Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars: D
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₁: l1(X₀, X₁, X₂) → l1(X₀-1, D, X₂) :|: 1 ≤ D ∧ 0 ≤ X₀
t₂: l1(X₀, X₁, X₂) → l1(X₀-1, D, X₂) :|: D+1 ≤ 0 ∧ 0 ≤ X₀
t₃: l1(X₀, X₁, X₂) → l1(X₀, 0, X₂) :|: 0 ≤ X₀
t₄: l1(X₀, X₁, X₂) → l2(X₀, X₁, D) :|: X₀+1 ≤ 0

Preprocessing

Eliminate variables {X₁,X₂} that do not contribute to the problem

Found invariant 1+X₀ ≤ 0 for location l2

Problem after Preprocessing

Start: l0
Program_Vars: X₀
Temp_Vars: D
Locations: l0, l1, l2
Transitions:
t₁₂: l0(X₀) → l1(X₀)
t₁₃: l1(X₀) → l1(X₀-1) :|: 1 ≤ D ∧ 0 ≤ X₀
t₁₄: l1(X₀) → l1(X₀-1) :|: D+1 ≤ 0 ∧ 0 ≤ X₀
t₁₅: l1(X₀) → l1(X₀) :|: 0 ≤ X₀
t₁₆: l1(X₀) → l2(X₀) :|: X₀+1 ≤ 0

MPRF for transition t₁₃: l1(X₀) → l1(X₀-1) :|: 1 ≤ D ∧ 0 ≤ X₀ of depth 1:

new bound:

X₀+1 {O(n)}

MPRF:

l1 [X₀+1 ]

MPRF for transition t₁₄: l1(X₀) → l1(X₀-1) :|: D+1 ≤ 0 ∧ 0 ≤ X₀ of depth 1:

new bound:

X₀+1 {O(n)}

MPRF:

l1 [X₀+1 ]

Analysing control-flow refined program

Cut unsatisfiable transition t₈₈: n_l1___1→l2

Found invariant 1+X₀ ≤ 0 for location l2

Found invariant 0 ≤ 1+X₀ for location n_l1___2

Found invariant 0 ≤ X₀ for location n_l1___1

MPRF for transition t₆₈: n_l1___1(X₀) → n_l1___2(Arg0_P) :|: 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ 1+X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ 1+X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ 1+Arg0_P ∧ X₀ ≤ Arg0_P+1 ∧ 1+Arg0_P ≤ X₀ ∧ 0 ≤ X₀ of depth 1:

new bound:

3⋅X₀+5 {O(n)}

MPRF:

n_l1___1 [X₀+1 ]
n_l1___2 [X₀+1 ]

MPRF for transition t₆₉: n_l1___1(X₀) → n_l1___2(Arg0_P) :|: 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ 1+X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ 1+X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ 1+Arg0_P ∧ X₀ ≤ Arg0_P+1 ∧ 1+Arg0_P ≤ X₀ ∧ 0 ≤ X₀ of depth 1:

new bound:

3⋅X₀+5 {O(n)}

MPRF:

n_l1___1 [X₀+1 ]
n_l1___2 [X₀+1 ]

MPRF for transition t₇₀: n_l1___2(X₀) → n_l1___1(X₀) :|: 0 ≤ 1+X₀ ∧ 0 ≤ 1+X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ 1+X₀ of depth 1:

new bound:

3⋅X₀+7 {O(n)}

MPRF:

n_l1___1 [X₀+1 ]
n_l1___2 [X₀+2 ]

MPRF for transition t₇₁: n_l1___2(X₀) → n_l1___2(Arg0_P) :|: 0 ≤ 1+X₀ ∧ 0 ≤ 1+X₀ ∧ 0 ≤ 1+Arg0_P ∧ X₀ ≤ Arg0_P+1 ∧ 1+Arg0_P ≤ X₀ ∧ 0 ≤ 1+X₀ of depth 1:

new bound:

3⋅X₀+7 {O(n)}

MPRF:

n_l1___1 [X₀+1 ]
n_l1___2 [X₀+2 ]

MPRF for transition t₇₂: n_l1___2(X₀) → n_l1___2(Arg0_P) :|: 0 ≤ 1+X₀ ∧ 0 ≤ 1+X₀ ∧ 0 ≤ 1+Arg0_P ∧ X₀ ≤ Arg0_P+1 ∧ 1+Arg0_P ≤ X₀ ∧ 0 ≤ 1+X₀ of depth 1:

new bound:

3⋅X₀+7 {O(n)}

MPRF:

n_l1___1 [X₀+1 ]
n_l1___2 [X₀+2 ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₁₂: 1 {O(1)}
t₁₃: X₀+1 {O(n)}
t₁₄: X₀+1 {O(n)}
t₁₅: inf {Infinity}
t₁₆: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₁₂: 1 {O(1)}
t₁₃: X₀+1 {O(n)}
t₁₄: X₀+1 {O(n)}
t₁₅: inf {Infinity}
t₁₆: 1 {O(1)}

Sizebounds

t₁₂, X₀: X₀ {O(n)}
t₁₃, X₀: 3⋅X₀+1 {O(n)}
t₁₄, X₀: 3⋅X₀+1 {O(n)}
t₁₅, X₀: 3⋅X₀+1 {O(n)}
t₁₆, X₀: 7⋅X₀+2 {O(n)}