KoAT2 Proof Output

Initial Problem

Start: eval_foo_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: eval_foo_bb0_in, eval_foo_bb1_in, eval_foo_bb2_in, eval_foo_bb3_in, eval_foo_start, eval_foo_stop
Transitions:
t₁: eval_foo_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_foo_bb1_in(X₃, X₄, X₅, X₃, X₄, X₅)
t₂: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 ≤ X₀
t₃: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₀ ≤ 0
t₄: eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_foo_bb1_in(X₀+X₁, X₂, -1-X₂, X₃, X₄, X₅)
t₅: eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_foo_stop(X₀, X₁, X₂, X₃, X₄, X₅)
t₀: eval_foo_start(X₀, X₁, X₂, X₃, X₄, X₅) → eval_foo_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅)

Preprocessing

Found invariant 0 ≤ X₀ for location eval_foo_bb2_in

Found invariant 1+X₀ ≤ 0 for location eval_foo_stop

Found invariant 1+X₀ ≤ 0 for location eval_foo_bb3_in

Problem after Preprocessing

Start: eval_foo_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: eval_foo_bb0_in, eval_foo_bb1_in, eval_foo_bb2_in, eval_foo_bb3_in, eval_foo_start, eval_foo_stop
Transitions:
t₁: eval_foo_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_foo_bb1_in(X₃, X₄, X₅, X₃, X₄, X₅)
t₂: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 ≤ X₀
t₃: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₀ ≤ 0
t₄: eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_foo_bb1_in(X₀+X₁, X₂, -1-X₂, X₃, X₄, X₅) :|: 0 ≤ X₀
t₅: eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_foo_stop(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₀ ≤ 0
t₀: eval_foo_start(X₀, X₁, X₂, X₃, X₄, X₅) → eval_foo_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅)

MPRF for transition t₂: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 ≤ X₀ of depth 3:

new bound:

162⋅X₃+27⋅X₅+81⋅X₄+55 {O(n)}

MPRF:

• eval_foo_bb1_in: [1+2⋅X₀+2⋅X₁+X₂; 1+3⋅X₀+X₁; X₀]
• eval_foo_bb2_in: [2⋅X₀+2⋅X₁+X₂; 1+3⋅X₀+3⋅X₁+X₂; X₀+X₁]

MPRF for transition t₄: eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_foo_bb1_in(X₀+X₁, X₂, -1-X₂, X₃, X₄, X₅) :|: 0 ≤ X₀ of depth 3:

new bound:

162⋅X₃+27⋅X₅+81⋅X₄+55 {O(n)}

MPRF:

• eval_foo_bb1_in: [1+2⋅X₀+2⋅X₁+X₂; 1+3⋅X₀+X₁; X₀]
• eval_foo_bb2_in: [1+2⋅X₀+2⋅X₁+X₂; 1+X₀+X₁; 0]

All Bounds

Timebounds

Overall timebound:162⋅X₄+324⋅X₃+54⋅X₅+114 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 162⋅X₃+27⋅X₅+81⋅X₄+55 {O(n)}
t₃: 1 {O(1)}
t₄: 162⋅X₃+27⋅X₅+81⋅X₄+55 {O(n)}
t₅: 1 {O(1)}

Costbounds

Overall costbound: 162⋅X₄+324⋅X₃+54⋅X₅+114 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 162⋅X₃+27⋅X₅+81⋅X₄+55 {O(n)}
t₃: 1 {O(1)}
t₄: 162⋅X₃+27⋅X₅+81⋅X₄+55 {O(n)}
t₅: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₀, X₄: X₄ {O(n)}
t₀, X₅: X₅ {O(n)}
t₁, X₀: X₃ {O(n)}
t₁, X₁: X₄ {O(n)}
t₁, X₂: X₅ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₁, X₅: X₅ {O(n)}
t₂, X₀: 164⋅X₃+29⋅X₅+83⋅X₄+57 {O(n)}
t₂, X₁: X₄+X₅+2 {O(n)}
t₂, X₂: X₅+2 {O(n)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: X₄ {O(n)}
t₂, X₅: X₅ {O(n)}
t₃, X₀: 10⋅X₅+26⋅X₄+27⋅X₃+11 {O(n)}
t₃, X₁: X₄+X₅+2 {O(n)}
t₃, X₂: 2⋅X₅+2 {O(n)}
t₃, X₃: 2⋅X₃ {O(n)}
t₃, X₄: 2⋅X₄ {O(n)}
t₃, X₅: 2⋅X₅ {O(n)}
t₄, X₀: 10⋅X₅+26⋅X₃+26⋅X₄+11 {O(n)}
t₄, X₁: X₅+2 {O(n)}
t₄, X₂: X₅+2 {O(n)}
t₄, X₃: X₃ {O(n)}
t₄, X₄: X₄ {O(n)}
t₄, X₅: X₅ {O(n)}
t₅, X₀: 10⋅X₅+26⋅X₄+27⋅X₃+11 {O(n)}
t₅, X₁: X₄+X₅+2 {O(n)}
t₅, X₂: 2⋅X₅+2 {O(n)}
t₅, X₃: 2⋅X₃ {O(n)}
t₅, X₄: 2⋅X₄ {O(n)}
t₅, X₅: 2⋅X₅ {O(n)}