Initial Problem

Start: eval_abc_start
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: eval_abc_0, eval_abc_1, eval_abc_2, eval_abc_3, eval_abc_4, eval_abc_bb0_in, eval_abc_bb1_in, eval_abc_bb2_in, eval_abc_bb3_in, eval_abc_start, eval_abc_stop
Transitions:
t₂: eval_abc_0(X₀, X₁, X₂) → eval_abc_1(X₀, X₁, X₂)
t₃: eval_abc_1(X₀, X₁, X₂) → eval_abc_2(X₀, X₁, X₂)
t₄: eval_abc_2(X₀, X₁, X₂) → eval_abc_3(X₀, X₁, X₂)
t₅: eval_abc_3(X₀, X₁, X₂) → eval_abc_4(X₀, X₁, X₂)
t₆: eval_abc_4(X₀, X₁, X₂) → eval_abc_bb1_in(X₀, X₁, X₀)
t₁: eval_abc_bb0_in(X₀, X₁, X₂) → eval_abc_0(X₀, X₁, X₂)
t₇: eval_abc_bb1_in(X₀, X₁, X₂) → eval_abc_bb2_in(X₀, X₁, X₂) :|: X₂ ≤ X₁
t₈: eval_abc_bb1_in(X₀, X₁, X₂) → eval_abc_bb3_in(X₀, X₁, X₂) :|: 1+X₁ ≤ X₂
t₉: eval_abc_bb2_in(X₀, X₁, X₂) → eval_abc_bb1_in(X₀, X₁, 1+X₂)
t₁₀: eval_abc_bb3_in(X₀, X₁, X₂) → eval_abc_stop(X₀, X₁, X₂)
t₀: eval_abc_start(X₀, X₁, X₂) → eval_abc_bb0_in(X₀, X₁, X₂)

Preprocessing

Found invariant X₂ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₁ for location eval_abc_bb2_in

Found invariant X₀ ≤ X₂ for location eval_abc_bb1_in

Found invariant 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ for location eval_abc_stop

Found invariant 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ for location eval_abc_bb3_in

Problem after Preprocessing

Start: eval_abc_start
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: eval_abc_0, eval_abc_1, eval_abc_2, eval_abc_3, eval_abc_4, eval_abc_bb0_in, eval_abc_bb1_in, eval_abc_bb2_in, eval_abc_bb3_in, eval_abc_start, eval_abc_stop
Transitions:
t₂: eval_abc_0(X₀, X₁, X₂) → eval_abc_1(X₀, X₁, X₂)
t₃: eval_abc_1(X₀, X₁, X₂) → eval_abc_2(X₀, X₁, X₂)
t₄: eval_abc_2(X₀, X₁, X₂) → eval_abc_3(X₀, X₁, X₂)
t₅: eval_abc_3(X₀, X₁, X₂) → eval_abc_4(X₀, X₁, X₂)
t₆: eval_abc_4(X₀, X₁, X₂) → eval_abc_bb1_in(X₀, X₁, X₀)
t₁: eval_abc_bb0_in(X₀, X₁, X₂) → eval_abc_0(X₀, X₁, X₂)
t₇: eval_abc_bb1_in(X₀, X₁, X₂) → eval_abc_bb2_in(X₀, X₁, X₂) :|: X₂ ≤ X₁ ∧ X₀ ≤ X₂
t₈: eval_abc_bb1_in(X₀, X₁, X₂) → eval_abc_bb3_in(X₀, X₁, X₂) :|: 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂
t₉: eval_abc_bb2_in(X₀, X₁, X₂) → eval_abc_bb1_in(X₀, X₁, 1+X₂) :|: X₀ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₁
t₁₀: eval_abc_bb3_in(X₀, X₁, X₂) → eval_abc_stop(X₀, X₁, X₂) :|: 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂
t₀: eval_abc_start(X₀, X₁, X₂) → eval_abc_bb0_in(X₀, X₁, X₂)

MPRF for transition t₇: eval_abc_bb1_in(X₀, X₁, X₂) → eval_abc_bb2_in(X₀, X₁, X₂) :|: X₂ ≤ X₁ ∧ X₀ ≤ X₂ of depth 1:

new bound:

X₀+X₁+1 {O(n)}

MPRF:

• eval_abc_bb1_in: [1+X₁-X₂]
• eval_abc_bb2_in: [X₁-X₂]

MPRF for transition t₉: eval_abc_bb2_in(X₀, X₁, X₂) → eval_abc_bb1_in(X₀, X₁, 1+X₂) :|: X₀ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₁ of depth 1:

new bound:

X₀+X₁+1 {O(n)}

MPRF:

• eval_abc_bb1_in: [1+X₁-X₂]
• eval_abc_bb2_in: [1+X₁-X₂]

All Bounds

Timebounds

Overall timebound:2⋅X₀+2⋅X₁+11 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: X₀+X₁+1 {O(n)}
t₈: 1 {O(1)}
t₉: X₀+X₁+1 {O(n)}
t₁₀: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₀+2⋅X₁+11 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: X₀+X₁+1 {O(n)}
t₈: 1 {O(1)}
t₉: X₀+X₁+1 {O(n)}
t₁₀: 1 {O(1)}

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: X₂ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: X₂ {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₂ {O(n)}
t₅, X₀: X₀ {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: X₂ {O(n)}
t₆, X₀: X₀ {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: X₀ {O(n)}
t₇, X₀: X₀ {O(n)}
t₇, X₁: X₁ {O(n)}
t₇, X₂: 2⋅X₀+X₁+1 {O(n)}
t₈, X₀: 2⋅X₀ {O(n)}
t₈, X₁: 2⋅X₁ {O(n)}
t₈, X₂: 3⋅X₀+X₁+1 {O(n)}
t₉, X₀: X₀ {O(n)}
t₉, X₁: X₁ {O(n)}
t₉, X₂: 2⋅X₀+X₁+1 {O(n)}
t₁₀, X₀: 2⋅X₀ {O(n)}
t₁₀, X₁: 2⋅X₁ {O(n)}
t₁₀, X₂: 3⋅X₀+X₁+1 {O(n)}