Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars: D, E
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂) → l7(X₀, X₁, X₂)
t₅: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₂+1 ≤ X₁
t₆: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: X₁ ≤ X₂
t₇: l2(X₀, X₁, X₂) → l1(X₀, X₁, X₂+1) :|: E+1 ≤ D
t₈: l2(X₀, X₁, X₂) → l1(X₀, X₁, X₂+1) :|: D ≤ E
t₉: l3(X₀, X₁, X₂) → l5(X₀+1, X₁, X₂)
t₄: l4(X₀, X₁, X₂) → l1(X₀, X₁, X₀+1)
t₂: l5(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: 2+X₀ ≤ X₁
t₃: l5(X₀, X₁, X₂) → l6(X₀, X₁, X₂) :|: X₁ ≤ X₀+1
t₁₀: l6(X₀, X₁, X₂) → l8(X₀, X₁, X₂)
t₁: l7(X₀, X₁, X₂) → l5(0, X₁, X₂)

Preprocessing

Found invariant 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l2

Found invariant X₁ ≤ 1+X₀ ∧ 0 ≤ X₀ for location l6

Found invariant 0 ≤ X₀ for location l5

Found invariant X₁ ≤ 1+X₀ ∧ 0 ≤ X₀ for location l8

Found invariant X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l1

Found invariant 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l4

Found invariant X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars: D, E
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂) → l7(X₀, X₁, X₂)
t₅: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₂+1 ≤ X₁ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₆: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₇: l2(X₀, X₁, X₂) → l1(X₀, X₁, X₂+1) :|: E+1 ≤ D ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₈: l2(X₀, X₁, X₂) → l1(X₀, X₁, X₂+1) :|: D ≤ E ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₉: l3(X₀, X₁, X₂) → l5(X₀+1, X₁, X₂) :|: X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₄: l4(X₀, X₁, X₂) → l1(X₀, X₁, X₀+1) :|: 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₂: l5(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: 2+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₃: l5(X₀, X₁, X₂) → l6(X₀, X₁, X₂) :|: X₁ ≤ X₀+1 ∧ 0 ≤ X₀
t₁₀: l6(X₀, X₁, X₂) → l8(X₀, X₁, X₂) :|: X₁ ≤ 1+X₀ ∧ 0 ≤ X₀
t₁: l7(X₀, X₁, X₂) → l5(0, X₁, X₂)

MPRF for transition t₂: l5(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁+1 {O(n)}

MPRF for transition t₄: l4(X₀, X₁, X₂) → l1(X₀, X₁, X₀+1) :|: 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁+1 {O(n)}

MPRF for transition t₆: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁ {O(n)}

MPRF for transition t₉: l3(X₀, X₁, X₂) → l5(X₀+1, X₁, X₂) :|: X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁+1 {O(n)}

MPRF for transition t₅: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₂+1 ≤ X₁ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁⋅X₁+2⋅X₁ {O(n^2)}

MPRF for transition t₇: l2(X₀, X₁, X₂) → l1(X₀, X₁, X₂+1) :|: E+1 ≤ D ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁⋅X₁+2⋅X₁ {O(n^2)}

MPRF for transition t₈: l2(X₀, X₁, X₂) → l1(X₀, X₁, X₂+1) :|: D ≤ E ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁⋅X₁+2⋅X₁ {O(n^2)}

Chain transitions t₄: l4→l1 and t₆: l1→l3 to t₇₀: l4→l3

Chain transitions t₈: l2→l1 and t₆: l1→l3 to t₇₁: l2→l3

Chain transitions t₈: l2→l1 and t₅: l1→l2 to t₇₂: l2→l2

Chain transitions t₄: l4→l1 and t₅: l1→l2 to t₇₃: l4→l2

Chain transitions t₇: l2→l1 and t₅: l1→l2 to t₇₄: l2→l2

Chain transitions t₇: l2→l1 and t₆: l1→l3 to t₇₅: l2→l3

Chain transitions t₇₀: l4→l3 and t₉: l3→l5 to t₇₆: l4→l5

Chain transitions t₇₅: l2→l3 and t₉: l3→l5 to t₇₇: l2→l5

Chain transitions t₇₁: l2→l3 and t₉: l3→l5 to t₇₈: l2→l5

Chain transitions t₂: l5→l4 and t₇₆: l4→l5 to t₇₉: l5→l5

Chain transitions t₂: l5→l4 and t₇₀: l4→l3 to t₈₀: l5→l3

Chain transitions t₂: l5→l4 and t₇₃: l4→l2 to t₈₁: l5→l2

Chain transitions t₂: l5→l4 and t₄: l4→l1 to t₈₂: l5→l1

Analysing control-flow refined program

Cut unsatisfiable transition t₇₉: l5→l5

Cut unsatisfiable transition t₈₀: l5→l3

Found invariant 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l2

Found invariant X₁ ≤ 1+X₀ ∧ 0 ≤ X₀ for location l6

Found invariant 0 ≤ X₀ for location l5

Found invariant X₁ ≤ 1+X₀ ∧ 0 ≤ X₀ for location l8

Found invariant X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l1

Found invariant 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l4

Found invariant X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l3

MPRF for transition t₇₇: l2(X₀, X₁, X₂) -{3}> l5(X₀+1, X₁, 1+X₂) :|: E+1 ≤ D ∧ X₁ ≤ X₂+1 ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₂+1 ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁ {O(n)}

MPRF for transition t₇₈: l2(X₀, X₁, X₂) -{3}> l5(X₀+1, X₁, 1+X₂) :|: D ≤ E ∧ X₁ ≤ X₂+1 ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₂+1 ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁ {O(n)}

MPRF for transition t₈₁: l5(X₀, X₁, X₂) -{3}> l2(X₀, X₁, 1+X₀) :|: 2+X₀ ≤ X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀+1 ≤ X₁ ∧ 0 ≤ X₀ ∧ 2 ≤ X₁+X₀ ∧ 0 ≤ 2⋅X₀ ∧ 0 ≤ 0 ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁+1 {O(n)}

MPRF for transition t₇₂: l2(X₀, X₁, X₂) -{2}> l2(X₀, X₁, 1+X₂) :|: D ≤ E ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₂+1 ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

5⋅X₁⋅X₁+8⋅X₁+3 {O(n^2)}

MPRF for transition t₇₄: l2(X₀, X₁, X₂) -{2}> l2(X₀, X₁, 1+X₂) :|: E+1 ≤ D ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₂+1 ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

5⋅X₁⋅X₁+8⋅X₁+3 {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 t₆: l1→l3

Found invariant X₁ ≤ 1+X₀ ∧ 0 ≤ X₀ for location l6

Found invariant X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l1___2

Found invariant 1+X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 3 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 3+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l2___1

Found invariant 1+X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l2___3

Found invariant 0 ≤ X₀ for location l5

Found invariant X₁ ≤ 1+X₀ ∧ 0 ≤ X₀ for location l8

Found invariant 1+X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l1

Found invariant 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l4

Found invariant X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l3

knowledge_propagation leads to new time bound X₁+1 {O(n)} for transition t₁₈₃: l1(X₀, X₁, X₂) → n_l2___3(X₀, X₁, X₂) :|: 1+X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₂ ∧ 0 ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀

knowledge_propagation leads to new time bound X₁+1 {O(n)} for transition t₁₈₆: n_l2___3(X₀, X₁, X₂) → n_l1___2(X₀, X₁, X₂+1) :|: X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀

knowledge_propagation leads to new time bound X₁+1 {O(n)} for transition t₁₈₇: n_l2___3(X₀, X₁, X₂) → n_l1___2(X₀, X₁, X₂+1) :|: X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀

MPRF for transition t₁₈₂: n_l1___2(X₀, X₁, X₂) → n_l2___1(X₀, X₁, X₂) :|: 2+X₀ ≤ X₂ ∧ 2+X₀ ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

4⋅X₁⋅X₁+12⋅X₁+8 {O(n^2)}

MPRF for transition t₁₈₄: n_l2___1(X₀, X₁, X₂) → n_l1___2(X₀, X₁, X₂+1) :|: 2+X₀ ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 3 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 3+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

4⋅X₁⋅X₁+10⋅X₁+6 {O(n^2)}

MPRF for transition t₁₈₅: n_l2___1(X₀, X₁, X₂) → n_l1___2(X₀, X₁, X₂+1) :|: 2+X₀ ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 3 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 3+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

4⋅X₁⋅X₁+10⋅X₁+6 {O(n^2)}

MPRF for transition t₁₉₄: n_l1___2(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁+1 {O(n)}

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:3⋅X₁⋅X₁+10⋅X₁+7 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₁+1 {O(n)}
t₃: 1 {O(1)}
t₄: X₁+1 {O(n)}
t₅: X₁⋅X₁+2⋅X₁ {O(n^2)}
t₆: X₁ {O(n)}
t₇: X₁⋅X₁+2⋅X₁ {O(n^2)}
t₈: X₁⋅X₁+2⋅X₁ {O(n^2)}
t₉: X₁+1 {O(n)}
t₁₀: 1 {O(1)}

Costbounds

Overall costbound: 3⋅X₁⋅X₁+10⋅X₁+7 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₁+1 {O(n)}
t₃: 1 {O(1)}
t₄: X₁+1 {O(n)}
t₅: X₁⋅X₁+2⋅X₁ {O(n^2)}
t₆: X₁ {O(n)}
t₇: X₁⋅X₁+2⋅X₁ {O(n^2)}
t₈: X₁⋅X₁+2⋅X₁ {O(n^2)}
t₉: X₁+1 {O(n)}
t₁₀: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₁, X₀: 0 {O(1)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₂, X₀: X₁+1 {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: 4⋅X₁⋅X₁+10⋅X₁+X₂+4 {O(n^2)}
t₃, X₀: X₁+1 {O(n)}
t₃, X₁: 2⋅X₁ {O(n)}
t₃, X₂: 4⋅X₁⋅X₁+10⋅X₁+X₂+4 {O(n^2)}
t₄, X₀: X₁+1 {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₁+2 {O(n)}
t₅, X₀: X₁+1 {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: 2⋅X₁⋅X₁+5⋅X₁+2 {O(n^2)}
t₆, X₀: X₁+1 {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: 4⋅X₁⋅X₁+10⋅X₁+4 {O(n^2)}
t₇, X₀: X₁+1 {O(n)}
t₇, X₁: X₁ {O(n)}
t₇, X₂: 2⋅X₁⋅X₁+5⋅X₁+2 {O(n^2)}
t₈, X₀: X₁+1 {O(n)}
t₈, X₁: X₁ {O(n)}
t₈, X₂: 2⋅X₁⋅X₁+5⋅X₁+2 {O(n^2)}
t₉, X₀: X₁+1 {O(n)}
t₉, X₁: X₁ {O(n)}
t₉, X₂: 4⋅X₁⋅X₁+10⋅X₁+4 {O(n^2)}
t₁₀, X₀: X₁+1 {O(n)}
t₁₀, X₁: 2⋅X₁ {O(n)}
t₁₀, X₂: 4⋅X₁⋅X₁+10⋅X₁+X₂+4 {O(n^2)}