Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: E
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃)
t₆: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: 0 ≤ X₃
t₅: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₃+1 ≤ 0
t₇: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₂+1 ≤ E
t₈: l2(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: E ≤ X₂
t₉: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃-1)
t₁₀: l4(X₀, X₁, X₂, X₃) → l6(X₀+1, X₁, X₂, X₃)
t₄: l5(X₀, X₁, X₂, X₃) → l1(X₀, X₁, E, X₀-1)
t₂: l6(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₀+1 ≤ X₁
t₃: l6(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₀
t₁₁: l7(X₀, X₁, X₂, X₃) → l9(X₀, X₁, X₂, X₃)
t₁: l8(X₀, X₁, X₂, X₃) → l6(1, X₁, X₂, X₃)
Preprocessing
Found invariant 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l2
Found invariant 1 ≤ X₀ for location l6
Found invariant X₁ ≤ X₀ ∧ 1 ≤ X₀ for location l7
Found invariant 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l5
Found invariant 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l1
Found invariant 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l4
Found invariant X₁ ≤ X₀ ∧ 1 ≤ X₀ for location l9
Found invariant 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: E
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃)
t₆: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: 0 ≤ X₃ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₅: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₃+1 ≤ 0 ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₇: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₂+1 ≤ E ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₈: l2(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: E ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₉: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃-1) :|: 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₁₀: l4(X₀, X₁, X₂, X₃) → l6(X₀+1, X₁, X₂, X₃) :|: 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₄: l5(X₀, X₁, X₂, X₃) → l1(X₀, X₁, E, X₀-1) :|: 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₂: l6(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₀+1 ≤ X₁ ∧ 1 ≤ X₀
t₃: l6(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₀ ∧ 1 ≤ X₀
t₁₁: l7(X₀, X₁, X₂, X₃) → l9(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₀ ∧ 1 ≤ X₀
t₁: l8(X₀, X₁, X₂, X₃) → l6(1, X₁, X₂, X₃)
MPRF for transition t₂: l6(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₀+1 ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁+2 {O(n)}
MPRF for transition t₄: l5(X₀, X₁, X₂, X₃) → l1(X₀, X₁, E, X₀-1) :|: 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁+1 {O(n)}
MPRF for transition t₅: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₃+1 ≤ 0 ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁+1 {O(n)}
MPRF for transition t₈: l2(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: E ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁+1 {O(n)}
MPRF for transition t₁₀: l4(X₀, X₁, X₂, X₃) → l6(X₀+1, X₁, X₂, X₃) :|: 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁+1 {O(n)}
MPRF for transition t₆: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: 0 ≤ X₃ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁⋅X₁+3⋅X₁+3 {O(n^2)}
MPRF for transition t₇: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₂+1 ≤ E ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁⋅X₁+3⋅X₁+3 {O(n^2)}
MPRF for transition t₉: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃-1) :|: 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁⋅X₁+3⋅X₁+3 {O(n^2)}
Chain transitions t₄: l5→l1 and t₅: l1→l4 to t₈₀: l5→l4
Chain transitions t₉: l3→l1 and t₅: l1→l4 to t₈₁: l3→l4
Chain transitions t₉: l3→l1 and t₆: l1→l2 to t₈₂: l3→l2
Chain transitions t₄: l5→l1 and t₆: l1→l2 to t₈₃: l5→l2
Chain transitions t₈₃: l5→l2 and t₈: l2→l4 to t₈₄: l5→l4
Chain transitions t₈₂: l3→l2 and t₈: l2→l4 to t₈₅: l3→l4
Chain transitions t₈₂: l3→l2 and t₇: l2→l3 to t₈₆: l3→l3
Chain transitions t₈₃: l5→l2 and t₇: l2→l3 to t₈₇: l5→l3
Chain transitions t₈₄: l5→l4 and t₁₀: l4→l6 to t₈₈: l5→l6
Chain transitions t₈₀: l5→l4 and t₁₀: l4→l6 to t₈₉: l5→l6
Chain transitions t₈₅: l3→l4 and t₁₀: l4→l6 to t₉₀: l3→l6
Chain transitions t₈₁: l3→l4 and t₁₀: l4→l6 to t₉₁: l3→l6
Chain transitions t₂: l6→l5 and t₈₉: l5→l6 to t₉₂: l6→l6
Chain transitions t₂: l6→l5 and t₈₈: l5→l6 to t₉₃: l6→l6
Chain transitions t₂: l6→l5 and t₈₄: l5→l4 to t₉₄: l6→l4
Chain transitions t₂: l6→l5 and t₈₀: l5→l4 to t₉₅: l6→l4
Chain transitions t₂: l6→l5 and t₈₇: l5→l3 to t₉₆: l6→l3
Chain transitions t₂: l6→l5 and t₈₃: l5→l2 to t₉₇: l6→l2
Chain transitions t₂: l6→l5 and t₄: l5→l1 to t₉₈: l6→l1
Analysing control-flow refined program
Cut unsatisfiable transition t₉₂: l6→l6
Cut unsatisfiable transition t₉₅: l6→l4
Found invariant 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l2
Found invariant 1 ≤ X₀ for location l6
Found invariant X₁ ≤ X₀ ∧ 1 ≤ X₀ for location l7
Found invariant 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l5
Found invariant 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l1
Found invariant 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l4
Found invariant X₁ ≤ X₀ ∧ 1 ≤ X₀ for location l9
Found invariant 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l3
MPRF for transition t₉₀: l3(X₀, X₁, X₂, X₃) -{4}> l6(X₀+1, X₁, X₂, X₃-1) :|: 1 ≤ X₃ ∧ Temp_Int₂₉₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁+1 {O(n)}
MPRF for transition t₉₁: l3(X₀, X₁, X₂, X₃) -{3}> l6(X₀+1, X₁, X₂, X₃-1) :|: X₃ ≤ 0 ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁+1 {O(n)}
MPRF for transition t₉₃: l6(X₀, X₁, X₂, X₃) -{5}> l6(X₀+1, X₁, Temp_Int₃₂₅, X₀-1) :|: X₀+1 ≤ X₁ ∧ 1 ≤ X₀ ∧ Temp_Int₃₂₆ ≤ Temp_Int₃₂₅ ∧ 1 ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ 0 ∧ 0 ≤ X₀ ∧ 2 ≤ X₁+X₀ ∧ 1 ≤ 2⋅X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ 0 ∧ 1 ≤ X₀ ∧ 3 ≤ X₁+X₀ ∧ 2 ≤ 2⋅X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ 0 ∧ 0 ≤ X₀ ∧ 2 ≤ X₁+X₀ ∧ 1 ≤ 2⋅X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁+1 {O(n)}
MPRF for transition t₉₆: l6(X₀, X₁, X₂, X₃) -{4}> l3(X₀, X₁, Temp_Int₃₃₆, X₀-1) :|: X₀+1 ≤ X₁ ∧ 1 ≤ X₀ ∧ Temp_Int₃₃₆+1 ≤ Temp_Int₃₃₇ ∧ 1 ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ 0 ∧ 0 ≤ X₀ ∧ 2 ≤ X₁+X₀ ∧ 1 ≤ 2⋅X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ 0 ∧ 1 ≤ X₀ ∧ 3 ≤ X₁+X₀ ∧ 2 ≤ 2⋅X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁+1 {O(n)}
MPRF for transition t₈₆: l3(X₀, X₁, X₂, X₃) -{3}> l3(X₀, X₁, X₂, X₃-1) :|: 1 ≤ X₃ ∧ X₂+1 ≤ Temp_Int₂₉₈ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
9⋅X₁⋅X₁+23⋅X₁+14 {O(n^2)}
CFR did not improve the program. Rolling back
CFR did not improve the program. Rolling back
Analysing control-flow refined program
Cut unsatisfiable transition t₂₄₆: n_l1___10→l4
Eliminate variables {NoDet0,X₂} that do not contribute to the problem
Found invariant 2+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ for location n_l6___3
Found invariant 3+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ 1+X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l1___6
Found invariant 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location n_l5___1
Found invariant 3+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ for location n_l3___4
Found invariant X₀ ≤ 1 ∧ 1 ≤ X₀ for location l6
Found invariant 1+X₂ ≤ 0 ∧ 4+X₂ ≤ X₁ ∧ 3+X₂ ≤ X₀ ∧ 0 ≤ 1+X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ for location n_l5___11
Found invariant 3+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ for location n_l2___5
Found invariant 1+X₂ ≤ 0 ∧ 3+X₂ ≤ X₁ ∧ 3+X₂ ≤ X₀ ∧ 0 ≤ 1+X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ for location n_l6___12
Found invariant 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l1___10
Found invariant 3+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ for location n_l5___2
Found invariant X₁ ≤ X₀ ∧ 1 ≤ X₀ for location l7
Found invariant 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l2___9
Found invariant 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l3___8
Found invariant 1+X₂ ≤ 0 ∧ 3+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ 1+X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l4
Found invariant X₁ ≤ X₀ ∧ 1 ≤ X₀ for location l9
Found invariant 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l4___7
MPRF for transition t₂₇₄: l4(X₀, X₁, X₂) → n_l6___12(X₀+1, X₁, X₂) :|: 1+X₂ ≤ 0 ∧ 1+X₂ ≤ 0 ∧ 3+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ 1+X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁+2 {O(n)}
MPRF for transition t₂₇₉: n_l1___10(X₀, X₁, X₂) → n_l2___9(X₀, X₁, X₂) :|: 0 ≤ X₂ ∧ 0 ≤ X₂ ∧ X₀ ≤ 1+X₂ ∧ 0 ≤ X₂ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁+1 {O(n)}
MPRF for transition t₂₈₀: n_l1___6(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₂+1 ≤ 0 ∧ 3+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ 1+X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁+1 {O(n)}
MPRF for transition t₂₈₃: n_l2___5(X₀, X₁, X₂) → n_l4___7(X₀, X₁, Arg3_P) :|: 2+X₂ ≤ X₀ ∧ 1+Arg3_P ≤ X₀ ∧ 0 ≤ Arg3_P ∧ X₂ ≤ Arg3_P ∧ Arg3_P ≤ X₂ ∧ 3+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₁+1 {O(n)}
MPRF for transition t₂₈₄: n_l2___9(X₀, X₁, X₂) → n_l3___8(X₀, X₁, Arg3_P) :|: X₀ ≤ X₂+1 ∧ 1+Arg3_P ≤ X₀ ∧ 0 ≤ Arg3_P ∧ X₂ ≤ Arg3_P ∧ Arg3_P ≤ X₂ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁+1 {O(n)}
MPRF for transition t₂₈₅: n_l2___9(X₀, X₁, X₂) → n_l4___7(X₀, X₁, Arg3_P) :|: X₀ ≤ X₂+1 ∧ 1+Arg3_P ≤ X₀ ∧ 0 ≤ Arg3_P ∧ X₂ ≤ Arg3_P ∧ Arg3_P ≤ X₂ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁+1 {O(n)}
MPRF for transition t₂₈₇: n_l3___8(X₀, X₁, X₂) → n_l1___6(X₀, X₁, X₂-1) :|: X₀ ≤ X₂+1 ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁+1 {O(n)}
MPRF for transition t₂₈₈: n_l4___7(X₀, X₁, X₂) → n_l6___3(X₀+1, X₁, X₂) :|: 0 ≤ X₂ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁+3 {O(n)}
MPRF for transition t₂₉₀: n_l5___11(X₀, X₁, X₂) → n_l1___10(X₀, X₁, X₀-1) :|: 2 ≤ X₀ ∧ X₂+1 ≤ 0 ∧ 0 ≤ 1+X₂ ∧ 1+X₂ ≤ 0 ∧ 4+X₂ ≤ X₁ ∧ 3+X₂ ≤ X₀ ∧ 0 ≤ 1+X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₁+2 {O(n)}
MPRF for transition t₂₉₁: n_l5___2(X₀, X₁, X₂) → n_l1___10(X₀, X₁, X₀-1) :|: 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 3+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₁+2 {O(n)}
MPRF for transition t₂₉₃: n_l6___12(X₀, X₁, X₂) → n_l5___11(X₀, X₁, X₂) :|: X₀ ≤ X₁ ∧ 2 ≤ X₀ ∧ X₂+1 ≤ 0 ∧ 0 ≤ 1+X₂ ∧ 1+X₀ ≤ X₁ ∧ 1+X₂ ≤ 0 ∧ 3+X₂ ≤ X₁ ∧ 3+X₂ ≤ X₀ ∧ 0 ≤ 1+X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₁+1 {O(n)}
MPRF for transition t₂₉₅: n_l6___3(X₀, X₁, X₂) → n_l5___2(X₀, X₁, X₂) :|: X₀ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ 2+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₁ {O(n)}
MPRF for transition t₂₈₁: n_l1___6(X₀, X₁, X₂) → n_l2___5(X₀, X₁, X₂) :|: 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 3+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ 1+X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
8⋅X₁⋅X₁+28⋅X₁+16 {O(n^2)}
MPRF for transition t₂₈₂: n_l2___5(X₀, X₁, X₂) → n_l3___4(X₀, X₁, Arg3_P) :|: 2+X₂ ≤ X₀ ∧ 1+Arg3_P ≤ X₀ ∧ 0 ≤ Arg3_P ∧ X₂ ≤ Arg3_P ∧ Arg3_P ≤ X₂ ∧ 3+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
3⋅X₁⋅X₁+7⋅X₁ {O(n^2)}
MPRF for transition t₂₈₆: n_l3___4(X₀, X₁, X₂) → n_l1___6(X₀, X₁, X₂-1) :|: 2+X₂ ≤ X₀ ∧ 3+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
8⋅X₁⋅X₁+28⋅X₁+14 {O(n^2)}
CFR did not improve the program. Rolling back
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:3⋅X₁⋅X₁+14⋅X₁+19 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₁+2 {O(n)}
t₃: 1 {O(1)}
t₄: X₁+1 {O(n)}
t₅: X₁+1 {O(n)}
t₆: X₁⋅X₁+3⋅X₁+3 {O(n^2)}
t₇: X₁⋅X₁+3⋅X₁+3 {O(n^2)}
t₈: X₁+1 {O(n)}
t₉: X₁⋅X₁+3⋅X₁+3 {O(n^2)}
t₁₀: X₁+1 {O(n)}
t₁₁: 1 {O(1)}
Costbounds
Overall costbound: 3⋅X₁⋅X₁+14⋅X₁+19 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₁+2 {O(n)}
t₃: 1 {O(1)}
t₄: X₁+1 {O(n)}
t₅: X₁+1 {O(n)}
t₆: X₁⋅X₁+3⋅X₁+3 {O(n^2)}
t₇: X₁⋅X₁+3⋅X₁+3 {O(n^2)}
t₈: X₁+1 {O(n)}
t₉: X₁⋅X₁+3⋅X₁+3 {O(n^2)}
t₁₀: X₁+1 {O(n)}
t₁₁: 1 {O(1)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₁, X₀: 1 {O(1)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₂, X₀: X₁+2 {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₃: X₁+X₃+4 {O(n)}
t₃, X₀: X₁+3 {O(n)}
t₃, X₁: 2⋅X₁ {O(n)}
t₃, X₃: X₁+X₃+4 {O(n)}
t₄, X₀: X₁+2 {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₃: X₁+2 {O(n)}
t₅, X₀: X₁+2 {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₃: 1 {O(1)}
t₆, X₀: X₁+2 {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₃: X₁+3 {O(n)}
t₇, X₀: X₁+2 {O(n)}
t₇, X₁: X₁ {O(n)}
t₇, X₃: X₁+3 {O(n)}
t₈, X₀: X₁+2 {O(n)}
t₈, X₁: X₁ {O(n)}
t₈, X₃: X₁+3 {O(n)}
t₉, X₀: X₁+2 {O(n)}
t₉, X₁: X₁ {O(n)}
t₉, X₃: X₁+3 {O(n)}
t₁₀, X₀: X₁+2 {O(n)}
t₁₀, X₁: X₁ {O(n)}
t₁₀, X₃: X₁+4 {O(n)}
t₁₁, X₀: X₁+3 {O(n)}
t₁₁, X₁: 2⋅X₁ {O(n)}
t₁₁, X₃: X₁+X₃+4 {O(n)}