KoAT2 Proof Output

Initial Problem

Start: eval_foo_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
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, X₆) → eval_foo_bb1_in(X₄, X₅, X₆, X₃, X₄, X₅, X₆)
t₂: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 ≤ X₀+X₁ ∧ X₀ ≤ X₃
t₃: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+X₀+X₁ ≤ 0
t₄: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+X₃ ≤ X₀
t₅: eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb1_in(2⋅X₀+X₁, X₂, 1+X₂, X₃, X₄, X₅, X₆)
t₆: eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₀: eval_foo_start(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆)

Preprocessing

Found invariant X₆ ≤ X₂ ∧ 0 ≤ X₁+X₃ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₀+X₁ for location eval_foo_bb2_in

Found invariant X₆ ≤ X₂ for location eval_foo_bb1_in

Found invariant X₆ ≤ X₂ for location eval_foo_stop

Found invariant X₆ ≤ X₂ for location eval_foo_bb3_in

Problem after Preprocessing

Start: eval_foo_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
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, X₆) → eval_foo_bb1_in(X₄, X₅, X₆, X₃, X₄, X₅, X₆)
t₂: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 ≤ X₀+X₁ ∧ X₀ ≤ X₃ ∧ X₆ ≤ X₂
t₃: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+X₀+X₁ ≤ 0 ∧ X₆ ≤ X₂
t₄: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+X₃ ≤ X₀ ∧ X₆ ≤ X₂
t₅: eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb1_in(2⋅X₀+X₁, X₂, 1+X₂, X₃, X₄, X₅, X₆) :|: 0 ≤ X₀+X₁ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₆ ≤ X₂
t₆: eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₆ ≤ X₂
t₀: eval_foo_start(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆)

MPRF for transition t₂: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 ≤ X₀+X₁ ∧ X₀ ≤ X₃ ∧ X₆ ≤ X₂ of depth 3:

new bound:

54⋅X₃+54⋅X₄+82 {O(n)}

MPRF:

• eval_foo_bb1_in: [2-X₀-X₂; 1+X₂+X₃-X₀-X₁; X₁+X₃]
• eval_foo_bb2_in: [1-X₀-X₂; 2+X₃-2⋅X₀-X₁; X₂+X₃]

MPRF for transition t₅: eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb1_in(2⋅X₀+X₁, X₂, 1+X₂, X₃, X₄, X₅, X₆) :|: 0 ≤ X₀+X₁ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₆ ≤ X₂ of depth 3:

new bound:

54⋅X₃+54⋅X₄+82 {O(n)}

MPRF:

• eval_foo_bb1_in: [2-X₀-X₂; 1+X₂+X₃-X₀-X₁; X₁+X₃]
• eval_foo_bb2_in: [2-X₀-X₂; 1+X₂+X₃-X₀-X₁; X₁+X₃]

All Bounds

Timebounds

Overall timebound:108⋅X₃+108⋅X₄+169 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 54⋅X₃+54⋅X₄+82 {O(n)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 54⋅X₃+54⋅X₄+82 {O(n)}
t₆: 1 {O(1)}

Costbounds

Overall costbound: 108⋅X₃+108⋅X₄+169 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 54⋅X₃+54⋅X₄+82 {O(n)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 54⋅X₃+54⋅X₄+82 {O(n)}
t₆: 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)}
t₀, X₆: X₆ {O(n)}
t₁, X₀: X₄ {O(n)}
t₁, X₁: X₅ {O(n)}
t₁, X₂: X₆ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₁, X₅: X₅ {O(n)}
t₁, X₆: X₆ {O(n)}
t₂, X₀: 2^(54⋅X₃)⋅2^(54⋅X₄)⋅2^(54⋅X₅)⋅2^(54⋅X₆)⋅4835703278458516698824704+2^(54⋅X₃)⋅2^(54⋅X₄)⋅2^(54⋅X₅)⋅2^(54⋅X₆)⋅4835703278458516698824704⋅X₄+2^(54⋅X₃)⋅2^(54⋅X₄)⋅2^(54⋅X₅)⋅2^(54⋅X₆)⋅4835703278458516698824704⋅X₅+2^(54⋅X₃)⋅2^(54⋅X₄)⋅2^(54⋅X₅)⋅2^(54⋅X₆)⋅4835703278458516698824704⋅X₆+54⋅X₃+55⋅X₅+55⋅X₆+56⋅X₄+82 {O(EXP)}
t₂, X₁: 54⋅X₃+54⋅X₄+X₅+X₆+82 {O(n)}
t₂, X₂: 54⋅X₃+54⋅X₄+X₆+82 {O(n)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: X₄ {O(n)}
t₂, X₅: X₅ {O(n)}
t₂, X₆: X₆ {O(n)}
t₃, X₀: 2^(24⋅X₄)⋅2^(8⋅X₃)⋅2^(8⋅X₅)⋅2^(8⋅X₆)⋅512+2^(24⋅X₄)⋅2^(8⋅X₃)⋅2^(8⋅X₅)⋅2^(8⋅X₆)⋅512⋅X₄+2^(24⋅X₄)⋅2^(8⋅X₃)⋅2^(8⋅X₅)⋅2^(8⋅X₆)⋅512⋅X₅+2^(24⋅X₄)⋅2^(8⋅X₃)⋅2^(8⋅X₅)⋅2^(8⋅X₆)⋅512⋅X₆+27⋅X₄+8⋅X₃+9⋅X₅+9⋅X₆+9 {O(EXP)}
t₃, X₁: 54⋅X₃+54⋅X₄+X₅+X₆+82 {O(n)}
t₃, X₂: 2⋅X₆+54⋅X₃+54⋅X₄+82 {O(n)}
t₃, X₃: 2⋅X₃ {O(n)}
t₃, X₄: 2⋅X₄ {O(n)}
t₃, X₅: 2⋅X₅ {O(n)}
t₃, X₆: 2⋅X₆ {O(n)}
t₄, X₀: 2^(24⋅X₄)⋅2^(8⋅X₃)⋅2^(8⋅X₅)⋅2^(8⋅X₆)⋅512+2^(24⋅X₄)⋅2^(8⋅X₃)⋅2^(8⋅X₅)⋅2^(8⋅X₆)⋅512⋅X₄+2^(24⋅X₄)⋅2^(8⋅X₃)⋅2^(8⋅X₅)⋅2^(8⋅X₆)⋅512⋅X₅+2^(24⋅X₄)⋅2^(8⋅X₃)⋅2^(8⋅X₅)⋅2^(8⋅X₆)⋅512⋅X₆+27⋅X₄+8⋅X₃+9⋅X₅+9⋅X₆+9 {O(EXP)}
t₄, X₁: 54⋅X₃+54⋅X₄+X₅+X₆+82 {O(n)}
t₄, X₂: 2⋅X₆+54⋅X₃+54⋅X₄+82 {O(n)}
t₄, X₃: 2⋅X₃ {O(n)}
t₄, X₄: 2⋅X₄ {O(n)}
t₄, X₅: 2⋅X₅ {O(n)}
t₄, X₆: 2⋅X₆ {O(n)}
t₅, X₀: 2^(24⋅X₄)⋅2^(8⋅X₃)⋅2^(8⋅X₅)⋅2^(8⋅X₆)⋅512+2^(24⋅X₄)⋅2^(8⋅X₃)⋅2^(8⋅X₅)⋅2^(8⋅X₆)⋅512⋅X₄+2^(24⋅X₄)⋅2^(8⋅X₃)⋅2^(8⋅X₅)⋅2^(8⋅X₆)⋅512⋅X₅+2^(24⋅X₄)⋅2^(8⋅X₃)⋅2^(8⋅X₅)⋅2^(8⋅X₆)⋅512⋅X₆+26⋅X₄+8⋅X₃+9⋅X₅+9⋅X₆+9 {O(EXP)}
t₅, X₁: 54⋅X₃+54⋅X₄+X₆+82 {O(n)}
t₅, X₂: 54⋅X₃+54⋅X₄+X₆+82 {O(n)}
t₅, X₃: X₃ {O(n)}
t₅, X₄: X₄ {O(n)}
t₅, X₅: X₅ {O(n)}
t₅, X₆: X₆ {O(n)}
t₆, X₀: 1024⋅2^(24⋅X₄)⋅2^(8⋅X₃)⋅2^(8⋅X₅)⋅2^(8⋅X₆)+1024⋅2^(24⋅X₄)⋅2^(8⋅X₃)⋅2^(8⋅X₅)⋅2^(8⋅X₆)⋅X₄+1024⋅2^(24⋅X₄)⋅2^(8⋅X₃)⋅2^(8⋅X₅)⋅2^(8⋅X₆)⋅X₅+1024⋅2^(24⋅X₄)⋅2^(8⋅X₃)⋅2^(8⋅X₅)⋅2^(8⋅X₆)⋅X₆+16⋅X₃+18⋅X₅+18⋅X₆+54⋅X₄+18 {O(EXP)}
t₆, X₁: 108⋅X₃+108⋅X₄+2⋅X₅+2⋅X₆+164 {O(n)}
t₆, X₂: 108⋅X₃+108⋅X₄+4⋅X₆+164 {O(n)}
t₆, X₃: 4⋅X₃ {O(n)}
t₆, X₄: 4⋅X₄ {O(n)}
t₆, X₅: 4⋅X₅ {O(n)}
t₆, X₆: 4⋅X₆ {O(n)}