Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars: D, E, F
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂) → l7(X₀, X₁, X₂)
t₆: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: 1 ≤ X₂
t₅: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₂ ≤ 0
t₇: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: X₂+1 ≤ 0 ∧ 0 ≤ 1+X₂
t₈: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: 0 ≤ X₂ ∧ 0 ≤ D ∧ 2⋅D ≤ X₂+1 ∧ X₂ ≤ 2⋅D
t₉: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: X₂+2 ≤ 0 ∧ D ≤ 0 ∧ X₂+1 ≤ 2⋅D ∧ 2⋅D ≤ 2+X₂
t₁₀: l2(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₂+1 ≤ 0 ∧ 0 ≤ 1+X₂
t₁₁: l2(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: 0 ≤ X₂ ∧ 0 ≤ D ∧ 2⋅D ≤ X₂+1 ∧ X₂ ≤ 2⋅D
t₁₂: l2(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₂+2 ≤ 0 ∧ D ≤ 0 ∧ X₂+1 ≤ 2⋅D ∧ 2⋅D ≤ 2+X₂
t₁₃: l3(X₀, X₁, X₂) → l1(X₀, X₁, -1) :|: X₂+1 ≤ 0 ∧ 0 ≤ 1+X₂
t₁₄: l3(X₀, X₁, X₂) → l1(X₀, X₁, D-1) :|: 1 ≤ 0 ∧ 0 ≤ D ∧ 2⋅D ≤ 0 ∧ 0 ≤ 1+2⋅D ∧ X₂+1 ≤ 0 ∧ 0 ≤ 1+X₂
t₁₅: l3(X₀, X₁, X₂) → l1(X₀, X₁, D-1) :|: 1 ≤ 0 ∧ D ≤ 0 ∧ X₂+1 ≤ 0 ∧ 0 ≤ 1+X₂ ∧ X₂+1 ≤ 2⋅D ∧ 2⋅D ≤ 2+X₂
t₁₆: l3(X₀, X₁, X₂) → l1(X₀, X₁, -1) :|: 1 ≤ 0 ∧ 0 ≤ D ∧ 2⋅D ≤ 0 ∧ 0 ≤ 1+2⋅D ∧ X₂+1 ≤ 0 ∧ 0 ≤ 1+X₂
t₁₇: l3(X₀, X₁, X₂) → l1(X₀, X₁, D-1) :|: 1 ≤ 0 ∧ 0 ≤ E ∧ 2⋅E ≤ 0 ∧ 0 ≤ 1+2⋅E ∧ 0 ≤ D ∧ 2⋅D ≤ 0 ∧ 0 ≤ 1+2⋅D ∧ X₂+1 ≤ 0 ∧ 0 ≤ 1+X₂
t₁₈: l3(X₀, X₁, X₂) → l1(X₀, X₁, D-1) :|: 1 ≤ 0 ∧ 0 ≤ E ∧ 2⋅E ≤ 0 ∧ 0 ≤ 1+2⋅E ∧ D ≤ 0 ∧ X₂+1 ≤ 0 ∧ 0 ≤ 1+X₂ ∧ X₂+1 ≤ 2⋅D ∧ 2⋅D ≤ 2+X₂
t₁₉: l3(X₀, X₁, X₂) → l1(X₀, X₁, -1) :|: 1 ≤ 0 ∧ D ≤ 0 ∧ X₂+1 ≤ 0 ∧ 0 ≤ 1+X₂ ∧ X₂+1 ≤ 2⋅D ∧ 2⋅D ≤ 2+X₂
t₂₀: l3(X₀, X₁, X₂) → l1(X₀, X₁, D-1) :|: 1 ≤ 0 ∧ E ≤ 0 ∧ 0 ≤ D ∧ 2⋅D ≤ 0 ∧ 0 ≤ 1+2⋅D ∧ X₂+1 ≤ 0 ∧ 0 ≤ 1+X₂ ∧ X₂+1 ≤ 2⋅E ∧ 2⋅E ≤ 2+X₂
t₂₁: l3(X₀, X₁, X₂) → l1(X₀, X₁, D-1) :|: 1 ≤ 0 ∧ E ≤ 0 ∧ D ≤ 0 ∧ X₂+1 ≤ 0 ∧ 0 ≤ 1+X₂ ∧ X₂+1 ≤ 2⋅E ∧ 2⋅E ≤ 2+X₂ ∧ X₂+1 ≤ 2⋅D ∧ 2⋅D ≤ 2+X₂
t₂₂: l3(X₀, X₁, X₂) → l1(X₀, X₁, -1) :|: 1 ≤ 0 ∧ 0 ≤ D ∧ 2⋅D ≤ 0 ∧ 0 ≤ 1+2⋅D ∧ X₂+1 ≤ 0 ∧ 0 ≤ 1+X₂
t₂₃: l3(X₀, X₁, X₂) → l1(X₀, X₁, D-1) :|: 1 ≤ 0 ∧ 0 ≤ E ∧ 2⋅E ≤ 0 ∧ 0 ≤ 1+2⋅E ∧ 0 ≤ D ∧ 2⋅D ≤ 0 ∧ 0 ≤ 1+2⋅D ∧ X₂+1 ≤ 0 ∧ 0 ≤ 1+X₂
t₂₄: l3(X₀, X₁, X₂) → l1(X₀, X₁, D-1) :|: 1 ≤ 0 ∧ 0 ≤ E ∧ 2⋅E ≤ 0 ∧ 0 ≤ 1+2⋅E ∧ D ≤ 0 ∧ X₂+1 ≤ 0 ∧ 0 ≤ 1+X₂ ∧ X₂+1 ≤ 2⋅D ∧ 2⋅D ≤ 2+X₂
t₂₅: l3(X₀, X₁, X₂) → l1(X₀, X₁, -1) :|: 1 ≤ 0 ∧ 0 ≤ D ∧ 2⋅D ≤ 0 ∧ 0 ≤ 1+2⋅D ∧ 0 ≤ E ∧ 2⋅E ≤ 0 ∧ 0 ≤ 1+2⋅E ∧ X₂+1 ≤ 0 ∧ 0 ≤ 1+X₂
t₂₆: l3(X₀, X₁, X₂) → l1(X₀, X₁, D-1) :|: 0 ≤ X₂ ∧ 0 ≤ E ∧ 2⋅E ≤ X₂+1 ∧ X₂ ≤ 2⋅E ∧ 0 ≤ F ∧ 2⋅F ≤ X₂+1 ∧ X₂ ≤ 2⋅F ∧ 0 ≤ D ∧ 2⋅D ≤ X₂+1 ∧ X₂ ≤ 2⋅D
t₂₇: l3(X₀, X₁, X₂) → l1(X₀, X₁, D-1) :|: 0 ≤ X₂ ∧ 0 ≤ E ∧ 2⋅E ≤ X₂+1 ∧ X₂ ≤ 2⋅E ∧ 0 ≤ F ∧ 2⋅F ≤ X₂+1 ∧ X₂ ≤ 2⋅F ∧ X₂+2 ≤ 0 ∧ D ≤ 0 ∧ X₂+1 ≤ 2⋅D ∧ 2⋅D ≤ 2+X₂
t₂₈: l3(X₀, X₁, X₂) → l1(X₀, X₁, -1) :|: 1 ≤ 0 ∧ 0 ≤ D ∧ 2⋅D ≤ 0 ∧ 0 ≤ 1+2⋅D ∧ E ≤ 0 ∧ X₂+1 ≤ 0 ∧ 0 ≤ 1+X₂ ∧ X₂+1 ≤ 2⋅E ∧ 2⋅E ≤ 2+X₂
t₂₉: l3(X₀, X₁, X₂) → l1(X₀, X₁, D-1) :|: 0 ≤ X₂ ∧ 0 ≤ E ∧ 2⋅E ≤ X₂+1 ∧ X₂ ≤ 2⋅E ∧ X₂+2 ≤ 0 ∧ F ≤ 0 ∧ 0 ≤ D ∧ 2⋅D ≤ X₂+1 ∧ X₂ ≤ 2⋅D ∧ X₂+1 ≤ 2⋅F ∧ 2⋅F ≤ 2+X₂
t₃₀: l3(X₀, X₁, X₂) → l1(X₀, X₁, D-1) :|: 0 ≤ X₂ ∧ 0 ≤ E ∧ 2⋅E ≤ X₂+1 ∧ X₂ ≤ 2⋅E ∧ X₂+2 ≤ 0 ∧ F ≤ 0 ∧ D ≤ 0 ∧ X₂+1 ≤ 2⋅F ∧ 2⋅F ≤ 2+X₂ ∧ X₂+1 ≤ 2⋅D ∧ 2⋅D ≤ 2+X₂
t₃₁: l3(X₀, X₁, X₂) → l1(X₀, X₁, -1) :|: 1 ≤ 0 ∧ D ≤ 0 ∧ X₂+1 ≤ 0 ∧ 0 ≤ 1+X₂ ∧ X₂+1 ≤ 2⋅D ∧ 2⋅D ≤ 2+X₂
t₃₂: l3(X₀, X₁, X₂) → l1(X₀, X₁, D-1) :|: 1 ≤ 0 ∧ E ≤ 0 ∧ 0 ≤ D ∧ 2⋅D ≤ 0 ∧ 0 ≤ 1+2⋅D ∧ X₂+1 ≤ 0 ∧ 0 ≤ 1+X₂ ∧ X₂+1 ≤ 2⋅E ∧ 2⋅E ≤ 2+X₂
t₃₃: l3(X₀, X₁, X₂) → l1(X₀, X₁, D-1) :|: 1 ≤ 0 ∧ E ≤ 0 ∧ D ≤ 0 ∧ X₂+1 ≤ 0 ∧ 0 ≤ 1+X₂ ∧ X₂+1 ≤ 2⋅E ∧ 2⋅E ≤ 2+X₂ ∧ X₂+1 ≤ 2⋅D ∧ 2⋅D ≤ 2+X₂
t₃₄: l3(X₀, X₁, X₂) → l1(X₀, X₁, -1) :|: 1 ≤ 0 ∧ D ≤ 0 ∧ 0 ≤ E ∧ 2⋅E ≤ 0 ∧ 0 ≤ 1+2⋅E ∧ X₂+1 ≤ 0 ∧ 0 ≤ 1+X₂ ∧ X₂+1 ≤ 2⋅D ∧ 2⋅D ≤ 2+X₂
t₃₅: l3(X₀, X₁, X₂) → l1(X₀, X₁, D-1) :|: X₂+2 ≤ 0 ∧ E ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ F ∧ 2⋅F ≤ X₂+1 ∧ X₂ ≤ 2⋅F ∧ 0 ≤ D ∧ 2⋅D ≤ X₂+1 ∧ X₂ ≤ 2⋅D ∧ X₂+1 ≤ 2⋅E ∧ 2⋅E ≤ 2+X₂
t₃₆: l3(X₀, X₁, X₂) → l1(X₀, X₁, D-1) :|: X₂+2 ≤ 0 ∧ E ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ F ∧ 2⋅F ≤ X₂+1 ∧ X₂ ≤ 2⋅F ∧ D ≤ 0 ∧ X₂+1 ≤ 2⋅E ∧ 2⋅E ≤ 2+X₂ ∧ X₂+1 ≤ 2⋅D ∧ 2⋅D ≤ 2+X₂
t₃₇: l3(X₀, X₁, X₂) → l1(X₀, X₁, -1) :|: 1 ≤ 0 ∧ D ≤ 0 ∧ E ≤ 0 ∧ X₂+1 ≤ 0 ∧ 0 ≤ 1+X₂ ∧ X₂+1 ≤ 2⋅D ∧ 2⋅D ≤ 2+X₂ ∧ X₂+1 ≤ 2⋅E ∧ 2⋅E ≤ 2+X₂
t₃₈: l3(X₀, X₁, X₂) → l1(X₀, X₁, D-1) :|: X₂+2 ≤ 0 ∧ E ≤ 0 ∧ F ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ D ∧ 2⋅D ≤ X₂+1 ∧ X₂ ≤ 2⋅D ∧ X₂+1 ≤ 2⋅E ∧ 2⋅E ≤ 2+X₂ ∧ X₂+1 ≤ 2⋅F ∧ 2⋅F ≤ 2+X₂
t₃₉: l3(X₀, X₁, X₂) → l1(X₀, X₁, D-1) :|: X₂+2 ≤ 0 ∧ E ≤ 0 ∧ F ≤ 0 ∧ D ≤ 0 ∧ X₂+1 ≤ 2⋅E ∧ 2⋅E ≤ 2+X₂ ∧ X₂+1 ≤ 2⋅F ∧ 2⋅F ≤ 2+X₂ ∧ X₂+1 ≤ 2⋅D ∧ 2⋅D ≤ 2+X₂
t₄₀: l4(X₀, X₁, X₂) → l5(X₀, X₁+1, X₂)
t₃: l5(X₀, X₁, X₂) → l1(X₀, X₁, X₁) :|: 1+X₁ ≤ X₀
t₄: l5(X₀, X₁, X₂) → l6(X₀, X₁, X₂) :|: X₀ ≤ X₁
t₄₁: l6(X₀, X₁, X₂) → l8(X₀, X₁, X₂)
t₁: l7(X₀, X₁, X₂) → l5(X₀, 1, X₂) :|: 3 ≤ X₀
t₂: l7(X₀, X₁, X₂) → l6(X₀, X₁, X₂) :|: X₀ ≤ 2

Preprocessing

Cut unsatisfiable transition t₇: l2→l3

Cut unsatisfiable transition t₉: l2→l3

Cut unsatisfiable transition t₁₀: l2→l4

Cut unsatisfiable transition t₁₂: l2→l4

Cut unsatisfiable transition t₁₄: l3→l1

Cut unsatisfiable transition t₁₅: l3→l1

Cut unsatisfiable transition t₁₆: l3→l1

Cut unsatisfiable transition t₁₇: l3→l1

Cut unsatisfiable transition t₁₈: l3→l1

Cut unsatisfiable transition t₁₉: l3→l1

Cut unsatisfiable transition t₂₀: l3→l1

Cut unsatisfiable transition t₂₁: l3→l1

Cut unsatisfiable transition t₂₂: l3→l1

Cut unsatisfiable transition t₂₃: l3→l1

Cut unsatisfiable transition t₂₄: l3→l1

Cut unsatisfiable transition t₂₅: l3→l1

Cut unsatisfiable transition t₂₇: l3→l1

Cut unsatisfiable transition t₂₈: l3→l1

Cut unsatisfiable transition t₂₉: l3→l1

Cut unsatisfiable transition t₃₀: l3→l1

Cut unsatisfiable transition t₃₁: l3→l1

Cut unsatisfiable transition t₃₂: l3→l1

Cut unsatisfiable transition t₃₃: l3→l1

Cut unsatisfiable transition t₃₄: l3→l1

Cut unsatisfiable transition t₃₅: l3→l1

Cut unsatisfiable transition t₃₆: l3→l1

Cut unsatisfiable transition t₃₇: l3→l1

Cut unsatisfiable transition t₃₈: l3→l1

Found invariant X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 3 ≤ X₀ for location l2

Found invariant X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 3 ≤ X₀ for location l5

Found invariant X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 3 ≤ X₀ for location l1

Found invariant X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 3 ≤ X₀ for location l4

Found invariant X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 3 ≤ X₀ for location l3

Cut unsatisfiable transition t₁₃: l3→l1

Cut unsatisfiable transition t₃₉: l3→l1

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars: D, E, F
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂) → l7(X₀, X₁, X₂)
t₆: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: 1 ≤ X₂ ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 3 ≤ X₀
t₅: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 3 ≤ X₀
t₈: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: 0 ≤ X₂ ∧ 0 ≤ D ∧ 2⋅D ≤ X₂+1 ∧ X₂ ≤ 2⋅D ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 3 ≤ X₀
t₁₁: l2(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: 0 ≤ X₂ ∧ 0 ≤ D ∧ 2⋅D ≤ X₂+1 ∧ X₂ ≤ 2⋅D ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 3 ≤ X₀
t₂₆: l3(X₀, X₁, X₂) → l1(X₀, X₁, D-1) :|: 0 ≤ X₂ ∧ 0 ≤ E ∧ 2⋅E ≤ X₂+1 ∧ X₂ ≤ 2⋅E ∧ 0 ≤ F ∧ 2⋅F ≤ X₂+1 ∧ X₂ ≤ 2⋅F ∧ 0 ≤ D ∧ 2⋅D ≤ X₂+1 ∧ X₂ ≤ 2⋅D ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 3 ≤ X₀
t₄₀: l4(X₀, X₁, X₂) → l5(X₀, X₁+1, X₂) :|: X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 3 ≤ X₀
t₃: l5(X₀, X₁, X₂) → l1(X₀, X₁, X₁) :|: 1+X₁ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 3 ≤ X₀
t₄: l5(X₀, X₁, X₂) → l6(X₀, X₁, X₂) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 3 ≤ X₀
t₄₁: l6(X₀, X₁, X₂) → l8(X₀, X₁, X₂)
t₁: l7(X₀, X₁, X₂) → l5(X₀, 1, X₂) :|: 3 ≤ X₀
t₂: l7(X₀, X₁, X₂) → l6(X₀, X₁, X₂) :|: X₀ ≤ 2

MPRF for transition t₅: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 3 ≤ X₀ of depth 1:

new bound:

X₀+1 {O(n)}

MPRF:

l2 [X₀-X₁ ]
l3 [X₀-X₁ ]
l4 [X₀-X₁-1 ]
l5 [X₀-X₁ ]
l1 [X₀-X₁ ]

MPRF for transition t₁₁: l2(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: 0 ≤ X₂ ∧ 0 ≤ D ∧ 2⋅D ≤ X₂+1 ∧ X₂ ≤ 2⋅D ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 3 ≤ X₀ of depth 1:

new bound:

X₀+1 {O(n)}

MPRF:

l2 [X₀-X₁ ]
l3 [X₀-X₁ ]
l4 [X₀-X₁-1 ]
l5 [X₀-X₁ ]
l1 [X₀-X₁ ]

MPRF for transition t₄₀: l4(X₀, X₁, X₂) → l5(X₀, X₁+1, X₂) :|: X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 3 ≤ X₀ of depth 1:

new bound:

X₀+3 {O(n)}

MPRF:

l2 [X₀+2-X₁ ]
l3 [X₀+2-X₁ ]
l4 [X₀+2-X₁ ]
l5 [X₀+2-X₁ ]
l1 [X₀+2-X₁ ]

MPRF for transition t₃: l5(X₀, X₁, X₂) → l1(X₀, X₁, X₁) :|: 1+X₁ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 3 ≤ X₀ of depth 1:

new bound:

X₀+2 {O(n)}

MPRF:

l2 [X₀-X₁ ]
l3 [X₀-X₁ ]
l4 [X₀-X₁ ]
l5 [X₀+1-X₁ ]
l1 [X₀-X₁ ]

MPRF for transition t₆: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: 1 ≤ X₂ ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 3 ≤ X₀ of depth 1:

new bound:

2⋅X₀⋅X₀+15⋅X₀+22 {O(n^2)}

MPRF:

l2 [2⋅X₂-1 ]
l3 [2⋅X₂-1 ]
l1 [2⋅X₂+1 ]
l4 [X₂ ]
l5 [0 ]

MPRF for transition t₈: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: 0 ≤ X₂ ∧ 0 ≤ D ∧ 2⋅D ≤ X₂+1 ∧ X₂ ≤ 2⋅D ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 3 ≤ X₀ of depth 1:

new bound:

4⋅X₀⋅X₀+25⋅X₀+34 {O(n^2)}

MPRF:

l2 [2⋅X₀+2⋅X₂-7 ]
l3 [2⋅X₀+2⋅X₂-9 ]
l1 [2⋅X₀+2⋅X₂-7 ]
l4 [2⋅X₀+X₂-7 ]
l5 [2⋅X₀-7 ]

MPRF for transition t₂₆: l3(X₀, X₁, X₂) → l1(X₀, X₁, D-1) :|: 0 ≤ X₂ ∧ 0 ≤ E ∧ 2⋅E ≤ X₂+1 ∧ X₂ ≤ 2⋅E ∧ 0 ≤ F ∧ 2⋅F ≤ X₂+1 ∧ X₂ ≤ 2⋅F ∧ 0 ≤ D ∧ 2⋅D ≤ X₂+1 ∧ X₂ ≤ 2⋅D ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 3 ≤ X₀ of depth 1:

new bound:

2⋅X₀⋅X₀+14⋅X₀+20 {O(n^2)}

MPRF:

l2 [2⋅X₂ ]
l3 [X₂+1 ]
l1 [2⋅X₂ ]
l4 [0 ]
l5 [0 ]

Analysing control-flow refined program

Cut unsatisfiable transition t₄: l5→l6

Cut unsatisfiable transition t₃₀₇: n_l1___8→l4

Found invariant 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 3 ≤ X₀ for location n_l5___1

Found invariant X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 3 ≤ X₀ for location n_l2___7

Found invariant X₂ ≤ 0 ∧ 2+X₂ ≤ X₁ ∧ 3+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 3 ≤ X₀ for location n_l5___9

Found invariant 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 3 ≤ X₀ for location n_l1___4

Found invariant X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 3 ≤ X₀ for location n_l3___6

Found invariant X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 3 ≤ X₀ for location n_l1___8

Found invariant 1+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 5 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 3 ≤ X₁ ∧ 7 ≤ X₀+X₁ ∧ 4 ≤ X₀ for location n_l2___3

Found invariant X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 3 ≤ X₀ for location n_l4___5

Found invariant X₁ ≤ 1 ∧ 2+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 3 ≤ X₀ for location l5

Found invariant 2+X₂ ≤ X₁ ∧ 3+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 5 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 3 ≤ X₁ ∧ 7 ≤ X₀+X₁ ∧ 4 ≤ X₀ for location n_l3___2

Found invariant X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 3+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 3 ≤ X₀ for location l4

MPRF for transition t₂₈₉: l4(X₀, X₁, X₂) → n_l5___9(X₀, X₁+1, X₂) :|: X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₂ ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ 3 ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 3+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 3 ≤ X₀ of depth 1:

new bound:

X₀+1 {O(n)}

MPRF:

l4 [X₀-X₁ ]
n_l2___3 [X₀-X₁ ]
n_l2___7 [X₀-X₂ ]
n_l3___2 [X₀-X₁ ]
n_l3___6 [X₀-X₂ ]
n_l1___4 [X₀-X₁ ]
n_l4___5 [X₀-X₁-1 ]
n_l5___1 [X₀-X₁ ]
n_l5___9 [X₀-X₁ ]
n_l1___8 [X₀-X₁ ]

MPRF for transition t₃₀₆: n_l1___4(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 3 ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 3 ≤ X₀ of depth 1:

new bound:

X₀+3 {O(n)}

MPRF:

l4 [X₀+1-X₁ ]
n_l2___3 [X₀+2-X₁ ]
n_l2___7 [X₀+2-X₂ ]
n_l3___2 [X₀+2-X₁ ]
n_l3___6 [X₀+2-X₁ ]
n_l1___4 [X₀+2-X₁ ]
n_l4___5 [X₀+2-X₁ ]
n_l5___1 [X₀+2-X₁ ]
n_l5___9 [X₀+2-X₁ ]
n_l1___8 [X₀+2-X₂ ]

MPRF for transition t₂₈₂: n_l1___8(X₀, X₁, X₂) → n_l2___7(X₀, X₁, X₂) :|: 1 ≤ X₂ ∧ 3 ≤ X₀ ∧ X₂ ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ X₂ ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀ ∧ 1+X₂ ≤ X₀ ∧ 3 ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 3 ≤ X₀ of depth 1:

new bound:

X₀+2 {O(n)}

MPRF:

l4 [X₀-X₁ ]
n_l2___3 [X₀-X₁ ]
n_l2___7 [X₀-X₁ ]
n_l3___2 [X₀-X₁ ]
n_l3___6 [X₀-X₁ ]
n_l1___4 [X₀-X₁ ]
n_l4___5 [X₀-X₁ ]
n_l5___1 [X₀+1-X₁ ]
n_l5___9 [X₀+1-X₁ ]
n_l1___8 [X₀+1-X₂ ]

MPRF for transition t₂₈₄: n_l2___3(X₀, X₁, X₂) → n_l4___5(X₀, X₁, Arg2_P) :|: 1+X₁ ≤ X₀ ∧ 1+2⋅X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ Arg2_P ∧ 3 ≤ X₀ ∧ Arg2_P ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ X₂ ≤ Arg2_P ∧ Arg2_P ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 5 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 3 ≤ X₁ ∧ 7 ≤ X₀+X₁ ∧ 4 ≤ X₀ of depth 1:

new bound:

X₀+1 {O(n)}

MPRF:

l4 [X₀-X₁ ]
n_l2___3 [X₀-X₁ ]
n_l2___7 [X₀-X₂ ]
n_l3___2 [X₀-X₁ ]
n_l3___6 [X₀+X₁-2⋅X₂ ]
n_l1___4 [X₀-X₁ ]
n_l4___5 [X₀-X₁-1 ]
n_l5___1 [X₀-X₁ ]
n_l5___9 [X₀-X₁ ]
n_l1___8 [X₀-X₂ ]

MPRF for transition t₂₈₅: n_l2___7(X₀, X₁, X₂) → n_l3___6(X₀, X₁, Arg2_P) :|: 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 1 ≤ Arg2_P ∧ 3 ≤ X₀ ∧ Arg2_P ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ X₂ ≤ Arg2_P ∧ Arg2_P ≤ X₂ ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 3 ≤ X₀ of depth 1:

new bound:

X₀+2 {O(n)}

MPRF:

l4 [X₀-X₁ ]
n_l2___3 [X₀-X₁ ]
n_l2___7 [X₀+1-X₂ ]
n_l3___2 [X₀-X₁ ]
n_l3___6 [X₀-X₁ ]
n_l1___4 [X₀-X₁ ]
n_l4___5 [X₀-X₁ ]
n_l5___1 [X₀+1-X₁ ]
n_l5___9 [X₀+1-X₁ ]
n_l1___8 [X₀+1-X₂ ]

MPRF for transition t₂₈₆: n_l2___7(X₀, X₁, X₂) → n_l4___5(X₀, X₁, Arg2_P) :|: 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 1 ≤ Arg2_P ∧ 3 ≤ X₀ ∧ Arg2_P ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ X₂ ≤ Arg2_P ∧ Arg2_P ≤ X₂ ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 3 ≤ X₀ of depth 1:

new bound:

X₀+1 {O(n)}

MPRF:

l4 [X₀-X₁ ]
n_l2___3 [X₀-X₁ ]
n_l2___7 [X₀-X₂ ]
n_l3___2 [X₀-X₁ ]
n_l3___6 [X₀-X₁ ]
n_l1___4 [X₀-X₁ ]
n_l4___5 [X₀-X₁-1 ]
n_l5___1 [X₀-X₁ ]
n_l5___9 [X₀-X₁ ]
n_l1___8 [X₀-X₁ ]

MPRF for transition t₂₈₈: n_l3___6(X₀, X₁, X₂) → n_l1___4(X₀, X₁, Arg2_P) :|: 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ X₂ ≤ 2+2⋅Arg2_P ∧ 1+2⋅Arg2_P ≤ X₂ ∧ X₂ ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ 3 ≤ X₀ ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 3 ≤ X₀ of depth 1:

new bound:

X₀+1 {O(n)}

MPRF:

l4 [X₀-X₁-1 ]
n_l2___3 [X₀-X₁-1 ]
n_l2___7 [X₀-X₂ ]
n_l3___2 [X₀-X₁-1 ]
n_l3___6 [X₀-X₂ ]
n_l1___4 [X₀-X₁-1 ]
n_l4___5 [X₀-X₁-1 ]
n_l5___1 [X₀-X₁ ]
n_l5___9 [X₀-X₁ ]
n_l1___8 [X₀-X₁ ]

MPRF for transition t₂₉₀: n_l4___5(X₀, X₁, X₂) → n_l5___1(X₀, X₁+1, X₂) :|: X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₂ ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀ ∧ X₂ ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ 3 ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 3 ≤ X₀ of depth 1:

new bound:

X₀+3 {O(n)}

MPRF:

l4 [X₀-X₁ ]
n_l2___3 [X₀-X₁ ]
n_l2___7 [X₀+X₂-2⋅X₁ ]
n_l3___2 [X₀-X₁ ]
n_l3___6 [X₀+X₂-2⋅X₁ ]
n_l1___4 [X₀-X₁ ]
n_l4___5 [X₀-X₁ ]
n_l5___1 [X₀-X₁ ]
n_l5___9 [X₀-X₁ ]
n_l1___8 [X₀+X₂-2⋅X₁ ]

MPRF for transition t₂₉₁: n_l5___1(X₀, X₁, X₂) → n_l1___8(X₀, X₁, X₁) :|: 1 ≤ X₂ ∧ 3 ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 3 ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 3 ≤ X₀ of depth 1:

new bound:

X₀+2 {O(n)}

MPRF:

l4 [X₀-X₁-1 ]
n_l2___3 [X₀-X₁-1 ]
n_l2___7 [X₀-X₂-1 ]
n_l3___2 [X₀-X₁-1 ]
n_l3___6 [X₀-X₁-1 ]
n_l1___4 [X₀-X₁-1 ]
n_l4___5 [X₀-X₁-1 ]
n_l5___1 [X₀-X₁ ]
n_l5___9 [X₀-X₁ ]
n_l1___8 [X₀-X₂-1 ]

MPRF for transition t₂₉₃: n_l5___9(X₀, X₁, X₂) → n_l1___8(X₀, X₁, X₁) :|: X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 3 ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ X₂ ≤ 0 ∧ 2+X₂ ≤ X₁ ∧ 3+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 3 ≤ X₀ of depth 1:

new bound:

X₀+2 {O(n)}

MPRF:

l4 [X₀+1-X₁ ]
n_l2___3 [X₀+1-X₁ ]
n_l2___7 [X₀+1-X₂ ]
n_l3___2 [X₀+1-X₁ ]
n_l3___6 [X₀+1-X₁ ]
n_l1___4 [X₀+1-X₁ ]
n_l4___5 [X₀-X₁ ]
n_l5___1 [X₀+1-X₁ ]
n_l5___9 [X₀+2-X₁ ]
n_l1___8 [X₀+1-X₂ ]

MPRF for transition t₂₈₁: n_l1___4(X₀, X₁, X₂) → n_l2___3(X₀, X₁, X₂) :|: 3 ≤ X₀ ∧ X₂ ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 3 ≤ X₀ ∧ 1+2⋅X₂ ≤ X₁ ∧ 0 ≤ 1+2⋅X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 3 ≤ X₀ of depth 1:

new bound:

4⋅X₀⋅X₀+18⋅X₀+21 {O(n^2)}

MPRF:

n_l5___9 [0 ]
l4 [0 ]
n_l1___8 [X₁ ]
n_l2___3 [2⋅X₂-1 ]
n_l2___7 [X₁ ]
n_l3___2 [X₂ ]
n_l3___6 [X₁ ]
n_l1___4 [2⋅X₂+1 ]
n_l4___5 [0 ]
n_l5___1 [0 ]

MPRF for transition t₂₈₃: n_l2___3(X₀, X₁, X₂) → n_l3___2(X₀, X₁, Arg2_P) :|: 1+X₁ ≤ X₀ ∧ 1+2⋅X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ Arg2_P ∧ 3 ≤ X₀ ∧ Arg2_P ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ X₂ ≤ Arg2_P ∧ Arg2_P ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 5 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 3 ≤ X₁ ∧ 7 ≤ X₀+X₁ ∧ 4 ≤ X₀ of depth 1:

new bound:

14⋅X₀⋅X₀+51⋅X₀+42 {O(n^2)}

MPRF:

n_l5___9 [2⋅X₀-2⋅X₁ ]
l4 [2⋅X₀-2⋅X₁-2 ]
n_l1___8 [3⋅X₀-2⋅X₂ ]
n_l2___3 [2⋅X₀+2⋅X₂-2⋅X₁-2 ]
n_l2___7 [3⋅X₀-2⋅X₂ ]
n_l3___2 [2⋅X₀+2⋅X₂-2⋅X₁-4 ]
n_l3___6 [3⋅X₀+X₁-3⋅X₂ ]
n_l1___4 [2⋅X₀+2⋅X₂-2⋅X₁-2 ]
n_l4___5 [2⋅X₀-2⋅X₁ ]
n_l5___1 [2⋅X₀-2⋅X₁ ]

MPRF for transition t₂₈₇: n_l3___2(X₀, X₁, X₂) → n_l1___4(X₀, X₁, Arg2_P) :|: 1+X₁ ≤ X₀ ∧ 1+2⋅X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ X₂ ≤ 2+2⋅Arg2_P ∧ 1+2⋅Arg2_P ≤ X₂ ∧ X₂ ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ 3 ≤ X₀ ∧ 2+X₂ ≤ X₁ ∧ 3+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 5 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 3 ≤ X₁ ∧ 7 ≤ X₀+X₁ ∧ 4 ≤ X₀ of depth 1:

new bound:

4⋅X₀⋅X₀+18⋅X₀+21 {O(n^2)}

MPRF:

n_l5___9 [0 ]
l4 [0 ]
n_l1___8 [X₂ ]
n_l2___3 [X₂ ]
n_l2___7 [X₂ ]
n_l3___2 [X₂ ]
n_l3___6 [X₁ ]
n_l1___4 [2⋅X₂ ]
n_l4___5 [0 ]
n_l5___1 [0 ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:8⋅X₀⋅X₀+58⋅X₀+88 {O(n^2)}
t₀: 1 {O(1)}
t₅: X₀+1 {O(n)}
t₆: 2⋅X₀⋅X₀+15⋅X₀+22 {O(n^2)}
t₈: 4⋅X₀⋅X₀+25⋅X₀+34 {O(n^2)}
t₁₁: X₀+1 {O(n)}
t₂₆: 2⋅X₀⋅X₀+14⋅X₀+20 {O(n^2)}
t₄₀: X₀+3 {O(n)}
t₃: X₀+2 {O(n)}
t₄: 1 {O(1)}
t₄₁: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}

Costbounds

Overall costbound: 8⋅X₀⋅X₀+58⋅X₀+88 {O(n^2)}
t₀: 1 {O(1)}
t₅: X₀+1 {O(n)}
t₆: 2⋅X₀⋅X₀+15⋅X₀+22 {O(n^2)}
t₈: 4⋅X₀⋅X₀+25⋅X₀+34 {O(n^2)}
t₁₁: X₀+1 {O(n)}
t₂₆: 2⋅X₀⋅X₀+14⋅X₀+20 {O(n^2)}
t₄₀: X₀+3 {O(n)}
t₃: X₀+2 {O(n)}
t₄: 1 {O(1)}
t₄₁: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₅, X₀: X₀ {O(n)}
t₅, X₁: X₀+4 {O(n)}
t₅, X₂: 0 {O(1)}
t₆, X₀: X₀ {O(n)}
t₆, X₁: X₀+4 {O(n)}
t₆, X₂: X₀+5 {O(n)}
t₈, X₀: X₀ {O(n)}
t₈, X₁: X₀+4 {O(n)}
t₈, X₂: X₀+5 {O(n)}
t₁₁, X₀: X₀ {O(n)}
t₁₁, X₁: X₀+4 {O(n)}
t₁₁, X₂: X₀+5 {O(n)}
t₂₆, X₀: X₀ {O(n)}
t₂₆, X₁: X₀+4 {O(n)}
t₂₆, X₂: X₀+5 {O(n)}
t₄₀, X₀: X₀ {O(n)}
t₄₀, X₁: X₀+4 {O(n)}
t₄₀, X₂: X₀+5 {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₀+4 {O(n)}
t₃, X₂: X₀+5 {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₀+4 {O(n)}
t₄, X₂: X₀+5 {O(n)}
t₄₁, X₀: 2⋅X₀ {O(n)}
t₄₁, X₁: X₀+X₁+4 {O(n)}
t₄₁, X₂: X₀+X₂+5 {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: 1 {O(1)}
t₁, X₂: X₂ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}