Initial Problem
Start: eval_ex2_start
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: eval_ex2_0, eval_ex2_1, eval_ex2_10, eval_ex2_2, eval_ex2_3, eval_ex2_4, eval_ex2_5, eval_ex2_6, eval_ex2_9, eval_ex2_bb0_in, eval_ex2_bb1_in, eval_ex2_bb2_in, eval_ex2_bb3_in, eval_ex2_bb4_in, eval_ex2_bb5_in, eval_ex2_start, eval_ex2_stop
Transitions:
t₂: eval_ex2_0(X₀, X₁, X₂, X₃) → eval_ex2_1(X₀, X₁, X₂, X₃)
t₃: eval_ex2_1(X₀, X₁, X₂, X₃) → eval_ex2_2(X₀, X₁, X₂, X₃)
t₁₆: eval_ex2_10(X₀, X₁, X₂, X₃) → eval_ex2_bb1_in(X₀, X₁, X₀, X₃)
t₄: eval_ex2_2(X₀, X₁, X₂, X₃) → eval_ex2_3(X₀, X₁, X₂, X₃)
t₅: eval_ex2_3(X₀, X₁, X₂, X₃) → eval_ex2_4(X₀, X₁, X₂, X₃)
t₆: eval_ex2_4(X₀, X₁, X₂, X₃) → eval_ex2_bb1_in(X₀, X₁, 1, X₃)
t₁₂: eval_ex2_5(X₀, X₁, X₂, X₃) → eval_ex2_6(X₀, X₁, X₂, X₃)
t₁₃: eval_ex2_6(X₀, X₁, X₂, X₃) → eval_ex2_bb2_in(X₀, X₁, X₂, 1+X₃)
t₁₅: eval_ex2_9(X₀, X₁, X₂, X₃) → eval_ex2_10(X₀, X₁, X₂, X₃)
t₁: eval_ex2_bb0_in(X₀, X₁, X₂, X₃) → eval_ex2_0(X₀, X₁, X₂, X₃)
t₇: eval_ex2_bb1_in(X₀, X₁, X₂, X₃) → eval_ex2_bb2_in(X₀, X₁, X₂, X₂) :|: X₂ ≤ X₁
t₈: eval_ex2_bb1_in(X₀, X₁, X₂, X₃) → eval_ex2_bb5_in(X₀, X₁, X₂, X₃) :|: 1+X₁ ≤ X₂
t₉: eval_ex2_bb2_in(X₀, X₁, X₂, X₃) → eval_ex2_bb3_in(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₁
t₁₀: eval_ex2_bb2_in(X₀, X₁, X₂, X₃) → eval_ex2_bb4_in(X₀, X₁, X₂, X₃) :|: 1+X₁ ≤ X₃
t₁₁: eval_ex2_bb3_in(X₀, X₁, X₂, X₃) → eval_ex2_5(X₀, X₁, X₂, X₃)
t₁₄: eval_ex2_bb4_in(X₀, X₁, X₂, X₃) → eval_ex2_9(1+X₂, X₁, X₂, X₃)
t₁₇: eval_ex2_bb5_in(X₀, X₁, X₂, X₃) → eval_ex2_stop(X₀, X₁, X₂, X₃)
t₀: eval_ex2_start(X₀, X₁, X₂, X₃) → eval_ex2_bb0_in(X₀, X₁, X₂, X₃)
Preprocessing
Found invariant X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location eval_ex2_bb3_in
Found invariant X₃ ≤ 1+X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location eval_ex2_bb4_in
Found invariant X₃ ≤ 1+X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 2 ≤ X₀ for location eval_ex2_9
Found invariant X₃ ≤ 1+X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location eval_ex2_bb2_in
Found invariant X₃ ≤ 1+X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 2 ≤ X₀ for location eval_ex2_10
Found invariant 1 ≤ X₂ ∧ 1+X₁ ≤ X₂ for location eval_ex2_bb5_in
Found invariant X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location eval_ex2_5
Found invariant 1 ≤ X₂ for location eval_ex2_bb1_in
Found invariant 1 ≤ X₂ ∧ 1+X₁ ≤ X₂ for location eval_ex2_stop
Found invariant X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location eval_ex2_6
Problem after Preprocessing
Start: eval_ex2_start
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: eval_ex2_0, eval_ex2_1, eval_ex2_10, eval_ex2_2, eval_ex2_3, eval_ex2_4, eval_ex2_5, eval_ex2_6, eval_ex2_9, eval_ex2_bb0_in, eval_ex2_bb1_in, eval_ex2_bb2_in, eval_ex2_bb3_in, eval_ex2_bb4_in, eval_ex2_bb5_in, eval_ex2_start, eval_ex2_stop
Transitions:
t₂: eval_ex2_0(X₀, X₁, X₂, X₃) → eval_ex2_1(X₀, X₁, X₂, X₃)
t₃: eval_ex2_1(X₀, X₁, X₂, X₃) → eval_ex2_2(X₀, X₁, X₂, X₃)
t₁₆: eval_ex2_10(X₀, X₁, X₂, X₃) → eval_ex2_bb1_in(X₀, X₁, X₀, X₃) :|: X₀ ≤ 1+X₁ ∧ X₀ ≤ 1+X₂ ∧ X₃ ≤ 1+X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₂+X₃ ∧ 4 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁
t₄: eval_ex2_2(X₀, X₁, X₂, X₃) → eval_ex2_3(X₀, X₁, X₂, X₃)
t₅: eval_ex2_3(X₀, X₁, X₂, X₃) → eval_ex2_4(X₀, X₁, X₂, X₃)
t₆: eval_ex2_4(X₀, X₁, X₂, X₃) → eval_ex2_bb1_in(X₀, X₁, 1, X₃)
t₁₂: eval_ex2_5(X₀, X₁, X₂, X₃) → eval_ex2_6(X₀, X₁, X₂, X₃) :|: 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₃
t₁₃: eval_ex2_6(X₀, X₁, X₂, X₃) → eval_ex2_bb2_in(X₀, X₁, X₂, 1+X₃) :|: 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₃
t₁₅: eval_ex2_9(X₀, X₁, X₂, X₃) → eval_ex2_10(X₀, X₁, X₂, X₃) :|: X₀ ≤ 1+X₁ ∧ X₀ ≤ 1+X₂ ∧ X₃ ≤ 1+X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₂+X₃ ∧ 4 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁
t₁: eval_ex2_bb0_in(X₀, X₁, X₂, X₃) → eval_ex2_0(X₀, X₁, X₂, X₃)
t₇: eval_ex2_bb1_in(X₀, X₁, X₂, X₃) → eval_ex2_bb2_in(X₀, X₁, X₂, X₂) :|: X₂ ≤ X₁ ∧ 1 ≤ X₂
t₈: eval_ex2_bb1_in(X₀, X₁, X₂, X₃) → eval_ex2_bb5_in(X₀, X₁, X₂, X₃) :|: 1+X₁ ≤ X₂ ∧ 1 ≤ X₂
t₉: eval_ex2_bb2_in(X₀, X₁, X₂, X₃) → eval_ex2_bb3_in(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₁ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₃
t₁₀: eval_ex2_bb2_in(X₀, X₁, X₂, X₃) → eval_ex2_bb4_in(X₀, X₁, X₂, X₃) :|: 1+X₁ ≤ X₃ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₃
t₁₁: eval_ex2_bb3_in(X₀, X₁, X₂, X₃) → eval_ex2_5(X₀, X₁, X₂, X₃) :|: 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₃
t₁₄: eval_ex2_bb4_in(X₀, X₁, X₂, X₃) → eval_ex2_9(1+X₂, X₁, X₂, X₃) :|: X₃ ≤ 1+X₁ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₂+X₃ ∧ X₂ ≤ X₁
t₁₇: eval_ex2_bb5_in(X₀, X₁, X₂, X₃) → eval_ex2_stop(X₀, X₁, X₂, X₃) :|: 1+X₁ ≤ X₂ ∧ 1 ≤ X₂
t₀: eval_ex2_start(X₀, X₁, X₂, X₃) → eval_ex2_bb0_in(X₀, X₁, X₂, X₃)
MPRF for transition t₇: eval_ex2_bb1_in(X₀, X₁, X₂, X₃) → eval_ex2_bb2_in(X₀, X₁, X₂, X₂) :|: X₂ ≤ X₁ ∧ 1 ≤ X₂ of depth 1:
new bound:
X₁+2 {O(n)}
MPRF:
• eval_ex2_10: [1+X₁-X₀]
• eval_ex2_5: [X₁-X₂]
• eval_ex2_6: [X₁-X₂]
• eval_ex2_9: [X₁-X₂]
• eval_ex2_bb1_in: [1+X₁-X₂]
• eval_ex2_bb2_in: [X₁-X₂]
• eval_ex2_bb3_in: [X₁-X₂]
• eval_ex2_bb4_in: [X₁-X₂]
MPRF for transition t₁₀: eval_ex2_bb2_in(X₀, X₁, X₂, X₃) → eval_ex2_bb4_in(X₀, X₁, X₂, X₃) :|: 1+X₁ ≤ X₃ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₃ of depth 1:
new bound:
X₁+3 {O(n)}
MPRF:
• eval_ex2_10: [2+X₁-X₀]
• eval_ex2_5: [2+X₁-X₂]
• eval_ex2_6: [2+X₁-X₂]
• eval_ex2_9: [2+X₁-X₀]
• eval_ex2_bb1_in: [2+X₁-X₂]
• eval_ex2_bb2_in: [2+X₁-X₂]
• eval_ex2_bb3_in: [2+X₁-X₂]
• eval_ex2_bb4_in: [1+X₁-X₂]
MPRF for transition t₁₄: eval_ex2_bb4_in(X₀, X₁, X₂, X₃) → eval_ex2_9(1+X₂, X₁, X₂, X₃) :|: X₃ ≤ 1+X₁ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₂+X₃ ∧ X₂ ≤ X₁ of depth 1:
new bound:
X₁+2 {O(n)}
MPRF:
• eval_ex2_10: [X₁-X₂]
• eval_ex2_5: [1+X₁-X₂]
• eval_ex2_6: [1+X₁-X₂]
• eval_ex2_9: [X₃-1-X₂]
• eval_ex2_bb1_in: [1+X₁-X₂]
• eval_ex2_bb2_in: [1+X₁-X₂]
• eval_ex2_bb3_in: [1+X₁-X₂]
• eval_ex2_bb4_in: [1+X₁-X₂]
MPRF for transition t₁₅: eval_ex2_9(X₀, X₁, X₂, X₃) → eval_ex2_10(X₀, X₁, X₂, X₃) :|: X₀ ≤ 1+X₁ ∧ X₀ ≤ 1+X₂ ∧ X₃ ≤ 1+X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₂+X₃ ∧ 4 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ of depth 1:
new bound:
X₁+2 {O(n)}
MPRF:
• eval_ex2_10: [X₃-1-X₂]
• eval_ex2_5: [1+X₁-X₂]
• eval_ex2_6: [1+X₁-X₂]
• eval_ex2_9: [1+X₁-X₂]
• eval_ex2_bb1_in: [1+X₁-X₂]
• eval_ex2_bb2_in: [1+X₁-X₂]
• eval_ex2_bb3_in: [1+X₁-X₂]
• eval_ex2_bb4_in: [1+X₁-X₂]
MPRF for transition t₁₆: eval_ex2_10(X₀, X₁, X₂, X₃) → eval_ex2_bb1_in(X₀, X₁, X₀, X₃) :|: X₀ ≤ 1+X₁ ∧ X₀ ≤ 1+X₂ ∧ X₃ ≤ 1+X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₂+X₃ ∧ 4 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ of depth 1:
new bound:
X₁+2 {O(n)}
MPRF:
• eval_ex2_10: [X₃-X₂]
• eval_ex2_5: [1+X₁-X₂]
• eval_ex2_6: [1+X₁-X₂]
• eval_ex2_9: [X₃-X₂]
• eval_ex2_bb1_in: [1+X₁-X₂]
• eval_ex2_bb2_in: [1+X₁-X₂]
• eval_ex2_bb3_in: [1+X₁-X₂]
• eval_ex2_bb4_in: [1+X₁-X₂]
MPRF for transition t₉: eval_ex2_bb2_in(X₀, X₁, X₂, X₃) → eval_ex2_bb3_in(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₁ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₃ of depth 1:
new bound:
2⋅X₁⋅X₁+9⋅X₁+10 {O(n^2)}
MPRF:
• eval_ex2_10: [X₁-X₃]
• eval_ex2_5: [X₁-X₃]
• eval_ex2_6: [X₁-X₃]
• eval_ex2_9: [X₁-X₃]
• eval_ex2_bb1_in: [1+X₁-X₂]
• eval_ex2_bb2_in: [1+X₁-X₃]
• eval_ex2_bb3_in: [X₁-X₃]
• eval_ex2_bb4_in: [X₁-X₃]
MPRF for transition t₁₁: eval_ex2_bb3_in(X₀, X₁, X₂, X₃) → eval_ex2_5(X₀, X₁, X₂, X₃) :|: 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₃ of depth 1:
new bound:
2⋅X₁⋅X₁+9⋅X₁+10 {O(n^2)}
MPRF:
• eval_ex2_10: [0]
• eval_ex2_5: [X₁-X₃]
• eval_ex2_6: [X₁-X₃]
• eval_ex2_9: [0]
• eval_ex2_bb1_in: [1+X₁-X₂]
• eval_ex2_bb2_in: [1+X₁-X₃]
• eval_ex2_bb3_in: [1+X₁-X₃]
• eval_ex2_bb4_in: [0]
MPRF for transition t₁₂: eval_ex2_5(X₀, X₁, X₂, X₃) → eval_ex2_6(X₀, X₁, X₂, X₃) :|: 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₃ of depth 1:
new bound:
2⋅X₁⋅X₁+9⋅X₁+10 {O(n^2)}
MPRF:
• eval_ex2_10: [X₁-X₃]
• eval_ex2_5: [1+X₁-X₃]
• eval_ex2_6: [X₁-X₃]
• eval_ex2_9: [X₁-X₃]
• eval_ex2_bb1_in: [1+X₁-X₂]
• eval_ex2_bb2_in: [1+X₁-X₃]
• eval_ex2_bb3_in: [1+X₁-X₃]
• eval_ex2_bb4_in: [X₁-X₃]
MPRF for transition t₁₃: eval_ex2_6(X₀, X₁, X₂, X₃) → eval_ex2_bb2_in(X₀, X₁, X₂, 1+X₃) :|: 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₃ of depth 1:
new bound:
3⋅X₁⋅X₁+11⋅X₁+7 {O(n^2)}
MPRF:
• eval_ex2_10: [X₃-2⋅X₂]
• eval_ex2_5: [2⋅X₁-X₃]
• eval_ex2_6: [2⋅X₁-X₃]
• eval_ex2_9: [X₃-2⋅X₂]
• eval_ex2_bb1_in: [2⋅X₁-X₂]
• eval_ex2_bb2_in: [2⋅X₁-X₃]
• eval_ex2_bb3_in: [2⋅X₁-X₃]
• eval_ex2_bb4_in: [X₃-2⋅X₂]
Cut unsatisfiable transition [t₁₀: eval_ex2_bb2_in→eval_ex2_bb4_in; t₉₂: eval_ex2_bb2_in→eval_ex2_bb4_in]
Found invariant X₃ ≤ 1+X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location eval_ex2_bb2_in_v1
Found invariant X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₁ for location eval_ex2_5_v2
Found invariant X₃ ≤ 1+X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location eval_ex2_bb4_in
Found invariant X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₁ for location eval_ex2_bb3_in_v2
Found invariant X₃ ≤ 1+X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 2 ≤ X₀ for location eval_ex2_9
Found invariant X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location eval_ex2_bb2_in
Found invariant X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location eval_ex2_5_v1
Found invariant X₃ ≤ 1+X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 2 ≤ X₀ for location eval_ex2_10
Found invariant X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location eval_ex2_6_v1
Found invariant 1 ≤ X₂ ∧ 1+X₁ ≤ X₂ for location eval_ex2_bb5_in
Found invariant 1 ≤ X₂ for location eval_ex2_bb1_in
Found invariant X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₁ for location eval_ex2_6_v2
Found invariant 1 ≤ X₂ ∧ 1+X₁ ≤ X₂ for location eval_ex2_stop
Found invariant X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location eval_ex2_bb3_in_v1
All Bounds
Timebounds
Overall timebound:9⋅X₁⋅X₁+43⋅X₁+57 {O(n^2)}
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: X₁+2 {O(n)}
t₈: 1 {O(1)}
t₉: 2⋅X₁⋅X₁+9⋅X₁+10 {O(n^2)}
t₁₀: X₁+3 {O(n)}
t₁₁: 2⋅X₁⋅X₁+9⋅X₁+10 {O(n^2)}
t₁₂: 2⋅X₁⋅X₁+9⋅X₁+10 {O(n^2)}
t₁₃: 3⋅X₁⋅X₁+11⋅X₁+7 {O(n^2)}
t₁₄: X₁+2 {O(n)}
t₁₅: X₁+2 {O(n)}
t₁₆: X₁+2 {O(n)}
t₁₇: 1 {O(1)}
Costbounds
Overall costbound: 9⋅X₁⋅X₁+43⋅X₁+57 {O(n^2)}
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: X₁+2 {O(n)}
t₈: 1 {O(1)}
t₉: 2⋅X₁⋅X₁+9⋅X₁+10 {O(n^2)}
t₁₀: X₁+3 {O(n)}
t₁₁: 2⋅X₁⋅X₁+9⋅X₁+10 {O(n^2)}
t₁₂: 2⋅X₁⋅X₁+9⋅X₁+10 {O(n^2)}
t₁₃: 3⋅X₁⋅X₁+11⋅X₁+7 {O(n^2)}
t₁₄: X₁+2 {O(n)}
t₁₅: X₁+2 {O(n)}
t₁₆: X₁+2 {O(n)}
t₁₇: 1 {O(1)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₅, X₀: X₀ {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₆, X₀: X₀ {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: 1 {O(1)}
t₆, X₃: X₃ {O(n)}
t₇, X₀: X₀+X₁+3 {O(n)}
t₇, X₁: X₁ {O(n)}
t₇, X₂: X₁+3 {O(n)}
t₇, X₃: X₁+4 {O(n)}
t₈, X₀: X₀+X₁+3 {O(n)}
t₈, X₁: 2⋅X₁ {O(n)}
t₈, X₂: X₁+4 {O(n)}
t₈, X₃: 3⋅X₁⋅X₁+12⋅X₁+X₃+11 {O(n^2)}
t₉, X₀: X₀+X₁+3 {O(n)}
t₉, X₁: X₁ {O(n)}
t₉, X₂: X₁+3 {O(n)}
t₉, X₃: 3⋅X₁⋅X₁+12⋅X₁+11 {O(n^2)}
t₁₀, X₀: X₀+X₁+3 {O(n)}
t₁₀, X₁: X₁ {O(n)}
t₁₀, X₂: X₁+3 {O(n)}
t₁₀, X₃: 3⋅X₁⋅X₁+12⋅X₁+11 {O(n^2)}
t₁₁, X₀: X₀+X₁+3 {O(n)}
t₁₁, X₁: X₁ {O(n)}
t₁₁, X₂: X₁+3 {O(n)}
t₁₁, X₃: 3⋅X₁⋅X₁+12⋅X₁+11 {O(n^2)}
t₁₂, X₀: X₀+X₁+3 {O(n)}
t₁₂, X₁: X₁ {O(n)}
t₁₂, X₂: X₁+3 {O(n)}
t₁₂, X₃: 3⋅X₁⋅X₁+12⋅X₁+11 {O(n^2)}
t₁₃, X₀: X₀+X₁+3 {O(n)}
t₁₃, X₁: X₁ {O(n)}
t₁₃, X₂: X₁+3 {O(n)}
t₁₃, X₃: 3⋅X₁⋅X₁+12⋅X₁+11 {O(n^2)}
t₁₄, X₀: X₁+3 {O(n)}
t₁₄, X₁: X₁ {O(n)}
t₁₄, X₂: X₁+3 {O(n)}
t₁₄, X₃: 3⋅X₁⋅X₁+12⋅X₁+11 {O(n^2)}
t₁₅, X₀: X₁+3 {O(n)}
t₁₅, X₁: X₁ {O(n)}
t₁₅, X₂: X₁+3 {O(n)}
t₁₅, X₃: 3⋅X₁⋅X₁+12⋅X₁+11 {O(n^2)}
t₁₆, X₀: X₁+3 {O(n)}
t₁₆, X₁: X₁ {O(n)}
t₁₆, X₂: X₁+3 {O(n)}
t₁₆, X₃: 3⋅X₁⋅X₁+12⋅X₁+11 {O(n^2)}
t₁₇, X₀: X₀+X₁+3 {O(n)}
t₁₇, X₁: 2⋅X₁ {O(n)}
t₁₇, X₂: X₁+4 {O(n)}
t₁₇, X₃: 3⋅X₁⋅X₁+12⋅X₁+X₃+11 {O(n^2)}