ ≤ X₁
t₁: f5(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) → 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) :|: X₁ ≤ X₀
t₃₃: f50(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) → f132(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) :|: X₀ ≤ X₁
t₉: f50(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) → f53(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) :|: 1+X₁ ≤ X₀
t₃₂: f53(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) → f50(X₀, 1+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) :|: 1+X₀ ≤ X₂
t₁₁: f53(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) → f53(X₀, X₁, 1+X₂, X₃, X₄, X₅, X₆, X₇, X₈, B1, 100⋅B1, C1, 100⋅B1+C1, D1, 100⋅B1+D1, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) :|: 5 ≤ X₄ ∧ X₂ ≤ X₀
t₁₂: f53(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) → f69(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, C1, B1, 100⋅B1, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) :|: X₄ ≤ 4 ∧ X₂ ≤ X₀
t₁₃: f53(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) → f69(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, F1, B1, 100⋅B1, C1, 100⋅B1+C1, D1, E1, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) :|: 1+100⋅B1+D1 ≤ E1 ∧ 5 ≤ X₄ ∧ X₂ ≤ X₀
t₁₄: f53(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) → f69(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, F1, B1, 100⋅B1, C1, 100⋅B1+C1, D1, E1, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) :|: 1+E1 ≤ 100⋅B1+D1 ∧ 5 ≤ X₄ ∧ X₂ ≤ X₀
t₁₅: f53(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) → f69(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, E1, B1, 100⋅B1, C1, D1, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) :|: 1+100⋅B1+C1 ≤ D1 ∧ 5 ≤ X₄ ∧ X₂ ≤ X₀
t₁₆: f53(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) → f69(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, E1, B1, 100⋅B1, C1, D1, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) :|: 1+D1 ≤ 100⋅B1+C1 ∧ 5 ≤ X₄ ∧ X₂ ≤ X₀
t₁₀: f69(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) → f53(X₀, X₁, 1+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) :|: X₈ ≤ X₇
t₁₇: f69(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) → f80(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, B1-C1, D1, E1, F1, K1, G1, I1, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) :|: G1*H1+H1*I1 ≤ 1 ∧ G1*J1+I1*J1 ≤ 1 ∧ 1+D1+X₁₀ ≤ E1 ∧ 1+X₇ ≤ X₈ ∧ 2 ≤ G1*H1+H1+H1*I1 ∧ 2 ≤ G1*J1+I1*J1+J1 ∧ H1 ≤ F1 ∧ F1 ≤ J1
t₁₈: f69(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) → f80(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, B1-C1, D1, E1, F1, K1, G1, I1, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) :|: G1*H1+H1*I1 ≤ 1 ∧ G1*J1+I1*J1 ≤ 1 ∧ 1+E1 ≤ D1+X₁₀ ∧ 1+X₇ ≤ X₈ ∧ 2 ≤ G1*H1+H1+H1*I1 ∧ 2 ≤ G1*J1+I1*J1+J1 ∧ H1 ≤ F1 ∧ F1 ≤ J1
t₂₀: f69(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) → f92(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, B1, C1, C1+X₁₀, D1, X₁₉, X₂₀, X₂₁, E1, F1, K1, G1, X₂₆) :|: D2*E1 ≤ 1 ∧ E1*K2 ≤ 1 ∧ E1*L2 ≤ 1 ∧ E1*X1 ≤ 1 ∧ 1+L1 ≤ A2+A2*E1*L1 ∧ 1+B2*C2+Z1 ≤ A2*C2+C2 ∧ 1+N1 ≤ B2+B2*E1*N1 ∧ 1+C2 ≤ D2*E2+2⋅E2 ∧ 1+H1 ≤ E1*H1*I1+I1 ∧ 1+H1 ≤ E1*H1*P1+P1 ∧ 1+H1 ≤ E1*H1*T1+T1 ∧ 1+H1 ≤ E1*H1*Z1+Z1 ∧ 1+L1 ≤ E1*J1*L1+J1 ∧ 1+L1 ≤ E1*L1*Q1+Q1 ∧ 1+L1 ≤ E1*L1*U1+U1 ∧ 1+N1 ≤ E1*M1*N1+M1 ∧ 1+N1 ≤ E1*N1*R1+R1 ∧ 1+N1 ≤ E1*N1*V1+V1 ∧ 1+F2*N1+H1 ≤ F2+F2*L1 ∧ 1+G2*N1+H1 ≤ G2+G2*L1 ∧ 1+H1*H2+H2*I2*N1 ≤ H2*I2*L1+I2 ∧ 1+H1*H2+H2*J2*N1 ≤ H2*J2*L1+J2 ∧ 1+I1+M1*O1 ≤ J1*O1+O1 ∧ 1+P1+R1*S1 ≤ Q1*S1+S1 ∧ 1+T1+V1*W1 ≤ U1*W1+W1 ∧ 1+W1 ≤ X1*Y1+2⋅Y1 ∧ 1+X₇ ≤ X₈ ∧ 2 ≤ D2+D2*E1 ∧ 2 ≤ E1*K2+K2 ∧ 2 ≤ E1*L2+L2 ∧ 2 ≤ E1*X1+X1 ∧ A2*C2 ≤ B2*C2+Z1 ∧ A2*E1*L1 ≤ L1 ∧ J2 ≤ B1 ∧ B1 ≤ I2 ∧ B2*E1*N1 ≤ N1 ∧ D2*E2+E2 ≤ C2 ∧ G2 ≤ D1 ∧ D1 ≤ F2 ∧ E1*H1*I1 ≤ H1 ∧ E1*H1*P1 ≤ H1 ∧ E1*H1*T1 ≤ H1 ∧ E1*H1*Z1 ≤ H1 ∧ E1*J1*L1 ≤ L1 ∧ E1*L1*Q1 ≤ L1 ∧ E1*L1*U1 ≤ L1 ∧ E1*M1*N1 ≤ N1 ∧ E1*N1*R1 ≤ N1 ∧ E1*N1*V1 ≤ N1 ∧ E2 ≤ G1 ∧ K2 ≤ F1 ∧ F1 ≤ L2 ∧ F2*L1 ≤ F2*N1+H1 ∧ G1 ≤ Y1 ∧ G2*L1 ≤ G2*N1+H1 ∧ H2*I2*L1 ≤ H1*H2+H2*I2*N1 ∧ H2*J2*L1 ≤ H1*H2+H2*J2*N1 ∧ J1*O1 ≤ I1+M1*O1 ∧ S1 ≤ K1 ∧ K1 ≤ O1 ∧ Q1*S1 ≤ P1+R1*S1 ∧ U1*W1 ≤ T1+V1*W1 ∧ X1*Y1+Y1 ≤ W1
t₄₀: 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) → f5(X₀, 1+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) :|: 1+X₀ ≤ X₂
t₂: 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) → f8(X₀, X₁, 1+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) :|: X₂ ≤ X₀
t₁₉: f80(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) → f92(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, B1*X₁₈, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, C1, D1, E1, F1, X₂₆) :|: C1*H1 ≤ 1 ∧ C1*I1 ≤ 1 ∧ C1*L1 ≤ 1 ∧ C1*O1 ≤ 1 ∧ 1+X₁₈ ≤ C1*G1*X₁₈+G1 ∧ 1+X₁₈ ≤ C1*J1*X₁₈+J1 ∧ 1+X₁₈ ≤ C1*K1*X₁₈+K1 ∧ 1+X₁₈ ≤ C1*N1*X₁₈+N1 ∧ 1+J1 ≤ L1*M1+2⋅M1 ∧ 1+N1 ≤ O1*P1+2⋅P1 ∧ 2 ≤ C1*H1+H1 ∧ 2 ≤ C1*I1+I1 ∧ 2 ≤ C1*L1+L1 ∧ 2 ≤ C1*O1+O1 ∧ C1*G1*X₁₈ ≤ X₁₈ ∧ C1*J1*X₁₈ ≤ X₁₈ ∧ C1*K1*X₁₈ ≤ X₁₈ ∧ C1*N1*X₁₈ ≤ X₁₈ ∧ I1 ≤ D1 ∧ D1 ≤ H1 ∧ G1 ≤ E1 ∧ E1 ≤ K1 ∧ P1 ≤ F1 ∧ F1 ≤ M1 ∧ L1*M1+M1 ≤ J1 ∧ O1*P1+P1 ≤ N1 ∧ 0 ≤ X₁₉
t₂₁: f80(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) → f92(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, -B1*X₁₈, X₁₆, X₁₇, -X₁₈, X₁₉, X₂₀, X₂₁, C1, D1, -E1*X₁₈, F1, X₂₆) :|: C1*E1 ≤ 1 ∧ C1*G1 ≤ 1 ∧ C1*H1 ≤ 1 ∧ C1*I1 ≤ 1 ∧ C1*K1 ≤ 1 ∧ C1*L1 ≤ 1 ∧ C1*M1 ≤ 1 ∧ 1 ≤ H1*J1+I1*X₁₈+2⋅J1 ∧ 1 ≤ L1*X₁₈+M1*N1+2⋅N1 ∧ 1+X₁₉ ≤ 0 ∧ 2 ≤ C1*E1+E1 ∧ 2 ≤ C1*G1+G1 ∧ 2 ≤ C1*H1+H1 ∧ 2 ≤ C1*I1+I1 ∧ 2 ≤ C1*K1+K1 ∧ 2 ≤ C1*L1+L1 ∧ 2 ≤ C1*M1+M1 ∧ K1 ≤ D1 ∧ D1 ≤ G1 ∧ J1 ≤ F1 ∧ F1 ≤ N1 ∧ H1*J1+I1*X₁₈+J1 ≤ 0 ∧ L1*X₁₈+M1*N1+N1 ≤ 0
t₃₁: f92(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) → f101(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) :|: X₁ ≤ X₂₆
t₂₂: f92(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) → f92(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, B1, X₁₁, X₁₂, X₁₃, X₁₄, C1, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, 1+X₂₆) :|: 1+X₂₆ ≤ X₁

Preprocessing

Cut unsatisfiable transition [t₃: f17→f17; t₂₅: f119→f119]

Eliminate variables [X₃; X₆; X₉; X₁₁; X₁₂; X₁₃; X₁₄; X₁₅; X₁₆; X₁₇; X₂₀; X₂₁; X₂₂; X₂₃; X₂₄; X₂₅] that do not contribute to the problem

Found invariant 1 ≤ 0 for location f80

Found invariant 1 ≤ 0 for location f69

Found invariant 1 ≤ 0 for location f101

Found invariant 1 ≤ 0 for location f110

Found invariant 1+X₀ ≤ X₁ for location f1

Found invariant 1 ≤ 0 for location f50

Found invariant 1 ≤ 0 for location f119

Found invariant X₄ ≤ 0 ∧ X₃+X₄ ≤ 50 ∧ 0 ≤ X₄ ∧ X₃ ≤ 50+X₄ ∧ X₃ ≤ 50 ∧ 1+X₀ ≤ X₁ for location f31

Found invariant 1 ≤ 0 for location f92

Found invariant 1 ≤ 0 for location f132

Found invariant 1+X₀ ≤ X₁ for location f17

Found invariant 1+X₀ ≤ X₁ for location f27

Found invariant X₁ ≤ X₀ for location f8

Found invariant 1 ≤ 0 for location f46

Found invariant 1 ≤ 0 for location f53

Found invariant 1 ≤ 0 for location f34

Cut unsatisfiable transition [t₈₉: f101→f101; t₉₀: f101→f110; t₉₁: f110→f110; t₉₂: f110→f119; t₉₃: f119→f53; t₉₄: f132→f132; t₉₅: f132→f27; t₁₀₁: f31→f34; t₁₀₂: f31→f46; t₁₀₃: f31→f46; t₁₀₄: f34→f31; t₁₀₅: f34→f34; t₁₀₆: f46→f50; t₁₀₇: f46→f50; t₁₁₀: f50→f132; t₁₁₁: f50→f53; t₁₁₂: f53→f50; t₁₁₃: f53→f53; t₁₁₄: f53→f69; t₁₁₅: f53→f69; t₁₁₆: f53→f69; t₁₁₇: f53→f69; t₁₁₈: f53→f69; t₁₁₉: f69→f53; t₁₂₀: f69→f80; t₁₂₁: f69→f80; t₁₂₂: f69→f92; t₁₂₅: f80→f92; t₁₂₆: f80→f92; t₁₂₇: f92→f101; t₁₂₈: f92→f92]

Cut unreachable locations [f101; f110; f119; f132; f34; f46; f50; f53; f69; f80; f92] from the program graph

Eliminate variables [X₅; X₆; X₇; X₈; X₉; X₁₀] that do not contribute to the problem

Problem after Preprocessing

Start: f2
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: f1, f17, f2, f27, f31, f5, f8
Transitions:
t₂₃₂: f17(X₀, X₁, X₂, X₃, X₄) → f27(X₀, X₁, X₂, X₃, X₄) :|: 1+X₀ ≤ X₁
t₂₃₃: f2(X₀, X₁, X₂, X₃, X₄) → f5(X₀, X₁, X₂, X₃, X₄)
t₂₃₄: f27(X₀, X₁, X₂, X₃, X₄) → f1(X₀, X₁, X₂, X₃, X₄) :|: 51 ≤ X₃
t₂₃₅: f27(X₀, X₁, X₂, X₃, X₄) → f31(X₀, X₁, X₂, X₃, 0) :|: X₃ ≤ 50
t₂₃₆: f31(X₀, X₁, X₂, X₃, X₄) → f1(X₀, X₁, X₂, X₃, 0) :|: X₀ ≤ X₁ ∧ 0 ≤ X₄ ∧ X₄ ≤ 0
t₂₃₇: f5(X₀, X₁, X₂, X₃, X₄) → f17(X₀, X₁, X₂, X₃, X₄) :|: 1+X₀ ≤ X₁
t₂₃₈: f5(X₀, X₁, X₂, X₃, X₄) → f8(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ X₀
t₂₃₉: f8(X₀, X₁, X₂, X₃, X₄) → f5(X₀, 1+X₁, X₂, X₃, X₄) :|: 1+X₀ ≤ X₂
t₂₄₀: f8(X₀, X₁, X₂, X₃, X₄) → f8(X₀, X₁, 1+X₂, X₃, X₄) :|: X₂ ≤ X₀

MPRF for transition t₂₃₈: f5(X₀, X₁, X₂, X₃, X₄) → f8(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ X₀ of depth 1:

new bound:

X₀+X₁+1 {O(n)}

MPRF:

• f5: [1+X₀-X₁]
• f8: [X₀-X₁]

MPRF for transition t₂₄₀: f8(X₀, X₁, X₂, X₃, X₄) → f8(X₀, X₁, 1+X₂, X₃, X₄) :|: X₂ ≤ X₀ of depth 1:

new bound:

X₀+X₂+1 {O(n)}

MPRF:

• f5: [1+X₀-X₂]
• f8: [1+X₀-X₂]

knowledge_propagation leads to new time bound 2⋅X₀+X₁+X₂+2 {O(n)} for transition t₂₃₉: f8(X₀, X₁, X₂, X₃, X₄) → f5(X₀, 1+X₁, X₂, X₃, X₄) :|: 1+X₀ ≤ X₂

All Bounds

Timebounds

Overall timebound:2⋅X₁+2⋅X₂+4⋅X₀+10 {O(n)}
t₂₃₂: 1 {O(1)}
t₂₃₃: 1 {O(1)}
t₂₃₄: 1 {O(1)}
t₂₃₅: 1 {O(1)}
t₂₃₆: 1 {O(1)}
t₂₃₇: 1 {O(1)}
t₂₃₈: X₀+X₁+1 {O(n)}
t₂₃₉: 2⋅X₀+X₁+X₂+2 {O(n)}
t₂₄₀: X₀+X₂+1 {O(n)}

Costbounds

Overall costbound: 2⋅X₁+2⋅X₂+4⋅X₀+10 {O(n)}
t₂₃₂: 1 {O(1)}
t₂₃₃: 1 {O(1)}
t₂₃₄: 1 {O(1)}
t₂₃₅: 1 {O(1)}
t₂₃₆: 1 {O(1)}
t₂₃₇: 1 {O(1)}
t₂₃₈: X₀+X₁+1 {O(n)}
t₂₃₉: 2⋅X₀+X₁+X₂+2 {O(n)}
t₂₄₀: X₀+X₂+1 {O(n)}

Sizebounds

t₂₃₂, X₀: 2⋅X₀ {O(n)}
t₂₃₂, X₁: 2⋅X₀+3⋅X₁+X₂+2 {O(n)}
t₂₃₂, X₂: 3⋅X₂+X₀+1 {O(n)}
t₂₃₂, X₃: 2⋅X₃ {O(n)}
t₂₃₂, X₄: 2⋅X₄ {O(n)}
t₂₃₃, X₀: X₀ {O(n)}
t₂₃₃, X₁: X₁ {O(n)}
t₂₃₃, X₂: X₂ {O(n)}
t₂₃₃, X₃: X₃ {O(n)}
t₂₃₃, X₄: X₄ {O(n)}
t₂₃₄, X₀: 2⋅X₀ {O(n)}
t₂₃₄, X₁: 2⋅X₀+3⋅X₁+X₂+2 {O(n)}
t₂₃₄, X₂: 3⋅X₂+X₀+1 {O(n)}
t₂₃₄, X₃: 2⋅X₃ {O(n)}
t₂₃₄, X₄: 2⋅X₄ {O(n)}
t₂₃₅, X₀: 2⋅X₀ {O(n)}
t₂₃₅, X₁: 2⋅X₀+3⋅X₁+X₂+2 {O(n)}
t₂₃₅, X₂: 3⋅X₂+X₀+1 {O(n)}
t₂₃₅, X₃: 2⋅X₃ {O(n)}
t₂₃₅, X₄: 0 {O(1)}
t₂₃₆, X₀: 2⋅X₀ {O(n)}
t₂₃₆, X₁: 2⋅X₀+3⋅X₁+X₂+2 {O(n)}
t₂₃₆, X₂: 3⋅X₂+X₀+1 {O(n)}
t₂₃₆, X₃: 2⋅X₃ {O(n)}
t₂₃₆, X₄: 0 {O(1)}
t₂₃₇, X₀: 2⋅X₀ {O(n)}
t₂₃₇, X₁: 2⋅X₀+3⋅X₁+X₂+2 {O(n)}
t₂₃₇, X₂: 3⋅X₂+X₀+1 {O(n)}
t₂₃₇, X₃: 2⋅X₃ {O(n)}
t₂₃₇, X₄: 2⋅X₄ {O(n)}
t₂₃₈, X₀: X₀ {O(n)}
t₂₃₈, X₁: 2⋅X₀+2⋅X₁+X₂+2 {O(n)}
t₂₃₈, X₂: 2⋅X₂+X₀+1 {O(n)}
t₂₃₈, X₃: X₃ {O(n)}
t₂₃₈, X₄: X₄ {O(n)}
t₂₃₉, X₀: X₀ {O(n)}
t₂₃₉, X₁: 2⋅X₀+2⋅X₁+X₂+2 {O(n)}
t₂₃₉, X₂: 2⋅X₂+X₀+1 {O(n)}
t₂₃₉, X₃: X₃ {O(n)}
t₂₃₉, X₄: X₄ {O(n)}
t₂₄₀, X₀: X₀ {O(n)}
t₂₄₀, X₁: 2⋅X₀+2⋅X₁+X₂+2 {O(n)}
t₂₄₀, X₂: 2⋅X₂+X₀+1 {O(n)}
t₂₄₀, X₃: X₃ {O(n)}
t₂₄₀, X₄: X₄ {O(n)}