Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l10, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂) → l7(X₀, X₁, X₂)
t₁₀: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂)
t₆: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂)
t₈: l3(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₁₁: l4(X₀, X₁, X₂) → l5(X₀, X₁+1, X₂)
t₄: l5(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₁+1 ≤ X₀
t₅: l5(X₀, X₁, X₂) → l9(X₀, X₁, X₂) :|: X₀ < 1+X₁
t₂: l6(X₀, X₁, X₂) → l5(X₀, 0, X₂) :|: 0 ≤ X₀
t₃: l6(X₀, X₁, X₂) → l8(X₀, X₁, X₂) :|: X₀ < 0
t₁: l7(X₀, X₁, X₂) → l6(X₂, X₁, X₂)
t₁₃: l8(X₀, X₁, X₂) → l10(X₀, X₁, X₂)
t₁₂: l9(X₀, X₁, X₂) → l6(X₀-1, X₁, X₂)

Preprocessing

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

Found invariant X₀ ≤ X₂ for location l6

Found invariant 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l5

Found invariant X₀ ≤ X₂ ∧ 1+X₀ ≤ 0 for location l8

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

Found invariant X₀ ≤ X₂ ∧ 1+X₀ ≤ 0 for location l10

Found invariant 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l4

Found invariant 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l9

Found invariant 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l10, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂) → l7(X₀, X₁, X₂)
t₁₀: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₆: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₈: l3(X₀, X₁, X₂) → l1(X₀, X₁, X₂) :|: 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₁: l4(X₀, X₁, X₂) → l5(X₀, X₁+1, X₂) :|: 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₄: l5(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₁+1 ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₅: l5(X₀, X₁, X₂) → l9(X₀, X₁, X₂) :|: X₀ < 1+X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₂: l6(X₀, X₁, X₂) → l5(X₀, 0, X₂) :|: 0 ≤ X₀ ∧ X₀ ≤ X₂
t₃: l6(X₀, X₁, X₂) → l8(X₀, X₁, X₂) :|: X₀ < 0 ∧ X₀ ≤ X₂
t₁: l7(X₀, X₁, X₂) → l6(X₂, X₁, X₂)
t₁₃: l8(X₀, X₁, X₂) → l10(X₀, X₁, X₂) :|: X₀ ≤ X₂ ∧ 1+X₀ ≤ 0
t₁₂: l9(X₀, X₁, X₂) → l6(X₀-1, X₁, X₂) :|: 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀

MPRF for transition t₂: l6(X₀, X₁, X₂) → l5(X₀, 0, X₂) :|: 0 ≤ X₀ ∧ X₀ ≤ X₂ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF for transition t₅: l5(X₀, X₁, X₂) → l9(X₀, X₁, X₂) :|: X₀ < 1+X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF for transition t₁₂: l9(X₀, X₁, X₂) → l6(X₀-1, X₁, X₂) :|: 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₂+1 {O(n)}

TWN: t₄: l5→l2

cycle: [t₄: l5→l2; t₆: l2→l3; t₈: l3→l1; t₁₀: l1→l4; t₁₁: l4→l5]
loop: (X₁+1 ≤ X₀,(X₀,X₁) -> (X₀,X₁+1)
order: [X₀; X₁]
closed-form:
X₀: X₀
X₁: X₁ + [[n != 0]] * n^1

Termination: true
Formula:

1 < 0
∨ X₁+1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁+1 ≤ X₀ ∧ X₀ ≤ X₁+1

Stabilization-Threshold for: X₁+1 ≤ X₀
alphas_abs: X₁+X₀+1
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+4 {O(n)}

TWN - Lifting for t₄: l5→l2 of 2⋅X₀+2⋅X₁+6 {O(n)}

relevant size-bounds w.r.t. t₂:
X₀: X₂+1 {O(n)}
X₁: 0 {O(1)}
Runtime-bound of t₂: X₂+1 {O(n)}
Results in: 2⋅X₂⋅X₂+10⋅X₂+8 {O(n^2)}

TWN: t₆: l2→l3

TWN - Lifting for t₆: l2→l3 of 2⋅X₀+2⋅X₁+6 {O(n)}

relevant size-bounds w.r.t. t₂:
X₀: X₂+1 {O(n)}
X₁: 0 {O(1)}
Runtime-bound of t₂: X₂+1 {O(n)}
Results in: 2⋅X₂⋅X₂+10⋅X₂+8 {O(n^2)}

TWN: t₈: l3→l1

TWN - Lifting for t₈: l3→l1 of 2⋅X₀+2⋅X₁+6 {O(n)}

relevant size-bounds w.r.t. t₂:
X₀: X₂+1 {O(n)}
X₁: 0 {O(1)}
Runtime-bound of t₂: X₂+1 {O(n)}
Results in: 2⋅X₂⋅X₂+10⋅X₂+8 {O(n^2)}

TWN: t₁₀: l1→l4

TWN - Lifting for t₁₀: l1→l4 of 2⋅X₀+2⋅X₁+6 {O(n)}

relevant size-bounds w.r.t. t₂:
X₀: X₂+1 {O(n)}
X₁: 0 {O(1)}
Runtime-bound of t₂: X₂+1 {O(n)}
Results in: 2⋅X₂⋅X₂+10⋅X₂+8 {O(n^2)}

TWN: t₁₁: l4→l5

TWN - Lifting for t₁₁: l4→l5 of 2⋅X₀+2⋅X₁+6 {O(n)}

relevant size-bounds w.r.t. t₂:
X₀: X₂+1 {O(n)}
X₁: 0 {O(1)}
Runtime-bound of t₂: X₂+1 {O(n)}
Results in: 2⋅X₂⋅X₂+10⋅X₂+8 {O(n^2)}

Chain transitions t₈: l3→l1 and t₁₀: l1→l4 to t₇₆: l3→l4

Chain transitions t₄: l5→l2 and t₆: l2→l3 to t₇₇: l5→l3

Chain transitions t₇₇: l5→l3 and t₇₆: l3→l4 to t₇₈: l5→l4

Chain transitions t₇₇: l5→l3 and t₈: l3→l1 to t₇₉: l5→l1

Chain transitions t₇₈: l5→l4 and t₁₁: l4→l5 to t₈₀: l5→l5

Chain transitions t₁₂: l9→l6 and t₃: l6→l8 to t₈₁: l9→l8

Chain transitions t₁: l7→l6 and t₃: l6→l8 to t₈₂: l7→l8

Chain transitions t₁: l7→l6 and t₂: l6→l5 to t₈₃: l7→l5

Chain transitions t₁₂: l9→l6 and t₂: l6→l5 to t₈₄: l9→l5

Chain transitions t₅: l5→l9 and t₈₁: l9→l8 to t₈₅: l5→l8

Chain transitions t₅: l5→l9 and t₁₂: l9→l6 to t₈₆: l5→l6

Chain transitions t₅: l5→l9 and t₈₄: l9→l5 to t₈₇: l5→l5

Analysing control-flow refined program

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

Found invariant X₀ ≤ X₂ for location l6

Found invariant 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l5

Found invariant X₀ ≤ X₂ ∧ 1+X₀ ≤ 0 for location l8

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

Found invariant X₀ ≤ X₂ ∧ 1+X₀ ≤ 0 for location l10

Found invariant 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l4

Found invariant 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l9

Found invariant 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l3

MPRF for transition t₈₇: l5(X₀, X₁, X₂) -{3}> l5(X₀-1, 0, X₂) :|: X₀ < 1+X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 1+X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₂+1 {O(n)}

TWN: t₈₀: l5→l5

cycle: [t₈₀: l5→l5]
loop: (X₁+1 ≤ X₀,(X₀,X₁) -> (X₀,X₁+1)
order: [X₀; X₁]
closed-form:
X₀: X₀
X₁: X₁ + [[n != 0]] * n^1

Termination: true
Formula:

1 < 0
∨ X₁+1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁+1 ≤ X₀ ∧ X₀ ≤ X₁+1

Stabilization-Threshold for: X₁+1 ≤ X₀
alphas_abs: X₁+X₀+1
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+4 {O(n)}
loop: (X₁+1 ≤ X₀,(X₀,X₁) -> (X₀,X₁+1)
order: [X₀; X₁]
closed-form:
X₀: X₀
X₁: X₁ + [[n != 0]] * n^1

Termination: true
Formula:

1 < 0
∨ X₁+1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁+1 ≤ X₀ ∧ X₀ ≤ X₁+1

Stabilization-Threshold for: X₁+1 ≤ X₀
alphas_abs: X₁+X₀+1
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+4 {O(n)}

TWN - Lifting for t₈₀: l5→l5 of 2⋅X₀+2⋅X₁+6 {O(n)}

relevant size-bounds w.r.t. t₈₃:
X₀: X₂ {O(n)}
X₁: 0 {O(1)}
Runtime-bound of t₈₃: 1 {O(1)}
Results in: 2⋅X₂+6 {O(n)}

TWN - Lifting for t₈₀: l5→l5 of 2⋅X₀+2⋅X₁+6 {O(n)}

relevant size-bounds w.r.t. t₈₇:
X₀: X₂ {O(n)}
X₁: 0 {O(1)}
Runtime-bound of t₈₇: X₂+1 {O(n)}
Results in: 2⋅X₂⋅X₂+8⋅X₂+6 {O(n^2)}

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

Analysing control-flow refined program

Found invariant X₀ ≤ X₂ for location l6

Found invariant 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l4___6

Found invariant 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l5___5

Found invariant 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l1___7

Found invariant 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l3___3

Found invariant 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l1___2

Found invariant 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l2___9

Found invariant 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l3___8

Found invariant 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l4___1

Found invariant 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l5

Found invariant X₀ ≤ X₂ ∧ 1+X₀ ≤ 0 for location l8

Found invariant X₀ ≤ X₂ ∧ 1+X₀ ≤ 0 for location l10

Found invariant 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l9

Found invariant 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l2___4

knowledge_propagation leads to new time bound X₂+1 {O(n)} for transition t₁₈₃: l5(X₀, X₁, X₂) → n_l2___9(X₀, X₁, X₂) :|: X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀

knowledge_propagation leads to new time bound X₂+1 {O(n)} for transition t₁₇₈: n_l2___9(X₀, X₁, X₂) → n_l3___8(X₀, X₁, X₂) :|: X₁ ≤ 0 ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀

knowledge_propagation leads to new time bound X₂+1 {O(n)} for transition t₁₈₀: n_l3___8(X₀, X₁, X₂) → n_l1___7(X₀, X₁, X₂) :|: X₁ ≤ 0 ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀

knowledge_propagation leads to new time bound X₂+1 {O(n)} for transition t₁₇₆: n_l1___7(X₀, X₁, X₂) → n_l4___6(X₀, X₁, X₂) :|: X₁ ≤ 0 ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀

knowledge_propagation leads to new time bound X₂+1 {O(n)} for transition t₁₈₂: n_l4___6(X₀, X₁, X₂) → n_l5___5(X₀, X₁+1, X₂) :|: X₁ ≤ 0 ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀

MPRF for transition t₁₇₅: n_l1___2(X₀, X₁, X₂) → n_l4___1(X₀, X₁, X₂) :|: 1 ≤ X₁ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₂⋅X₂+X₂ {O(n^2)}

MPRF for transition t₁₇₇: n_l2___4(X₀, X₁, X₂) → n_l3___3(X₀, X₁, X₂) :|: 1 ≤ X₁ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₂⋅X₂+X₂ {O(n^2)}

MPRF for transition t₁₇₉: n_l3___3(X₀, X₁, X₂) → n_l1___2(X₀, X₁, X₂) :|: 1 ≤ X₁ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₂⋅X₂+4⋅X₂+1 {O(n^2)}

MPRF for transition t₁₈₁: n_l4___1(X₀, X₁, X₂) → n_l5___5(X₀, X₁+1, X₂) :|: 1 ≤ X₁ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₂⋅X₂+X₂ {O(n^2)}

MPRF for transition t₁₈₄: n_l5___5(X₀, X₁, X₂) → n_l2___4(X₀, X₁, X₂) :|: 1 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₂⋅X₂+4⋅X₂+2 {O(n^2)}

MPRF for transition t₁₉₁: n_l5___5(X₀, X₁, X₂) → l9(X₀, X₁, X₂) :|: X₀ < 1+X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₂+1 {O(n)}

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:10⋅X₂⋅X₂+53⋅X₂+47 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₂+1 {O(n)}
t₃: 1 {O(1)}
t₄: 2⋅X₂⋅X₂+10⋅X₂+8 {O(n^2)}
t₅: X₂+1 {O(n)}
t₆: 2⋅X₂⋅X₂+10⋅X₂+8 {O(n^2)}
t₈: 2⋅X₂⋅X₂+10⋅X₂+8 {O(n^2)}
t₁₀: 2⋅X₂⋅X₂+10⋅X₂+8 {O(n^2)}
t₁₁: 2⋅X₂⋅X₂+10⋅X₂+8 {O(n^2)}
t₁₂: X₂+1 {O(n)}
t₁₃: 1 {O(1)}

Costbounds

Overall costbound: 10⋅X₂⋅X₂+53⋅X₂+47 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₂+1 {O(n)}
t₃: 1 {O(1)}
t₄: 2⋅X₂⋅X₂+10⋅X₂+8 {O(n^2)}
t₅: X₂+1 {O(n)}
t₆: 2⋅X₂⋅X₂+10⋅X₂+8 {O(n^2)}
t₈: 2⋅X₂⋅X₂+10⋅X₂+8 {O(n^2)}
t₁₀: 2⋅X₂⋅X₂+10⋅X₂+8 {O(n^2)}
t₁₁: 2⋅X₂⋅X₂+10⋅X₂+8 {O(n^2)}
t₁₂: X₂+1 {O(n)}
t₁₃: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₁, X₀: X₂ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₂, X₀: X₂+1 {O(n)}
t₂, X₁: 0 {O(1)}
t₂, X₂: X₂ {O(n)}
t₃, X₀: 2⋅X₂+1 {O(n)}
t₃, X₁: 2⋅X₂⋅X₂+10⋅X₂+X₁+8 {O(n^2)}
t₃, X₂: 2⋅X₂ {O(n)}
t₄, X₀: X₂+1 {O(n)}
t₄, X₁: 2⋅X₂⋅X₂+10⋅X₂+8 {O(n^2)}
t₄, X₂: X₂ {O(n)}
t₅, X₀: X₂+1 {O(n)}
t₅, X₁: 2⋅X₂⋅X₂+10⋅X₂+8 {O(n^2)}
t₅, X₂: X₂ {O(n)}
t₆, X₀: X₂+1 {O(n)}
t₆, X₁: 2⋅X₂⋅X₂+10⋅X₂+8 {O(n^2)}
t₆, X₂: X₂ {O(n)}
t₈, X₀: X₂+1 {O(n)}
t₈, X₁: 2⋅X₂⋅X₂+10⋅X₂+8 {O(n^2)}
t₈, X₂: X₂ {O(n)}
t₁₀, X₀: X₂+1 {O(n)}
t₁₀, X₁: 2⋅X₂⋅X₂+10⋅X₂+8 {O(n^2)}
t₁₀, X₂: X₂ {O(n)}
t₁₁, X₀: X₂+1 {O(n)}
t₁₁, X₁: 2⋅X₂⋅X₂+10⋅X₂+8 {O(n^2)}
t₁₁, X₂: X₂ {O(n)}
t₁₂, X₀: X₂+1 {O(n)}
t₁₂, X₁: 2⋅X₂⋅X₂+10⋅X₂+8 {O(n^2)}
t₁₂, X₂: X₂ {O(n)}
t₁₃, X₀: 2⋅X₂+1 {O(n)}
t₁₃, X₁: 2⋅X₂⋅X₂+10⋅X₂+X₁+8 {O(n^2)}
t₁₃, X₂: 2⋅X₂ {O(n)}