Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 0 ≤ X₀ ∧ X₀ ≤ X₁
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ < 0
t₄: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₁ < X₀
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₂, 20, X₂, X₃)
t₅: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃) :|: 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀
t₆: l3(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: 0 < X₀
t₇: l3(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₀ < 0
t₈: l3(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₀ < X₁
t₉: l3(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₁ < X₀
t₁₉: l4(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃)
t₁₀: l5(X₀, X₁, X₂, X₃) → l1(0, X₁-1, X₂, X₃) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀
t₁₁: l5(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁-1, X₂, X₃) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ < X₁
t₁₂: l5(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁-1, X₂, X₃) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₁ < X₀
t₁₃: l5(X₀, X₁, X₂, X₃) → l1(0, X₁, X₂, X₃) :|: X₀ < X₁ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀
t₁₄: l5(X₀, X₁, X₂, X₃) → l1(0, X₁, X₂, X₃) :|: X₁ < X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀
t₁₅: l5(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁, X₂, X₃) :|: X₀ < X₁ ∧ X₀ < X₁
t₁₆: l5(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁, X₂, X₃) :|: X₀ < X₁ ∧ X₁ < X₀
t₁₇: l5(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁, X₂, X₃) :|: X₁ < X₀ ∧ X₀ < X₁
t₁₈: l5(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁, X₂, X₃) :|: X₁ < X₀ ∧ X₁ < X₀

Preprocessing

Cut unsatisfiable transition t₇: l3→l5

Cut unsatisfiable transition t₉: l3→l5

Cut unsatisfiable transition t₁₁: l5→l1

Cut unsatisfiable transition t₁₂: l5→l1

Cut unsatisfiable transition t₁₃: l5→l1

Cut unsatisfiable transition t₁₄: l5→l1

Cut unsatisfiable transition t₁₆: l5→l1

Cut unsatisfiable transition t₁₇: l5→l1

Eliminate variables {X₃} that do not contribute to the problem

Found invariant X₁ ≤ 20 ∧ 0 ≤ X₁ for location l6

Found invariant X₁ ≤ 20 ∧ X₁ ≤ 20+X₀ ∧ X₀+X₁ ≤ 40 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 20 ∧ 0 ≤ X₀ for location l5

Found invariant X₁ ≤ 20 ∧ 0 ≤ X₁ for location l1

Found invariant X₁ ≤ 20 ∧ 0 ≤ X₁ for location l4

Found invariant X₁ ≤ 20 ∧ X₁ ≤ 20+X₀ ∧ X₀+X₁ ≤ 40 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 20 ∧ 0 ≤ X₀ for location l3

Cut unsatisfiable transition t₇₄: l5→l1

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6
Transitions:
t₆₃: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₆₄: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: 0 ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ 20 ∧ 0 ≤ X₁
t₆₅: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₀ < 0 ∧ X₁ ≤ 20 ∧ 0 ≤ X₁
t₆₆: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₁ < X₀ ∧ X₁ ≤ 20 ∧ 0 ≤ X₁
t₆₇: l2(X₀, X₁, X₂) → l1(X₂, 20, X₂)
t₆₈: l3(X₀, X₁, X₂) → l1(X₀, X₁, X₂) :|: 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₁ ≤ 20 ∧ X₁ ≤ 20+X₀ ∧ X₀+X₁ ≤ 40 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 20 ∧ 0 ≤ X₀
t₆₉: l3(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: 0 < X₀ ∧ X₁ ≤ 20 ∧ X₁ ≤ 20+X₀ ∧ X₀+X₁ ≤ 40 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 20 ∧ 0 ≤ X₀
t₇₀: l3(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₀ < X₁ ∧ X₁ ≤ 20 ∧ X₁ ≤ 20+X₀ ∧ X₀+X₁ ≤ 40 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 20 ∧ 0 ≤ X₀
t₇₁: l4(X₀, X₁, X₂) → l6(X₀, X₁, X₂) :|: X₁ ≤ 20 ∧ 0 ≤ X₁
t₇₂: l5(X₀, X₁, X₂) → l1(0, X₁-1, X₂) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₁ ≤ 20 ∧ X₁ ≤ 20+X₀ ∧ X₀+X₁ ≤ 40 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 20 ∧ 0 ≤ X₀
t₇₃: l5(X₀, X₁, X₂) → l1(X₀+1, X₁, X₂) :|: X₀ < X₁ ∧ X₀ < X₁ ∧ X₁ ≤ 20 ∧ X₁ ≤ 20+X₀ ∧ X₀+X₁ ≤ 40 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 20 ∧ 0 ≤ X₀

MPRF for transition t₆₉: l3(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: 0 < X₀ ∧ X₁ ≤ 20 ∧ X₁ ≤ 20+X₀ ∧ X₀+X₁ ≤ 40 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 20 ∧ 0 ≤ X₀ of depth 1:

new bound:

X₂+441 {O(n)}

MPRF for transition t₇₀: l3(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₀ < X₁ ∧ X₁ ≤ 20 ∧ X₁ ≤ 20+X₀ ∧ X₀+X₁ ≤ 40 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 20 ∧ 0 ≤ X₀ of depth 1:

new bound:

X₂+439 {O(n)}

MPRF for transition t₇₂: l5(X₀, X₁, X₂) → l1(0, X₁-1, X₂) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₁ ≤ 20 ∧ X₁ ≤ 20+X₀ ∧ X₀+X₁ ≤ 40 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 20 ∧ 0 ≤ X₀ of depth 1:

new bound:

20 {O(1)}

MPRF for transition t₇₃: l5(X₀, X₁, X₂) → l1(X₀+1, X₁, X₂) :|: X₀ < X₁ ∧ X₀ < X₁ ∧ X₁ ≤ 20 ∧ X₁ ≤ 20+X₀ ∧ X₀+X₁ ≤ 40 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 20 ∧ 0 ≤ X₀ of depth 1:

new bound:

X₂+420 {O(n)}

Chain transitions t₇₃: l5→l1 and t₆₆: l1→l4 to t₁₅₇: l5→l4

Chain transitions t₇₂: l5→l1 and t₆₆: l1→l4 to t₁₅₈: l5→l4

Chain transitions t₇₂: l5→l1 and t₆₅: l1→l4 to t₁₅₉: l5→l4

Chain transitions t₇₃: l5→l1 and t₆₅: l1→l4 to t₁₆₀: l5→l4

Chain transitions t₆₈: l3→l1 and t₆₅: l1→l4 to t₁₆₁: l3→l4

Chain transitions t₆₈: l3→l1 and t₆₆: l1→l4 to t₁₆₂: l3→l4

Chain transitions t₆₈: l3→l1 and t₆₄: l1→l3 to t₁₆₃: l3→l3

Chain transitions t₇₂: l5→l1 and t₆₄: l1→l3 to t₁₆₄: l5→l3

Chain transitions t₇₃: l5→l1 and t₆₄: l1→l3 to t₁₆₅: l5→l3

Chain transitions t₆₇: l2→l1 and t₆₄: l1→l3 to t₁₆₆: l2→l3

Chain transitions t₆₇: l2→l1 and t₆₅: l1→l4 to t₁₆₇: l2→l4

Chain transitions t₆₇: l2→l1 and t₆₆: l1→l4 to t₁₆₈: l2→l4

Chain transitions t₇₀: l3→l5 and t₁₆₀: l5→l4 to t₁₆₉: l3→l4

Chain transitions t₆₉: l3→l5 and t₁₆₀: l5→l4 to t₁₇₀: l3→l4

Chain transitions t₆₉: l3→l5 and t₁₅₉: l5→l4 to t₁₇₁: l3→l4

Chain transitions t₇₀: l3→l5 and t₁₅₉: l5→l4 to t₁₇₂: l3→l4

Chain transitions t₆₉: l3→l5 and t₁₅₈: l5→l4 to t₁₇₃: l3→l4

Chain transitions t₇₀: l3→l5 and t₁₅₈: l5→l4 to t₁₇₄: l3→l4

Chain transitions t₆₉: l3→l5 and t₁₅₇: l5→l4 to t₁₇₅: l3→l4

Chain transitions t₇₀: l3→l5 and t₁₅₇: l5→l4 to t₁₇₆: l3→l4

Chain transitions t₆₉: l3→l5 and t₁₆₅: l5→l3 to t₁₇₇: l3→l3

Chain transitions t₇₀: l3→l5 and t₁₆₅: l5→l3 to t₁₇₈: l3→l3

Chain transitions t₆₉: l3→l5 and t₁₆₄: l5→l3 to t₁₇₉: l3→l3

Chain transitions t₇₀: l3→l5 and t₁₆₄: l5→l3 to t₁₈₀: l3→l3

Chain transitions t₆₉: l3→l5 and t₇₃: l5→l1 to t₁₈₁: l3→l1

Chain transitions t₇₀: l3→l5 and t₇₃: l5→l1 to t₁₈₂: l3→l1

Chain transitions t₆₉: l3→l5 and t₇₂: l5→l1 to t₁₈₃: l3→l1

Chain transitions t₇₀: l3→l5 and t₇₂: l5→l1 to t₁₈₄: l3→l1

Analysing control-flow refined program

Cut unsatisfiable transition t₁₆₁: l3→l4

Cut unsatisfiable transition t₁₆₂: l3→l4

Cut unsatisfiable transition t₁₆₉: l3→l4

Cut unsatisfiable transition t₁₇₀: l3→l4

Cut unsatisfiable transition t₁₇₁: l3→l4

Cut unsatisfiable transition t₁₇₂: l3→l4

Cut unsatisfiable transition t₁₇₃: l3→l4

Cut unsatisfiable transition t₁₇₄: l3→l4

Cut unsatisfiable transition t₁₇₅: l3→l4

Cut unsatisfiable transition t₁₇₆: l3→l4

Cut unsatisfiable transition t₁₈₀: l3→l3

Cut unsatisfiable transition t₁₈₄: l3→l1

Found invariant X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 20 ∧ 20 ≤ X₁ for location l6

Found invariant X₂ ≤ 20 ∧ X₂ ≤ 19+X₁ ∧ X₁+X₂ ≤ 40 ∧ X₂ ≤ 20+X₀ ∧ X₀+X₂ ≤ 40 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₁ ≤ 20+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ 20+X₂ ∧ X₁ ≤ 20 ∧ X₁ ≤ 20+X₀ ∧ X₀+X₁ ≤ 40 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 20 ∧ 0 ≤ X₀ for location l5

Found invariant X₂ ≤ 20+X₀ ∧ X₁ ≤ 20 ∧ 0 ≤ X₁ for location l1

Found invariant X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 20 ∧ 20 ≤ X₁ for location l4

Found invariant X₂ ≤ 20 ∧ X₂ ≤ 20+X₁ ∧ X₁+X₂ ≤ 40 ∧ X₂ ≤ 20+X₀ ∧ X₀+X₂ ≤ 40 ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ 20+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ 20+X₂ ∧ X₁ ≤ 20 ∧ X₁ ≤ 20+X₀ ∧ X₀+X₁ ≤ 40 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 20 ∧ 0 ≤ X₀ for location l3

MPRF for transition t₁₇₇: l3(X₀, X₁, X₂) -{3}> l3(1+X₀, X₁, X₂) :|: 0 < X₀ ∧ X₀ < X₁ ∧ X₀ < X₁ ∧ 0 ≤ 1+X₀ ∧ 1+X₀ ≤ X₁ ∧ X₁ ≤ 20 ∧ X₁ ≤ 20+X₀ ∧ X₀+X₁ ≤ 40 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 20 ∧ 0 ≤ X₀ ∧ X₁ ≤ 20 ∧ X₁ ≤ 20+X₀ ∧ X₀+X₁ ≤ 40 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 20 ∧ 0 ≤ X₀ ∧ X₁ ≤ 20 ∧ 0 ≤ X₁ ∧ X₂ ≤ 20 ∧ X₂ ≤ 20+X₁ ∧ X₁+X₂ ≤ 40 ∧ X₂ ≤ 20+X₀ ∧ X₀+X₂ ≤ 40 ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ 20+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ 20+X₂ ∧ X₁ ≤ 20 ∧ X₁ ≤ 20+X₀ ∧ X₀+X₁ ≤ 40 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 20 ∧ 0 ≤ X₀ of depth 1:

new bound:

X₂+421 {O(n)}

MPRF for transition t₁₇₈: l3(X₀, X₁, X₂) -{3}> l3(1+X₀, X₁, X₂) :|: X₀ < X₁ ∧ X₀ < X₁ ∧ X₀ < X₁ ∧ 0 ≤ 1+X₀ ∧ 1+X₀ ≤ X₁ ∧ X₁ ≤ 20 ∧ X₁ ≤ 20+X₀ ∧ X₀+X₁ ≤ 40 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 20 ∧ 0 ≤ X₀ ∧ X₁ ≤ 20 ∧ X₁ ≤ 20+X₀ ∧ X₀+X₁ ≤ 40 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 20 ∧ 0 ≤ X₀ ∧ X₁ ≤ 20 ∧ 0 ≤ X₁ ∧ X₂ ≤ 20 ∧ X₂ ≤ 20+X₁ ∧ X₁+X₂ ≤ 40 ∧ X₂ ≤ 20+X₀ ∧ X₀+X₂ ≤ 40 ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ 20+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ 20+X₂ ∧ X₁ ≤ 20 ∧ X₁ ≤ 20+X₀ ∧ X₀+X₁ ≤ 40 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 20 ∧ 0 ≤ X₀ of depth 1:

new bound:

X₂+421 {O(n)}

MPRF for transition t₁₇₉: l3(X₀, X₁, X₂) -{3}> l3(0, X₁-1, X₂) :|: 0 < X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ 0 ∧ 1 ≤ X₁ ∧ X₁ ≤ 20 ∧ X₁ ≤ 20+X₀ ∧ X₀+X₁ ≤ 40 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 20 ∧ 0 ≤ X₀ ∧ X₁ ≤ 20 ∧ X₁ ≤ 20+X₀ ∧ X₀+X₁ ≤ 40 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 20 ∧ 0 ≤ X₀ ∧ X₁ ≤ 21 ∧ 1 ≤ X₁ ∧ X₂ ≤ 20 ∧ X₂ ≤ 20+X₁ ∧ X₁+X₂ ≤ 40 ∧ X₂ ≤ 20+X₀ ∧ X₀+X₂ ≤ 40 ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ 20+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ 20+X₂ ∧ X₁ ≤ 20 ∧ X₁ ≤ 20+X₀ ∧ X₀+X₁ ≤ 40 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 20 ∧ 0 ≤ X₀ of depth 1:

new bound:

21 {O(1)}

TWN: t₁₆₃: l3→l3

cycle: [t₁₆₃: l3→l3]
loop: (0 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₁,(X₀,X₁) -> (X₀,X₁)
order: [X₀; X₁]
closed-form:
X₀: X₀
X₁: X₁

Termination: true
Formula:

X₀ < X₁ ∧ 0 < X₀ ∧ X₁ < X₀ ∧ X₀ < 0
∨ X₀ < X₁ ∧ 0 < X₀ ∧ X₁ < X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
∨ X₀ < X₁ ∧ 0 < X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ < 0
∨ X₀ < X₁ ∧ 0 < X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
∨ X₀ < X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₁ < X₀ ∧ X₀ < 0
∨ X₀ < X₁ ∧ X₁ < X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
∨ X₀ < X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ < 0
∨ X₀ < X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
∨ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 < X₀ ∧ X₁ < X₀ ∧ X₀ < 0
∨ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 < X₀ ∧ X₁ < X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
∨ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 < X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ < 0
∨ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 < X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
∨ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₁ < X₀ ∧ X₀ < 0
∨ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₁ < X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
∨ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ < 0
∨ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀

TWN - Lifting for t₁₆₃: l3→l3 of 6 {O(1)}

relevant size-bounds w.r.t. t₁₇₉:
Runtime-bound of t₁₇₉: 21 {O(1)}
Results in: 126 {O(1)}

Analysing control-flow refined program

Cut unsatisfiable transition t₄₀₉: n_l3___2→l5

Cut unsatisfiable transition t₄₁₀: n_l3___4→l5

Cut unsatisfiable transition t₄₁₃: n_l3___2→l5

Found invariant X₁ ≤ 19 ∧ X₁ ≤ 19+X₀ ∧ X₀+X₁ ≤ 19 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l3___4

Found invariant X₁ ≤ 20 ∧ 0 ≤ X₁ for location l6

Found invariant X₂ ≤ 20 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 40 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 40 ∧ 0 ≤ X₂ ∧ 20 ≤ X₁+X₂ ∧ X₁ ≤ 20+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 20 ∧ X₁ ≤ 20+X₀ ∧ X₀+X₁ ≤ 40 ∧ 20 ≤ X₁ ∧ 20 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 20 ∧ 0 ≤ X₀ for location n_l3___5

Found invariant X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l1___3

Found invariant X₁ ≤ 20 ∧ X₁ ≤ 20+X₀ ∧ X₀+X₁ ≤ 40 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 20 ∧ 0 ≤ X₀ for location l5

Found invariant X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l3___2

Found invariant X₁ ≤ 20 ∧ 0 ≤ X₁ for location l1

Found invariant X₁ ≤ 20 ∧ 0 ≤ X₁ for location l4

Found invariant X₁ ≤ 20 ∧ X₁ ≤ 20+X₀ ∧ X₀+X₁ ≤ 40 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 20 ∧ 0 ≤ X₀ for location n_l3___1

knowledge_propagation leads to new time bound X₂+441 {O(n)} for transition t₃₉₆: l1(X₀, X₁, X₂) → n_l3___1(X₀, X₁, X₂) :|: 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ 20 ∧ 0 ≤ X₁ ∧ X₁ ≤ 20 ∧ X₁ ≤ 20 ∧ 0 ≤ X₁

knowledge_propagation leads to new time bound 20 {O(1)} for transition t₃₉₇: l1(X₀, X₁, X₂) → n_l3___4(X₀, X₁, X₂) :|: X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ X₁ ≤ 19 ∧ 0 ≤ X₀ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ 20 ∧ 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ X₁ ≤ 20 ∧ X₁ ≤ 20 ∧ X₁ ≤ 20 ∧ 0 ≤ X₁

knowledge_propagation leads to new time bound X₂+421 {O(n)} for transition t₃₉₈: l1(X₀, X₁, X₂) → n_l3___5(X₀, X₁, X₂) :|: 20 ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ 20 ∧ 0 ≤ X₁ ∧ X₁ ≤ 20 ∧ X₁ ≤ 20 ∧ X₁ ≤ 20 ∧ 0 ≤ X₁

knowledge_propagation leads to new time bound X₂+441 {O(n)} for transition t₄₀₈: n_l3___1(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: 0 < X₀ ∧ X₁ ≤ 20 ∧ X₁ ≤ 20+X₀ ∧ X₀+X₁ ≤ 40 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 20 ∧ 0 ≤ X₀ ∧ X₁ ≤ 20 ∧ X₁ ≤ 20+X₀ ∧ X₀+X₁ ≤ 40 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 20 ∧ 0 ≤ X₀

knowledge_propagation leads to new time bound X₂+421 {O(n)} for transition t₄₁₁: n_l3___5(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: 0 < X₀ ∧ X₁ ≤ 20 ∧ X₁ ≤ 20+X₀ ∧ X₀+X₁ ≤ 40 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 20 ∧ 0 ≤ X₀ ∧ X₂ ≤ 20 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 40 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 40 ∧ 0 ≤ X₂ ∧ 20 ≤ X₁+X₂ ∧ X₁ ≤ 20+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 20 ∧ X₁ ≤ 20+X₀ ∧ X₀+X₁ ≤ 40 ∧ 20 ≤ X₁ ∧ 20 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 20 ∧ 0 ≤ X₀

knowledge_propagation leads to new time bound X₂+441 {O(n)} for transition t₄₁₂: n_l3___1(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₀ < X₁ ∧ X₁ ≤ 20 ∧ X₁ ≤ 20+X₀ ∧ X₀+X₁ ≤ 40 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 20 ∧ 0 ≤ X₀ ∧ X₁ ≤ 20 ∧ X₁ ≤ 20+X₀ ∧ X₀+X₁ ≤ 40 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 20 ∧ 0 ≤ X₀

knowledge_propagation leads to new time bound 20 {O(1)} for transition t₄₁₄: n_l3___4(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₀ < X₁ ∧ X₁ ≤ 20 ∧ X₁ ≤ 20+X₀ ∧ X₀+X₁ ≤ 40 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 20 ∧ 0 ≤ X₀ ∧ X₁ ≤ 19 ∧ X₁ ≤ 19+X₀ ∧ X₀+X₁ ≤ 19 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀

knowledge_propagation leads to new time bound X₂+421 {O(n)} for transition t₄₁₅: n_l3___5(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₀ < X₁ ∧ X₁ ≤ 20 ∧ X₁ ≤ 20+X₀ ∧ X₀+X₁ ≤ 40 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 20 ∧ 0 ≤ X₀ ∧ X₂ ≤ 20 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 40 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 40 ∧ 0 ≤ X₂ ∧ 20 ≤ X₁+X₂ ∧ X₁ ≤ 20+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 20 ∧ X₁ ≤ 20+X₀ ∧ X₀+X₁ ≤ 40 ∧ 20 ≤ X₁ ∧ 20 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 20 ∧ 0 ≤ X₀

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₆₃: 1 {O(1)}
t₆₄: inf {Infinity}
t₆₅: 1 {O(1)}
t₆₆: 1 {O(1)}
t₆₇: 1 {O(1)}
t₆₈: inf {Infinity}
t₆₉: X₂+441 {O(n)}
t₇₀: X₂+439 {O(n)}
t₇₁: 1 {O(1)}
t₇₂: 20 {O(1)}
t₇₃: X₂+420 {O(n)}

Costbounds

Overall costbound: inf {Infinity}
t₆₃: 1 {O(1)}
t₆₄: inf {Infinity}
t₆₅: 1 {O(1)}
t₆₆: 1 {O(1)}
t₆₇: 1 {O(1)}
t₆₈: inf {Infinity}
t₆₉: X₂+441 {O(n)}
t₇₀: X₂+439 {O(n)}
t₇₁: 1 {O(1)}
t₇₂: 20 {O(1)}
t₇₃: X₂+420 {O(n)}

Sizebounds

t₆₃, X₀: X₀ {O(n)}
t₆₃, X₁: X₁ {O(n)}
t₆₃, X₂: X₂ {O(n)}
t₆₄, X₀: 20 {O(1)}
t₆₄, X₁: 20 {O(1)}
t₆₄, X₂: X₂ {O(n)}
t₆₅, X₀: X₂ {O(n)}
t₆₅, X₁: 20 {O(1)}
t₆₅, X₂: X₂ {O(n)}
t₆₆, X₀: X₂ {O(n)}
t₆₆, X₁: 20 {O(1)}
t₆₆, X₂: X₂ {O(n)}
t₆₇, X₀: X₂ {O(n)}
t₆₇, X₁: 20 {O(1)}
t₆₇, X₂: X₂ {O(n)}
t₆₈, X₀: 0 {O(1)}
t₆₈, X₁: 0 {O(1)}
t₆₈, X₂: X₂ {O(n)}
t₆₉, X₀: 20 {O(1)}
t₆₉, X₁: 20 {O(1)}
t₆₉, X₂: X₂ {O(n)}
t₇₀, X₀: 19 {O(1)}
t₇₀, X₁: 20 {O(1)}
t₇₀, X₂: X₂ {O(n)}
t₇₁, X₀: 2⋅X₂ {O(n)}
t₇₁, X₁: 20 {O(1)}
t₇₁, X₂: 2⋅X₂ {O(n)}
t₇₂, X₀: 0 {O(1)}
t₇₂, X₁: 19 {O(1)}
t₇₂, X₂: X₂ {O(n)}
t₇₃, X₀: 20 {O(1)}
t₇₃, X₁: 20 {O(1)}
t₇₃, X₂: X₂ {O(n)}