Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₁: l1(X₀, X₁, X₂) → l1(X₀-1, X₁, (X₁)²+X₂) :|: 1 ≤ X₀
t₂: l1(X₀, X₁, X₂) → l1(X₀-1, X₁, 1+(X₁)²+X₂) :|: 1 ≤ X₀
t₃: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₄: l2(X₀, X₁, X₂) → l2(X₀, X₁, X₂-1) :|: 1 ≤ X₂

Preprocessing

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₁: l1(X₀, X₁, X₂) → l1(X₀-1, X₁, (X₁)²+X₂) :|: 1 ≤ X₀
t₂: l1(X₀, X₁, X₂) → l1(X₀-1, X₁, 1+(X₁)²+X₂) :|: 1 ≤ X₀
t₃: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₄: l2(X₀, X₁, X₂) → l2(X₀, X₁, X₂-1) :|: 1 ≤ X₂

MPRF for transition t₁: l1(X₀, X₁, X₂) → l1(X₀-1, X₁, Temp_Int₇₅+X₂) :|: 1 ≤ X₀ ∧ 0 ≤ Temp_Int₇₅ of depth 1:

new bound:

X₀ {O(n)}

• l1: [X₀]

MPRF for transition t₂: l1(X₀, X₁, X₂) → l1(X₀-1, X₁, Temp_Int₇₆+Temp_Int₇₇+X₂) :|: 1 ≤ X₀ ∧ 0 ≤ Temp_Int₇₇ of depth 1:

new bound:

X₀ {O(n)}

• l1: [X₀]

MPRF for transition t₄: l2(X₀, X₁, X₂) → l2(X₀, X₁, X₂-1) :|: 1 ≤ X₂ of depth 1:

new bound:

8⋅X₀⋅X₁⋅X₁+16⋅X₁⋅X₁+4⋅X₂+6⋅X₀+10 {O(n^3)}

• l2: [X₂]

Found invariant 0 ≤ X₂ for location l2_v1

All Bounds

Timebounds

Overall timebound:8⋅X₀⋅X₁⋅X₁+16⋅X₁⋅X₁+4⋅X₂+8⋅X₀+12 {O(n^3)}
t₀: 1 {O(1)}
t₁: X₀ {O(n)}
t₂: X₀ {O(n)}
t₃: 1 {O(1)}
t₄: 8⋅X₀⋅X₁⋅X₁+16⋅X₁⋅X₁+4⋅X₂+6⋅X₀+10 {O(n^3)}

Costbounds

Overall costbound: 8⋅X₀⋅X₁⋅X₁+16⋅X₁⋅X₁+4⋅X₂+8⋅X₀+12 {O(n^3)}
t₀: 1 {O(1)}
t₁: X₀ {O(n)}
t₂: X₀ {O(n)}
t₃: 1 {O(1)}
t₄: 8⋅X₀⋅X₁⋅X₁+16⋅X₁⋅X₁+4⋅X₂+6⋅X₀+10 {O(n^3)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: 3⋅X₀⋅X₁⋅X₁+6⋅X₁⋅X₁+2⋅X₀+X₂+3 {O(n^3)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: 5⋅X₀⋅X₁⋅X₁+10⋅X₁⋅X₁+2⋅X₂+4⋅X₀+7 {O(n^3)}
t₃, X₀: 3⋅X₀ {O(n)}
t₃, X₁: 3⋅X₁ {O(n)}
t₃, X₂: 8⋅X₀⋅X₁⋅X₁+16⋅X₁⋅X₁+4⋅X₂+6⋅X₀+10 {O(n^3)}
t₄, X₀: 3⋅X₀ {O(n)}
t₄, X₁: 3⋅X₁ {O(n)}
t₄, X₂: 8⋅X₀⋅X₁⋅X₁+16⋅X₁⋅X₁+4⋅X₂+6⋅X₀+10 {O(n^3)}