Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 < X₂
t₄: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₂ ≤ 0
t₁₁: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₁: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₄, X₁, X₆, X₃, X₄, X₅, X₆) :|: 0 < X₄
t₂: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₄ ≤ 0
t₅: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀+X₂, X₁, X₂-1, X₃, X₄, X₅, X₆)
t₇: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 < X₂
t₆: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₀, X₅, X₂, X₀, X₄, X₅, X₆) :|: X₂ ≤ 0
t₉: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: (X₁)² ≤ X₃
t₈: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₃ < (X₁)²
t₁₀: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₀, 2⋅X₁, X₂, 5⋅X₃+(X₁)⁴, X₄, X₅, X₆)

Preprocessing

Cut unsatisfiable transition t₇: l5→l2

Found invariant X₂ ≤ X₆ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₀ for location l6

Found invariant X₂ ≤ X₆ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₀ for location l7

Found invariant X₂ ≤ X₆ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₂ ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₀ for location l5

Found invariant X₂ ≤ X₆ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₀ for location l1

Found invariant 1 ≤ X₆ ∧ 2 ≤ X₄+X₆ ∧ 2 ≤ X₂+X₆ ∧ X₂ ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₀ for location l4

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 < X₂ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₀
t₄: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₂ ≤ 0 ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₀
t₁₁: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₁: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₄, X₁, X₆, X₃, X₄, X₅, X₆) :|: 0 < X₄
t₂: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₄ ≤ 0
t₅: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀+X₂, X₁, X₂-1, X₃, X₄, X₅, X₆) :|: 1 ≤ X₆ ∧ 2 ≤ X₄+X₆ ∧ 2 ≤ X₂+X₆ ∧ X₂ ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₀
t₆: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₀, X₅, X₂, X₀, X₄, X₅, X₆) :|: X₂ ≤ 0 ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₂ ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₀
t₉: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: (X₁)² ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₀
t₈: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₃ < (X₁)² ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₀
t₁₀: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₀, 2⋅X₁, X₂, 5⋅X₃+(X₁)⁴, X₄, X₅, X₆) :|: X₂ ≤ X₆ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₀

MPRF for transition t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 < X₂ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₆ {O(n)}

MPRF for transition t₅: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀+X₂, X₁, X₂-1, X₃, X₄, X₅, X₆) :|: 1 ≤ X₆ ∧ 2 ≤ X₄+X₆ ∧ 2 ≤ X₂+X₆ ∧ X₂ ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₆ {O(n)}

Chain transitions t₁₀: l7→l6 and t₈: l6→l7 to t₇₀: l7→l7

Chain transitions t₆: l5→l6 and t₈: l6→l7 to t₇₁: l5→l7

Chain transitions t₆: l5→l6 and t₉: l6→l2 to t₇₂: l5→l2

Chain transitions t₁₀: l7→l6 and t₉: l6→l2 to t₇₃: l7→l2

Analysing control-flow refined program

Found invariant X₂ ≤ X₆ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₀ for location l6

Found invariant X₂ ≤ X₆ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₀ for location l7

Found invariant X₂ ≤ X₆ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₂ ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₀ for location l5

Found invariant X₂ ≤ X₆ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₀ for location l1

Found invariant 1 ≤ X₆ ∧ 2 ≤ X₄+X₆ ∧ 2 ≤ X₂+X₆ ∧ X₂ ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₀ for location l4

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

Analysing control-flow refined program

Found invariant X₂ ≤ X₆ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₂ ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₀ for location n_l6___2

Found invariant X₂ ≤ X₆ ∧ X₅ ≤ X₁ ∧ X₁ ≤ X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₀ for location l6

Found invariant X₂ ≤ X₆ ∧ X₅ ≤ X₁ ∧ X₁ ≤ X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₀ for location n_l7___3

Found invariant X₂ ≤ X₆ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₂ ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₀ for location l5

Found invariant X₂ ≤ X₆ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₀ for location l1

Found invariant 1 ≤ X₆ ∧ 2 ≤ X₄+X₆ ∧ 2 ≤ X₂+X₆ ∧ X₂ ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₀ for location l4

Found invariant X₂ ≤ X₆ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₀ for location n_l7___1

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: X₆ {O(n)}
t₄: 1 {O(1)}
t₅: X₆ {O(n)}
t₆: 1 {O(1)}
t₈: inf {Infinity}
t₉: 1 {O(1)}
t₁₀: inf {Infinity}
t₁₁: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: X₆ {O(n)}
t₄: 1 {O(1)}
t₅: X₆ {O(n)}
t₆: 1 {O(1)}
t₈: inf {Infinity}
t₉: 1 {O(1)}
t₁₀: inf {Infinity}
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)}
t₀, X₄: X₄ {O(n)}
t₀, X₅: X₅ {O(n)}
t₀, X₆: X₆ {O(n)}
t₁, X₀: X₄ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₆ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₁, X₅: X₅ {O(n)}
t₁, X₆: X₆ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: X₄ {O(n)}
t₂, X₅: X₅ {O(n)}
t₂, X₆: X₆ {O(n)}
t₃, X₀: X₆⋅X₆+X₄+X₆ {O(n^2)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: X₆ {O(n)}
t₃, X₃: X₃ {O(n)}
t₃, X₄: X₄ {O(n)}
t₃, X₅: X₅ {O(n)}
t₃, X₆: X₆ {O(n)}
t₄, X₀: X₆⋅X₆+2⋅X₄+X₆ {O(n^2)}
t₄, X₁: 2⋅X₁ {O(n)}
t₄, X₂: 2⋅X₆ {O(n)}
t₄, X₃: 2⋅X₃ {O(n)}
t₄, X₄: 2⋅X₄ {O(n)}
t₄, X₅: 2⋅X₅ {O(n)}
t₄, X₆: 2⋅X₆ {O(n)}
t₅, X₀: X₆⋅X₆+X₄+X₆ {O(n^2)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: X₆ {O(n)}
t₅, X₃: X₃ {O(n)}
t₅, X₄: X₄ {O(n)}
t₅, X₅: X₅ {O(n)}
t₅, X₆: X₆ {O(n)}
t₆, X₀: X₆⋅X₆+2⋅X₄+X₆ {O(n^2)}
t₆, X₁: 2⋅X₅ {O(n)}
t₆, X₂: 2⋅X₆ {O(n)}
t₆, X₃: X₆⋅X₆+2⋅X₄+X₆ {O(n^2)}
t₆, X₄: 2⋅X₄ {O(n)}
t₆, X₅: 2⋅X₅ {O(n)}
t₆, X₆: 2⋅X₆ {O(n)}
t₈, X₀: X₆⋅X₆+2⋅X₄+X₆ {O(n^2)}
t₈, X₂: 2⋅X₆ {O(n)}
t₈, X₄: 2⋅X₄ {O(n)}
t₈, X₅: 2⋅X₅ {O(n)}
t₈, X₆: 2⋅X₆ {O(n)}
t₉, X₀: 2⋅X₆⋅X₆+2⋅X₆+4⋅X₄ {O(n^2)}
t₉, X₂: 4⋅X₆ {O(n)}
t₉, X₄: 4⋅X₄ {O(n)}
t₉, X₅: 4⋅X₅ {O(n)}
t₉, X₆: 4⋅X₆ {O(n)}
t₁₀, X₀: X₆⋅X₆+2⋅X₄+X₆ {O(n^2)}
t₁₀, X₂: 2⋅X₆ {O(n)}
t₁₀, X₄: 2⋅X₄ {O(n)}
t₁₀, X₅: 2⋅X₅ {O(n)}
t₁₀, X₆: 2⋅X₆ {O(n)}
t₁₁, X₀: 2⋅X₆⋅X₆+2⋅X₆+4⋅X₄+X₀ {O(n^2)}
t₁₁, X₂: 4⋅X₆+X₂ {O(n)}
t₁₁, X₄: 5⋅X₄ {O(n)}
t₁₁, X₅: 5⋅X₅ {O(n)}
t₁₁, X₆: 5⋅X₆ {O(n)}