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, X₂
Temp_Vars: H, I
Locations: l0, l1, l2
Transitions:
t₁₁: l0(X₀, X₂) → l1(X₀, X₂)
t₁₃: l1(X₀, X₂) → l1(X₀, X₂-1) :|: 1 ≤ X₀ ∧ 3 ≤ X₂
t₁₄: l1(X₀, X₂) → l1(X₀-1, I) :|: H+1 ≤ 0 ∧ 1 ≤ X₀
t₁₅: l1(X₀, X₂) → l1(X₀-1, I) :|: 1 ≤ H ∧ 1 ≤ X₀
t₁₂: l1(X₀, X₂) → l2(X₀, X₂) :|: X₀ ≤ 0

MPRF for transition t₁₄: l1(X₀, X₂) → l1(X₀-1, I) :|: H+1 ≤ 0 ∧ 1 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

MPRF:

l1 [X₀ ]

MPRF for transition t₁₅: l1(X₀, X₂) → l1(X₀-1, I) :|: 1 ≤ H ∧ 1 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

MPRF:

l1 [X₀ ]

Found invariant 1 ≤ 0 for location l2

Found invariant 1 ≤ 0 for location l1

Found invariant 1 ≤ 0 for location l2

Found invariant 1 ≤ 0 for location l1

Found invariant X₀ ≤ 0 for location l2

Analysing control-flow refined program

Cut unsatisfiable transition t₉₇: n_l1___2→l2

Found invariant X₀ ≤ 0 for location l2

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

Found invariant 0 ≤ X₀ for location n_l1___1

MPRF for transition t₇₅: n_l1___1(X₀, X₂) → 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:

n_l1___1 [X₀+1 ]
n_l1___2 [X₀ ]

MPRF for transition t₇₆: n_l1___1(X₀, X₂) → 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:

n_l1___1 [X₀+1 ]
n_l1___2 [X₀ ]

MPRF for transition t₇₇: n_l1___1(X₀, X₂) → n_l1___2(X₀, X₂-1) :|: 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀ ∧ 3 ≤ X₂ ∧ 0 ≤ X₀ of depth 1:

new bound:

3⋅X₀+2 {O(n)}

MPRF:

n_l1___1 [X₀+1 ]
n_l1___2 [X₀ ]

MPRF for transition t₇₈: n_l1___2(X₀, X₂) → n_l1___1(Arg0_P, NoDet0) :|: 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 2 ≤ X₂ ∧ 1 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ Arg0_P ∧ X₀ ≤ Arg0_P+1 ∧ 1+Arg0_P ≤ X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1 ≤ X₀ of depth 1:

new bound:

3⋅X₀+3 {O(n)}

MPRF:

n_l1___1 [X₀+1 ]
n_l1___2 [X₀+1 ]

MPRF for transition t₇₉: n_l1___2(X₀, X₂) → n_l1___1(Arg0_P, NoDet0) :|: 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 2 ≤ X₂ ∧ 1 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ Arg0_P ∧ X₀ ≤ Arg0_P+1 ∧ 1+Arg0_P ≤ X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1 ≤ X₀ of depth 1:

new bound:

3⋅X₀+3 {O(n)}

MPRF:

n_l1___1 [X₀+1 ]
n_l1___2 [X₀+1 ]

Found invariant X₀ ≤ 0 for location l2

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

Found invariant 0 ≤ X₀ for location n_l1___1

Found invariant X₀ ≤ 0 for location l2

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

Found invariant 0 ≤ X₀ for location n_l1___1

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₁₁: 1 {O(1)}
t₁₂: 1 {O(1)}
t₁₃: inf {Infinity}
t₁₄: X₀ {O(n)}
t₁₅: X₀ {O(n)}

Costbounds

Overall costbound: inf {Infinity}
t₁₁: 1 {O(1)}
t₁₂: 1 {O(1)}
t₁₃: inf {Infinity}
t₁₄: X₀ {O(n)}
t₁₅: X₀ {O(n)}

Sizebounds

t₁₁, X₀: X₀ {O(n)}
t₁₁, X₂: X₂ {O(n)}
t₁₂, X₀: 7⋅X₀ {O(n)}
t₁₃, X₀: 3⋅X₀ {O(n)}
t₁₄, X₀: 3⋅X₀ {O(n)}
t₁₅, X₀: 3⋅X₀ {O(n)}