Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars: D
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂) → l7(X₀, X₁, X₂)
t₉: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂-1)
t₁₀: l2(X₀, X₁, X₂) → l3(X₀, X₁-1, X₁-1)
t₄: l3(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₀ ≤ X₂
t₅: l3(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₂+1 ≤ X₀
t₆: l4(X₀, X₁, X₂) → l1(X₀, X₁, X₂) :|: D+1 ≤ 0
t₇: l4(X₀, X₁, X₂) → l1(X₀, X₁, X₂) :|: 1 ≤ D
t₈: l4(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₁₁: l5(X₀, X₁, X₂) → l8(X₀, X₁, X₂)
t₃: l6(X₀, X₁, X₂) → l3(X₀, 2⋅X₀, 2⋅X₀)
t₂: l7(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₀+1 ≤ 0
t₁: l7(X₀, X₁, X₂) → l6(X₀, X₁, X₂) :|: 0 ≤ X₀
Preprocessing
Found invariant 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₀ for location l2
Found invariant 0 ≤ X₀ for location l6
Found invariant 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₀ for location l1
Found invariant 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₀ for location l4
Found invariant 0 ≤ X₀ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars: D
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂) → l7(X₀, X₁, X₂)
t₉: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂-1) :|: 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₀
t₁₀: l2(X₀, X₁, X₂) → l3(X₀, X₁-1, X₁-1) :|: 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₀
t₄: l3(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₀ ≤ X₂ ∧ 0 ≤ X₀
t₅: l3(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₂+1 ≤ X₀ ∧ 0 ≤ X₀
t₆: l4(X₀, X₁, X₂) → l1(X₀, X₁, X₂) :|: D+1 ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₀
t₇: l4(X₀, X₁, X₂) → l1(X₀, X₁, X₂) :|: 1 ≤ D ∧ 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₀
t₈: l4(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₀
t₁₁: l5(X₀, X₁, X₂) → l8(X₀, X₁, X₂)
t₃: l6(X₀, X₁, X₂) → l3(X₀, 2⋅X₀, 2⋅X₀) :|: 0 ≤ X₀
t₂: l7(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₀+1 ≤ 0
t₁: l7(X₀, X₁, X₂) → l6(X₀, X₁, X₂) :|: 0 ≤ X₀
MPRF for transition t₈: l4(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₀ of depth 2:
new bound:
32⋅X₀+9 {O(n)}
MPRF for transition t₁₀: l2(X₀, X₁, X₂) → l3(X₀, X₁-1, X₁-1) :|: 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₀ of depth 2:
new bound:
32⋅X₀+1 {O(n)}
MPRF for transition t₄: l3(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₀ ≤ X₂ ∧ 0 ≤ X₀ of depth 1:
new bound:
1088⋅X₀⋅X₀+164⋅X₀+6 {O(n^2)}
MPRF for transition t₆: l4(X₀, X₁, X₂) → l1(X₀, X₁, X₂) :|: D+1 ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₀ of depth 1:
new bound:
1088⋅X₀⋅X₀+132⋅X₀+4 {O(n^2)}
MPRF for transition t₇: l4(X₀, X₁, X₂) → l1(X₀, X₁, X₂) :|: 1 ≤ D ∧ 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₀ of depth 1:
new bound:
1088⋅X₀⋅X₀+132⋅X₀+4 {O(n^2)}
MPRF for transition t₉: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂-1) :|: 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₀ of depth 1:
new bound:
1088⋅X₀⋅X₀+132⋅X₀+4 {O(n^2)}
Chain transitions t₇: l4→l1 and t₉: l1→l3 to t₇₉: l4→l3
Chain transitions t₆: l4→l1 and t₉: l1→l3 to t₈₀: l4→l3
Chain transitions t₈: l4→l2 and t₁₀: l2→l3 to t₈₁: l4→l3
Chain transitions t₃: l6→l3 and t₅: l3→l5 to t₈₂: l6→l5
Chain transitions t₈₁: l4→l3 and t₅: l3→l5 to t₈₃: l4→l5
Chain transitions t₈₁: l4→l3 and t₄: l3→l4 to t₈₄: l4→l4
Chain transitions t₃: l6→l3 and t₄: l3→l4 to t₈₅: l6→l4
Chain transitions t₈₀: l4→l3 and t₄: l3→l4 to t₈₆: l4→l4
Chain transitions t₈₀: l4→l3 and t₅: l3→l5 to t₈₇: l4→l5
Chain transitions t₇₉: l4→l3 and t₄: l3→l4 to t₈₈: l4→l4
Chain transitions t₇₉: l4→l3 and t₅: l3→l5 to t₈₉: l4→l5
Analysing control-flow refined program
Cut unsatisfiable transition t₈₂: l6→l5
Found invariant 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l2
Found invariant 0 ≤ X₀ for location l6
Found invariant 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l1
Found invariant 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l4
Found invariant 0 ≤ 1+X₂ ∧ 0 ≤ 2+X₁+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 0 ≤ X₀ for location l3
MPRF for transition t₈₄: l4(X₀, X₁, X₂) -{3}> l4(X₀, X₁-1, X₁-1) :|: X₀+1 ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
2⋅X₀+1 {O(n)}
TWN: t₈₆: l4→l4
cycle: [t₈₆: l4→l4; t₈₈: l4→l4]
loop: (X₀+1 ≤ X₂ ∨ X₀+1 ≤ X₂,(X₀,X₂) -> (X₀,X₂-1)
order: [X₀; X₂]
closed-form:
X₀: X₀
X₂: X₂ + [[n != 0]] * -1 * n^1
Termination: true
Formula:
1 < 0
∨ X₀+1 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ X₀+1
∨ 1 < 0
∨ X₀+1 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ X₀+1
Stabilization-Threshold for: X₀+1 ≤ X₂
alphas_abs: X₀+X₂+1
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₂+4 {O(n)}
loop: (X₀+1 ≤ X₂ ∨ X₀+1 ≤ X₂,(X₀,X₂) -> (X₀,X₂-1)
order: [X₀; X₂]
closed-form:
X₀: X₀
X₂: X₂ + [[n != 0]] * -1 * n^1
Termination: true
Formula:
1 < 0
∨ X₀+1 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ X₀+1
∨ 1 < 0
∨ X₀+1 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ X₀+1
Stabilization-Threshold for: X₀+1 ≤ X₂
alphas_abs: X₀+X₂+1
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₂+4 {O(n)}
loop: (X₀+1 ≤ X₂ ∨ X₀+1 ≤ X₂,(X₀,X₂) -> (X₀,X₂-1)
order: [X₀; X₂]
closed-form:
X₀: X₀
X₂: X₂ + [[n != 0]] * -1 * n^1
Termination: true
Formula:
1 < 0
∨ X₀+1 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ X₀+1
∨ 1 < 0
∨ X₀+1 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ X₀+1
Stabilization-Threshold for: X₀+1 ≤ X₂
alphas_abs: X₀+X₂+1
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₂+4 {O(n)}
loop: (X₀+1 ≤ X₂ ∨ X₀+1 ≤ X₂,(X₀,X₂) -> (X₀,X₂-1)
order: [X₀; X₂]
closed-form:
X₀: X₀
X₂: X₂ + [[n != 0]] * -1 * n^1
Termination: true
Formula:
1 < 0
∨ X₀+1 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ X₀+1
∨ 1 < 0
∨ X₀+1 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ X₀+1
Stabilization-Threshold for: X₀+1 ≤ X₂
alphas_abs: X₀+X₂+1
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₂+4 {O(n)}
TWN - Lifting for t₈₆: l4→l4 of 2⋅X₀+2⋅X₂+6 {O(n)}
relevant size-bounds w.r.t. t₈₅:
X₀: X₀ {O(n)}
X₂: 2⋅X₀ {O(n)}
Runtime-bound of t₈₅: 1 {O(1)}
Results in: 6⋅X₀+6 {O(n)}
TWN - Lifting for t₈₆: l4→l4 of 2⋅X₀+2⋅X₂+6 {O(n)}
relevant size-bounds w.r.t. t₈₄:
X₀: X₀ {O(n)}
X₂: 8⋅X₀ {O(n)}
Runtime-bound of t₈₄: 2⋅X₀+1 {O(n)}
Results in: 36⋅X₀⋅X₀+30⋅X₀+6 {O(n^2)}
TWN - Lifting for t₈₆: l4→l4 of 2⋅X₀+2⋅X₂+6 {O(n)}
relevant size-bounds w.r.t. t₈₅:
X₀: X₀ {O(n)}
X₂: 2⋅X₀ {O(n)}
Runtime-bound of t₈₅: 1 {O(1)}
Results in: 6⋅X₀+6 {O(n)}
TWN - Lifting for t₈₆: l4→l4 of 2⋅X₀+2⋅X₂+6 {O(n)}
relevant size-bounds w.r.t. t₈₄:
X₀: X₀ {O(n)}
X₂: 8⋅X₀ {O(n)}
Runtime-bound of t₈₄: 2⋅X₀+1 {O(n)}
Results in: 36⋅X₀⋅X₀+30⋅X₀+6 {O(n^2)}
TWN: t₈₈: l4→l4
TWN - Lifting for t₈₈: l4→l4 of 2⋅X₀+2⋅X₂+6 {O(n)}
relevant size-bounds w.r.t. t₈₅:
X₀: X₀ {O(n)}
X₂: 2⋅X₀ {O(n)}
Runtime-bound of t₈₅: 1 {O(1)}
Results in: 6⋅X₀+6 {O(n)}
TWN - Lifting for t₈₈: l4→l4 of 2⋅X₀+2⋅X₂+6 {O(n)}
relevant size-bounds w.r.t. t₈₄:
X₀: X₀ {O(n)}
X₂: 8⋅X₀ {O(n)}
Runtime-bound of t₈₄: 2⋅X₀+1 {O(n)}
Results in: 36⋅X₀⋅X₀+30⋅X₀+6 {O(n^2)}
TWN - Lifting for t₈₈: l4→l4 of 2⋅X₀+2⋅X₂+6 {O(n)}
relevant size-bounds w.r.t. t₈₅:
X₀: X₀ {O(n)}
X₂: 2⋅X₀ {O(n)}
Runtime-bound of t₈₅: 1 {O(1)}
Results in: 6⋅X₀+6 {O(n)}
TWN - Lifting for t₈₈: l4→l4 of 2⋅X₀+2⋅X₂+6 {O(n)}
relevant size-bounds w.r.t. t₈₄:
X₀: X₀ {O(n)}
X₂: 8⋅X₀ {O(n)}
Runtime-bound of t₈₄: 2⋅X₀+1 {O(n)}
Results in: 36⋅X₀⋅X₀+30⋅X₀+6 {O(n^2)}
CFR did not improve the program. Rolling back
CFR did not improve the program. Rolling back
Analysing control-flow refined program
Cut unsatisfiable transition t₅: l3→l5
Found invariant 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l2___6
Found invariant 0 ≤ X₀ for location l6
Found invariant X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l1___11
Found invariant X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l4___4
Found invariant 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l1___7
Found invariant X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l3___5
Found invariant X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l4___12
Found invariant X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l1___3
Found invariant X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l2___2
Found invariant 1+X₂ ≤ X₁ ∧ 0 ≤ 1+X₂ ∧ 0 ≤ 1+X₁+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l3___9
Found invariant X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l2___10
Found invariant X₂ ≤ X₁ ∧ 0 ≤ 1+X₂ ∧ 0 ≤ 2+X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 0 ≤ X₀ for location n_l3___1
Found invariant 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l4___8
Found invariant 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l3
Cut unsatisfiable transition t₂₄₆: n_l3___5→l5
MPRF for transition t₂₁₇: n_l1___3(X₀, X₁, X₂) → n_l3___9(X₀, X₁, X₂-1) :|: X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
6⋅X₀+2 {O(n)}
MPRF for transition t₂₂₀: n_l2___2(X₀, X₁, X₂) → n_l3___1(X₀, X₁-1, X₁-1) :|: X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
6⋅X₀+2 {O(n)}
MPRF for transition t₂₂₁: n_l2___6(X₀, X₁, X₂) → n_l3___5(X₀, X₁-1, X₁-1) :|: X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
6⋅X₀+1 {O(n)}
MPRF for transition t₂₂₂: n_l3___1(X₀, X₁, X₂) → n_l4___4(X₀, X₁, X₂) :|: X₀ ≤ 1+X₂ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₂ ≤ X₁ ∧ 0 ≤ 1+X₂ ∧ 0 ≤ 2+X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
6⋅X₀+2 {O(n)}
MPRF for transition t₂₂₄: n_l3___5(X₀, X₁, X₂) → n_l4___4(X₀, X₁, X₂) :|: X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
6⋅X₀+1 {O(n)}
MPRF for transition t₂₂₉: n_l4___4(X₀, X₁, X₂) → n_l1___3(Arg0_P, X₁, Arg2_P) :|: X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ Arg0_P ≤ Arg2_P ∧ 0 ≤ Arg0_P ∧ X₀ ≤ Arg0_P ∧ Arg0_P ≤ X₀ ∧ X₂ ≤ Arg2_P ∧ Arg2_P ≤ X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
6⋅X₀+2 {O(n)}
MPRF for transition t₂₃₀: n_l4___4(X₀, X₁, X₂) → n_l1___3(Arg0_P, X₁, Arg2_P) :|: X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ Arg0_P ≤ Arg2_P ∧ 0 ≤ Arg0_P ∧ X₀ ≤ Arg0_P ∧ Arg0_P ≤ X₀ ∧ X₂ ≤ Arg2_P ∧ Arg2_P ≤ X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
6⋅X₀+2 {O(n)}
MPRF for transition t₂₃₁: n_l4___4(X₀, X₁, X₂) → n_l2___2(X₀, X₁, X₂) :|: X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
6⋅X₀+2 {O(n)}
MPRF for transition t₂₃₄: n_l4___8(X₀, X₁, X₂) → n_l2___6(X₀, X₁, X₂) :|: X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
6⋅X₀+1 {O(n)}
MPRF for transition t₂₁₈: n_l1___7(X₀, X₁, X₂) → n_l3___9(X₀, X₁, X₂-1) :|: X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
36⋅X₀⋅X₀+28⋅X₀+8 {O(n^2)}
MPRF for transition t₂₂₅: n_l3___9(X₀, X₁, X₂) → n_l4___8(X₀, X₁, X₂) :|: X₀ ≤ 1+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ 1+X₂ ∧ 0 ≤ 1+X₁+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
36⋅X₀⋅X₀+24⋅X₀+8 {O(n^2)}
MPRF for transition t₂₃₂: n_l4___8(X₀, X₁, X₂) → n_l1___7(Arg0_P, X₁, Arg2_P) :|: Arg0_P ≤ Arg2_P ∧ 0 ≤ Arg0_P ∧ X₀ ≤ Arg0_P ∧ Arg0_P ≤ X₀ ∧ X₂ ≤ Arg2_P ∧ Arg2_P ≤ X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
36⋅X₀⋅X₀+24⋅X₀+6 {O(n^2)}
MPRF for transition t₂₃₃: n_l4___8(X₀, X₁, X₂) → n_l1___7(Arg0_P, X₁, Arg2_P) :|: Arg0_P ≤ Arg2_P ∧ 0 ≤ Arg0_P ∧ X₀ ≤ Arg0_P ∧ Arg0_P ≤ X₀ ∧ X₂ ≤ Arg2_P ∧ Arg2_P ≤ X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
36⋅X₀⋅X₀+24⋅X₀+6 {O(n^2)}
CFR did not improve the program. Rolling back
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:4352⋅X₀⋅X₀+624⋅X₀+34 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1088⋅X₀⋅X₀+164⋅X₀+6 {O(n^2)}
t₅: 1 {O(1)}
t₆: 1088⋅X₀⋅X₀+132⋅X₀+4 {O(n^2)}
t₇: 1088⋅X₀⋅X₀+132⋅X₀+4 {O(n^2)}
t₈: 32⋅X₀+9 {O(n)}
t₉: 1088⋅X₀⋅X₀+132⋅X₀+4 {O(n^2)}
t₁₀: 32⋅X₀+1 {O(n)}
t₁₁: 1 {O(1)}
Costbounds
Overall costbound: 4352⋅X₀⋅X₀+624⋅X₀+34 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1088⋅X₀⋅X₀+164⋅X₀+6 {O(n^2)}
t₅: 1 {O(1)}
t₆: 1088⋅X₀⋅X₀+132⋅X₀+4 {O(n^2)}
t₇: 1088⋅X₀⋅X₀+132⋅X₀+4 {O(n^2)}
t₈: 32⋅X₀+9 {O(n)}
t₉: 1088⋅X₀⋅X₀+132⋅X₀+4 {O(n^2)}
t₁₀: 32⋅X₀+1 {O(n)}
t₁₁: 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: 2⋅X₀ {O(n)}
t₃, X₂: 2⋅X₀ {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: 34⋅X₀+1 {O(n)}
t₄, X₂: 36⋅X₀+3 {O(n)}
t₅, X₀: 2⋅X₀ {O(n)}
t₅, X₁: 68⋅X₀+2 {O(n)}
t₅, X₂: 70⋅X₀+5 {O(n)}
t₆, X₀: X₀ {O(n)}
t₆, X₁: 34⋅X₀+1 {O(n)}
t₆, X₂: 36⋅X₀+3 {O(n)}
t₇, X₀: X₀ {O(n)}
t₇, X₁: 34⋅X₀+1 {O(n)}
t₇, X₂: 36⋅X₀+3 {O(n)}
t₈, X₀: X₀ {O(n)}
t₈, X₁: 34⋅X₀+1 {O(n)}
t₈, X₂: 36⋅X₀+3 {O(n)}
t₉, X₀: X₀ {O(n)}
t₉, X₁: 34⋅X₀+1 {O(n)}
t₉, X₂: 36⋅X₀+3 {O(n)}
t₁₀, X₀: X₀ {O(n)}
t₁₀, X₁: 34⋅X₀+1 {O(n)}
t₁₀, X₂: 34⋅X₀+2 {O(n)}
t₁₁, X₀: 3⋅X₀ {O(n)}
t₁₁, X₁: 68⋅X₀+X₁+2 {O(n)}
t₁₁, X₂: 70⋅X₀+X₂+5 {O(n)}