Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars: G, H, I
Locations: l0, l1, l2
Transitions:
t₄: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₃, X₄, X₅)
t₁: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂-1, G, 0, H) :|: 1 ≤ X₀ ∧ 3 ≤ X₂
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀-1, X₁, I, G, H, X₅) :|: H+1 ≤ 0 ∧ 1 ≤ X₀
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀-1, X₁, I, G, H, X₅) :|: 1 ≤ H ∧ 1 ≤ X₀
t₀: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, G, X₂, X₃, X₄, X₅) :|: X₀ ≤ 0

Preprocessing

Eliminate variables {G,X₁,X₃,X₄,X₅} that do not contribute to the problem

Found invariant X₀ ≤ 0 for location l2

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars: H, I
Locations: l0, l1, l2
Transitions:
t₁₀: l0(X₀, X₁) → l1(X₀, X₁)
t₁₁: l1(X₀, X₁) → l1(X₀, X₁-1) :|: 1 ≤ X₀ ∧ 3 ≤ X₁
t₁₂: l1(X₀, X₁) → l1(X₀-1, I) :|: H+1 ≤ 0 ∧ 1 ≤ X₀
t₁₃: l1(X₀, X₁) → l1(X₀-1, I) :|: 1 ≤ H ∧ 1 ≤ X₀
t₁₄: l1(X₀, X₁) → l2(X₀, X₁) :|: X₀ ≤ 0

MPRF for transition t₁₂: l1(X₀, X₁) → l1(X₀-1, I) :|: H+1 ≤ 0 ∧ 1 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

MPRF for transition t₁₃: l1(X₀, X₁) → l1(X₀-1, I) :|: 1 ≤ H ∧ 1 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

Analysing control-flow refined program

Cut unsatisfiable transition t₉₂: n_l1___2→l2

Found invariant X₀ ≤ 0 for location l2

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

Found invariant 0 ≤ X₀ for location n_l1___1

MPRF for transition t₇₀: n_l1___1(X₀, X₁) → n_l1___1(Arg0_P, NoDet0) :|: 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ Arg0_P ∧ X₀ ≤ Arg0_P+1 ∧ 1+Arg0_P ≤ X₀ ∧ 0 ≤ X₀ of depth 1:

new bound:

3⋅X₀+2 {O(n)}

MPRF for transition t₇₁: n_l1___1(X₀, X₁) → n_l1___1(Arg0_P, NoDet0) :|: 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ Arg0_P ∧ X₀ ≤ Arg0_P+1 ∧ 1+Arg0_P ≤ X₀ ∧ 0 ≤ X₀ of depth 1:

new bound:

3⋅X₀+2 {O(n)}

MPRF for transition t₇₂: n_l1___1(X₀, X₁) → n_l1___2(X₀, X₁-1) :|: 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀ ∧ 3 ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

3⋅X₀+2 {O(n)}

MPRF for transition t₇₃: n_l1___2(X₀, X₁) → n_l1___1(Arg0_P, NoDet0) :|: 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 2 ≤ X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ Arg0_P ∧ X₀ ≤ Arg0_P+1 ∧ 1+Arg0_P ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

3⋅X₀+3 {O(n)}

MPRF for transition t₇₄: n_l1___2(X₀, X₁) → n_l1___1(Arg0_P, NoDet0) :|: 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 2 ≤ X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ Arg0_P ∧ X₀ ≤ Arg0_P+1 ∧ 1+Arg0_P ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

3⋅X₀+3 {O(n)}

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₁₀: 1 {O(1)}
t₁₁: inf {Infinity}
t₁₂: X₀ {O(n)}
t₁₃: X₀ {O(n)}
t₁₄: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₁₀: 1 {O(1)}
t₁₁: inf {Infinity}
t₁₂: X₀ {O(n)}
t₁₃: X₀ {O(n)}
t₁₄: 1 {O(1)}

Sizebounds

t₁₀, X₀: X₀ {O(n)}
t₁₀, X₁: X₁ {O(n)}
t₁₁, X₀: X₀ {O(n)}
t₁₂, X₀: X₀ {O(n)}
t₁₃, X₀: X₀ {O(n)}
t₁₄, X₀: 3⋅X₀ {O(n)}