KoAT2 Proof Output

Initial Problem

Start: f0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars: H, I
Locations: f0, f15, f25, f33, f42, f52, f60, f69
Transitions:
t₀: f0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f15(0, H, I, 0, X₄, X₅, X₆)
t₁: f15(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f15(X₀, X₁, X₂, 1+X₃, X₄, X₅, X₆) :|: X₃ ≤ 49
t₁₂: f15(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f25(X₀, X₁, X₂, X₃, 0, X₅, X₆) :|: 50 ≤ X₃
t₂: f25(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f25(X₀, X₁, X₂, X₃, 1+X₄, X₅, X₆) :|: X₄ ≤ 49
t₁₁: f25(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f33(0, X₁, X₂, X₃, X₄, X₅, X₆) :|: 50 ≤ X₄
t₃: f33(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f33(1+X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₀ ≤ 49
t₁₀: f33(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f42(X₀, X₁, X₂, X₃, X₄, 0, X₆) :|: 50 ≤ X₀
t₄: f42(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f42(X₀, X₁, X₂, X₃, X₄, 1+X₅, X₆) :|: X₅ ≤ 49
t₉: f42(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f52(X₀, X₁, X₂, X₃, X₄, X₅, 0) :|: 50 ≤ X₅
t₅: f52(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f52(X₀, X₁, X₂, X₃, X₄, X₅, 1+X₆) :|: X₆ ≤ 49
t₈: f52(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f60(0, X₁, X₂, X₃, X₄, X₅, X₆) :|: 50 ≤ X₆
t₆: f60(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f60(1+X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₀ ≤ 49
t₇: f60(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f69(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 50 ≤ X₀

Preprocessing

Eliminate variables [H; I; X₁; X₂] that do not contribute to the problem

Found invariant X₁ ≤ 50 ∧ X₁ ≤ 50+X₀ ∧ X₀+X₁ ≤ 50 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location f15

Found invariant X₄ ≤ 50 ∧ X₄ ≤ X₃ ∧ X₃+X₄ ≤ 100 ∧ X₄ ≤ X₂ ∧ X₂+X₄ ≤ 100 ∧ X₄ ≤ X₁ ∧ X₁+X₄ ≤ 100 ∧ X₄ ≤ X₀ ∧ X₀+X₄ ≤ 100 ∧ 50 ≤ X₄ ∧ 100 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 100 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 100 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 100 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₃ ≤ 50 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 100 ∧ X₃ ≤ X₁ ∧ X₁+X₃ ≤ 100 ∧ X₃ ≤ X₀ ∧ X₀+X₃ ≤ 100 ∧ 50 ≤ X₃ ∧ 100 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 100 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 100 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 50 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 100 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 100 ∧ 50 ≤ X₂ ∧ 100 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 100 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 50 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 100 ∧ 50 ≤ X₁ ∧ 100 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 50 ∧ 50 ≤ X₀ for location f69

Found invariant X₃ ≤ 50 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 100 ∧ X₃ ≤ X₁ ∧ X₁+X₃ ≤ 100 ∧ X₃ ≤ X₀ ∧ X₀+X₃ ≤ 100 ∧ 0 ≤ X₃ ∧ 50 ≤ X₂+X₃ ∧ X₂ ≤ 50+X₃ ∧ 50 ≤ X₁+X₃ ∧ X₁ ≤ 50+X₃ ∧ 50 ≤ X₀+X₃ ∧ X₀ ≤ 50+X₃ ∧ X₂ ≤ 50 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 100 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 100 ∧ 50 ≤ X₂ ∧ 100 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 100 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 50 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 100 ∧ 50 ≤ X₁ ∧ 100 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 50 ∧ 50 ≤ X₀ for location f42

Found invariant X₂ ≤ 50 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 100 ∧ X₂ ≤ 50+X₀ ∧ X₀+X₂ ≤ 100 ∧ 50 ≤ X₂ ∧ 100 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 50 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 50 ∧ X₁ ≤ 50+X₀ ∧ X₀+X₁ ≤ 100 ∧ 50 ≤ X₁ ∧ 50 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 50 ∧ 0 ≤ X₀ for location f33

Found invariant X₄ ≤ 50 ∧ X₄ ≤ X₃ ∧ X₃+X₄ ≤ 100 ∧ X₄ ≤ X₂ ∧ X₂+X₄ ≤ 100 ∧ X₄ ≤ X₁ ∧ X₁+X₄ ≤ 100 ∧ X₄ ≤ X₀ ∧ X₀+X₄ ≤ 100 ∧ 0 ≤ X₄ ∧ 50 ≤ X₃+X₄ ∧ X₃ ≤ 50+X₄ ∧ 50 ≤ X₂+X₄ ∧ X₂ ≤ 50+X₄ ∧ 50 ≤ X₁+X₄ ∧ X₁ ≤ 50+X₄ ∧ 50 ≤ X₀+X₄ ∧ X₀ ≤ 50+X₄ ∧ X₃ ≤ 50 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 100 ∧ X₃ ≤ X₁ ∧ X₁+X₃ ≤ 100 ∧ X₃ ≤ X₀ ∧ X₀+X₃ ≤ 100 ∧ 50 ≤ X₃ ∧ 100 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 100 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 100 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 50 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 100 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 100 ∧ 50 ≤ X₂ ∧ 100 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 100 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 50 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 100 ∧ 50 ≤ X₁ ∧ 100 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 50 ∧ 50 ≤ X₀ for location f52

Found invariant X₂ ≤ 50 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 100 ∧ X₂ ≤ 50+X₀ ∧ X₀+X₂ ≤ 50 ∧ 0 ≤ X₂ ∧ 50 ≤ X₁+X₂ ∧ X₁ ≤ 50+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 50 ∧ X₁ ≤ 50+X₀ ∧ X₀+X₁ ≤ 50 ∧ 50 ≤ X₁ ∧ 50 ≤ X₀+X₁ ∧ 50+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location f25

Found invariant X₄ ≤ 50 ∧ X₄ ≤ X₃ ∧ X₃+X₄ ≤ 100 ∧ X₄ ≤ X₂ ∧ X₂+X₄ ≤ 100 ∧ X₄ ≤ X₁ ∧ X₁+X₄ ≤ 100 ∧ X₄ ≤ 50+X₀ ∧ X₀+X₄ ≤ 100 ∧ 50 ≤ X₄ ∧ 100 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 100 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 100 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 50 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₃ ≤ 50 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 100 ∧ X₃ ≤ X₁ ∧ X₁+X₃ ≤ 100 ∧ X₃ ≤ 50+X₀ ∧ X₀+X₃ ≤ 100 ∧ 50 ≤ X₃ ∧ 100 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 100 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 50 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 50 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 100 ∧ X₂ ≤ 50+X₀ ∧ X₀+X₂ ≤ 100 ∧ 50 ≤ X₂ ∧ 100 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 50 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 50 ∧ X₁ ≤ 50+X₀ ∧ X₀+X₁ ≤ 100 ∧ 50 ≤ X₁ ∧ 50 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 50 ∧ 0 ≤ X₀ for location f60

Problem after Preprocessing

Start: f0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: f0, f15, f25, f33, f42, f52, f60, f69
Transitions:
t₃₁: f0(X₀, X₁, X₂, X₃, X₄) → f15(0, 0, X₂, X₃, X₄)
t₃₂: f15(X₀, X₁, X₂, X₃, X₄) → f15(X₀, 1+X₁, X₂, X₃, X₄) :|: X₁ ≤ 49 ∧ X₁ ≤ 50+X₀ ∧ X₀+X₁ ≤ 50 ∧ X₁ ≤ 50 ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₁ ∧ 0 ≤ X₁
t₃₃: f15(X₀, X₁, X₂, X₃, X₄) → f25(X₀, X₁, 0, X₃, X₄) :|: 50 ≤ X₁ ∧ X₁ ≤ 50+X₀ ∧ X₀+X₁ ≤ 50 ∧ X₁ ≤ 50 ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₁ ∧ 0 ≤ X₁
t₃₄: f25(X₀, X₁, X₂, X₃, X₄) → f25(X₀, X₁, 1+X₂, X₃, X₄) :|: X₂ ≤ 49 ∧ X₁+X₂ ≤ 100 ∧ X₁ ≤ 50+X₀ ∧ X₂ ≤ 50+X₀ ∧ X₀+X₁ ≤ 50 ∧ X₀+X₂ ≤ 50 ∧ X₁ ≤ 50 ∧ X₁ ≤ 50+X₂ ∧ X₂ ≤ 50 ∧ 50 ≤ X₀+X₁ ∧ 50+X₀ ≤ X₁ ∧ 50 ≤ X₁ ∧ 50 ≤ X₁+X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂
t₃₅: f25(X₀, X₁, X₂, X₃, X₄) → f33(0, X₁, X₂, X₃, X₄) :|: 50 ≤ X₂ ∧ X₁+X₂ ≤ 100 ∧ X₁ ≤ 50+X₀ ∧ X₂ ≤ 50+X₀ ∧ X₀+X₁ ≤ 50 ∧ X₀+X₂ ≤ 50 ∧ X₁ ≤ 50 ∧ X₁ ≤ 50+X₂ ∧ X₂ ≤ 50 ∧ 50 ≤ X₀+X₁ ∧ 50+X₀ ≤ X₁ ∧ 50 ≤ X₁ ∧ 50 ≤ X₁+X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂
t₃₆: f33(X₀, X₁, X₂, X₃, X₄) → f33(1+X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ 49 ∧ X₀+X₁ ≤ 100 ∧ X₀+X₂ ≤ 100 ∧ X₁+X₂ ≤ 100 ∧ X₁ ≤ 50+X₀ ∧ X₂ ≤ 50+X₀ ∧ X₀ ≤ 50 ∧ X₁ ≤ 50 ∧ X₂ ≤ 50 ∧ 50 ≤ X₀+X₁ ∧ 50 ≤ X₀+X₂ ∧ 50 ≤ X₁ ∧ 50 ≤ X₂ ∧ 100 ≤ X₁+X₂ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂
t₃₇: f33(X₀, X₁, X₂, X₃, X₄) → f42(X₀, X₁, X₂, 0, X₄) :|: 50 ≤ X₀ ∧ X₀+X₁ ≤ 100 ∧ X₀+X₂ ≤ 100 ∧ X₁+X₂ ≤ 100 ∧ X₁ ≤ 50+X₀ ∧ X₂ ≤ 50+X₀ ∧ X₀ ≤ 50 ∧ X₁ ≤ 50 ∧ X₂ ≤ 50 ∧ 50 ≤ X₀+X₁ ∧ 50 ≤ X₀+X₂ ∧ 50 ≤ X₁ ∧ 50 ≤ X₂ ∧ 100 ≤ X₁+X₂ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂
t₃₈: f42(X₀, X₁, X₂, X₃, X₄) → f42(X₀, X₁, X₂, 1+X₃, X₄) :|: X₃ ≤ 49 ∧ X₀+X₁ ≤ 100 ∧ X₀+X₂ ≤ 100 ∧ X₀+X₃ ≤ 100 ∧ X₁+X₂ ≤ 100 ∧ X₁+X₃ ≤ 100 ∧ X₂+X₃ ≤ 100 ∧ X₀ ≤ 50 ∧ X₀ ≤ 50+X₃ ∧ X₁ ≤ 50 ∧ X₁ ≤ 50+X₃ ∧ X₂ ≤ 50 ∧ X₂ ≤ 50+X₃ ∧ X₃ ≤ 50 ∧ 50 ≤ X₀ ∧ 50 ≤ X₀+X₃ ∧ 50 ≤ X₁ ∧ 50 ≤ X₁+X₃ ∧ 50 ≤ X₂ ∧ 50 ≤ X₂+X₃ ∧ 100 ≤ X₀+X₁ ∧ 100 ≤ X₀+X₂ ∧ 100 ≤ X₁+X₂ ∧ X₁ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃
t₃₉: f42(X₀, X₁, X₂, X₃, X₄) → f52(X₀, X₁, X₂, X₃, 0) :|: 50 ≤ X₃ ∧ X₀+X₁ ≤ 100 ∧ X₀+X₂ ≤ 100 ∧ X₀+X₃ ≤ 100 ∧ X₁+X₂ ≤ 100 ∧ X₁+X₃ ≤ 100 ∧ X₂+X₃ ≤ 100 ∧ X₀ ≤ 50 ∧ X₀ ≤ 50+X₃ ∧ X₁ ≤ 50 ∧ X₁ ≤ 50+X₃ ∧ X₂ ≤ 50 ∧ X₂ ≤ 50+X₃ ∧ X₃ ≤ 50 ∧ 50 ≤ X₀ ∧ 50 ≤ X₀+X₃ ∧ 50 ≤ X₁ ∧ 50 ≤ X₁+X₃ ∧ 50 ≤ X₂ ∧ 50 ≤ X₂+X₃ ∧ 100 ≤ X₀+X₁ ∧ 100 ≤ X₀+X₂ ∧ 100 ≤ X₁+X₂ ∧ X₁ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃
t₄₀: f52(X₀, X₁, X₂, X₃, X₄) → f52(X₀, X₁, X₂, X₃, 1+X₄) :|: X₄ ≤ 49 ∧ X₀+X₁ ≤ 100 ∧ X₀+X₂ ≤ 100 ∧ X₀+X₃ ≤ 100 ∧ X₀+X₄ ≤ 100 ∧ X₁+X₂ ≤ 100 ∧ X₁+X₃ ≤ 100 ∧ X₁+X₄ ≤ 100 ∧ X₂+X₃ ≤ 100 ∧ X₂+X₄ ≤ 100 ∧ X₃+X₄ ≤ 100 ∧ X₀ ≤ 50 ∧ X₀ ≤ 50+X₄ ∧ X₁ ≤ 50 ∧ X₁ ≤ 50+X₄ ∧ X₂ ≤ 50 ∧ X₂ ≤ 50+X₄ ∧ X₃ ≤ 50 ∧ X₃ ≤ 50+X₄ ∧ X₄ ≤ 50 ∧ 50 ≤ X₀ ∧ 50 ≤ X₀+X₄ ∧ 50 ≤ X₁ ∧ 50 ≤ X₁+X₄ ∧ 50 ≤ X₂ ∧ 50 ≤ X₂+X₄ ∧ 50 ≤ X₃ ∧ 50 ≤ X₃+X₄ ∧ 100 ≤ X₀+X₁ ∧ 100 ≤ X₀+X₂ ∧ 100 ≤ X₀+X₃ ∧ 100 ≤ X₁+X₂ ∧ 100 ≤ X₁+X₃ ∧ 100 ≤ X₂+X₃ ∧ X₁ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₄ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₄ ≤ X₂ ∧ X₂ ≤ X₃ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₄
t₄₁: f52(X₀, X₁, X₂, X₃, X₄) → f60(0, X₁, X₂, X₃, X₄) :|: 50 ≤ X₄ ∧ X₀+X₁ ≤ 100 ∧ X₀+X₂ ≤ 100 ∧ X₀+X₃ ≤ 100 ∧ X₀+X₄ ≤ 100 ∧ X₁+X₂ ≤ 100 ∧ X₁+X₃ ≤ 100 ∧ X₁+X₄ ≤ 100 ∧ X₂+X₃ ≤ 100 ∧ X₂+X₄ ≤ 100 ∧ X₃+X₄ ≤ 100 ∧ X₀ ≤ 50 ∧ X₀ ≤ 50+X₄ ∧ X₁ ≤ 50 ∧ X₁ ≤ 50+X₄ ∧ X₂ ≤ 50 ∧ X₂ ≤ 50+X₄ ∧ X₃ ≤ 50 ∧ X₃ ≤ 50+X₄ ∧ X₄ ≤ 50 ∧ 50 ≤ X₀ ∧ 50 ≤ X₀+X₄ ∧ 50 ≤ X₁ ∧ 50 ≤ X₁+X₄ ∧ 50 ≤ X₂ ∧ 50 ≤ X₂+X₄ ∧ 50 ≤ X₃ ∧ 50 ≤ X₃+X₄ ∧ 100 ≤ X₀+X₁ ∧ 100 ≤ X₀+X₂ ∧ 100 ≤ X₀+X₃ ∧ 100 ≤ X₁+X₂ ∧ 100 ≤ X₁+X₃ ∧ 100 ≤ X₂+X₃ ∧ X₁ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₄ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₄ ≤ X₂ ∧ X₂ ≤ X₃ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₄
t₄₂: f60(X₀, X₁, X₂, X₃, X₄) → f60(1+X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ 49 ∧ X₀+X₁ ≤ 100 ∧ X₀+X₂ ≤ 100 ∧ X₀+X₃ ≤ 100 ∧ X₀+X₄ ≤ 100 ∧ X₁+X₂ ≤ 100 ∧ X₁+X₃ ≤ 100 ∧ X₁+X₄ ≤ 100 ∧ X₂+X₃ ≤ 100 ∧ X₂+X₄ ≤ 100 ∧ X₃+X₄ ≤ 100 ∧ X₁ ≤ 50+X₀ ∧ X₂ ≤ 50+X₀ ∧ X₃ ≤ 50+X₀ ∧ X₄ ≤ 50+X₀ ∧ X₀ ≤ 50 ∧ X₁ ≤ 50 ∧ X₂ ≤ 50 ∧ X₃ ≤ 50 ∧ X₄ ≤ 50 ∧ 50 ≤ X₀+X₁ ∧ 50 ≤ X₀+X₂ ∧ 50 ≤ X₀+X₃ ∧ 50 ≤ X₀+X₄ ∧ 50 ≤ X₁ ∧ 50 ≤ X₂ ∧ 50 ≤ X₃ ∧ 50 ≤ X₄ ∧ 100 ≤ X₁+X₂ ∧ 100 ≤ X₁+X₃ ∧ 100 ≤ X₁+X₄ ∧ 100 ≤ X₂+X₃ ∧ 100 ≤ X₂+X₄ ∧ 100 ≤ X₃+X₄ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₃ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₄ ≤ X₂ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₄ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₄
t₄₃: f60(X₀, X₁, X₂, X₃, X₄) → f69(X₀, X₁, X₂, X₃, X₄) :|: 50 ≤ X₀ ∧ X₀+X₁ ≤ 100 ∧ X₀+X₂ ≤ 100 ∧ X₀+X₃ ≤ 100 ∧ X₀+X₄ ≤ 100 ∧ X₁+X₂ ≤ 100 ∧ X₁+X₃ ≤ 100 ∧ X₁+X₄ ≤ 100 ∧ X₂+X₃ ≤ 100 ∧ X₂+X₄ ≤ 100 ∧ X₃+X₄ ≤ 100 ∧ X₁ ≤ 50+X₀ ∧ X₂ ≤ 50+X₀ ∧ X₃ ≤ 50+X₀ ∧ X₄ ≤ 50+X₀ ∧ X₀ ≤ 50 ∧ X₁ ≤ 50 ∧ X₂ ≤ 50 ∧ X₃ ≤ 50 ∧ X₄ ≤ 50 ∧ 50 ≤ X₀+X₁ ∧ 50 ≤ X₀+X₂ ∧ 50 ≤ X₀+X₃ ∧ 50 ≤ X₀+X₄ ∧ 50 ≤ X₁ ∧ 50 ≤ X₂ ∧ 50 ≤ X₃ ∧ 50 ≤ X₄ ∧ 100 ≤ X₁+X₂ ∧ 100 ≤ X₁+X₃ ∧ 100 ≤ X₁+X₄ ∧ 100 ≤ X₂+X₃ ∧ 100 ≤ X₂+X₄ ∧ 100 ≤ X₃+X₄ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₃ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₄ ≤ X₂ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₄ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₄

MPRF for transition t₃₂: f15(X₀, X₁, X₂, X₃, X₄) → f15(X₀, 1+X₁, X₂, X₃, X₄) :|: X₁ ≤ 49 ∧ X₁ ≤ 50+X₀ ∧ X₀+X₁ ≤ 50 ∧ X₁ ≤ 50 ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₁ ∧ 0 ≤ X₁ of depth 1:

new bound:

50 {O(1)}

MPRF:

• f15: [50-X₁]

MPRF for transition t₃₄: f25(X₀, X₁, X₂, X₃, X₄) → f25(X₀, X₁, 1+X₂, X₃, X₄) :|: X₂ ≤ 49 ∧ X₁+X₂ ≤ 100 ∧ X₁ ≤ 50+X₀ ∧ X₂ ≤ 50+X₀ ∧ X₀+X₁ ≤ 50 ∧ X₀+X₂ ≤ 50 ∧ X₁ ≤ 50 ∧ X₁ ≤ 50+X₂ ∧ X₂ ≤ 50 ∧ 50 ≤ X₀+X₁ ∧ 50+X₀ ≤ X₁ ∧ 50 ≤ X₁ ∧ 50 ≤ X₁+X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ of depth 1:

new bound:

51 {O(1)}

MPRF:

• f25: [51-X₂]

MPRF for transition t₃₆: f33(X₀, X₁, X₂, X₃, X₄) → f33(1+X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ 49 ∧ X₀+X₁ ≤ 100 ∧ X₀+X₂ ≤ 100 ∧ X₁+X₂ ≤ 100 ∧ X₁ ≤ 50+X₀ ∧ X₂ ≤ 50+X₀ ∧ X₀ ≤ 50 ∧ X₁ ≤ 50 ∧ X₂ ≤ 50 ∧ 50 ≤ X₀+X₁ ∧ 50 ≤ X₀+X₂ ∧ 50 ≤ X₁ ∧ 50 ≤ X₂ ∧ 100 ≤ X₁+X₂ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ of depth 1:

new bound:

51 {O(1)}

MPRF:

• f33: [51-X₀]

MPRF for transition t₃₈: f42(X₀, X₁, X₂, X₃, X₄) → f42(X₀, X₁, X₂, 1+X₃, X₄) :|: X₃ ≤ 49 ∧ X₀+X₁ ≤ 100 ∧ X₀+X₂ ≤ 100 ∧ X₀+X₃ ≤ 100 ∧ X₁+X₂ ≤ 100 ∧ X₁+X₃ ≤ 100 ∧ X₂+X₃ ≤ 100 ∧ X₀ ≤ 50 ∧ X₀ ≤ 50+X₃ ∧ X₁ ≤ 50 ∧ X₁ ≤ 50+X₃ ∧ X₂ ≤ 50 ∧ X₂ ≤ 50+X₃ ∧ X₃ ≤ 50 ∧ 50 ≤ X₀ ∧ 50 ≤ X₀+X₃ ∧ 50 ≤ X₁ ∧ 50 ≤ X₁+X₃ ∧ 50 ≤ X₂ ∧ 50 ≤ X₂+X₃ ∧ 100 ≤ X₀+X₁ ∧ 100 ≤ X₀+X₂ ∧ 100 ≤ X₁+X₂ ∧ X₁ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ of depth 1:

new bound:

51 {O(1)}

MPRF:

• f42: [1+X₀-X₃]

MPRF for transition t₄₀: f52(X₀, X₁, X₂, X₃, X₄) → f52(X₀, X₁, X₂, X₃, 1+X₄) :|: X₄ ≤ 49 ∧ X₀+X₁ ≤ 100 ∧ X₀+X₂ ≤ 100 ∧ X₀+X₃ ≤ 100 ∧ X₀+X₄ ≤ 100 ∧ X₁+X₂ ≤ 100 ∧ X₁+X₃ ≤ 100 ∧ X₁+X₄ ≤ 100 ∧ X₂+X₃ ≤ 100 ∧ X₂+X₄ ≤ 100 ∧ X₃+X₄ ≤ 100 ∧ X₀ ≤ 50 ∧ X₀ ≤ 50+X₄ ∧ X₁ ≤ 50 ∧ X₁ ≤ 50+X₄ ∧ X₂ ≤ 50 ∧ X₂ ≤ 50+X₄ ∧ X₃ ≤ 50 ∧ X₃ ≤ 50+X₄ ∧ X₄ ≤ 50 ∧ 50 ≤ X₀ ∧ 50 ≤ X₀+X₄ ∧ 50 ≤ X₁ ∧ 50 ≤ X₁+X₄ ∧ 50 ≤ X₂ ∧ 50 ≤ X₂+X₄ ∧ 50 ≤ X₃ ∧ 50 ≤ X₃+X₄ ∧ 100 ≤ X₀+X₁ ∧ 100 ≤ X₀+X₂ ∧ 100 ≤ X₀+X₃ ∧ 100 ≤ X₁+X₂ ∧ 100 ≤ X₁+X₃ ∧ 100 ≤ X₂+X₃ ∧ X₁ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₄ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₄ ≤ X₂ ∧ X₂ ≤ X₃ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₄ of depth 1:

new bound:

50 {O(1)}

MPRF:

• f52: [50-X₄]

MPRF for transition t₄₂: f60(X₀, X₁, X₂, X₃, X₄) → f60(1+X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ 49 ∧ X₀+X₁ ≤ 100 ∧ X₀+X₂ ≤ 100 ∧ X₀+X₃ ≤ 100 ∧ X₀+X₄ ≤ 100 ∧ X₁+X₂ ≤ 100 ∧ X₁+X₃ ≤ 100 ∧ X₁+X₄ ≤ 100 ∧ X₂+X₃ ≤ 100 ∧ X₂+X₄ ≤ 100 ∧ X₃+X₄ ≤ 100 ∧ X₁ ≤ 50+X₀ ∧ X₂ ≤ 50+X₀ ∧ X₃ ≤ 50+X₀ ∧ X₄ ≤ 50+X₀ ∧ X₀ ≤ 50 ∧ X₁ ≤ 50 ∧ X₂ ≤ 50 ∧ X₃ ≤ 50 ∧ X₄ ≤ 50 ∧ 50 ≤ X₀+X₁ ∧ 50 ≤ X₀+X₂ ∧ 50 ≤ X₀+X₃ ∧ 50 ≤ X₀+X₄ ∧ 50 ≤ X₁ ∧ 50 ≤ X₂ ∧ 50 ≤ X₃ ∧ 50 ≤ X₄ ∧ 100 ≤ X₁+X₂ ∧ 100 ≤ X₁+X₃ ∧ 100 ≤ X₁+X₄ ∧ 100 ≤ X₂+X₃ ∧ 100 ≤ X₂+X₄ ∧ 100 ≤ X₃+X₄ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₃ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₄ ≤ X₂ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₄ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₄ of depth 1:

new bound:

51 {O(1)}

MPRF:

• f60: [51-X₀]

All Bounds

Timebounds

Overall timebound:311 {O(1)}
t₃₁: 1 {O(1)}
t₃₂: 50 {O(1)}
t₃₃: 1 {O(1)}
t₃₄: 51 {O(1)}
t₃₅: 1 {O(1)}
t₃₆: 51 {O(1)}
t₃₇: 1 {O(1)}
t₃₈: 51 {O(1)}
t₃₉: 1 {O(1)}
t₄₀: 50 {O(1)}
t₄₁: 1 {O(1)}
t₄₂: 51 {O(1)}
t₄₃: 1 {O(1)}

Costbounds

Overall costbound: 311 {O(1)}
t₃₁: 1 {O(1)}
t₃₂: 50 {O(1)}
t₃₃: 1 {O(1)}
t₃₄: 51 {O(1)}
t₃₅: 1 {O(1)}
t₃₆: 51 {O(1)}
t₃₇: 1 {O(1)}
t₃₈: 51 {O(1)}
t₃₉: 1 {O(1)}
t₄₀: 50 {O(1)}
t₄₁: 1 {O(1)}
t₄₂: 51 {O(1)}
t₄₃: 1 {O(1)}

Sizebounds

t₃₁, X₀: 0 {O(1)}
t₃₁, X₁: 0 {O(1)}
t₃₁, X₂: X₂ {O(n)}
t₃₁, X₃: X₃ {O(n)}
t₃₁, X₄: X₄ {O(n)}
t₃₂, X₀: 0 {O(1)}
t₃₂, X₁: 50 {O(1)}
t₃₂, X₂: X₂ {O(n)}
t₃₂, X₃: X₃ {O(n)}
t₃₂, X₄: X₄ {O(n)}
t₃₃, X₀: 0 {O(1)}
t₃₃, X₁: 50 {O(1)}
t₃₃, X₂: 0 {O(1)}
t₃₃, X₃: X₃ {O(n)}
t₃₃, X₄: X₄ {O(n)}
t₃₄, X₀: 0 {O(1)}
t₃₄, X₁: 50 {O(1)}
t₃₄, X₂: 50 {O(1)}
t₃₄, X₃: X₃ {O(n)}
t₃₄, X₄: X₄ {O(n)}
t₃₅, X₀: 0 {O(1)}
t₃₅, X₁: 50 {O(1)}
t₃₅, X₂: 50 {O(1)}
t₃₅, X₃: X₃ {O(n)}
t₃₅, X₄: X₄ {O(n)}
t₃₆, X₀: 50 {O(1)}
t₃₆, X₁: 50 {O(1)}
t₃₆, X₂: 50 {O(1)}
t₃₆, X₃: X₃ {O(n)}
t₃₆, X₄: X₄ {O(n)}
t₃₇, X₀: 50 {O(1)}
t₃₇, X₁: 50 {O(1)}
t₃₇, X₂: 50 {O(1)}
t₃₇, X₃: 0 {O(1)}
t₃₇, X₄: X₄ {O(n)}
t₃₈, X₀: 50 {O(1)}
t₃₈, X₁: 50 {O(1)}
t₃₈, X₂: 50 {O(1)}
t₃₈, X₃: 50 {O(1)}
t₃₈, X₄: X₄ {O(n)}
t₃₉, X₀: 50 {O(1)}
t₃₉, X₁: 50 {O(1)}
t₃₉, X₂: 50 {O(1)}
t₃₉, X₃: 50 {O(1)}
t₃₉, X₄: 0 {O(1)}
t₄₀, X₀: 50 {O(1)}
t₄₀, X₁: 50 {O(1)}
t₄₀, X₂: 50 {O(1)}
t₄₀, X₃: 50 {O(1)}
t₄₀, X₄: 50 {O(1)}
t₄₁, X₀: 0 {O(1)}
t₄₁, X₁: 50 {O(1)}
t₄₁, X₂: 50 {O(1)}
t₄₁, X₃: 50 {O(1)}
t₄₁, X₄: 50 {O(1)}
t₄₂, X₀: 50 {O(1)}
t₄₂, X₁: 50 {O(1)}
t₄₂, X₂: 50 {O(1)}
t₄₂, X₃: 50 {O(1)}
t₄₂, X₄: 50 {O(1)}
t₄₃, X₀: 50 {O(1)}
t₄₃, X₁: 50 {O(1)}
t₄₃, X₂: 50 {O(1)}
t₄₃, X₃: 50 {O(1)}
t₄₃, X₄: 50 {O(1)}